Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(656,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.656");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.s (of order \(6\), degree \(2\), not 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 656.17 | ||
Character | \(\chi\) | \(=\) | 1323.656 |
Dual form | 1323.2.s.d.962.17 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58658 | − | 0.916012i | 1.12188 | − | 0.647718i | 0.180001 | − | 0.983667i | \(-0.442390\pi\) |
0.941880 | + | 0.335948i | \(0.109057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.678156 | − | 1.17460i | 0.339078 | − | 0.587300i | ||||
\(5\) | −0.645568 | −0.288707 | −0.144353 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144353 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.17925i | 0.416928i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.02425 | + | 0.591348i | −0.323895 | + | 0.187001i | ||||
\(11\) | 5.31595i | 1.60282i | 0.598116 | + | 0.801410i | \(0.295916\pi\) | ||||
−0.598116 | + | 0.801410i | \(0.704084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.44045 | + | 2.56370i | −1.23156 | + | 0.711041i | −0.967355 | − | 0.253425i | \(-0.918443\pi\) |
−0.264205 | + | 0.964467i | \(0.585110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.43652 | + | 4.22018i | 0.609130 | + | 1.05504i | ||||
\(17\) | −0.814931 | − | 1.41150i | −0.197650 | − | 0.342339i | 0.750116 | − | 0.661306i | \(-0.229998\pi\) |
−0.947766 | + | 0.318967i | \(0.896664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.09039 | + | 1.20689i | 0.479569 | + | 0.276879i | 0.720237 | − | 0.693728i | \(-0.244033\pi\) |
−0.240668 | + | 0.970608i | \(0.577366\pi\) | |||||||
\(20\) | −0.437796 | + | 0.758285i | −0.0978942 | + | 0.169558i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.86947 | + | 8.43418i | 1.03818 | + | 1.79817i | ||||
\(23\) | 1.47157i | 0.306843i | 0.988161 | + | 0.153422i | \(0.0490292\pi\) | ||||
−0.988161 | + | 0.153422i | \(0.950971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58324 | −0.916648 | ||||||||
\(26\) | −4.69675 | + | 8.13502i | −0.921109 | + | 1.59541i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.43846 | + | 3.71724i | 1.19559 | + | 0.690275i | 0.959569 | − | 0.281473i | \(-0.0908229\pi\) |
0.236022 | + | 0.971748i | \(0.424156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.90799 | − | 2.83363i | −0.881501 | − | 0.508935i | −0.0103477 | − | 0.999946i | \(-0.503294\pi\) |
−0.871153 | + | 0.491012i | \(0.836627\pi\) | |||||||
\(32\) | 5.68894 | + | 3.28451i | 1.00567 | + | 0.580625i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.58590 | − | 1.49297i | −0.443479 | − | 0.256043i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.99736 | − | 6.92362i | 0.657161 | − | 1.13824i | −0.324186 | − | 0.945993i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615763\pi\) | |||||||
\(38\) | 4.42210 | 0.717359 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.761288i | − | 0.120370i | ||||||
\(41\) | 5.99052 | + | 10.3759i | 0.935562 | + | 1.62044i | 0.773628 | + | 0.633640i | \(0.218440\pi\) |
0.161934 | + | 0.986802i | \(0.448227\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51281 | + | 2.62026i | −0.230701 | + | 0.399586i | −0.958015 | − | 0.286719i | \(-0.907435\pi\) |
0.727314 | + | 0.686305i | \(0.240769\pi\) | |||||||
\(44\) | 6.24412 | + | 3.60504i | 0.941336 | + | 0.543481i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.34797 | + | 2.33476i | 0.198748 | + | 0.344241i | ||||
\(47\) | −1.54176 | − | 2.67041i | −0.224889 | − | 0.389520i | 0.731397 | − | 0.681952i | \(-0.238869\pi\) |
−0.956286 | + | 0.292432i | \(0.905535\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.27168 | + | 4.19830i | −1.02837 | + | 0.593730i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.95434i | 0.964394i | ||||||||
\(53\) | 2.04554 | − | 1.18100i | 0.280977 | − | 0.162222i | −0.352889 | − | 0.935665i | \(-0.614801\pi\) |
0.633866 | + | 0.773443i | \(0.281467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.43181i | − | 0.462745i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.6202 | 1.78841 | ||||||||
\(59\) | 1.47918 | − | 2.56202i | 0.192573 | − | 0.333546i | −0.753529 | − | 0.657414i | \(-0.771650\pi\) |
0.946102 | + | 0.323868i | \(0.104983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.18018 | + | 5.30018i | −1.17540 | + | 0.678618i | −0.954946 | − | 0.296779i | \(-0.904088\pi\) |
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(62\) | −10.3825 | −1.31859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.28853 | 0.286066 | ||||||||
\(65\) | 2.86662 | − | 1.65504i | 0.355560 | − | 0.205283i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.07747 | − | 8.79444i | 0.620312 | − | 1.07441i | −0.369116 | − | 0.929383i | \(-0.620339\pi\) |
0.989428 | − | 0.145028i | \(-0.0463273\pi\) | |||||||
\(68\) | −2.21060 | −0.268075 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.76597i | 0.565617i | 0.959176 | + | 0.282808i | \(0.0912661\pi\) | ||||
−0.959176 | + | 0.282808i | \(0.908734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2239 | − | 5.90277i | 1.19662 | − | 0.690867i | 0.236817 | − | 0.971554i | \(-0.423896\pi\) |
0.959799 | + | 0.280687i | \(0.0905624\pi\) | |||||||
\(74\) | − | 14.6465i | − | 1.70262i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.83523 | − | 1.63692i | 0.325223 | − | 0.187767i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.48104 | − | 6.02934i | −0.391648 | − | 0.678354i | 0.601019 | − | 0.799235i | \(-0.294762\pi\) |
−0.992667 | + | 0.120881i | \(0.961428\pi\) | |||||||
\(80\) | −1.57294 | − | 2.72441i | −0.175860 | − | 0.304599i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.0089 | + | 10.9748i | 2.09918 | + | 1.21196i | ||||
\(83\) | 3.51618 | − | 6.09021i | 0.385951 | − | 0.668487i | −0.605949 | − | 0.795503i | \(-0.707207\pi\) |
0.991901 | + | 0.127016i | \(0.0405399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.526093 | + | 0.911221i | 0.0570628 | + | 0.0988357i | ||||
\(86\) | 5.54300i | 0.597717i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.26884 | −0.668261 | ||||||||
\(89\) | −2.16337 | + | 3.74706i | −0.229317 | + | 0.397188i | −0.957606 | − | 0.288082i | \(-0.906982\pi\) |
0.728289 | + | 0.685270i | \(0.240316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.72850 | + | 0.997953i | 0.180209 | + | 0.104044i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.89226 | − | 2.82455i | −0.504598 | − | 0.291330i | ||||
\(95\) | −1.34949 | − | 0.779129i | −0.138455 | − | 0.0799370i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3946 | + | 8.31075i | 1.46156 | + | 0.843829i | 0.999083 | − | 0.0428048i | \(-0.0136294\pi\) |
0.462472 | + | 0.886634i | \(0.346963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.10815 | + | 5.38348i | −0.310815 | + | 0.538348i | ||||
\(101\) | −4.65154 | −0.462846 | −0.231423 | − | 0.972853i | \(-0.574338\pi\) | ||||
−0.231423 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3043i | 1.01532i | 0.861559 | + | 0.507658i | \(0.169489\pi\) | ||||
−0.861559 | + | 0.507658i | \(0.830511\pi\) | |||||||
\(104\) | −3.02324 | − | 5.23641i | −0.296453 | − | 0.513472i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.16361 | − | 3.74749i | 0.210149 | − | 0.363988i | ||||
\(107\) | 0.267212 | + | 0.154275i | 0.0258324 | + | 0.0149143i | 0.512861 | − | 0.858472i | \(-0.328586\pi\) |
−0.487028 | + | 0.873386i | \(0.661919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.14423 | + | 5.44596i | 0.301162 | + | 0.521628i | 0.976399 | − | 0.215972i | \(-0.0692921\pi\) |
−0.675237 | + | 0.737601i | \(0.735959\pi\) | |||||||
\(110\) | −3.14358 | − | 5.44484i | −0.299728 | − | 0.519145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.72869 | + | 4.46216i | −0.727054 | + | 0.419765i | −0.817343 | − | 0.576151i | \(-0.804554\pi\) |
0.0902895 | + | 0.995916i | \(0.471221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.949998i | − | 0.0885877i | ||||||
\(116\) | 8.73256 | − | 5.04174i | 0.810797 | − | 0.468114i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.41979i | − | 0.498932i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.2593 | −1.56903 | ||||||||
\(122\) | −9.71006 | + | 16.8183i | −0.879107 | + | 1.52266i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.65676 | + | 3.84328i | −0.597795 | + | 0.345137i | ||||
\(125\) | 6.18664 | 0.553350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.49989 | −0.221829 | −0.110915 | − | 0.993830i | \(-0.535378\pi\) | ||||
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(128\) | −7.74695 | + | 4.47270i | −0.684740 | + | 0.395335i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.03208 | − | 5.25171i | 0.265931 | − | 0.460605i | ||||
\(131\) | −2.53450 | −0.221440 | −0.110720 | − | 0.993852i | \(-0.535316\pi\) | ||||
−0.110720 | + | 0.993852i | \(0.535316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.6041i | − | 1.60715i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.66452 | − | 0.961008i | 0.142731 | − | 0.0824058i | ||||
\(137\) | 1.21291i | 0.103626i | 0.998657 | + | 0.0518131i | \(0.0165000\pi\) | ||||
−0.998657 | + | 0.0518131i | \(0.983500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.11754 | − | 3.53196i | 0.518883 | − | 0.299577i | −0.217594 | − | 0.976039i | \(-0.569821\pi\) |
0.736478 | + | 0.676462i | \(0.236488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.36569 | + | 7.56159i | 0.366360 | + | 0.634555i | ||||
\(143\) | −13.6285 | − | 23.6052i | −1.13967 | − | 1.97397i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.15646 | − | 2.39974i | −0.345175 | − | 0.199287i | ||||
\(146\) | 10.8140 | − | 18.7304i | 0.894974 | − | 1.55014i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.42166 | − | 9.39060i | −0.445658 | − | 0.771902i | ||||
\(149\) | − | 6.93132i | − | 0.567836i | −0.958849 | − | 0.283918i | \(-0.908366\pi\) | ||
0.958849 | − | 0.283918i | \(-0.0916343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.31878 | 0.514215 | 0.257108 | − | 0.966383i | \(-0.417231\pi\) | ||||
0.257108 | + | 0.966383i | \(0.417231\pi\) | |||||||
\(152\) | −1.42323 | + | 2.46510i | −0.115439 | + | 0.199946i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.16844 | + | 1.82930i | 0.254495 | + | 0.146933i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.72363 | + | 0.995139i | 0.137561 | + | 0.0794208i | 0.567201 | − | 0.823579i | \(-0.308026\pi\) |
−0.429640 | + | 0.903000i | \(0.641360\pi\) | |||||||
\(158\) | −11.0459 | − | 6.37735i | −0.878765 | − | 0.507355i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.67260 | − | 2.12038i | −0.290345 | − | 0.167631i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.99365 | − | 5.18515i | 0.234480 | − | 0.406132i | −0.724641 | − | 0.689126i | \(-0.757994\pi\) |
0.959122 | + | 0.282994i | \(0.0913278\pi\) | |||||||
\(164\) | 16.2500 | 1.26891 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.8835i | − | 0.999951i | ||||||
\(167\) | −0.697990 | − | 1.20895i | −0.0540121 | − | 0.0935516i | 0.837755 | − | 0.546046i | \(-0.183868\pi\) |
−0.891767 | + | 0.452494i | \(0.850534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.64508 | − | 11.5096i | 0.511160 | − | 0.885355i | ||||
\(170\) | 1.66938 | + | 0.963816i | 0.128035 | + | 0.0739213i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.05184 | + | 3.55389i | 0.156451 | + | 0.270982i | ||||
\(173\) | 3.80506 | + | 6.59055i | 0.289293 | + | 0.501071i | 0.973641 | − | 0.228085i | \(-0.0732464\pi\) |
−0.684348 | + | 0.729156i | \(0.739913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.4343 | + | 12.9524i | −1.69105 | + | 0.976326i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.92669i | 0.594130i | ||||||||
\(179\) | −8.00888 | + | 4.62393i | −0.598612 | + | 0.345609i | −0.768495 | − | 0.639855i | \(-0.778994\pi\) |
0.169883 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.9634i | − | 0.889234i | −0.895721 | − | 0.444617i | \(-0.853340\pi\) | ||
0.895721 | − | 0.444617i | \(-0.146660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.73535 | −0.127932 | ||||||||
\(185\) | −2.58057 | + | 4.46967i | −0.189727 | + | 0.328617i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50347 | − | 4.33213i | 0.548708 | − | 0.316797i | ||||
\(188\) | −4.18223 | −0.305020 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.85477 | −0.207107 | ||||||||
\(191\) | −17.5586 | + | 10.1375i | −1.27050 | + | 0.733521i | −0.975081 | − | 0.221847i | \(-0.928791\pi\) |
−0.295415 | + | 0.955369i | \(0.595458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.44583 | − | 14.6286i | 0.607944 | − | 1.05299i | −0.383634 | − | 0.923485i | \(-0.625328\pi\) |
0.991579 | − | 0.129505i | \(-0.0413389\pi\) | |||||||
\(194\) | 30.4510 | 2.18625 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.7102i | − | 1.33305i | −0.745484 | − | 0.666524i | \(-0.767781\pi\) | ||
0.745484 | − | 0.666524i | \(-0.232219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6271 | + | 9.02231i | −1.10778 | + | 0.639574i | −0.938252 | − | 0.345952i | \(-0.887556\pi\) |
−0.169523 | + | 0.985526i | \(0.554223\pi\) | |||||||
\(200\) | − | 5.40480i | − | 0.382177i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.38004 | + | 4.26087i | −0.519258 | + | 0.299794i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.86729 | − | 6.69834i | −0.270103 | − | 0.467833i | ||||
\(206\) | 9.43889 | + | 16.3486i | 0.657639 | + | 1.13906i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.6385 | − | 12.4930i | −1.50036 | − | 0.866234i | ||||
\(209\) | −6.41576 | + | 11.1124i | −0.443788 | + | 0.768663i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.03491 | − | 6.98868i | −0.277775 | − | 0.481120i | 0.693057 | − | 0.720883i | \(-0.256264\pi\) |
−0.970831 | + | 0.239763i | \(0.922930\pi\) | |||||||
\(212\) | − | 3.20360i | − | 0.220024i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.565272 | 0.0386412 | ||||||||
\(215\) | 0.976621 | − | 1.69156i | 0.0666050 | − | 0.115363i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.97713 | + | 5.76030i | 0.675736 | + | 0.390137i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.03101 | − | 2.32730i | −0.271770 | − | 0.156907i | ||||
\(221\) | 7.23732 | + | 4.17847i | 0.486835 | + | 0.281074i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2450 | + | 11.6884i | 1.35570 | + | 0.782716i | 0.989041 | − | 0.147638i | \(-0.0471671\pi\) |
0.366662 | + | 0.930354i | \(0.380500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.17479 | + | 14.1591i | −0.543779 | + | 0.941852i | ||||
\(227\) | 14.4431 | 0.958620 | 0.479310 | − | 0.877646i | \(-0.340887\pi\) | ||||
0.479310 | + | 0.877646i | \(0.340887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.1137i | − | 0.866578i | −0.901255 | − | 0.433289i | \(-0.857353\pi\) | ||
0.901255 | − | 0.433289i | \(-0.142647\pi\) | |||||||
\(230\) | −0.870209 | − | 1.50725i | −0.0573799 | − | 0.0993849i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.38357 | + | 7.59256i | −0.287795 | + | 0.498476i | ||||
\(233\) | −7.31966 | − | 4.22601i | −0.479527 | − | 0.276855i | 0.240692 | − | 0.970601i | \(-0.422626\pi\) |
−0.720219 | + | 0.693746i | \(0.755959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.995314 | + | 1.72393i | 0.0649271 | + | 0.112457i | ||||
\(236\) | −2.00623 | − | 3.47489i | −0.130594 | − | 0.226196i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.2111 | − | 13.9783i | 1.56608 | − | 0.904179i | 0.569466 | − | 0.822015i | \(-0.307150\pi\) |
0.996619 | − | 0.0821642i | \(-0.0261832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.4079i | − | 1.44342i | −0.692196 | − | 0.721710i | \(-0.743357\pi\) | ||
0.692196 | − | 0.721710i | \(-0.256643\pi\) | |||||||
\(242\) | −27.3833 | + | 15.8097i | −1.76026 | + | 1.01629i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.3774i | 0.920418i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.3764 | −0.787491 | ||||||||
\(248\) | 3.34156 | − | 5.78775i | 0.212189 | − | 0.367523i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.81559 | − | 5.66703i | 0.620792 | − | 0.358415i | ||||
\(251\) | −6.39587 | −0.403704 | −0.201852 | − | 0.979416i | \(-0.564696\pi\) | ||||
−0.201852 | + | 0.979416i | \(0.564696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.82278 | −0.491814 | ||||||||
\(254\) | −3.96627 | + | 2.28993i | −0.248866 | + | 0.143683i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4826 | + | 18.1565i | −0.655165 | + | 1.13478i | ||||
\(257\) | 3.31409 | 0.206727 | 0.103364 | − | 0.994644i | \(-0.467039\pi\) | ||||
0.103364 | + | 0.994644i | \(0.467039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.48950i | − | 0.278427i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.02118 | + | 2.32163i | −0.248429 | + | 0.143431i | ||||
\(263\) | 22.6901i | 1.39913i | 0.714567 | + | 0.699567i | \(0.246624\pi\) | ||||
−0.714567 | + | 0.699567i | \(0.753376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.32054 | + | 0.762413i | −0.0811200 | + | 0.0468347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.88664 | − | 11.9280i | −0.420668 | − | 0.728619i | ||||
\(269\) | 1.38050 | + | 2.39110i | 0.0841707 | + | 0.145788i | 0.905038 | − | 0.425332i | \(-0.139843\pi\) |
−0.820867 | + | 0.571120i | \(0.806509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.27342 | − | 3.04461i | −0.320337 | − | 0.184947i | 0.331206 | − | 0.943559i | \(-0.392545\pi\) |
−0.651543 | + | 0.758612i | \(0.725878\pi\) | |||||||
\(272\) | 3.97119 | − | 6.87830i | 0.240789 | − | 0.417058i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11104 | + | 1.92438i | 0.0671205 | + | 0.116256i | ||||
\(275\) | − | 24.3643i | − | 1.46922i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.43367 | −0.566814 | −0.283407 | − | 0.959000i | \(-0.591465\pi\) | ||||
−0.283407 | + | 0.959000i | \(0.591465\pi\) | |||||||
\(278\) | 6.47064 | − | 11.2075i | 0.388083 | − | 0.672180i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.57153 | − | 2.63938i | −0.272715 | − | 0.157452i | 0.357406 | − | 0.933949i | \(-0.383661\pi\) |
−0.630121 | + | 0.776497i | \(0.716995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0346 | + | 9.83496i | 1.01260 | + | 0.584628i | 0.911953 | − | 0.410294i | \(-0.134574\pi\) |
0.100651 | + | 0.994922i | \(0.467907\pi\) | |||||||
\(284\) | 5.59811 | + | 3.23207i | 0.332187 | + | 0.191788i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −43.2453 | − | 24.9677i | −2.55715 | − | 1.47637i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.17178 | − | 12.4219i | 0.421869 | − | 0.730699i | ||||
\(290\) | −8.79274 | −0.516328 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 16.0120i | − | 0.937031i | ||||||
\(293\) | 9.11647 | + | 15.7902i | 0.532590 | + | 0.922473i | 0.999276 | + | 0.0380495i | \(0.0121145\pi\) |
−0.466686 | + | 0.884423i | \(0.654552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.954912 | + | 1.65396i | −0.0555971 | + | 0.0962970i | ||||
\(296\) | 8.16470 | + | 4.71389i | 0.474563 | + | 0.273989i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.34917 | − | 10.9971i | −0.367797 | − | 0.637044i | ||||
\(299\) | −3.77265 | − | 6.53443i | −0.218178 | − | 0.377896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.0253 | − | 5.78808i | 0.576888 | − | 0.333067i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.7624i | 0.674622i | ||||||||
\(305\) | 5.92643 | − | 3.42163i | 0.339347 | − | 0.195922i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0447i | 1.48645i | 0.669042 | + | 0.743224i | \(0.266704\pi\) | ||||
−0.669042 | + | 0.743224i | \(0.733296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.70265 | 0.380685 | ||||||||
\(311\) | −14.1433 | + | 24.4969i | −0.801992 | + | 1.38909i | 0.116311 | + | 0.993213i | \(0.462893\pi\) |
−0.918303 | + | 0.395878i | \(0.870440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.82891 | − | 2.78797i | 0.272946 | − | 0.157586i | −0.357280 | − | 0.933998i | \(-0.616296\pi\) |
0.630226 | + | 0.776412i | \(0.282962\pi\) | |||||||
\(314\) | 3.64624 | 0.205769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.44276 | −0.531197 | ||||||||
\(317\) | 29.0708 | − | 16.7841i | 1.63278 | − | 0.942686i | 0.649550 | − | 0.760319i | \(-0.274957\pi\) |
0.983230 | − | 0.182367i | \(-0.0583760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.7607 | + | 34.2265i | −1.10639 | + | 1.91632i | ||||
\(320\) | −1.47740 | −0.0825893 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.93412i | − | 0.218901i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.3517 | − | 11.7500i | 1.12891 | − | 0.651775i | ||||
\(326\) | − | 10.9689i | − | 0.607509i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.2358 | + | 7.06433i | −0.675608 | + | 0.390063i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1867 | + | 26.3042i | 0.834739 | + | 1.44581i | 0.894243 | + | 0.447582i | \(0.147715\pi\) |
−0.0595042 | + | 0.998228i | \(0.518952\pi\) | |||||||
\(332\) | −4.76904 | − | 8.26023i | −0.261735 | − | 0.453339i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.21483 | − | 1.27873i | −0.121190 | − | 0.0699692i | ||||
\(335\) | −3.27785 | + | 5.67741i | −0.179088 | + | 0.310190i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86121 | + | 3.22371i | 0.101387 | + | 0.175607i | 0.912256 | − | 0.409620i | \(-0.134339\pi\) |
−0.810870 | + | 0.585227i | \(0.801005\pi\) | |||||||
\(338\) | − | 24.3479i | − | 1.32435i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.42709 | 0.0773950 | ||||||||
\(341\) | 15.0634 | − | 26.0906i | 0.815730 | − | 1.41289i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.08995 | − | 1.78398i | −0.166599 | − | 0.0961858i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0741 | + | 6.97096i | 0.649105 | + | 0.374761i | ||||
\(347\) | 6.18028 | + | 3.56818i | 0.331775 | + | 0.191550i | 0.656629 | − | 0.754214i | \(-0.271982\pi\) |
−0.324854 | + | 0.945764i | \(0.605315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.2087 | − | 7.62607i | −0.707047 | − | 0.408214i | 0.102920 | − | 0.994690i | \(-0.467182\pi\) |
−0.809967 | + | 0.586476i | \(0.800515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.4603 | + | 30.2421i | −0.930637 | + | 1.61191i | ||||
\(353\) | 34.4718 | 1.83475 | 0.917373 | − | 0.398028i | \(-0.130305\pi\) | ||||
0.917373 | + | 0.398028i | \(0.130305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.07676i | − | 0.163297i | ||||||
\(356\) | 2.93420 | + | 5.08219i | 0.155512 | + | 0.269355i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.47115 | + | 14.6725i | −0.447714 | + | 0.775464i | ||||
\(359\) | −5.73791 | − | 3.31278i | −0.302835 | − | 0.174842i | 0.340881 | − | 0.940107i | \(-0.389275\pi\) |
−0.643716 | + | 0.765265i | \(0.722608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58684 | − | 11.4087i | −0.346676 | − | 0.600460i | ||||
\(362\) | −10.9586 | − | 18.9809i | −0.575973 | − | 0.997614i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.60022 | + | 3.81064i | −0.345472 | + | 0.199458i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.09716i | − | 0.161670i | −0.996727 | − | 0.0808352i | \(-0.974241\pi\) | ||
0.996727 | − | 0.0808352i | \(-0.0257587\pi\) | |||||||
\(368\) | −6.21028 | + | 3.58551i | −0.323733 | + | 0.186907i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.45532i | 0.491559i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.69999 | 0.502246 | 0.251123 | − | 0.967955i | \(-0.419200\pi\) | ||||
0.251123 | + | 0.967955i | \(0.419200\pi\) | |||||||
\(374\) | 7.93657 | − | 13.7465i | 0.410390 | − | 0.710816i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.14909 | − | 1.81813i | 0.162402 | − | 0.0937628i | ||||
\(377\) | −38.1195 | −1.96326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.76103 | 0.398657 | 0.199329 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199329 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(380\) | −1.83033 | + | 1.05674i | −0.0938941 | + | 0.0542098i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.5721 | + | 32.1678i | −0.950231 | + | 1.64585i | ||||
\(383\) | −24.6127 | −1.25765 | −0.628825 | − | 0.777547i | \(-0.716464\pi\) | ||||
−0.628825 | + | 0.777547i | \(0.716464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 30.9459i | − | 1.57511i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.5236 | − | 11.2720i | 0.991162 | − | 0.572248i | ||||
\(389\) | 6.42681i | 0.325852i | 0.986638 | + | 0.162926i | \(0.0520932\pi\) | ||||
−0.986638 | + | 0.162926i | \(0.947907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.07712 | − | 1.19923i | 0.105044 | − | 0.0606474i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.1388 | − | 29.6852i | −0.863439 | − | 1.49552i | ||||
\(395\) | 2.24725 | + | 3.89235i | 0.113071 | + | 0.195846i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4835 | − | 6.62998i | −0.576338 | − | 0.332749i | 0.183339 | − | 0.983050i | \(-0.441310\pi\) |
−0.759677 | + | 0.650301i | \(0.774643\pi\) | |||||||
\(398\) | −16.5291 | + | 28.6292i | −0.828528 | + | 1.43505i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.1672 | − | 19.3421i | −0.558358 | − | 0.967105i | ||||
\(401\) | 15.8052i | 0.789273i | 0.918837 | + | 0.394636i | \(0.129129\pi\) | ||||
−0.918837 | + | 0.394636i | \(0.870871\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.0582 | 1.44749 | ||||||||
\(404\) | −3.15447 | + | 5.46370i | −0.156941 | + | 0.271829i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.8056 | + | 21.2497i | 1.82439 | + | 1.05331i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.69257 | + | 2.70926i | 0.232033 | + | 0.133964i | 0.611509 | − | 0.791237i | \(-0.290563\pi\) |
−0.379477 | + | 0.925201i | \(0.623896\pi\) | |||||||
\(410\) | −12.2715 | − | 7.08497i | −0.606048 | − | 0.349902i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.1035 | + | 6.98795i | 0.596296 | + | 0.344271i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.26994 | + | 3.93165i | −0.111427 | + | 0.192997i | ||||
\(416\) | −33.6820 | −1.65139 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.5077i | 1.14980i | ||||||||
\(419\) | 12.2469 | + | 21.2123i | 0.598302 | + | 1.03629i | 0.993072 | + | 0.117509i | \(0.0374909\pi\) |
−0.394770 | + | 0.918780i | \(0.629176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.99347 | − | 10.3810i | 0.292104 | − | 0.505939i | −0.682203 | − | 0.731163i | \(-0.738978\pi\) |
0.974307 | + | 0.225224i | \(0.0723113\pi\) | |||||||
\(422\) | −12.8034 | − | 7.39206i | −0.623261 | − | 0.359840i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.39269 | + | 2.41221i | 0.0676350 | + | 0.117147i | ||||
\(425\) | 3.73502 | + | 6.46925i | 0.181175 | + | 0.313805i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.362424 | − | 0.209245i | 0.0175184 | − | 0.0101143i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 3.57839i | − | 0.172565i | ||||||
\(431\) | 26.6926 | − | 15.4110i | 1.28574 | − | 0.742320i | 0.307845 | − | 0.951437i | \(-0.400392\pi\) |
0.977891 | + | 0.209117i | \(0.0670590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.06173i | − | 0.291308i | −0.989336 | − | 0.145654i | \(-0.953471\pi\) | ||
0.989336 | − | 0.145654i | \(-0.0465287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.52910 | 0.408470 | ||||||||
\(437\) | −1.77602 | + | 3.07616i | −0.0849585 | + | 0.147152i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.5081 | − | 13.5724i | 1.12198 | − | 0.647776i | 0.180075 | − | 0.983653i | \(-0.442366\pi\) |
0.941906 | + | 0.335877i | \(0.109033\pi\) | |||||||
\(440\) | 4.04697 | 0.192932 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.3101 | 0.728228 | ||||||||
\(443\) | −4.63465 | + | 2.67582i | −0.220199 | + | 0.127132i | −0.606042 | − | 0.795432i | \(-0.707244\pi\) |
0.385843 | + | 0.922564i | \(0.373910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.39660 | − | 2.41899i | 0.0662053 | − | 0.114671i | ||||
\(446\) | 42.8270 | 2.02792 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.2418i | 1.61597i | 0.589204 | + | 0.807985i | \(0.299442\pi\) | ||||
−0.589204 | + | 0.807985i | \(0.700558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −55.1577 | + | 31.8453i | −2.59727 | + | 1.49954i | ||||
\(452\) | 12.1042i | 0.569332i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.9151 | − | 13.2300i | 1.07546 | − | 0.620916i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.93019 | + | 13.7355i | 0.370958 | + | 0.642519i | 0.989713 | − | 0.143065i | \(-0.0456959\pi\) |
−0.618755 | + | 0.785584i | \(0.712363\pi\) | |||||||
\(458\) | −12.0123 | − | 20.8059i | −0.561299 | − | 0.972198i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.11587 | − | 0.644247i | −0.0520276 | − | 0.0300382i | ||||
\(461\) | 6.50676 | − | 11.2700i | 0.303050 | − | 0.524898i | −0.673775 | − | 0.738936i | \(-0.735328\pi\) |
0.976825 | + | 0.214038i | \(0.0686618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.01941 | − | 10.4259i | −0.279746 | − | 0.484534i | 0.691576 | − | 0.722304i | \(-0.256917\pi\) |
−0.971321 | + | 0.237770i | \(0.923583\pi\) | |||||||
\(464\) | 36.2286i | 1.68187i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.4843 | −0.717297 | ||||||||
\(467\) | −10.1728 | + | 17.6199i | −0.470743 | + | 0.815351i | −0.999440 | − | 0.0334596i | \(-0.989347\pi\) |
0.528697 | + | 0.848811i | \(0.322681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.15829 | + | 1.82344i | 0.145681 | + | 0.0841090i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.02126 | + | 1.74433i | 0.139065 | + | 0.0802891i | ||||
\(473\) | −13.9292 | − | 8.04201i | −0.640464 | − | 0.369772i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.58078 | − | 5.53146i | −0.439596 | − | 0.253801i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.6085 | − | 44.3553i | 1.17131 | − | 2.02876i | ||||
\(479\) | −24.2983 | −1.11022 | −0.555109 | − | 0.831778i | \(-0.687324\pi\) | ||||
−0.555109 | + | 0.831778i | \(0.687324\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.9920i | 1.86908i | ||||||||
\(482\) | −20.5259 | − | 35.5519i | −0.934929 | − | 1.61934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.7045 | + | 20.2728i | −0.532023 | + | 0.921491i | ||||
\(485\) | −9.29273 | − | 5.36516i | −0.421961 | − | 0.243619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6546 | + | 23.6504i | 0.618747 | + | 1.07170i | 0.989715 | + | 0.143055i | \(0.0456927\pi\) |
−0.370968 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(488\) | −6.25025 | − | 10.8257i | −0.282935 | − | 0.490058i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2899 | − | 7.67290i | 0.599763 | − | 0.346273i | −0.169185 | − | 0.985584i | \(-0.554114\pi\) |
0.768948 | + | 0.639311i | \(0.220780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.1172i | − | 0.545731i | ||||||
\(494\) | −19.6361 | + | 11.3369i | −0.883471 | + | 0.510072i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 27.6168i | − | 1.24003i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3101 | −0.461542 | −0.230771 | − | 0.973008i | \(-0.574125\pi\) | ||||
−0.230771 | + | 0.973008i | \(0.574125\pi\) | |||||||
\(500\) | 4.19551 | − | 7.26683i | 0.187629 | − | 0.324982i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.1476 | + | 5.85869i | −0.452907 | + | 0.261486i | ||||
\(503\) | 24.6770 | 1.10029 | 0.550146 | − | 0.835068i | \(-0.314572\pi\) | ||||
0.550146 | + | 0.835068i | \(0.314572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00289 | 0.133627 | ||||||||
\(506\) | −12.4115 | + | 7.16576i | −0.551757 | + | 0.318557i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.69531 | + | 2.93637i | −0.0752174 | + | 0.130280i | ||||
\(509\) | −5.17203 | −0.229246 | −0.114623 | − | 0.993409i | \(-0.536566\pi\) | ||||
−0.114623 | + | 0.993409i | \(0.536566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5181i | 0.906778i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.25807 | − | 3.03575i | 0.231924 | − | 0.133901i | ||||
\(515\) | − | 6.65215i | − | 0.293129i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1958 | − | 8.19594i | 0.624330 | − | 0.360457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.95171 | + | 3.38046i | 0.0855882 | + | 0.148243i | ||||
\(521\) | 19.1664 | + | 33.1972i | 0.839696 | + | 1.45440i | 0.890149 | + | 0.455669i | \(0.150600\pi\) |
−0.0504538 | + | 0.998726i | \(0.516067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6468 | − | 13.6525i | −1.03400 | − | 0.596982i | −0.115874 | − | 0.993264i | \(-0.536967\pi\) |
−0.918129 | + | 0.396282i | \(0.870300\pi\) | |||||||
\(524\) | −1.71878 | + | 2.97702i | −0.0750855 | + | 0.130052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.7844 | + | 35.9997i | 0.906245 | + | 1.56966i | ||||
\(527\) | 9.23684i | 0.402363i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8345 | 0.905847 | ||||||||
\(530\) | −1.39676 | + | 2.41926i | −0.0606714 | + | 0.105086i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −53.2012 | − | 30.7158i | −2.30440 | − | 1.33045i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.172504 | − | 0.0995952i | −0.00745799 | − | 0.00430588i | ||||
\(536\) | 10.3709 | + | 5.98762i | 0.447953 | + | 0.258626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.38055 | + | 2.52911i | 0.188859 | + | 0.109038i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.78052 | + | 16.9404i | −0.420498 | + | 0.728323i | −0.995988 | − | 0.0894853i | \(-0.971478\pi\) |
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(542\) | −11.1556 | −0.479174 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 10.7066i | − | 0.459042i | ||||||
\(545\) | −2.02981 | − | 3.51574i | −0.0869476 | − | 0.150598i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6246 | − | 21.8665i | 0.539790 | − | 0.934944i | −0.459125 | − | 0.888372i | \(-0.651837\pi\) |
0.998915 | − | 0.0465723i | \(-0.0148298\pi\) | |||||||
\(548\) | 1.42469 | + | 0.822544i | 0.0608597 | + | 0.0351373i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.3180 | − | 38.6559i | −0.951642 | − | 1.64829i | ||||
\(551\) | 8.97260 | + | 15.5410i | 0.382246 | + | 0.662069i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.9673 | + | 8.64136i | −0.635898 | + | 0.367136i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.58089i | − | 0.406320i | ||||||
\(557\) | 28.8204 | − | 16.6395i | 1.22116 | − | 0.705036i | 0.255994 | − | 0.966678i | \(-0.417597\pi\) |
0.965165 | + | 0.261642i | \(0.0842640\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.5135i | − | 0.656152i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.67080 | −0.407938 | ||||||||
\(563\) | 15.2587 | − | 26.4289i | 0.643079 | − | 1.11385i | −0.341663 | − | 0.939823i | \(-0.610990\pi\) |
0.984742 | − | 0.174023i | \(-0.0556767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.98940 | − | 2.88063i | 0.209905 | − | 0.121189i | ||||
\(566\) | 36.0358 | 1.51470 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.62028 | −0.235822 | ||||||||
\(569\) | 13.4044 | − | 7.73906i | 0.561943 | − | 0.324438i | −0.191982 | − | 0.981398i | \(-0.561491\pi\) |
0.753925 | + | 0.656960i | \(0.228158\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2042 | − | 21.1384i | 0.510731 | − | 0.884613i | −0.489191 | − | 0.872177i | \(-0.662708\pi\) |
0.999923 | − | 0.0124362i | \(-0.00395868\pi\) | |||||||
\(572\) | −36.9689 | −1.54575 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.74455i | − | 0.281267i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6901 | + | 7.32664i | −0.528296 | + | 0.305012i | −0.740322 | − | 0.672252i | \(-0.765327\pi\) |
0.212026 | + | 0.977264i | \(0.431994\pi\) | |||||||
\(578\) | − | 26.2777i | − | 1.09301i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.63746 | + | 3.25479i | −0.234083 | + | 0.135148i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.27811 | + | 10.8740i | 0.260013 | + | 0.450355i | ||||
\(584\) | 6.96085 | + | 12.0565i | 0.288042 | + | 0.498904i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.9280 | + | 16.7016i | 1.19500 | + | 0.689936i | ||||
\(587\) | 11.6129 | − | 20.1141i | 0.479314 | − | 0.830197i | −0.520404 | − | 0.853920i | \(-0.674219\pi\) |
0.999719 | + | 0.0237232i | \(0.00755204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.83975 | − | 11.8468i | −0.281827 | − | 0.488139i | ||||
\(590\) | 3.49884i | 0.144045i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 38.9586 | 1.60119 | ||||||||
\(593\) | −5.55605 | + | 9.62337i | −0.228160 | + | 0.395184i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684404i | \(0.239938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.14153 | − | 4.70051i | −0.333490 | − | 0.192541i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.9712 | − | 6.91159i | −0.489540 | − | 0.282636i | ||||
\(599\) | −13.5581 | − | 7.82776i | −0.553968 | − | 0.319833i | 0.196753 | − | 0.980453i | \(-0.436960\pi\) |
−0.750721 | + | 0.660620i | \(0.770294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.5665 | + | 17.6476i | 1.24684 | + | 0.719861i | 0.970477 | − | 0.241194i | \(-0.0775390\pi\) |
0.276358 | + | 0.961055i | \(0.410872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.28512 | − | 7.42205i | 0.174359 | − | 0.301999i | ||||
\(605\) | 11.1421 | 0.452990 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.8051i | 1.57505i | 0.616284 | + | 0.787524i | \(0.288637\pi\) | ||||
−0.616284 | + | 0.787524i | \(0.711363\pi\) | |||||||
\(608\) | 7.92809 | + | 13.7318i | 0.321526 | + | 0.556900i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.26850 | − | 10.8574i | 0.253804 | − | 0.439602i | ||||
\(611\) | 13.6923 | + | 7.90523i | 0.553929 | + | 0.319811i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8786 | − | 27.5025i | −0.641330 | − | 1.11082i | −0.985136 | − | 0.171776i | \(-0.945049\pi\) |
0.343806 | − | 0.939041i | \(-0.388284\pi\) | |||||||
\(614\) | 23.8572 | + | 41.3220i | 0.962800 | + | 1.66762i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.25518 | + | 0.724680i | −0.0505317 | + | 0.0291745i | −0.525053 | − | 0.851070i | \(-0.675955\pi\) |
0.474521 | + | 0.880244i | \(0.342621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.1666i | 1.17230i | 0.810201 | + | 0.586152i | \(0.199358\pi\) | ||||
−0.810201 | + | 0.586152i | \(0.800642\pi\) | |||||||
\(620\) | 4.29740 | − | 2.48110i | 0.172588 | − | 0.0996435i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 51.8217i | 2.07786i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9223 | 0.756892 | ||||||||
\(626\) | 5.10764 | − | 8.84668i | 0.204142 | − | 0.353585i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.33778 | − | 1.34972i | 0.0932877 | − | 0.0538597i | ||||
\(629\) | −13.0303 | −0.519551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7428 | 0.467473 | 0.233736 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233736 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(632\) | 7.11011 | − | 4.10503i | 0.282825 | − | 0.163289i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.7488 | − | 53.2585i | 1.22119 | − | 2.11516i | ||||
\(635\) | 1.61385 | 0.0640436 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 72.4041i | 2.86651i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.00119 | − | 2.88744i | 0.197689 | − | 0.114136i | ||||
\(641\) | − | 11.5778i | − | 0.457296i | −0.973509 | − | 0.228648i | \(-0.926569\pi\) | ||
0.973509 | − | 0.228648i | \(-0.0734305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.1240 | + | 7.57712i | −0.517558 | + | 0.298812i | −0.735935 | − | 0.677052i | \(-0.763257\pi\) |
0.218377 | + | 0.975865i | \(0.429924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.60370 | − | 6.24180i | −0.141786 | − | 0.245580i | ||||
\(647\) | −6.22057 | − | 10.7743i | −0.244556 | − | 0.423583i | 0.717451 | − | 0.696609i | \(-0.245309\pi\) |
−0.962007 | + | 0.273026i | \(0.911975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6195 | + | 7.86325i | 0.534614 | + | 0.308659i | ||||
\(650\) | 21.5264 | − | 37.2847i | 0.844333 | − | 1.46243i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.06032 | − | 7.03268i | −0.159014 | − | 0.275421i | ||||
\(653\) | 4.58431i | 0.179398i | 0.995969 | + | 0.0896990i | \(0.0285905\pi\) | ||||
−0.995969 | + | 0.0896990i | \(0.971410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.63619 | 0.0639313 | ||||||||
\(656\) | −29.1921 | + | 50.5621i | −1.13976 | + | 1.97412i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.6110 | − | 9.01301i | −0.608118 | − | 0.351097i | 0.164111 | − | 0.986442i | \(-0.447525\pi\) |
−0.772228 | + | 0.635345i | \(0.780858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.554932 | − | 0.320390i | −0.0215844 | − | 0.0124617i | 0.489169 | − | 0.872189i | \(-0.337300\pi\) |
−0.510753 | + | 0.859727i | \(0.670633\pi\) | |||||||
\(662\) | 48.1899 | + | 27.8225i | 1.87296 | + | 1.08135i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.18189 | + | 4.14647i | 0.278711 | + | 0.160914i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.47018 | + | 9.47462i | −0.211806 | + | 0.366859i | ||||
\(668\) | −1.89338 | −0.0732572 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.0102i | 0.463995i | ||||||||
\(671\) | −28.1755 | − | 48.8014i | −1.08770 | − | 1.88396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0695 | + | 19.1729i | −0.426697 | + | 0.739061i | −0.996577 | − | 0.0826667i | \(-0.973656\pi\) |
0.569880 | + | 0.821728i | \(0.306990\pi\) | |||||||
\(674\) | 5.90591 | + | 3.40978i | 0.227487 | + | 0.131340i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.01280 | − | 15.6106i | −0.346646 | − | 0.600409i | ||||
\(677\) | −10.0160 | − | 17.3482i | −0.384947 | − | 0.666747i | 0.606815 | − | 0.794843i | \(-0.292447\pi\) |
−0.991762 | + | 0.128096i | \(0.959114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.07456 | + | 0.620397i | −0.0412074 | + | 0.0237911i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 55.1931i | − | 2.11345i | ||||||
\(683\) | −18.1316 | + | 10.4683i | −0.693786 | + | 0.400558i | −0.805029 | − | 0.593235i | \(-0.797850\pi\) |
0.111243 | + | 0.993793i | \(0.464517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.783018i | − | 0.0299176i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.7440 | −0.562108 | ||||||||
\(689\) | −6.05543 | + | 10.4883i | −0.230693 | + | 0.399573i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.33430 | − | 0.770358i | 0.0507591 | − | 0.0293058i | −0.474406 | − | 0.880306i | \(-0.657337\pi\) |
0.525165 | + | 0.851001i | \(0.324004\pi\) | |||||||
\(692\) | 10.3217 | 0.392372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0740 | 0.496282 | ||||||||
\(695\) | −3.94929 | + | 2.28012i | −0.149805 | + | 0.0864900i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.76372 | − | 16.9113i | 0.369827 | − | 0.640560i | ||||
\(698\) | −27.9423 | −1.05763 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.6641i | − | 1.19593i | −0.801520 | − | 0.597967i | \(-0.795975\pi\) | ||
0.801520 | − | 0.597967i | \(-0.204025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7121 | − | 9.64873i | 0.630309 | − | 0.363909i | ||||
\(704\) | 12.1657i | 0.458513i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.6922 | − | 31.5766i | 2.05837 | − | 1.18840i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1762 | − | 19.3578i | −0.419732 | − | 0.726996i | 0.576181 | − | 0.817322i | \(-0.304542\pi\) |
−0.995912 | + | 0.0903259i | \(0.971209\pi\) | |||||||
\(710\) | −2.81835 | − | 4.88152i | −0.105771 | − | 0.183200i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.41873 | − | 2.55116i | −0.165599 | − | 0.0956086i | ||||
\(713\) | 4.16988 | − | 7.22244i | 0.156163 | − | 0.270482i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.79812 | + | 15.2388i | 0.329031 | + | 0.569898i | ||||
\(716\) | 12.5430i | 0.468754i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.1382 | −0.452994 | ||||||||
\(719\) | 19.4544 | − | 33.6959i | 0.725525 | − | 1.25665i | −0.233232 | − | 0.972421i | \(-0.574930\pi\) |
0.958757 | − | 0.284226i | \(-0.0917365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.9011 | − | 12.0672i | −0.777858 | − | 0.449096i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0522 | − | 8.11306i | −0.522247 | − | 0.301520i | ||||
\(725\) | −29.5090 | − | 17.0370i | −1.09594 | − | 0.632739i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4647 | − | 6.61915i | −0.425202 | − | 0.245491i | 0.272098 | − | 0.962269i | \(-0.412282\pi\) |
−0.697301 | + | 0.716779i | \(0.745616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.98119 | + | 12.0918i | −0.258385 | + | 0.447536i | ||||
\(731\) | 4.93133 | 0.182392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 32.4727i | − | 1.19941i | −0.800222 | − | 0.599704i | \(-0.795285\pi\) | ||
0.800222 | − | 0.599704i | \(-0.204715\pi\) | |||||||
\(734\) | −2.83703 | − | 4.91389i | −0.104717 | − | 0.181375i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.83338 | + | 8.37167i | −0.178161 | + | 0.308584i | ||||
\(737\) | 46.7508 | + | 26.9916i | 1.72209 | + | 0.994248i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.91965 | + | 11.9852i | 0.254543 | + | 0.440882i | 0.964771 | − | 0.263090i | \(-0.0847415\pi\) |
−0.710228 | + | 0.703972i | \(0.751408\pi\) | |||||||
\(740\) | 3.50005 | + | 6.06227i | 0.128665 | + | 0.222854i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.8593 | + | 18.3940i | −1.16880 | + | 0.674810i | −0.953398 | − | 0.301715i | \(-0.902441\pi\) |
−0.215406 | + | 0.976525i | \(0.569108\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.47464i | 0.163938i | ||||||||
\(746\) | 15.3898 | − | 8.88530i | 0.563461 | − | 0.325314i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 11.7514i | − | 0.429675i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.65905 | −0.133520 | −0.0667602 | − | 0.997769i | \(-0.521266\pi\) | ||||
−0.0667602 | + | 0.997769i | \(0.521266\pi\) | |||||||
\(752\) | 7.51308 | − | 13.0130i | 0.273974 | − | 0.474537i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −60.4797 | + | 34.9180i | −2.20254 | + | 1.27164i | ||||
\(755\) | −4.07921 | −0.148458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8901 | 0.504842 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(758\) | 12.3135 | − | 7.10920i | 0.447246 | − | 0.258218i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.918790 | − | 1.59139i | 0.0333280 | − | 0.0577258i | ||||
\(761\) | −13.6417 | −0.494510 | −0.247255 | − | 0.968950i | \(-0.579529\pi\) | ||||
−0.247255 | + | 0.968950i | \(0.579529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.4991i | 0.994884i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −39.0500 | + | 22.5455i | −1.41093 | + | 0.814602i | ||||
\(767\) | 15.1687i | 0.547709i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.9328 | + | 13.2402i | −0.826976 | + | 0.477455i | −0.852816 | − | 0.522211i | \(-0.825107\pi\) |
0.0258399 | + | 0.999666i | \(0.491774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.4552 | − | 19.8410i | −0.412281 | − | 0.714092i | ||||
\(773\) | 13.1109 | + | 22.7087i | 0.471566 | + | 0.816776i | 0.999471 | − | 0.0325274i | \(-0.0103556\pi\) |
−0.527905 | + | 0.849303i | \(0.677022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.4945 | + | 12.9872i | 0.808026 | + | 0.466514i | ||||
\(776\) | −9.80047 | + | 16.9749i | −0.351816 | + | 0.609364i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.88703 | + | 10.1966i | 0.211060 | + | 0.365567i | ||||
\(779\) | 28.9196i | 1.03615i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.3357 | −0.906581 | ||||||||
\(782\) | 2.19701 | − | 3.80533i | 0.0785649 | − | 0.136078i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.11272 | − | 0.642430i | −0.0397148 | − | 0.0229293i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.1554 | − | 14.5235i | −0.896694 | − | 0.517706i | −0.0205676 | − | 0.999788i | \(-0.506547\pi\) |
−0.876126 | + | 0.482082i | \(0.839881\pi\) | |||||||
\(788\) | −21.9770 | − | 12.6884i | −0.782899 | − | 0.452007i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.13088 | + | 4.11702i | 0.253705 | + | 0.146477i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1761 | − | 47.0704i | 0.965052 | − | 1.67152i | ||||
\(794\) | −24.2926 | −0.862111 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.4741i | 0.867462i | ||||||||
\(797\) | 15.8184 | + | 27.3983i | 0.560317 | + | 0.970498i | 0.997469 | + | 0.0711097i | \(0.0226540\pi\) |
−0.437151 | + | 0.899388i | \(0.644013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.51286 | + | 4.35240i | −0.0888986 | + | 0.153977i | ||||
\(800\) | −26.0738 | − | 15.0537i | −0.921848 | − | 0.532229i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.4777 | + | 25.0762i | 0.511227 | + | 0.885470i | ||||
\(803\) | 31.3788 | + | 54.3497i | 1.10733 | + | 1.91796i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 46.1032 | − | 26.6177i | 1.62392 | − | 0.937569i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 5.48534i | − | 0.192974i | ||||||
\(809\) | 34.5466 | − | 19.9455i | 1.21459 | − | 0.701245i | 0.250836 | − | 0.968029i | \(-0.419294\pi\) |
0.963756 | + | 0.266784i | \(0.0859610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.9516i | − | 1.01663i | −0.861172 | − | 0.508314i | \(-0.830269\pi\) | ||
0.861172 | − | 0.508314i | \(-0.169731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 77.8601 | 2.72899 | ||||||||
\(815\) | −1.93260 | + | 3.34737i | −0.0676961 | + | 0.117253i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.32473 | + | 3.65158i | −0.221274 | + | 0.127753i | ||||
\(818\) | 9.92684 | 0.347084 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.4905 | −0.366344 | ||||||||
\(821\) | 0.359377 | − | 0.207486i | 0.0125423 | − | 0.00724132i | −0.493716 | − | 0.869623i | \(-0.664362\pi\) |
0.506258 | + | 0.862382i | \(0.331028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.54814 | − | 11.3417i | 0.228254 | − | 0.395347i | −0.729037 | − | 0.684475i | \(-0.760032\pi\) |
0.957291 | + | 0.289127i | \(0.0933650\pi\) | |||||||
\(824\) | −12.1514 | −0.423314 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2637i | 1.22624i | 0.789990 | + | 0.613120i | \(0.210086\pi\) | ||||
−0.789990 | + | 0.613120i | \(0.789914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.0164 | − | 16.7526i | 1.00778 | − | 0.581842i | 0.0972388 | − | 0.995261i | \(-0.468999\pi\) |
0.910541 | + | 0.413419i | \(0.135666\pi\) | |||||||
\(830\) | 8.31716i | 0.288693i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.1621 | + | 5.86710i | −0.352308 | + | 0.203405i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.450600 | + | 0.780462i | 0.0155937 | + | 0.0270090i | ||||
\(836\) | 8.70178 | + | 15.0719i | 0.300957 | + | 0.521273i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 38.8615 | + | 22.4367i | 1.34245 | + | 0.775062i | ||||
\(839\) | −22.4984 | + | 38.9684i | −0.776731 | + | 1.34534i | 0.157085 | + | 0.987585i | \(0.449790\pi\) |
−0.933816 | + | 0.357753i | \(0.883543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1358 | + | 22.7519i | 0.452959 | + | 0.784548i | ||||
\(842\) | − | 21.9604i | − | 0.756805i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.9452 | −0.376749 | ||||||||
\(845\) | −4.28985 | + | 7.43024i | −0.147575 | + | 0.255608i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.96802 | + | 5.75504i | 0.342303 | + | 0.197629i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.8518 | + | 6.84265i | 0.406514 | + | 0.234701i | ||||
\(851\) | 10.1886 | + | 5.88238i | 0.349260 | + | 0.201645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.8457 | − | 9.14854i | −0.542548 | − | 0.313240i | 0.203563 | − | 0.979062i | \(-0.434748\pi\) |
−0.746111 | + | 0.665822i | \(0.768081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.181929 | + | 0.315111i | −0.00621822 | + | 0.0107703i | ||||
\(857\) | −10.5785 | −0.361355 | −0.180678 | − | 0.983542i | \(-0.557829\pi\) | ||||
−0.180678 | + | 0.983542i | \(0.557829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32.6748i | − | 1.11485i | −0.830227 | − | 0.557425i | \(-0.811790\pi\) | ||
0.830227 | − | 0.557425i | \(-0.188210\pi\) | |||||||
\(860\) | −1.32460 | − | 2.29428i | −0.0451686 | − | 0.0782343i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2332 | − | 48.9014i | 0.961628 | − | 1.66559i | ||||
\(863\) | −8.09878 | − | 4.67583i | −0.275686 | − | 0.159167i | 0.355783 | − | 0.934569i | \(-0.384214\pi\) |
−0.631469 | + | 0.775401i | \(0.717548\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.45643 | − | 4.25465i | −0.0835210 | − | 0.144663i | ||||
\(866\) | −5.55262 | − | 9.61742i | −0.188686 | − | 0.326813i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0517 | − | 18.5050i | 1.08728 | − | 0.627741i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.0684i | 1.76427i | ||||||||
\(872\) | −6.42216 | + | 3.70783i | −0.217482 | + | 0.125563i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.50742i | 0.220117i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.23815 | 0.0418095 | 0.0209048 | − | 0.999781i | \(-0.493345\pi\) | ||||
0.0209048 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(878\) | 24.8650 | − | 43.0674i | 0.839153 | − | 1.45346i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.4828 | − | 8.36167i | 0.488217 | − | 0.281872i | ||||
\(881\) | 37.3480 | 1.25828 | 0.629142 | − | 0.777290i | \(-0.283406\pi\) | ||||
0.629142 | + | 0.777290i | \(0.283406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90708 | 0.131484 | 0.0657419 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657419 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(884\) | 9.81607 | − | 5.66731i | 0.330150 | − | 0.190612i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.90216 | + | 8.49079i | −0.164691 | + | 0.285254i | ||||
\(887\) | −14.5116 | −0.487251 | −0.243625 | − | 0.969869i | \(-0.578337\pi\) | ||||
−0.243625 | + | 0.969869i | \(0.578337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 5.11722i | − | 0.171530i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.4585 | − | 15.8532i | 0.919379 | − | 0.530804i | ||||
\(893\) | − | 7.44295i | − | 0.249069i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.17028 | − | 2.98506i | 0.172823 | − | 0.0997797i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3659 | + | 54.3273i | 1.04669 | + | 1.81293i | ||||
\(899\) | −21.0666 | − | 36.4884i | −0.702610 | − | 1.21696i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.33395 | − | 1.92486i | −0.111070 | − | 0.0641263i | ||||
\(902\) | −58.3414 | + | 101.050i | −1.94256 | + | 3.36460i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.26201 | − | 9.11407i | −0.175012 | − | 0.303129i | ||||
\(905\) | 7.72320i | 0.256728i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.2139 | −0.637987 | −0.318993 | − | 0.947757i | \(-0.603345\pi\) | ||||
−0.318993 | + | 0.947757i | \(0.603345\pi\) | |||||||
\(908\) | 9.79466 | − | 16.9648i | 0.325047 | − | 0.562998i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1252 | − | 5.84579i | −0.335463 | − | 0.193680i | 0.322801 | − | 0.946467i | \(-0.395376\pi\) |
−0.658264 | + | 0.752787i | \(0.728709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.3752 | + | 18.6919i | 1.07146 | + | 0.618610i | ||||
\(914\) | 25.1637 | + | 14.5283i | 0.832342 | + | 0.480553i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.4034 | − | 8.89314i | −0.508942 | − | 0.293838i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9930 | + | 34.6289i | −0.659508 | + | 1.14230i | 0.321236 | + | 0.946999i | \(0.395902\pi\) |
−0.980743 | + | 0.195301i | \(0.937432\pi\) | |||||||
\(920\) | 1.12029 | 0.0369347 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 23.8411i | − | 0.785164i | ||||||
\(923\) | −12.2185 | − | 21.1631i | −0.402177 | − | 0.696591i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3209 | + | 31.7326i | −0.602386 | + | 1.04336i | ||||
\(926\) | −19.1005 | − | 11.0277i | −0.627683 | − | 0.362393i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.4187 | + | 42.2944i | 0.801582 | + | 1.38838i | ||||
\(929\) | −6.38359 | − | 11.0567i | −0.209439 | − | 0.362759i | 0.742099 | − | 0.670290i | \(-0.233830\pi\) |
−0.951538 | + | 0.307532i | \(0.900497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.92775 | + | 5.73179i | −0.325194 | + | 0.187751i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.2738i | 1.21964i | ||||||||
\(935\) | −4.84400 | + | 2.79669i | −0.158416 | + | 0.0914614i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.9436i | − | 0.390179i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||
0.980785 | − | 0.195090i | \(-0.0624997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.69991 | 0.0880614 | ||||||||
\(941\) | 12.5159 | − | 21.6781i | 0.408006 | − | 0.706686i | −0.586661 | − | 0.809833i | \(-0.699558\pi\) |
0.994666 | + | 0.103146i | \(0.0328910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.2688 | + | 8.81546i | −0.497221 | + | 0.287071i | ||||
\(944\) | 14.4162 | 0.469208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.4663 | −0.958032 | ||||||||
\(947\) | −28.3671 | + | 16.3777i | −0.921806 | + | 0.532205i | −0.884211 | − | 0.467088i | \(-0.845303\pi\) |
−0.0375955 | + | 0.999293i | \(0.511970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.2658 | + | 52.4219i | −0.982470 | + | 1.70169i | ||||
\(950\) | −20.2676 | −0.657566 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.77705i | 0.219530i | 0.993958 | + | 0.109765i | \(0.0350099\pi\) | ||||
−0.993958 | + | 0.109765i | \(0.964990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.3353 | − | 6.54443i | 0.366801 | − | 0.211773i | ||||
\(956\) | − | 37.9178i | − | 1.22635i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.5512 | + | 22.2575i | −1.24553 | + | 0.719109i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.558897 | + | 0.968037i | 0.0180289 | + | 0.0312270i | ||||
\(962\) | 37.5492 | + | 65.0371i | 1.21063 | + | 2.09688i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.3203 | − | 15.1960i | −0.847721 | − | 0.489432i | ||||
\(965\) | −5.45236 | + | 9.44377i | −0.175518 | + | 0.304006i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7901 | + | 36.0096i | 0.668566 | + | 1.15799i | 0.978305 | + | 0.207169i | \(0.0664249\pi\) |
−0.309739 | + | 0.950822i | \(0.600242\pi\) | |||||||
\(968\) | − | 20.3531i | − | 0.654173i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.6582 | −0.631187 | ||||||||
\(971\) | 20.6257 | − | 35.7248i | 0.661910 | − | 1.14646i | −0.318203 | − | 0.948023i | \(-0.603079\pi\) |
0.980113 | − | 0.198439i | \(-0.0635873\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.3281 | + | 25.0155i | 1.38832 | + | 0.801547i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.7354 | − | 25.8280i | −1.43195 | − | 0.826734i | ||||
\(977\) | 3.96507 | + | 2.28924i | 0.126854 | + | 0.0732391i | 0.562084 | − | 0.827080i | \(-0.310000\pi\) |
−0.435230 | + | 0.900319i | \(0.643333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9192 | − | 11.5004i | −0.636621 | − | 0.367553i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.0569 | − | 24.3473i | 0.448575 | − | 0.776955i | ||||
\(983\) | −24.4801 | −0.780794 | −0.390397 | − | 0.920647i | \(-0.627662\pi\) | ||||
−0.390397 | + | 0.920647i | \(0.627662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0787i | 0.384860i | ||||||||
\(986\) | −11.0995 | − | 19.2249i | −0.353480 | − | 0.612245i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39312 | + | 14.5373i | −0.267021 | + | 0.462494i | ||||
\(989\) | −3.85589 | − | 2.22620i | −0.122610 | − | 0.0707890i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.0927 | + | 36.5337i | 0.670032 | + | 1.16053i | 0.977894 | + | 0.209099i | \(0.0670531\pi\) |
−0.307862 | + | 0.951431i | \(0.599614\pi\) | |||||||
\(992\) | −18.6142 | − | 32.2407i | −0.591001 | − | 1.02364i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0884 | − | 5.82452i | 0.319822 | − | 0.184650i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.67834i | 0.306516i | 0.988186 | + | 0.153258i | \(0.0489765\pi\) | ||||
−0.988186 | + | 0.153258i | \(0.951023\pi\) | |||||||
\(998\) | −16.3578 | + | 9.44415i | −0.517796 | + | 0.298949i | ||||
\(999\) | 0 | 0 |
(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 | 1323.2.s.d.656.17 | 48 | ||
3.2 | odd | 2 | 441.2.s.d.362.8 | 48 | |||
7.2 | even | 3 | 1323.2.o.e.440.7 | 48 | |||
7.3 | odd | 6 | 1323.2.i.d.521.17 | 48 | |||
7.4 | even | 3 | 1323.2.i.d.521.15 | 48 | |||
7.5 | odd | 6 | 1323.2.o.e.440.8 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.s.d.656.18 | 48 | ||
9.4 | even | 3 | 441.2.i.d.68.18 | 48 | |||
9.5 | odd | 6 | 1323.2.i.d.1097.17 | 48 | |||
21.2 | odd | 6 | 441.2.o.e.146.18 | yes | 48 | ||
21.5 | even | 6 | 441.2.o.e.146.17 | ✓ | 48 | ||
21.11 | odd | 6 | 441.2.i.d.227.7 | 48 | |||
21.17 | even | 6 | 441.2.i.d.227.8 | 48 | |||
21.20 | even | 2 | 441.2.s.d.362.7 | 48 | |||
63.4 | even | 3 | 441.2.s.d.374.7 | 48 | |||
63.5 | even | 6 | 1323.2.o.e.881.7 | 48 | |||
63.13 | odd | 6 | 441.2.i.d.68.17 | 48 | |||
63.23 | odd | 6 | 1323.2.o.e.881.8 | 48 | |||
63.31 | odd | 6 | 441.2.s.d.374.8 | 48 | |||
63.32 | odd | 6 | inner | 1323.2.s.d.962.18 | 48 | ||
63.40 | odd | 6 | 441.2.o.e.293.18 | yes | 48 | ||
63.41 | even | 6 | 1323.2.i.d.1097.15 | 48 | |||
63.58 | even | 3 | 441.2.o.e.293.17 | yes | 48 | ||
63.59 | even | 6 | inner | 1323.2.s.d.962.17 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.17 | 48 | 63.13 | odd | 6 | |||
441.2.i.d.68.18 | 48 | 9.4 | even | 3 | |||
441.2.i.d.227.7 | 48 | 21.11 | odd | 6 | |||
441.2.i.d.227.8 | 48 | 21.17 | even | 6 | |||
441.2.o.e.146.17 | ✓ | 48 | 21.5 | even | 6 | ||
441.2.o.e.146.18 | yes | 48 | 21.2 | odd | 6 | ||
441.2.o.e.293.17 | yes | 48 | 63.58 | even | 3 | ||
441.2.o.e.293.18 | yes | 48 | 63.40 | odd | 6 | ||
441.2.s.d.362.7 | 48 | 21.20 | even | 2 | |||
441.2.s.d.362.8 | 48 | 3.2 | odd | 2 | |||
441.2.s.d.374.7 | 48 | 63.4 | even | 3 | |||
441.2.s.d.374.8 | 48 | 63.31 | odd | 6 | |||
1323.2.i.d.521.15 | 48 | 7.4 | even | 3 | |||
1323.2.i.d.521.17 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.1097.15 | 48 | 63.41 | even | 6 | |||
1323.2.i.d.1097.17 | 48 | 9.5 | odd | 6 | |||
1323.2.o.e.440.7 | 48 | 7.2 | even | 3 | |||
1323.2.o.e.440.8 | 48 | 7.5 | odd | 6 | |||
1323.2.o.e.881.7 | 48 | 63.5 | even | 6 | |||
1323.2.o.e.881.8 | 48 | 63.23 | odd | 6 | |||
1323.2.s.d.656.17 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.s.d.656.18 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.s.d.962.17 | 48 | 63.59 | even | 6 | inner | ||
1323.2.s.d.962.18 | 48 | 63.32 | odd | 6 | inner |