Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (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 | 440.7 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.7 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58658 | − | 0.916012i | −1.12188 | − | 0.647718i | −0.180001 | − | 0.983667i | \(-0.557610\pi\) |
−0.941880 | + | 0.335948i | \(0.890943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.678156 | + | 1.17460i | 0.339078 | + | 0.587300i | ||||
\(5\) | 0.322784 | + | 0.559079i | 0.144353 | + | 0.250028i | 0.929132 | − | 0.369749i | \(-0.120556\pi\) |
−0.784778 | + | 0.619777i | \(0.787223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.17925i | 0.416928i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.18270i | − | 0.374002i | ||||||
\(11\) | −4.60375 | − | 2.65797i | −1.38808 | − | 0.801410i | −0.394983 | − | 0.918688i | \(-0.629250\pi\) |
−0.993099 | + | 0.117279i | \(0.962583\pi\) | |||||||
\(12\) | 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 | ||||
\(17\) | 1.62986 | 0.395299 | 0.197650 | − | 0.980273i | \(-0.436669\pi\) | ||||
0.197650 | + | 0.980273i | \(0.436669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.41378i | − | 0.553759i | −0.960905 | − | 0.276879i | \(-0.910700\pi\) | ||
0.960905 | − | 0.276879i | \(-0.0893002\pi\) | |||||||
\(20\) | −0.437796 | + | 0.758285i | −0.0978942 | + | 0.169558i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.86947 | + | 8.43418i | 1.03818 | + | 1.79817i | ||||
\(23\) | 1.27442 | − | 0.735784i | 0.265734 | − | 0.153422i | −0.361213 | − | 0.932483i | \(-0.617637\pi\) |
0.626947 | + | 0.779062i | \(0.284304\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.29162 | − | 3.96920i | 0.458324 | − | 0.793841i | ||||
\(26\) | 9.39351 | 1.84222 | ||||||||
\(27\) | 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 | \(-0.496706\pi\) |
0.871153 | + | 0.491012i | \(0.163373\pi\) | |||||||
\(32\) | −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 | ||||||||
\(37\) | −7.99471 | −1.31432 | −0.657161 | − | 0.753750i | \(-0.728243\pi\) | ||||
−0.657161 | + | 0.753750i | \(0.728243\pi\) | |||||||
\(38\) | −2.21105 | + | 3.82965i | −0.358680 | + | 0.621251i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.659294 | + | 0.380644i | −0.104244 | + | 0.0601851i | ||||
\(41\) | 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 | \(0.240769\pi\) | |||||||
\(44\) | − | 7.21009i | − | 1.08696i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.69595 | −0.397496 | ||||||||
\(47\) | −1.54176 | + | 2.67041i | −0.224889 | + | 0.389520i | −0.956286 | − | 0.292432i | \(-0.905535\pi\) |
0.731397 | + | 0.681952i | \(0.238869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.27168 | + | 4.19830i | −1.02837 | + | 0.593730i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.02264 | − | 3.47717i | −0.835190 | − | 0.482197i | ||||
\(53\) | 2.36199i | 0.324444i | 0.986754 | + | 0.162222i | \(0.0518661\pi\) | ||||
−0.986754 | + | 0.162222i | \(0.948134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.43181i | − | 0.462745i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.81008 | − | 11.7954i | −0.894207 | − | 1.54881i | ||||
\(59\) | 1.47918 | + | 2.56202i | 0.192573 | + | 0.333546i | 0.946102 | − | 0.323868i | \(-0.104983\pi\) |
−0.753529 | + | 0.657414i | \(0.771650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.18018 | + | 5.30018i | 1.17540 | + | 0.678618i | 0.954946 | − | 0.296779i | \(-0.0959124\pi\) |
0.220455 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(62\) | −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 | 0.989428 | + | 0.145028i | \(0.0463273\pi\) |
−0.369116 | + | 0.929383i | \(0.620339\pi\) | |||||||
\(68\) | 1.10530 | + | 1.91444i | 0.134037 | + | 0.232159i | ||||
\(69\) | 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 | ||||||||
\(73\) | 11.8055i | 1.38173i | 0.722982 | + | 0.690867i | \(0.242771\pi\) | ||||
−0.722982 | + | 0.690867i | \(0.757229\pi\) | |||||||
\(74\) | 12.6842 | + | 7.32325i | 1.47451 | + | 0.851311i | ||||
\(75\) | 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 | −0.992667 | − | 0.120881i | \(-0.961428\pi\) |
0.601019 | + | 0.799235i | \(0.294762\pi\) | |||||||
\(80\) | 3.14588 | 0.351720 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 21.9496i | − | 2.42392i | ||||||
\(83\) | 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 | ||||
\(86\) | 4.80038 | − | 2.77150i | 0.517638 | − | 0.298859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.13442 | − | 5.42898i | 0.334130 | − | 0.578731i | ||||
\(89\) | 4.32674 | 0.458633 | 0.229317 | − | 0.973352i | \(-0.426351\pi\) | ||||
0.229317 | + | 0.973352i | \(0.426351\pi\) | |||||||
\(90\) | 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 | ||||||||
\(100\) | 6.21631 | 0.621631 | ||||||||
\(101\) | 2.32577 | − | 4.02835i | 0.231423 | − | 0.400836i | −0.726804 | − | 0.686845i | \(-0.758995\pi\) |
0.958227 | + | 0.286009i | \(0.0923286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.92382 | − | 5.15217i | 0.879290 | − | 0.507658i | 0.00886554 | − | 0.999961i | \(-0.497178\pi\) |
0.870424 | + | 0.492303i | \(0.163845\pi\) | |||||||
\(104\) | −3.02324 | − | 5.23641i | −0.296453 | − | 0.513472i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.16361 | − | 3.74749i | 0.210149 | − | 0.363988i | ||||
\(107\) | − | 0.308550i | − | 0.0298287i | −0.999889 | − | 0.0149143i | \(-0.995252\pi\) | ||
0.999889 | − | 0.0149143i | \(-0.00474756\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.28845 | −0.602324 | −0.301162 | − | 0.953573i | \(-0.597375\pi\) | ||||
−0.301162 | + | 0.953573i | \(0.597375\pi\) | |||||||
\(110\) | −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 | ||||||||
\(115\) | 0.822722 | + | 0.474999i | 0.0767192 | + | 0.0442939i | ||||
\(116\) | 10.0835i | 0.936228i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.41979i | − | 0.498932i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62966 | + | 14.9470i | 0.784515 | + | 1.35882i | ||||
\(122\) | −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 | ||||
\(131\) | 1.26725 | + | 2.19494i | 0.110720 | + | 0.191773i | 0.916061 | − | 0.401039i | \(-0.131351\pi\) |
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.6041i | − | 1.60715i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.92202i | 0.164812i | ||||||||
\(137\) | −1.05041 | − | 0.606456i | −0.0897429 | − | 0.0518131i | 0.454457 | − | 0.890769i | \(-0.349833\pi\) |
−0.544200 | + | 0.838956i | \(0.683167\pi\) | |||||||
\(138\) | 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 | ||||
\(143\) | 27.2570 | 2.27934 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.79947i | 0.398574i | ||||||||
\(146\) | 10.8140 | − | 18.7304i | 0.894974 | − | 1.55014i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.42166 | − | 9.39060i | −0.445658 | − | 0.771902i | ||||
\(149\) | −6.00270 | + | 3.46566i | −0.491760 | + | 0.283918i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) |
0.233544 | + | 0.972346i | \(0.424968\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.15939 | + | 5.47223i | −0.257108 | + | 0.445323i | −0.965466 | − | 0.260530i | \(-0.916103\pi\) |
0.708358 | + | 0.705853i | \(0.249436\pi\) | |||||||
\(152\) | 2.84645 | 0.230878 | ||||||||
\(153\) | 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 | \(-0.691974\pi\) |
0.429640 | + | 0.903000i | \(0.358640\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −5.98729 | −0.468961 | −0.234480 | − | 0.972121i | \(-0.575339\pi\) | ||||
−0.234480 | + | 0.972121i | \(0.575339\pi\) | |||||||
\(164\) | −8.12502 | + | 14.0729i | −0.634457 | + | 1.09891i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1574 | + | 6.44173i | −0.865983 | + | 0.499976i | ||||
\(167\) | −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 | ||||
\(170\) | − | 1.92763i | − | 0.147843i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.10368 | −0.312903 | ||||||||
\(173\) | 3.80506 | − | 6.59055i | 0.289293 | − | 0.501071i | −0.684348 | − | 0.729156i | \(-0.739913\pi\) |
0.973641 | + | 0.228085i | \(0.0732464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.4343 | + | 12.9524i | −1.69105 | + | 0.976326i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.86471 | − | 3.96334i | −0.514532 | − | 0.297065i | ||||
\(179\) | − | 9.24786i | − | 0.691218i | −0.938379 | − | 0.345609i | \(-0.887672\pi\) | ||
0.938379 | − | 0.345609i | \(-0.112328\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | 0.867674 | + | 1.50286i | 0.0639658 | + | 0.110792i | ||||
\(185\) | −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 | \(-0.0712087\pi\) |
0.295415 | + | 0.955369i | \(0.404542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.44583 | + | 14.6286i | 0.607944 | + | 1.05299i | 0.991579 | + | 0.129505i | \(0.0413389\pi\) |
−0.383634 | + | 0.923485i | \(0.625328\pi\) | |||||||
\(194\) | −15.2255 | − | 26.3713i | −1.09313 | − | 1.89335i | ||||
\(195\) | 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 | ||||||||
\(199\) | − | 18.0446i | − | 1.27915i | −0.768729 | − | 0.639574i | \(-0.779111\pi\) | ||
0.768729 | − | 0.639574i | \(-0.220889\pi\) | |||||||
\(200\) | 4.68069 | + | 2.70240i | 0.330975 | + | 0.191088i | ||||
\(201\) | 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 | ||||
\(206\) | −18.8778 | −1.31528 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.9860i | 1.73247i | ||||||||
\(209\) | −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 | \(0.922930\pi\) | |||||||
\(212\) | −2.77440 | + | 1.60180i | −0.190546 | + | 0.110012i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.282636 | + | 0.489540i | −0.0193206 | + | 0.0334642i | ||||
\(215\) | −1.95324 | −0.133210 | ||||||||
\(216\) | 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 | ||||||||
\(226\) | 16.3496 | 1.08756 | ||||||||
\(227\) | −7.22154 | + | 12.5081i | −0.479310 | + | 0.830190i | −0.999718 | − | 0.0237280i | \(-0.992446\pi\) |
0.520408 | + | 0.853918i | \(0.325780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3568 | + | 6.55685i | −0.750479 | + | 0.433289i | −0.825867 | − | 0.563865i | \(-0.809314\pi\) |
0.0753881 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(230\) | −0.870209 | − | 1.50725i | −0.0573799 | − | 0.0993849i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.38357 | + | 7.59256i | −0.287795 | + | 0.498476i | ||||
\(233\) | 8.45202i | 0.553710i | 0.960912 | + | 0.276855i | \(0.0892922\pi\) | ||||
−0.960912 | + | 0.276855i | \(0.910708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.99063 | −0.129854 | ||||||||
\(236\) | −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 | ||||||||
\(241\) | 19.4058 | + | 11.2039i | 1.25004 | + | 0.721710i | 0.971117 | − | 0.238605i | \(-0.0766900\pi\) |
0.278921 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(242\) | − | 31.6195i | − | 2.03258i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.3774i | 0.920418i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.18819 | + | 10.7183i | 0.393745 | + | 0.681987i | ||||
\(248\) | 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 | ||||
\(257\) | −1.65705 | − | 2.87009i | −0.103364 | − | 0.179031i | 0.809705 | − | 0.586837i | \(-0.199627\pi\) |
−0.913069 | + | 0.407806i | \(0.866294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.48950i | − | 0.278427i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 4.64326i | − | 0.286862i | ||||||
\(263\) | −19.6502 | − | 11.3451i | −1.21169 | − | 0.699567i | −0.248559 | − | 0.968617i | \(-0.579957\pi\) |
−0.963126 | + | 0.269050i | \(0.913290\pi\) | |||||||
\(264\) | 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 | ||||
\(269\) | −2.76100 | −0.168341 | −0.0841707 | − | 0.996451i | \(-0.526824\pi\) | ||||
−0.0841707 | + | 0.996451i | \(0.526824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.08922i | 0.369894i | 0.982749 | + | 0.184947i | \(0.0592113\pi\) | ||||
−0.982749 | + | 0.184947i | \(0.940789\pi\) | |||||||
\(272\) | 3.97119 | − | 6.87830i | 0.240789 | − | 0.417058i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11104 | + | 1.92438i | 0.0671205 | + | 0.116256i | ||||
\(275\) | −21.1001 | + | 12.1821i | −1.27238 | + | 0.734611i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.71684 | − | 8.16980i | 0.283407 | − | 0.490876i | −0.688814 | − | 0.724938i | \(-0.741869\pi\) |
0.972222 | + | 0.234062i | \(0.0752019\pi\) | |||||||
\(278\) | −12.9413 | −0.776167 | ||||||||
\(279\) | 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 | \(-0.865426\pi\) |
−0.100651 | + | 0.994922i | \(0.532093\pi\) | |||||||
\(284\) | −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 | ||||||||
\(289\) | −14.3436 | −0.843738 | ||||||||
\(290\) | 4.39637 | − | 7.61474i | 0.258164 | − | 0.447153i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.8668 | + | 8.00600i | −0.811493 | + | 0.468516i | ||||
\(293\) | 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 | ||||
\(296\) | − | 9.42778i | − | 0.547979i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.6983 | 0.735595 | ||||||||
\(299\) | −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 | ||||||||
\(304\) | −10.1866 | − | 5.88122i | −0.584240 | − | 0.337311i | ||||
\(305\) | 6.84326i | 0.391844i | ||||||||
\(306\) | 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 | ||||||||
\(310\) | −3.35132 | − | 5.80466i | −0.190342 | − | 0.329683i | ||||
\(311\) | −14.1433 | − | 24.4969i | −0.801992 | − | 1.38909i | −0.918303 | − | 0.395878i | \(-0.870440\pi\) |
0.116311 | − | 0.993213i | \(-0.462893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.82891 | − | 2.78797i | −0.272946 | − | 0.157586i | 0.357280 | − | 0.933998i | \(-0.383704\pi\) |
−0.630226 | + | 0.776412i | \(0.717038\pi\) | |||||||
\(314\) | 3.64624 | 0.205769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.44276 | −0.531197 | ||||||||
\(317\) | −29.0708 | − | 16.7841i | −1.63278 | − | 0.942686i | −0.983230 | − | 0.182367i | \(-0.941624\pi\) |
−0.649550 | − | 0.760319i | \(-0.725043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.7607 | − | 34.2265i | −1.10639 | − | 1.91632i | ||||
\(320\) | 0.738701 | + | 1.27947i | 0.0412947 | + | 0.0715244i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.93412i | − | 0.218901i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.5001i | 1.30355i | ||||||||
\(326\) | 9.49931 | + | 5.48443i | 0.526118 | + | 0.303755i | ||||
\(327\) | 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 | −0.0595042 | − | 0.998228i | \(-0.518952\pi\) |
0.894243 | − | 0.447582i | \(-0.147715\pi\) | |||||||
\(332\) | 9.53809 | 0.523470 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.55747i | 0.139938i | ||||||||
\(335\) | −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 | \(0.801005\pi\) | |||||||
\(338\) | −21.0859 | + | 12.1739i | −1.14692 | + | 0.662175i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.713547 | + | 1.23590i | −0.0386975 | + | 0.0670261i | ||||
\(341\) | −30.1268 | −1.63146 | ||||||||
\(342\) | 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 | \(-0.728018\pi\) |
0.324854 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 34.9206 | 1.86127 | ||||||||
\(353\) | −17.2359 | + | 29.8534i | −0.917373 | + | 1.58894i | −0.113985 | + | 0.993482i | \(0.536362\pi\) |
−0.803389 | + | 0.595455i | \(0.796972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.66455 | + | 1.53838i | −0.141420 | + | 0.0816487i | ||||
\(356\) | 2.93420 | + | 5.08219i | 0.155512 | + | 0.269355i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.47115 | + | 14.6725i | −0.447714 | + | 0.775464i | ||||
\(359\) | 6.62557i | 0.349684i | 0.984596 | + | 0.174842i | \(0.0559415\pi\) | ||||
−0.984596 | + | 0.174842i | \(0.944059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1737 | 0.693351 | ||||||||
\(362\) | −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 | ||||||||
\(367\) | 2.68222 | + | 1.54858i | 0.140011 | + | 0.0808352i | 0.568369 | − | 0.822774i | \(-0.307575\pi\) |
−0.428358 | + | 0.903609i | \(0.640908\pi\) | |||||||
\(368\) | − | 7.17101i | − | 0.373815i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.45532i | 0.491559i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.84999 | − | 8.40043i | −0.251123 | − | 0.434958i | 0.712712 | − | 0.701457i | \(-0.247467\pi\) |
−0.963835 | + | 0.266499i | \(0.914133\pi\) | |||||||
\(374\) | 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 | ||||
\(383\) | 12.3063 | + | 21.3152i | 0.628825 | + | 1.08916i | 0.987788 | + | 0.155804i | \(0.0497970\pi\) |
−0.358963 | + | 0.933352i | \(0.616870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 30.9459i | − | 1.57511i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.5440i | 1.14450i | ||||||||
\(389\) | −5.56578 | − | 3.21340i | −0.282196 | − | 0.162926i | 0.352221 | − | 0.935917i | \(-0.385427\pi\) |
−0.634417 | + | 0.772991i | \(0.718760\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | −4.49450 | −0.226143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.2600i | 0.665498i | 0.943015 | + | 0.332749i | \(0.107976\pi\) | ||||
−0.943015 | + | 0.332749i | \(0.892024\pi\) | |||||||
\(398\) | −16.5291 | + | 28.6292i | −0.828528 | + | 1.43505i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.1672 | − | 19.3421i | −0.558358 | − | 0.967105i | ||||
\(401\) | 13.6877 | − | 7.90259i | 0.683530 | − | 0.394636i | −0.117653 | − | 0.993055i | \(-0.537537\pi\) |
0.801184 | + | 0.598418i | \(0.204204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5291 | + | 25.1652i | −0.723747 | + | 1.25357i | ||||
\(404\) | 6.30894 | 0.313882 | ||||||||
\(405\) | 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 | \(-0.709437\pi\) |
0.379477 | + | 0.925201i | \(0.376104\pi\) | |||||||
\(410\) | 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 | ||||||||
\(415\) | 4.53987 | 0.222854 | ||||||||
\(416\) | 16.8410 | − | 29.1694i | 0.825697 | − | 1.43015i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.3582 | − | 11.7538i | 0.995754 | − | 0.574899i | ||||
\(419\) | 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 | \(0.0723113\pi\) | |||||||
\(422\) | 14.7841i | 0.719680i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.78538 | −0.135270 | ||||||||
\(425\) | 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 | ||||||||
\(430\) | 3.09897 | + | 1.78919i | 0.149446 | + | 0.0862825i | ||||
\(431\) | 30.8219i | 1.48464i | 0.670046 | + | 0.742320i | \(0.266274\pi\) | ||||
−0.670046 | + | 0.742320i | \(0.733726\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −4.26455 | − | 7.38642i | −0.204235 | − | 0.353745i | ||||
\(437\) | −1.77602 | − | 3.07616i | −0.0849585 | − | 0.147152i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.5081 | − | 13.5724i | −1.12198 | − | 0.647776i | −0.180075 | − | 0.983653i | \(-0.557634\pi\) |
−0.941906 | + | 0.335877i | \(0.890967\pi\) | |||||||
\(440\) | 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 | \(-0.292756\pi\) |
−0.385843 | + | 0.922564i | \(0.626090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.39660 | + | 2.41899i | 0.0662053 | + | 0.114671i | ||||
\(446\) | −21.4135 | − | 37.0893i | −1.01396 | − | 1.75623i | ||||
\(447\) | 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 | ||||||||
\(451\) | − | 63.6906i | − | 2.99907i | ||||||
\(452\) | −10.4825 | − | 6.05208i | −0.493056 | − | 0.284666i | ||||
\(453\) | 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 | −0.618755 | − | 0.785584i | \(-0.712363\pi\) |
0.989713 | + | 0.143065i | \(0.0456959\pi\) | |||||||
\(458\) | 24.0246 | 1.12260 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.28849i | 0.0600763i | ||||||||
\(461\) | 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 | \(0.923583\pi\) | |||||||
\(464\) | 31.3749 | − | 18.1143i | 1.45654 | − | 0.840935i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.74215 | − | 13.4098i | 0.358648 | − | 0.621197i | ||||
\(467\) | 20.3457 | 0.941486 | 0.470743 | − | 0.882270i | \(-0.343986\pi\) | ||||
0.470743 | + | 0.882270i | \(0.343986\pi\) | |||||||
\(468\) | 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 | ||||||||
\(478\) | −51.2171 | −2.34261 | ||||||||
\(479\) | 12.1492 | − | 21.0430i | 0.555109 | − | 0.961477i | −0.442786 | − | 0.896627i | \(-0.646010\pi\) |
0.997895 | − | 0.0648499i | \(-0.0206569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.5001 | − | 20.4960i | 1.61867 | − | 0.934538i | ||||
\(482\) | −20.5259 | − | 35.5519i | −0.934929 | − | 1.61934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.7045 | + | 20.2728i | −0.532023 | + | 0.921491i | ||||
\(485\) | 10.7303i | 0.487239i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.3091 | −1.23749 | −0.618747 | − | 0.785590i | \(-0.712359\pi\) | ||||
−0.618747 | + | 0.785590i | \(0.712359\pi\) | |||||||
\(488\) | −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 | ||||||||
\(493\) | 10.4938 | + | 6.05859i | 0.472616 | + | 0.272865i | ||||
\(494\) | − | 22.6738i | − | 1.02014i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 27.6168i | − | 1.24003i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.15504 | + | 8.92879i | 0.230771 | + | 0.399707i | 0.958035 | − | 0.286650i | \(-0.0925418\pi\) |
−0.727264 | + | 0.686358i | \(0.759208\pi\) | |||||||
\(500\) | 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 | ||||
\(509\) | 2.58601 | + | 4.47911i | 0.114623 | + | 0.198533i | 0.917629 | − | 0.397438i | \(-0.130101\pi\) |
−0.803006 | + | 0.595971i | \(0.796767\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5181i | 0.906778i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.07150i | 0.267802i | ||||||||
\(515\) | 5.76093 | + | 3.32608i | 0.253857 | + | 0.146564i | ||||
\(516\) | 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 | ||||
\(521\) | −38.3328 | −1.67939 | −0.839696 | − | 0.543058i | \(-0.817267\pi\) | ||||
−0.839696 | + | 0.543058i | \(0.817267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3050i | 1.19396i | 0.802255 | + | 0.596982i | \(0.203634\pi\) | ||||
−0.802255 | + | 0.596982i | \(0.796366\pi\) | |||||||
\(524\) | −1.71878 | + | 2.97702i | −0.0750855 | + | 0.130052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.7844 | + | 35.9997i | 0.906245 | + | 1.56966i | ||||
\(527\) | 7.99934 | − | 4.61842i | 0.348457 | − | 0.201182i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4172 | + | 18.0432i | −0.452924 | + | 0.784487i | ||||
\(530\) | 2.79352 | 0.121343 | ||||||||
\(531\) | 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 | ||||||||
\(541\) | 19.5610 | 0.840995 | 0.420498 | − | 0.907294i | \(-0.361856\pi\) | ||||
0.420498 | + | 0.907294i | \(0.361856\pi\) | |||||||
\(542\) | 5.57779 | − | 9.66102i | 0.239587 | − | 0.414977i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.27219 | + | 5.35330i | −0.397542 | + | 0.229521i | ||||
\(545\) | −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 | \(-0.0148298\pi\) | |||||||
\(548\) | − | 1.64509i | − | 0.0702747i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 44.6359 | 1.90328 | ||||||||
\(551\) | 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 | ||||||||
\(556\) | 8.29730 | + | 4.79045i | 0.351884 | + | 0.203160i | ||||
\(557\) | 33.2789i | 1.41007i | 0.709171 | + | 0.705036i | \(0.249069\pi\) | ||||
−0.709171 | + | 0.705036i | \(0.750931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.5135i | − | 0.656152i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.83540 | + | 8.37516i | 0.203969 | + | 0.353285i | ||||
\(563\) | 15.2587 | + | 26.4289i | 0.643079 | + | 1.11385i | 0.984742 | + | 0.174023i | \(0.0556767\pi\) |
−0.341663 | + | 0.939823i | \(0.610990\pi\) | |||||||
\(564\) | 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 | \(-0.438509\pi\) |
−0.753925 | + | 0.656960i | \(0.771842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2042 | + | 21.1384i | 0.510731 | + | 0.884613i | 0.999923 | + | 0.0124362i | \(0.00395868\pi\) |
−0.489191 | + | 0.872177i | \(0.662708\pi\) | |||||||
\(572\) | 18.4845 | + | 32.0160i | 0.772875 | + | 1.33866i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.74455i | − | 0.281267i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.6533i | − | 0.610024i | −0.952349 | − | 0.305012i | \(-0.901340\pi\) | ||
0.952349 | − | 0.305012i | \(-0.0986605\pi\) | |||||||
\(578\) | 22.7572 | + | 13.1389i | 0.946574 | + | 0.546505i | ||||
\(579\) | 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 | ||||
\(584\) | −13.9217 | −0.576084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 33.4032i | − | 1.37987i | ||||||
\(587\) | 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 | ||||
\(590\) | 3.03009 | − | 1.74942i | 0.124747 | − | 0.0720225i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.4793 | + | 33.7391i | −0.800594 | + | 1.38667i | ||||
\(593\) | 11.1121 | 0.456319 | 0.228160 | − | 0.973624i | \(-0.426729\pi\) | ||||
0.228160 | + | 0.973624i | \(0.426729\pi\) | |||||||
\(594\) | 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 | \(-0.563040\pi\) |
0.750721 | + | 0.660620i | \(0.229706\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | −8.57024 | −0.348718 | ||||||||
\(605\) | −5.57104 | + | 9.64932i | −0.226495 | + | 0.392301i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.6062 | − | 19.4025i | 1.36403 | − | 0.787524i | 0.373874 | − | 0.927479i | \(-0.378029\pi\) |
0.990158 | + | 0.139955i | \(0.0446959\pi\) | |||||||
\(608\) | 7.92809 | + | 13.7318i | 0.321526 | + | 0.556900i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.26850 | − | 10.8574i | 0.253804 | − | 0.439602i | ||||
\(611\) | − | 15.8105i | − | 0.639623i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.7572 | 1.28266 | 0.641330 | − | 0.767265i | \(-0.278383\pi\) | ||||
0.641330 | + | 0.767265i | \(0.278383\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −25.2590 | − | 14.5833i | −1.01524 | − | 0.586152i | −0.102522 | − | 0.994731i | \(-0.532691\pi\) |
−0.912723 | + | 0.408579i | \(0.866024\pi\) | |||||||
\(620\) | 4.96220i | 0.199287i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 51.8217i | 2.07786i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.46116 | − | 16.3872i | −0.378446 | − | 0.655488i | ||||
\(626\) | 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 | ||||
\(635\) | −0.806924 | − | 1.39763i | −0.0320218 | − | 0.0554634i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 72.4041i | 2.86651i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.77487i | 0.228272i | ||||||||
\(641\) | 10.0267 | + | 5.78891i | 0.396030 | + | 0.228648i | 0.684770 | − | 0.728760i | \(-0.259903\pi\) |
−0.288740 | + | 0.957408i | \(0.593236\pi\) | |||||||
\(642\) | 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 | ||||
\(647\) | 12.4411 | 0.489111 | 0.244556 | − | 0.969635i | \(-0.421358\pi\) | ||||
0.244556 | + | 0.969635i | \(0.421358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.7265i | − | 0.617319i | ||||||
\(650\) | 21.5264 | − | 37.2847i | 0.844333 | − | 1.46243i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.06032 | − | 7.03268i | −0.159014 | − | 0.275421i | ||||
\(653\) | 3.97013 | − | 2.29216i | 0.155363 | − | 0.0896990i | −0.420303 | − | 0.907384i | \(-0.638076\pi\) |
0.575666 | + | 0.817685i | \(0.304743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.818096 | + | 1.41698i | −0.0319656 | + | 0.0553661i | ||||
\(656\) | 58.3841 | 2.27952 | ||||||||
\(657\) | 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 | \(-0.662700\pi\) |
0.510753 | + | 0.859727i | \(0.329367\pi\) | |||||||
\(662\) | −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 | ||||||||
\(667\) | 10.9404 | 0.423612 | ||||||||
\(668\) | 0.946692 | − | 1.63972i | 0.0366286 | − | 0.0634426i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.4012 | − | 6.00511i | 0.401832 | − | 0.231998i | ||||
\(671\) | −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 | \(0.306990\pi\) | |||||||
\(674\) | − | 6.81956i | − | 0.262680i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.0256 | 0.693292 | ||||||||
\(677\) | −10.0160 | + | 17.3482i | −0.384947 | + | 0.666747i | −0.991762 | − | 0.128096i | \(-0.959114\pi\) |
0.606815 | + | 0.794843i | \(0.292447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.07456 | + | 0.620397i | −0.0412074 | + | 0.0237911i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 47.7986 | + | 27.5966i | 1.83030 | + | 1.05673i | ||||
\(683\) | − | 20.9366i | − | 0.801116i | −0.916271 | − | 0.400558i | \(-0.868816\pi\) | ||
0.916271 | − | 0.400558i | \(-0.131184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.783018i | − | 0.0299176i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.37198 | + | 12.7686i | 0.281054 | + | 0.486800i | ||||
\(689\) | −6.05543 | − | 10.4883i | −0.230693 | − | 0.399573i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.33430 | − | 0.770358i | −0.0507591 | − | 0.0293058i | 0.474406 | − | 0.880306i | \(-0.342663\pi\) |
−0.525165 | + | 0.851001i | \(0.675996\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | 13.9711 | + | 24.1987i | 0.528815 | + | 0.915935i | ||||
\(699\) | 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 | ||||||||
\(703\) | 19.2975i | 0.727818i | ||||||||
\(704\) | −10.5358 | − | 6.08286i | −0.397083 | − | 0.229256i | ||||
\(705\) | 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 | −0.995912 | − | 0.0903259i | \(-0.971209\pi\) |
0.576181 | + | 0.817322i | \(0.304542\pi\) | |||||||
\(710\) | 5.63670 | 0.211542 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.10231i | 0.191217i | ||||||||
\(713\) | 4.16988 | − | 7.22244i | 0.156163 | − | 0.270482i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.79812 | + | 15.2388i | 0.329031 | + | 0.569898i | ||||
\(716\) | 10.8625 | − | 6.27149i | 0.405952 | − | 0.234377i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.06910 | − | 10.5120i | 0.226497 | − | 0.392304i | ||||
\(719\) | −38.9087 | −1.45105 | −0.725525 | − | 0.688195i | \(-0.758403\pi\) | ||||
−0.725525 | + | 0.688195i | \(0.758403\pi\) | |||||||
\(720\) | 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 | ||||||||
\(730\) | 13.9624 | 0.516771 | ||||||||
\(731\) | −2.46567 | + | 4.27066i | −0.0911960 | + | 0.157956i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.1222 | + | 16.2364i | −1.03872 | + | 0.599704i | −0.919470 | − | 0.393161i | \(-0.871382\pi\) |
−0.119248 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(734\) | −2.83703 | − | 4.91389i | −0.104717 | − | 0.181375i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.83338 | + | 8.37167i | −0.178161 | + | 0.308584i | ||||
\(737\) | − | 53.9832i | − | 1.98850i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8393 | −0.509087 | −0.254543 | − | 0.967061i | \(-0.581925\pi\) | ||||
−0.254543 | + | 0.967061i | \(0.581925\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | −3.87515 | − | 2.23732i | −0.141975 | − | 0.0819690i | ||||
\(746\) | 17.7706i | 0.650628i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 11.7514i | − | 0.429675i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82952 | + | 3.16883i | 0.0667602 | + | 0.115632i | 0.897473 | − | 0.441068i | \(-0.145400\pi\) |
−0.830713 | + | 0.556701i | \(0.812067\pi\) | |||||||
\(752\) | 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 | ||||
\(761\) | 6.82083 | + | 11.8140i | 0.247255 | + | 0.428258i | 0.962763 | − | 0.270346i | \(-0.0871381\pi\) |
−0.715508 | + | 0.698604i | \(0.753805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.4991i | 0.994884i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 45.0910i | − | 1.62920i | ||||||
\(767\) | −13.1365 | − | 7.58434i | −0.474330 | − | 0.273855i | ||||
\(768\) | 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 | ||||
\(773\) | −26.2218 | −0.943132 | −0.471566 | − | 0.881831i | \(-0.656311\pi\) | ||||
−0.471566 | + | 0.881831i | \(0.656311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 25.9744i | − | 0.933028i | ||||||
\(776\) | −9.80047 | + | 16.9749i | −0.351816 | + | 0.609364i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.88703 | + | 10.1966i | 0.211060 | + | 0.365567i | ||||
\(779\) | 25.0451 | − | 14.4598i | 0.897334 | − | 0.518076i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6678 | − | 21.9413i | 0.453291 | − | 0.785123i | ||||
\(782\) | −4.39402 | −0.157130 | ||||||||
\(783\) | 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 | \(-0.493453\pi\) |
0.876126 | + | 0.482082i | \(0.160119\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −54.3522 | −1.93010 | ||||||||
\(794\) | 12.1463 | − | 21.0380i | 0.431055 | − | 0.746610i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.1952 | − | 12.2371i | 0.751245 | − | 0.433731i | ||||
\(797\) | 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 | ||||
\(800\) | 30.1074i | 1.06446i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.9555 | −1.02245 | ||||||||
\(803\) | 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 | ||||||||
\(808\) | 4.75044 | + | 2.74267i | 0.167120 | + | 0.0964868i | ||||
\(809\) | 39.8909i | 1.40249i | 0.712920 | + | 0.701245i | \(0.247372\pi\) | ||||
−0.712920 | + | 0.701245i | \(0.752628\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | −38.9300 | − | 67.4288i | −1.36450 | − | 2.36338i | ||||
\(815\) | −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 | \(-0.335638\pi\) |
−0.506258 | + | 0.862382i | \(0.668972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.54814 | + | 11.3417i | 0.228254 | + | 0.395347i | 0.957291 | − | 0.289127i | \(-0.0933650\pi\) |
−0.729037 | + | 0.684475i | \(0.760032\pi\) | |||||||
\(824\) | 6.07570 | + | 10.5234i | 0.211657 | + | 0.366601i | ||||
\(825\) | 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 | ||||||||
\(829\) | 33.5052i | 1.16368i | 0.813302 | + | 0.581842i | \(0.197668\pi\) | ||||
−0.813302 | + | 0.581842i | \(0.802332\pi\) | |||||||
\(830\) | −7.20287 | − | 4.15858i | −0.250015 | − | 0.144346i | ||||
\(831\) | 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 | ||||
\(836\) | −17.4036 | −0.601914 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 44.8733i | − | 1.55012i | ||||||
\(839\) | −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 | ||||
\(842\) | −19.0182 | + | 10.9802i | −0.655412 | + | 0.378402i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.47260 | − | 9.47882i | 0.188375 | − | 0.326275i | ||||
\(845\) | 8.57970 | 0.295151 | ||||||||
\(846\) | 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 | ||||||||
\(856\) | 0.363859 | 0.0124364 | ||||||||
\(857\) | 5.28926 | − | 9.16126i | 0.180678 | − | 0.312943i | −0.761434 | − | 0.648243i | \(-0.775504\pi\) |
0.942111 | + | 0.335300i | \(0.108838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2972 | + | 16.3374i | −0.965488 | + | 0.557425i | −0.897858 | − | 0.440286i | \(-0.854877\pi\) |
−0.0676303 | + | 0.997710i | \(0.521544\pi\) | |||||||
\(860\) | −1.32460 | − | 2.29428i | −0.0451686 | − | 0.0782343i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2332 | − | 48.9014i | 0.961628 | − | 1.66559i | ||||
\(863\) | 9.35166i | 0.318334i | 0.987252 | + | 0.159167i | \(0.0508809\pi\) | ||||
−0.987252 | + | 0.159167i | \(0.949119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.91285 | 0.167042 | ||||||||
\(866\) | −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 | ||||||||
\(871\) | −45.0925 | − | 26.0342i | −1.52790 | − | 0.882135i | ||||
\(872\) | − | 7.41567i | − | 0.251126i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.50742i | 0.220117i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.619077 | − | 1.07227i | −0.0209048 | − | 0.0362081i | 0.855384 | − | 0.517995i | \(-0.173321\pi\) |
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(878\) | 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 | ||||
\(887\) | 7.25578 | + | 12.5674i | 0.243625 | + | 0.421972i | 0.961744 | − | 0.273949i | \(-0.0883299\pi\) |
−0.718119 | + | 0.695920i | \(0.754997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 5.11722i | − | 0.171530i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31.7063i | 1.06161i | ||||||||
\(893\) | 6.44579 | + | 3.72148i | 0.215700 | + | 0.124534i | ||||
\(894\) | 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 | ||||
\(899\) | 42.1331 | 1.40522 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84972i | 0.128253i | ||||||||
\(902\) | −58.3414 | + | 101.050i | −1.94256 | + | 3.36460i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.26201 | − | 9.11407i | −0.175012 | − | 0.303129i | ||||
\(905\) | 6.68849 | − | 3.86160i | 0.222333 | − | 0.128364i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.60695 | − | 16.6397i | 0.318993 | − | 0.552513i | −0.661285 | − | 0.750135i | \(-0.729989\pi\) |
0.980278 | + | 0.197622i | \(0.0633219\pi\) | |||||||
\(908\) | −19.5893 | −0.650094 | ||||||||
\(909\) | 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 | ||||||||
\(919\) | 39.9860 | 1.31902 | 0.659508 | − | 0.751698i | \(-0.270765\pi\) | ||||
0.659508 | + | 0.751698i | \(0.270765\pi\) | |||||||
\(920\) | −0.560143 | + | 0.970196i | −0.0184674 | + | 0.0319864i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.6470 | + | 11.9205i | −0.679972 | + | 0.392582i | ||||
\(923\) | −12.2185 | − | 21.1631i | −0.402177 | − | 0.696591i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3209 | + | 31.7326i | −0.602386 | + | 1.04336i | ||||
\(926\) | 22.0554i | 0.724786i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −48.8373 | −1.60316 | ||||||||
\(929\) | −6.38359 | + | 11.0567i | −0.209439 | + | 0.362759i | −0.951538 | − | 0.307532i | \(-0.900497\pi\) |
0.742099 | + | 0.670290i | \(0.233830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.92775 | + | 5.73179i | −0.325194 | + | 0.187751i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.2801 | − | 18.6369i | −1.05624 | − | 0.609818i | ||||
\(935\) | − | 5.59337i | − | 0.182923i | ||||||
\(936\) | 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 | ||||||||
\(940\) | −1.34996 | − | 2.33819i | −0.0440307 | − | 0.0762634i | ||||
\(941\) | 12.5159 | + | 21.6781i | 0.408006 | + | 0.706686i | 0.994666 | − | 0.103146i | \(-0.0328910\pi\) |
−0.586661 | + | 0.809833i | \(0.699558\pi\) | |||||||
\(942\) | 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 | \(-0.154697\pi\) |
0.0375955 | + | 0.999293i | \(0.488030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.2658 | − | 52.4219i | −0.982470 | − | 1.70169i | ||||
\(950\) | 10.1338 | + | 17.5522i | 0.328783 | + | 0.569469i | ||||
\(951\) | 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 | ||||||||
\(955\) | 13.0889i | 0.423545i | ||||||||
\(956\) | 32.8378 | + | 18.9589i | 1.06205 | + | 0.613175i | ||||
\(957\) | 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 | ||||
\(962\) | −75.0984 | −2.42127 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.3921i | 0.978863i | ||||||||
\(965\) | −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 | \(0.600242\pi\) | |||||||
\(968\) | −17.6263 | + | 10.1765i | −0.566530 | + | 0.327086i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.82910 | − | 17.0245i | 0.315593 | − | 0.546624i | ||||
\(971\) | −41.2514 | −1.32382 | −0.661910 | − | 0.749583i | \(-0.730254\pi\) | ||||
−0.661910 | + | 0.749583i | \(0.730254\pi\) | |||||||
\(972\) | 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 | \(-0.690000\pi\) |
0.435230 | + | 0.900319i | \(0.356667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9192 | − | 11.5004i | −0.636621 | − | 0.367553i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.1139 | −0.897150 | ||||||||
\(983\) | 12.2401 | − | 21.2004i | 0.390397 | − | 0.676188i | −0.602105 | − | 0.798417i | \(-0.705671\pi\) |
0.992502 | + | 0.122229i | \(0.0390044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.4605 | − | 6.03936i | 0.333299 | − | 0.192430i | ||||
\(986\) | −11.0995 | − | 19.2249i | −0.353480 | − | 0.612245i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.39312 | + | 14.5373i | −0.267021 | + | 0.462494i | ||||
\(989\) | 4.45240i | 0.141578i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.1854 | −1.34006 | −0.670032 | − | 0.742332i | \(-0.733720\pi\) | ||||
−0.670032 | + | 0.742332i | \(0.733720\pi\) | |||||||
\(992\) | −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 | ||||||||
\(997\) | −8.38168 | − | 4.83917i | −0.265451 | − | 0.153258i | 0.361368 | − | 0.932423i | \(-0.382310\pi\) |
−0.626818 | + | 0.779165i | \(0.715643\pi\) | |||||||
\(998\) | − | 18.8883i | − | 0.597899i | ||||||
\(999\) | 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.o.e.440.7 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.18 | yes | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.15 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.18 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.17 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.17 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.8 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.17 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.8 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.7 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.8 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.8 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.7 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.17 | ✓ | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.18 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.17 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.18 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.18 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.17 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.17 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.8 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.7 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.7 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.15 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.17 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.68.18 | 48 | 63.4 | even | 3 | |||
441.2.i.d.227.7 | 48 | 21.2 | odd | 6 | |||
441.2.i.d.227.8 | 48 | 21.5 | even | 6 | |||
441.2.o.e.146.17 | ✓ | 48 | 21.20 | even | 2 | ||
441.2.o.e.146.18 | yes | 48 | 3.2 | odd | 2 | ||
441.2.o.e.293.17 | yes | 48 | 9.4 | even | 3 | ||
441.2.o.e.293.18 | yes | 48 | 63.13 | odd | 6 | ||
441.2.s.d.362.7 | 48 | 21.17 | even | 6 | |||
441.2.s.d.362.8 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.374.7 | 48 | 63.58 | even | 3 | |||
441.2.s.d.374.8 | 48 | 63.40 | odd | 6 | |||
1323.2.i.d.521.15 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.521.17 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.1097.15 | 48 | 63.59 | even | 6 | |||
1323.2.i.d.1097.17 | 48 | 63.32 | odd | 6 | |||
1323.2.o.e.440.7 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.440.8 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.7 | 48 | 63.41 | even | 6 | inner | ||
1323.2.o.e.881.8 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.s.d.656.17 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.656.18 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.962.17 | 48 | 63.5 | even | 6 | |||
1323.2.s.d.962.18 | 48 | 63.23 | odd | 6 |