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 | 961.1 | ||
Root | \(-2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.e.961.3 |
$q$-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 | \(-0.771423\pi\) | ||
0.753059 | − | 0.657952i | \(-0.228577\pi\) | |||||||
\(14\) | 2.37228i | 0.634019i | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.372281i | 0.0902915i | 0.998980 | + | 0.0451457i | \(0.0143752\pi\) | ||||
−0.998980 | + | 0.0451457i | \(0.985625\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 2.37228 | 0.517674 | ||||||||
\(22\) | − | 6.37228i | − | 1.35857i | ||||||
\(23\) | − | 8.74456i | − | 1.82337i | −0.410893 | − | 0.911684i | \(-0.634783\pi\) | ||
0.410893 | − | 0.911684i | \(-0.365217\pi\) | |||||||
\(24\) | − | 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 | \(0.109353\pi\) | ||||
−0.941567 | + | 0.336825i | \(0.890647\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − | 8.37228i | − | 1.50371i | −0.659331 | − | 0.751853i | \(-0.729160\pi\) | ||
0.659331 | − | 0.751853i | \(-0.270840\pi\) | |||||||
\(32\) | − | 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 | \(-0.891810\pi\) | ||
0.942791 | − | 0.333383i | \(-0.108190\pi\) | |||||||
\(44\) | −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 | \(-0.825650\pi\) | ||
0.853706 | − | 0.520756i | \(-0.174350\pi\) | |||||||
\(60\) | − | 1.00000i | − | 0.129099i | ||||||
\(61\) | − | 5.62772i | − | 0.720556i | −0.932845 | − | 0.360278i | \(-0.882682\pi\) | ||
0.932845 | − | 0.360278i | \(-0.117318\pi\) | |||||||
\(62\) | −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 | \(-0.876127\pi\) | ||
0.925228 | − | 0.379411i | \(-0.123873\pi\) | |||||||
\(80\) | − | 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 | \(0.0464667\pi\) | ||||
−0.989364 | + | 0.145462i | \(0.953533\pi\) | |||||||
\(90\) | −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 | \(-0.882332\pi\) | ||
0.932448 | − | 0.361303i | \(-0.117668\pi\) | |||||||
\(98\) | 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 | \(-0.879713\pi\) | ||
0.929444 | − | 0.368963i | \(-0.120287\pi\) | |||||||
\(104\) | 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 | \(0.0476923\pi\) | ||||
−0.988797 | + | 0.149270i | \(0.952308\pi\) | |||||||
\(110\) | −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 | \(0.153529\pi\) | ||||
−0.885918 | + | 0.463842i | \(0.846471\pi\) | |||||||
\(114\) | −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 | \(-0.863944\pi\) | ||
0.910034 | − | 0.414534i | \(-0.136056\pi\) | |||||||
\(132\) | 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 | \(-0.883785\pi\) | ||
0.934088 | − | 0.357043i | \(-0.116215\pi\) | |||||||
\(164\) | 9.11684 | 0.711906 | ||||||||
\(165\) | 6.37228i | 0.496081i | ||||||||
\(166\) | 5.48913i | 0.426039i | ||||||||
\(167\) | 3.25544i | 0.251913i | 0.992036 | + | 0.125957i | \(0.0402000\pi\) | ||||
−0.992036 | + | 0.125957i | \(0.959800\pi\) | |||||||
\(168\) | 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 | \(0.105970\pi\) | ||||
−0.945094 | + | 0.326800i | \(0.894030\pi\) | |||||||
\(180\) | 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 | \(-0.917108\pi\) | ||
0.966284 | − | 0.257478i | \(-0.0828916\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 18.2337i | 1.31249i | 0.754548 | + | 0.656245i | \(0.227856\pi\) | ||||
−0.754548 | + | 0.656245i | \(0.772144\pi\) | |||||||
\(194\) | −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 | \(-0.875638\pi\) | ||
0.924645 | − | 0.380831i | \(-0.124362\pi\) | |||||||
\(200\) | − | 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 | \(-0.932174\pi\) | ||
0.977384 | − | 0.211472i | \(-0.0678256\pi\) | |||||||
\(228\) | 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 | \(0.0818306\pi\) | ||||
−0.967137 | + | 0.254256i | \(0.918169\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | − | 21.4891i | − | 1.38424i | −0.721784 | − | 0.692118i | \(-0.756678\pi\) | ||
0.721784 | − | 0.692118i | \(-0.243322\pi\) | |||||||
\(242\) | − | 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 | \(-0.959709\pi\) | ||
0.992000 | − | 0.126239i | \(-0.0402906\pi\) | |||||||
\(252\) | 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 | \(-0.738304\pi\) | ||
0.680653 | − | 0.732606i | \(-0.261696\pi\) | |||||||
\(258\) | 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 | \(0.0920179\pi\) | ||||
−0.958506 | + | 0.285073i | \(0.907982\pi\) | |||||||
\(278\) | 1.62772i | 0.0976241i | ||||||||
\(279\) | − | 8.37228i | − | 0.501235i | ||||||
\(280\) | −2.37228 | −0.141771 | ||||||||
\(281\) | 20.9783i | 1.25146i | 0.780041 | + | 0.625729i | \(0.215198\pi\) | ||||
−0.780041 | + | 0.625729i | \(0.784802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.7446i | 1.82757i | 0.406193 | + | 0.913787i | \(0.366856\pi\) | ||||
−0.406193 | + | 0.913787i | \(0.633144\pi\) | |||||||
\(284\) | 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 | \(-0.809601\pi\) | ||
0.826376 | − | 0.563119i | \(-0.190399\pi\) | |||||||
\(312\) | −4.74456 | −0.268608 | ||||||||
\(313\) | − | 18.2337i | − | 1.03063i | −0.857001 | − | 0.515314i | \(-0.827675\pi\) | ||
0.857001 | − | 0.515314i | \(-0.172325\pi\) | |||||||
\(314\) | 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 | \(-0.969430\pi\) | ||
0.995392 | − | 0.0958898i | \(-0.0305697\pi\) | |||||||
\(332\) | 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 | \(-0.687483\pi\) | ||
0.555525 | − | 0.831500i | \(-0.312517\pi\) | |||||||
\(348\) | 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 | \(0.0434797\pi\) | ||||
−0.990685 | + | 0.136171i | \(0.956520\pi\) | |||||||
\(354\) | 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 | \(0.365987\pi\) | ||||
−0.408686 | + | 0.912675i | \(0.634013\pi\) | |||||||
\(384\) | − | 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 | \(-0.952526\pi\) | ||
0.988899 | − | 0.148593i | \(-0.0474743\pi\) | |||||||
\(390\) | − | 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 | \(0.257492\pi\) | ||||
−0.690269 | + | 0.723552i | \(0.742508\pi\) | |||||||
\(402\) | 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 | \(-0.821710\pi\) | ||
0.847194 | − | 0.531284i | \(-0.178290\pi\) | |||||||
\(410\) | 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 | \(-0.931647\pi\) | ||
0.977032 | − | 0.213092i | \(-0.0683534\pi\) | |||||||
\(422\) | − | 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 | \(0.106446\pi\) | ||||
−0.944604 | + | 0.328212i | \(0.893554\pi\) | |||||||
\(432\) | −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 | \(0.0954024\pi\) | ||||
−0.955421 | + | 0.295248i | \(0.904598\pi\) | |||||||
\(440\) | 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 | \(0.337539\pi\) | ||||
−0.488515 | + | 0.872556i | \(0.662461\pi\) | |||||||
\(450\) | 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 | \(-0.957980\pi\) | ||
0.991299 | − | 0.131627i | \(-0.0420200\pi\) | |||||||
\(458\) | − | 4.51087i | − | 0.210779i | ||||||
\(459\) | − | 0.372281i | − | 0.0173766i | ||||||
\(460\) | 8.74456 | 0.407717 | ||||||||
\(461\) | 14.6060i | 0.680268i | 0.940377 | + | 0.340134i | \(0.110472\pi\) | ||||
−0.940377 | + | 0.340134i | \(0.889528\pi\) | |||||||
\(462\) | − | 15.1168i | − | 0.703299i | ||||||
\(463\) | 12.2337i | 0.568548i | 0.958743 | + | 0.284274i | \(0.0917525\pi\) | ||||
−0.958743 | + | 0.284274i | \(0.908248\pi\) | |||||||
\(464\) | 3.62772i | 0.168413i | ||||||||
\(465\) | 8.37228 | 0.388255 | ||||||||
\(466\) | − | 14.7446i | − | 0.683029i | ||||||
\(467\) | 26.3723i | 1.22036i | 0.792261 | + | 0.610182i | \(0.208904\pi\) | ||||
−0.792261 | + | 0.610182i | \(0.791096\pi\) | |||||||
\(468\) | 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 | \(0.0806951\pi\) | ||||
−0.968038 | + | 0.250805i | \(0.919305\pi\) | |||||||
\(480\) | 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 | \(-0.860380\pi\) | ||
0.905335 | − | 0.424699i | \(-0.139620\pi\) | |||||||
\(488\) | 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 | \(-0.811151\pi\) | ||
0.829107 | − | 0.559090i | \(-0.188849\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | − | 3.25544i | − | 0.145442i | ||||||
\(502\) | −4.00000 | −0.178529 | ||||||||
\(503\) | 21.4891i | 0.958153i | 0.877773 | + | 0.479076i | \(0.159028\pi\) | ||||
−0.877773 | + | 0.479076i | \(0.840972\pi\) | |||||||
\(504\) | − | 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 | \(-0.779089\pi\) | ||
0.768687 | − | 0.639625i | \(-0.220911\pi\) | |||||||
\(524\) | 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 | \(0.203224\pi\) | ||||
−0.803023 | + | 0.595948i | \(0.796776\pi\) | |||||||
\(542\) | − | 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 | \(0.0780189\pi\) | ||||
−0.970112 | + | 0.242657i | \(0.921981\pi\) | |||||||
\(548\) | 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 | \(0.171617\pi\) | ||||
−0.858145 | + | 0.513407i | \(0.828383\pi\) | |||||||
\(558\) | −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 | \(-0.974071\pi\) | ||
0.996684 | − | 0.0813694i | \(-0.0259294\pi\) | |||||||
\(564\) | 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 | \(-0.853013\pi\) | ||
0.895263 | − | 0.445537i | \(-0.146987\pi\) | |||||||
\(570\) | 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 | \(0.266874\pi\) | ||||
−0.668647 | + | 0.743580i | \(0.733126\pi\) | |||||||
\(578\) | − | 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 | \(0.0106945\pi\) | ||||
−0.999436 | + | 0.0335916i | \(0.989305\pi\) | |||||||
\(588\) | −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 | \(0.0243538\pi\) | ||||
−0.997075 | + | 0.0764349i | \(0.975646\pi\) | |||||||
\(608\) | 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 | \(-0.981723\pi\) | ||
0.998352 | − | 0.0573883i | \(-0.0182773\pi\) | |||||||
\(632\) | 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 | \(-0.805341\pi\) | ||
0.818765 | − | 0.574128i | \(-0.194659\pi\) | |||||||
\(644\) | − | 20.7446i | − | 0.817450i | ||||||
\(645\) | 4.37228 | 0.172158 | ||||||||
\(646\) | 2.23369i | 0.0878833i | ||||||||
\(647\) | 9.76631i | 0.383953i | 0.981399 | + | 0.191977i | \(0.0614898\pi\) | ||||
−0.981399 | + | 0.191977i | \(0.938510\pi\) | |||||||
\(648\) | 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 | \(-0.901989\pi\) | ||
0.952969 | − | 0.303068i | \(-0.0980110\pi\) | |||||||
\(654\) | −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 | \(-0.806633\pi\) | ||
0.821088 | − | 0.570802i | \(-0.193367\pi\) | |||||||
\(662\) | −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 | \(-0.885672\pi\) | ||
0.936189 | − | 0.351498i | \(-0.114328\pi\) | |||||||
\(684\) | − | 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 | \(-0.815676\pi\) | ||
0.836971 | − | 0.547247i | \(-0.184324\pi\) | |||||||
\(702\) | 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 | \(-0.730768\pi\) | ||
0.663120 | − | 0.748513i | \(-0.269232\pi\) | |||||||
\(710\) | 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 | \(0.111260\pi\) | ||||
−0.939533 | + | 0.342459i | \(0.888740\pi\) | |||||||
\(728\) | −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 | \(0.134152\pi\) | ||||
−0.912496 | + | 0.409086i | \(0.865848\pi\) | |||||||
\(758\) | − | 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 | \(0.195767\pi\) | ||||
−0.816762 | + | 0.576975i | \(0.804233\pi\) | |||||||
\(770\) | 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 | \(0.0609448\pi\) | ||||
−0.981727 | + | 0.190296i | \(0.939055\pi\) | |||||||
\(798\) | 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 | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | −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 | \(-0.978614\pi\) | ||
0.997744 | − | 0.0671371i | \(-0.0213865\pi\) | |||||||
\(828\) | 8.74456i | 0.303895i | ||||||||
\(829\) | 23.8614i | 0.828741i | 0.910108 | + | 0.414370i | \(0.135998\pi\) | ||||
−0.910108 | + | 0.414370i | \(0.864002\pi\) | |||||||
\(830\) | 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 | \(-0.810580\pi\) | ||
0.828103 | − | 0.560576i | \(-0.189420\pi\) | |||||||
\(854\) | 13.3505 | 0.456846 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 3.25544i | 0.111269i | ||||||||
\(857\) | 18.6060i | 0.635568i | 0.948163 | + | 0.317784i | \(0.102939\pi\) | ||||
−0.948163 | + | 0.317784i | \(0.897061\pi\) | |||||||
\(858\) | 30.2337 | 1.03216 | ||||||||
\(859\) | − | 30.0000i | − | 1.02359i | −0.859109 | − | 0.511793i | \(-0.828981\pi\) | ||
0.859109 | − | 0.511793i | \(-0.171019\pi\) | |||||||
\(860\) | 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 | \(-0.807035\pi\) | ||
0.821809 | − | 0.569764i | \(-0.192965\pi\) | |||||||
\(884\) | −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 | \(0.164270\pi\) | ||||
−0.869766 | + | 0.493465i | \(0.835730\pi\) | |||||||
\(908\) | 6.37228i | 0.211472i | ||||||||
\(909\) | −5.25544 | −0.174312 | ||||||||
\(910\) | − | 11.2554i | − | 0.373114i | ||||||
\(911\) | 53.4891i | 1.77217i | 0.463519 | + | 0.886087i | \(0.346587\pi\) | ||||
−0.463519 | + | 0.886087i | \(0.653413\pi\) | |||||||
\(912\) | − | 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 | \(-0.812256\pi\) | ||
0.831044 | − | 0.556206i | \(-0.187744\pi\) | |||||||
\(920\) | − | 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 | \(-0.681003\pi\) | ||
0.538486 | − | 0.842635i | \(-0.318997\pi\) | |||||||
\(948\) | − | 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 | \(-0.898544\pi\) | ||
0.949633 | − | 0.313364i | \(-0.101456\pi\) | |||||||
\(968\) | 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 | \(0.238691\pi\) | ||||
−0.731778 | + | 0.681543i | \(0.761309\pi\) | |||||||
\(978\) | 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 | \(0.157295\pi\) | ||||
−0.880369 | + | 0.474289i | \(0.842705\pi\) | |||||||
\(992\) | −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 | \(-0.721506\pi\) | ||
0.641063 | − | 0.767489i | \(-0.278494\pi\) | |||||||
\(998\) | −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.961.1 | ✓ | 4 | |
3.2 | odd | 2 | 3330.2.h.k.2071.3 | 4 | |||
37.36 | even | 2 | inner | 1110.2.h.e.961.3 | yes | 4 | |
111.110 | odd | 2 | 3330.2.h.k.2071.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.e.961.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1110.2.h.e.961.3 | yes | 4 | 37.36 | even | 2 | inner | |
3330.2.h.k.2071.1 | 4 | 111.110 | odd | 2 | |||
3330.2.h.k.2071.3 | 4 | 3.2 | odd | 2 |