Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1224,2,Mod(611,1224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1224.611");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1224.h (of order \(2\), degree \(1\), 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: | \(9.77368920740\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 611.40 | ||
Character | \(\chi\) | \(=\) | 1224.611 |
Dual form | 1224.2.h.c.611.38 |
$q$-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 \(\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times\).
\(n\) | \(137\) | \(613\) | \(649\) | \(919\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.933778 | + | 1.06210i | 0.660281 | + | 0.751019i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.256118 | + | 1.98353i | −0.128059 | + | 0.991767i | ||||
\(5\) | − | 3.62179i | − | 1.61972i | −0.586626 | − | 0.809858i | \(-0.699544\pi\) | ||
0.586626 | − | 0.809858i | \(-0.300456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.18114 | −0.446429 | −0.223215 | − | 0.974769i | \(-0.571655\pi\) | ||||
−0.223215 | + | 0.974769i | \(0.571655\pi\) | |||||||
\(8\) | −2.34587 | + | 1.58016i | −0.829390 | + | 0.558669i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.84671 | − | 3.38195i | 1.21644 | − | 1.06947i | ||||
\(11\) | −5.34326 | −1.61105 | −0.805527 | − | 0.592559i | \(-0.798118\pi\) | ||||
−0.805527 | + | 0.592559i | \(0.798118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.66295i | 1.84797i | 0.382428 | + | 0.923985i | \(0.375088\pi\) | ||||
−0.382428 | + | 0.923985i | \(0.624912\pi\) | |||||||
\(14\) | −1.10292 | − | 1.25449i | −0.294768 | − | 0.335277i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.86881 | − | 1.01604i | −0.967202 | − | 0.254009i | ||||
\(17\) | −1.54823 | − | 3.82139i | −0.375500 | − | 0.926822i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.692491 | 0.158868 | 0.0794342 | − | 0.996840i | \(-0.474689\pi\) | ||||
0.0794342 | + | 0.996840i | \(0.474689\pi\) | |||||||
\(20\) | 7.18395 | + | 0.927607i | 1.60638 | + | 0.207419i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.98942 | − | 5.67509i | −1.06375 | − | 1.20993i | ||||
\(23\) | 5.64119i | 1.17627i | 0.808763 | + | 0.588134i | \(0.200137\pi\) | ||||
−0.808763 | + | 0.588134i | \(0.799863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.11740 | −1.62348 | ||||||||
\(26\) | −7.07673 | + | 6.22172i | −1.38786 | + | 1.22018i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.302511 | − | 2.34283i | 0.0571693 | − | 0.442753i | ||||
\(29\) | 1.90843i | 0.354387i | 0.984176 | + | 0.177194i | \(0.0567019\pi\) | ||||
−0.984176 | + | 0.177194i | \(0.943298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.08929 | −1.45288 | −0.726440 | − | 0.687230i | \(-0.758827\pi\) | ||||
−0.726440 | + | 0.687230i | \(0.758827\pi\) | |||||||
\(32\) | −2.53347 | − | 5.05782i | −0.447859 | − | 0.894104i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61300 | − | 5.21270i | 0.448125 | − | 0.893971i | ||||
\(35\) | 4.27785i | 0.723088i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.32659 | 1.36888 | 0.684442 | − | 0.729068i | \(-0.260046\pi\) | ||||
0.684442 | + | 0.729068i | \(0.260046\pi\) | |||||||
\(38\) | 0.646633 | + | 0.735496i | 0.104898 | + | 0.119313i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.72300 | + | 8.49626i | 0.904886 | + | 1.34338i | ||||
\(41\) | −3.42928 | −0.535564 | −0.267782 | − | 0.963480i | \(-0.586291\pi\) | ||||
−0.267782 | + | 0.963480i | \(0.586291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.89610 | −1.05164 | −0.525822 | − | 0.850594i | \(-0.676242\pi\) | ||||
−0.525822 | + | 0.850594i | \(0.676242\pi\) | |||||||
\(44\) | 1.36851 | − | 10.5985i | 0.206310 | − | 1.59779i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.99151 | + | 5.26762i | −0.883400 | + | 0.776668i | ||||
\(47\) | −9.04763 | −1.31973 | −0.659867 | − | 0.751383i | \(-0.729387\pi\) | ||||
−0.659867 | + | 0.751383i | \(0.729387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.60491 | −0.800701 | ||||||||
\(50\) | −7.57985 | − | 8.62150i | −1.07195 | − | 1.21926i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.2162 | − | 1.70650i | −1.83276 | − | 0.236649i | ||||
\(53\) | 6.65539 | 0.914188 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.3522i | 2.60945i | ||||||||
\(56\) | 2.77080 | − | 1.86639i | 0.370264 | − | 0.249406i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.02695 | + | 1.78205i | −0.266152 | + | 0.233995i | ||||
\(59\) | − | 1.66078i | − | 0.216214i | −0.994139 | − | 0.108107i | \(-0.965521\pi\) | ||
0.994139 | − | 0.108107i | \(-0.0344790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.88629 | −0.625626 | −0.312813 | − | 0.949815i | \(-0.601271\pi\) | ||||
−0.312813 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(62\) | −7.55360 | − | 8.59165i | −0.959309 | − | 1.09114i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.00622 | − | 7.41368i | 0.375777 | − | 0.926710i | ||||
\(65\) | 24.1318 | 2.99319 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.55229 | 1.04483 | 0.522415 | − | 0.852692i | \(-0.325031\pi\) | ||||
0.522415 | + | 0.852692i | \(0.325031\pi\) | |||||||
\(68\) | 7.97637 | − | 2.09223i | 0.967278 | − | 0.253721i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.54351 | + | 3.99456i | −0.543053 | + | 0.477441i | ||||
\(71\) | − | 1.73403i | − | 0.205791i | −0.994692 | − | 0.102896i | \(-0.967189\pi\) | ||
0.994692 | − | 0.102896i | \(-0.0328108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.99143i | 1.05237i | 0.850371 | + | 0.526184i | \(0.176378\pi\) | ||||
−0.850371 | + | 0.526184i | \(0.823622\pi\) | |||||||
\(74\) | 7.77519 | + | 8.84368i | 0.903847 | + | 1.02806i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.177360 | + | 1.37358i | −0.0203445 | + | 0.157560i | ||||
\(77\) | 6.31114 | 0.719222 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.44027 | −0.724587 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(80\) | −3.67988 | + | 14.0120i | −0.411423 | + | 1.56659i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.20219 | − | 3.64224i | −0.353622 | − | 0.402219i | ||||
\(83\) | − | 11.3835i | − | 1.24950i | −0.780823 | − | 0.624752i | \(-0.785200\pi\) | ||
0.780823 | − | 0.624752i | \(-0.214800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8403 | + | 5.60736i | −1.50119 | + | 0.608204i | ||||
\(86\) | −6.43942 | − | 7.32435i | −0.694381 | − | 0.789805i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.5346 | − | 8.44319i | 1.33619 | − | 0.900047i | ||||
\(89\) | − | 8.13825i | − | 0.862653i | −0.902196 | − | 0.431326i | \(-0.858046\pi\) | ||
0.902196 | − | 0.431326i | \(-0.141954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 7.86988i | − | 0.824988i | ||||||
\(92\) | −11.1895 | − | 1.44481i | −1.16658 | − | 0.150632i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.44848 | − | 9.60950i | −0.871394 | − | 0.991145i | ||||
\(95\) | − | 2.50806i | − | 0.257322i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.89086i | − | 0.699661i | −0.936813 | − | 0.349831i | \(-0.886239\pi\) | ||
0.936813 | − | 0.349831i | \(-0.113761\pi\) | |||||||
\(98\) | −5.23374 | − | 5.95298i | −0.528687 | − | 0.601342i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.07901 | − | 16.1011i | 0.207901 | − | 1.61011i | ||||
\(101\) | 7.21896 | 0.718313 | 0.359157 | − | 0.933277i | \(-0.383064\pi\) | ||||
0.359157 | + | 0.933277i | \(0.383064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.72196i | 0.859400i | 0.902972 | + | 0.429700i | \(0.141381\pi\) | ||||
−0.902972 | + | 0.429700i | \(0.858619\pi\) | |||||||
\(104\) | −10.5285 | − | 15.6304i | −1.03240 | − | 1.53269i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.21466 | + | 7.06870i | 0.603621 | + | 0.686573i | ||||
\(107\) | 13.6474 | 1.31934 | 0.659671 | − | 0.751554i | \(-0.270696\pi\) | ||||
0.659671 | + | 0.751554i | \(0.270696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9038 | 1.23596 | 0.617982 | − | 0.786192i | \(-0.287951\pi\) | ||||
0.617982 | + | 0.786192i | \(0.287951\pi\) | |||||||
\(110\) | −20.5540 | + | 18.0707i | −1.95975 | + | 1.72297i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.56960 | + | 1.20008i | 0.431787 | + | 0.113397i | ||||
\(113\) | −3.28872 | −0.309377 | −0.154688 | − | 0.987963i | \(-0.549437\pi\) | ||||
−0.154688 | + | 0.987963i | \(0.549437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.4312 | 1.90522 | ||||||||
\(116\) | −3.78544 | − | 0.488785i | −0.351470 | − | 0.0453825i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.76391 | − | 1.55079i | 0.162381 | − | 0.142762i | ||||
\(119\) | 1.82867 | + | 4.51359i | 0.167634 | + | 0.413760i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5505 | 1.59550 | ||||||||
\(122\) | −4.56271 | − | 5.18974i | −0.413089 | − | 0.469857i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.07181 | − | 16.0454i | 0.186054 | − | 1.44092i | ||||
\(125\) | 11.2906i | 1.00986i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.07890i | − | 0.450680i | −0.974280 | − | 0.225340i | \(-0.927651\pi\) | ||
0.974280 | − | 0.225340i | \(-0.0723492\pi\) | |||||||
\(128\) | 10.6812 | − | 3.72983i | 0.944095 | − | 0.329673i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 22.5338 | + | 25.6305i | 1.97634 | + | 2.24794i | ||||
\(131\) | −10.6767 | −0.932830 | −0.466415 | − | 0.884566i | \(-0.654455\pi\) | ||||
−0.466415 | + | 0.884566i | \(0.654455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.817930 | −0.0709235 | ||||||||
\(134\) | 7.98594 | + | 9.08340i | 0.689880 | + | 0.784686i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.67033 | + | 6.51803i | 0.829224 | + | 0.558917i | ||||
\(137\) | − | 0.0369638i | − | 0.00315803i | −0.999999 | − | 0.00157901i | \(-0.999497\pi\) | ||
0.999999 | − | 0.00157901i | \(-0.000502616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.5586i | − | 1.57412i | −0.616874 | − | 0.787062i | \(-0.711601\pi\) | ||
0.616874 | − | 0.787062i | \(-0.288399\pi\) | |||||||
\(140\) | −8.48525 | − | 1.09563i | −0.717135 | − | 0.0925980i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.84172 | − | 1.61920i | 0.154553 | − | 0.135880i | ||||
\(143\) | − | 35.6019i | − | 2.97718i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.91196 | 0.574007 | ||||||||
\(146\) | −9.54981 | + | 8.39600i | −0.790348 | + | 0.694858i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.13259 | + | 16.5161i | −0.175298 | + | 1.35761i | ||||
\(149\) | 4.85767 | 0.397956 | 0.198978 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198978 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8039i | 1.20473i | 0.798222 | + | 0.602363i | \(0.205774\pi\) | ||||
−0.798222 | + | 0.602363i | \(0.794226\pi\) | |||||||
\(152\) | −1.62450 | + | 1.09424i | −0.131764 | + | 0.0887549i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.89321 | + | 6.70307i | 0.474888 | + | 0.540149i | ||||
\(155\) | 29.2978i | 2.35325i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.35906i | − | 0.746934i | −0.927643 | − | 0.373467i | \(-0.878169\pi\) | ||
0.927643 | − | 0.373467i | \(-0.121831\pi\) | |||||||
\(158\) | −6.01378 | − | 6.84022i | −0.478431 | − | 0.544179i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −18.3184 | + | 9.17571i | −1.44819 | + | 0.725404i | ||||
\(161\) | − | 6.66303i | − | 0.525121i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9278i | 1.32589i | 0.748668 | + | 0.662945i | \(0.230694\pi\) | ||||
−0.748668 | + | 0.662945i | \(0.769306\pi\) | |||||||
\(164\) | 0.878301 | − | 6.80209i | 0.0685838 | − | 0.531154i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0905 | − | 10.6297i | 0.938401 | − | 0.825023i | ||||
\(167\) | 9.17661i | 0.710108i | 0.934846 | + | 0.355054i | \(0.115537\pi\) | ||||
−0.934846 | + | 0.355054i | \(0.884463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −31.3949 | −2.41499 | ||||||||
\(170\) | −18.8793 | − | 9.46374i | −1.44798 | − | 0.725836i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.76621 | − | 13.6786i | 0.134673 | − | 1.04299i | ||||
\(173\) | 3.40214i | 0.258660i | 0.991602 | + | 0.129330i | \(0.0412827\pi\) | ||||
−0.991602 | + | 0.129330i | \(0.958717\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.58779 | 0.724768 | ||||||||
\(176\) | 20.6721 | + | 5.42896i | 1.55821 | + | 0.409223i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.64364 | − | 7.59932i | 0.647869 | − | 0.569593i | ||||
\(179\) | 25.9810i | 1.94191i | 0.239264 | + | 0.970955i | \(0.423094\pi\) | ||||
−0.239264 | + | 0.970955i | \(0.576906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.3228 | −1.36192 | −0.680960 | − | 0.732321i | \(-0.738437\pi\) | ||||
−0.680960 | + | 0.732321i | \(0.738437\pi\) | |||||||
\(182\) | 8.35861 | − | 7.34872i | 0.619581 | − | 0.544723i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.91396 | − | 13.2335i | −0.657146 | − | 0.975586i | ||||
\(185\) | − | 30.1572i | − | 2.21720i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.27259 | + | 20.4187i | 0.604952 | + | 1.49316i | ||||
\(188\) | 2.31726 | − | 17.9463i | 0.169004 | − | 1.30887i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.66382 | − | 2.34197i | 0.193253 | − | 0.169905i | ||||
\(191\) | 5.00973 | 0.362491 | 0.181246 | − | 0.983438i | \(-0.441987\pi\) | ||||
0.181246 | + | 0.983438i | \(0.441987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.7563i | − | 1.78199i | −0.454009 | − | 0.890997i | \(-0.650007\pi\) | ||
0.454009 | − | 0.890997i | \(-0.349993\pi\) | |||||||
\(194\) | 7.31880 | − | 6.43454i | 0.525459 | − | 0.461973i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.43552 | − | 11.1175i | 0.102537 | − | 0.794109i | ||||
\(197\) | 17.2594i | 1.22968i | 0.788650 | + | 0.614842i | \(0.210780\pi\) | ||||
−0.788650 | + | 0.614842i | \(0.789220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.16648 | 0.153578 | 0.0767889 | − | 0.997047i | \(-0.475533\pi\) | ||||
0.0767889 | + | 0.997047i | \(0.475533\pi\) | |||||||
\(200\) | 19.0424 | − | 12.8268i | 1.34650 | − | 0.906988i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.74090 | + | 7.66727i | 0.474288 | + | 0.539467i | ||||
\(203\) | − | 2.25413i | − | 0.158209i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4202i | 0.867461i | ||||||||
\(206\) | −9.26361 | + | 8.14437i | −0.645426 | + | 0.567445i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.76981 | − | 25.7777i | 0.469402 | − | 1.78736i | ||||
\(209\) | −3.70016 | −0.255946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.7291i | 1.15168i | 0.817564 | + | 0.575838i | \(0.195324\pi\) | ||||
−0.817564 | + | 0.575838i | \(0.804676\pi\) | |||||||
\(212\) | −1.70457 | + | 13.2012i | −0.117070 | + | 0.906662i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.7436 | + | 14.4949i | 0.871136 | + | 0.990851i | ||||
\(215\) | 24.9762i | 1.70337i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.55459 | 0.648608 | ||||||||
\(218\) | 12.0493 | + | 13.7052i | 0.816083 | + | 0.928232i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −38.3857 | − | 4.95645i | −2.58797 | − | 0.334164i | ||||
\(221\) | 25.4617 | − | 10.3158i | 1.71274 | − | 0.693914i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.53097i | 0.102521i | 0.998685 | + | 0.0512605i | \(0.0163239\pi\) | ||||
−0.998685 | + | 0.0512605i | \(0.983676\pi\) | |||||||
\(224\) | 2.99239 | + | 5.97399i | 0.199937 | + | 0.399154i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.07093 | − | 3.49295i | −0.204275 | − | 0.232348i | ||||
\(227\) | −16.6745 | −1.10673 | −0.553364 | − | 0.832940i | \(-0.686656\pi\) | ||||
−0.553364 | + | 0.832940i | \(0.686656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.69611i | 0.178164i | 0.996024 | + | 0.0890819i | \(0.0283933\pi\) | ||||
−0.996024 | + | 0.0890819i | \(0.971607\pi\) | |||||||
\(230\) | 19.0782 | + | 21.7000i | 1.25798 | + | 1.43086i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.01562 | − | 4.47694i | −0.197985 | − | 0.293926i | ||||
\(233\) | −26.8316 | −1.75780 | −0.878899 | − | 0.477008i | \(-0.841721\pi\) | ||||
−0.878899 | + | 0.477008i | \(0.841721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7687i | 2.13759i | ||||||||
\(236\) | 3.29420 | + | 0.425355i | 0.214434 | + | 0.0276882i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.08632 | + | 6.15693i | −0.200056 | + | 0.399095i | ||||
\(239\) | 8.76006 | 0.566641 | 0.283321 | − | 0.959025i | \(-0.408564\pi\) | ||||
0.283321 | + | 0.959025i | \(0.408564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.75236i | 0.177295i | 0.996063 | + | 0.0886476i | \(0.0282545\pi\) | ||||
−0.996063 | + | 0.0886476i | \(0.971745\pi\) | |||||||
\(242\) | 16.3882 | + | 18.6404i | 1.05348 | + | 1.19825i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.25147 | − | 9.69213i | 0.0801170 | − | 0.620475i | ||||
\(245\) | 20.2998i | 1.29691i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.61404i | 0.293584i | ||||||||
\(248\) | 18.9764 | − | 12.7823i | 1.20500 | − | 0.811680i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.9917 | + | 10.5429i | −0.758424 | + | 0.666791i | ||||
\(251\) | 2.61985i | 0.165364i | 0.996576 | + | 0.0826818i | \(0.0263485\pi\) | ||||
−0.996576 | + | 0.0826818i | \(0.973651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 30.1424i | − | 1.89503i | ||||||
\(254\) | 5.39431 | − | 4.74257i | 0.338469 | − | 0.297575i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.9353 | + | 7.86171i | 0.870958 | + | 0.491357i | ||||
\(257\) | − | 3.00640i | − | 0.187534i | −0.995594 | − | 0.0937669i | \(-0.970109\pi\) | ||
0.995594 | − | 0.0937669i | \(-0.0298908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.83487 | −0.611109 | ||||||||
\(260\) | −6.18060 | + | 47.8663i | −0.383305 | + | 2.96854i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.96969 | − | 11.3398i | −0.615930 | − | 0.700573i | ||||
\(263\) | −16.1476 | −0.995703 | −0.497852 | − | 0.867262i | \(-0.665878\pi\) | ||||
−0.497852 | + | 0.867262i | \(0.665878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.1045i | − | 1.48073i | ||||||
\(266\) | −0.763764 | − | 0.868724i | −0.0468294 | − | 0.0532649i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.19040 | + | 16.9638i | −0.133800 | + | 1.03623i | ||||
\(269\) | 11.8650i | 0.723423i | 0.932290 | + | 0.361711i | \(0.117807\pi\) | ||||
−0.932290 | + | 0.361711i | \(0.882193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.12428i | − | 0.0682950i | −0.999417 | − | 0.0341475i | \(-0.989128\pi\) | ||
0.999417 | − | 0.0341475i | \(-0.0108716\pi\) | |||||||
\(272\) | 2.10712 | + | 16.3573i | 0.127763 | + | 0.991805i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0392592 | − | 0.0345159i | 0.00237174 | − | 0.00208518i | ||||
\(275\) | 43.3734 | 2.61551 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3663 | 0.983358 | 0.491679 | − | 0.870777i | \(-0.336383\pi\) | ||||
0.491679 | + | 0.870777i | \(0.336383\pi\) | |||||||
\(278\) | 19.7112 | − | 17.3297i | 1.18220 | − | 1.03936i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.75967 | − | 10.0353i | −0.403967 | − | 0.599722i | ||||
\(281\) | 0.186718i | 0.0111387i | 0.999984 | + | 0.00556934i | \(0.00177279\pi\) | ||||
−0.999984 | + | 0.00556934i | \(0.998227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 15.4116i | − | 0.916125i | −0.888920 | − | 0.458063i | \(-0.848544\pi\) | ||
0.888920 | − | 0.458063i | \(-0.151456\pi\) | |||||||
\(284\) | 3.43951 | + | 0.444116i | 0.204097 | + | 0.0263535i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 37.8128 | − | 33.2443i | 2.23592 | − | 1.96577i | ||||
\(287\) | 4.05046 | 0.239091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2060 | + | 11.8328i | −0.717999 | + | 0.696044i | ||||
\(290\) | 6.45423 | + | 7.34120i | 0.379006 | + | 0.431090i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.8348 | − | 2.30287i | −1.04370 | − | 0.134765i | ||||
\(293\) | −17.2373 | −1.00701 | −0.503507 | − | 0.863991i | \(-0.667957\pi\) | ||||
−0.503507 | + | 0.863991i | \(0.667957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.01499 | −0.350206 | ||||||||
\(296\) | −19.5331 | + | 13.1573i | −1.13534 | + | 0.764753i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.53599 | + | 5.15934i | 0.262763 | + | 0.298872i | ||||
\(299\) | −37.5870 | −2.17371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.14526 | 0.469485 | ||||||||
\(302\) | −15.7233 | + | 13.8236i | −0.904772 | + | 0.795457i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.67912 | − | 0.703597i | −0.153658 | − | 0.0403541i | ||||
\(305\) | 17.6972i | 1.01334i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0720 | 0.631911 | 0.315955 | − | 0.948774i | \(-0.397675\pi\) | ||||
0.315955 | + | 0.948774i | \(0.397675\pi\) | |||||||
\(308\) | −1.61640 | + | 12.5184i | −0.0921028 | + | 0.713300i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31.1172 | + | 27.3576i | −1.76734 | + | 1.55381i | ||||
\(311\) | − | 0.535200i | − | 0.0303484i | −0.999885 | − | 0.0151742i | \(-0.995170\pi\) | ||
0.999885 | − | 0.0151742i | \(-0.00483029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.9542i | 1.63659i | 0.574800 | + | 0.818294i | \(0.305080\pi\) | ||||
−0.574800 | + | 0.818294i | \(0.694920\pi\) | |||||||
\(314\) | 9.94027 | − | 8.73928i | 0.560962 | − | 0.493186i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.64947 | − | 12.7745i | 0.0927900 | − | 0.718622i | ||||
\(317\) | − | 32.4690i | − | 1.82364i | −0.410588 | − | 0.911821i | \(-0.634676\pi\) | ||
0.410588 | − | 0.911821i | \(-0.365324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.1973i | − | 0.570937i | ||||||
\(320\) | −26.8508 | − | 10.8879i | −1.50101 | − | 0.608652i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.07682 | − | 6.22179i | 0.394376 | − | 0.346727i | ||||
\(323\) | −1.07213 | − | 2.64628i | −0.0596552 | − | 0.147243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 54.0858i | − | 3.00014i | ||||||
\(326\) | −17.9791 | + | 15.8068i | −0.995769 | + | 0.875460i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.04465 | − | 5.41880i | 0.444192 | − | 0.299203i | ||||
\(329\) | 10.6865 | 0.589167 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5963 | −0.582428 | −0.291214 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291214 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(332\) | 22.5796 | + | 2.91553i | 1.23922 | + | 0.160010i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.74649 | + | 8.56892i | −0.533304 | + | 0.468870i | ||||
\(335\) | − | 30.9747i | − | 1.69233i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.48046i | − | 0.135119i | −0.997715 | − | 0.0675596i | \(-0.978479\pi\) | ||
0.997715 | − | 0.0675596i | \(-0.0215213\pi\) | |||||||
\(338\) | −29.3159 | − | 33.3446i | −1.59457 | − | 1.81371i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.57765 | − | 28.8888i | −0.410956 | − | 1.56671i | ||||
\(341\) | 43.2232 | 2.34067 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.8882 | 0.803885 | ||||||||
\(344\) | 16.1773 | − | 10.8969i | 0.872224 | − | 0.587522i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.61342 | + | 3.17684i | −0.194259 | + | 0.170788i | ||||
\(347\) | −4.66781 | −0.250581 | −0.125291 | − | 0.992120i | \(-0.539986\pi\) | ||||
−0.125291 | + | 0.992120i | \(0.539986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8707i | 0.956597i | 0.878197 | + | 0.478298i | \(0.158746\pi\) | ||||
−0.878197 | + | 0.478298i | \(0.841254\pi\) | |||||||
\(350\) | 8.95286 | + | 10.1832i | 0.478551 | + | 0.544315i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.5370 | + | 27.0253i | 0.721525 | + | 1.44045i | ||||
\(353\) | − | 4.04601i | − | 0.215347i | −0.994186 | − | 0.107674i | \(-0.965660\pi\) | ||
0.994186 | − | 0.107674i | \(-0.0343401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.28030 | −0.333324 | ||||||||
\(356\) | 16.1425 | + | 2.08435i | 0.855550 | + | 0.110470i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.5944 | + | 24.2605i | −1.45841 | + | 1.28221i | ||||
\(359\) | 23.4791 | 1.23918 | 0.619590 | − | 0.784926i | \(-0.287299\pi\) | ||||
0.619590 | + | 0.784926i | \(0.287299\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5205 | −0.974761 | ||||||||
\(362\) | −17.1094 | − | 19.4606i | −0.899249 | − | 1.02283i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.6102 | + | 2.01562i | 0.818195 | + | 0.105647i | ||||
\(365\) | 32.5651 | 1.70454 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1347 | −0.685627 | −0.342813 | − | 0.939404i | \(-0.611380\pi\) | ||||
−0.342813 | + | 0.939404i | \(0.611380\pi\) | |||||||
\(368\) | 5.73166 | − | 21.8247i | 0.298783 | − | 1.13769i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 32.0300 | − | 28.1601i | 1.66516 | − | 1.46398i | ||||
\(371\) | −7.86095 | −0.408120 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.51304i | 0.389011i | 0.980901 | + | 0.194505i | \(0.0623101\pi\) | ||||
−0.980901 | + | 0.194505i | \(0.937690\pi\) | |||||||
\(374\) | −13.9619 | + | 27.8528i | −0.721955 | + | 1.44024i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.2246 | − | 14.2967i | 1.09457 | − | 0.737295i | ||||
\(377\) | −12.7158 | −0.654897 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.69855i | − | 0.498181i | −0.968480 | − | 0.249090i | \(-0.919868\pi\) | ||
0.968480 | − | 0.249090i | \(-0.0801317\pi\) | |||||||
\(380\) | 4.97482 | + | 0.642360i | 0.255203 | + | 0.0329524i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.67797 | + | 5.32084i | 0.239346 | + | 0.272238i | ||||
\(383\) | −26.7791 | −1.36835 | −0.684175 | − | 0.729318i | \(-0.739838\pi\) | ||||
−0.684175 | + | 0.729318i | \(0.739838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 22.8577i | − | 1.16493i | ||||||
\(386\) | 26.2937 | − | 23.1168i | 1.33831 | − | 1.17662i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.6683 | + | 1.76488i | 0.693901 | + | 0.0895980i | ||||
\(389\) | −23.0611 | −1.16924 | −0.584621 | − | 0.811306i | \(-0.698757\pi\) | ||||
−0.584621 | + | 0.811306i | \(0.698757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5572 | − | 8.73384i | 1.09019 | − | 0.441689i | ||||
\(392\) | 13.1484 | − | 8.85663i | 0.664094 | − | 0.447327i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.3313 | + | 16.1165i | −0.923516 | + | 0.811937i | ||||
\(395\) | 23.3253i | 1.17363i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9301 | 0.648944 | 0.324472 | − | 0.945895i | \(-0.394813\pi\) | ||||
0.324472 | + | 0.945895i | \(0.394813\pi\) | |||||||
\(398\) | 2.02301 | + | 2.30102i | 0.101404 | + | 0.115340i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 31.4046 | + | 8.24758i | 1.57023 | + | 0.412379i | ||||
\(401\) | 21.9768 | 1.09747 | 0.548734 | − | 0.835997i | \(-0.315110\pi\) | ||||
0.548734 | + | 0.835997i | \(0.315110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 53.8986i | − | 2.68488i | ||||||
\(404\) | −1.84891 | + | 14.3190i | −0.0919865 | + | 0.712399i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.39411 | − | 2.10486i | 0.118818 | − | 0.104462i | ||||
\(407\) | −44.4912 | −2.20535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7032 | −0.727026 | −0.363513 | − | 0.931589i | \(-0.618423\pi\) | ||||
−0.363513 | + | 0.931589i | \(0.618423\pi\) | |||||||
\(410\) | −13.1915 | + | 11.5977i | −0.651480 | + | 0.572768i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.3003 | − | 2.23385i | −0.852325 | − | 0.110054i | ||||
\(413\) | 1.96161i | 0.0965244i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.2288 | −2.02384 | ||||||||
\(416\) | 33.7000 | − | 16.8804i | 1.65228 | − | 0.827630i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.45513 | − | 3.92995i | −0.168996 | − | 0.192220i | ||||
\(419\) | −28.4797 | −1.39132 | −0.695662 | − | 0.718370i | \(-0.744889\pi\) | ||||
−0.695662 | + | 0.718370i | \(0.744889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.5326i | − | 0.757013i | −0.925599 | − | 0.378506i | \(-0.876438\pi\) | ||
0.925599 | − | 0.378506i | \(-0.123562\pi\) | |||||||
\(422\) | −17.7679 | + | 15.6212i | −0.864930 | + | 0.760429i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.6127 | + | 10.5166i | −0.758219 | + | 0.510729i | ||||
\(425\) | 12.5676 | + | 31.0197i | 0.609617 | + | 1.50468i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.77140 | 0.279298 | ||||||||
\(428\) | −3.49534 | + | 27.0700i | −0.168954 | + | 1.30848i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.5273 | + | 23.3223i | −1.27926 | + | 1.12470i | ||||
\(431\) | − | 10.4813i | − | 0.504867i | −0.967614 | − | 0.252434i | \(-0.918769\pi\) | ||
0.967614 | − | 0.252434i | \(-0.0812309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96586 | 0.382815 | 0.191407 | − | 0.981511i | \(-0.438695\pi\) | ||||
0.191407 | + | 0.981511i | \(0.438695\pi\) | |||||||
\(434\) | 8.92187 | + | 10.1479i | 0.428263 | + | 0.487117i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.30491 | + | 25.5952i | −0.158276 | + | 1.22579i | ||||
\(437\) | 3.90647i | 0.186872i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.7122 | 1.51354 | 0.756770 | − | 0.653681i | \(-0.226776\pi\) | ||||
0.756770 | + | 0.653681i | \(0.226776\pi\) | |||||||
\(440\) | −30.5795 | − | 45.3978i | −1.45782 | − | 2.16425i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 34.7320 | + | 17.4103i | 1.65203 | + | 0.828123i | ||||
\(443\) | − | 13.3688i | − | 0.635171i | −0.948230 | − | 0.317586i | \(-0.897128\pi\) | ||
0.948230 | − | 0.317586i | \(-0.102872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.4751 | −1.39725 | ||||||||
\(446\) | −1.62604 | + | 1.42958i | −0.0769952 | + | 0.0676926i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.55076 | + | 8.75660i | −0.167758 | + | 0.413710i | ||||
\(449\) | 2.01452 | 0.0950712 | 0.0475356 | − | 0.998870i | \(-0.484863\pi\) | ||||
0.0475356 | + | 0.998870i | \(0.484863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.3236 | 0.862823 | ||||||||
\(452\) | 0.842301 | − | 6.52329i | 0.0396185 | − | 0.306830i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.5703 | − | 17.7100i | −0.730751 | − | 0.831174i | ||||
\(455\) | −28.5031 | −1.33625 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3281 | 1.23158 | 0.615788 | − | 0.787912i | \(-0.288838\pi\) | ||||
0.615788 | + | 0.787912i | \(0.288838\pi\) | |||||||
\(458\) | −2.86354 | + | 2.51757i | −0.133804 | + | 0.117638i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.23281 | + | 40.5260i | −0.243981 | + | 1.88953i | ||||
\(461\) | −19.3286 | −0.900225 | −0.450112 | − | 0.892972i | \(-0.648616\pi\) | ||||
−0.450112 | + | 0.892972i | \(0.648616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.3567i | 1.03901i | 0.854469 | + | 0.519503i | \(0.173883\pi\) | ||||
−0.854469 | + | 0.519503i | \(0.826117\pi\) | |||||||
\(464\) | 1.93904 | − | 7.38337i | 0.0900177 | − | 0.342764i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.0548 | − | 28.4979i | −1.16064 | − | 1.32014i | ||||
\(467\) | 19.0174i | 0.880022i | 0.897992 | + | 0.440011i | \(0.145025\pi\) | ||||
−0.897992 | + | 0.440011i | \(0.854975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1015 | −0.466442 | ||||||||
\(470\) | −34.8037 | + | 30.5987i | −1.60537 | + | 1.41141i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.62428 | + | 3.89596i | 0.120792 | + | 0.179326i | ||||
\(473\) | 36.8477 | 1.69426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.62123 | −0.257920 | ||||||||
\(476\) | −9.42122 | + | 2.47122i | −0.431821 | + | 0.113268i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.17995 | + | 9.30407i | 0.374142 | + | 0.425558i | ||||
\(479\) | 8.69335i | 0.397209i | 0.980080 | + | 0.198605i | \(0.0636409\pi\) | ||||
−0.980080 | + | 0.198605i | \(0.936359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.4797i | 2.52966i | ||||||||
\(482\) | −2.92329 | + | 2.57009i | −0.133152 | + | 0.117065i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.49499 | + | 34.8119i | −0.204318 | + | 1.58236i | ||||
\(485\) | −24.9573 | −1.13325 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7910 | 0.579616 | 0.289808 | − | 0.957085i | \(-0.406409\pi\) | ||||
0.289808 | + | 0.957085i | \(0.406409\pi\) | |||||||
\(488\) | 11.4626 | − | 7.72111i | 0.518888 | − | 0.349518i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.5605 | + | 18.9555i | −0.974003 | + | 0.856323i | ||||
\(491\) | 5.78080i | 0.260884i | 0.991456 | + | 0.130442i | \(0.0416396\pi\) | ||||
−0.991456 | + | 0.130442i | \(0.958360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.29287 | − | 2.95469i | 0.328454 | − | 0.133073i | ||||
\(494\) | −4.90057 | + | 4.30849i | −0.220487 | + | 0.193848i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.2959 | + | 8.21903i | 1.40523 | + | 0.369045i | ||||
\(497\) | 2.04813i | 0.0918713i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.8967i | − | 0.622100i | −0.950394 | − | 0.311050i | \(-0.899319\pi\) | ||
0.950394 | − | 0.311050i | \(-0.100681\pi\) | |||||||
\(500\) | −22.3952 | − | 2.89172i | −1.00155 | − | 0.129322i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.78255 | + | 2.44636i | −0.124191 | + | 0.109186i | ||||
\(503\) | 23.3528i | 1.04125i | 0.853785 | + | 0.520625i | \(0.174301\pi\) | ||||
−0.853785 | + | 0.520625i | \(0.825699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.1456i | − | 1.16346i | ||||||
\(506\) | 32.0142 | − | 28.1463i | 1.42321 | − | 1.25125i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0742 | + | 1.30080i | 0.446969 | + | 0.0577136i | ||||
\(509\) | −31.6573 | −1.40319 | −0.701593 | − | 0.712578i | \(-0.747527\pi\) | ||||
−0.701593 | + | 0.712578i | \(0.747527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.6201i | − | 0.469808i | ||||||
\(512\) | 4.66258 | + | 22.1418i | 0.206059 | + | 0.978540i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.19310 | − | 2.80730i | 0.140841 | − | 0.123825i | ||||
\(515\) | 31.5892 | 1.39198 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.3439 | 2.12616 | ||||||||
\(518\) | −9.18359 | − | 10.4456i | −0.403504 | − | 0.458955i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −56.6102 | + | 38.1321i | −2.48252 | + | 1.67220i | ||||
\(521\) | 26.9722 | 1.18167 | 0.590836 | − | 0.806791i | \(-0.298798\pi\) | ||||
0.590836 | + | 0.806791i | \(0.298798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9078 | 1.13287 | 0.566434 | − | 0.824107i | \(-0.308323\pi\) | ||||
0.566434 | + | 0.824107i | \(0.308323\pi\) | |||||||
\(524\) | 2.73450 | − | 21.1776i | 0.119457 | − | 0.925150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0783 | − | 17.1504i | −0.657443 | − | 0.747792i | ||||
\(527\) | 12.5241 | + | 30.9123i | 0.545557 | + | 1.34656i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.82300 | −0.383609 | ||||||||
\(530\) | 25.6014 | − | 22.5082i | 1.11205 | − | 0.977694i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.209487 | − | 1.62239i | 0.00908239 | − | 0.0703395i | ||||
\(533\) | − | 22.8491i | − | 0.989706i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 49.4280i | − | 2.13696i | ||||||
\(536\) | −20.0626 | + | 13.5140i | −0.866571 | + | 0.583714i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.6018 | + | 11.0793i | −0.543304 | + | 0.477662i | ||||
\(539\) | 29.9485 | 1.28997 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.8418 | 1.06803 | 0.534017 | − | 0.845474i | \(-0.320682\pi\) | ||||
0.534017 | + | 0.845474i | \(0.320682\pi\) | |||||||
\(542\) | 1.19410 | − | 1.04983i | 0.0512909 | − | 0.0450939i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.4055 | + | 17.5120i | −0.660505 | + | 0.750822i | ||||
\(545\) | − | 46.7351i | − | 2.00191i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4825i | 1.68815i | 0.536227 | + | 0.844074i | \(0.319849\pi\) | ||||
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(548\) | 0.0733188 | + | 0.00946709i | 0.00313203 | + | 0.000404414i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 40.5011 | + | 46.0669i | 1.72697 | + | 1.96430i | ||||
\(551\) | 1.32157i | 0.0563010i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.60687 | 0.323477 | ||||||||
\(554\) | 15.2825 | + | 17.3827i | 0.649292 | + | 0.738521i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.8117 | + | 4.75321i | 1.56116 | + | 0.201581i | ||||
\(557\) | −30.3318 | −1.28520 | −0.642599 | − | 0.766203i | \(-0.722144\pi\) | ||||
−0.642599 | + | 0.766203i | \(0.722144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 45.9484i | − | 1.94341i | ||||||
\(560\) | 4.34645 | − | 16.5502i | 0.183671 | − | 0.699372i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.198314 | + | 0.174353i | −0.00836536 | + | 0.00735466i | ||||
\(563\) | − | 38.1522i | − | 1.60792i | −0.594681 | − | 0.803962i | \(-0.702721\pi\) | ||
0.594681 | − | 0.803962i | \(-0.297279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9111i | 0.501102i | ||||||||
\(566\) | 16.3687 | − | 14.3910i | 0.688027 | − | 0.604900i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.74004 | + | 4.06781i | 0.114969 | + | 0.170681i | ||||
\(569\) | 3.84130i | 0.161036i | 0.996753 | + | 0.0805179i | \(0.0256574\pi\) | ||||
−0.996753 | + | 0.0805179i | \(0.974343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.9874i | − | 0.669051i | −0.942387 | − | 0.334526i | \(-0.891424\pi\) | ||
0.942387 | − | 0.334526i | \(-0.108576\pi\) | |||||||
\(572\) | 70.6176 | + | 9.11829i | 2.95267 | + | 0.381255i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.78223 | + | 4.30200i | 0.157867 | + | 0.179562i | ||||
\(575\) | − | 45.7918i | − | 1.90965i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9708 | −1.03955 | −0.519774 | − | 0.854304i | \(-0.673984\pi\) | ||||
−0.519774 | + | 0.854304i | \(0.673984\pi\) | |||||||
\(578\) | −23.9653 | − | 1.91483i | −0.996823 | − | 0.0796463i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.77028 | + | 13.7101i | −0.0735068 | + | 0.569281i | ||||
\(581\) | 13.4455i | 0.557815i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.5615 | −1.47281 | ||||||||
\(584\) | −14.2079 | − | 21.0927i | −0.587926 | − | 0.872824i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0958 | − | 18.3078i | −0.664912 | − | 0.756287i | ||||
\(587\) | 28.2425i | 1.16569i | 0.812582 | + | 0.582847i | \(0.198061\pi\) | ||||
−0.812582 | + | 0.582847i | \(0.801939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.60177 | −0.230817 | ||||||||
\(590\) | −5.61666 | − | 6.38852i | −0.231234 | − | 0.263011i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.2140 | − | 8.46013i | −1.32399 | − | 0.347709i | ||||
\(593\) | − | 20.5555i | − | 0.844115i | −0.906569 | − | 0.422057i | \(-0.861308\pi\) | ||
0.906569 | − | 0.422057i | \(-0.138692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3473 | − | 6.62308i | 0.670174 | − | 0.271520i | ||||
\(596\) | −1.24414 | + | 9.63535i | −0.0509619 | + | 0.394679i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −35.0979 | − | 39.9212i | −1.43526 | − | 1.63250i | ||||
\(599\) | 13.8198 | 0.564661 | 0.282330 | − | 0.959317i | \(-0.408893\pi\) | ||||
0.282330 | + | 0.959317i | \(0.408893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.46980i | 0.223118i | 0.993758 | + | 0.111559i | \(0.0355844\pi\) | ||||
−0.993758 | + | 0.111559i | \(0.964416\pi\) | |||||||
\(602\) | 7.60586 | + | 8.65109i | 0.309992 | + | 0.352592i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −29.3641 | − | 3.79155i | −1.19481 | − | 0.154276i | ||||
\(605\) | − | 63.5642i | − | 2.58425i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.9372 | −1.45864 | −0.729322 | − | 0.684170i | \(-0.760164\pi\) | ||||
−0.729322 | + | 0.684170i | \(0.760164\pi\) | |||||||
\(608\) | −1.75441 | − | 3.50250i | −0.0711506 | − | 0.142045i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.7962 | + | 16.5252i | −0.761035 | + | 0.669086i | ||||
\(611\) | − | 60.2840i | − | 2.43883i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6849i | 0.673899i | 0.941523 | + | 0.336949i | \(0.109395\pi\) | ||||
−0.941523 | + | 0.336949i | \(0.890605\pi\) | |||||||
\(614\) | 10.3388 | + | 11.7596i | 0.417238 | + | 0.474577i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.8051 | + | 9.97259i | −0.596515 | + | 0.401807i | ||||
\(617\) | −28.5025 | −1.14747 | −0.573734 | − | 0.819042i | \(-0.694506\pi\) | ||||
−0.573734 | + | 0.819042i | \(0.694506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.1142i | − | 1.04962i | −0.851219 | − | 0.524810i | \(-0.824136\pi\) | ||
0.851219 | − | 0.524810i | \(-0.175864\pi\) | |||||||
\(620\) | −58.1131 | − | 7.50369i | −2.33388 | − | 0.301355i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.568437 | − | 0.499758i | 0.0227922 | − | 0.0200385i | ||||
\(623\) | 9.61241i | 0.385113i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.305155 | 0.0122062 | ||||||||
\(626\) | −30.7523 | + | 27.0368i | −1.22911 | + | 1.08061i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.5640 | + | 2.39702i | 0.740785 | + | 0.0956517i | ||||
\(629\) | −12.8915 | − | 31.8191i | −0.514016 | − | 1.26871i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.2773i | − | 1.00627i | −0.864207 | − | 0.503136i | \(-0.832180\pi\) | ||
0.864207 | − | 0.503136i | \(-0.167820\pi\) | |||||||
\(632\) | 15.1080 | − | 10.1766i | 0.600966 | − | 0.404805i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.4854 | − | 30.3189i | 1.36959 | − | 1.20412i | ||||
\(635\) | −18.3947 | −0.729973 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 37.3452i | − | 1.47967i | ||||||
\(638\) | 10.8305 | − | 9.52198i | 0.428785 | − | 0.376979i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.5087 | − | 38.6852i | −0.533977 | − | 1.52917i | ||||
\(641\) | −33.8918 | −1.33864 | −0.669322 | − | 0.742972i | \(-0.733415\pi\) | ||||
−0.669322 | + | 0.742972i | \(0.733415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.7558i | 1.05514i | 0.849510 | + | 0.527572i | \(0.176897\pi\) | ||||
−0.849510 | + | 0.527572i | \(0.823103\pi\) | |||||||
\(644\) | 13.2163 | + | 1.70652i | 0.520797 | + | 0.0672465i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.80948 | − | 3.60975i | 0.0711930 | − | 0.142024i | ||||
\(647\) | −14.6489 | −0.575907 | −0.287954 | − | 0.957644i | \(-0.592975\pi\) | ||||
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.87396i | 0.348333i | ||||||||
\(650\) | 57.4446 | − | 50.5041i | 2.25316 | − | 1.98094i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.5769 | − | 4.33553i | −1.31497 | − | 0.169792i | ||||
\(653\) | 39.0328i | 1.52747i | 0.645528 | + | 0.763736i | \(0.276637\pi\) | ||||
−0.645528 | + | 0.763736i | \(0.723363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.6689i | 1.51092i | ||||||||
\(656\) | 13.2672 | + | 3.48428i | 0.517998 | + | 0.136038i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.97884 | + | 11.3502i | 0.389016 | + | 0.442476i | ||||
\(659\) | − | 36.4228i | − | 1.41883i | −0.704790 | − | 0.709416i | \(-0.748959\pi\) | ||
0.704790 | − | 0.709416i | \(-0.251041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8077i | 1.15938i | 0.814835 | + | 0.579692i | \(0.196827\pi\) | ||||
−0.814835 | + | 0.579692i | \(0.803173\pi\) | |||||||
\(662\) | −9.89464 | − | 11.2544i | −0.384566 | − | 0.437415i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.9877 | + | 26.7043i | 0.698060 | + | 1.03633i | ||||
\(665\) | 2.96237i | 0.114876i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.7658 | −0.416855 | ||||||||
\(668\) | −18.2021 | − | 2.35030i | −0.704261 | − | 0.0909357i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.8982 | − | 28.9234i | 1.27097 | − | 1.11741i | ||||
\(671\) | 26.1088 | 1.00792 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.12932i | 0.0435321i | 0.999763 | + | 0.0217661i | \(0.00692890\pi\) | ||||
−0.999763 | + | 0.0217661i | \(0.993071\pi\) | |||||||
\(674\) | 2.63450 | − | 2.31620i | 0.101477 | − | 0.0892166i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.04081 | − | 62.2729i | 0.309262 | − | 2.39511i | ||||
\(677\) | − | 18.5385i | − | 0.712493i | −0.934392 | − | 0.356247i | \(-0.884056\pi\) | ||
0.934392 | − | 0.356247i | \(-0.115944\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.13908i | 0.312349i | ||||||||
\(680\) | 23.6070 | − | 35.0239i | 0.905287 | − | 1.34311i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 40.3609 | + | 45.9074i | 1.54550 | + | 1.75789i | ||||
\(683\) | −32.0323 | −1.22568 | −0.612841 | − | 0.790206i | \(-0.709974\pi\) | ||||
−0.612841 | + | 0.790206i | \(0.709974\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.133875 | −0.00511511 | ||||||||
\(686\) | 13.9022 | + | 15.8127i | 0.530790 | + | 0.603733i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 26.6797 | + | 7.00669i | 1.01715 | + | 0.267128i | ||||
\(689\) | 44.3446i | 1.68939i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8752i | 0.756087i | 0.925788 | + | 0.378043i | \(0.123403\pi\) | ||||
−0.925788 | + | 0.378043i | \(0.876597\pi\) | |||||||
\(692\) | −6.74826 | − | 0.871350i | −0.256530 | − | 0.0331238i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.35870 | − | 4.95769i | −0.165454 | − | 0.188191i | ||||
\(695\) | −67.2156 | −2.54963 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.30931 | + | 13.1046i | 0.201104 | + | 0.496373i | ||||
\(698\) | −18.9805 | + | 16.6873i | −0.718422 | + | 0.631622i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.45561 | + | 19.0177i | −0.0928132 | + | 0.718801i | ||||
\(701\) | −10.8001 | −0.407915 | −0.203958 | − | 0.978980i | \(-0.565380\pi\) | ||||
−0.203958 | + | 0.978980i | \(0.565380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.76609 | 0.217472 | ||||||||
\(704\) | −16.0630 | + | 39.6132i | −0.605397 | + | 1.49298i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.29727 | − | 3.77807i | 0.161730 | − | 0.142190i | ||||
\(707\) | −8.52661 | −0.320676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6286 | 0.586945 | 0.293473 | − | 0.955968i | \(-0.405189\pi\) | ||||
0.293473 | + | 0.955968i | \(0.405189\pi\) | |||||||
\(710\) | −5.86440 | − | 6.67031i | −0.220087 | − | 0.250332i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.8597 | + | 19.0913i | 0.481938 | + | 0.715476i | ||||
\(713\) | − | 45.6332i | − | 1.70898i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −128.943 | −4.82219 | ||||||||
\(716\) | −51.5341 | − | 6.65420i | −1.92592 | − | 0.248679i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.9243 | + | 24.9372i | 0.818206 | + | 0.930647i | ||||
\(719\) | 1.93732i | 0.0722499i | 0.999347 | + | 0.0361250i | \(0.0115014\pi\) | ||||
−0.999347 | + | 0.0361250i | \(0.988499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.3019i | − | 0.383661i | ||||||
\(722\) | −17.2940 | − | 19.6706i | −0.643616 | − | 0.732064i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.69279 | − | 36.3438i | 0.174406 | − | 1.35071i | ||||
\(725\) | − | 15.4915i | − | 0.575341i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.5491i | − | 1.05883i | −0.848363 | − | 0.529414i | \(-0.822412\pi\) | ||
0.848363 | − | 0.529414i | \(-0.177588\pi\) | |||||||
\(728\) | 12.4356 | + | 18.4617i | 0.460895 | + | 0.684237i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 30.4086 | + | 34.5875i | 1.12547 | + | 1.28014i | ||||
\(731\) | 10.6767 | + | 26.3526i | 0.394893 | + | 0.974688i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.4163i | − | 0.421671i | −0.977522 | − | 0.210836i | \(-0.932382\pi\) | ||
0.977522 | − | 0.210836i | \(-0.0676185\pi\) | |||||||
\(734\) | −12.2649 | − | 13.9504i | −0.452706 | − | 0.514919i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.5321 | − | 14.2918i | 1.05171 | − | 0.526802i | ||||
\(737\) | −45.6972 | −1.68328 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0328 | 1.39906 | 0.699529 | − | 0.714604i | \(-0.253393\pi\) | ||||
0.699529 | + | 0.714604i | \(0.253393\pi\) | |||||||
\(740\) | 59.8178 | + | 7.72381i | 2.19895 | + | 0.283933i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.34038 | − | 8.34913i | −0.269474 | − | 0.306506i | ||||
\(743\) | − | 20.6846i | − | 0.758844i | −0.925224 | − | 0.379422i | \(-0.876123\pi\) | ||
0.925224 | − | 0.379422i | \(-0.123877\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 17.5935i | − | 0.644576i | ||||||
\(746\) | −7.97961 | + | 7.01551i | −0.292154 | + | 0.256856i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −42.6199 | + | 11.1794i | −1.55834 | + | 0.408758i | ||||
\(749\) | −16.1195 | −0.588993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.04847 | −0.293693 | −0.146846 | − | 0.989159i | \(-0.546912\pi\) | ||||
−0.146846 | + | 0.989159i | \(0.546912\pi\) | |||||||
\(752\) | 35.0036 | + | 9.19274i | 1.27645 | + | 0.335225i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.8737 | − | 13.5055i | −0.432416 | − | 0.491840i | ||||
\(755\) | 53.6168 | 1.95131 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6017i | 0.603399i | 0.953403 | + | 0.301700i | \(0.0975539\pi\) | ||||
−0.953403 | + | 0.301700i | \(0.902446\pi\) | |||||||
\(758\) | 10.3008 | − | 9.05629i | 0.374143 | − | 0.328939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.96313 | + | 5.88359i | 0.143758 | + | 0.213420i | ||||
\(761\) | 20.8942i | 0.757415i | 0.925516 | + | 0.378708i | \(0.123631\pi\) | ||||
−0.925516 | + | 0.378708i | \(0.876369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.2412 | −0.551770 | ||||||||
\(764\) | −1.28308 | + | 9.93696i | −0.0464203 | + | 0.359507i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.0058 | − | 28.4422i | −0.903495 | − | 1.02766i | ||||
\(767\) | 11.0657 | 0.399558 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0767 | 0.435496 | 0.217748 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217748 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(770\) | 24.2772 | − | 21.3440i | 0.874888 | − | 0.769184i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 49.1049 | + | 6.34053i | 1.76732 | + | 0.228201i | ||||
\(773\) | −8.74673 | −0.314598 | −0.157299 | − | 0.987551i | \(-0.550279\pi\) | ||||
−0.157299 | + | 0.987551i | \(0.550279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.6640 | 2.35872 | ||||||||
\(776\) | 10.8886 | + | 16.1651i | 0.390879 | + | 0.580292i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.5339 | − | 24.4932i | −0.772028 | − | 0.878123i | ||||
\(779\) | −2.37475 | −0.0850842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.26538i | 0.331541i | ||||||||
\(782\) | 29.4058 | + | 14.7404i | 1.05155 | + | 0.527116i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.6843 | + | 5.69480i | 0.774439 | + | 0.203386i | ||||
\(785\) | −33.8966 | −1.20982 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.83239i | 0.100964i | 0.998725 | + | 0.0504819i | \(0.0160757\pi\) | ||||
−0.998725 | + | 0.0504819i | \(0.983924\pi\) | |||||||
\(788\) | −34.2347 | − | 4.42046i | −1.21956 | − | 0.157472i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.7739 | + | 21.7807i | −0.881415 | + | 0.774922i | ||||
\(791\) | 3.88444 | 0.138115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 32.5571i | − | 1.15614i | ||||||
\(794\) | 12.0739 | + | 13.7331i | 0.428485 | + | 0.487369i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.554875 | + | 4.29729i | −0.0196670 | + | 0.152313i | ||||
\(797\) | 4.90753 | 0.173834 | 0.0869168 | − | 0.996216i | \(-0.472299\pi\) | ||||
0.0869168 | + | 0.996216i | \(0.472299\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0078 | + | 34.5745i | 0.495560 | + | 1.22316i | ||||
\(800\) | 20.5652 | + | 41.0563i | 0.727089 | + | 1.45156i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.5214 | + | 23.3415i | 0.724636 | + | 0.824219i | ||||
\(803\) | − | 48.0436i | − | 1.69542i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.1321 | −0.850546 | ||||||||
\(806\) | 57.2458 | − | 50.3293i | 2.01640 | − | 1.77277i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.9347 | + | 11.4071i | −0.595762 | + | 0.401300i | ||||
\(809\) | 9.49156 | 0.333705 | 0.166853 | − | 0.985982i | \(-0.446640\pi\) | ||||
0.166853 | + | 0.985982i | \(0.446640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.48311i | 0.297882i | 0.988846 | + | 0.148941i | \(0.0475865\pi\) | ||||
−0.988846 | + | 0.148941i | \(0.952414\pi\) | |||||||
\(812\) | 4.47114 | + | 0.577323i | 0.156906 | + | 0.0202601i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −41.5449 | − | 47.2541i | −1.45615 | − | 1.65626i | ||||
\(815\) | 61.3092 | 2.14757 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.77549 | −0.167073 | ||||||||
\(818\) | −13.7295 | − | 15.6163i | −0.480041 | − | 0.546010i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.6358 | − | 3.18103i | −0.860319 | − | 0.111086i | ||||
\(821\) | 8.83437i | 0.308322i | 0.988046 | + | 0.154161i | \(0.0492674\pi\) | ||||
−0.988046 | + | 0.154161i | \(0.950733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.67818 | −0.197929 | −0.0989644 | − | 0.995091i | \(-0.531553\pi\) | ||||
−0.0989644 | + | 0.995091i | \(0.531553\pi\) | |||||||
\(824\) | −13.7821 | − | 20.4606i | −0.480121 | − | 0.712778i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08343 | + | 1.83171i | −0.0724917 | + | 0.0637332i | ||||
\(827\) | −13.2629 | −0.461195 | −0.230597 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230597 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.07928i | 0.0722165i | 0.999348 | + | 0.0361083i | \(0.0114961\pi\) | ||||
−0.999348 | + | 0.0361083i | \(0.988504\pi\) | |||||||
\(830\) | −38.4985 | − | 43.7892i | −1.33630 | − | 1.51994i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 49.3970 | + | 20.0303i | 1.71253 | + | 0.694425i | ||||
\(833\) | 8.67767 | + | 21.4185i | 0.300664 | + | 0.742108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.2358 | 1.15017 | ||||||||
\(836\) | 0.947679 | − | 7.33940i | 0.0327762 | − | 0.253838i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.5937 | − | 30.2483i | −0.918664 | − | 1.04491i | ||||
\(839\) | 15.0806i | 0.520641i | 0.965522 | + | 0.260321i | \(0.0838283\pi\) | ||||
−0.965522 | + | 0.260321i | \(0.916172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.3579 | 0.874410 | ||||||||
\(842\) | 16.4972 | − | 14.5040i | 0.568531 | − | 0.499841i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.1826 | − | 4.28461i | −1.14219 | − | 0.147482i | ||||
\(845\) | 113.706i | 3.91160i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.7296 | −0.712276 | ||||||||
\(848\) | −25.7484 | − | 6.76213i | −0.884205 | − | 0.232212i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.2107 | + | 42.3136i | −0.727523 | + | 1.45134i | ||||
\(851\) | 46.9719i | 1.61017i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.3284 | −0.456356 | −0.228178 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228178 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(854\) | 5.38920 | + | 6.12981i | 0.184415 | + | 0.209758i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.0150 | + | 21.5650i | −1.09425 | + | 0.737076i | ||||
\(857\) | 17.5303 | 0.598825 | 0.299412 | − | 0.954124i | \(-0.403209\pi\) | ||||
0.299412 | + | 0.954124i | \(0.403209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.7587 | −1.73187 | −0.865933 | − | 0.500160i | \(-0.833274\pi\) | ||||
−0.865933 | + | 0.500160i | \(0.833274\pi\) | |||||||
\(860\) | −49.5412 | − | 6.39687i | −1.68934 | − | 0.218131i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.1322 | − | 9.78722i | 0.379165 | − | 0.333354i | ||||
\(863\) | −48.9159 | −1.66512 | −0.832558 | − | 0.553938i | \(-0.813125\pi\) | ||||
−0.832558 | + | 0.553938i | \(0.813125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3219 | 0.418956 | ||||||||
\(866\) | 7.43835 | + | 8.46055i | 0.252765 | + | 0.287501i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.44710 | + | 18.9519i | −0.0830601 | + | 0.643268i | ||||
\(869\) | 34.4121 | 1.16735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.9835i | 1.93081i | ||||||||
\(872\) | −30.2707 | + | 20.3901i | −1.02510 | + | 0.690495i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.14907 | + | 3.64778i | −0.140344 | + | 0.123388i | ||||
\(875\) | − | 13.3358i | − | 0.450831i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.26891 | 0.177919 | 0.0889593 | − | 0.996035i | \(-0.471646\pi\) | ||||
0.0889593 | + | 0.996035i | \(0.471646\pi\) | |||||||
\(878\) | 29.6121 | + | 33.6816i | 0.999361 | + | 1.13670i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.6626 | − | 74.8699i | 0.662825 | − | 2.52387i | ||||
\(881\) | −37.7030 | −1.27025 | −0.635123 | − | 0.772411i | \(-0.719050\pi\) | ||||
−0.635123 | + | 0.772411i | \(0.719050\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.8547 | −0.600857 | −0.300428 | − | 0.953804i | \(-0.597130\pi\) | ||||
−0.300428 | + | 0.953804i | \(0.597130\pi\) | |||||||
\(884\) | 13.9405 | + | 53.1462i | 0.468868 | + | 1.78750i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.1990 | − | 12.4835i | 0.477026 | − | 0.419391i | ||||
\(887\) | − | 39.8319i | − | 1.33743i | −0.743521 | − | 0.668713i | \(-0.766846\pi\) | ||
0.743521 | − | 0.668713i | \(-0.233154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.99890i | 0.201196i | ||||||||
\(890\) | −27.5232 | − | 31.3055i | −0.922579 | − | 1.04936i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.03672 | − | 0.392108i | −0.101677 | − | 0.0131287i | ||||
\(893\) | −6.26541 | −0.209664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 94.0978 | 3.14534 | ||||||||
\(896\) | −12.6160 | + | 4.40545i | −0.421472 | + | 0.147176i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.88112 | + | 2.13963i | 0.0627736 | + | 0.0714002i | ||||
\(899\) | − | 15.4379i | − | 0.514883i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.3041 | − | 25.4328i | −0.343278 | − | 0.847290i | ||||
\(902\) | 17.1101 | + | 19.4615i | 0.569705 | + | 0.647996i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.71491 | − | 5.19669i | 0.256594 | − | 0.172839i | ||||
\(905\) | 66.3613i | 2.20592i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.27025i | − | 0.307814i | −0.988085 | − | 0.153907i | \(-0.950814\pi\) | ||
0.988085 | − | 0.153907i | \(-0.0491856\pi\) | |||||||
\(908\) | 4.27065 | − | 33.0745i | 0.141726 | − | 1.09762i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.6156 | − | 30.2732i | −0.882297 | − | 1.00355i | ||||
\(911\) | 13.7439i | 0.455356i | 0.973737 | + | 0.227678i | \(0.0731133\pi\) | ||||
−0.973737 | + | 0.227678i | \(0.926887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.8252i | 2.01302i | ||||||||
\(914\) | 24.5846 | + | 27.9631i | 0.813186 | + | 0.924938i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.34782 | − | 0.690522i | −0.176697 | − | 0.0228155i | ||||
\(917\) | 12.6107 | 0.416442 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.85281i | − | 0.193066i | −0.995330 | − | 0.0965332i | \(-0.969225\pi\) | ||
0.995330 | − | 0.0965332i | \(-0.0307754\pi\) | |||||||
\(920\) | −47.9290 | + | 32.2845i | −1.58017 | + | 1.06439i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.0487 | − | 20.5290i | −0.594401 | − | 0.676086i | ||||
\(923\) | 11.5538 | 0.380297 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −67.5903 | −2.22235 | ||||||||
\(926\) | −23.7451 | + | 20.8762i | −0.780312 | + | 0.686035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.65252 | − | 4.83497i | 0.316859 | − | 0.158716i | ||||
\(929\) | 23.8045 | 0.780999 | 0.390500 | − | 0.920603i | \(-0.372302\pi\) | ||||
0.390500 | + | 0.920603i | \(0.372302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.88135 | −0.127206 | ||||||||
\(932\) | 6.87206 | − | 53.2214i | 0.225102 | − | 1.74332i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.1984 | + | 17.7581i | −0.660913 | + | 0.581061i | ||||
\(935\) | 73.9522 | − | 29.9616i | 2.41850 | − | 0.979850i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.7531 | −0.873986 | −0.436993 | − | 0.899465i | \(-0.643956\pi\) | ||||
−0.436993 | + | 0.899465i | \(0.643956\pi\) | |||||||
\(938\) | −9.43252 | − | 10.7288i | −0.307983 | − | 0.350307i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −64.9978 | − | 8.39265i | −2.11999 | − | 0.273738i | ||||
\(941\) | − | 3.36287i | − | 0.109627i | −0.998497 | − | 0.0548133i | \(-0.982544\pi\) | ||
0.998497 | − | 0.0548133i | \(-0.0174564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.3452i | − | 0.629967i | ||||||
\(944\) | −1.68741 | + | 6.42522i | −0.0549205 | + | 0.209123i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.4075 | + | 39.1359i | 1.11868 | + | 1.27242i | ||||
\(947\) | 45.7558 | 1.48686 | 0.743432 | − | 0.668812i | \(-0.233197\pi\) | ||||
0.743432 | + | 0.668812i | \(0.233197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −59.9095 | −1.94474 | ||||||||
\(950\) | −5.24898 | − | 5.97031i | −0.170299 | − | 0.193703i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.4220 | − | 7.69871i | −0.370190 | − | 0.249517i | ||||
\(953\) | 22.5083i | 0.729115i | 0.931181 | + | 0.364557i | \(0.118780\pi\) | ||||
−0.931181 | + | 0.364557i | \(0.881220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 18.1442i | − | 0.587133i | ||||||
\(956\) | −2.24361 | + | 17.3759i | −0.0725636 | + | 0.561976i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.23321 | + | 8.11765i | −0.298312 | + | 0.262269i | ||||
\(959\) | 0.0436594i | 0.00140983i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.4367 | 1.11086 | ||||||||
\(962\) | −58.9250 | + | 51.8057i | −1.89982 | + | 1.67028i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.45940 | − | 0.704930i | −0.175836 | − | 0.0227043i | ||||
\(965\) | −89.6621 | −2.88632 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27.3288i | − | 0.878834i | −0.898283 | − | 0.439417i | \(-0.855185\pi\) | ||
0.898283 | − | 0.439417i | \(-0.144815\pi\) | |||||||
\(968\) | −41.1711 | + | 27.7325i | −1.32329 | + | 0.891355i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.3046 | − | 26.5072i | −0.748265 | − | 0.851094i | ||||
\(971\) | − | 49.4412i | − | 1.58664i | −0.608803 | − | 0.793321i | \(-0.708350\pi\) | ||
0.608803 | − | 0.793321i | \(-0.291650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.9204i | 0.702735i | ||||||||
\(974\) | 11.9440 | + | 13.5854i | 0.382709 | + | 0.435303i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.9041 | + | 4.96466i | 0.605106 | + | 0.158915i | ||||
\(977\) | 9.91996i | 0.317368i | 0.987329 | + | 0.158684i | \(0.0507251\pi\) | ||||
−0.987329 | + | 0.158684i | \(0.949275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.4848i | 1.38978i | ||||||||
\(980\) | −40.2654 | − | 5.19915i | −1.28623 | − | 0.166081i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.13979 | + | 5.39798i | −0.195929 | + | 0.172256i | ||||
\(983\) | 34.8952i | 1.11298i | 0.830853 | + | 0.556491i | \(0.187853\pi\) | ||||
−0.830853 | + | 0.556491i | \(0.812147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62.5102 | 1.99174 | ||||||||
\(986\) | 9.94810 | + | 4.98674i | 0.316812 | + | 0.158810i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.15209 | − | 1.18174i | −0.291167 | − | 0.0375961i | ||||
\(989\) | − | 38.9022i | − | 1.23702i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1366 | −0.353766 | −0.176883 | − | 0.984232i | \(-0.556601\pi\) | ||||
−0.176883 | + | 0.984232i | \(0.556601\pi\) | |||||||
\(992\) | 20.4940 | + | 40.9142i | 0.650685 | + | 1.29903i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.17532 | + | 1.91250i | −0.0689971 | + | 0.0606608i | ||||
\(995\) | − | 7.84656i | − | 0.248753i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5272 | 0.460082 | 0.230041 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230041 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(998\) | 14.7597 | − | 12.9764i | 0.467209 | − | 0.410761i | ||||
\(999\) | 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 | 1224.2.h.c.611.40 | yes | 56 | |
3.2 | odd | 2 | inner | 1224.2.h.c.611.17 | ✓ | 56 | |
4.3 | odd | 2 | 4896.2.h.c.2447.51 | 56 | |||
8.3 | odd | 2 | inner | 1224.2.h.c.611.20 | yes | 56 | |
8.5 | even | 2 | 4896.2.h.c.2447.48 | 56 | |||
12.11 | even | 2 | 4896.2.h.c.2447.10 | 56 | |||
17.16 | even | 2 | inner | 1224.2.h.c.611.39 | yes | 56 | |
24.5 | odd | 2 | 4896.2.h.c.2447.5 | 56 | |||
24.11 | even | 2 | inner | 1224.2.h.c.611.37 | yes | 56 | |
51.50 | odd | 2 | inner | 1224.2.h.c.611.18 | yes | 56 | |
68.67 | odd | 2 | 4896.2.h.c.2447.6 | 56 | |||
136.67 | odd | 2 | inner | 1224.2.h.c.611.19 | yes | 56 | |
136.101 | even | 2 | 4896.2.h.c.2447.9 | 56 | |||
204.203 | even | 2 | 4896.2.h.c.2447.47 | 56 | |||
408.101 | odd | 2 | 4896.2.h.c.2447.52 | 56 | |||
408.203 | even | 2 | inner | 1224.2.h.c.611.38 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1224.2.h.c.611.17 | ✓ | 56 | 3.2 | odd | 2 | inner | |
1224.2.h.c.611.18 | yes | 56 | 51.50 | odd | 2 | inner | |
1224.2.h.c.611.19 | yes | 56 | 136.67 | odd | 2 | inner | |
1224.2.h.c.611.20 | yes | 56 | 8.3 | odd | 2 | inner | |
1224.2.h.c.611.37 | yes | 56 | 24.11 | even | 2 | inner | |
1224.2.h.c.611.38 | yes | 56 | 408.203 | even | 2 | inner | |
1224.2.h.c.611.39 | yes | 56 | 17.16 | even | 2 | inner | |
1224.2.h.c.611.40 | yes | 56 | 1.1 | even | 1 | trivial | |
4896.2.h.c.2447.5 | 56 | 24.5 | odd | 2 | |||
4896.2.h.c.2447.6 | 56 | 68.67 | odd | 2 | |||
4896.2.h.c.2447.9 | 56 | 136.101 | even | 2 | |||
4896.2.h.c.2447.10 | 56 | 12.11 | even | 2 | |||
4896.2.h.c.2447.47 | 56 | 204.203 | even | 2 | |||
4896.2.h.c.2447.48 | 56 | 8.5 | even | 2 | |||
4896.2.h.c.2447.51 | 56 | 4.3 | odd | 2 | |||
4896.2.h.c.2447.52 | 56 | 408.101 | odd | 2 |