Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Character | \(\chi\) | \(=\) | 1152.191 |
Dual form | 1152.2.p.g.959.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68783 | + | 0.388876i | −0.974470 | + | 0.224518i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.538609 | − | 0.932899i | −0.240873 | − | 0.417205i | 0.720090 | − | 0.693881i | \(-0.244101\pi\) |
−0.960963 | + | 0.276676i | \(0.910767\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.07105 | − | 2.35042i | −1.53871 | − | 0.888376i | −0.998914 | − | 0.0465815i | \(-0.985167\pi\) |
−0.539798 | − | 0.841795i | \(-0.681499\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.69755 | − | 1.31271i | 0.899184 | − | 0.437571i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.28563 | + | 2.47431i | 1.29216 | + | 0.746032i | 0.979038 | − | 0.203679i | \(-0.0652900\pi\) |
0.313127 | + | 0.949711i | \(0.398623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.05002 | − | 0.606232i | 0.291225 | − | 0.168139i | −0.347269 | − | 0.937765i | \(-0.612891\pi\) |
0.638494 | + | 0.769627i | \(0.279558\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.27186 | + | 1.36512i | 0.328394 | + | 0.352474i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.12017i | − | 0.756753i | −0.925652 | − | 0.378376i | \(-0.876482\pi\) | ||
0.925652 | − | 0.378376i | \(-0.123518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.05903 | −0.472375 | −0.236187 | − | 0.971708i | \(-0.575898\pi\) | ||||
−0.236187 | + | 0.971708i | \(0.575898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.78527 | + | 2.38398i | 1.69889 | + | 0.520228i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.71835 | − | 2.97627i | −0.358301 | − | 0.620596i | 0.629376 | − | 0.777101i | \(-0.283311\pi\) |
−0.987677 | + | 0.156505i | \(0.949977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.91980 | − | 3.32519i | 0.383960 | − | 0.665038i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.04253 | + | 3.26465i | −0.777985 | + | 0.628283i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.723042 | + | 1.25234i | −0.134265 | + | 0.232555i | −0.925317 | − | 0.379195i | \(-0.876201\pi\) |
0.791051 | + | 0.611750i | \(0.209534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.45450 | + | 3.72651i | −1.15926 | + | 0.669301i | −0.951127 | − | 0.308799i | \(-0.900073\pi\) |
−0.208136 | + | 0.978100i | \(0.566740\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.19561 | − | 2.50964i | −1.42667 | − | 0.436872i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.06384i | 0.855945i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.04031i | 1.48622i | 0.669171 | + | 0.743109i | \(0.266649\pi\) | ||||
−0.669171 | + | 0.743109i | \(0.733351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.53652 | + | 1.43155i | −0.246040 | + | 0.229231i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.75630 | + | 5.05545i | −1.36750 | + | 0.789529i | −0.990609 | − | 0.136726i | \(-0.956342\pi\) |
−0.376896 | + | 0.926256i | \(0.623009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0592540 | + | 0.102631i | −0.00903614 | + | 0.0156511i | −0.870508 | − | 0.492154i | \(-0.836210\pi\) |
0.861472 | + | 0.507805i | \(0.169543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.67756 | − | 1.80950i | −0.399146 | − | 0.269745i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.98823 | − | 3.44372i | 0.290014 | − | 0.502319i | −0.683799 | − | 0.729671i | \(-0.739673\pi\) |
0.973813 | + | 0.227352i | \(0.0730068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.54897 | + | 13.0752i | 1.07842 | + | 1.86789i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.21336 | + | 5.26632i | 0.169904 | + | 0.737433i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.401027 | −0.0550853 | −0.0275426 | − | 0.999621i | \(-0.508768\pi\) | ||||
−0.0275426 | + | 0.999621i | \(0.508768\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.33074i | − | 0.718797i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.47530 | − | 0.800709i | 0.460315 | − | 0.106056i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.97357 | + | 5.18089i | −1.16826 | + | 0.674495i | −0.953269 | − | 0.302121i | \(-0.902305\pi\) |
−0.214990 | + | 0.976616i | \(0.568972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7417 | − | 6.77909i | −1.50337 | − | 0.867973i | −0.999992 | − | 0.00390851i | \(-0.998756\pi\) |
−0.503381 | − | 0.864065i | \(-0.667911\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.0673 | − | 0.996260i | −1.77231 | − | 0.125517i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.13111 | − | 0.653045i | −0.140297 | − | 0.0810002i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.94046 | + | 8.55712i | 0.603573 | + | 1.04542i | 0.992275 | + | 0.124056i | \(0.0395901\pi\) |
−0.388702 | + | 0.921363i | \(0.627077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.05769 | + | 4.35522i | 0.488488 | + | 0.524307i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8855 | −1.52922 | −0.764612 | − | 0.644491i | \(-0.777069\pi\) | ||||
−0.764612 | + | 0.644491i | \(0.777069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.327300 | 0.0383076 | 0.0191538 | − | 0.999817i | \(-0.493903\pi\) | ||||
0.0191538 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.94721 | + | 6.35893i | −0.224845 | + | 0.734265i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.6313 | − | 20.1461i | −1.32551 | − | 2.29586i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.98705 | + | 5.18867i | 1.01112 | + | 0.583771i | 0.911520 | − | 0.411256i | \(-0.134910\pi\) |
0.0996017 | + | 0.995027i | \(0.468243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.55357 | − | 7.08223i | 0.617063 | − | 0.786914i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.21751 | − | 4.74438i | −0.901989 | − | 0.520764i | −0.0241442 | − | 0.999708i | \(-0.507686\pi\) |
−0.877845 | + | 0.478945i | \(0.841019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.91081 | + | 1.68055i | −0.315721 | + | 0.182282i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.733366 | − | 2.39492i | 0.0786251 | − | 0.256762i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.80272i | 1.03909i | 0.854444 | + | 0.519543i | \(0.173898\pi\) | ||||
−0.854444 | + | 0.519543i | \(0.826102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.69961 | −0.597481 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.44496 | − | 8.79972i | 0.979397 | − | 0.912488i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.10902 | + | 1.92087i | 0.113783 | + | 0.197077i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.79591 | − | 4.84266i | 0.283882 | − | 0.491698i | −0.688455 | − | 0.725279i | \(-0.741711\pi\) |
0.972337 | + | 0.233581i | \(0.0750443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.8088 | + | 1.04877i | 1.48834 | + | 0.105405i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.29078 | − | 5.69980i | 0.327445 | − | 0.567152i | −0.654559 | − | 0.756011i | \(-0.727146\pi\) |
0.982004 | + | 0.188859i | \(0.0604790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.27010 | − | 3.04270i | 0.519279 | − | 0.299806i | −0.217361 | − | 0.976091i | \(-0.569745\pi\) |
0.736639 | + | 0.676286i | \(0.236411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.96920 | − | 8.54691i | −0.192175 | − | 0.834093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.55222i | − | 0.826774i | −0.910555 | − | 0.413387i | \(-0.864346\pi\) | ||
0.910555 | − | 0.413387i | \(-0.135654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0641i | 1.34710i | 0.739142 | + | 0.673550i | \(0.235231\pi\) | ||||
−0.739142 | + | 0.673550i | \(0.764769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.51556 | − | 15.2585i | −0.333682 | − | 1.44827i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4863 | + | 6.63162i | −1.08054 | + | 0.623850i | −0.931042 | − | 0.364911i | \(-0.881099\pi\) |
−0.149498 | + | 0.988762i | \(0.547766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.85104 | + | 3.20610i | −0.172610 | + | 0.298970i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.03669 | − | 3.01372i | 0.188292 | − | 0.278619i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.33372 | + | 12.7024i | −0.672281 | + | 1.16443i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.74439 | + | 11.6816i | 0.613127 | + | 1.06197i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8132 | − | 11.9379i | 1.15533 | − | 1.07640i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.52218 | −0.851690 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.69445i | − | 0.150358i | −0.997170 | − | 0.0751791i | \(-0.976047\pi\) | ||
0.997170 | − | 0.0751791i | \(-0.0239529\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0601000 | − | 0.196266i | 0.00529151 | − | 0.0172803i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.75341 | − | 2.74438i | 0.415308 | − | 0.239778i | −0.277760 | − | 0.960650i | \(-0.589592\pi\) |
0.693068 | + | 0.720873i | \(0.256259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.38243 | + | 4.83960i | 0.726849 | + | 0.419646i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.22294 | + | 2.01290i | 0.449519 | + | 0.173243i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6559 | − | 6.72954i | −0.995832 | − | 0.574944i | −0.0888193 | − | 0.996048i | \(-0.528309\pi\) |
−0.907012 | + | 0.421104i | \(0.861643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.33263 | + | 10.9684i | 0.537126 | + | 0.930330i | 0.999057 | + | 0.0434141i | \(0.0138235\pi\) |
−0.461931 | + | 0.886916i | \(0.652843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.01662 | + | 6.58560i | −0.169830 | + | 0.554608i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00002 | 0.501747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.55775 | 0.129364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.8260 | − | 19.1331i | −1.47026 | − | 1.57807i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.82503 | + | 8.35719i | 0.395282 | + | 0.684648i | 0.993137 | − | 0.116956i | \(-0.0373136\pi\) |
−0.597855 | + | 0.801604i | \(0.703980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.55145 | + | 2.05043i | 0.289013 | + | 0.166862i | 0.637497 | − | 0.770453i | \(-0.279970\pi\) |
−0.348484 | + | 0.937315i | \(0.613303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.09589 | − | 8.41682i | −0.331133 | − | 0.680460i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.95291 | + | 4.01427i | 0.558471 | + | 0.322434i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0033 | + | 10.9716i | −1.51663 | + | 0.875625i | −0.516818 | + | 0.856095i | \(0.672884\pi\) |
−0.999809 | + | 0.0195297i | \(0.993783\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.676866 | − | 0.155950i | 0.0536789 | − | 0.0123676i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.1554i | 1.27322i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.42867 | −0.660185 | −0.330092 | − | 0.943949i | \(-0.607080\pi\) | ||||
−0.330092 | + | 0.943949i | \(0.607080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.07300 | + | 8.99739i | 0.161383 | + | 0.700446i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.04030 | + | 13.9262i | 0.622177 | + | 1.07764i | 0.989080 | + | 0.147383i | \(0.0470849\pi\) |
−0.366903 | + | 0.930259i | \(0.619582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.76497 | + | 9.98521i | −0.443459 | + | 0.768093i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.55435 | + | 2.70292i | −0.424752 | + | 0.206698i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.55535 | − | 16.5504i | 0.726480 | − | 1.25830i | −0.231882 | − | 0.972744i | \(-0.574488\pi\) |
0.958362 | − | 0.285556i | \(-0.0921784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6312 | + | 9.02468i | −1.18161 | + | 0.682202i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1312 | − | 12.2341i | 0.986998 | − | 0.919570i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.424929i | 0.0317607i | 0.999874 | + | 0.0158803i | \(0.00505508\pi\) | ||||
−0.999874 | + | 0.0158803i | \(0.994945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0403i | 0.969278i | 0.874714 | + | 0.484639i | \(0.161049\pi\) | ||||
−0.874714 | + | 0.484639i | \(0.838951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.4543 | + | 6.87588i | 1.65987 | + | 0.508280i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.43369 | − | 4.86920i | 0.620057 | − | 0.357990i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.72026 | − | 13.3719i | 0.564562 | − | 0.977849i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.1307 | − | 3.78891i | 1.75525 | − | 0.275603i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3515 | − | 17.9294i | 0.749010 | − | 1.29732i | −0.199288 | − | 0.979941i | \(-0.563863\pi\) |
0.948298 | − | 0.317382i | \(-0.102804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.46861 | − | 6.00782i | −0.249676 | − | 0.432452i | 0.713760 | − | 0.700391i | \(-0.246991\pi\) |
−0.963436 | + | 0.267939i | \(0.913658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.16307 | + | 0.662370i | 0.154901 | + | 0.0474333i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.30640 | −0.449312 | −0.224656 | − | 0.974438i | \(-0.572126\pi\) | ||||
−0.224656 | + | 0.974438i | \(0.572126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.7691i | − | 1.61406i | −0.590510 | − | 0.807031i | \(-0.701073\pi\) | ||
0.590510 | − | 0.807031i | \(-0.298927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6663 | − | 12.5218i | −0.822879 | − | 0.883217i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.88708 | − | 3.39891i | 0.413192 | − | 0.238556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.43246 | + | 5.44583i | 0.658791 | + | 0.380353i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.54234 | − | 5.77294i | −0.593733 | − | 0.401247i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.82425 | − | 5.09468i | −0.610386 | − | 0.352407i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.45859 | − | 9.45455i | −0.375785 | − | 0.650878i | 0.614660 | − | 0.788792i | \(-0.289293\pi\) |
−0.990444 | + | 0.137915i | \(0.955960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.7485 | − | 5.01085i | 1.49018 | − | 0.343338i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.127659 | 0.00870627 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.0355 | 2.37836 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.552427 | + | 0.127279i | −0.0373296 | + | 0.00860072i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.89155 | − | 3.27626i | −0.127239 | − | 0.220385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8367 | + | 9.14333i | 1.06050 | + | 0.612283i | 0.925572 | − | 0.378572i | \(-0.123585\pi\) |
0.134933 | + | 0.990855i | \(0.456918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.813735 | − | 11.4900i | 0.0542490 | − | 0.766001i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.01058 | + | 1.73816i | 0.199819 | + | 0.115366i | 0.596571 | − | 0.802560i | \(-0.296529\pi\) |
−0.396752 | + | 0.917926i | \(0.629863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.77911 | + | 3.91392i | −0.447976 | + | 0.258639i | −0.706975 | − | 0.707238i | \(-0.749941\pi\) |
0.258999 | + | 0.965878i | \(0.416607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.4660 | + | 29.4800i | 1.80713 | + | 1.93964i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.9622i | − | 0.783669i | −0.920036 | − | 0.391835i | \(-0.871841\pi\) | ||
0.920036 | − | 0.391835i | \(-0.128159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.28353 | −0.279426 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.1864 | − | 5.26276i | −1.11637 | − | 0.341853i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.26987 | − | 2.19948i | −0.0821412 | − | 0.142273i | 0.822028 | − | 0.569447i | \(-0.192843\pi\) |
−0.904169 | + | 0.427174i | \(0.859509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.01191 | − | 3.48473i | 0.129599 | − | 0.224471i | −0.793923 | − | 0.608019i | \(-0.791964\pi\) |
0.923521 | + | 0.383548i | \(0.125298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.61938 | + | 14.1133i | −0.424633 | + | 0.905365i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.13189 | − | 14.0849i | 0.519528 | − | 0.899848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.16204 | + | 1.24825i | −0.137567 | + | 0.0794244i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.7148 | + | 4.81213i | 0.995882 | + | 0.304956i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.64335i | − | 0.545563i | −0.962076 | − | 0.272782i | \(-0.912056\pi\) | ||
0.962076 | − | 0.272782i | \(-0.0879437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 17.0069i | − | 1.06922i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.25942 | − | 3.96843i | 0.266735 | − | 0.248513i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1468 | + | 6.43561i | −0.695319 | + | 0.401443i | −0.805602 | − | 0.592458i | \(-0.798158\pi\) |
0.110283 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.2485 | − | 36.8035i | 1.32032 | − | 2.28686i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.306472 | + | 4.32741i | −0.0189701 | + | 0.267860i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.90296 | − | 5.02808i | 0.179004 | − | 0.310045i | −0.762535 | − | 0.646946i | \(-0.776046\pi\) |
0.941540 | + | 0.336902i | \(0.109379\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.215997 | + | 0.374117i | 0.0132686 | + | 0.0229819i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.81204 | − | 16.5453i | −0.233293 | − | 1.01256i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.75093 | 0.228699 | 0.114349 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114349 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3745i | 1.35916i | 0.733603 | + | 0.679578i | \(0.237837\pi\) | ||||
−0.733603 | + | 0.679578i | \(0.762163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.61998 | − | 2.21644i | 0.582227 | − | 0.134145i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4551 | − | 9.50035i | 0.992279 | − | 0.572893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.37669 | − | 4.25893i | −0.443222 | − | 0.255894i | 0.261741 | − | 0.965138i | \(-0.415703\pi\) |
−0.704963 | + | 0.709244i | \(0.749037\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.5195 | + | 18.5254i | −0.749524 | + | 1.10908i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7826 | + | 6.22534i | 0.643236 | + | 0.371373i | 0.785860 | − | 0.618404i | \(-0.212221\pi\) |
−0.142624 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.15797 | − | 14.1300i | −0.484941 | − | 0.839942i | 0.514910 | − | 0.857244i | \(-0.327825\pi\) |
−0.999850 | + | 0.0173026i | \(0.994492\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.61881 | − | 2.81084i | −0.155125 | − | 0.166500i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 47.5298 | 2.80560 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.26453 | 0.427325 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.83584 | + | 9.26087i | −0.166240 | + | 0.542882i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.80318 | − | 11.7835i | −0.397446 | − | 0.688397i | 0.595964 | − | 0.803011i | \(-0.296770\pi\) |
−0.993410 | + | 0.114614i | \(0.963437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.66650 | + | 5.58096i | 0.562805 | + | 0.324936i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.4025 | + | 3.98862i | −1.47400 | + | 0.231443i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.60862 | − | 2.08344i | −0.208692 | − | 0.120488i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.482452 | − | 0.278544i | 0.0278081 | − | 0.0160550i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.33777 | + | 10.9000i | −0.191750 | + | 0.626189i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6051i | 0.836287i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.53173 | 0.429859 | 0.214929 | − | 0.976630i | \(-0.431048\pi\) | ||||
0.214929 | + | 0.976630i | \(0.431048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.71182 | + | 7.18497i | −0.438710 | + | 0.408739i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7246 | − | 18.5755i | −0.608136 | − | 1.05332i | −0.991547 | − | 0.129745i | \(-0.958584\pi\) |
0.383411 | − | 0.923578i | \(-0.374749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.12564 | + | 12.3420i | −0.402765 | + | 0.697609i | −0.994058 | − | 0.108847i | \(-0.965284\pi\) |
0.591294 | + | 0.806456i | \(0.298617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.64737 | + | 13.6600i | 0.374537 | + | 0.769652i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3799 | + | 30.1029i | −0.976153 | + | 1.69075i | −0.300078 | + | 0.953915i | \(0.597013\pi\) |
−0.676075 | + | 0.736833i | \(0.736321\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.19737 | + | 3.57805i | −0.346986 | + | 0.200333i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.32575 | + | 14.4347i | 0.185625 | + | 0.805667i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42454i | 0.357471i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.65538i | − | 0.258234i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.46920 | − | 23.7379i | −0.302447 | − | 1.31271i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.1884 | + | 9.34638i | −0.892496 | + | 0.515283i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.85837 | − | 11.8791i | 0.376970 | − | 0.652932i | −0.613650 | − | 0.789579i | \(-0.710299\pi\) |
0.990620 | + | 0.136647i | \(0.0436325\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.8673 | + | 24.3867i | 0.650326 | + | 1.33638i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.32195 | − | 9.21790i | 0.290769 | − | 0.503627i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.12713 | − | 3.68431i | −0.115872 | − | 0.200697i | 0.802256 | − | 0.596981i | \(-0.203633\pi\) |
−0.918128 | + | 0.396284i | \(0.870300\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.8081 | − | 15.6598i | 0.912889 | − | 0.850524i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.8821 | −1.99728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 38.0671i | − | 2.05543i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.87747 | − | 6.13118i | 0.101080 | − | 0.330092i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.9663 | + | 7.48608i | −0.696066 | + | 0.401874i | −0.805881 | − | 0.592078i | \(-0.798308\pi\) |
0.109814 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.1751 | + | 8.18402i | 0.758777 | + | 0.438080i | 0.828857 | − | 0.559461i | \(-0.188992\pi\) |
−0.0700793 | + | 0.997541i | \(0.522325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.26562 | + | 5.87868i | −0.120930 | + | 0.313781i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6621 | − | 8.46517i | −0.780385 | − | 0.450555i | 0.0561818 | − | 0.998421i | \(-0.482107\pi\) |
−0.836567 | + | 0.547865i | \(0.815441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.94024 | + | 12.0208i | 0.368350 | + | 0.638000i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.43844 | − | 24.2914i | 0.393684 | − | 1.28564i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.9540 | −1.10591 | −0.552955 | − | 0.833211i | \(-0.686500\pi\) | ||||
−0.552955 | + | 0.833211i | \(0.686500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7604 | −0.776862 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.9261 | − | 17.0939i | −0.835904 | − | 0.897197i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.176287 | − | 0.305338i | −0.00922728 | − | 0.0159821i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1275 | + | 8.73384i | 0.789647 | + | 0.455903i | 0.839838 | − | 0.542837i | \(-0.182650\pi\) |
−0.0501914 | + | 0.998740i | \(0.515983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.9842 | + | 25.1319i | −0.884163 | + | 1.30831i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.63260 | + | 0.942582i | 0.0847604 | + | 0.0489364i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5467 | + | 10.1306i | −0.908534 | + | 0.524542i | −0.879959 | − | 0.475049i | \(-0.842430\pi\) |
−0.0285749 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.0718 | − | 3.70295i | 0.829946 | − | 0.191219i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.75332i | 0.0903008i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0937 | −1.03214 | −0.516072 | − | 0.856545i | \(-0.672606\pi\) | ||||
−0.516072 | + | 0.856545i | \(0.672606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.658931 | + | 2.85995i | 0.0337581 | + | 0.146520i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.82133 | + | 3.15464i | 0.0930659 | + | 0.161195i | 0.908800 | − | 0.417233i | \(-0.137000\pi\) |
−0.815734 | + | 0.578427i | \(0.803667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.5295 | + | 21.7017i | −0.638562 | + | 1.10602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0251156 | + | 0.354636i | −0.00127670 | + | 0.0180271i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.87792 | − | 17.1091i | 0.500831 | − | 0.867464i | −0.499169 | − | 0.866505i | \(-0.666361\pi\) |
1.00000 | 0.000959266i | \(-0.000305344\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.28648 | + | 5.36155i | −0.469638 | + | 0.271145i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.95573 | + | 6.48054i | −0.350870 | + | 0.326900i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.1787i | − | 0.562460i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.63889i | − | 0.232819i | −0.993201 | − | 0.116410i | \(-0.962861\pi\) | ||
0.993201 | − | 0.116410i | \(-0.0371385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.0301 | − | 4.90870i | −0.802511 | − | 0.245743i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.4727 | − | 12.3972i | 1.07229 | − | 0.619089i | 0.143486 | − | 0.989652i | \(-0.454169\pi\) |
0.928807 | + | 0.370564i | \(0.120835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.51826 | + | 7.82585i | −0.225070 | + | 0.389834i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.59820 | − | 1.36636i | −0.476939 | − | 0.0678951i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.3685 | + | 38.7434i | −1.10877 | + | 1.92044i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.97230 | − | 12.0764i | −0.344758 | − | 0.597138i | 0.640552 | − | 0.767915i | \(-0.278706\pi\) |
−0.985310 | + | 0.170777i | \(0.945372\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.2902 | + | 6.82563i | 1.09949 | + | 0.336684i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 48.7091 | 2.39682 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2215i | 0.501753i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.9538 | − | 16.0503i | −0.732289 | − | 0.785984i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0259 | + | 8.67521i | −0.734063 | + | 0.423812i | −0.819907 | − | 0.572497i | \(-0.805975\pi\) |
0.0858435 | + | 0.996309i | \(0.472642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.33241 | − | 4.23337i | −0.357360 | − | 0.206322i | 0.310562 | − | 0.950553i | \(-0.399483\pi\) |
−0.667922 | + | 0.744231i | \(0.732816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.842741 | − | 11.8996i | 0.0409755 | − | 0.578578i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3752 | − | 5.99010i | −0.503269 | − | 0.290563i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.8674 | + | 55.1960i | 1.54217 | + | 2.67112i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.1270 | + | 2.33326i | −0.488937 | + | 0.112651i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.1512 | −0.585302 | −0.292651 | − | 0.956219i | \(-0.594537\pi\) | ||||
−0.292651 | + | 0.956219i | \(0.594537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.4672 | 0.935532 | 0.467766 | − | 0.883852i | \(-0.345059\pi\) | ||||
0.467766 | + | 0.883852i | \(0.345059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.62922 | + | 0.605771i | −0.126061 | + | 0.0290445i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.53815 | + | 6.12825i | 0.169252 | + | 0.293154i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.44979 | + | 4.30114i | 0.355559 | + | 0.205282i | 0.667131 | − | 0.744940i | \(-0.267522\pi\) |
−0.311572 | + | 0.950223i | \(0.600855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.5277 | + | 25.3614i | 1.78703 | + | 1.20768i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6579 | − | 8.46276i | −0.696419 | − | 0.402078i | 0.109593 | − | 0.993977i | \(-0.465045\pi\) |
−0.806012 | + | 0.591899i | \(0.798379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.14494 | − | 5.27984i | 0.433512 | − | 0.250288i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.3937 | − | 12.2292i | −0.538906 | − | 0.578421i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 40.9499i | − | 1.93255i | −0.257522 | − | 0.966273i | \(-0.582906\pi\) | ||
0.257522 | − | 0.966273i | \(-0.417094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50.0350 | −2.35606 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.79162 | − | 2.07971i | −0.319098 | − | 0.0977133i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.06986 | + | 5.31716i | 0.143917 | + | 0.249272i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.34163 | − | 12.7161i | 0.343427 | − | 0.594833i | −0.641640 | − | 0.767006i | \(-0.721745\pi\) |
0.985067 | + | 0.172173i | \(0.0550788\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.1863 | + | 12.6134i | 0.475455 | + | 0.588742i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6860 | + | 32.3651i | −0.870294 | + | 1.50739i | −0.00860141 | + | 0.999963i | \(0.502738\pi\) |
−0.861693 | + | 0.507431i | \(0.830595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.24136 | + | 0.716699i | −0.0576909 | + | 0.0333078i | −0.528568 | − | 0.848891i | \(-0.677271\pi\) |
0.470877 | + | 0.882199i | \(0.343938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.2964 | − | 4.07159i | −0.616606 | − | 0.188815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 14.7591i | − | 0.682970i | −0.939887 | − | 0.341485i | \(-0.889070\pi\) | ||
0.939887 | − | 0.341485i | \(-0.110930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 46.4486i | − | 2.14480i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.8078 | − | 25.9080i | 1.28131 | − | 1.19378i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.507881 | + | 0.293225i | −0.0233524 | + | 0.0134825i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.95293 | + | 6.84668i | −0.181373 | + | 0.314147i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.08179 | + | 0.526433i | −0.0495318 | + | 0.0241037i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.3517 | + | 21.3938i | −0.564365 | + | 0.977509i | 0.432743 | + | 0.901517i | \(0.357546\pi\) |
−0.997108 | + | 0.0759917i | \(0.975788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.48052 | + | 9.49255i | 0.249890 | + | 0.432823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.28245 | − | 27.2676i | −0.285861 | − | 1.24072i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.02362 | −0.273519 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.5414i | − | 1.56522i | −0.622513 | − | 0.782610i | \(-0.713888\pi\) | ||
0.622513 | − | 0.782610i | \(-0.286112\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.2262 | − | 3.27771i | 0.643330 | − | 0.148223i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.8995 | − | 18.4172i | 1.43961 | − | 0.831156i | 0.441783 | − | 0.897122i | \(-0.354346\pi\) |
0.997822 | + | 0.0659653i | \(0.0210127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.90753 | + | 2.25601i | 0.175986 | + | 0.101606i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.99774 | − | 14.3799i | −0.314525 | − | 0.646331i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.4574 | + | 30.2863i | 2.35304 | + | 1.35853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9375 | + | 36.2648i | 0.937291 | + | 1.62344i | 0.770497 | + | 0.637443i | \(0.220008\pi\) |
0.166793 | + | 0.985992i | \(0.446659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9862 | − | 20.3784i | −0.848242 | − | 0.910440i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4048 | −0.463929 | −0.231964 | − | 0.972724i | \(-0.574515\pi\) | ||||
−0.231964 | + | 0.972724i | \(0.574515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.08979 | −0.315491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.84728 | − | 19.0952i | 0.259687 | − | 0.848048i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.73328 | − | 13.3944i | −0.342771 | − | 0.593698i | 0.642175 | − | 0.766558i | \(-0.278032\pi\) |
−0.984946 | + | 0.172861i | \(0.944699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.33245 | − | 0.769293i | −0.0589443 | − | 0.0340315i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.32371 | − | 6.72203i | 0.367501 | − | 0.296785i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.67706 | − | 3.27765i | −0.250161 | − | 0.144430i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.0417 | − | 9.83900i | 0.749491 | − | 0.432719i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.69179 | + | 31.6501i | −0.425423 | + | 1.38928i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.2431i | 0.624002i | 0.950082 | + | 0.312001i | \(0.100999\pi\) | ||||
−0.950082 | + | 0.312001i | \(0.899001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.33839 | −0.102251 | −0.0511254 | − | 0.998692i | \(-0.516281\pi\) | ||||
−0.0511254 | + | 0.998692i | \(0.516281\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.8734 | − | 21.3107i | 0.998275 | − | 0.930077i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6273 | + | 20.1392i | 0.506495 | + | 0.877275i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.59453 | − | 9.69002i | 0.243241 | − | 0.421305i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.4056 | + | 25.7555i | −0.755340 | + | 1.11769i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.12956 | + | 10.6167i | −0.265501 | + | 0.459861i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.97836 | + | 4.60631i | −0.344934 | + | 0.199148i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.165244 | − | 0.717208i | −0.00713082 | − | 0.0309498i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 74.7139i | 3.21815i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7952i | 1.10902i | 0.832176 | + | 0.554512i | \(0.187095\pi\) | ||||
−0.832176 | + | 0.554512i | \(0.812905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.07106 | − | 22.0098i | −0.217620 | − | 0.944533i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.1204 | − | 7.57507i | 0.562017 | − | 0.324480i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.47104 | + | 12.9402i | −0.319439 | + | 0.553284i | −0.980371 | − | 0.197162i | \(-0.936828\pi\) |
0.660932 | + | 0.750445i | \(0.270161\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.5729 | − | 2.87341i | −1.73161 | − | 0.122634i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.48877 | − | 2.57862i | 0.0634236 | − | 0.109853i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.3911 | − | 42.2467i | −1.03722 | − | 1.79651i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.3411 | + | 11.4980i | −0.523852 | + | 0.488065i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.4302 | 1.07751 | 0.538756 | − | 0.842462i | \(-0.318895\pi\) | ||||
0.538756 | + | 0.842462i | \(0.318895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.143687i | 0.00607730i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.83050 | + | 25.5717i | −0.330604 | + | 1.07964i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.5279 | + | 12.4291i | −0.907292 | + | 0.523825i | −0.879559 | − | 0.475790i | \(-0.842162\pi\) |
−0.0277333 | + | 0.999615i | \(0.508829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.3733 | + | 7.14371i | 0.520547 | + | 0.300538i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −39.2551 | + | 15.7789i | −1.64856 | + | 0.662650i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6202 | + | 10.7504i | 0.780600 | + | 0.450680i | 0.836643 | − | 0.547749i | \(-0.184515\pi\) |
−0.0560427 | + | 0.998428i | \(0.517848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5882 | − | 25.2675i | −0.610498 | − | 1.05741i | −0.991157 | − | 0.132698i | \(-0.957636\pi\) |
0.380658 | − | 0.924716i | \(-0.375697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.4993 | + | 34.2872i | −0.438616 | + | 1.43237i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.1956 | −0.550293 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.8813 | −1.45213 | −0.726063 | − | 0.687628i | \(-0.758652\pi\) | ||||
−0.726063 | + | 0.687628i | \(0.758652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.19073 | + | 8.79132i | 0.340395 | + | 0.365355i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.3026 | + | 38.6293i | 0.925268 | + | 1.60261i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.71865 | − | 0.992263i | −0.0711792 | − | 0.0410954i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.90848 | − | 0.276802i | −0.161596 | − | 0.0114444i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5905 | − | 11.8879i | −0.849862 | − | 0.490668i | 0.0107423 | − | 0.999942i | \(-0.496581\pi\) |
−0.860604 | + | 0.509274i | \(0.829914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2900 | − | 7.67301i | 0.547607 | − | 0.316161i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.6441 | − | 2.45241i | 0.437841 | − | 0.100879i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.9535i | − | 1.39430i | −0.716923 | − | 0.697152i | \(-0.754450\pi\) | ||
0.716923 | − | 0.697152i | \(-0.245550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.8000 | 0.647739 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.85437 | + | 38.4305i | 0.362385 | + | 1.57285i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.46524 | − | 14.6622i | −0.345881 | − | 0.599083i | 0.639633 | − | 0.768681i | \(-0.279086\pi\) |
−0.985513 | + | 0.169598i | \(0.945753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5145 | − | 18.2116i | 0.428895 | − | 0.742868i | −0.567880 | − | 0.823111i | \(-0.692236\pi\) |
0.996775 | + | 0.0802433i | \(0.0255697\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.5602 | + | 16.5979i | 1.00017 | + | 0.675918i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.26519 | − | 12.5837i | 0.295372 | − | 0.511599i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0727 | + | 13.8984i | −0.977082 | + | 0.564119i | −0.901388 | − | 0.433012i | \(-0.857451\pi\) |
−0.0756944 | + | 0.997131i | \(0.524117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.61464 | + | 8.02612i | −0.349083 | + | 0.325235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.82133i | − | 0.195050i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.4417i | − | 0.542906i | −0.962452 | − | 0.271453i | \(-0.912496\pi\) | ||
0.962452 | − | 0.271453i | \(-0.0875042\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0382 | − | 5.52359i | −0.727368 | − | 0.222733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1656 | − | 6.44644i | 0.449509 | − | 0.259524i | −0.258114 | − | 0.966114i | \(-0.583101\pi\) |
0.707623 | + | 0.706591i | \(0.249768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.59418 | + | 11.4215i | −0.265043 | + | 0.459067i | −0.967575 | − | 0.252585i | \(-0.918719\pi\) |
0.702532 | + | 0.711652i | \(0.252053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.6630 | + | 6.42185i | 0.668663 | + | 0.257700i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.0405 | − | 39.9073i | 0.923099 | − | 1.59885i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.47026 | − | 7.74272i | −0.178810 | − | 0.309709i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.8750 | + | 5.16743i | 0.673924 | + | 0.206367i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.2073 | 1.12470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.49548i | − | 0.258581i | −0.991607 | − | 0.129290i | \(-0.958730\pi\) | ||
0.991607 | − | 0.129290i | \(-0.0412699\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.8898 | + | 13.8350i | 0.512324 | + | 0.549891i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.58075 | + | 0.912648i | −0.0627302 | + | 0.0362173i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8532 | + | 9.15285i | 0.628127 | + | 0.362649i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.7592 | + | 16.9149i | −1.37505 | + | 0.669145i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.0483 | − | 15.6164i | −1.06835 | − | 0.616809i | −0.140616 | − | 0.990064i | \(-0.544908\pi\) |
−0.927729 | + | 0.373255i | \(0.878242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.12404 | − | 14.0713i | −0.320381 | − | 0.554916i | 0.660186 | − | 0.751102i | \(-0.270478\pi\) |
−0.980567 | + | 0.196186i | \(0.937144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.215467 | + | 0.0496435i | −0.00848400 | + | 0.00195471i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.1277 | −0.869929 | −0.434964 | − | 0.900448i | \(-0.643239\pi\) | ||||
−0.434964 | + | 0.900448i | \(0.643239\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.2765 | −2.01278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −59.1340 | + | 13.6244i | −2.31764 | + | 0.533984i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.5882 | + | 32.1957i | 0.727412 | + | 1.25991i | 0.957974 | + | 0.286856i | \(0.0926102\pi\) |
−0.230562 | + | 0.973058i | \(0.574056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.12047 | − | 2.95630i | −0.200073 | − | 0.115512i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.882908 | − | 0.429651i | 0.0344455 | − | 0.0167623i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.8491 | + | 23.5842i | 1.59125 | + | 0.918711i | 0.993092 | + | 0.117334i | \(0.0374349\pi\) |
0.598161 | + | 0.801376i | \(0.295898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1291 | − | 19.1271i | 1.28857 | − | 0.743957i | 0.310172 | − | 0.950680i | \(-0.399613\pi\) |
0.978399 | + | 0.206723i | \(0.0662799\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.46667 | + | 4.79419i | 0.173471 | + | 0.186191i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 10.4266i | − | 0.404327i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.96976 | 0.192430 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.2853 | − | 9.27389i | −1.17090 | − | 0.358549i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.5471 | − | 58.1053i | −1.29507 | − | 2.24313i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.66960 | − | 4.62389i | 0.102906 | − | 0.178238i | −0.809975 | − | 0.586465i | \(-0.800519\pi\) |
0.912881 | + | 0.408227i | \(0.133853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.09474 | + | 19.7097i | 0.119117 | + | 0.758625i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.31625 | + | 4.01186i | −0.0890206 | + | 0.154188i | −0.907097 | − | 0.420921i | \(-0.861707\pi\) |
0.818077 | + | 0.575109i | \(0.195040\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.7646 | + | 13.1432i | −0.873626 | + | 0.504388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.75727 | − | 1.76298i | −0.220619 | − | 0.0675574i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 6.06774i | − | 0.232175i | −0.993239 | − | 0.116088i | \(-0.962965\pi\) | ||
0.993239 | − | 0.116088i | \(-0.0370354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4984i | 0.553955i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.91997 | − | 9.24227i | 0.378470 | − | 0.352615i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.421088 | + | 0.243115i | −0.0160422 | + | 0.00926196i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0823 | − | 19.1951i | 0.421590 | − | 0.730216i | −0.574505 | − | 0.818501i | \(-0.694805\pi\) |
0.996095 | + | 0.0882853i | \(0.0281387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −57.8221 | − | 39.0764i | −2.19648 | − | 1.48439i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.82162 | − | 11.8154i | 0.258759 | − | 0.448184i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7739 | + | 27.3212i | 0.597479 | + | 1.03486i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.65181 | + | 20.1902i | 0.175947 | + | 0.763662i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.47732 | 0.282414 | 0.141207 | − | 0.989980i | \(-0.454902\pi\) | ||||
0.141207 | + | 0.989980i | \(0.454902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 18.6143i | − | 0.702052i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.22987 | − | 1.66576i | 0.272293 | − | 0.0627362i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.7939 | + | 15.4695i | −1.00769 | + | 0.581789i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.8031 | − | 22.4030i | −1.45728 | − | 0.841362i | −0.458404 | − | 0.888744i | \(-0.651579\pi\) |
−0.998877 | + | 0.0473824i | \(0.984912\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.0543 | + | 2.19929i | 1.16463 | + | 0.0824799i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.1822 | + | 12.8069i | 0.830730 | + | 0.479622i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.23167 | − | 5.59741i | −0.120857 | − | 0.209331i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.99866 | + | 3.21854i | 0.111987 | + | 0.120198i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.62241 | 0.172387 | 0.0861933 | − | 0.996278i | \(-0.472530\pi\) | ||||
0.0861933 | + | 0.996278i | \(0.472530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.6065 | −1.06536 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.04064 | + | 6.66402i | −0.0758922 | + | 0.247838i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.77619 | + | 4.80850i | 0.103105 | + | 0.178583i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.19976 | − | 0.692682i | −0.0444967 | − | 0.0256902i | 0.477587 | − | 0.878585i | \(-0.341512\pi\) |
−0.522083 | + | 0.852894i | \(0.674845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.68409 | − | 26.3949i | 0.210522 | − | 0.977589i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.320226 | + | 0.184883i | 0.0118440 | + | 0.00683813i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.9391 | − | 18.4400i | 1.17970 | − | 0.681098i | 0.223752 | − | 0.974646i | \(-0.428169\pi\) |
0.955944 | + | 0.293548i | \(0.0948361\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.24801 | + | 26.9352i | −0.304232 | + | 0.993518i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.8968i | 1.80114i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.13367 | 0.225631 | 0.112815 | − | 0.993616i | \(-0.464013\pi\) | ||||
0.112815 | + | 0.993616i | \(0.464013\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.16374 | − | 2.94760i | 0.116223 | − | 0.108283i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.31592 | + | 7.47540i | 0.158336 | + | 0.274246i | 0.934269 | − | 0.356570i | \(-0.116054\pi\) |
−0.775933 | + | 0.630816i | \(0.782720\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.19761 | − | 9.00253i | 0.190426 | − | 0.329827i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.3952 | − | 2.01097i | −1.03893 | − | 0.0735777i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.1013 | + | 34.8165i | −0.734486 | + | 1.27217i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0911 | + | 10.4449i | −0.660153 | + | 0.381140i | −0.792335 | − | 0.610086i | \(-0.791135\pi\) |
0.132182 | + | 0.991225i | \(0.457802\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.36119 | + | 14.5885i | 0.122489 | + | 0.531635i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.41753i | − | 0.160770i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5413i | 0.928313i | 0.885753 | + | 0.464157i | \(0.153643\pi\) | ||||
−0.885753 | + | 0.464157i | \(0.846357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.61358 | + | 28.7048i | 0.240058 | + | 1.04192i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.8817 | − | 20.7163i | 1.30071 | − | 0.750965i | 0.320184 | − | 0.947355i | \(-0.396255\pi\) |
0.980526 | + | 0.196390i | \(0.0629218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.0566 | − | 57.2558i | 1.19673 | − | 2.07280i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.64596 | + | 8.35444i | −0.204130 | + | 0.302055i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.28165 | + | 10.8801i | −0.226817 | + | 0.392859i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.41361 | − | 14.5728i | −0.303403 | − | 0.525509i | 0.673502 | − | 0.739186i | \(-0.264789\pi\) |
−0.976904 | + | 0.213677i | \(0.931456\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3113 | − | 15.1970i | 0.587437 | − | 0.547305i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.3934 | −1.63269 | −0.816344 | − | 0.577566i | \(-0.804002\pi\) | ||||
−0.816344 | + | 0.577566i | \(0.804002\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.6166i | 1.02794i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.5519 | + | 70.3812i | −0.773172 | + | 2.52491i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.0295 | − | 10.4094i | 0.645975 | − | 0.372954i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.2223 | − | 31.8826i | −1.97601 | − | 1.14085i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.16555 | − | 7.42312i | −0.0416535 | − | 0.265281i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.4707 | + | 11.8188i | 0.730631 | + | 0.421830i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6788 | + | 21.9603i | 0.451950 | + | 0.782800i | 0.998507 | − | 0.0546214i | \(-0.0173952\pi\) |
−0.546557 | + | 0.837422i | \(0.684062\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.94441 | + | 9.61544i | −0.104824 | + | 0.342319i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.3484 | 2.21686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.4388 | −0.583759 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.510052 | − | 0.547451i | −0.0180897 | − | 0.0194161i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.96853 | − | 6.87370i | −0.140573 | − | 0.243479i | 0.787140 | − | 0.616775i | \(-0.211561\pi\) |
−0.927712 | + | 0.373296i | \(0.878228\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7450 | − | 6.20363i | −0.380131 | − | 0.219469i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.8682 | + | 26.4433i | 0.454674 | + | 0.934329i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.40269 | + | 0.809841i | 0.0494997 | + | 0.0285787i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0714 | − | 8.70146i | 0.531196 | − | 0.306686i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.33095 | + | 1.45865i | −0.222860 | + | 0.0513468i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.0973i | − | 1.09332i | −0.837354 | − | 0.546661i | \(-0.815899\pi\) | ||
0.837354 | − | 0.546661i | \(-0.184101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.1896 | −1.16544 | −0.582722 | − | 0.812671i | \(-0.698012\pi\) | ||||
−0.582722 | + | 0.812671i | \(0.698012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.70091 | − | 37.7644i | −0.305154 | − | 1.32446i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.53976 | + | 7.86310i | 0.159021 | + | 0.275432i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.122006 | − | 0.211320i | 0.00426845 | − | 0.00739317i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.3750 | + | 7.48195i | −0.537245 | + | 0.261441i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8779 | − | 46.5538i | 0.938044 | − | 1.62474i | 0.168931 | − | 0.985628i | \(-0.445968\pi\) |
0.769113 | − | 0.639112i | \(-0.220698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.166035 | + | 0.0958606i | −0.00578763 | + | 0.00334149i | −0.502891 | − | 0.864350i | \(-0.667730\pi\) |
0.497103 | + | 0.867691i | \(0.334397\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.0790 | + | 22.4340i | −0.838322 | + | 0.781051i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.8393i | 0.794202i | 0.917775 | + | 0.397101i | \(0.129984\pi\) | ||||
−0.917775 | + | 0.397101i | \(0.870016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 32.7863i | − | 1.13872i | −0.822089 | − | 0.569358i | \(-0.807192\pi\) | ||
0.822089 | − | 0.569358i | \(-0.192808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1068 | + | 4.31975i | 0.489360 | + | 0.149850i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.7969 | − | 23.5541i | 1.41353 | − | 0.816100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.66116 | − | 15.0016i | 0.299732 | − | 0.519151i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.9268 | − | 36.1362i | 0.481379 | − | 1.24905i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.80362 | − | 11.7842i | 0.234887 | − | 0.406836i | −0.724353 | − | 0.689430i | \(-0.757861\pi\) |
0.959240 | + | 0.282593i | \(0.0911946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4544 | + | 23.3037i | 0.463946 | + | 0.803577i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.6201 | − | 6.31423i | −0.710194 | − | 0.217474i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4203 | 0.427270 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 63.4087i | − | 2.17875i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.2641 | + | 20.6766i | 0.661142 | + | 0.709621i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.9064 | − | 15.5344i | 0.922340 | − | 0.532513i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.31821 | − | 0.761067i | −0.0451345 | − | 0.0260584i | 0.477263 | − | 0.878761i | \(-0.341629\pi\) |
−0.522397 | + | 0.852702i | \(0.674962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.51318 | + | 3.72583i | 0.188547 | + | 0.127421i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.7528 | − | 8.51753i | −0.503946 | − | 0.290953i | 0.226396 | − | 0.974035i | \(-0.427306\pi\) |
−0.730342 | + | 0.683082i | \(0.760639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3773 | + | 17.9740i | 0.354069 | + | 0.613265i | 0.986958 | − | 0.160977i | \(-0.0514645\pi\) |
−0.632889 | + | 0.774242i | \(0.718131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −80.2223 | + | 18.4832i | −2.73397 | + | 0.629905i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.4712 | −0.424525 | −0.212263 | − | 0.977213i | \(-0.568083\pi\) | ||||
−0.212263 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.5864 | −0.699959 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.2613 | + | 2.82500i | −0.416416 | + | 0.0959420i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.6767 | + | 44.4734i | 0.871024 | + | 1.50866i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3752 | + | 5.99013i | 0.351550 | + | 0.202968i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.18509 | − | 16.7336i | 0.0401092 | − | 0.566346i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.7653 | + | 22.3812i | 1.31051 | + | 0.756621i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7116 | − | 9.07108i | 0.530542 | − | 0.306309i | −0.210695 | − | 0.977552i | \(-0.567573\pi\) |
0.741237 | + | 0.671243i | \(0.234239\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.0649 | + | 17.2429i | 0.541856 | + | 0.581588i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.15687i | − | 0.0389760i | −0.999810 | − | 0.0194880i | \(-0.993796\pi\) | ||
0.999810 | − | 0.0194880i | \(-0.00620362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.9132 | −0.804744 | −0.402372 | − | 0.915476i | \(-0.631814\pi\) | ||||
−0.402372 | + | 0.915476i | \(0.631814\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.4857 | − | 5.66065i | −0.621391 | − | 0.190281i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.97669 | + | 5.15578i | 0.0999474 | + | 0.173114i | 0.911663 | − | 0.410939i | \(-0.134799\pi\) |
−0.811715 | + | 0.584053i | \(0.801466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.98268 | + | 6.89820i | −0.133575 | + | 0.231358i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.3241 | − | 16.6105i | 1.38441 | − | 0.556474i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.09384 | + | 7.09074i | −0.136995 | + | 0.237283i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.396415 | − | 0.228871i | 0.0132507 | − | 0.00765030i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.90095 | + | 2.11319i | 0.230416 | + | 0.0705574i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10.7777i | − | 0.359456i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.25127i | 0.0416859i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.705978 | + | 0.657749i | −0.0234935 | + | 0.0218885i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.1653 | − | 7.02363i | 0.404388 | − | 0.233473i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.1801 | + | 21.0965i | −0.404433 | + | 0.700499i | −0.994255 | − | 0.107034i | \(-0.965865\pi\) |
0.589822 | + | 0.807533i | \(0.299198\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.39485 | − | 19.6954i | 0.0462641 | − | 0.653254i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.2288 | + | 19.4488i | −0.372026 | + | 0.644367i | −0.989877 | − | 0.141928i | \(-0.954670\pi\) |
0.617851 | + | 0.786295i | \(0.288003\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.4781 | − | 40.6653i | −0.777013 | − | 1.34583i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.67958 | − | 24.6510i | −0.187761 | − | 0.814936i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.8018 | −0.852052 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.5861i | 1.17388i | 0.809631 | + | 0.586939i | \(0.199667\pi\) | ||||
−0.809631 | + | 0.586939i | \(0.800333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.7123 | + | 2.92891i | −0.418884 | + | 0.0965108i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.5301 | + | 7.81159i | −0.445348 | + | 0.257122i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0607 | + | 17.3556i | 0.988391 | + | 0.570648i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.2222 | − | 15.1260i | 0.335741 | − | 0.496802i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.4661 | − | 6.61995i | −0.376190 | − | 0.217194i | 0.299969 | − | 0.953949i | \(-0.403024\pi\) |
−0.676159 | + | 0.736755i | \(0.736357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.5436 | − | 26.9223i | −0.509420 | − | 0.882342i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.3249 | + | 27.1819i | 0.829100 | + | 0.889894i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.6328 | −0.543952 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.4996 | 0.343007 | 0.171504 | − | 0.985183i | \(-0.445137\pi\) | ||||
0.171504 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.22738 | − | 23.6021i | 0.235857 | − | 0.770227i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.713336 | + | 1.23553i | 0.0232541 | + | 0.0402773i | 0.877418 | − | 0.479726i | \(-0.159264\pi\) |
−0.854164 | + | 0.520003i | \(0.825931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0928 | + | 17.3741i | 0.979957 | + | 0.565779i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.5317 | − | 20.4707i | −0.537775 | − | 0.665913i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.2243 | − | 11.6765i | −0.657202 | − | 0.379436i | 0.134008 | − | 0.990980i | \(-0.457215\pi\) |
−0.791210 | + | 0.611545i | \(0.790549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.343673 | − | 0.198420i | 0.0111561 | − | 0.00644098i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.6281 | − | 57.5673i | 0.571630 | − | 1.86675i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.6044i | 0.343511i | 0.985140 | + | 0.171756i | \(0.0549440\pi\) | ||||
−0.985140 | + | 0.171756i | \(0.945056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.3017 | −0.721666 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.06870 | − | 8.44916i | 0.293149 | − | 0.273123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.6345 | + | 54.7926i | 1.02153 | + | 1.76935i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2737 | − | 21.2587i | 0.395927 | − | 0.685765i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.2266 | − | 23.0700i | −0.361773 | − | 0.743422i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.73646 | + | 6.47173i | −0.120281 | + | 0.208332i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7081 | − | 13.6879i | 0.762401 | − | 0.440172i | −0.0677564 | − | 0.997702i | \(-0.521584\pi\) |
0.830157 | + | 0.557530i | \(0.188251\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.49835 | − | 10.8435i | −0.0802585 | − | 0.348345i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 57.0592i | − | 1.83112i | −0.402185 | − | 0.915558i | \(-0.631749\pi\) | ||
0.402185 | − | 0.915558i | \(-0.368251\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 59.5374i | − | 1.90868i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.81036 | + | 7.85749i | 0.0579780 | + | 0.251641i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.8184 | + | 24.7212i | −1.36988 | + | 0.790902i | −0.990913 | − | 0.134506i | \(-0.957055\pi\) |
−0.378970 | + | 0.925409i | \(0.623722\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.2549 | + | 42.0108i | −0.775191 | + | 1.34267i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.4622 | + | 37.9387i | 0.589452 | + | 1.21129i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.51615 | + | 14.7504i | −0.271623 | + | 0.470465i | −0.969278 | − | 0.245970i | \(-0.920894\pi\) |
0.697655 | + | 0.716434i | \(0.254227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.39669 | + | 5.88323i | 0.108227 | + | 0.187455i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.6887 | − | 22.0704i | 0.754020 | − | 0.702508i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.407277 | 0.0129506 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.85317i | − | 0.0906340i | −0.998973 | − | 0.0453170i | \(-0.985570\pi\) | ||
0.998973 | − | 0.0453170i | \(-0.0144298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.95630 | + | 22.7169i | −0.220752 | + | 0.720899i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.2413 | + | 12.2637i | −0.673395 | + | 0.388785i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8113 | + | 14.9022i | 0.817452 | + | 0.471956i | 0.849537 | − | 0.527529i | \(-0.176881\pi\) |
−0.0320848 | + | 0.999485i | \(0.510215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.5135 | − | 36.5457i | −0.933764 | − | 1.15626i |
(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 | 1152.2.p.g.191.1 | yes | 24 | |
3.2 | odd | 2 | 3456.2.p.g.575.7 | 24 | |||
4.3 | odd | 2 | 1152.2.p.f.191.12 | yes | 24 | ||
8.3 | odd | 2 | 1152.2.p.f.191.1 | ✓ | 24 | ||
8.5 | even | 2 | inner | 1152.2.p.g.191.12 | yes | 24 | |
9.4 | even | 3 | 3456.2.p.f.2879.6 | 24 | |||
9.5 | odd | 6 | 1152.2.p.f.959.1 | yes | 24 | ||
12.11 | even | 2 | 3456.2.p.f.575.7 | 24 | |||
24.5 | odd | 2 | 3456.2.p.g.575.6 | 24 | |||
24.11 | even | 2 | 3456.2.p.f.575.6 | 24 | |||
36.23 | even | 6 | inner | 1152.2.p.g.959.12 | yes | 24 | |
36.31 | odd | 6 | 3456.2.p.g.2879.6 | 24 | |||
72.5 | odd | 6 | 1152.2.p.f.959.12 | yes | 24 | ||
72.13 | even | 6 | 3456.2.p.f.2879.7 | 24 | |||
72.59 | even | 6 | inner | 1152.2.p.g.959.1 | yes | 24 | |
72.67 | odd | 6 | 3456.2.p.g.2879.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.f.191.1 | ✓ | 24 | 8.3 | odd | 2 | ||
1152.2.p.f.191.12 | yes | 24 | 4.3 | odd | 2 | ||
1152.2.p.f.959.1 | yes | 24 | 9.5 | odd | 6 | ||
1152.2.p.f.959.12 | yes | 24 | 72.5 | odd | 6 | ||
1152.2.p.g.191.1 | yes | 24 | 1.1 | even | 1 | trivial | |
1152.2.p.g.191.12 | yes | 24 | 8.5 | even | 2 | inner | |
1152.2.p.g.959.1 | yes | 24 | 72.59 | even | 6 | inner | |
1152.2.p.g.959.12 | yes | 24 | 36.23 | even | 6 | inner | |
3456.2.p.f.575.6 | 24 | 24.11 | even | 2 | |||
3456.2.p.f.575.7 | 24 | 12.11 | even | 2 | |||
3456.2.p.f.2879.6 | 24 | 9.4 | even | 3 | |||
3456.2.p.f.2879.7 | 24 | 72.13 | even | 6 | |||
3456.2.p.g.575.6 | 24 | 24.5 | odd | 2 | |||
3456.2.p.g.575.7 | 24 | 3.2 | odd | 2 | |||
3456.2.p.g.2879.6 | 24 | 36.31 | odd | 6 | |||
3456.2.p.g.2879.7 | 24 | 72.67 | odd | 6 |