Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(521,1323)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.i (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 | 521.15 | ||
Character | \(\chi\) | \(=\) | 1323.521 |
Dual form | 1323.2.i.d.1097.15 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.83202i | 1.29544i | 0.761880 | + | 0.647718i | \(0.224277\pi\) | ||||
−0.761880 | + | 0.647718i | \(0.775723\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.35631 | −0.678156 | ||||||||
\(5\) | 0.322784 | − | 0.559079i | 0.144353 | − | 0.250028i | −0.784778 | − | 0.619777i | \(-0.787223\pi\) |
0.929132 | + | 0.369749i | \(0.120556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.17925i | 0.416928i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.02425 | + | 0.591348i | 0.323895 | + | 0.187001i | ||||
\(11\) | 4.60375 | − | 2.65797i | 1.38808 | − | 0.801410i | 0.394983 | − | 0.918688i | \(-0.370750\pi\) |
0.993099 | + | 0.117279i | \(0.0374171\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | −4.87304 | −1.21826 | ||||||||
\(17\) | −0.814931 | + | 1.41150i | −0.197650 | + | 0.342339i | −0.947766 | − | 0.318967i | \(-0.896664\pi\) |
0.750116 | + | 0.661306i | \(0.229998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09039 | + | 1.20689i | −0.479569 | + | 0.276879i | −0.720237 | − | 0.693728i | \(-0.755967\pi\) |
0.240668 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(20\) | −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 | \(-0.382363\pi\) |
−0.626947 | + | 0.779062i | \(0.715696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.29162 | + | 3.96920i | 0.458324 | + | 0.793841i | ||||
\(26\) | −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 | ||||||||
\(31\) | 5.66726i | 1.01787i | 0.860805 | + | 0.508935i | \(0.169961\pi\) | ||||
−0.860805 | + | 0.508935i | \(0.830039\pi\) | |||||||
\(32\) | − | 6.56903i | − | 1.16125i | ||||||
\(33\) | 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 | 0.981347 | + | 0.192244i | \(0.0615763\pi\) |
−0.324186 | + | 0.945993i | \(0.605090\pi\) | |||||||
\(38\) | −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 | \(0.240769\pi\) | |||||||
\(44\) | −6.24412 | + | 3.60504i | −0.941336 | + | 0.543481i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.34797 | − | 2.33476i | 0.198748 | − | 0.344241i | ||||
\(47\) | 3.08353 | 0.449779 | 0.224889 | − | 0.974384i | \(-0.427798\pi\) | ||||
0.224889 | + | 0.974384i | \(0.427798\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | −2.04554 | − | 1.18100i | −0.280977 | − | 0.162222i | 0.352889 | − | 0.935665i | \(-0.385199\pi\) |
−0.633866 | + | 0.773443i | \(0.718533\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.43181i | − | 0.462745i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.81008 | + | 11.7954i | −0.894207 | + | 1.54881i | ||||
\(59\) | −2.95836 | −0.385146 | −0.192573 | − | 0.981283i | \(-0.561683\pi\) | ||||
−0.192573 | + | 0.981283i | \(0.561683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.6004i | − | 1.35724i | −0.734491 | − | 0.678618i | \(-0.762579\pi\) | ||
0.734491 | − | 0.678618i | \(-0.237421\pi\) | |||||||
\(62\) | −10.3825 | −1.31859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.28853 | 0.286066 | ||||||||
\(65\) | 3.31008i | 0.410565i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1549 | −1.24062 | −0.620312 | − | 0.784355i | \(-0.712994\pi\) | ||||
−0.620312 | + | 0.784355i | \(0.712994\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −10.2239 | − | 5.90277i | −1.19662 | − | 0.690867i | −0.236817 | − | 0.971554i | \(-0.576104\pi\) |
−0.959799 | + | 0.280687i | \(0.909438\pi\) | |||||||
\(74\) | −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 | ||||||||
\(79\) | 6.96209 | 0.783296 | 0.391648 | − | 0.920115i | \(-0.371905\pi\) | ||||
0.391648 | + | 0.920115i | \(0.371905\pi\) | |||||||
\(80\) | −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 | ||||
\(86\) | −4.80038 | − | 2.77150i | −0.517638 | − | 0.298859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.13442 | + | 5.42898i | 0.334130 | + | 0.578731i | ||||
\(89\) | −2.16337 | − | 3.74706i | −0.229317 | − | 0.397188i | 0.728289 | − | 0.685270i | \(-0.240316\pi\) |
−0.957606 | + | 0.288082i | \(0.906982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.72850 | + | 0.997953i | 0.180209 | + | 0.104044i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.64910i | 0.582660i | ||||||||
\(95\) | 1.55826i | 0.159874i | ||||||||
\(96\) | 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 | ||||
\(101\) | 2.32577 | + | 4.02835i | 0.231423 | + | 0.400836i | 0.958227 | − | 0.286009i | \(-0.0923286\pi\) |
−0.726804 | + | 0.686845i | \(0.758995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.92382 | − | 5.15217i | −0.879290 | − | 0.507658i | −0.00886554 | − | 0.999961i | \(-0.502822\pi\) |
−0.870424 | + | 0.492303i | \(0.836155\pi\) | |||||||
\(104\) | −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 | \(-0.671414\pi\) |
0.487028 | + | 0.873386i | \(0.338081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.14423 | − | 5.44596i | 0.301162 | − | 0.521628i | −0.675237 | − | 0.737601i | \(-0.735959\pi\) |
0.976399 | + | 0.215972i | \(0.0692921\pi\) | |||||||
\(110\) | 6.28716 | 0.599457 | ||||||||
\(111\) | 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 | ||||
\(116\) | −8.73256 | − | 5.04174i | −0.810797 | − | 0.468114i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.41979i | − | 0.498932i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62966 | − | 14.9470i | 0.784515 | − | 1.35882i | ||||
\(122\) | 19.4201 | 1.75821 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 7.68657i | − | 0.690274i | ||||||
\(125\) | 6.18664 | 0.553350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.49989 | −0.221829 | −0.110915 | − | 0.993830i | \(-0.535378\pi\) | ||||
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(128\) | − | 8.94541i | − | 0.790670i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.06415 | −0.531861 | ||||||||
\(131\) | 1.26725 | − | 2.19494i | 0.110720 | − | 0.191773i | −0.805341 | − | 0.592812i | \(-0.798018\pi\) |
0.916061 | + | 0.401039i | \(0.131351\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.6041i | − | 1.60715i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.66452 | − | 0.961008i | −0.142731 | − | 0.0824058i | ||||
\(137\) | 1.05041 | − | 0.606456i | 0.0897429 | − | 0.0518131i | −0.454457 | − | 0.890769i | \(-0.650167\pi\) |
0.544200 | + | 0.838956i | \(0.316833\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −8.73137 | −0.732721 | ||||||||
\(143\) | −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 | ||||
\(149\) | 6.00270 | + | 3.46566i | 0.491760 | + | 0.283918i | 0.725304 | − | 0.688428i | \(-0.241699\pi\) |
−0.233544 | + | 0.972346i | \(0.575032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.15939 | − | 5.47223i | −0.257108 | − | 0.445323i | 0.708358 | − | 0.705853i | \(-0.249436\pi\) |
−0.965466 | + | 0.260530i | \(0.916103\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | − | 1.99028i | − | 0.158842i | −0.996841 | − | 0.0794208i | \(-0.974693\pi\) | ||
0.996841 | − | 0.0794208i | \(-0.0253071\pi\) | |||||||
\(158\) | 12.7547i | 1.01471i | ||||||||
\(159\) | 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 | 0.959122 | − | 0.282994i | \(-0.0913278\pi\) |
−0.724641 | + | 0.689126i | \(0.757994\pi\) | |||||||
\(164\) | −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 | ||||
\(170\) | −1.66938 | + | 0.963816i | −0.128035 | + | 0.0739213i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.05184 | − | 3.55389i | 0.156451 | − | 0.270982i | ||||
\(173\) | −7.61012 | −0.578586 | −0.289293 | − | 0.957241i | \(-0.593420\pi\) | ||||
−0.289293 | + | 0.957241i | \(0.593420\pi\) | |||||||
\(174\) | 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 | ||||
\(179\) | 8.00888 | + | 4.62393i | 0.598612 | + | 0.345609i | 0.768495 | − | 0.639855i | \(-0.221006\pi\) |
−0.169883 | + | 0.985464i | \(0.554339\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | 5.16113 | 0.379454 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.66426i | 0.633593i | ||||||||
\(188\) | −4.18223 | −0.305020 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.85477 | −0.207107 | ||||||||
\(191\) | − | 20.2749i | − | 1.46704i | −0.679666 | − | 0.733521i | \(-0.737875\pi\) | ||
0.679666 | − | 0.733521i | \(-0.262125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8917 | −1.21589 | −0.607944 | − | 0.793980i | \(-0.708006\pi\) | ||||
−0.607944 | + | 0.793980i | \(0.708006\pi\) | |||||||
\(194\) | −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 | ||||||||
\(199\) | 15.6271 | + | 9.02231i | 1.10778 | + | 0.639574i | 0.938252 | − | 0.345952i | \(-0.112444\pi\) |
0.169523 | + | 0.985526i | \(0.445777\pi\) | |||||||
\(200\) | −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 | ||||||||
\(205\) | 7.73458 | 0.540207 | ||||||||
\(206\) | 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 | \(0.922930\pi\) | |||||||
\(212\) | 2.77440 | + | 1.60180i | 0.190546 | + | 0.110012i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.282636 | − | 0.489540i | −0.0193206 | − | 0.0334642i | ||||
\(215\) | 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 | ||||||||
\(220\) | 4.65460i | 0.313813i | ||||||||
\(221\) | − | 8.35694i | − | 0.562148i | ||||||
\(222\) | 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 | ||||
\(227\) | −7.22154 | − | 12.5081i | −0.479310 | − | 0.830190i | 0.520408 | − | 0.853918i | \(-0.325780\pi\) |
−0.999718 | + | 0.0237280i | \(0.992446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3568 | + | 6.55685i | 0.750479 | + | 0.433289i | 0.825867 | − | 0.563865i | \(-0.190686\pi\) |
−0.0753881 | + | 0.997154i | \(0.524020\pi\) | |||||||
\(230\) | −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 | \(-0.577374\pi\) |
0.720219 | + | 0.693746i | \(0.244041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.995314 | − | 1.72393i | 0.0649271 | − | 0.112457i | ||||
\(236\) | 4.01246 | 0.261189 | ||||||||
\(237\) | 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 | \(-0.923310\pi\) |
−0.278921 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(242\) | 27.3833 | + | 15.8097i | 1.76026 | + | 1.01629i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.3774i | 0.920418i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.18819 | − | 10.7183i | 0.393745 | − | 0.681987i | ||||
\(248\) | −6.68312 | −0.424379 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.3341i | 0.716829i | ||||||||
\(251\) | −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 | ||||||||
\(254\) | − | 4.57985i | − | 0.287366i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9653 | 1.31033 | ||||||||
\(257\) | −1.65705 | + | 2.87009i | −0.103364 | + | 0.179031i | −0.913069 | − | 0.407806i | \(-0.866294\pi\) |
0.809705 | + | 0.586837i | \(0.199627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.48950i | − | 0.278427i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.02118 | + | 2.32163i | 0.248429 | + | 0.143431i | ||||
\(263\) | 19.6502 | − | 11.3451i | 1.21169 | − | 0.699567i | 0.248559 | − | 0.968617i | \(-0.420043\pi\) |
0.963126 | + | 0.269050i | \(0.0867096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.32054 | + | 0.762413i | −0.0811200 | + | 0.0468347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.7733 | 0.841336 | ||||||||
\(269\) | 1.38050 | − | 2.39110i | 0.0841707 | − | 0.145788i | −0.820867 | − | 0.571120i | \(-0.806509\pi\) |
0.905038 | + | 0.425332i | \(0.139843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.27342 | − | 3.04461i | 0.320337 | − | 0.184947i | −0.331206 | − | 0.943559i | \(-0.607455\pi\) |
0.651543 | + | 0.758612i | \(0.274122\pi\) | |||||||
\(272\) | 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 | 0.972222 | − | 0.234062i | \(-0.0752019\pi\) |
−0.688814 | + | 0.724938i | \(0.741869\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | − | 19.6699i | − | 1.16926i | −0.811302 | − | 0.584628i | \(-0.801241\pi\) | ||
0.811302 | − | 0.584628i | \(-0.198759\pi\) | |||||||
\(284\) | − | 6.46414i | − | 0.383576i | ||||||
\(285\) | 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 | ||||
\(290\) | 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 | ||||
\(296\) | −8.16470 | + | 4.71389i | −0.474563 | + | 0.273989i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.34917 | + | 10.9971i | −0.367797 | + | 0.637044i | ||||
\(299\) | 7.54531 | 0.436356 | ||||||||
\(300\) | 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 | ||||
\(305\) | −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 | ||||||||
\(310\) | −3.35132 | + | 5.80466i | −0.190342 | + | 0.329683i | ||||
\(311\) | 28.2866 | 1.60398 | 0.801992 | − | 0.597334i | \(-0.203773\pi\) | ||||
0.801992 | + | 0.597334i | \(0.203773\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.57595i | 0.315171i | 0.987505 | + | 0.157586i | \(0.0503710\pi\) | ||||
−0.987505 | + | 0.157586i | \(0.949629\pi\) | |||||||
\(314\) | 3.64624 | 0.205769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.44276 | −0.531197 | ||||||||
\(317\) | 33.5681i | 1.88537i | 0.333680 | + | 0.942686i | \(0.391709\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.5214 | 2.21277 | ||||||||
\(320\) | 0.738701 | − | 1.27947i | 0.0412947 | − | 0.0715244i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.93412i | − | 0.218901i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.3517 | − | 11.7500i | −1.12891 | − | 0.651775i | ||||
\(326\) | −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 | ||||||||
\(331\) | −30.3735 | −1.66948 | −0.834739 | − | 0.550646i | \(-0.814381\pi\) | ||||
−0.834739 | + | 0.550646i | \(0.814381\pi\) | |||||||
\(332\) | −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 | \(0.801005\pi\) | |||||||
\(338\) | 21.0859 | + | 12.1739i | 1.14692 | + | 0.662175i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.713547 | − | 1.23590i | −0.0386975 | − | 0.0670261i | ||||
\(341\) | 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 | ||||||||
\(346\) | − | 13.9419i | − | 0.749522i | ||||||
\(347\) | − | 7.13637i | − | 0.383100i | −0.981483 | − | 0.191550i | \(-0.938649\pi\) | ||
0.981483 | − | 0.191550i | \(-0.0613515\pi\) | |||||||
\(348\) | 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 | ||||
\(353\) | −17.2359 | − | 29.8534i | −0.917373 | − | 1.58894i | −0.803389 | − | 0.595455i | \(-0.796972\pi\) |
−0.113985 | − | 0.993482i | \(-0.536362\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | 5.73791 | − | 3.31278i | 0.302835 | − | 0.174842i | −0.340881 | − | 0.940107i | \(-0.610725\pi\) |
0.643716 | + | 0.765265i | \(0.277392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58684 | + | 11.4087i | −0.346676 | + | 0.600460i | ||||
\(362\) | 21.9173 | 1.15195 | ||||||||
\(363\) | 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 | \(-0.692425\pi\) |
0.428358 | + | 0.903609i | \(0.359092\pi\) | |||||||
\(368\) | 6.21028 | + | 3.58551i | 0.323733 | + | 0.186907i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.45532i | 0.491559i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.84999 | + | 8.40043i | −0.251123 | + | 0.434958i | −0.963835 | − | 0.266499i | \(-0.914133\pi\) |
0.712712 | + | 0.701457i | \(0.247467\pi\) | |||||||
\(374\) | −15.8731 | −0.820780 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.63625i | 0.187526i | ||||||||
\(377\) | −38.1195 | −1.96326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.76103 | 0.398657 | 0.199329 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199329 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(380\) | − | 2.11349i | − | 0.108420i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.1442 | 1.90046 | ||||||||
\(383\) | 12.3063 | − | 21.3152i | 0.628825 | − | 1.08916i | −0.358963 | − | 0.933352i | \(-0.616870\pi\) |
0.987788 | − | 0.155804i | \(-0.0497970\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 30.9459i | − | 1.57511i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.5236 | − | 11.2720i | −0.991162 | − | 0.572248i | ||||
\(389\) | 5.56578 | − | 3.21340i | 0.282196 | − | 0.162926i | −0.352221 | − | 0.935917i | \(-0.614573\pi\) |
0.634417 | + | 0.772991i | \(0.281240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.07712 | − | 1.19923i | 0.105044 | − | 0.0606474i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.2776 | 1.72688 | ||||||||
\(395\) | 2.24725 | − | 3.89235i | 0.113071 | − | 0.195846i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4835 | − | 6.62998i | 0.576338 | − | 0.332749i | −0.183339 | − | 0.983050i | \(-0.558690\pi\) |
0.759677 | + | 0.650301i | \(0.225357\pi\) | |||||||
\(398\) | −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 | \(-0.462463\pi\) |
−0.801184 | + | 0.598418i | \(0.795796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5291 | − | 25.1652i | −0.723747 | − | 1.25357i | ||||
\(404\) | −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 | ||||||||
\(409\) | − | 5.41851i | − | 0.267928i | −0.990986 | − | 0.133964i | \(-0.957229\pi\) | ||
0.990986 | − | 0.133964i | \(-0.0427707\pi\) | |||||||
\(410\) | 14.1699i | 0.699803i | ||||||||
\(411\) | 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 | ||||
\(416\) | 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 | \(0.0723113\pi\) | |||||||
\(422\) | 12.8034 | − | 7.39206i | 0.623261 | − | 0.359840i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.39269 | − | 2.41221i | 0.0676350 | − | 0.117147i | ||||
\(425\) | −7.47005 | −0.362351 | ||||||||
\(426\) | 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 | ||||
\(431\) | −26.6926 | − | 15.4110i | −1.28574 | − | 0.742320i | −0.307845 | − | 0.951437i | \(-0.599608\pi\) |
−0.977891 | + | 0.209117i | \(0.932941\pi\) | |||||||
\(432\) | 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 | ||||
\(437\) | 3.55204 | 0.169917 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.1448i | 1.29555i | 0.761831 | + | 0.647776i | \(0.224301\pi\) | ||||
−0.761831 | + | 0.647776i | \(0.775699\pi\) | |||||||
\(440\) | 4.04697 | 0.192932 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.3101 | 0.728228 | ||||||||
\(443\) | − | 5.35163i | − | 0.254264i | −0.991886 | − | 0.127132i | \(-0.959423\pi\) | ||
0.991886 | − | 0.127132i | \(-0.0405771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.79320 | −0.132411 | ||||||||
\(446\) | −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 | ||||||||
\(451\) | 55.1577 | + | 31.8453i | 2.59727 | + | 1.49954i | ||||
\(452\) | 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 | ||||||||
\(457\) | −15.8604 | −0.741917 | −0.370958 | − | 0.928649i | \(-0.620971\pi\) | ||||
−0.370958 | + | 0.928649i | \(0.620971\pi\) | |||||||
\(458\) | −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 | \(0.923583\pi\) | |||||||
\(464\) | −31.3749 | − | 18.1143i | −1.45654 | − | 0.840935i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.74215 | + | 13.4098i | 0.358648 | + | 0.621197i | ||||
\(467\) | −10.1728 | − | 17.6199i | −0.470743 | − | 0.815351i | 0.528697 | − | 0.848811i | \(-0.322681\pi\) |
−0.999440 | + | 0.0334596i | \(0.989347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.15829 | + | 1.82344i | 0.145681 | + | 0.0841090i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 3.48865i | − | 0.160578i | ||||||
\(473\) | 16.0840i | 0.739544i | ||||||||
\(474\) | 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 | ||||
\(479\) | 12.1492 | + | 21.0430i | 0.555109 | + | 0.961477i | 0.997895 | + | 0.0648499i | \(0.0206569\pi\) |
−0.442786 | + | 0.896627i | \(0.646010\pi\) | |||||||
\(480\) | 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 | ||||
\(485\) | 9.29273 | − | 5.36516i | 0.421961 | − | 0.243619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6546 | − | 23.6504i | 0.618747 | − | 1.07170i | −0.370968 | − | 0.928646i | \(-0.620974\pi\) |
0.989715 | − | 0.143055i | \(-0.0456927\pi\) | |||||||
\(488\) | 12.5005 | 0.565871 | ||||||||
\(489\) | 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 | ||||
\(494\) | 19.6361 | + | 11.3369i | 0.883471 | + | 0.510072i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 27.6168i | − | 1.24003i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.15504 | − | 8.92879i | 0.230771 | − | 0.399707i | −0.727264 | − | 0.686358i | \(-0.759208\pi\) |
0.958035 | + | 0.286650i | \(0.0925418\pi\) | |||||||
\(500\) | −8.39101 | −0.375257 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 11.7174i | − | 0.522972i | ||||||
\(503\) | 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 | ||||||||
\(506\) | − | 14.3315i | − | 0.637114i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.39063 | 0.150435 | ||||||||
\(509\) | 2.58601 | − | 4.47911i | 0.114623 | − | 0.198533i | −0.803006 | − | 0.595971i | \(-0.796767\pi\) |
0.917629 | + | 0.397438i | \(0.130101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5181i | 0.906778i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.25807 | − | 3.03575i | −0.231924 | − | 0.133901i | ||||
\(515\) | −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 | ||||||||
\(520\) | −3.90342 | −0.171176 | ||||||||
\(521\) | 19.1664 | − | 33.1972i | 0.839696 | − | 1.45440i | −0.0504538 | − | 0.998726i | \(-0.516067\pi\) |
0.890149 | − | 0.455669i | \(-0.150600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.6468 | − | 13.6525i | 1.03400 | − | 0.596982i | 0.115874 | − | 0.993264i | \(-0.463033\pi\) |
0.918129 | + | 0.396282i | \(0.129700\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −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 | ||||||||
\(535\) | 0.199190i | 0.00861175i | ||||||||
\(536\) | − | 11.9752i | − | 0.517251i | ||||||
\(537\) | 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 | 0.575491 | − | 0.817808i | \(-0.304811\pi\) |
−0.995988 | + | 0.0894853i | \(0.971478\pi\) | |||||||
\(542\) | 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 | \(-0.0148298\pi\) | |||||||
\(548\) | −1.42469 | + | 0.822544i | −0.0608597 | + | 0.0351373i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.3180 | + | 38.6559i | −0.951642 | + | 1.64829i | ||||
\(551\) | −17.9452 | −0.764492 | ||||||||
\(552\) | 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 | ||||
\(557\) | −28.8204 | − | 16.6395i | −1.22116 | − | 0.705036i | −0.255994 | − | 0.966678i | \(-0.582403\pi\) |
−0.965165 | + | 0.261642i | \(0.915736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.5135i | − | 0.656152i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.83540 | − | 8.37516i | 0.203969 | − | 0.353285i | ||||
\(563\) | −30.5175 | −1.28616 | −0.643079 | − | 0.765800i | \(-0.722343\pi\) | ||||
−0.643079 | + | 0.765800i | \(0.722343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.76126i | 0.242378i | ||||||||
\(566\) | 36.0358 | 1.51470 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.62028 | −0.235822 | ||||||||
\(569\) | 15.4781i | 0.648876i | 0.945907 | + | 0.324438i | \(0.105175\pi\) | ||||
−0.945907 | + | 0.324438i | \(0.894825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4085 | −1.02146 | −0.510731 | − | 0.859740i | \(-0.670625\pi\) | ||||
−0.510731 | + | 0.859740i | \(0.670625\pi\) | |||||||
\(572\) | 18.4845 | − | 32.0160i | 0.772875 | − | 1.33866i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.74455i | − | 0.281267i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6901 | + | 7.32664i | 0.528296 | + | 0.305012i | 0.740322 | − | 0.672252i | \(-0.234673\pi\) |
−0.212026 | + | 0.977264i | \(0.568006\pi\) | |||||||
\(578\) | −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 | ||||||||
\(583\) | −12.5562 | −0.520026 | ||||||||
\(584\) | 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 | ||||
\(590\) | −3.03009 | − | 1.74942i | −0.124747 | − | 0.0720225i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.4793 | − | 33.7391i | −0.800594 | − | 1.38667i | ||||
\(593\) | −5.55605 | − | 9.62337i | −0.228160 | − | 0.395184i | 0.729103 | − | 0.684404i | \(-0.239938\pi\) |
−0.957263 | + | 0.289220i | \(0.906604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.14153 | − | 4.70051i | −0.333490 | − | 0.192541i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.8232i | 0.565272i | ||||||||
\(599\) | 15.6555i | 0.639667i | 0.947474 | + | 0.319833i | \(0.103627\pi\) | ||||
−0.947474 | + | 0.319833i | \(0.896373\pi\) | |||||||
\(600\) | 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 | ||||
\(605\) | −5.57104 | − | 9.64932i | −0.226495 | − | 0.392301i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.6062 | − | 19.4025i | −1.36403 | − | 0.787524i | −0.373874 | − | 0.927479i | \(-0.621971\pi\) |
−0.990158 | + | 0.139955i | \(0.955304\pi\) | |||||||
\(608\) | 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 | 0.343806 | + | 0.939041i | \(0.388284\pi\) |
−0.985136 | + | 0.171776i | \(0.945049\pi\) | |||||||
\(614\) | −47.7145 | −1.92560 | ||||||||
\(615\) | 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 | \(-0.467309\pi\) |
0.912723 | + | 0.408579i | \(0.133976\pi\) | |||||||
\(620\) | −4.29740 | − | 2.48110i | −0.172588 | − | 0.0996435i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 51.8217i | 2.07786i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.46116 | + | 16.3872i | −0.378446 | + | 0.655488i | ||||
\(626\) | −10.2153 | −0.408284 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.69944i | 0.107719i | ||||||||
\(629\) | −13.0303 | −0.519551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7428 | 0.467473 | 0.233736 | − | 0.972300i | \(-0.424905\pi\) | ||||
0.233736 | + | 0.972300i | \(0.424905\pi\) | |||||||
\(632\) | 8.21005i | 0.326578i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −61.4976 | −2.44238 | ||||||||
\(635\) | −0.806924 | + | 1.39763i | −0.0320218 | + | 0.0554634i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 72.4041i | 2.86651i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.00119 | − | 2.88744i | −0.197689 | − | 0.114136i | ||||
\(641\) | −10.0267 | + | 5.78891i | −0.396030 | + | 0.228648i | −0.684770 | − | 0.728760i | \(-0.740097\pi\) |
0.288740 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 7.20741 | 0.283572 | ||||||||
\(647\) | −6.22057 | + | 10.7743i | −0.244556 | + | 0.423583i | −0.962007 | − | 0.273026i | \(-0.911975\pi\) |
0.717451 | + | 0.696609i | \(0.245309\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | −3.97013 | − | 2.29216i | −0.155363 | − | 0.0896990i | 0.420303 | − | 0.907384i | \(-0.361924\pi\) |
−0.575666 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.818096 | − | 1.41698i | −0.0319656 | − | 0.0553661i | ||||
\(656\) | −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 | ||||||||
\(661\) | 0.640781i | 0.0249235i | 0.999922 | + | 0.0124617i | \(0.00396680\pi\) | ||||
−0.999922 | + | 0.0124617i | \(0.996033\pi\) | |||||||
\(662\) | − | 55.6449i | − | 2.16270i | ||||||
\(663\) | 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 | ||||
\(668\) | 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 | \(0.306990\pi\) | |||||||
\(674\) | −5.90591 | + | 3.40978i | −0.227487 | + | 0.131340i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.01280 | + | 15.6106i | −0.346646 | + | 0.600409i | ||||
\(677\) | 20.0320 | 0.769893 | 0.384947 | − | 0.922939i | \(-0.374220\pi\) | ||||
0.384947 | + | 0.922939i | \(0.374220\pi\) | |||||||
\(678\) | 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 | ||||
\(683\) | 18.1316 | + | 10.4683i | 0.693786 | + | 0.400558i | 0.805029 | − | 0.593235i | \(-0.202150\pi\) |
−0.111243 | + | 0.993793i | \(0.535483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.783018i | − | 0.0299176i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.37198 | − | 12.7686i | 0.281054 | − | 0.486800i | ||||
\(689\) | 12.1109 | 0.461387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.54072i | 0.0586116i | 0.999570 | + | 0.0293058i | \(0.00932966\pi\) | ||||
−0.999570 | + | 0.0293058i | \(0.990670\pi\) | |||||||
\(692\) | 10.3217 | 0.392372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0740 | 0.496282 | ||||||||
\(695\) | − | 4.56025i | − | 0.172980i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5274 | −0.739654 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −16.7121 | − | 9.64873i | −0.630309 | − | 0.363909i | ||||
\(704\) | 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 | ||||||||
\(709\) | 22.3524 | 0.839463 | 0.419732 | − | 0.907648i | \(-0.362124\pi\) | ||||
0.419732 | + | 0.907648i | \(0.362124\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | −10.8625 | − | 6.27149i | −0.405952 | − | 0.234377i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.06910 | + | 10.5120i | 0.226497 | + | 0.392304i | ||||
\(719\) | 19.4544 | + | 33.6959i | 0.725525 | + | 1.25665i | 0.958757 | + | 0.284226i | \(0.0917365\pi\) |
−0.233232 | + | 0.972421i | \(0.574930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −20.9011 | − | 12.0672i | −0.777858 | − | 0.449096i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.2261i | 0.603039i | ||||||||
\(725\) | 34.0741i | 1.26548i | ||||||||
\(726\) | 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 | ||||
\(731\) | −2.46567 | − | 4.27066i | −0.0911960 | − | 0.157956i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1222 | + | 16.2364i | 1.03872 | + | 0.599704i | 0.919470 | − | 0.393161i | \(-0.128618\pi\) |
0.119248 | + | 0.992865i | \(0.461952\pi\) | |||||||
\(734\) | −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 | −0.710228 | − | 0.703972i | \(-0.751408\pi\) |
0.964771 | + | 0.263090i | \(0.0847415\pi\) | |||||||
\(740\) | −7.00011 | −0.257329 | ||||||||
\(741\) | 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 | ||||
\(746\) | −15.3898 | − | 8.88530i | −0.563461 | − | 0.325314i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 11.7514i | − | 0.429675i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82952 | − | 3.16883i | 0.0667602 | − | 0.115632i | −0.830713 | − | 0.556701i | \(-0.812067\pi\) |
0.897473 | + | 0.441068i | \(0.145400\pi\) | |||||||
\(752\) | −15.0262 | −0.547948 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 69.8359i | − | 2.54327i | ||||||
\(755\) | −4.07921 | −0.148458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8901 | 0.504842 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(758\) | 14.2184i | 0.516435i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.83758 | −0.0666560 | ||||||||
\(761\) | 6.82083 | − | 11.8140i | 0.247255 | − | 0.428258i | −0.715508 | − | 0.698604i | \(-0.753805\pi\) |
0.962763 | + | 0.270346i | \(0.0871381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.4991i | 0.994884i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.0500 | + | 22.5455i | 1.41093 | + | 0.814602i | ||||
\(767\) | 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 | ||||||||
\(772\) | 22.9104 | 0.824562 | ||||||||
\(773\) | 13.1109 | − | 22.7087i | 0.471566 | − | 0.816776i | −0.527905 | − | 0.849303i | \(-0.677022\pi\) |
0.999471 | + | 0.0325274i | \(0.0103556\pi\) | |||||||
\(774\) | 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 | ||||
\(779\) | −25.0451 | − | 14.4598i | −0.897334 | − | 0.518076i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6678 | + | 21.9413i | 0.453291 | + | 0.785123i | ||||
\(782\) | 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 | ||||||||
\(787\) | 29.0470i | 1.03541i | 0.855558 | + | 0.517706i | \(0.173214\pi\) | ||||
−0.855558 | + | 0.517706i | \(0.826786\pi\) | |||||||
\(788\) | 25.3769i | 0.904014i | ||||||||
\(789\) | 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 | ||||
\(794\) | 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 | ||||
\(800\) | 26.0738 | − | 15.0537i | 0.921848 | − | 0.532229i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.4777 | − | 25.0762i | 0.511227 | − | 0.885470i | ||||
\(803\) | −62.7577 | −2.21467 | ||||||||
\(804\) | 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 | ||||
\(809\) | −34.5466 | − | 19.9455i | −1.21459 | − | 0.701245i | −0.250836 | − | 0.968029i | \(-0.580706\pi\) |
−0.963756 | + | 0.266784i | \(0.914039\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | 3.86521 | 0.135392 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.30317i | − | 0.255505i | ||||||
\(818\) | 9.92684 | 0.347084 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.4905 | −0.366344 | ||||||||
\(821\) | 0.414973i | 0.0144826i | 0.999974 | + | 0.00724132i | \(0.00230500\pi\) | ||||
−0.999974 | + | 0.00724132i | \(0.997695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0963 | −0.456508 | −0.228254 | − | 0.973602i | \(-0.573302\pi\) | ||||
−0.228254 | + | 0.973602i | \(0.573302\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | −29.0164 | − | 16.7526i | −1.00778 | − | 0.581842i | −0.0972388 | − | 0.995261i | \(-0.531001\pi\) |
−0.910541 | + | 0.413419i | \(0.864334\pi\) | |||||||
\(830\) | 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 | ||||||||
\(835\) | −0.901200 | −0.0311873 | ||||||||
\(836\) | 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 | ||||
\(842\) | 19.0182 | + | 10.9802i | 0.655412 | + | 0.378402i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.47260 | + | 9.47882i | 0.188375 | + | 0.326275i | ||||
\(845\) | −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 | ||||||||
\(850\) | − | 13.6853i | − | 0.469402i | ||||||
\(851\) | − | 11.7648i | − | 0.403291i | ||||||
\(852\) | 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 | ||||
\(857\) | 5.28926 | + | 9.16126i | 0.180678 | + | 0.312943i | 0.942111 | − | 0.335300i | \(-0.108838\pi\) |
−0.761434 | + | 0.648243i | \(0.775504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.2972 | + | 16.3374i | 0.965488 | + | 0.557425i | 0.897858 | − | 0.440286i | \(-0.145123\pi\) |
0.0676303 | + | 0.997710i | \(0.478456\pi\) | |||||||
\(860\) | −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 | \(-0.615786\pi\) |
0.631469 | + | 0.775401i | \(0.282452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.45643 | + | 4.25465i | −0.0835210 | + | 0.144663i | ||||
\(866\) | 11.1052 | 0.377372 | ||||||||
\(867\) | 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 | ||||
\(872\) | 6.42216 | + | 3.70783i | 0.217482 | + | 0.125563i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.50742i | 0.220117i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.619077 | + | 1.07227i | −0.0209048 | + | 0.0362081i | −0.876289 | − | 0.481787i | \(-0.839988\pi\) |
0.855384 | + | 0.517995i | \(0.173321\pi\) | |||||||
\(878\) | −49.7300 | −1.67831 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.7233i | 0.563744i | ||||||||
\(881\) | 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 | \(0.479059\pi\) | |||||||
\(884\) | 11.3346i | 0.381224i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.80432 | 0.329383 | ||||||||
\(887\) | 7.25578 | − | 12.5674i | 0.243625 | − | 0.421972i | −0.718119 | − | 0.695920i | \(-0.754997\pi\) |
0.961744 | + | 0.273949i | \(0.0883299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 5.11722i | − | 0.171530i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.4585 | − | 15.8532i | −0.919379 | − | 0.530804i | ||||
\(893\) | −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 | ||||||||
\(898\) | −62.7317 | −2.09339 | ||||||||
\(899\) | −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 | ||||
\(905\) | −6.68849 | − | 3.86160i | −0.222333 | − | 0.128364i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.60695 | + | 16.6397i | 0.318993 | + | 0.552513i | 0.980278 | − | 0.197622i | \(-0.0633219\pi\) |
−0.661285 | + | 0.750135i | \(0.729989\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 37.3837i | − | 1.23722i | ||||||
\(914\) | − | 29.0566i | − | 0.961106i | ||||||
\(915\) | 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 | −0.980743 | − | 0.195301i | \(-0.937432\pi\) |
0.321236 | − | 0.946999i | \(-0.395902\pi\) | |||||||
\(920\) | −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 | ||||
\(926\) | 19.1005 | − | 11.0277i | 0.627683 | − | 0.362393i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.4187 | − | 42.2944i | 0.801582 | − | 1.38838i | ||||
\(929\) | 12.7672 | 0.418877 | 0.209439 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209439 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | 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 | ||||||||
\(940\) | −1.34996 | + | 2.33819i | −0.0440307 | + | 0.0762634i | ||||
\(941\) | −25.0317 | −0.816011 | −0.408006 | − | 0.912979i | \(-0.633776\pi\) | ||||
−0.408006 | + | 0.912979i | \(0.633776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17.6309i | − | 0.574142i | ||||||
\(944\) | 14.4162 | 0.469208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.4663 | −0.958032 | ||||||||
\(947\) | − | 32.7555i | − | 1.06441i | −0.846615 | − | 0.532205i | \(-0.821363\pi\) | ||
0.846615 | − | 0.532205i | \(-0.178637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.5316 | 1.96494 | ||||||||
\(950\) | 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 | ||||||||
\(955\) | −11.3353 | − | 6.54443i | −0.366801 | − | 0.211773i | ||||
\(956\) | −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 | ||||||||
\(961\) | −1.11779 | −0.0360578 | ||||||||
\(962\) | 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 | \(0.600242\pi\) | |||||||
\(968\) | 17.6263 | + | 10.1765i | 0.566530 | + | 0.327086i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.82910 | + | 17.0245i | 0.315593 | + | 0.546624i | ||||
\(971\) | 20.6257 | + | 35.7248i | 0.661910 | + | 1.14646i | 0.980113 | + | 0.198439i | \(0.0635873\pi\) |
−0.318203 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.3281 | + | 25.0155i | 1.38832 | + | 0.801547i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51.6560i | 1.65347i | ||||||||
\(977\) | − | 4.57847i | − | 0.146478i | −0.997314 | − | 0.0732391i | \(-0.976666\pi\) | ||
0.997314 | − | 0.0732391i | \(-0.0233336\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 12.2401 | + | 21.2004i | 0.390397 | + | 0.676188i | 0.992502 | − | 0.122229i | \(-0.0390044\pi\) |
−0.602105 | + | 0.798417i | \(0.705671\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | 3.85589 | − | 2.22620i | 0.122610 | − | 0.0707890i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.0927 | − | 36.5337i | 0.670032 | − | 1.16053i | −0.307862 | − | 0.951431i | \(-0.599614\pi\) |
0.977894 | − | 0.209099i | \(-0.0670531\pi\) | |||||||
\(992\) | 37.2284 | 1.18200 | ||||||||
\(993\) | 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 | \(-0.617690\pi\) |
0.626818 | + | 0.779165i | \(0.284357\pi\) | |||||||
\(998\) | 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.i.d.521.15 | 48 | ||
3.2 | odd | 2 | 441.2.i.d.227.7 | 48 | |||
7.2 | even | 3 | 1323.2.s.d.656.17 | 48 | |||
7.3 | odd | 6 | 1323.2.o.e.440.8 | 48 | |||
7.4 | even | 3 | 1323.2.o.e.440.7 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.656.18 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.i.d.521.17 | 48 | ||
9.4 | even | 3 | 441.2.s.d.374.7 | 48 | |||
9.5 | odd | 6 | 1323.2.s.d.962.18 | 48 | |||
21.2 | odd | 6 | 441.2.s.d.362.8 | 48 | |||
21.5 | even | 6 | 441.2.s.d.362.7 | 48 | |||
21.11 | odd | 6 | 441.2.o.e.146.18 | yes | 48 | ||
21.17 | even | 6 | 441.2.o.e.146.17 | ✓ | 48 | ||
21.20 | even | 2 | 441.2.i.d.227.8 | 48 | |||
63.4 | even | 3 | 441.2.o.e.293.17 | yes | 48 | ||
63.5 | even | 6 | inner | 1323.2.i.d.1097.15 | 48 | ||
63.13 | odd | 6 | 441.2.s.d.374.8 | 48 | |||
63.23 | odd | 6 | inner | 1323.2.i.d.1097.17 | 48 | ||
63.31 | odd | 6 | 441.2.o.e.293.18 | yes | 48 | ||
63.32 | odd | 6 | 1323.2.o.e.881.8 | 48 | |||
63.40 | odd | 6 | 441.2.i.d.68.17 | 48 | |||
63.41 | even | 6 | 1323.2.s.d.962.17 | 48 | |||
63.58 | even | 3 | 441.2.i.d.68.18 | 48 | |||
63.59 | even | 6 | 1323.2.o.e.881.7 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.17 | 48 | 63.40 | odd | 6 | |||
441.2.i.d.68.18 | 48 | 63.58 | even | 3 | |||
441.2.i.d.227.7 | 48 | 3.2 | odd | 2 | |||
441.2.i.d.227.8 | 48 | 21.20 | even | 2 | |||
441.2.o.e.146.17 | ✓ | 48 | 21.17 | even | 6 | ||
441.2.o.e.146.18 | yes | 48 | 21.11 | odd | 6 | ||
441.2.o.e.293.17 | yes | 48 | 63.4 | even | 3 | ||
441.2.o.e.293.18 | yes | 48 | 63.31 | odd | 6 | ||
441.2.s.d.362.7 | 48 | 21.5 | even | 6 | |||
441.2.s.d.362.8 | 48 | 21.2 | odd | 6 | |||
441.2.s.d.374.7 | 48 | 9.4 | even | 3 | |||
441.2.s.d.374.8 | 48 | 63.13 | odd | 6 | |||
1323.2.i.d.521.15 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.i.d.521.17 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.i.d.1097.15 | 48 | 63.5 | even | 6 | inner | ||
1323.2.i.d.1097.17 | 48 | 63.23 | odd | 6 | inner | ||
1323.2.o.e.440.7 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.440.8 | 48 | 7.3 | odd | 6 | |||
1323.2.o.e.881.7 | 48 | 63.59 | even | 6 | |||
1323.2.o.e.881.8 | 48 | 63.32 | odd | 6 | |||
1323.2.s.d.656.17 | 48 | 7.2 | even | 3 | |||
1323.2.s.d.656.18 | 48 | 7.5 | odd | 6 | |||
1323.2.s.d.962.17 | 48 | 63.41 | even | 6 | |||
1323.2.s.d.962.18 | 48 | 9.5 | odd | 6 |