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 | 881.17 | ||
Character | \(\chi\) | \(=\) | 1323.881 |
Dual form | 1323.2.o.e.440.17 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.02035 | − | 0.589100i | 0.721498 | − | 0.416557i | −0.0938059 | − | 0.995591i | \(-0.529903\pi\) |
0.815304 | + | 0.579034i | \(0.196570\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.305921 | + | 0.529871i | −0.152961 | + | 0.264936i | ||||
\(5\) | −2.16601 | + | 3.75164i | −0.968670 | + | 1.67778i | −0.269254 | + | 0.963069i | \(0.586777\pi\) |
−0.699415 | + | 0.714716i | \(0.746556\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07728i | 1.08798i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.10399i | 1.61402i | ||||||||
\(11\) | 1.87238 | − | 1.08102i | 0.564545 | − | 0.325940i | −0.190423 | − | 0.981702i | \(-0.560986\pi\) |
0.754968 | + | 0.655762i | \(0.227653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.25256 | − | 1.30052i | −0.624748 | − | 0.360698i | 0.153967 | − | 0.988076i | \(-0.450795\pi\) |
−0.778715 | + | 0.627378i | \(0.784128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.20098 | + | 2.08016i | 0.300245 | + | 0.520040i | ||||
\(17\) | −1.17115 | −0.284046 | −0.142023 | − | 0.989863i | \(-0.545361\pi\) | ||||
−0.142023 | + | 0.989863i | \(0.545361\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41658i | 0.554402i | 0.960812 | + | 0.277201i | \(0.0894067\pi\) | ||||
−0.960812 | + | 0.277201i | \(0.910593\pi\) | |||||||
\(20\) | −1.32526 | − | 2.29541i | −0.296337 | − | 0.513270i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.27366 | − | 2.20604i | 0.271545 | − | 0.470330i | ||||
\(23\) | 3.16186 | + | 1.82550i | 0.659294 | + | 0.380644i | 0.792008 | − | 0.610511i | \(-0.209036\pi\) |
−0.132714 | + | 0.991154i | \(0.542369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.88321 | − | 11.9221i | −1.37664 | − | 2.38441i | ||||
\(26\) | −3.06454 | −0.601006 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.589262 | + | 0.340210i | −0.109423 | + | 0.0631755i | −0.553713 | − | 0.832708i | \(-0.686789\pi\) |
0.444290 | + | 0.895883i | \(0.353456\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.67723 | − | 3.27775i | −1.01966 | − | 0.588702i | −0.105655 | − | 0.994403i | \(-0.533694\pi\) |
−0.914006 | + | 0.405701i | \(0.867027\pi\) | |||||||
\(32\) | −2.87915 | − | 1.66228i | −0.508967 | − | 0.293852i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.19499 | + | 0.689926i | −0.204939 | + | 0.118321i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.10692 | −0.839572 | −0.419786 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419786 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(38\) | 1.42361 | + | 2.46576i | 0.230940 | + | 0.399999i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.5448 | − | 6.66541i | −1.82540 | − | 1.05389i | ||||
\(41\) | −3.68473 | + | 6.38214i | −0.575458 | + | 0.996723i | 0.420534 | + | 0.907277i | \(0.361843\pi\) |
−0.995992 | + | 0.0894458i | \(0.971490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12577 | − | 3.68194i | −0.324176 | − | 0.561490i | 0.657169 | − | 0.753743i | \(-0.271754\pi\) |
−0.981345 | + | 0.192253i | \(0.938420\pi\) | |||||||
\(44\) | 1.32283i | 0.199424i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.30162 | 0.634239 | ||||||||
\(47\) | 3.57157 | + | 6.18614i | 0.520967 | + | 0.902341i | 0.999703 | + | 0.0243819i | \(0.00776176\pi\) |
−0.478736 | + | 0.877959i | \(0.658905\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.0466 | − | 8.10980i | −1.98649 | − | 1.14690i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37821 | − | 0.795711i | 0.191124 | − | 0.110345i | ||||
\(53\) | − | 3.23289i | − | 0.444071i | −0.975039 | − | 0.222036i | \(-0.928730\pi\) | ||
0.975039 | − | 0.222036i | \(-0.0712702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.36601i | 1.26291i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.400836 | + | 0.694269i | −0.0526324 | + | 0.0911619i | ||||
\(59\) | 2.91810 | − | 5.05430i | 0.379905 | − | 0.658014i | −0.611143 | − | 0.791520i | \(-0.709290\pi\) |
0.991048 | + | 0.133506i | \(0.0426234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.21638 | + | 3.58903i | −0.795925 | + | 0.459528i | −0.842044 | − | 0.539408i | \(-0.818648\pi\) |
0.0461190 | + | 0.998936i | \(0.485315\pi\) | |||||||
\(62\) | −7.72370 | −0.980911 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.72092 | −1.09012 | ||||||||
\(65\) | 9.75814 | − | 5.63387i | 1.21035 | − | 0.698795i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.32682 | + | 5.76221i | −0.406435 | + | 0.703966i | −0.994487 | − | 0.104857i | \(-0.966562\pi\) |
0.588052 | + | 0.808823i | \(0.299895\pi\) | |||||||
\(68\) | 0.358281 | − | 0.620560i | 0.0434479 | − | 0.0752540i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.95976i | − | 0.232580i | −0.993215 | − | 0.116290i | \(-0.962900\pi\) | ||
0.993215 | − | 0.116290i | \(-0.0371003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.9069i | − | 1.39360i | −0.717266 | − | 0.696799i | \(-0.754607\pi\) | ||
0.717266 | − | 0.696799i | \(-0.245393\pi\) | |||||||
\(74\) | −5.21085 | + | 3.00849i | −0.605749 | + | 0.349729i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.28048 | − | 0.739283i | −0.146881 | − | 0.0848016i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.87702 | + | 8.44725i | 0.548708 | + | 0.950390i | 0.998363 | + | 0.0571879i | \(0.0182134\pi\) |
−0.449656 | + | 0.893202i | \(0.648453\pi\) | |||||||
\(80\) | −10.4054 | −1.16335 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.68270i | 0.958844i | ||||||||
\(83\) | 0.796736 | + | 1.37999i | 0.0874531 | + | 0.151473i | 0.906434 | − | 0.422348i | \(-0.138794\pi\) |
−0.818981 | + | 0.573821i | \(0.805461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.53673 | − | 4.39374i | 0.275147 | − | 0.476568i | ||||
\(86\) | −4.33806 | − | 2.50458i | −0.467785 | − | 0.270076i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.32660 | + | 5.76184i | 0.354617 | + | 0.614214i | ||||
\(89\) | −6.09921 | −0.646515 | −0.323258 | − | 0.946311i | \(-0.604778\pi\) | ||||
−0.323258 | + | 0.946311i | \(0.604778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.93456 | + | 1.11692i | −0.201692 | + | 0.116447i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.28851 | + | 4.20802i | 0.751753 | + | 0.434025i | ||||
\(95\) | −9.06614 | − | 5.23434i | −0.930166 | − | 0.537032i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.36387 | − | 1.36478i | 0.240014 | − | 0.138572i | −0.375169 | − | 0.926956i | \(-0.622415\pi\) |
0.615183 | + | 0.788384i | \(0.289082\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.42288 | 0.842288 | ||||||||
\(101\) | 7.99849 | + | 13.8538i | 0.795880 | + | 1.37850i | 0.922279 | + | 0.386524i | \(0.126324\pi\) |
−0.126400 | + | 0.991979i | \(0.540342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.61251 | + | 1.50834i | 0.257419 | + | 0.148621i | 0.623156 | − | 0.782097i | \(-0.285850\pi\) |
−0.365738 | + | 0.930718i | \(0.619183\pi\) | |||||||
\(104\) | 4.00205 | − | 6.93175i | 0.392433 | − | 0.679714i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.90450 | − | 3.29868i | −0.184981 | − | 0.320397i | ||||
\(107\) | 11.8484i | 1.14543i | 0.819754 | + | 0.572716i | \(0.194110\pi\) | ||||
−0.819754 | + | 0.572716i | \(0.805890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.16157 | 0.685954 | 0.342977 | − | 0.939344i | \(-0.388565\pi\) | ||||
0.342977 | + | 0.939344i | \(0.388565\pi\) | |||||||
\(110\) | 5.51752 | + | 9.55662i | 0.526075 | + | 0.911188i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.46102 | − | 1.42087i | −0.231514 | − | 0.133664i | 0.379756 | − | 0.925086i | \(-0.376008\pi\) |
−0.611270 | + | 0.791422i | \(0.709341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.6973 | + | 7.90812i | −1.27728 | + | 0.737436i | ||||
\(116\) | − | 0.416310i | − | 0.0386535i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.87623i | − | 0.633008i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.16279 | + | 5.47811i | −0.287526 | + | 0.498010i | ||||
\(122\) | −4.22859 | + | 7.32414i | −0.382839 | + | 0.663096i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.47357 | − | 2.00547i | 0.311936 | − | 0.180096i | ||||
\(125\) | 37.9763 | 3.39670 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5344 | 1.64466 | 0.822332 | − | 0.569009i | \(-0.192673\pi\) | ||||
0.822332 | + | 0.569009i | \(0.192673\pi\) | |||||||
\(128\) | −3.14011 | + | 1.81294i | −0.277549 | + | 0.160243i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.63783 | − | 11.4971i | 0.582176 | − | 1.00836i | ||||
\(131\) | 3.35221 | − | 5.80619i | 0.292884 | − | 0.507289i | −0.681607 | − | 0.731719i | \(-0.738718\pi\) |
0.974490 | + | 0.224429i | \(0.0720518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.83931i | 0.677214i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.60396i | − | 0.309037i | ||||||
\(137\) | −11.8181 | + | 6.82316i | −1.00969 | + | 0.582942i | −0.911099 | − | 0.412187i | \(-0.864765\pi\) |
−0.0985856 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.74126 | − | 4.46942i | −0.656605 | − | 0.379091i | 0.134377 | − | 0.990930i | \(-0.457097\pi\) |
−0.790982 | + | 0.611839i | \(0.790430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.15449 | − | 1.99964i | −0.0968830 | − | 0.167806i | ||||
\(143\) | −5.62354 | −0.470264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.94760i | − | 0.244785i | ||||||
\(146\) | −7.01436 | − | 12.1492i | −0.580513 | − | 1.00548i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.56231 | − | 2.70601i | 0.128421 | − | 0.222432i | ||||
\(149\) | 3.29003 | + | 1.89950i | 0.269530 | + | 0.155613i | 0.628674 | − | 0.777669i | \(-0.283598\pi\) |
−0.359144 | + | 0.933282i | \(0.616931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.91083 | + | 3.30965i | 0.155501 | + | 0.269336i | 0.933241 | − | 0.359250i | \(-0.116967\pi\) |
−0.777740 | + | 0.628586i | \(0.783634\pi\) | |||||||
\(152\) | −7.43648 | −0.603178 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5939 | − | 14.1993i | 1.97543 | − | 1.14051i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6081 | + | 10.7434i | 1.48509 | + | 0.857417i | 0.999856 | − | 0.0169675i | \(-0.00540117\pi\) |
0.485234 | + | 0.874384i | \(0.338735\pi\) | |||||||
\(158\) | 9.95256 | + | 5.74611i | 0.791783 | + | 0.457136i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.4725 | − | 7.20102i | 0.986041 | − | 0.569291i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5175 | 0.980447 | 0.490223 | − | 0.871597i | \(-0.336915\pi\) | ||||
0.490223 | + | 0.871597i | \(0.336915\pi\) | |||||||
\(164\) | −2.25448 | − | 3.90487i | −0.176045 | − | 0.304919i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.62590 | + | 0.938715i | 0.126194 | + | 0.0728584i | ||||
\(167\) | −7.70819 | + | 13.3510i | −0.596477 | + | 1.03313i | 0.396859 | + | 0.917880i | \(0.370100\pi\) |
−0.993337 | + | 0.115250i | \(0.963233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.11731 | − | 5.39935i | −0.239793 | − | 0.415334i | ||||
\(170\) | − | 5.97755i | − | 0.458457i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.60127 | 0.198345 | ||||||||
\(173\) | −4.30737 | − | 7.46059i | −0.327483 | − | 0.567218i | 0.654528 | − | 0.756037i | \(-0.272867\pi\) |
−0.982012 | + | 0.188820i | \(0.939534\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.49739 | + | 2.59657i | 0.339004 | + | 0.195724i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.22334 | + | 3.59305i | −0.466459 | + | 0.269310i | ||||
\(179\) | 19.1384i | 1.43047i | 0.698882 | + | 0.715237i | \(0.253681\pi\) | ||||
−0.698882 | + | 0.715237i | \(0.746319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.69817i | − | 0.572200i | −0.958200 | − | 0.286100i | \(-0.907641\pi\) | ||
0.958200 | − | 0.286100i | \(-0.0923590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.61758 | + | 9.72993i | −0.414133 | + | 0.717300i | ||||
\(185\) | 11.0616 | − | 19.1593i | 0.813268 | − | 1.40862i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.19285 | + | 1.26604i | −0.160357 | + | 0.0925820i | ||||
\(188\) | −4.37047 | −0.318750 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.3342 | −0.894817 | ||||||||
\(191\) | −16.1203 | + | 9.30704i | −1.16642 | + | 0.673433i | −0.952834 | − | 0.303491i | \(-0.901848\pi\) |
−0.213587 | + | 0.976924i | \(0.568515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.05721 | + | 15.6875i | −0.651952 | + | 1.12921i | 0.330696 | + | 0.943737i | \(0.392716\pi\) |
−0.982649 | + | 0.185477i | \(0.940617\pi\) | |||||||
\(194\) | 1.60799 | − | 2.78511i | 0.115447 | − | 0.199959i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5945i | 1.18231i | 0.806559 | + | 0.591154i | \(0.201328\pi\) | ||||
−0.806559 | + | 0.591154i | \(0.798672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.71887i | − | 0.192735i | −0.995346 | − | 0.0963677i | \(-0.969278\pi\) | ||
0.995346 | − | 0.0963677i | \(-0.0307225\pi\) | |||||||
\(200\) | 36.6875 | − | 21.1815i | 2.59420 | − | 1.49776i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.3225 | + | 9.42383i | 1.14845 | + | 0.663058i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9623 | − | 27.6476i | −1.11486 | − | 1.93099i | ||||
\(206\) | 3.55425 | 0.247636 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.24759i | − | 0.433192i | ||||||
\(209\) | 2.61237 | + | 4.52476i | 0.180702 | + | 0.312984i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9445 | + | 24.1526i | −0.959979 | + | 1.66273i | −0.237440 | + | 0.971402i | \(0.576308\pi\) |
−0.722539 | + | 0.691330i | \(0.757025\pi\) | |||||||
\(212\) | 1.71301 | + | 0.989010i | 0.117650 | + | 0.0679255i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.97992 | + | 12.0896i | 0.477138 | + | 0.826427i | ||||
\(215\) | 18.4177 | 1.25608 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.30732 | − | 4.21888i | 0.494914 | − | 0.285739i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.96278 | − | 2.86526i | −0.334590 | − | 0.193176i | ||||
\(221\) | 2.63809 | + | 1.52310i | 0.177457 | + | 0.102455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.64349 | + | 3.83562i | −0.444881 | + | 0.256852i | −0.705666 | − | 0.708545i | \(-0.749352\pi\) |
0.260785 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.34815 | −0.222715 | ||||||||
\(227\) | 1.16439 | + | 2.01677i | 0.0772829 | + | 0.133858i | 0.902077 | − | 0.431576i | \(-0.142042\pi\) |
−0.824794 | + | 0.565434i | \(0.808709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3653 | + | 5.98443i | 0.684961 | + | 0.395463i | 0.801722 | − | 0.597698i | \(-0.203918\pi\) |
−0.116760 | + | 0.993160i | \(0.537251\pi\) | |||||||
\(230\) | −9.31735 | + | 16.1381i | −0.614368 | + | 1.06412i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.04692 | − | 1.81332i | −0.0687337 | − | 0.119050i | ||||
\(233\) | 2.52779i | 0.165601i | 0.996566 | + | 0.0828007i | \(0.0263865\pi\) | ||||
−0.996566 | + | 0.0828007i | \(0.973614\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.9442 | −2.01858 | ||||||||
\(236\) | 1.78542 | + | 3.09244i | 0.116221 | + | 0.201301i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4587 | − | 10.0798i | −1.12931 | − | 0.652006i | −0.185546 | − | 0.982636i | \(-0.559405\pi\) |
−0.943761 | + | 0.330630i | \(0.892739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1254 | − | 10.4647i | 1.16756 | − | 0.674091i | 0.214455 | − | 0.976734i | \(-0.431202\pi\) |
0.953104 | + | 0.302643i | \(0.0978690\pi\) | |||||||
\(242\) | 7.45280i | 0.479084i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4.39184i | − | 0.281159i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.14280 | − | 5.44349i | 0.199972 | − | 0.346361i | ||||
\(248\) | 10.0865 | − | 17.4704i | 0.640496 | − | 1.10937i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 38.7492 | − | 22.3718i | 2.45071 | − | 1.41492i | ||||
\(251\) | −25.5747 | −1.61426 | −0.807130 | − | 0.590374i | \(-0.798980\pi\) | ||||
−0.807130 | + | 0.590374i | \(0.798980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.89363 | 0.496268 | ||||||||
\(254\) | 18.9116 | − | 10.9186i | 1.18662 | − | 0.685096i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.58491 | − | 11.4054i | 0.411557 | − | 0.712837i | ||||
\(257\) | 5.93725 | − | 10.2836i | 0.370355 | − | 0.641474i | −0.619265 | − | 0.785182i | \(-0.712569\pi\) |
0.989620 | + | 0.143708i | \(0.0459026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.89408i | 0.427553i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 7.89915i | − | 0.488011i | ||||||
\(263\) | −19.3705 | + | 11.1836i | −1.19444 | + | 0.689608i | −0.959309 | − | 0.282357i | \(-0.908884\pi\) |
−0.235127 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1286 | + | 7.00247i | 0.745056 | + | 0.430158i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.03549 | − | 3.52557i | −0.124337 | − | 0.215358i | ||||
\(269\) | 4.22669 | 0.257706 | 0.128853 | − | 0.991664i | \(-0.458870\pi\) | ||||
0.128853 | + | 0.991664i | \(0.458870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.3943i | − | 1.36036i | −0.733046 | − | 0.680179i | \(-0.761902\pi\) | ||
0.733046 | − | 0.680179i | \(-0.238098\pi\) | |||||||
\(272\) | −1.40653 | − | 2.43619i | −0.0852836 | − | 0.147715i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.03905 | + | 13.9240i | −0.485657 | + | 0.841183i | ||||
\(275\) | −25.7760 | − | 14.8818i | −1.55435 | − | 0.897405i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.69230 | − | 9.85935i | −0.342017 | − | 0.592391i | 0.642790 | − | 0.766042i | \(-0.277777\pi\) |
−0.984807 | + | 0.173651i | \(0.944443\pi\) | |||||||
\(278\) | −10.5317 | −0.631652 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.702700 | − | 0.405704i | 0.0419196 | − | 0.0242023i | −0.478894 | − | 0.877873i | \(-0.658962\pi\) |
0.520813 | + | 0.853671i | \(0.325629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8740 | − | 9.16486i | −0.943611 | − | 0.544794i | −0.0525206 | − | 0.998620i | \(-0.516726\pi\) |
−0.891090 | + | 0.453826i | \(0.850059\pi\) | |||||||
\(284\) | 1.03842 | + | 0.599532i | 0.0616188 | + | 0.0355757i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.73799 | + | 3.31283i | −0.339294 | + | 0.195892i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6284 | −0.919318 | ||||||||
\(290\) | −1.73643 | − | 3.00759i | −0.101967 | − | 0.176612i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.30913 | + | 3.64258i | 0.369214 | + | 0.213166i | ||||
\(293\) | 6.23639 | − | 10.8017i | 0.364334 | − | 0.631044i | −0.624335 | − | 0.781156i | \(-0.714630\pi\) |
0.988669 | + | 0.150112i | \(0.0479634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6413 | + | 21.8954i | 0.736004 | + | 1.27480i | ||||
\(296\) | − | 15.7154i | − | 0.913438i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.47599 | 0.259287 | ||||||||
\(299\) | −4.74819 | − | 8.22411i | −0.274595 | − | 0.475613i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.89943 | + | 2.25134i | 0.224387 | + | 0.129550i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.02688 | + | 2.90227i | −0.288311 | + | 0.166457i | ||||
\(305\) | − | 31.0955i | − | 1.78052i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.3241i | 1.21703i | 0.793543 | + | 0.608514i | \(0.208234\pi\) | ||||
−0.793543 | + | 0.608514i | \(0.791766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.7296 | − | 28.9765i | 0.950178 | − | 1.64576i | ||||
\(311\) | −3.92094 | + | 6.79126i | −0.222336 | + | 0.385097i | −0.955517 | − | 0.294936i | \(-0.904702\pi\) |
0.733181 | + | 0.680034i | \(0.238035\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.57593 | + | 4.95131i | −0.484740 | + | 0.279865i | −0.722390 | − | 0.691486i | \(-0.756956\pi\) |
0.237650 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(314\) | 25.3158 | 1.42865 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.96794 | −0.335723 | ||||||||
\(317\) | −20.8358 | + | 12.0296i | −1.17025 | + | 0.675647i | −0.953740 | − | 0.300632i | \(-0.902802\pi\) |
−0.216515 | + | 0.976279i | \(0.569469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.735549 | + | 1.27401i | −0.0411828 | + | 0.0713308i | ||||
\(320\) | 18.8896 | − | 32.7178i | 1.05596 | − | 1.82898i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.83018i | − | 0.157476i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35.8069i | 1.98621i | ||||||||
\(326\) | 12.7723 | − | 7.37407i | 0.707390 | − | 0.408412i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.6396 | − | 11.3389i | −1.08442 | − | 0.626088i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.53686 | + | 7.85807i | 0.249368 | + | 0.431918i | 0.963351 | − | 0.268245i | \(-0.0864437\pi\) |
−0.713982 | + | 0.700164i | \(0.753110\pi\) | |||||||
\(332\) | −0.974954 | −0.0535075 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.1636i | 0.993867i | ||||||||
\(335\) | −14.4118 | − | 24.9620i | −0.787403 | − | 1.36382i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.02012 | − | 6.96304i | 0.218990 | − | 0.379301i | −0.735510 | − | 0.677514i | \(-0.763057\pi\) |
0.954499 | + | 0.298213i | \(0.0963906\pi\) | |||||||
\(338\) | −6.36152 | − | 3.67282i | −0.346021 | − | 0.199775i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.55208 | + | 2.68828i | 0.0841733 | + | 0.145792i | ||||
\(341\) | −14.1733 | −0.767525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.3303 | − | 6.54157i | 0.610891 | − | 0.352698i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.79007 | − | 5.07495i | −0.472557 | − | 0.272831i | ||||
\(347\) | 30.6345 | + | 17.6868i | 1.64454 | + | 0.949478i | 0.979189 | + | 0.202952i | \(0.0650536\pi\) |
0.665356 | + | 0.746526i | \(0.268280\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.1868 | + | 12.2322i | −1.13411 | + | 0.654776i | −0.944964 | − | 0.327174i | \(-0.893904\pi\) |
−0.189141 | + | 0.981950i | \(0.560570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.18783 | −0.383112 | ||||||||
\(353\) | −0.485949 | − | 0.841688i | −0.0258644 | − | 0.0447985i | 0.852803 | − | 0.522232i | \(-0.174900\pi\) |
−0.878668 | + | 0.477433i | \(0.841567\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.35231 | + | 4.24486i | 0.390220 | + | 0.225294i | ||||
\(356\) | 1.86588 | − | 3.23180i | 0.0988914 | − | 0.171285i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2745 | + | 19.5279i | 0.595874 | + | 1.03208i | ||||
\(359\) | − | 15.9210i | − | 0.840276i | −0.907460 | − | 0.420138i | \(-0.861982\pi\) | ||
0.907460 | − | 0.420138i | \(-0.138018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1601 | 0.692639 | ||||||||
\(362\) | −4.53499 | − | 7.85484i | −0.238354 | − | 0.412841i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.6704 | + | 25.7905i | 2.33816 | + | 1.34994i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3983 | − | 12.3543i | 1.11698 | − | 0.644891i | 0.176355 | − | 0.984327i | \(-0.443569\pi\) |
0.940629 | + | 0.339435i | \(0.110236\pi\) | |||||||
\(368\) | 8.76958i | 0.457146i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 26.0657i | − | 1.35509i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.71810 | − | 8.17200i | 0.244294 | − | 0.423130i | −0.717639 | − | 0.696416i | \(-0.754777\pi\) |
0.961933 | + | 0.273286i | \(0.0881104\pi\) | |||||||
\(374\) | −1.49165 | + | 2.58361i | −0.0771314 | + | 0.133595i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.0364 | + | 10.9907i | −0.981730 | + | 0.566802i | ||||
\(377\) | 1.76980 | 0.0911492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8031 | 1.06858 | 0.534292 | − | 0.845300i | \(-0.320578\pi\) | ||||
0.534292 | + | 0.845300i | \(0.320578\pi\) | |||||||
\(380\) | 5.54705 | − | 3.20259i | 0.284558 | − | 0.164289i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.9656 | + | 18.9929i | −0.561047 | + | 0.971761i | ||||
\(383\) | −3.23008 | + | 5.59467i | −0.165050 | + | 0.285874i | −0.936673 | − | 0.350205i | \(-0.886112\pi\) |
0.771623 | + | 0.636080i | \(0.219445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.3424i | 1.08630i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.67006i | 0.0847845i | ||||||||
\(389\) | 0.0445846 | − | 0.0257409i | 0.00226053 | − | 0.00130512i | −0.498869 | − | 0.866677i | \(-0.666251\pi\) |
0.501130 | + | 0.865372i | \(0.332918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.70303 | − | 2.13794i | −0.187270 | − | 0.108120i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.77582 | + | 16.9322i | 0.492499 | + | 0.853033i | ||||
\(395\) | −42.2547 | −2.12607 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7131i | 0.638052i | 0.947746 | + | 0.319026i | \(0.103356\pi\) | ||||
−0.947746 | + | 0.319026i | \(0.896644\pi\) | |||||||
\(398\) | −1.60169 | − | 2.77420i | −0.0802853 | − | 0.139058i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.5332 | − | 28.6364i | 0.826660 | − | 1.43182i | ||||
\(401\) | 2.19725 | + | 1.26858i | 0.109725 | + | 0.0633500i | 0.553858 | − | 0.832611i | \(-0.313155\pi\) |
−0.444133 | + | 0.895961i | \(0.646488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.52554 | + | 14.7667i | 0.424687 | + | 0.735580i | ||||
\(404\) | −9.78764 | −0.486953 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.56210 | + | 5.52068i | −0.473976 | + | 0.273650i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0495655 | + | 0.0286167i | 0.00245086 | + | 0.00141500i | 0.501225 | − | 0.865317i | \(-0.332883\pi\) |
−0.498774 | + | 0.866732i | \(0.666216\pi\) | |||||||
\(410\) | −32.5744 | − | 18.8068i | −1.60873 | − | 0.928803i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.59845 | + | 0.922864i | −0.0787499 | + | 0.0454663i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.90295 | −0.338853 | ||||||||
\(416\) | 4.32364 | + | 7.48876i | 0.211984 | + | 0.367167i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.33108 | + | 3.07790i | 0.260752 | + | 0.150545i | ||||
\(419\) | 3.08007 | − | 5.33484i | 0.150471 | − | 0.260624i | −0.780930 | − | 0.624619i | \(-0.785254\pi\) |
0.931401 | + | 0.363995i | \(0.118588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0693 | + | 26.1007i | 0.734431 | + | 1.27207i | 0.954973 | + | 0.296694i | \(0.0958842\pi\) |
−0.220542 | + | 0.975378i | \(0.570783\pi\) | |||||||
\(422\) | 32.8588i | 1.59954i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.94849 | 0.483141 | ||||||||
\(425\) | 8.06128 | + | 13.9626i | 0.391030 | + | 0.677283i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.27815 | − | 3.62469i | −0.303466 | − | 0.175206i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.7926 | − | 10.8499i | 0.906258 | − | 0.523228i | ||||
\(431\) | − | 8.07140i | − | 0.388785i | −0.980924 | − | 0.194393i | \(-0.937726\pi\) | ||
0.980924 | − | 0.194393i | \(-0.0622736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4938i | 1.36933i | 0.728860 | + | 0.684663i | \(0.240051\pi\) | ||||
−0.728860 | + | 0.684663i | \(0.759949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19088 | + | 3.79471i | −0.104924 | + | 0.181734i | ||||
\(437\) | −4.41147 | + | 7.64090i | −0.211029 | + | 0.365514i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.77067 | + | 1.02230i | −0.0845096 | + | 0.0487916i | −0.541659 | − | 0.840598i | \(-0.682204\pi\) |
0.457150 | + | 0.889390i | \(0.348870\pi\) | |||||||
\(440\) | −28.8218 | −1.37402 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.58904 | 0.170713 | ||||||||
\(443\) | 21.1324 | − | 12.2008i | 1.00403 | − | 0.579677i | 0.0945924 | − | 0.995516i | \(-0.469845\pi\) |
0.909438 | + | 0.415839i | \(0.136512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.2110 | − | 22.8821i | 0.626260 | − | 1.08471i | ||||
\(446\) | −4.51913 | + | 7.82737i | −0.213987 | + | 0.370637i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.293539i | − | 0.0138529i | −0.999976 | − | 0.00692647i | \(-0.997795\pi\) | ||
0.999976 | − | 0.00692647i | \(-0.00220478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.9331i | 0.750259i | ||||||||
\(452\) | 1.50576 | − | 0.869351i | 0.0708250 | − | 0.0408908i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.37616 | + | 1.37188i | 0.111519 | + | 0.0643855i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.27470 | − | 14.3322i | −0.387074 | − | 0.670432i | 0.604981 | − | 0.796240i | \(-0.293181\pi\) |
−0.992055 | + | 0.125808i | \(0.959848\pi\) | |||||||
\(458\) | 14.1017 | 0.658931 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 9.67705i | − | 0.451195i | ||||||
\(461\) | 10.0560 | + | 17.4175i | 0.468354 | + | 0.811213i | 0.999346 | − | 0.0361638i | \(-0.0115138\pi\) |
−0.530992 | + | 0.847377i | \(0.678180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.34602 | − | 16.1878i | 0.434346 | − | 0.752310i | −0.562896 | − | 0.826528i | \(-0.690313\pi\) |
0.997242 | + | 0.0742181i | \(0.0236461\pi\) | |||||||
\(464\) | −1.41538 | − | 0.817173i | −0.0657076 | − | 0.0379363i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.48912 | + | 2.57924i | 0.0689824 | + | 0.119481i | ||||
\(467\) | 29.3605 | 1.35864 | 0.679322 | − | 0.733841i | \(-0.262274\pi\) | ||||
0.679322 | + | 0.733841i | \(0.262274\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −31.5740 | + | 18.2293i | −1.45640 | + | 0.840853i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.5535 | + | 8.97981i | 0.715907 | + | 0.413329i | ||||
\(473\) | −7.96050 | − | 4.59599i | −0.366024 | − | 0.211324i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8106 | − | 16.6338i | 1.32192 | − | 0.763212i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.7520 | −1.08639 | ||||||||
\(479\) | 10.9660 | + | 18.9938i | 0.501051 | + | 0.867847i | 0.999999 | + | 0.00121455i | \(0.000386605\pi\) |
−0.498948 | + | 0.866632i | \(0.666280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5036 | + | 6.64163i | 0.524521 | + | 0.302832i | ||||
\(482\) | 12.3295 | − | 21.3554i | 0.561594 | − | 0.972710i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.93513 | − | 3.35174i | −0.0879604 | − | 0.152352i | ||||
\(485\) | 11.8245i | 0.536923i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.07779 | 0.0488394 | 0.0244197 | − | 0.999702i | \(-0.492226\pi\) | ||||
0.0244197 | + | 0.999702i | \(0.492226\pi\) | |||||||
\(488\) | −11.0444 | − | 19.1295i | −0.499957 | − | 0.865952i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3708 | − | 9.45168i | −0.738804 | − | 0.426549i | 0.0828305 | − | 0.996564i | \(-0.473604\pi\) |
−0.821634 | + | 0.570015i | \(0.806937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.690115 | − | 0.398438i | 0.0310812 | − | 0.0179448i | ||||
\(494\) | − | 7.40570i | − | 0.333198i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 15.7461i | − | 0.707020i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.34290 | − | 14.4503i | 0.373479 | − | 0.646885i | −0.616619 | − | 0.787262i | \(-0.711498\pi\) |
0.990098 | + | 0.140377i | \(0.0448314\pi\) | |||||||
\(500\) | −11.6178 | + | 20.1225i | −0.519562 | + | 0.899908i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.0952 | + | 15.0661i | −1.16468 | + | 0.672431i | ||||
\(503\) | 21.2386 | 0.946981 | 0.473491 | − | 0.880799i | \(-0.342994\pi\) | ||||
0.473491 | + | 0.880799i | \(0.342994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.2993 | −3.08378 | ||||||||
\(506\) | 8.05428 | − | 4.65014i | 0.358056 | − | 0.206724i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.67007 | + | 9.82085i | −0.251569 | + | 0.435730i | ||||
\(509\) | −5.72252 | + | 9.91170i | −0.253646 | + | 0.439328i | −0.964527 | − | 0.263984i | \(-0.914963\pi\) |
0.710881 | + | 0.703313i | \(0.248297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.7685i | − | 1.00623i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 13.9905i | − | 0.617096i | ||||||
\(515\) | −11.3175 | + | 6.53414i | −0.498707 | + | 0.287929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3747 | + | 7.72188i | 0.588218 | + | 0.339608i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.3370 | + | 30.0285i | 0.760276 | + | 1.31684i | ||||
\(521\) | 20.7998 | 0.911254 | 0.455627 | − | 0.890171i | \(-0.349415\pi\) | ||||
0.455627 | + | 0.890171i | \(0.349415\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.9338i | − | 0.653009i | −0.945196 | − | 0.326505i | \(-0.894129\pi\) | ||
0.945196 | − | 0.326505i | \(-0.105871\pi\) | |||||||
\(524\) | 2.05102 | + | 3.55248i | 0.0895994 | + | 0.155191i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1765 | + | 22.8223i | −0.574522 | + | 0.995101i | ||||
\(527\) | 6.64890 | + | 3.83875i | 0.289631 | + | 0.167218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.83508 | − | 8.37460i | −0.210221 | − | 0.364113i | ||||
\(530\) | 16.5006 | 0.716742 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.6002 | − | 9.58410i | 0.719033 | − | 0.415134i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.4511 | − | 25.6639i | −1.92179 | − | 1.10955i | ||||
\(536\) | −17.7319 | − | 10.2375i | −0.765902 | − | 0.442194i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.31272 | − | 2.48995i | 0.185934 | − | 0.107349i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1677 | 1.34000 | 0.670002 | − | 0.742360i | \(-0.266293\pi\) | ||||
0.670002 | + | 0.742360i | \(0.266293\pi\) | |||||||
\(542\) | −13.1925 | − | 22.8501i | −0.566667 | − | 0.981496i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.37192 | + | 1.94678i | 0.144570 | + | 0.0834675i | ||||
\(545\) | −15.5120 | + | 26.8676i | −0.664462 | + | 1.15088i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7410 | − | 27.2642i | −0.673035 | − | 1.16573i | −0.977039 | − | 0.213061i | \(-0.931657\pi\) |
0.304004 | − | 0.952671i | \(-0.401677\pi\) | |||||||
\(548\) | − | 8.34940i | − | 0.356669i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −35.0674 | −1.49528 | ||||||||
\(551\) | −0.822146 | − | 1.42400i | −0.0350246 | − | 0.0606644i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.6163 | − | 6.70667i | −0.493529 | − | 0.284939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.73643 | − | 2.73458i | 0.200870 | − | 0.115972i | ||||
\(557\) | 27.2389i | 1.15415i | 0.816692 | + | 0.577074i | \(0.195806\pi\) | ||||
−0.816692 | + | 0.577074i | \(0.804194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0584i | 0.467720i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.478001 | − | 0.827922i | 0.0201633 | − | 0.0349238i | ||||
\(563\) | 14.1871 | − | 24.5728i | 0.597916 | − | 1.03562i | −0.395212 | − | 0.918590i | \(-0.629329\pi\) |
0.993128 | − | 0.117031i | \(-0.0373377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.6612 | − | 6.15525i | 0.448521 | − | 0.258953i | ||||
\(566\) | −21.5961 | −0.907751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.03071 | 0.253043 | ||||||||
\(569\) | −29.4616 | + | 17.0097i | −1.23509 | + | 0.713082i | −0.968087 | − | 0.250613i | \(-0.919368\pi\) |
−0.267007 | + | 0.963695i | \(0.586035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.3455 | − | 38.7035i | 0.935130 | − | 1.61969i | 0.160727 | − | 0.986999i | \(-0.448616\pi\) |
0.774402 | − | 0.632693i | \(-0.218051\pi\) | |||||||
\(572\) | 1.72036 | − | 2.97975i | 0.0719319 | − | 0.124590i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 50.2613i | − | 2.09604i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.34738i | 0.305875i | 0.988236 | + | 0.152938i | \(0.0488734\pi\) | ||||
−0.988236 | + | 0.152938i | \(0.951127\pi\) | |||||||
\(578\) | −15.9465 | + | 9.20670i | −0.663286 | + | 0.382948i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.56185 | + | 0.901733i | 0.0648522 | + | 0.0374424i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.49482 | − | 6.05320i | −0.144741 | − | 0.250698i | ||||
\(584\) | 36.6408 | 1.51621 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 14.6954i | − | 0.607063i | ||||||
\(587\) | 13.1328 | + | 22.7466i | 0.542048 | + | 0.938855i | 0.998786 | + | 0.0492535i | \(0.0156842\pi\) |
−0.456738 | + | 0.889601i | \(0.650982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.92095 | − | 13.7195i | 0.326377 | − | 0.565302i | ||||
\(590\) | 25.7971 | + | 14.8940i | 1.06205 | + | 0.613175i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.13331 | − | 10.6232i | −0.252078 | − | 0.436611i | ||||
\(593\) | 9.12418 | 0.374685 | 0.187343 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187343 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.01298 | + | 1.16220i | −0.0824550 | + | 0.0476054i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.68966 | − | 5.59433i | −0.396240 | − | 0.228769i | ||||
\(599\) | 20.0987 | + | 11.6040i | 0.821210 | + | 0.474126i | 0.850834 | − | 0.525435i | \(-0.176097\pi\) |
−0.0296234 | + | 0.999561i | \(0.509431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0021 | + | 10.9709i | −0.775111 | + | 0.447510i | −0.834695 | − | 0.550713i | \(-0.814356\pi\) |
0.0595840 | + | 0.998223i | \(0.481023\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.33825 | −0.0951421 | ||||||||
\(605\) | −13.7013 | − | 23.7313i | −0.557036 | − | 0.964815i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.6289 | − | 22.3024i | −1.56790 | − | 0.905226i | −0.996414 | − | 0.0846136i | \(-0.973034\pi\) |
−0.571484 | − | 0.820613i | \(-0.693632\pi\) | |||||||
\(608\) | 4.01703 | − | 6.95770i | 0.162912 | − | 0.282172i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.3184 | − | 31.7283i | −0.741689 | − | 1.28464i | ||||
\(611\) | − | 18.5795i | − | 0.751647i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6560 | 0.470780 | 0.235390 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235390 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(614\) | 12.5620 | + | 21.7580i | 0.506961 | + | 0.878083i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.6143 | − | 21.1393i | −1.47403 | − | 0.851034i | −0.474462 | − | 0.880276i | \(-0.657357\pi\) |
−0.999572 | + | 0.0292416i | \(0.990691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.0633 | + | 17.3571i | −1.20835 | + | 0.697640i | −0.962398 | − | 0.271643i | \(-0.912433\pi\) |
−0.245949 | + | 0.969283i | \(0.579100\pi\) | |||||||
\(620\) | 17.3755i | 0.697815i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.23930i | 0.370462i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −47.8410 | + | 82.8631i | −1.91364 | + | 3.31452i | ||||
\(626\) | −5.83364 | + | 10.1042i | −0.233159 | + | 0.403844i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.3852 | + | 6.57327i | −0.454321 | + | 0.262302i | ||||
\(629\) | 5.98098 | 0.238477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8860 | −0.512982 | −0.256491 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256491 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(632\) | −25.9945 | + | 15.0079i | −1.03401 | + | 0.596984i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.1732 | + | 24.5488i | −0.562891 | + | 0.974956i | ||||
\(635\) | −40.1457 | + | 69.5345i | −1.59314 | + | 2.75939i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.73325i | 0.0686200i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 15.7074i | − | 0.620890i | ||||||
\(641\) | 16.5666 | − | 9.56474i | 0.654342 | − | 0.377785i | −0.135776 | − | 0.990740i | \(-0.543353\pi\) |
0.790118 | + | 0.612955i | \(0.210019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.77521 | − | 5.64372i | −0.385497 | − | 0.222567i | 0.294710 | − | 0.955587i | \(-0.404777\pi\) |
−0.680207 | + | 0.733020i | \(0.738110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66726 | − | 2.88778i | −0.0655976 | − | 0.113618i | ||||
\(647\) | 5.08677 | 0.199982 | 0.0999909 | − | 0.994988i | \(-0.468119\pi\) | ||||
0.0999909 | + | 0.994988i | \(0.468119\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.6181i | − | 0.495305i | ||||||
\(650\) | 21.0939 | + | 36.5356i | 0.827369 | + | 1.43305i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.82937 | + | 6.63267i | −0.149970 | + | 0.259755i | ||||
\(653\) | 32.9044 | + | 18.9974i | 1.28765 | + | 0.743424i | 0.978234 | − | 0.207503i | \(-0.0665338\pi\) |
0.309414 | + | 0.950927i | \(0.399867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5218 | + | 25.1526i | 0.567415 | + | 0.982792i | ||||
\(656\) | −17.7012 | −0.691115 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.97949 | + | 5.76166i | −0.388746 | + | 0.224442i | −0.681617 | − | 0.731710i | \(-0.738723\pi\) |
0.292871 | + | 0.956152i | \(0.405389\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0928 | + | 21.9929i | 1.48164 | + | 0.855424i | 0.999783 | − | 0.0208274i | \(-0.00663005\pi\) |
0.481854 | + | 0.876251i | \(0.339963\pi\) | |||||||
\(662\) | 9.25838 | + | 5.34533i | 0.359837 | + | 0.207752i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.24660 | + | 2.45178i | −0.164800 | + | 0.0951473i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.48422 | −0.0961894 | ||||||||
\(668\) | −4.71620 | − | 8.16869i | −0.182475 | − | 0.316056i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.4103 | − | 16.9800i | −1.13622 | − | 0.655996i | ||||
\(671\) | −7.75962 | + | 13.4401i | −0.299557 | + | 0.518848i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.9316 | − | 37.9866i | −0.845400 | − | 1.46428i | −0.885273 | − | 0.465071i | \(-0.846029\pi\) |
0.0398735 | − | 0.999205i | \(-0.487305\pi\) | |||||||
\(674\) | − | 9.47301i | − | 0.364887i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.81461 | 0.146716 | ||||||||
\(677\) | 0.738999 | + | 1.27998i | 0.0284020 | + | 0.0491938i | 0.879877 | − | 0.475201i | \(-0.157625\pi\) |
−0.851475 | + | 0.524395i | \(0.824291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.5208 | + | 7.80621i | 0.518497 | + | 0.299355i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.4617 | + | 8.34948i | −0.553768 | + | 0.319718i | ||||
\(683\) | − | 10.3259i | − | 0.395111i | −0.980292 | − | 0.197555i | \(-0.936700\pi\) | ||
0.980292 | − | 0.197555i | \(-0.0633002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 59.1162i | − | 2.25871i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.10601 | − | 8.84388i | 0.194665 | − | 0.337170i | ||||
\(689\) | −4.20442 | + | 7.28228i | −0.160176 | + | 0.277433i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.58166 | + | 3.79992i | −0.250378 | + | 0.144556i | −0.619937 | − | 0.784651i | \(-0.712842\pi\) |
0.369559 | + | 0.929207i | \(0.379509\pi\) | |||||||
\(692\) | 5.27087 | 0.200368 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.6773 | 1.58205 | ||||||||
\(695\) | 33.5353 | − | 19.3616i | 1.27207 | − | 0.734428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31538 | − | 7.47446i | 0.163457 | − | 0.283115i | ||||
\(698\) | −14.4120 | + | 24.9624i | −0.545503 | + | 0.944839i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.35907i | 0.240179i | 0.992763 | + | 0.120089i | \(0.0383181\pi\) | ||||
−0.992763 | + | 0.120089i | \(0.961682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.3413i | − | 0.465460i | ||||||
\(704\) | −16.3289 | + | 9.42749i | −0.615419 | + | 0.355312i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.991677 | − | 0.572545i | −0.0373223 | − | 0.0215480i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8048 | + | 41.2311i | 0.894007 | + | 1.54847i | 0.835029 | + | 0.550206i | \(0.185451\pi\) |
0.0589776 | + | 0.998259i | \(0.481216\pi\) | |||||||
\(710\) | 10.0026 | 0.375390 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 18.7690i | − | 0.703396i | ||||||
\(713\) | −11.9671 | − | 20.7276i | −0.448171 | − | 0.776255i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1806 | − | 21.0975i | 0.455530 | − | 0.789002i | ||||
\(716\) | −10.1409 | − | 5.85486i | −0.378983 | − | 0.218806i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.37904 | − | 16.2450i | −0.350023 | − | 0.606257i | ||||
\(719\) | −14.1470 | −0.527594 | −0.263797 | − | 0.964578i | \(-0.584975\pi\) | ||||
−0.263797 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.4280 | − | 7.75264i | 0.499737 | − | 0.288524i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.07904 | + | 2.35503i | 0.151596 | + | 0.0875241i | ||||
\(725\) | 8.11202 | + | 4.68348i | 0.301273 | + | 0.173940i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.1828 | − | 23.1996i | 1.49030 | − | 0.860424i | 0.490360 | − | 0.871520i | \(-0.336865\pi\) |
0.999938 | + | 0.0110955i | \(0.00353187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 60.7728 | 2.24930 | ||||||||
\(731\) | 2.48960 | + | 4.31211i | 0.0920811 | + | 0.159489i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8893 | + | 13.2151i | 0.845436 | + | 0.488112i | 0.859108 | − | 0.511794i | \(-0.171019\pi\) |
−0.0136726 | + | 0.999907i | \(0.504352\pi\) | |||||||
\(734\) | 14.5559 | − | 25.2115i | 0.537268 | − | 0.930575i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.06899 | − | 10.5118i | −0.223706 | − | 0.387470i | ||||
\(737\) | 14.3854i | 0.529894i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.2670 | −1.70196 | −0.850979 | − | 0.525200i | \(-0.823991\pi\) | ||||
−0.850979 | + | 0.525200i | \(0.823991\pi\) | |||||||
\(740\) | 6.76798 | + | 11.7225i | 0.248796 | + | 0.430927i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.5640 | + | 21.1102i | 1.34140 | + | 0.774458i | 0.987013 | − | 0.160640i | \(-0.0513558\pi\) |
0.354388 | + | 0.935098i | \(0.384689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2525 | + | 8.22868i | −0.522171 | + | 0.301476i | ||||
\(746\) | − | 11.1177i | − | 0.407050i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.54923i | − | 0.0566456i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.02320 | − | 13.8966i | 0.292771 | − | 0.507094i | −0.681693 | − | 0.731638i | \(-0.738756\pi\) |
0.974464 | + | 0.224544i | \(0.0720894\pi\) | |||||||
\(752\) | −8.57877 | + | 14.8589i | −0.312836 | + | 0.541847i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.80582 | − | 1.04259i | 0.0657639 | − | 0.0379688i | ||||
\(755\) | −16.5555 | −0.602516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0149 | 0.909183 | 0.454591 | − | 0.890700i | \(-0.349785\pi\) | ||||
0.454591 | + | 0.890700i | \(0.349785\pi\) | |||||||
\(758\) | 21.2265 | − | 12.2551i | 0.770981 | − | 0.445126i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.1075 | − | 27.8990i | 0.584281 | − | 1.01200i | ||||
\(761\) | −3.00365 | + | 5.20247i | −0.108882 | + | 0.188589i | −0.915318 | − | 0.402733i | \(-0.868060\pi\) |
0.806436 | + | 0.591322i | \(0.201394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 11.3889i | − | 0.412035i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.61138i | 0.275010i | ||||||||
\(767\) | −13.1464 | + | 7.59008i | −0.474689 | + | 0.274062i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9946 | + | 16.7400i | 1.04557 | + | 0.603661i | 0.921406 | − | 0.388600i | \(-0.127041\pi\) |
0.124166 | + | 0.992262i | \(0.460375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.54159 | − | 9.59831i | −0.199446 | − | 0.345451i | ||||
\(773\) | −36.2016 | −1.30208 | −0.651040 | − | 0.759043i | \(-0.725667\pi\) | ||||
−0.651040 | + | 0.759043i | \(0.725667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90.2458i | 3.24172i | ||||||||
\(776\) | 4.19980 | + | 7.27427i | 0.150764 | + | 0.261131i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0303280 | − | 0.0525296i | 0.00108731 | − | 0.00188328i | ||||
\(779\) | −15.4230 | − | 8.90445i | −0.552585 | − | 0.319035i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.11854 | − | 3.66942i | −0.0758073 | − | 0.131302i | ||||
\(782\) | −5.03785 | −0.180153 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −80.6108 | + | 46.5407i | −2.87712 | + | 1.66111i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1930 | + | 8.19433i | 0.505926 | + | 0.292096i | 0.731157 | − | 0.682209i | \(-0.238981\pi\) |
−0.225232 | + | 0.974305i | \(0.572314\pi\) | |||||||
\(788\) | −8.79294 | − | 5.07661i | −0.313236 | − | 0.180847i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −43.1147 | + | 24.8923i | −1.53395 | + | 0.885628i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.6703 | 0.663004 | ||||||||
\(794\) | 7.48929 | + | 12.9718i | 0.265785 | + | 0.460353i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.44065 | + | 0.831760i | 0.0510625 | + | 0.0294809i | ||||
\(797\) | 23.3328 | − | 40.4137i | 0.826492 | − | 1.43153i | −0.0742821 | − | 0.997237i | \(-0.523667\pi\) |
0.900774 | − | 0.434288i | \(-0.143000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.18285 | − | 7.24491i | −0.147979 | − | 0.256306i | ||||
\(800\) | 45.7672i | 1.61811i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.98929 | 0.105555 | ||||||||
\(803\) | −12.8716 | − | 22.2943i | −0.454229 | − | 0.786748i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.3981 | + | 10.0448i | 0.612822 | + | 0.353813i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −42.6319 | + | 24.6136i | −1.49979 | + | 0.865902i | ||||
\(809\) | − | 29.8980i | − | 1.05116i | −0.850744 | − | 0.525580i | \(-0.823849\pi\) | ||
0.850744 | − | 0.525580i | \(-0.176151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.3404i | − | 0.889821i | −0.895575 | − | 0.444911i | \(-0.853235\pi\) | ||
0.895575 | − | 0.444911i | \(-0.146765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.50447 | + | 11.2661i | −0.227982 | + | 0.394876i | ||||
\(815\) | −27.1131 | + | 46.9612i | −0.949729 | + | 1.64498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.89769 | − | 5.13709i | 0.311291 | − | 0.179724i | ||||
\(818\) | 0.0674323 | 0.00235772 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5329 | 0.682117 | ||||||||
\(821\) | −9.23012 | + | 5.32901i | −0.322133 | + | 0.185984i | −0.652343 | − | 0.757924i | \(-0.726214\pi\) |
0.330210 | + | 0.943908i | \(0.392881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.55239 | + | 14.8132i | −0.298118 | + | 0.516355i | −0.975705 | − | 0.219087i | \(-0.929692\pi\) |
0.677588 | + | 0.735442i | \(0.263025\pi\) | |||||||
\(824\) | −4.64156 | + | 8.03943i | −0.161697 | + | 0.280067i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.3221i | − | 0.637121i | −0.947903 | − | 0.318560i | \(-0.896801\pi\) | ||
0.947903 | − | 0.318560i | \(-0.103199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.73341i | 0.268592i | 0.990941 | + | 0.134296i | \(0.0428774\pi\) | ||||
−0.990941 | + | 0.134296i | \(0.957123\pi\) | |||||||
\(830\) | −7.04344 | + | 4.06653i | −0.244481 | + | 0.141151i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.6444 | + | 11.3417i | 0.681047 | + | 0.393203i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.3920 | − | 57.8367i | −1.15558 | − | 2.00152i | ||||
\(836\) | −3.19672 | −0.110561 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 7.25788i | − | 0.250719i | ||||||
\(839\) | 9.73588 | + | 16.8630i | 0.336120 | + | 0.582177i | 0.983699 | − | 0.179821i | \(-0.0575519\pi\) |
−0.647579 | + | 0.761998i | \(0.724219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.2685 | + | 24.7138i | −0.492018 | + | 0.852200i | ||||
\(842\) | 30.7519 | + | 17.7546i | 1.05978 | + | 0.611865i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.53184 | − | 14.7776i | −0.293678 | − | 0.508665i | ||||
\(845\) | 27.0085 | 0.929122 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.72493 | − | 3.88264i | 0.230935 | − | 0.133330i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.4507 | + | 9.49781i | 0.564254 | + | 0.325772i | ||||
\(851\) | −16.1474 | − | 9.32269i | −0.553525 | − | 0.319578i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.812274 | + | 0.468967i | −0.0278117 | + | 0.0160571i | −0.513841 | − | 0.857885i | \(-0.671778\pi\) |
0.486030 | + | 0.873942i | \(0.338445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.4609 | −1.24621 | ||||||||
\(857\) | 9.00087 | + | 15.5900i | 0.307464 | + | 0.532543i | 0.977807 | − | 0.209509i | \(-0.0671864\pi\) |
−0.670343 | + | 0.742051i | \(0.733853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1160 | − | 13.3460i | −0.788709 | − | 0.455361i | 0.0507989 | − | 0.998709i | \(-0.483823\pi\) |
−0.839508 | + | 0.543348i | \(0.817157\pi\) | |||||||
\(860\) | −5.63438 | + | 9.75903i | −0.192131 | + | 0.332780i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.75486 | − | 8.23566i | −0.161951 | − | 0.280508i | ||||
\(863\) | − | 27.7596i | − | 0.944946i | −0.881345 | − | 0.472473i | \(-0.843361\pi\) | ||
0.881345 | − | 0.472473i | \(-0.156639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.3193 | 1.26889 | ||||||||
\(866\) | 16.7857 | + | 29.0737i | 0.570402 | + | 0.987966i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.2633 | + | 10.5443i | 0.619540 | + | 0.357692i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.9877 | − | 8.65316i | 0.507839 | − | 0.293201i | ||||
\(872\) | 22.0381i | 0.746305i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.3952i | 0.351623i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.90978 | + | 11.9681i | −0.233327 | + | 0.404134i | −0.958785 | − | 0.284132i | \(-0.908295\pi\) |
0.725458 | + | 0.688266i | \(0.241628\pi\) | |||||||
\(878\) | −1.20447 | + | 2.08621i | −0.0406490 | + | 0.0704061i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.4828 | + | 11.2484i | −0.656765 | + | 0.379184i | ||||
\(881\) | −43.9006 | −1.47905 | −0.739525 | − | 0.673129i | \(-0.764950\pi\) | ||||
−0.739525 | + | 0.673129i | \(0.764950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.96743 | 0.268125 | 0.134063 | − | 0.990973i | \(-0.457198\pi\) | ||||
0.134063 | + | 0.990973i | \(0.457198\pi\) | |||||||
\(884\) | −1.61410 | + | 0.931899i | −0.0542880 | + | 0.0313432i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.3750 | − | 24.8982i | 0.482937 | − | 0.836472i | ||||
\(887\) | 10.6080 | − | 18.3736i | 0.356181 | − | 0.616924i | −0.631138 | − | 0.775670i | \(-0.717412\pi\) |
0.987319 | + | 0.158747i | \(0.0507453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 31.1303i | − | 1.04349i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.69359i | − | 0.157153i | ||||||
\(893\) | −14.9493 | + | 8.63098i | −0.500259 | + | 0.288825i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.8005 | − | 41.4541i | −2.40003 | − | 1.38566i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.172924 | − | 0.299513i | −0.00577054 | − | 0.00999487i | ||||
\(899\) | 4.46050 | 0.148766 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.78621i | 0.126137i | ||||||||
\(902\) | 9.38618 | + | 16.2573i | 0.312526 | + | 0.541310i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.37242 | − | 7.57325i | 0.145424 | − | 0.251883i | ||||
\(905\) | 28.8808 | + | 16.6743i | 0.960029 | + | 0.554273i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.88344 | − | 3.26221i | −0.0625385 | − | 0.108320i | 0.833061 | − | 0.553181i | \(-0.186586\pi\) |
−0.895599 | + | 0.444861i | \(0.853253\pi\) | |||||||
\(908\) | −1.42484 | −0.0472850 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0013 | + | 23.0947i | −1.32530 | + | 0.765163i | −0.984569 | − | 0.174998i | \(-0.944008\pi\) |
−0.340732 | + | 0.940160i | \(0.610675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.98359 | + | 1.72258i | 0.0987423 | + | 0.0570089i | ||||
\(914\) | −16.8862 | − | 9.74926i | −0.558546 | − | 0.322477i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.34196 | + | 3.66153i | −0.209544 | + | 0.120980i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.21522 | 0.0400864 | 0.0200432 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200432 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(920\) | −24.3355 | − | 42.1503i | −0.802316 | − | 1.38965i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.5213 | + | 11.8480i | 0.675833 | + | 0.390192i | ||||
\(923\) | −2.54870 | + | 4.41447i | −0.0838914 | + | 0.145304i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.1520 | + | 60.8850i | 1.15579 | + | 2.00189i | ||||
\(926\) | − | 22.0230i | − | 0.723720i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.26210 | 0.0742570 | ||||||||
\(929\) | −9.44516 | − | 16.3595i | −0.309886 | − | 0.536737i | 0.668452 | − | 0.743756i | \(-0.266957\pi\) |
−0.978337 | + | 0.207018i | \(0.933624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.33941 | − | 0.773306i | −0.0438737 | − | 0.0253305i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.9581 | − | 17.2963i | 0.980258 | − | 0.565952i | ||||
\(935\) | − | 10.9690i | − | 0.358725i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0448i | 0.883516i | 0.897134 | + | 0.441758i | \(0.145645\pi\) | ||||
−0.897134 | + | 0.441758i | \(0.854355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.46650 | − | 16.3965i | 0.308763 | − | 0.534793i | ||||
\(941\) | −8.16024 | + | 14.1339i | −0.266016 | + | 0.460754i | −0.967829 | − | 0.251607i | \(-0.919041\pi\) |
0.701813 | + | 0.712361i | \(0.252374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3012 | + | 13.4530i | −0.758793 | + | 0.438089i | ||||
\(944\) | 14.0184 | 0.456259 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.8300 | −0.352114 | ||||||||
\(947\) | 24.8567 | − | 14.3510i | 0.807734 | − | 0.466345i | −0.0384343 | − | 0.999261i | \(-0.512237\pi\) |
0.846168 | + | 0.532916i | \(0.178904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4851 | + | 26.8210i | −0.502668 | + | 0.870647i | ||||
\(950\) | 19.5980 | − | 33.9447i | 0.635842 | − | 1.10131i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 34.5757i | − | 1.12002i | −0.828486 | − | 0.560009i | \(-0.810798\pi\) | ||
0.828486 | − | 0.560009i | \(-0.189202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 80.6366i | − | 2.60934i | ||||||
\(956\) | 10.6820 | − | 6.16723i | 0.345479 | − | 0.199462i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.3785 | + | 12.9202i | 0.723015 | + | 0.417433i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.98731 | + | 10.3703i | 0.193139 | + | 0.334527i | ||||
\(962\) | 15.6503 | 0.504587 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.8055i | 0.412437i | ||||||||
\(965\) | −39.2360 | − | 67.9588i | −1.26305 | − | 2.18767i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25000 | + | 9.09327i | −0.168829 | + | 0.292420i | −0.938008 | − | 0.346613i | \(-0.887332\pi\) |
0.769180 | + | 0.639033i | \(0.220665\pi\) | |||||||
\(968\) | −16.8577 | − | 9.73277i | −0.541826 | − | 0.312823i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.96583 | + | 12.0652i | 0.223659 | + | 0.387389i | ||||
\(971\) | −22.8312 | −0.732689 | −0.366345 | − | 0.930479i | \(-0.619391\pi\) | ||||
−0.366345 | + | 0.930479i | \(0.619391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.09973 | − | 0.634927i | 0.0352375 | − | 0.0203444i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.9315 | − | 8.62071i | −0.477946 | − | 0.275942i | ||||
\(977\) | 8.88551 | + | 5.13005i | 0.284273 | + | 0.164125i | 0.635356 | − | 0.772219i | \(-0.280853\pi\) |
−0.351083 | + | 0.936344i | \(0.614187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4201 | + | 6.59337i | −0.364987 | + | 0.210725i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.2720 | −0.710727 | ||||||||
\(983\) | −16.9599 | − | 29.3754i | −0.540937 | − | 0.936930i | −0.998851 | − | 0.0479337i | \(-0.984736\pi\) |
0.457913 | − | 0.888997i | \(-0.348597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −62.2566 | − | 35.9438i | −1.98366 | − | 1.14527i | ||||
\(986\) | 0.469440 | − | 0.813095i | 0.0149500 | − | 0.0258942i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.92290 | + | 3.33056i | 0.0611756 | + | 0.105959i | ||||
\(989\) | − | 15.5224i | − | 0.493583i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8556 | 0.726031 | 0.363015 | − | 0.931783i | \(-0.381747\pi\) | ||||
0.363015 | + | 0.931783i | \(0.381747\pi\) | |||||||
\(992\) | 10.8971 | + | 18.8743i | 0.345982 | + | 0.599259i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2002 | + | 5.88910i | 0.323369 | + | 0.186697i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.65867 | − | 3.26704i | 0.179212 | − | 0.103468i | −0.407710 | − | 0.913111i | \(-0.633673\pi\) |
0.586922 | + | 0.809643i | \(0.300339\pi\) | |||||||
\(998\) | − | 19.6592i | − | 0.622302i | ||||||
\(999\) | 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.881.17 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.293.7 | yes | 48 | ||
7.2 | even | 3 | 1323.2.s.d.962.8 | 48 | |||
7.3 | odd | 6 | 1323.2.i.d.1097.1 | 48 | |||
7.4 | even | 3 | 1323.2.i.d.1097.20 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.962.7 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.881.18 | 48 | ||
9.2 | odd | 6 | inner | 1323.2.o.e.440.18 | 48 | ||
9.7 | even | 3 | 441.2.o.e.146.8 | yes | 48 | ||
21.2 | odd | 6 | 441.2.s.d.374.18 | 48 | |||
21.5 | even | 6 | 441.2.s.d.374.17 | 48 | |||
21.11 | odd | 6 | 441.2.i.d.68.8 | 48 | |||
21.17 | even | 6 | 441.2.i.d.68.7 | 48 | |||
21.20 | even | 2 | 441.2.o.e.293.8 | yes | 48 | ||
63.2 | odd | 6 | 1323.2.i.d.521.1 | 48 | |||
63.11 | odd | 6 | 1323.2.s.d.656.7 | 48 | |||
63.16 | even | 3 | 441.2.i.d.227.17 | 48 | |||
63.20 | even | 6 | inner | 1323.2.o.e.440.17 | 48 | ||
63.25 | even | 3 | 441.2.s.d.362.17 | 48 | |||
63.34 | odd | 6 | 441.2.o.e.146.7 | ✓ | 48 | ||
63.38 | even | 6 | 1323.2.s.d.656.8 | 48 | |||
63.47 | even | 6 | 1323.2.i.d.521.20 | 48 | |||
63.52 | odd | 6 | 441.2.s.d.362.18 | 48 | |||
63.61 | odd | 6 | 441.2.i.d.227.18 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.7 | 48 | 21.17 | even | 6 | |||
441.2.i.d.68.8 | 48 | 21.11 | odd | 6 | |||
441.2.i.d.227.17 | 48 | 63.16 | even | 3 | |||
441.2.i.d.227.18 | 48 | 63.61 | odd | 6 | |||
441.2.o.e.146.7 | ✓ | 48 | 63.34 | odd | 6 | ||
441.2.o.e.146.8 | yes | 48 | 9.7 | even | 3 | ||
441.2.o.e.293.7 | yes | 48 | 3.2 | odd | 2 | ||
441.2.o.e.293.8 | yes | 48 | 21.20 | even | 2 | ||
441.2.s.d.362.17 | 48 | 63.25 | even | 3 | |||
441.2.s.d.362.18 | 48 | 63.52 | odd | 6 | |||
441.2.s.d.374.17 | 48 | 21.5 | even | 6 | |||
441.2.s.d.374.18 | 48 | 21.2 | odd | 6 | |||
1323.2.i.d.521.1 | 48 | 63.2 | odd | 6 | |||
1323.2.i.d.521.20 | 48 | 63.47 | even | 6 | |||
1323.2.i.d.1097.1 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.1097.20 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.440.17 | 48 | 63.20 | even | 6 | inner | ||
1323.2.o.e.440.18 | 48 | 9.2 | odd | 6 | inner | ||
1323.2.o.e.881.17 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.881.18 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.s.d.656.7 | 48 | 63.11 | odd | 6 | |||
1323.2.s.d.656.8 | 48 | 63.38 | even | 6 | |||
1323.2.s.d.962.7 | 48 | 7.5 | odd | 6 | |||
1323.2.s.d.962.8 | 48 | 7.2 | even | 3 |