Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2091141441.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.335492 + 1.69925i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.337 |
Dual form | 504.2.r.e.169.1 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.30385 | − | 1.14017i | −0.752776 | − | 0.658277i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.164508 | + | 0.284936i | −0.0735702 | + | 0.127427i | −0.900464 | − | 0.434931i | \(-0.856773\pi\) |
0.826893 | + | 0.562359i | \(0.190106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.400030 | + | 2.97321i | 0.133343 | + | 0.991070i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.664508 | + | 1.15096i | 0.200357 | + | 0.347028i | 0.948643 | − | 0.316348i | \(-0.102457\pi\) |
−0.748287 | + | 0.663375i | \(0.769123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.53937 | + | 2.66626i | −0.426944 | + | 0.739489i | −0.996600 | − | 0.0823948i | \(-0.973743\pi\) |
0.569656 | + | 0.821883i | \(0.307076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.539368 | − | 0.183946i | 0.139264 | − | 0.0474946i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.35741 | 1.78443 | 0.892217 | − | 0.451606i | \(-0.149149\pi\) | ||||
0.892217 | + | 0.451606i | \(0.149149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.93671 | −0.673727 | −0.336864 | − | 0.941553i | \(-0.609366\pi\) | ||||
−0.336864 | + | 0.941553i | \(0.609366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.335492 | − | 1.69925i | 0.0732104 | − | 0.370806i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34321 | − | 5.79062i | 0.697108 | − | 1.20743i | −0.272356 | − | 0.962196i | \(-0.587803\pi\) |
0.969465 | − | 0.245231i | \(-0.0788637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44587 | + | 4.23638i | 0.489175 | + | 0.847276i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.86838 | − | 4.33271i | 0.552021 | − | 0.833830i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.88258 | + | 6.72483i | 0.720977 | + | 1.24877i | 0.960608 | + | 0.277906i | \(0.0896402\pi\) |
−0.239631 | + | 0.970864i | \(0.577026\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63555 | − | 2.83286i | 0.293754 | − | 0.508796i | −0.680940 | − | 0.732339i | \(-0.738429\pi\) |
0.974694 | + | 0.223542i | \(0.0717621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.445874 | − | 2.25833i | 0.0776168 | − | 0.393124i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.329016 | −0.0556138 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.329016 | 0.0540899 | 0.0270449 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270449 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.04709 | − | 1.72126i | 0.808181 | − | 0.275622i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.135552 | + | 0.234783i | −0.0211696 | + | 0.0366669i | −0.876416 | − | 0.481555i | \(-0.840072\pi\) |
0.855247 | + | 0.518221i | \(0.173406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.48255 | + | 9.49606i | 0.836081 | + | 1.44814i | 0.893147 | + | 0.449765i | \(0.148492\pi\) |
−0.0570654 | + | 0.998370i | \(0.518174\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.912983 | − | 0.375134i | −0.136099 | − | 0.0559216i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.571014 | − | 0.989025i | −0.0832910 | − | 0.144264i | 0.821371 | − | 0.570395i | \(-0.193210\pi\) |
−0.904662 | + | 0.426131i | \(0.859876\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.59293 | − | 8.38869i | −1.34328 | − | 1.17465i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.42828 | 0.882992 | 0.441496 | − | 0.897263i | \(-0.354448\pi\) | ||||
0.441496 | + | 0.897263i | \(0.354448\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.437267 | −0.0589611 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.82902 | + | 3.34834i | 0.507166 | + | 0.443499i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.372170 | + | 0.644618i | −0.0484525 | + | 0.0839221i | −0.889234 | − | 0.457452i | \(-0.848762\pi\) |
0.840782 | + | 0.541374i | \(0.182096\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.42195 | − | 7.65904i | −0.566173 | − | 0.980640i | −0.996940 | − | 0.0781767i | \(-0.975090\pi\) |
0.430767 | − | 0.902463i | \(-0.358243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.37486 | + | 1.83304i | −0.299204 | + | 0.230941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.506476 | − | 0.877243i | −0.0628207 | − | 0.108809i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.28640 | + | 7.42426i | −0.523667 | + | 0.907018i | 0.475954 | + | 0.879470i | \(0.342103\pi\) |
−0.999620 | + | 0.0275474i | \(0.991230\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.9613 | + | 3.73825i | −1.31959 | + | 0.450032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60769 | 0.190798 | 0.0953990 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0953990 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.4941 | −1.57936 | −0.789680 | − | 0.613519i | \(-0.789754\pi\) | ||||
−0.789680 | + | 0.613519i | \(0.789754\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.64114 | − | 8.31230i | 0.189503 | − | 0.959821i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.664508 | + | 1.15096i | −0.0757277 | + | 0.131164i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.628926 | + | 1.08933i | 0.0707597 | + | 0.122559i | 0.899234 | − | 0.437467i | \(-0.144124\pi\) |
−0.828475 | + | 0.560026i | \(0.810791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.67995 | + | 2.37875i | −0.964439 | + | 0.264305i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0316459 | + | 0.0548124i | 0.00347359 | + | 0.00601644i | 0.867757 | − | 0.496989i | \(-0.165561\pi\) |
−0.864283 | + | 0.503005i | \(0.832228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21035 | + | 2.09639i | −0.131281 | + | 0.227386i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60515 | − | 13.1949i | 0.279302 | − | 1.41465i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3071 | 1.19855 | 0.599274 | − | 0.800544i | \(-0.295456\pi\) | ||||
0.599274 | + | 0.800544i | \(0.295456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.07874 | −0.322739 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.36245 | + | 1.82881i | −0.556060 | + | 0.189638i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.483112 | − | 0.836774i | 0.0495662 | − | 0.0858512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.51420 | + | 9.55087i | 0.559882 | + | 0.969744i | 0.997506 | + | 0.0705859i | \(0.0224869\pi\) |
−0.437624 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.15623 | + | 2.43614i | −0.317213 | + | 0.244841i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12079 | − | 12.3336i | −0.708546 | − | 1.22724i | −0.965397 | − | 0.260786i | \(-0.916018\pi\) |
0.256851 | − | 0.966451i | \(-0.417315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.29288 | + | 9.16753i | −0.521522 | + | 0.903303i | 0.478164 | + | 0.878270i | \(0.341302\pi\) |
−0.999687 | + | 0.0250330i | \(0.992031\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.428986 | + | 0.375134i | 0.0418647 | + | 0.0366093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5574 | −1.50399 | −0.751993 | − | 0.659171i | \(-0.770907\pi\) | ||||
−0.751993 | + | 0.659171i | \(0.770907\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3574 | −1.37519 | −0.687595 | − | 0.726094i | \(-0.741334\pi\) | ||||
−0.687595 | + | 0.726094i | \(0.741334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.428986 | − | 0.375134i | −0.0407175 | − | 0.0356061i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94966 | − | 3.37691i | 0.183409 | − | 0.317673i | −0.759630 | − | 0.650355i | \(-0.774620\pi\) |
0.943039 | + | 0.332682i | \(0.107954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.09997 | + | 1.90520i | 0.102573 | + | 0.177661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.54315 | − | 3.51028i | −0.789815 | − | 0.324525i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.67871 | + | 6.37171i | 0.337226 | + | 0.584093i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.61686 | − | 7.99663i | 0.419714 | − | 0.726967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.444430 | − | 0.151568i | 0.0400729 | − | 0.0136665i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.25454 | −0.291095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00787 | −0.621848 | −0.310924 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310924 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.67871 | − | 18.6324i | 0.323892 | − | 1.64049i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.33280 | + | 5.77258i | −0.291188 | + | 0.504353i | −0.974091 | − | 0.226156i | \(-0.927384\pi\) |
0.682903 | + | 0.730509i | \(0.260717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.46835 | − | 2.54326i | −0.127322 | − | 0.220529i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.762673 | + | 1.53007i | 0.0656405 | + | 0.131688i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.41926 | + | 14.5826i | 0.719306 | + | 1.24587i | 0.961275 | + | 0.275591i | \(0.0888734\pi\) |
−0.241969 | + | 0.970284i | \(0.577793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.81032 | − | 13.5279i | 0.662463 | − | 1.14742i | −0.317504 | − | 0.948257i | \(-0.602845\pi\) |
0.979967 | − | 0.199162i | \(-0.0638221\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.383141 | + | 1.94059i | −0.0322663 | + | 0.163427i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.09169 | −0.342164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.55486 | −0.212170 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.63934 | − | 0.559079i | 0.135210 | − | 0.0461121i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.53233 | − | 13.0464i | 0.617073 | − | 1.06880i | −0.372944 | − | 0.927854i | \(-0.621652\pi\) |
0.990017 | − | 0.140948i | \(-0.0450149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.86714 | + | 6.69808i | 0.314703 | + | 0.545082i | 0.979374 | − | 0.202054i | \(-0.0647617\pi\) |
−0.664671 | + | 0.747136i | \(0.731428\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.94318 | + | 21.8751i | 0.237942 | + | 1.76850i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.538122 | + | 0.932055i | 0.0432230 | + | 0.0748645i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.35812 | − | 7.54849i | 0.347816 | − | 0.602435i | −0.638045 | − | 0.769999i | \(-0.720257\pi\) |
0.985861 | + | 0.167564i | \(0.0535901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.38149 | − | 7.32932i | −0.664695 | − | 0.581253i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.68643 | 0.526964 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4513 | 1.05359 | 0.526793 | − | 0.849993i | \(-0.323394\pi\) | ||||
0.526793 | + | 0.849993i | \(0.323394\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.570129 | + | 0.498558i | 0.0443845 | + | 0.0388127i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.81804 | − | 10.0771i | 0.450214 | − | 0.779793i | −0.548185 | − | 0.836357i | \(-0.684681\pi\) |
0.998399 | + | 0.0565638i | \(0.0180144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.76069 | + | 3.04961i | 0.135438 | + | 0.234585i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17477 | − | 8.73145i | −0.0898370 | − | 0.667711i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.885831 | − | 1.53430i | −0.0673485 | − | 0.116651i | 0.830385 | − | 0.557190i | \(-0.188121\pi\) |
−0.897733 | + | 0.440539i | \(0.854787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.44587 | + | 4.23638i | −0.184891 | + | 0.320240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.22023 | − | 0.416146i | 0.0917178 | − | 0.0312794i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.73139 | −0.503128 | −0.251564 | − | 0.967841i | \(-0.580945\pi\) | ||||
−0.251564 | + | 0.967841i | \(0.580945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2711 | −0.986433 | −0.493217 | − | 0.869906i | \(-0.664179\pi\) | ||||
−0.493217 | + | 0.869906i | \(0.664179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.96706 | + | 15.0280i | −0.219331 | + | 1.11090i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0541257 | + | 0.0937484i | −0.00397940 | + | 0.00689252i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.88906 | + | 8.46810i | 0.357523 | + | 0.619249i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.18643 | + | 0.317738i | 0.377257 | + | 0.0231121i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4083 | − | 18.0277i | −0.753117 | − | 1.30444i | −0.946305 | − | 0.323276i | \(-0.895216\pi\) |
0.193187 | − | 0.981162i | \(-0.438117\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2585 | − | 17.7683i | 0.738426 | − | 1.27899i | −0.214778 | − | 0.976663i | \(-0.568903\pi\) |
0.953204 | − | 0.302328i | \(-0.0977638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.339838 | + | 1.72126i | −0.0243363 | + | 0.123262i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.20781 | 0.513535 | 0.256768 | − | 0.966473i | \(-0.417342\pi\) | ||||
0.256768 | + | 0.966473i | \(0.417342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3276 | −1.01566 | −0.507828 | − | 0.861458i | \(-0.669552\pi\) | ||||
−0.507828 | + | 0.861458i | \(0.669552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0537 | − | 4.79288i | 0.991273 | − | 0.338063i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.88258 | + | 6.72483i | −0.272504 | + | 0.471991i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0445987 | − | 0.0772471i | −0.00311491 | − | 0.00539517i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.5541 | + | 7.62366i | 1.28960 | + | 0.529881i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.95147 | − | 3.38004i | −0.134986 | − | 0.233802i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.68897 | − | 6.38948i | 0.253959 | − | 0.439870i | −0.710653 | − | 0.703543i | \(-0.751600\pi\) |
0.964612 | + | 0.263672i | \(0.0849338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.09618 | − | 1.83304i | −0.143628 | − | 0.125598i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.60769 | −0.246043 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27110 | 0.222057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.5942 | + | 15.3855i | 1.18890 | + | 1.03966i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.3258 | + | 19.6168i | −0.761854 | + | 1.31957i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3549 | + | 23.1313i | 0.894308 | + | 1.54899i | 0.834658 | + | 0.550768i | \(0.185665\pi\) |
0.0596502 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.6172 | + | 8.96678i | −0.774481 | + | 0.597785i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.46386 | + | 14.6598i | 0.561766 | + | 0.973007i | 0.997342 | + | 0.0728556i | \(0.0232112\pi\) |
−0.435576 | + | 0.900152i | \(0.643455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.22580 | − | 14.2475i | 0.543576 | − | 0.941501i | −0.455119 | − | 0.890431i | \(-0.650403\pi\) |
0.998695 | − | 0.0510706i | \(-0.0162633\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.17871 | − | 0.743025i | 0.143348 | − | 0.0488875i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.10855 | 0.269160 | 0.134580 | − | 0.990903i | \(-0.457031\pi\) | ||||
0.134580 | + | 0.990903i | \(0.457031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.375745 | 0.0245109 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.422000 | − | 2.13740i | 0.0274118 | − | 0.138839i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4182 | + | 18.0448i | −0.673895 | + | 1.16722i | 0.302896 | + | 0.953024i | \(0.402047\pi\) |
−0.976791 | + | 0.214197i | \(0.931287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3477 | − | 19.6548i | −0.730969 | − | 1.26608i | −0.956470 | − | 0.291832i | \(-0.905735\pi\) |
0.225501 | − | 0.974243i | \(-0.427598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.0295 | + | 6.79509i | 0.899992 | + | 0.435905i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.164508 | − | 0.284936i | −0.0105100 | − | 0.0182039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.52067 | − | 7.83004i | 0.287644 | − | 0.498213i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0212339 | − | 0.107549i | 0.00134564 | − | 0.00681561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00030 | 0.252497 | 0.126248 | − | 0.991999i | \(-0.459706\pi\) | ||||
0.126248 | + | 0.991999i | \(0.459706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.88637 | 0.558681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.96835 | − | 1.35337i | 0.248508 | − | 0.0847511i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.254753 | + | 0.441245i | −0.0158911 | + | 0.0275241i | −0.873862 | − | 0.486175i | \(-0.838392\pi\) |
0.857971 | + | 0.513699i | \(0.171725\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.164508 | + | 0.284936i | 0.0102220 | + | 0.0177051i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.4412 | + | 14.2339i | −1.14148 | + | 0.881054i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.56344 | + | 2.70796i | 0.0964059 | + | 0.166980i | 0.910194 | − | 0.414181i | \(-0.135932\pi\) |
−0.813789 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05750 | + | 1.83165i | −0.0649619 | + | 0.112517i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7427 | − | 12.8920i | −0.902238 | − | 0.788976i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.16505 | −0.253947 | −0.126974 | − | 0.991906i | \(-0.540526\pi\) | ||||
−0.126974 | + | 0.991906i | \(0.540526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0230 | −0.791092 | −0.395546 | − | 0.918446i | \(-0.629445\pi\) | ||||
−0.395546 | + | 0.918446i | \(0.629445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.01420 | + | 3.51028i | 0.242950 | + | 0.212452i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.25061 | + | 5.63021i | −0.196019 | + | 0.339515i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.347709 | + | 0.602250i | 0.0208918 | + | 0.0361857i | 0.876282 | − | 0.481798i | \(-0.160016\pi\) |
−0.855390 | + | 0.517984i | \(0.826683\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.07695 | + | 3.72961i | 0.543423 | + | 0.223286i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1488 | − | 27.9706i | −0.963359 | − | 1.66859i | −0.713960 | − | 0.700186i | \(-0.753100\pi\) |
−0.249399 | − | 0.968401i | \(-0.580233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.06383 | − | 12.2349i | 0.419901 | − | 0.727290i | −0.576028 | − | 0.817430i | \(-0.695398\pi\) |
0.995929 | + | 0.0901399i | \(0.0287314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.58397 | + | 0.540196i | −0.0938261 | + | 0.0319984i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.271104 | −0.0160027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.1315 | 2.18421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.69994 | − | 18.7400i | 0.216894 | − | 1.09856i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.33818 | + | 14.4422i | −0.487122 | + | 0.843720i | −0.999890 | − | 0.0148072i | \(-0.995287\pi\) |
0.512769 | + | 0.858527i | \(0.328620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.122450 | − | 0.212090i | −0.00712931 | − | 0.0123483i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.89285 | + | 0.422279i | 0.399963 | + | 0.0245031i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2929 | + | 17.8278i | 0.595252 | + | 1.03101i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.48255 | + | 9.49606i | −0.316009 | + | 0.547344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.77794 | + | 24.2000i | −0.274486 | + | 1.39025i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.90978 | 0.166614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.0345 | 1.54294 | 0.771469 | − | 0.636267i | \(-0.219522\pi\) | ||||
0.771469 | + | 0.636267i | \(0.219522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.3536 | − | 5.91828i | 0.987213 | − | 0.336679i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7377 | − | 20.3302i | 0.665581 | − | 1.15282i | −0.313546 | − | 0.949573i | \(-0.601517\pi\) |
0.979127 | − | 0.203248i | \(-0.0651496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.364597 | + | 0.631501i | 0.0206083 | + | 0.0356946i | 0.876146 | − | 0.482047i | \(-0.160106\pi\) |
−0.855537 | + | 0.517741i | \(0.826773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.131616 | − | 0.978233i | −0.00741573 | − | 0.0551172i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7398 | − | 28.9943i | −0.940203 | − | 1.62848i | −0.765082 | − | 0.643933i | \(-0.777301\pi\) |
−0.175122 | − | 0.984547i | \(-0.556032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.16001 | + | 8.93741i | −0.288905 | + | 0.500399i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2844 | + | 17.7380i | 1.13216 | + | 0.990039i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6066 | −1.20222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0604 | −0.835401 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.7199 | + | 16.3699i | 1.03521 | + | 0.905256i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.571014 | − | 0.989025i | 0.0314810 | − | 0.0545267i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.92051 | + | 8.52257i | 0.270456 | + | 0.468443i | 0.968979 | − | 0.247145i | \(-0.0794924\pi\) |
−0.698523 | + | 0.715588i | \(0.746159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.131616 | + | 0.978233i | 0.00721252 | + | 0.0536068i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41029 | − | 2.44270i | −0.0770525 | − | 0.133459i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.93490 | − | 6.81545i | 0.214348 | − | 0.371261i | −0.738723 | − | 0.674009i | \(-0.764571\pi\) |
0.953071 | + | 0.302748i | \(0.0979041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.39231 | + | 2.18003i | −0.347182 | + | 0.118403i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.34735 | 0.235422 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.738063 | − | 3.73825i | 0.0397360 | − | 0.201260i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.14721 | − | 14.1114i | 0.437365 | − | 0.757539i | −0.560120 | − | 0.828411i | \(-0.689245\pi\) |
0.997485 | + | 0.0708727i | \(0.0225784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.79219 | + | 3.10416i | 0.0959336 | + | 0.166162i | 0.909998 | − | 0.414613i | \(-0.136083\pi\) |
−0.814064 | + | 0.580775i | \(0.802750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.13665 | + | 14.3175i | 0.380926 | + | 0.764212i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.80329 | + | 16.9798i | 0.521776 | + | 0.903743i | 0.999679 | + | 0.0253304i | \(0.00806378\pi\) |
−0.477903 | + | 0.878413i | \(0.658603\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.264478 | + | 0.458089i | −0.0140370 | + | 0.0243129i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.46835 | − | 12.5021i | 0.130639 | − | 0.661680i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.8040 | −0.886882 | −0.443441 | − | 0.896303i | \(-0.646243\pi\) | ||||
−0.443441 | + | 0.896303i | \(0.646243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3757 | −0.546092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.1372 | + | 5.16238i | −0.794496 | + | 0.270955i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.21988 | − | 3.84494i | 0.116194 | − | 0.201254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.8160 | − | 29.1262i | −0.877790 | − | 1.52038i | −0.853760 | − | 0.520666i | \(-0.825684\pi\) |
−0.0240298 | − | 0.999711i | \(-0.507650\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.752282 | − | 0.309104i | −0.0391623 | − | 0.0160913i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.21414 | + | 5.56705i | 0.166870 | + | 0.289027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.2159 | − | 29.8189i | 0.891407 | − | 1.54396i | 0.0532169 | − | 0.998583i | \(-0.483053\pi\) |
0.838190 | − | 0.545379i | \(-0.183614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.24342 | + | 3.71073i | 0.219129 | + | 0.191621i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.9069 | −1.23127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0913 | 0.929287 | 0.464644 | − | 0.885498i | \(-0.346182\pi\) | ||||
0.464644 | + | 0.885498i | \(0.346182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.13719 | + | 7.99016i | 0.468112 | + | 0.409348i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.03792 | − | 8.72594i | 0.257426 | − | 0.445875i | −0.708126 | − | 0.706086i | \(-0.750459\pi\) |
0.965552 | + | 0.260212i | \(0.0837923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.218634 | − | 0.378684i | −0.0111426 | − | 0.0192995i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.0406 | + | 20.0995i | −1.32372 | + | 1.02171i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.715236 | + | 1.23882i | 0.0362639 | + | 0.0628109i | 0.883588 | − | 0.468266i | \(-0.155121\pi\) |
−0.847324 | + | 0.531077i | \(0.821788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.5974 | − | 42.6040i | 1.24394 | − | 2.15457i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9272 | − | 3.72660i | 0.551203 | − | 0.187982i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.413853 | −0.0208232 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5433 | −0.529152 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.985242 | + | 4.99020i | −0.0493238 | + | 0.249822i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.804044 | + | 1.39265i | −0.0401521 | + | 0.0695454i | −0.885403 | − | 0.464824i | \(-0.846118\pi\) |
0.845251 | + | 0.534369i | \(0.179451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.03543 | + | 8.72162i | 0.250833 | + | 0.434455i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.750130 | − | 2.86455i | 0.0372743 | − | 0.142341i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.218634 | + | 0.378684i | 0.0108373 | + | 0.0187707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0174 | + | 22.5468i | −0.643670 | + | 1.11487i | 0.340937 | + | 0.940086i | \(0.389256\pi\) |
−0.984607 | + | 0.174783i | \(0.944077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.64919 | − | 28.6128i | 0.278654 | − | 1.41137i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.744341 | −0.0366266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0208240 | −0.00102221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.6075 | + | 8.73318i | −1.25401 | + | 0.427666i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.00882 | + | 3.47938i | −0.0981372 | + | 0.169979i | −0.910914 | − | 0.412597i | \(-0.864622\pi\) |
0.812776 | + | 0.582576i | \(0.197955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.63431 | − | 4.56275i | −0.128388 | − | 0.222375i | 0.794664 | − | 0.607049i | \(-0.207647\pi\) |
−0.923052 | + | 0.384675i | \(0.874314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.71216 | − | 2.09338i | 0.131870 | − | 0.101784i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.9953 | + | 31.1688i | 0.872901 | + | 1.51191i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.42195 | − | 7.65904i | 0.213993 | − | 0.370647i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.33493 | + | 4.66522i | 0.257573 | + | 0.225239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7343 | −0.854230 | −0.427115 | − | 0.904197i | \(-0.640470\pi\) | ||||
−0.427115 | + | 0.904197i | \(0.640470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.76835 | −0.229152 | −0.114576 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114576 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.33115 | + | 2.91297i | 0.159716 | + | 0.139666i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.81804 | + | 17.0054i | −0.469661 | + | 0.813476i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1134 | − | 31.3733i | −0.864506 | − | 1.49737i | −0.867537 | − | 0.497373i | \(-0.834298\pi\) |
0.00303091 | − | 0.999995i | \(-0.499035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.77489 | − | 1.14017i | −0.132138 | − | 0.0542938i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.81211 | − | 13.5310i | −0.371164 | − | 0.642876i | 0.618581 | − | 0.785721i | \(-0.287708\pi\) |
−0.989745 | + | 0.142846i | \(0.954375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.86010 | + | 3.22179i | −0.0881773 | + | 0.152728i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.6961 | + | 8.42235i | −1.16808 | + | 0.398363i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.4142 | −0.727441 | −0.363721 | − | 0.931508i | \(-0.618494\pi\) | ||||
−0.363721 | + | 0.931508i | \(0.618494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.360301 | −0.0169659 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.59479 | − | 13.1425i | 0.121914 | − | 0.617486i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.506476 | − | 0.877243i | 0.0237440 | − | 0.0411258i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.71214 | + | 8.16166i | 0.220424 | + | 0.381786i | 0.954937 | − | 0.296809i | \(-0.0959224\pi\) |
−0.734512 | + | 0.678595i | \(0.762589\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.1039 | − | 31.8775i | 0.985045 | − | 1.48792i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0406 | − | 34.7113i | −0.933383 | − | 1.61667i | −0.777491 | − | 0.628893i | \(-0.783508\pi\) |
−0.155892 | − | 0.987774i | \(-0.549825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9717 | + | 19.0036i | −0.509900 | + | 0.883172i | 0.490035 | + | 0.871703i | \(0.336984\pi\) |
−0.999934 | + | 0.0114690i | \(0.996349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.361072 | − | 1.82881i | 0.0167443 | − | 0.0848089i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9808 | −0.970878 | −0.485439 | − | 0.874271i | \(-0.661340\pi\) | ||||
−0.485439 | + | 0.874271i | \(0.661340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.57280 | −0.395855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2889 | + | 4.87307i | −0.658396 | + | 0.224539i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.28640 | + | 12.6204i | −0.335029 | + | 0.580287i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.18282 | − | 12.4410i | −0.329570 | − | 0.570833i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.57150 | + | 19.1126i | 0.117741 | + | 0.875107i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.65194 | + | 11.5215i | 0.303935 | + | 0.526431i | 0.977024 | − | 0.213131i | \(-0.0683661\pi\) |
−0.673089 | + | 0.739562i | \(0.735033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.506476 | + | 0.877243i | −0.0230933 | + | 0.0399988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.71807 | − | 7.62366i | −0.396686 | − | 0.346888i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.62852 | −0.164762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.5519 | −1.74695 | −0.873477 | − | 0.486865i | \(-0.838140\pi\) | ||||
−0.873477 | + | 0.486865i | \(0.838140\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.5384 | − | 15.3367i | −0.793115 | − | 0.693552i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.25959 | − | 5.64578i | 0.147103 | − | 0.254791i | −0.783052 | − | 0.621956i | \(-0.786338\pi\) |
0.930156 | + | 0.367165i | \(0.119672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.5658 | + | 49.4774i | 1.28654 | + | 2.22835i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.174920 | − | 1.30009i | −0.00786206 | − | 0.0584346i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.803846 | + | 1.39230i | 0.0360574 | + | 0.0624533i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.3259 | + | 24.8132i | −0.641316 | + | 1.11079i | 0.343823 | + | 0.939034i | \(0.388278\pi\) |
−0.985139 | + | 0.171758i | \(0.945055\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.0755 | + | 6.50550i | −0.852230 | + | 0.290644i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2801 | 0.725892 | 0.362946 | − | 0.931810i | \(-0.381771\pi\) | ||||
0.362946 | + | 0.931810i | \(0.381771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.68571 | 0.208511 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.18140 | − | 5.98370i | 0.0524676 | − | 0.265746i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2296 | + | 22.9143i | −0.586391 | + | 1.01566i | 0.408309 | + | 0.912844i | \(0.366118\pi\) |
−0.994700 | + | 0.102815i | \(0.967215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.74703 | − | 11.6862i | −0.298471 | − | 0.516967i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.42361 | + | 12.7239i | −0.371911 | + | 0.561774i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.74144 | − | 3.01626i | −0.0767370 | − | 0.132912i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.758887 | − | 1.31443i | 0.0333758 | − | 0.0578086i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.594379 | + | 3.01049i | −0.0260903 | + | 0.132146i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.72559 | −0.338464 | −0.169232 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169232 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.9546 | −0.741375 | −0.370687 | − | 0.928758i | \(-0.620878\pi\) | ||||
−0.370687 | + | 0.928758i | \(0.620878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.01923 | − | 2.73488i | 0.349988 | − | 0.119360i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0334 | − | 20.8425i | 0.524184 | − | 0.907914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8542 | − | 18.8000i | −0.471920 | − | 0.817390i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.06546 | − | 0.848674i | −0.0896335 | − | 0.0368293i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.417328 | − | 0.722833i | −0.0180765 | − | 0.0313094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.55931 | − | 4.43285i | 0.110648 | − | 0.191649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.77669 | + | 7.67492i | 0.378742 | + | 0.331197i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.32902 | −0.0572448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9353 | 0.943072 | 0.471536 | − | 0.881847i | \(-0.343700\pi\) | ||||
0.471536 | + | 0.881847i | \(0.343700\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3035 | + | 15.1313i | 0.742563 | + | 0.649346i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.36191 | − | 4.09094i | 0.101173 | − | 0.175237i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4034 | − | 37.0718i | −0.915144 | − | 1.58508i | −0.806691 | − | 0.590974i | \(-0.798744\pi\) |
−0.108453 | − | 0.994102i | \(-0.534590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.0030 | − | 16.2112i | 0.896387 | − | 0.691879i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.4020 | − | 19.7489i | −0.485742 | − | 0.841330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.628926 | + | 1.08933i | −0.0267447 | + | 0.0463231i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.177461 | − | 0.0605211i | 0.00753278 | − | 0.00256898i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.5498 | 1.54866 | 0.774332 | − | 0.632780i | \(-0.218086\pi\) | ||||
0.774332 | + | 0.632780i | \(0.218086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7587 | −1.42784 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.28048 | − | 16.6155i | 0.138502 | − | 0.701505i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8582 | + | 34.3955i | −0.836925 | + | 1.44960i | 0.0555277 | + | 0.998457i | \(0.482316\pi\) |
−0.892453 | + | 0.451140i | \(0.851017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.641469 | + | 1.11106i | 0.0269868 | + | 0.0467425i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.40003 | − | 6.32769i | −0.268776 | − | 0.265738i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.4173 | − | 26.7035i | −0.646325 | − | 1.11947i | −0.983994 | − | 0.178203i | \(-0.942972\pi\) |
0.337669 | − | 0.941265i | \(-0.390362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4009 | − | 33.6033i | 0.811901 | − | 1.40625i | −0.0996310 | − | 0.995024i | \(-0.531766\pi\) |
0.911532 | − | 0.411229i | \(-0.134900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.98380 | + | 35.3725i | −0.291752 | + | 1.47771i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.7083 | 1.36403 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.10713 | −0.0877211 | −0.0438606 | − | 0.999038i | \(-0.513966\pi\) | ||||
−0.0438606 | + | 0.999038i | \(0.513966\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.6344 | + | 11.4707i | −1.39780 | + | 0.476705i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0316459 | + | 0.0548124i | −0.00131289 | + | 0.00227400i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.27164 | + | 7.39870i | 0.176913 | + | 0.306423i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.40562 | − | 1.85678i | 0.0994602 | − | 0.0767686i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.46457 | − | 6.00081i | −0.142998 | − | 0.247680i | 0.785626 | − | 0.618701i | \(-0.212341\pi\) |
−0.928624 | + | 0.371022i | \(0.879008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.80314 | + | 8.31928i | −0.197910 | + | 0.342790i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.39788 | − | 8.21812i | −0.386577 | − | 0.338048i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.0323 | −0.411977 | −0.205989 | − | 0.978554i | \(-0.566041\pi\) | ||||
−0.205989 | + | 0.978554i | \(0.566041\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.42070 | −0.0992392 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6810 | + | 16.3359i | 0.764562 | + | 0.668583i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.6645 | − | 37.5240i | 0.885187 | − | 1.53319i | 0.0396877 | − | 0.999212i | \(-0.487364\pi\) |
0.845499 | − | 0.533977i | \(-0.179303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2578 | + | 40.2837i | 0.948707 | + | 1.64321i | 0.748154 | + | 0.663525i | \(0.230941\pi\) |
0.200553 | + | 0.979683i | \(0.435726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.7886 | − | 9.77444i | −0.968746 | − | 0.398046i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.51902 | + | 2.63102i | 0.0617569 | + | 0.106966i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9227 | + | 32.7751i | −0.768048 | + | 1.33030i | 0.170572 | + | 0.985345i | \(0.445439\pi\) |
−0.938620 | + | 0.344953i | \(0.887895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.7297 | − | 4.34134i | 0.515835 | − | 0.175920i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.51600 | 0.142242 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2811 | 1.22304 | 0.611522 | − | 0.791228i | \(-0.290558\pi\) | ||||
0.611522 | + | 0.791228i | \(0.290558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0299250 | + | 0.151568i | −0.00120669 | + | 0.00611183i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.08770 | − | 14.0083i | 0.325599 | − | 0.563954i | −0.656035 | − | 0.754731i | \(-0.727767\pi\) |
0.981633 | + | 0.190777i | \(0.0611008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.9377 | + | 22.4088i | 0.520012 | + | 0.900687i | 0.999729 | + | 0.0232638i | \(0.00740578\pi\) |
−0.479718 | + | 0.877423i | \(0.659261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.4994 | − | 31.0949i | −0.621971 | − | 1.24779i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65354 | + | 9.79221i | 0.226504 | + | 0.392317i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.6940 | + | 20.2546i | −0.467759 | + | 0.810182i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.30940 | + | 6.63205i | −0.0522925 | + | 0.264859i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.42070 | 0.0965198 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2969 | 1.16629 | 0.583146 | − | 0.812368i | \(-0.301822\pi\) | ||||
0.583146 | + | 0.812368i | \(0.301822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0949 | + | 4.12485i | −0.480731 | + | 0.163948i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.15285 | − | 1.99679i | 0.0457495 | − | 0.0792404i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.53937 | − | 2.66626i | −0.0609920 | − | 0.105641i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.643125 | + | 4.78001i | 0.0254416 | + | 0.189094i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.82630 | + | 15.2876i | 0.348618 | + | 0.603824i | 0.986004 | − | 0.166720i | \(-0.0533177\pi\) |
−0.637386 | + | 0.770545i | \(0.719984\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5426 | − | 25.1885i | 0.573504 | − | 0.993338i | −0.422698 | − | 0.906270i | \(-0.638917\pi\) |
0.996202 | − | 0.0870676i | \(-0.0277496\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.70388 | + | 4.11338i | 0.185215 | + | 0.161964i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.8747 | 1.56764 | 0.783819 | − | 0.620989i | \(-0.213269\pi\) | ||||
0.783819 | + | 0.620989i | \(0.213269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.989241 | −0.0388311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.26502 | − | 3.72961i | −0.167159 | − | 0.146175i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.08986 | + | 12.2800i | −0.277448 | + | 0.480553i | −0.970750 | − | 0.240094i | \(-0.922822\pi\) |
0.693302 | + | 0.720647i | \(0.256155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.09654 | − | 1.89927i | −0.0428455 | − | 0.0742106i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.39803 | − | 40.1207i | −0.210597 | − | 1.56526i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3592 | + | 19.6747i | 0.442491 | + | 0.766418i | 0.997874 | − | 0.0651775i | \(-0.0207614\pi\) |
−0.555382 | + | 0.831595i | \(0.687428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0052 | + | 34.6500i | −0.778111 | + | 1.34773i | 0.154919 | + | 0.987927i | \(0.450488\pi\) |
−0.933030 | + | 0.359800i | \(0.882845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.1335 | − | 12.6640i | 1.44215 | − | 0.491829i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.966223 | 0.0374685 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.9212 | 2.01040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.96091 | − | 45.3865i | 0.346449 | − | 1.75474i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.87684 | − | 10.1790i | 0.226873 | − | 0.392956i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.913881 | + | 1.58289i | 0.0352275 | + | 0.0610159i | 0.883102 | − | 0.469182i | \(-0.155451\pi\) |
−0.847874 | + | 0.530198i | \(0.822118\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.3707 | + | 1.55430i | 0.976519 | + | 0.0598249i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2246 | + | 24.6376i | 0.546694 | + | 0.946902i | 0.998498 | + | 0.0547845i | \(0.0174472\pi\) |
−0.451804 | + | 0.892117i | \(0.649219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.51420 | + | 9.55087i | −0.211616 | + | 0.366529i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.67912 | − | 28.7644i | 0.217624 | − | 1.10225i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.868335 | 0.0332259 | 0.0166130 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166130 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.54014 | −0.211678 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9697 | + | 9.19775i | −1.02896 | + | 0.350916i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.89549 | + | 17.1395i | −0.376988 | + | 0.652962i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.71932 | + | 15.1023i | 0.331699 | + | 0.574519i | 0.982845 | − | 0.184433i | \(-0.0590450\pi\) |
−0.651146 | + | 0.758952i | \(0.725712\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.68787 | − | 1.51530i | −0.140091 | − | 0.0575616i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.56972 | + | 4.45088i | 0.0974750 | + | 0.168832i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.997310 | + | 1.72739i | −0.0377758 | + | 0.0654296i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.35692 | − | 4.68444i | −0.202617 | − | 0.177182i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.23113 | 0.348655 | 0.174327 | − | 0.984688i | \(-0.444225\pi\) | ||||
0.174327 | + | 0.984688i | \(0.444225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.966223 | −0.0364418 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.489914 | − | 0.428413i | −0.0184512 | − | 0.0161350i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.12079 | − | 12.3336i | 0.267805 | − | 0.463852i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.8231 | − | 18.7461i | −0.406469 | − | 0.704025i | 0.588022 | − | 0.808845i | \(-0.299907\pi\) |
−0.994491 | + | 0.104820i | \(0.966573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.98722 | + | 2.30570i | −0.112030 | + | 0.0864703i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.9360 | − | 18.9417i | −0.409556 | − | 0.709373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.673115 | − | 1.16587i | 0.0251731 | − | 0.0436010i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.1578 | − | 11.6492i | 1.27565 | − | 0.435046i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.6526 | 1.81444 | 0.907218 | − | 0.420661i | \(-0.138202\pi\) | ||||
0.907218 | + | 0.420661i | \(0.138202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5858 | −0.394234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.61412 | + | 38.5651i | −0.283172 | + | 1.43425i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.9926 | + | 32.8962i | −0.705368 | + | 1.22173i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.11417 | − | 1.92980i | −0.0413222 | − | 0.0715722i | 0.844625 | − | 0.535359i | \(-0.179824\pi\) |
−0.885947 | + | 0.463787i | \(0.846490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.5447 | − | 24.8557i | −0.390546 | − | 0.920583i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.3374 | + | 69.8664i | 1.49193 | + | 2.58410i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0129 | + | 32.9313i | −0.702258 | + | 1.21635i | 0.265415 | + | 0.964134i | \(0.414491\pi\) |
−0.967672 | + | 0.252211i | \(0.918842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.110382 | + | 0.559079i | −0.00407151 | + | 0.0206220i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.3934 | −0.419681 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.6048 | −1.78796 | −0.893978 | − | 0.448112i | \(-0.852097\pi\) | ||||
−0.893978 | + | 0.448112i | \(0.852097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.8218 | + | 5.05483i | −0.544494 | + | 0.185694i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2700 | − | 36.8408i | 0.780322 | − | 1.35156i | −0.151432 | − | 0.988468i | \(-0.548388\pi\) |
0.931754 | − | 0.363090i | \(-0.118278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47826 | + | 4.29247i | 0.0907963 | + | 0.157264i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.150309 | + | 0.116017i | −0.00549953 | + | 0.00424482i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.77868 | − | 13.4731i | −0.284227 | − | 0.492295i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.62893 | + | 8.01754i | −0.168912 | + | 0.292564i | −0.938038 | − | 0.346534i | \(-0.887359\pi\) |
0.769126 | + | 0.639098i | \(0.220692\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.21577 | − | 4.56102i | −0.190073 | − | 0.166213i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.54470 | −0.0926111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0363 | 1.49149 | 0.745744 | − | 0.666232i | \(-0.232094\pi\) | ||||
0.745744 | + | 0.666232i | \(0.232094\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.5865 | − | 10.1320i | −0.420562 | − | 0.367767i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1859 | − | 33.2309i | 0.695487 | − | 1.20462i | −0.274529 | − | 0.961579i | \(-0.588522\pi\) |
0.970016 | − | 0.243040i | \(-0.0781448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.17871 | − | 12.4339i | −0.259887 | − | 0.450137i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.71719 | − | 2.76001i | −0.242861 | − | 0.0997885i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.14581 | − | 1.98461i | −0.0413730 | − | 0.0716601i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.149772 | − | 0.259412i | 0.00540090 | − | 0.00935463i | −0.863312 | − | 0.504670i | \(-0.831614\pi\) |
0.868713 | + | 0.495315i | \(0.164947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.835252 | − | 0.284854i | 0.0300809 | − | 0.0102588i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.2941 | 1.44928 | 0.724639 | − | 0.689128i | \(-0.242006\pi\) | ||||
0.724639 | + | 0.689128i | \(0.242006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0014 | 0.574788 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.110382 | − | 0.559079i | 0.00395994 | − | 0.0200569i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.398076 | − | 0.689488i | 0.0142626 | − | 0.0247035i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06832 | + | 1.85039i | 0.0382276 | + | 0.0662122i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.2735 | + | 2.46729i | 1.43926 | + | 0.0881738i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.43389 | + | 2.48357i | 0.0511777 | + | 0.0886425i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2565 | + | 21.2289i | −0.436897 | + | 0.756728i | −0.997448 | − | 0.0713920i | \(-0.977256\pi\) |
0.560551 | + | 0.828120i | \(0.310589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.04904 | − | 5.31335i | 0.0373470 | − | 0.189160i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.89932 | 0.138644 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.2280 | 0.966896 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.46721 | − | 1.18246i | 0.122969 | − | 0.0419374i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.9140 | − | 46.6164i | 0.953343 | − | 1.65124i | 0.215228 | − | 0.976564i | \(-0.430951\pi\) |
0.738115 | − | 0.674675i | \(-0.235716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.20119 | − | 7.27667i | −0.148627 | − | 0.257430i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.52317 | + | 33.6183i | 0.159818 | + | 1.18784i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.96691 | − | 15.5311i | −0.316435 | − | 0.548082i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09997 | + | 1.90520i | −0.0387689 | + | 0.0671496i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.43058 | + | 4.74886i | 0.191165 | + | 0.167168i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.44011 | 0.261580 | 0.130790 | − | 0.991410i | \(-0.458249\pi\) | ||||
0.130790 | + | 0.991410i | \(0.458249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.94854 | 0.103537 | 0.0517687 | − | 0.998659i | \(-0.483514\pi\) | ||||
0.0517687 | + | 0.998659i | \(0.483514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.9800 | + | 14.8484i | 0.595515 | + | 0.520758i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.21284 | + | 3.83276i | −0.0775125 | + | 0.134256i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1007 | − | 27.8872i | −0.563291 | − | 0.975648i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.23159 | − | 9.15373i | −0.0430351 | − | 0.319857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.44331 | + | 14.6242i | 0.294674 | + | 0.510390i | 0.974909 | − | 0.222604i | \(-0.0714557\pi\) |
−0.680235 | + | 0.732994i | \(0.738122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.3829 | + | 42.2325i | −0.849935 | + | 1.47213i | 0.0313301 | + | 0.999509i | \(0.490026\pi\) |
−0.881265 | + | 0.472622i | \(0.843308\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.6577 | − | 3.63469i | 0.371053 | − | 0.126544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.4541 | −0.502618 | −0.251309 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251309 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.5659 | −1.13106 | −0.565530 | − | 0.824728i | \(-0.691328\pi\) | ||||
−0.565530 | + | 0.824728i | \(0.691328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.233307 | − | 1.18169i | 0.00809334 | − | 0.0409923i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.67871 | + | 6.37171i | −0.127460 | + | 0.220767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.91423 | + | 3.31554i | 0.0662446 | + | 0.114739i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.58256 | − | 15.2121i | −0.262092 | − | 0.525807i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.4412 | + | 42.3334i | 0.843803 | + | 1.46151i | 0.886656 | + | 0.462429i | \(0.153022\pi\) |
−0.0428531 | + | 0.999081i | \(0.513645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6489 | + | 27.1047i | −0.539617 | + | 0.934644i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.8356 | + | 54.8818i | −0.373199 | + | 1.89023i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.15859 | −0.0398567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.23372 | 0.317274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.1600 | + | 7.89848i | −0.794850 | + | 0.271075i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09997 | − | 1.90520i | 0.0377065 | − | 0.0653096i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5285 | + | 18.2360i | 0.360491 | + | 0.624388i | 0.988042 | − | 0.154187i | \(-0.0492760\pi\) |
−0.627551 | + | 0.778575i | \(0.715943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.68116 | + | 1.10166i | 0.0916939 | + | 0.0376759i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.7290 | − | 32.4396i | −0.639771 | − | 1.10812i | −0.985483 | − | 0.169776i | \(-0.945696\pi\) |
0.345711 | − | 0.938341i | \(-0.387638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.2123 | + | 22.8844i | −0.450799 | + | 0.780807i | −0.998436 | − | 0.0559093i | \(-0.982194\pi\) |
0.547637 | + | 0.836716i | \(0.315528\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.353477 | + | 0.309104i | 0.0120465 | + | 0.0105342i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.1888 | −0.993597 | −0.496798 | − | 0.867866i | \(-0.665491\pi\) | ||||
−0.496798 | + | 0.867866i | \(0.665491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.582905 | 0.0198194 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −48.4138 | − | 42.3362i | −1.64422 | − | 1.43781i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.835853 | + | 1.44774i | −0.0283544 | + | 0.0491112i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.1967 | − | 22.8573i | −0.447153 | − | 0.774491i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.1909 | + | 20.2155i | −0.886428 | + | 0.684191i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.62727 | − | 2.81852i | −0.0550118 | − | 0.0952832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.70263 | + | 9.87725i | −0.192564 | + | 0.333531i | −0.946099 | − | 0.323877i | \(-0.895014\pi\) |
0.753535 | + | 0.657408i | \(0.228347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.3382 | − | 9.32341i | 0.922095 | − | 0.314471i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.7109 | −0.563005 | −0.281503 | − | 0.959560i | \(-0.590833\pi\) | ||||
−0.281503 | + | 0.959560i | \(0.590833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8347 | 0.398268 | 0.199134 | − | 0.979972i | \(-0.436187\pi\) | ||||
0.199134 | + | 0.979972i | \(0.436187\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0821620 | + | 0.416146i | −0.00276184 | + | 0.0139886i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8800 | + | 30.9691i | −0.600353 | + | 1.03984i | 0.392414 | + | 0.919789i | \(0.371640\pi\) |
−0.992767 | + | 0.120053i | \(0.961693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50394 | − | 6.06899i | −0.117518 | − | 0.203548i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.50574 | − | 8.40960i | −0.284953 | − | 0.281732i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.67690 | + | 2.90448i | 0.0561154 | + | 0.0971947i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.10737 | − | 1.91801i | 0.0370152 | − | 0.0641122i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.90636 | − | 34.9803i | 0.230597 | − | 1.16796i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.4007 | 0.847159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.2955 | 1.57564 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.9755 | − | 6.13037i | 0.598188 | − | 0.204006i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.18320 | − | 3.78142i | 0.0725721 | − | 0.125698i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.32308 | + | 14.4160i | 0.276363 | + | 0.478675i | 0.970478 | − | 0.241189i | \(-0.0775374\pi\) |
−0.694115 | + | 0.719864i | \(0.744204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.8218 | − | 26.1054i | 1.12180 | − | 0.865862i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.88258 | − | 17.1171i | −0.327425 | − | 0.567116i | 0.654575 | − | 0.755997i | \(-0.272847\pi\) |
−0.982000 | + | 0.188881i | \(0.939514\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0420579 | + | 0.0728465i | −0.00139191 | + | 0.00241087i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.79391 | − | 3.31764i | −0.125423 | − | 0.109678i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.66560 | −0.220118 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.2384 | −0.337734 | −0.168867 | − | 0.985639i | \(-0.554011\pi\) | ||||
−0.168867 | + | 0.985639i | \(0.554011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.2488 | − | 30.8238i | −1.16149 | − | 1.01568i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.47483 | + | 4.28653i | −0.0814600 | + | 0.141093i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.804731 | + | 1.39384i | 0.0264594 | + | 0.0458290i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.3743 | − | 12.0695i | −0.964778 | − | 0.396416i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.5842 | + | 30.4567i | 0.576917 | + | 0.999250i | 0.995830 | + | 0.0912240i | \(0.0290779\pi\) |
−0.418913 | + | 0.908026i | \(0.637589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46835 | − | 2.54326i | 0.0481234 | − | 0.0833521i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.4840 | + | 13.1246i | −1.25991 | + | 0.429679i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.21715 | −0.105212 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.5829 | −1.03177 | −0.515884 | − | 0.856659i | \(-0.672536\pi\) | ||||
−0.515884 | + | 0.856659i | \(0.672536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.244639 | − | 1.23908i | 0.00798349 | − | 0.0404359i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.49641 | + | 11.2521i | −0.211777 | + | 0.366808i | −0.952271 | − | 0.305255i | \(-0.901258\pi\) |
0.740494 | + | 0.672063i | \(0.234592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.906357 | + | 1.56986i | 0.0295150 | + | 0.0511216i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.943743 | + | 1.42553i | −0.0307000 | + | 0.0463725i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7246 | + | 30.6998i | 0.575971 | + | 0.997610i | 0.995935 | + | 0.0900699i | \(0.0287090\pi\) |
−0.419965 | + | 0.907540i | \(0.637958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7723 | − | 35.9787i | 0.674298 | − | 1.16792i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2322 | + | 56.8903i | −0.364228 | + | 1.84479i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0040 | −1.29586 | −0.647928 | − | 0.761702i | \(-0.724364\pi\) | ||||
−0.647928 | + | 0.761702i | \(0.724364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.84898 | 0.221628 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9180 | − | 5.76972i | 0.546882 | − | 0.186508i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.41926 | + | 14.5826i | −0.271872 | + | 0.470896i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1499 | + | 17.5802i | 0.327417 | + | 0.567104i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.22341 | − | 46.2553i | −0.200546 | − | 1.49056i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.37522 | + | 5.84605i | 0.108652 | + | 0.188191i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.03814 | + | 5.26222i | −0.0977001 | + | 0.169222i | −0.910732 | − | 0.412997i | \(-0.864482\pi\) |
0.813032 | + | 0.582219i | \(0.197815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.1716 | + | 24.6351i | 0.905004 | + | 0.791395i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.1397 | 1.83370 | 0.916850 | − | 0.399232i | \(-0.130723\pi\) | ||||
0.916850 | + | 0.399232i | \(0.130723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6206 | 0.500775 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.6365 | + | 17.1714i | 0.628870 | + | 0.549925i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.91064 | − | 10.2375i | 0.189098 | − | 0.327528i | −0.755852 | − | 0.654743i | \(-0.772777\pi\) |
0.944950 | + | 0.327215i | \(0.106110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.51364 | + | 13.0140i | 0.240137 | + | 0.415929i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.74339 | − | 42.6876i | −0.183372 | − | 1.36291i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.26336 | − | 16.0446i | −0.295455 | − | 0.511744i | 0.679635 | − | 0.733550i | \(-0.262138\pi\) |
−0.975091 | + | 0.221806i | \(0.928805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18574 | + | 2.05377i | −0.0377809 | + | 0.0654384i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.87217 | + | 0.638484i | −0.0595918 | + | 0.0203232i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 73.3174 | 2.33136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5408 | 0.398371 | 0.199186 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199186 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.30158 | − | 16.7223i | 0.104773 | − | 0.530667i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.35700 | − | 4.08245i | 0.0747220 | − | 0.129422i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.94209 | − | 13.7561i | −0.251528 | − | 0.435660i | 0.712418 | − | 0.701755i | \(-0.247600\pi\) |
−0.963947 | + | 0.266095i | \(0.914267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.943743 | − | 1.42553i | 0.0298587 | − | 0.0451018i |
(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 | 504.2.r.e.337.1 | yes | 8 | |
3.2 | odd | 2 | 1512.2.r.e.1009.2 | 8 | |||
4.3 | odd | 2 | 1008.2.r.l.337.4 | 8 | |||
9.2 | odd | 6 | 1512.2.r.e.505.2 | 8 | |||
9.4 | even | 3 | 4536.2.a.z.1.2 | 4 | |||
9.5 | odd | 6 | 4536.2.a.y.1.3 | 4 | |||
9.7 | even | 3 | inner | 504.2.r.e.169.1 | ✓ | 8 | |
12.11 | even | 2 | 3024.2.r.m.1009.2 | 8 | |||
36.7 | odd | 6 | 1008.2.r.l.673.4 | 8 | |||
36.11 | even | 6 | 3024.2.r.m.2017.2 | 8 | |||
36.23 | even | 6 | 9072.2.a.cg.1.3 | 4 | |||
36.31 | odd | 6 | 9072.2.a.cj.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.e.169.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
504.2.r.e.337.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1008.2.r.l.337.4 | 8 | 4.3 | odd | 2 | |||
1008.2.r.l.673.4 | 8 | 36.7 | odd | 6 | |||
1512.2.r.e.505.2 | 8 | 9.2 | odd | 6 | |||
1512.2.r.e.1009.2 | 8 | 3.2 | odd | 2 | |||
3024.2.r.m.1009.2 | 8 | 12.11 | even | 2 | |||
3024.2.r.m.2017.2 | 8 | 36.11 | even | 6 | |||
4536.2.a.y.1.3 | 4 | 9.5 | odd | 6 | |||
4536.2.a.z.1.2 | 4 | 9.4 | even | 3 | |||
9072.2.a.cg.1.3 | 4 | 36.23 | even | 6 | |||
9072.2.a.cj.1.2 | 4 | 36.31 | odd | 6 |