Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [345,3,Mod(229,345)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(345, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("345.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 345 = 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 345.d (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: | \(9.40056912043\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.16 | ||
Character | \(\chi\) | \(=\) | 345.229 |
Dual form | 345.3.d.a.229.34 |
$q$-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 \(\left(\mathbb{Z}/345\mathbb{Z}\right)^\times\).
\(n\) | \(116\) | \(166\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.48820i | − | 0.744102i | −0.928212 | − | 0.372051i | \(-0.878655\pi\) | ||
0.928212 | − | 0.372051i | \(-0.121345\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 1.78525 | 0.446312 | ||||||||
\(5\) | 0.794027 | − | 4.93655i | 0.158805 | − | 0.987310i | ||||
\(6\) | −2.57765 | −0.429608 | ||||||||
\(7\) | 12.7168 | 1.81668 | 0.908341 | − | 0.418230i | \(-0.137349\pi\) | ||||
0.908341 | + | 0.418230i | \(0.137349\pi\) | |||||||
\(8\) | − | 8.60963i | − | 1.07620i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −7.34659 | − | 1.18167i | −0.734659 | − | 0.118167i | ||||
\(11\) | − | 4.27531i | − | 0.388664i | −0.980936 | − | 0.194332i | \(-0.937746\pi\) | ||
0.980936 | − | 0.194332i | \(-0.0622540\pi\) | |||||||
\(12\) | − | 3.09214i | − | 0.257678i | ||||||
\(13\) | 15.4363i | 1.18741i | 0.804683 | + | 0.593705i | \(0.202335\pi\) | ||||
−0.804683 | + | 0.593705i | \(0.797665\pi\) | |||||||
\(14\) | − | 18.9252i | − | 1.35180i | ||||||
\(15\) | −8.55035 | − | 1.37530i | −0.570024 | − | 0.0916864i | ||||
\(16\) | −5.67190 | −0.354493 | ||||||||
\(17\) | 30.8454 | 1.81443 | 0.907216 | − | 0.420664i | \(-0.138203\pi\) | ||||
0.907216 | + | 0.420664i | \(0.138203\pi\) | |||||||
\(18\) | 4.46461i | 0.248034i | ||||||||
\(19\) | 10.7704i | 0.566864i | 0.958992 | + | 0.283432i | \(0.0914730\pi\) | ||||
−0.958992 | + | 0.283432i | \(0.908527\pi\) | |||||||
\(20\) | 1.41754 | − | 8.81297i | 0.0708768 | − | 0.440648i | ||||
\(21\) | − | 22.0261i | − | 1.04886i | ||||||
\(22\) | −6.36253 | −0.289206 | ||||||||
\(23\) | −7.86140 | + | 21.6148i | −0.341800 | + | 0.939773i | ||||
\(24\) | −14.9123 | −0.621347 | ||||||||
\(25\) | −23.7390 | − | 7.83951i | −0.949562 | − | 0.313580i | ||||
\(26\) | 22.9724 | 0.883554 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 22.7026 | 0.810807 | ||||||||
\(29\) | −26.8805 | −0.926914 | −0.463457 | − | 0.886120i | \(-0.653391\pi\) | ||||
−0.463457 | + | 0.886120i | \(0.653391\pi\) | |||||||
\(30\) | −2.04672 | + | 12.7247i | −0.0682240 | + | 0.424156i | ||||
\(31\) | 0.696771 | 0.0224765 | 0.0112382 | − | 0.999937i | \(-0.496423\pi\) | ||||
0.0112382 | + | 0.999937i | \(0.496423\pi\) | |||||||
\(32\) | − | 25.9976i | − | 0.812424i | ||||||
\(33\) | −7.40505 | −0.224396 | ||||||||
\(34\) | − | 45.9042i | − | 1.35012i | ||||||
\(35\) | 10.0975 | − | 62.7770i | 0.288499 | − | 1.79363i | ||||
\(36\) | −5.35574 | −0.148771 | ||||||||
\(37\) | −27.3072 | −0.738032 | −0.369016 | − | 0.929423i | \(-0.620305\pi\) | ||||
−0.369016 | + | 0.929423i | \(0.620305\pi\) | |||||||
\(38\) | 16.0286 | 0.421805 | ||||||||
\(39\) | 26.7365 | 0.685551 | ||||||||
\(40\) | −42.5019 | − | 6.83628i | −1.06255 | − | 0.170907i | ||||
\(41\) | −65.4795 | −1.59706 | −0.798530 | − | 0.601955i | \(-0.794389\pi\) | ||||
−0.798530 | + | 0.601955i | \(0.794389\pi\) | |||||||
\(42\) | −32.7793 | −0.780461 | ||||||||
\(43\) | −34.1462 | −0.794097 | −0.397049 | − | 0.917798i | \(-0.629966\pi\) | ||||
−0.397049 | + | 0.917798i | \(0.629966\pi\) | |||||||
\(44\) | − | 7.63249i | − | 0.173466i | ||||||
\(45\) | −2.38208 | + | 14.8096i | −0.0529352 | + | 0.329103i | ||||
\(46\) | 32.1672 | + | 11.6994i | 0.699287 | + | 0.254334i | ||||
\(47\) | 64.8134i | 1.37901i | 0.724281 | + | 0.689504i | \(0.242172\pi\) | ||||
−0.724281 | + | 0.689504i | \(0.757828\pi\) | |||||||
\(48\) | 9.82401i | 0.204667i | ||||||||
\(49\) | 112.716 | 2.30034 | ||||||||
\(50\) | −11.6668 | + | 35.3285i | −0.233336 | + | 0.706571i | ||||
\(51\) | − | 53.4257i | − | 1.04756i | ||||||
\(52\) | 27.5577i | 0.529955i | ||||||||
\(53\) | −35.9160 | −0.677661 | −0.338830 | − | 0.940848i | \(-0.610031\pi\) | ||||
−0.338830 | + | 0.940848i | \(0.610031\pi\) | |||||||
\(54\) | 7.73294 | 0.143203 | ||||||||
\(55\) | −21.1053 | − | 3.39471i | −0.383732 | − | 0.0617220i | ||||
\(56\) | − | 109.487i | − | 1.95512i | ||||||
\(57\) | 18.6549 | 0.327279 | ||||||||
\(58\) | 40.0037i | 0.689718i | ||||||||
\(59\) | −26.3025 | −0.445806 | −0.222903 | − | 0.974841i | \(-0.571553\pi\) | ||||
−0.222903 | + | 0.974841i | \(0.571553\pi\) | |||||||
\(60\) | −15.2645 | − | 2.45524i | −0.254408 | − | 0.0409207i | ||||
\(61\) | 81.6109i | 1.33788i | 0.743315 | + | 0.668941i | \(0.233252\pi\) | ||||
−0.743315 | + | 0.668941i | \(0.766748\pi\) | |||||||
\(62\) | − | 1.03694i | − | 0.0167248i | ||||||
\(63\) | −38.1503 | −0.605561 | ||||||||
\(64\) | −61.3773 | −0.959020 | ||||||||
\(65\) | 76.2022 | + | 12.2569i | 1.17234 | + | 0.188567i | ||||
\(66\) | 11.0202i | 0.166973i | ||||||||
\(67\) | −6.00979 | −0.0896983 | −0.0448491 | − | 0.998994i | \(-0.514281\pi\) | ||||
−0.0448491 | + | 0.998994i | \(0.514281\pi\) | |||||||
\(68\) | 55.0666 | 0.809803 | ||||||||
\(69\) | 37.4379 | + | 13.6163i | 0.542578 | + | 0.197338i | ||||
\(70\) | −93.4250 | − | 15.0271i | −1.33464 | − | 0.214673i | ||||
\(71\) | 37.9228 | 0.534124 | 0.267062 | − | 0.963679i | \(-0.413947\pi\) | ||||
0.267062 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(72\) | 25.8289i | 0.358735i | ||||||||
\(73\) | − | 90.5168i | − | 1.23996i | −0.784619 | − | 0.619978i | \(-0.787142\pi\) | ||
0.784619 | − | 0.619978i | \(-0.212858\pi\) | |||||||
\(74\) | 40.6387i | 0.549171i | ||||||||
\(75\) | −13.5784 | + | 41.1172i | −0.181046 | + | 0.548230i | ||||
\(76\) | 19.2279i | 0.252998i | ||||||||
\(77\) | − | 54.3682i | − | 0.706080i | ||||||
\(78\) | − | 39.7894i | − | 0.510120i | ||||||
\(79\) | − | 53.2816i | − | 0.674450i | −0.941424 | − | 0.337225i | \(-0.890512\pi\) | ||
0.941424 | − | 0.337225i | \(-0.109488\pi\) | |||||||
\(80\) | −4.50364 | + | 27.9996i | −0.0562955 | + | 0.349995i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 97.4468i | 1.18838i | ||||||||
\(83\) | 85.0565 | 1.02478 | 0.512388 | − | 0.858754i | \(-0.328761\pi\) | ||||
0.512388 | + | 0.858754i | \(0.328761\pi\) | |||||||
\(84\) | − | 39.3221i | − | 0.468120i | ||||||
\(85\) | 24.4921 | − | 152.270i | 0.288142 | − | 1.79141i | ||||
\(86\) | 50.8165i | 0.590890i | ||||||||
\(87\) | 46.5584i | 0.535154i | ||||||||
\(88\) | −36.8088 | −0.418282 | ||||||||
\(89\) | 5.80872i | 0.0652665i | 0.999467 | + | 0.0326333i | \(0.0103893\pi\) | ||||
−0.999467 | + | 0.0326333i | \(0.989611\pi\) | |||||||
\(90\) | 22.0398 | + | 3.54502i | 0.244886 | + | 0.0393892i | ||||
\(91\) | 196.300i | 2.15715i | ||||||||
\(92\) | −14.0346 | + | 38.5877i | −0.152549 | + | 0.419432i | ||||
\(93\) | − | 1.20684i | − | 0.0129768i | ||||||
\(94\) | 96.4556 | 1.02612 | ||||||||
\(95\) | 53.1687 | + | 8.55200i | 0.559670 | + | 0.0900211i | ||||
\(96\) | −45.0291 | −0.469054 | ||||||||
\(97\) | 39.7405 | 0.409696 | 0.204848 | − | 0.978794i | \(-0.434330\pi\) | ||||
0.204848 | + | 0.978794i | \(0.434330\pi\) | |||||||
\(98\) | − | 167.745i | − | 1.71168i | ||||||
\(99\) | 12.8259i | 0.129555i | ||||||||
\(100\) | −42.3801 | − | 13.9955i | −0.423801 | − | 0.139955i | ||||
\(101\) | −99.0469 | −0.980663 | −0.490331 | − | 0.871536i | \(-0.663124\pi\) | ||||
−0.490331 | + | 0.871536i | \(0.663124\pi\) | |||||||
\(102\) | −79.5084 | −0.779494 | ||||||||
\(103\) | −29.4647 | −0.286065 | −0.143033 | − | 0.989718i | \(-0.545685\pi\) | ||||
−0.143033 | + | 0.989718i | \(0.545685\pi\) | |||||||
\(104\) | 132.901 | 1.27789 | ||||||||
\(105\) | −108.733 | − | 17.4893i | −1.03555 | − | 0.166565i | ||||
\(106\) | 53.4504i | 0.504249i | ||||||||
\(107\) | 64.3564 | 0.601462 | 0.300731 | − | 0.953709i | \(-0.402769\pi\) | ||||
0.300731 | + | 0.953709i | \(0.402769\pi\) | |||||||
\(108\) | 9.27642i | 0.0858928i | ||||||||
\(109\) | 78.7776i | 0.722731i | 0.932424 | + | 0.361365i | \(0.117689\pi\) | ||||
−0.932424 | + | 0.361365i | \(0.882311\pi\) | |||||||
\(110\) | −5.05203 | + | 31.4090i | −0.0459275 | + | 0.285536i | ||||
\(111\) | 47.2974i | 0.426103i | ||||||||
\(112\) | −72.1282 | −0.644002 | ||||||||
\(113\) | 141.420 | 1.25150 | 0.625751 | − | 0.780023i | \(-0.284793\pi\) | ||||
0.625751 | + | 0.780023i | \(0.284793\pi\) | |||||||
\(114\) | − | 27.7623i | − | 0.243529i | ||||||
\(115\) | 100.460 | + | 55.9709i | 0.873567 | + | 0.486704i | ||||
\(116\) | −47.9884 | −0.413693 | ||||||||
\(117\) | − | 46.3090i | − | 0.395803i | ||||||
\(118\) | 39.1435i | 0.331725i | ||||||||
\(119\) | 392.254 | 3.29625 | ||||||||
\(120\) | −11.8408 | + | 73.6154i | −0.0986732 | + | 0.613462i | ||||
\(121\) | 102.722 | 0.848940 | ||||||||
\(122\) | 121.454 | 0.995521 | ||||||||
\(123\) | 113.414i | 0.922063i | ||||||||
\(124\) | 1.24391 | 0.0100315 | ||||||||
\(125\) | −57.5496 | + | 110.964i | −0.460397 | + | 0.887713i | ||||
\(126\) | 56.7755i | 0.450599i | ||||||||
\(127\) | 179.193i | 1.41096i | 0.708727 | + | 0.705482i | \(0.249270\pi\) | ||||
−0.708727 | + | 0.705482i | \(0.750730\pi\) | |||||||
\(128\) | − | 12.6484i | − | 0.0988155i | ||||||
\(129\) | 59.1429i | 0.458472i | ||||||||
\(130\) | 18.2407 | − | 113.404i | 0.140313 | − | 0.872341i | ||||
\(131\) | −98.4288 | −0.751365 | −0.375682 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375682 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(132\) | −13.2199 | −0.100150 | ||||||||
\(133\) | 136.965i | 1.02981i | ||||||||
\(134\) | 8.94379i | 0.0667447i | ||||||||
\(135\) | 25.6511 | + | 4.12589i | 0.190008 | + | 0.0305621i | ||||
\(136\) | − | 265.567i | − | 1.95270i | ||||||
\(137\) | −105.119 | −0.767295 | −0.383648 | − | 0.923480i | \(-0.625332\pi\) | ||||
−0.383648 | + | 0.923480i | \(0.625332\pi\) | |||||||
\(138\) | 20.2639 | − | 55.7152i | 0.146840 | − | 0.403733i | ||||
\(139\) | 84.8078 | 0.610128 | 0.305064 | − | 0.952332i | \(-0.401322\pi\) | ||||
0.305064 | + | 0.952332i | \(0.401322\pi\) | |||||||
\(140\) | 18.0265 | − | 112.073i | 0.128761 | − | 0.800518i | ||||
\(141\) | 112.260 | 0.796171 | ||||||||
\(142\) | − | 56.4368i | − | 0.397443i | ||||||
\(143\) | 65.9950 | 0.461504 | ||||||||
\(144\) | 17.0157 | 0.118164 | ||||||||
\(145\) | −21.3439 | + | 132.697i | −0.147199 | + | 0.915151i | ||||
\(146\) | −134.707 | −0.922654 | ||||||||
\(147\) | − | 195.231i | − | 1.32810i | ||||||
\(148\) | −48.7501 | −0.329393 | ||||||||
\(149\) | − | 140.350i | − | 0.941949i | −0.882147 | − | 0.470974i | \(-0.843902\pi\) | ||
0.882147 | − | 0.470974i | \(-0.156098\pi\) | |||||||
\(150\) | 61.1908 | + | 20.2075i | 0.407939 | + | 0.134717i | ||||
\(151\) | −214.230 | −1.41874 | −0.709372 | − | 0.704834i | \(-0.751021\pi\) | ||||
−0.709372 | + | 0.704834i | \(0.751021\pi\) | |||||||
\(152\) | 92.7293 | 0.610061 | ||||||||
\(153\) | −92.5361 | −0.604811 | ||||||||
\(154\) | −80.9109 | −0.525396 | ||||||||
\(155\) | 0.553255 | − | 3.43965i | 0.00356939 | − | 0.0221913i | ||||
\(156\) | 47.7313 | 0.305970 | ||||||||
\(157\) | 217.731 | 1.38682 | 0.693412 | − | 0.720541i | \(-0.256107\pi\) | ||||
0.693412 | + | 0.720541i | \(0.256107\pi\) | |||||||
\(158\) | −79.2939 | −0.501860 | ||||||||
\(159\) | 62.2084i | 0.391248i | ||||||||
\(160\) | −128.338 | − | 20.6428i | −0.802115 | − | 0.129017i | ||||
\(161\) | −99.9717 | + | 274.870i | −0.620942 | + | 1.70727i | ||||
\(162\) | − | 13.3938i | − | 0.0826780i | ||||||
\(163\) | − | 96.6805i | − | 0.593132i | −0.955012 | − | 0.296566i | \(-0.904159\pi\) | ||
0.955012 | − | 0.296566i | \(-0.0958415\pi\) | |||||||
\(164\) | −116.897 | −0.712787 | ||||||||
\(165\) | −5.87981 | + | 36.5554i | −0.0356352 | + | 0.221548i | ||||
\(166\) | − | 126.581i | − | 0.762539i | ||||||
\(167\) | − | 146.668i | − | 0.878252i | −0.898426 | − | 0.439126i | \(-0.855288\pi\) | ||
0.898426 | − | 0.439126i | \(-0.144712\pi\) | |||||||
\(168\) | −189.637 | −1.12879 | ||||||||
\(169\) | −69.2801 | −0.409941 | ||||||||
\(170\) | −226.608 | − | 36.4492i | −1.33299 | − | 0.214407i | ||||
\(171\) | − | 32.3112i | − | 0.188955i | ||||||
\(172\) | −60.9594 | −0.354415 | ||||||||
\(173\) | − | 6.56628i | − | 0.0379554i | −0.999820 | − | 0.0189777i | \(-0.993959\pi\) | ||
0.999820 | − | 0.0189777i | \(-0.00604115\pi\) | |||||||
\(174\) | 69.2884 | 0.398209 | ||||||||
\(175\) | −301.884 | − | 99.6933i | −1.72505 | − | 0.569676i | ||||
\(176\) | 24.2491i | 0.137779i | ||||||||
\(177\) | 45.5573i | 0.257386i | ||||||||
\(178\) | 8.64456 | 0.0485649 | ||||||||
\(179\) | 69.6886 | 0.389322 | 0.194661 | − | 0.980871i | \(-0.437639\pi\) | ||||
0.194661 | + | 0.980871i | \(0.437639\pi\) | |||||||
\(180\) | −4.25261 | + | 26.4389i | −0.0236256 | + | 0.146883i | ||||
\(181\) | − | 122.019i | − | 0.674137i | −0.941480 | − | 0.337068i | \(-0.890565\pi\) | ||
0.941480 | − | 0.337068i | \(-0.109435\pi\) | |||||||
\(182\) | 292.135 | 1.60514 | ||||||||
\(183\) | 141.354 | 0.772427 | ||||||||
\(184\) | 186.095 | + | 67.6838i | 1.01139 | + | 0.367847i | ||||
\(185\) | −21.6827 | + | 134.803i | −0.117204 | + | 0.728666i | ||||
\(186\) | −1.79603 | −0.00965607 | ||||||||
\(187\) | − | 131.873i | − | 0.705205i | ||||||
\(188\) | 115.708i | 0.615468i | ||||||||
\(189\) | 66.0783i | 0.349621i | ||||||||
\(190\) | 12.7271 | − | 79.1258i | 0.0669849 | − | 0.416452i | ||||
\(191\) | 10.4188i | 0.0545487i | 0.999628 | + | 0.0272744i | \(0.00868278\pi\) | ||||
−0.999628 | + | 0.0272744i | \(0.991317\pi\) | |||||||
\(192\) | 106.309i | 0.553691i | ||||||||
\(193\) | 350.458i | 1.81584i | 0.419140 | + | 0.907922i | \(0.362332\pi\) | ||||
−0.419140 | + | 0.907922i | \(0.637668\pi\) | |||||||
\(194\) | − | 59.1420i | − | 0.304856i | ||||||
\(195\) | 21.2295 | − | 131.986i | 0.108869 | − | 0.676851i | ||||
\(196\) | 201.227 | 1.02667 | ||||||||
\(197\) | − | 132.632i | − | 0.673258i | −0.941637 | − | 0.336629i | \(-0.890713\pi\) | ||
0.941637 | − | 0.336629i | \(-0.109287\pi\) | |||||||
\(198\) | 19.0876 | 0.0964020 | ||||||||
\(199\) | − | 339.036i | − | 1.70370i | −0.523788 | − | 0.851849i | \(-0.675482\pi\) | ||
0.523788 | − | 0.851849i | \(-0.324518\pi\) | |||||||
\(200\) | −67.4953 | + | 204.384i | −0.337476 | + | 1.02192i | ||||
\(201\) | 10.4093i | 0.0517873i | ||||||||
\(202\) | 147.402i | 0.729713i | ||||||||
\(203\) | −341.833 | −1.68391 | ||||||||
\(204\) | − | 95.3782i | − | 0.467540i | ||||||
\(205\) | −51.9925 | + | 323.243i | −0.253622 | + | 1.57679i | ||||
\(206\) | 43.8496i | 0.212862i | ||||||||
\(207\) | 23.5842 | − | 64.8443i | 0.113933 | − | 0.313258i | ||||
\(208\) | − | 87.5532i | − | 0.420929i | ||||||
\(209\) | 46.0468 | 0.220320 | ||||||||
\(210\) | −26.0277 | + | 161.817i | −0.123941 | + | 0.770556i | ||||
\(211\) | −141.472 | −0.670482 | −0.335241 | − | 0.942132i | \(-0.608818\pi\) | ||||
−0.335241 | + | 0.942132i | \(0.608818\pi\) | |||||||
\(212\) | −64.1190 | −0.302448 | ||||||||
\(213\) | − | 65.6842i | − | 0.308376i | ||||||
\(214\) | − | 95.7755i | − | 0.447549i | ||||||
\(215\) | −27.1130 | + | 168.564i | −0.126107 | + | 0.784020i | ||||
\(216\) | 44.7370 | 0.207116 | ||||||||
\(217\) | 8.86068 | 0.0408326 | ||||||||
\(218\) | 117.237 | 0.537785 | ||||||||
\(219\) | −156.780 | −0.715889 | ||||||||
\(220\) | −37.6782 | − | 6.06040i | −0.171264 | − | 0.0275473i | ||||
\(221\) | 476.139i | 2.15447i | ||||||||
\(222\) | 70.3882 | 0.317064 | ||||||||
\(223\) | − | 375.406i | − | 1.68343i | −0.539920 | − | 0.841717i | \(-0.681545\pi\) | ||
0.539920 | − | 0.841717i | \(-0.318455\pi\) | |||||||
\(224\) | − | 330.605i | − | 1.47592i | ||||||
\(225\) | 71.2171 | + | 23.5185i | 0.316521 | + | 0.104527i | ||||
\(226\) | − | 210.461i | − | 0.931245i | ||||||
\(227\) | −322.505 | −1.42073 | −0.710363 | − | 0.703836i | \(-0.751469\pi\) | ||||
−0.710363 | + | 0.703836i | \(0.751469\pi\) | |||||||
\(228\) | 33.3036 | 0.146069 | ||||||||
\(229\) | 20.6760i | 0.0902884i | 0.998980 | + | 0.0451442i | \(0.0143747\pi\) | ||||
−0.998980 | + | 0.0451442i | \(0.985625\pi\) | |||||||
\(230\) | 83.2962 | − | 149.505i | 0.362157 | − | 0.650023i | ||||
\(231\) | −94.1684 | −0.407655 | ||||||||
\(232\) | 231.431i | 0.997548i | ||||||||
\(233\) | 176.353i | 0.756881i | 0.925626 | + | 0.378440i | \(0.123539\pi\) | ||||
−0.925626 | + | 0.378440i | \(0.876461\pi\) | |||||||
\(234\) | −68.9172 | −0.294518 | ||||||||
\(235\) | 319.955 | + | 51.4636i | 1.36151 | + | 0.218994i | ||||
\(236\) | −46.9565 | −0.198968 | ||||||||
\(237\) | −92.2864 | −0.389394 | ||||||||
\(238\) | − | 583.753i | − | 2.45275i | ||||||
\(239\) | 318.851 | 1.33410 | 0.667052 | − | 0.745012i | \(-0.267556\pi\) | ||||
0.667052 | + | 0.745012i | \(0.267556\pi\) | |||||||
\(240\) | 48.4967 | + | 7.80053i | 0.202070 | + | 0.0325022i | ||||
\(241\) | − | 232.825i | − | 0.966077i | −0.875599 | − | 0.483039i | \(-0.839533\pi\) | ||
0.875599 | − | 0.483039i | \(-0.160467\pi\) | |||||||
\(242\) | − | 152.871i | − | 0.631698i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 145.696i | 0.597113i | ||||||||
\(245\) | 89.4999 | − | 556.430i | 0.365306 | − | 2.27114i | ||||
\(246\) | 168.783 | 0.686109 | ||||||||
\(247\) | −166.256 | −0.673099 | ||||||||
\(248\) | − | 5.99894i | − | 0.0241893i | ||||||
\(249\) | − | 147.322i | − | 0.591655i | ||||||
\(250\) | 165.137 | + | 85.6455i | 0.660549 | + | 0.342582i | ||||
\(251\) | − | 388.651i | − | 1.54841i | −0.632936 | − | 0.774205i | \(-0.718150\pi\) | ||
0.632936 | − | 0.774205i | \(-0.281850\pi\) | |||||||
\(252\) | −68.1078 | −0.270269 | ||||||||
\(253\) | 92.4098 | + | 33.6099i | 0.365256 | + | 0.132846i | ||||
\(254\) | 266.675 | 1.04990 | ||||||||
\(255\) | −263.739 | − | 42.4215i | −1.03427 | − | 0.166359i | ||||
\(256\) | −264.333 | −1.03255 | ||||||||
\(257\) | − | 49.0820i | − | 0.190981i | −0.995430 | − | 0.0954904i | \(-0.969558\pi\) | ||
0.995430 | − | 0.0954904i | \(-0.0304419\pi\) | |||||||
\(258\) | 88.0168 | 0.341150 | ||||||||
\(259\) | −347.259 | −1.34077 | ||||||||
\(260\) | 136.040 | + | 21.8815i | 0.523230 | + | 0.0841598i | ||||
\(261\) | 80.6415 | 0.308971 | ||||||||
\(262\) | 146.482i | 0.559092i | ||||||||
\(263\) | −338.647 | −1.28763 | −0.643815 | − | 0.765181i | \(-0.722650\pi\) | ||||
−0.643815 | + | 0.765181i | \(0.722650\pi\) | |||||||
\(264\) | 63.7548i | 0.241495i | ||||||||
\(265\) | −28.5183 | + | 177.301i | −0.107616 | + | 0.669061i | ||||
\(266\) | 203.832 | 0.766285 | ||||||||
\(267\) | 10.0610 | 0.0376816 | ||||||||
\(268\) | −10.7290 | −0.0400334 | ||||||||
\(269\) | −156.589 | −0.582114 | −0.291057 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291057 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(270\) | 6.14016 | − | 38.1740i | 0.0227413 | − | 0.141385i | ||||
\(271\) | 142.248 | 0.524901 | 0.262451 | − | 0.964945i | \(-0.415469\pi\) | ||||
0.262451 | + | 0.964945i | \(0.415469\pi\) | |||||||
\(272\) | −174.952 | −0.643205 | ||||||||
\(273\) | 340.002 | 1.24543 | ||||||||
\(274\) | 156.439i | 0.570946i | ||||||||
\(275\) | −33.5163 | + | 101.492i | −0.121878 | + | 0.369061i | ||||
\(276\) | 66.8359 | + | 24.3086i | 0.242159 | + | 0.0880745i | ||||
\(277\) | 190.799i | 0.688805i | 0.938822 | + | 0.344403i | \(0.111919\pi\) | ||||
−0.938822 | + | 0.344403i | \(0.888081\pi\) | |||||||
\(278\) | − | 126.211i | − | 0.453997i | ||||||
\(279\) | −2.09031 | −0.00749216 | ||||||||
\(280\) | −540.487 | − | 86.9355i | −1.93031 | − | 0.310484i | ||||
\(281\) | − | 315.889i | − | 1.12416i | −0.827083 | − | 0.562079i | \(-0.810002\pi\) | ||
0.827083 | − | 0.562079i | \(-0.189998\pi\) | |||||||
\(282\) | − | 167.066i | − | 0.592433i | ||||||
\(283\) | −208.215 | −0.735742 | −0.367871 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367871 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(284\) | 67.7016 | 0.238386 | ||||||||
\(285\) | 14.8125 | − | 92.0908i | 0.0519737 | − | 0.323126i | ||||
\(286\) | − | 98.2141i | − | 0.343406i | ||||||
\(287\) | −832.688 | −2.90135 | ||||||||
\(288\) | 77.9928i | 0.270808i | ||||||||
\(289\) | 662.436 | 2.29217 | ||||||||
\(290\) | 197.480 | + | 31.7640i | 0.680966 | + | 0.109531i | ||||
\(291\) | − | 68.8326i | − | 0.236538i | ||||||
\(292\) | − | 161.595i | − | 0.553407i | ||||||
\(293\) | 31.8358 | 0.108655 | 0.0543273 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543273 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(294\) | −290.543 | −0.988241 | ||||||||
\(295\) | −20.8849 | + | 129.844i | −0.0707964 | + | 0.440148i | ||||
\(296\) | 235.105i | 0.794273i | ||||||||
\(297\) | 22.2152 | 0.0747985 | ||||||||
\(298\) | −208.870 | −0.700906 | ||||||||
\(299\) | −333.653 | − | 121.351i | −1.11590 | − | 0.405857i | ||||
\(300\) | −24.2409 | + | 73.4045i | −0.0808029 | + | 0.244682i | ||||
\(301\) | −434.229 | −1.44262 | ||||||||
\(302\) | 318.819i | 1.05569i | ||||||||
\(303\) | 171.554i | 0.566186i | ||||||||
\(304\) | − | 61.0887i | − | 0.200950i | ||||||
\(305\) | 402.876 | + | 64.8013i | 1.32090 | + | 0.212463i | ||||
\(306\) | 137.713i | 0.450041i | ||||||||
\(307\) | − | 246.986i | − | 0.804515i | −0.915526 | − | 0.402258i | \(-0.868226\pi\) | ||
0.915526 | − | 0.402258i | \(-0.131774\pi\) | |||||||
\(308\) | − | 97.0606i | − | 0.315132i | ||||||
\(309\) | 51.0344i | 0.165160i | ||||||||
\(310\) | −5.11889 | − | 0.823357i | −0.0165126 | − | 0.00265599i | ||||
\(311\) | −422.720 | −1.35923 | −0.679614 | − | 0.733570i | \(-0.737853\pi\) | ||||
−0.679614 | + | 0.733570i | \(0.737853\pi\) | |||||||
\(312\) | − | 230.191i | − | 0.737793i | ||||||
\(313\) | 436.906 | 1.39587 | 0.697933 | − | 0.716163i | \(-0.254103\pi\) | ||||
0.697933 | + | 0.716163i | \(0.254103\pi\) | |||||||
\(314\) | − | 324.029i | − | 1.03194i | ||||||
\(315\) | −30.2924 | + | 188.331i | −0.0961664 | + | 0.597876i | ||||
\(316\) | − | 95.1208i | − | 0.301015i | ||||||
\(317\) | − | 256.740i | − | 0.809905i | −0.914338 | − | 0.404953i | \(-0.867288\pi\) | ||
0.914338 | − | 0.404953i | \(-0.132712\pi\) | |||||||
\(318\) | 92.5787 | 0.291128 | ||||||||
\(319\) | 114.922i | 0.360258i | ||||||||
\(320\) | −48.7353 | + | 302.992i | −0.152298 | + | 0.946850i | ||||
\(321\) | − | 111.469i | − | 0.347254i | ||||||
\(322\) | 409.063 | + | 148.778i | 1.27038 | + | 0.462044i | ||||
\(323\) | 332.217i | 1.02854i | ||||||||
\(324\) | 16.0672 | 0.0495902 | ||||||||
\(325\) | 121.013 | − | 366.444i | 0.372348 | − | 1.12752i | ||||
\(326\) | −143.880 | −0.441351 | ||||||||
\(327\) | 136.447 | 0.417269 | ||||||||
\(328\) | 563.754i | 1.71876i | ||||||||
\(329\) | 824.218i | 2.50522i | ||||||||
\(330\) | 54.4019 | + | 8.75036i | 0.164854 | + | 0.0265163i | ||||
\(331\) | 585.027 | 1.76745 | 0.883727 | − | 0.468003i | \(-0.155026\pi\) | ||||
0.883727 | + | 0.468003i | \(0.155026\pi\) | |||||||
\(332\) | 151.847 | 0.457370 | ||||||||
\(333\) | 81.9216 | 0.246011 | ||||||||
\(334\) | −218.272 | −0.653509 | ||||||||
\(335\) | −4.77193 | + | 29.6676i | −0.0142446 | + | 0.0885600i | ||||
\(336\) | 124.930i | 0.371815i | ||||||||
\(337\) | 386.269 | 1.14620 | 0.573099 | − | 0.819486i | \(-0.305741\pi\) | ||||
0.573099 | + | 0.819486i | \(0.305741\pi\) | |||||||
\(338\) | 103.103i | 0.305038i | ||||||||
\(339\) | − | 244.946i | − | 0.722555i | ||||||
\(340\) | 43.7244 | − | 271.839i | 0.128601 | − | 0.799527i | ||||
\(341\) | − | 2.97891i | − | 0.00873581i | ||||||
\(342\) | −48.0857 | −0.140602 | ||||||||
\(343\) | 810.268 | 2.36230 | ||||||||
\(344\) | 293.986i | 0.854611i | ||||||||
\(345\) | 96.9445 | − | 174.002i | 0.280998 | − | 0.504354i | ||||
\(346\) | −9.77197 | −0.0282427 | ||||||||
\(347\) | 244.267i | 0.703938i | 0.936012 | + | 0.351969i | \(0.114488\pi\) | ||||
−0.936012 | + | 0.351969i | \(0.885512\pi\) | |||||||
\(348\) | 83.1183i | 0.238846i | ||||||||
\(349\) | 309.800 | 0.887678 | 0.443839 | − | 0.896107i | \(-0.353616\pi\) | ||||
0.443839 | + | 0.896107i | \(0.353616\pi\) | |||||||
\(350\) | −148.364 | + | 449.265i | −0.423897 | + | 1.28361i | ||||
\(351\) | −80.2095 | −0.228517 | ||||||||
\(352\) | −111.148 | −0.315761 | ||||||||
\(353\) | 547.232i | 1.55023i | 0.631818 | + | 0.775116i | \(0.282309\pi\) | ||||
−0.631818 | + | 0.775116i | \(0.717691\pi\) | |||||||
\(354\) | 67.7986 | 0.191521 | ||||||||
\(355\) | 30.1117 | − | 187.208i | 0.0848218 | − | 0.527346i | ||||
\(356\) | 10.3700i | 0.0291292i | ||||||||
\(357\) | − | 679.403i | − | 1.90309i | ||||||
\(358\) | − | 103.711i | − | 0.289695i | ||||||
\(359\) | − | 505.030i | − | 1.40677i | −0.710810 | − | 0.703384i | \(-0.751671\pi\) | ||
0.710810 | − | 0.703384i | \(-0.248329\pi\) | |||||||
\(360\) | 127.506 | + | 20.5088i | 0.354182 | + | 0.0569690i | ||||
\(361\) | 244.998 | 0.678665 | ||||||||
\(362\) | −181.589 | −0.501627 | ||||||||
\(363\) | − | 177.919i | − | 0.490136i | ||||||
\(364\) | 350.445i | 0.962760i | ||||||||
\(365\) | −446.841 | − | 71.8728i | −1.22422 | − | 0.196912i | ||||
\(366\) | − | 210.364i | − | 0.574765i | ||||||
\(367\) | 40.2534 | 0.109682 | 0.0548411 | − | 0.998495i | \(-0.482535\pi\) | ||||
0.0548411 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(368\) | 44.5890 | − | 122.597i | 0.121166 | − | 0.333143i | ||||
\(369\) | 196.438 | 0.532354 | ||||||||
\(370\) | 200.615 | + | 32.2682i | 0.542202 | + | 0.0872114i | ||||
\(371\) | −456.736 | −1.23109 | ||||||||
\(372\) | − | 2.15451i | − | 0.00579171i | ||||||
\(373\) | −579.554 | −1.55376 | −0.776882 | − | 0.629646i | \(-0.783200\pi\) | ||||
−0.776882 | + | 0.629646i | \(0.783200\pi\) | |||||||
\(374\) | −196.255 | −0.524745 | ||||||||
\(375\) | 192.196 | + | 99.6788i | 0.512522 | + | 0.265810i | ||||
\(376\) | 558.020 | 1.48409 | ||||||||
\(377\) | − | 414.936i | − | 1.10063i | ||||||
\(378\) | 98.3380 | 0.260154 | ||||||||
\(379\) | − | 334.998i | − | 0.883900i | −0.897040 | − | 0.441950i | \(-0.854287\pi\) | ||
0.897040 | − | 0.441950i | \(-0.145713\pi\) | |||||||
\(380\) | 94.9193 | + | 15.2674i | 0.249788 | + | 0.0401775i | ||||
\(381\) | 310.371 | 0.814621 | ||||||||
\(382\) | 15.5053 | 0.0405898 | ||||||||
\(383\) | 508.087 | 1.32660 | 0.663299 | − | 0.748354i | \(-0.269156\pi\) | ||||
0.663299 | + | 0.748354i | \(0.269156\pi\) | |||||||
\(384\) | −21.9076 | −0.0570512 | ||||||||
\(385\) | −268.391 | − | 43.1698i | −0.697120 | − | 0.112129i | ||||
\(386\) | 521.553 | 1.35117 | ||||||||
\(387\) | 102.439 | 0.264699 | ||||||||
\(388\) | 70.9467 | 0.182852 | ||||||||
\(389\) | 370.320i | 0.951979i | 0.879451 | + | 0.475990i | \(0.157910\pi\) | ||||
−0.879451 | + | 0.475990i | \(0.842090\pi\) | |||||||
\(390\) | −196.422 | − | 31.5938i | −0.503647 | − | 0.0810099i | ||||
\(391\) | −242.488 | + | 666.715i | −0.620173 | + | 1.70515i | ||||
\(392\) | − | 970.447i | − | 2.47563i | ||||||
\(393\) | 170.484i | 0.433801i | ||||||||
\(394\) | −197.383 | −0.500972 | ||||||||
\(395\) | −263.027 | − | 42.3070i | −0.665891 | − | 0.107106i | ||||
\(396\) | 22.8975i | 0.0578219i | ||||||||
\(397\) | 242.477i | 0.610773i | 0.952228 | + | 0.305387i | \(0.0987857\pi\) | ||||
−0.952228 | + | 0.305387i | \(0.901214\pi\) | |||||||
\(398\) | −504.554 | −1.26772 | ||||||||
\(399\) | 237.230 | 0.594562 | ||||||||
\(400\) | 134.645 | + | 44.4649i | 0.336613 | + | 0.111162i | ||||
\(401\) | 502.129i | 1.25219i | 0.779746 | + | 0.626096i | \(0.215348\pi\) | ||||
−0.779746 | + | 0.626096i | \(0.784652\pi\) | |||||||
\(402\) | 15.4911 | 0.0385351 | ||||||||
\(403\) | 10.7556i | 0.0266888i | ||||||||
\(404\) | −176.823 | −0.437682 | ||||||||
\(405\) | 7.14625 | − | 44.4289i | 0.0176451 | − | 0.109701i | ||||
\(406\) | 508.718i | 1.25300i | ||||||||
\(407\) | 116.747i | 0.286847i | ||||||||
\(408\) | −459.976 | −1.12739 | ||||||||
\(409\) | −165.369 | −0.404325 | −0.202163 | − | 0.979352i | \(-0.564797\pi\) | ||||
−0.202163 | + | 0.979352i | \(0.564797\pi\) | |||||||
\(410\) | 481.051 | + | 77.3755i | 1.17330 | + | 0.188721i | ||||
\(411\) | 182.072i | 0.442998i | ||||||||
\(412\) | −52.6019 | −0.127674 | ||||||||
\(413\) | −334.483 | −0.809887 | ||||||||
\(414\) | −96.5016 | − | 35.0981i | −0.233096 | − | 0.0847780i | ||||
\(415\) | 67.5372 | − | 419.885i | 0.162740 | − | 1.01177i | ||||
\(416\) | 401.307 | 0.964681 | ||||||||
\(417\) | − | 146.891i | − | 0.352257i | ||||||
\(418\) | − | 68.5271i | − | 0.163940i | ||||||
\(419\) | 97.8982i | 0.233647i | 0.993153 | + | 0.116824i | \(0.0372712\pi\) | ||||
−0.993153 | + | 0.116824i | \(0.962729\pi\) | |||||||
\(420\) | −194.115 | − | 31.2228i | −0.462179 | − | 0.0743400i | ||||
\(421\) | 580.162i | 1.37806i | 0.724734 | + | 0.689029i | \(0.241963\pi\) | ||||
−0.724734 | + | 0.689029i | \(0.758037\pi\) | |||||||
\(422\) | 210.539i | 0.498907i | ||||||||
\(423\) | − | 194.440i | − | 0.459670i | ||||||
\(424\) | 309.224i | 0.729301i | ||||||||
\(425\) | −732.239 | − | 241.813i | −1.72292 | − | 0.568971i | ||||
\(426\) | −97.7515 | −0.229464 | ||||||||
\(427\) | 1037.83i | 2.43051i | ||||||||
\(428\) | 114.892 | 0.268440 | ||||||||
\(429\) | − | 114.307i | − | 0.266449i | ||||||
\(430\) | 250.858 | + | 40.3497i | 0.583391 | + | 0.0938365i | ||||
\(431\) | − | 717.474i | − | 1.66467i | −0.554271 | − | 0.832336i | \(-0.687003\pi\) | ||
0.554271 | − | 0.832336i | \(-0.312997\pi\) | |||||||
\(432\) | − | 29.4720i | − | 0.0682223i | ||||||
\(433\) | 407.798 | 0.941797 | 0.470899 | − | 0.882187i | \(-0.343930\pi\) | ||||
0.470899 | + | 0.882187i | \(0.343930\pi\) | |||||||
\(434\) | − | 13.1865i | − | 0.0303837i | ||||||
\(435\) | 229.838 | + | 36.9686i | 0.528363 | + | 0.0849854i | ||||
\(436\) | 140.638i | 0.322563i | ||||||||
\(437\) | −232.800 | − | 84.6705i | −0.532723 | − | 0.193754i | ||||
\(438\) | 233.320i | 0.532694i | ||||||||
\(439\) | −411.873 | −0.938207 | −0.469104 | − | 0.883143i | \(-0.655423\pi\) | ||||
−0.469104 | + | 0.883143i | \(0.655423\pi\) | |||||||
\(440\) | −29.2272 | + | 181.709i | −0.0664255 | + | 0.412974i | ||||
\(441\) | −338.149 | −0.766778 | ||||||||
\(442\) | 708.592 | 1.60315 | ||||||||
\(443\) | 431.371i | 0.973748i | 0.873472 | + | 0.486874i | \(0.161863\pi\) | ||||
−0.873472 | + | 0.486874i | \(0.838137\pi\) | |||||||
\(444\) | 84.4377i | 0.190175i | ||||||||
\(445\) | 28.6750 | + | 4.61228i | 0.0644383 | + | 0.0103647i | ||||
\(446\) | −558.680 | −1.25265 | ||||||||
\(447\) | −243.094 | −0.543834 | ||||||||
\(448\) | −780.521 | −1.74224 | ||||||||
\(449\) | −428.495 | −0.954331 | −0.477166 | − | 0.878813i | \(-0.658336\pi\) | ||||
−0.477166 | + | 0.878813i | \(0.658336\pi\) | |||||||
\(450\) | 35.0004 | − | 105.986i | 0.0777786 | − | 0.235524i | ||||
\(451\) | 279.945i | 0.620721i | ||||||||
\(452\) | 252.469 | 0.558560 | ||||||||
\(453\) | 371.058i | 0.819113i | ||||||||
\(454\) | 479.953i | 1.05716i | ||||||||
\(455\) | 969.046 | + | 155.868i | 2.12977 | + | 0.342567i | ||||
\(456\) | − | 160.612i | − | 0.352219i | ||||||
\(457\) | 418.532 | 0.915826 | 0.457913 | − | 0.888997i | \(-0.348597\pi\) | ||||
0.457913 | + | 0.888997i | \(0.348597\pi\) | |||||||
\(458\) | 30.7702 | 0.0671838 | ||||||||
\(459\) | 160.277i | 0.349188i | ||||||||
\(460\) | 179.346 | + | 99.9220i | 0.389884 | + | 0.217222i | ||||
\(461\) | 187.102 | 0.405860 | 0.202930 | − | 0.979193i | \(-0.434954\pi\) | ||||
0.202930 | + | 0.979193i | \(0.434954\pi\) | |||||||
\(462\) | 140.142i | 0.303337i | ||||||||
\(463\) | − | 916.641i | − | 1.97979i | −0.141814 | − | 0.989893i | \(-0.545293\pi\) | ||
0.141814 | − | 0.989893i | \(-0.454707\pi\) | |||||||
\(464\) | 152.463 | 0.328585 | ||||||||
\(465\) | −5.95764 | − | 0.958266i | −0.0128121 | − | 0.00206079i | ||||
\(466\) | 262.450 | 0.563197 | ||||||||
\(467\) | −295.215 | −0.632153 | −0.316077 | − | 0.948734i | \(-0.602366\pi\) | ||||
−0.316077 | + | 0.948734i | \(0.602366\pi\) | |||||||
\(468\) | − | 82.6730i | − | 0.176652i | ||||||
\(469\) | −76.4251 | −0.162953 | ||||||||
\(470\) | 76.5884 | − | 476.158i | 0.162954 | − | 1.01310i | ||||
\(471\) | − | 377.122i | − | 0.800683i | ||||||
\(472\) | 226.455i | 0.479778i | ||||||||
\(473\) | 145.986i | 0.308637i | ||||||||
\(474\) | 137.341i | 0.289749i | ||||||||
\(475\) | 84.4348 | − | 255.679i | 0.177757 | − | 0.538272i | ||||
\(476\) | 700.270 | 1.47116 | ||||||||
\(477\) | 107.748 | 0.225887 | ||||||||
\(478\) | − | 474.515i | − | 0.992709i | ||||||
\(479\) | 473.694i | 0.988923i | 0.869200 | + | 0.494461i | \(0.164635\pi\) | ||||
−0.869200 | + | 0.494461i | \(0.835365\pi\) | |||||||
\(480\) | −35.7544 | + | 222.289i | −0.0744883 | + | 0.463101i | ||||
\(481\) | − | 421.523i | − | 0.876346i | ||||||
\(482\) | −346.491 | −0.718860 | ||||||||
\(483\) | 476.089 | + | 173.156i | 0.985692 | + | 0.358501i | ||||
\(484\) | 183.384 | 0.378892 | ||||||||
\(485\) | 31.5550 | − | 196.181i | 0.0650620 | − | 0.404497i | ||||
\(486\) | −23.1988 | −0.0477342 | ||||||||
\(487\) | 92.1170i | 0.189152i | 0.995518 | + | 0.0945760i | \(0.0301495\pi\) | ||||
−0.995518 | + | 0.0945760i | \(0.969850\pi\) | |||||||
\(488\) | 702.639 | 1.43983 | ||||||||
\(489\) | −167.456 | −0.342445 | ||||||||
\(490\) | −828.082 | − | 133.194i | −1.68996 | − | 0.271825i | ||||
\(491\) | −197.753 | −0.402756 | −0.201378 | − | 0.979514i | \(-0.564542\pi\) | ||||
−0.201378 | + | 0.979514i | \(0.564542\pi\) | |||||||
\(492\) | 202.472i | 0.411528i | ||||||||
\(493\) | −829.138 | −1.68182 | ||||||||
\(494\) | 247.422i | 0.500855i | ||||||||
\(495\) | 63.3158 | + | 10.1841i | 0.127911 | + | 0.0205740i | ||||
\(496\) | −3.95201 | −0.00796777 | ||||||||
\(497\) | 482.256 | 0.970333 | ||||||||
\(498\) | −219.245 | −0.440252 | ||||||||
\(499\) | −872.447 | −1.74839 | −0.874195 | − | 0.485575i | \(-0.838610\pi\) | ||||
−0.874195 | + | 0.485575i | \(0.838610\pi\) | |||||||
\(500\) | −102.740 | + | 198.099i | −0.205481 | + | 0.396197i | ||||
\(501\) | −254.037 | −0.507059 | ||||||||
\(502\) | −578.392 | −1.15217 | ||||||||
\(503\) | 199.518 | 0.396655 | 0.198328 | − | 0.980136i | \(-0.436449\pi\) | ||||
0.198328 | + | 0.980136i | \(0.436449\pi\) | |||||||
\(504\) | 328.460i | 0.651707i | ||||||||
\(505\) | −78.6460 | + | 488.950i | −0.155735 | + | 0.968218i | ||||
\(506\) | 50.0184 | − | 137.525i | 0.0988506 | − | 0.271788i | ||||
\(507\) | 119.997i | 0.236680i | ||||||||
\(508\) | 319.903i | 0.629731i | ||||||||
\(509\) | −179.473 | −0.352599 | −0.176299 | − | 0.984337i | \(-0.556413\pi\) | ||||
−0.176299 | + | 0.984337i | \(0.556413\pi\) | |||||||
\(510\) | −63.1318 | + | 392.497i | −0.123788 | + | 0.769602i | ||||
\(511\) | − | 1151.08i | − | 2.25261i | ||||||
\(512\) | 342.787i | 0.669506i | ||||||||
\(513\) | −55.9647 | −0.109093 | ||||||||
\(514\) | −73.0441 | −0.142109 | ||||||||
\(515\) | −23.3958 | + | 145.454i | −0.0454288 | + | 0.282435i | ||||
\(516\) | 105.585i | 0.204622i | ||||||||
\(517\) | 277.097 | 0.535972 | ||||||||
\(518\) | 516.793i | 0.997670i | ||||||||
\(519\) | −11.3731 | −0.0219136 | ||||||||
\(520\) | 105.527 | − | 656.073i | 0.202937 | − | 1.26168i | ||||
\(521\) | 137.997i | 0.264870i | 0.991192 | + | 0.132435i | \(0.0422796\pi\) | ||||
−0.991192 | + | 0.132435i | \(0.957720\pi\) | |||||||
\(522\) | − | 120.011i | − | 0.229906i | ||||||
\(523\) | 179.904 | 0.343985 | 0.171992 | − | 0.985098i | \(-0.444980\pi\) | ||||
0.171992 | + | 0.985098i | \(0.444980\pi\) | |||||||
\(524\) | −175.720 | −0.335343 | ||||||||
\(525\) | −172.674 | + | 522.879i | −0.328903 | + | 0.995959i | ||||
\(526\) | 503.976i | 0.958129i | ||||||||
\(527\) | 21.4922 | 0.0407821 | ||||||||
\(528\) | 42.0007 | 0.0795468 | ||||||||
\(529\) | −405.397 | − | 339.845i | −0.766345 | − | 0.642429i | ||||
\(530\) | 263.860 | + | 42.4411i | 0.497850 | + | 0.0800775i | ||||
\(531\) | 78.9076 | 0.148602 | ||||||||
\(532\) | 244.516i | 0.459617i | ||||||||
\(533\) | − | 1010.76i | − | 1.89636i | ||||||
\(534\) | − | 14.9728i | − | 0.0280390i | ||||||
\(535\) | 51.1008 | − | 317.699i | 0.0955155 | − | 0.593829i | ||||
\(536\) | 51.7420i | 0.0965336i | ||||||||
\(537\) | − | 120.704i | − | 0.224775i | ||||||
\(538\) | 233.036i | 0.433152i | ||||||||
\(539\) | − | 481.898i | − | 0.894059i | ||||||
\(540\) | 45.7935 | + | 7.36573i | 0.0848028 | + | 0.0136402i | ||||
\(541\) | −358.999 | −0.663585 | −0.331792 | − | 0.943352i | \(-0.607653\pi\) | ||||
−0.331792 | + | 0.943352i | \(0.607653\pi\) | |||||||
\(542\) | − | 211.695i | − | 0.390580i | ||||||
\(543\) | −211.343 | −0.389213 | ||||||||
\(544\) | − | 801.905i | − | 1.47409i | ||||||
\(545\) | 388.890 | + | 62.5516i | 0.713559 | + | 0.114774i | ||||
\(546\) | − | 505.993i | − | 0.926726i | ||||||
\(547\) | 70.3378i | 0.128588i | 0.997931 | + | 0.0642942i | \(0.0204796\pi\) | ||||
−0.997931 | + | 0.0642942i | \(0.979520\pi\) | |||||||
\(548\) | −187.664 | −0.342453 | ||||||||
\(549\) | − | 244.833i | − | 0.445961i | ||||||
\(550\) | 151.040 | + | 49.8791i | 0.274619 | + | 0.0906894i | ||||
\(551\) | − | 289.514i | − | 0.525434i | ||||||
\(552\) | 117.232 | − | 322.326i | 0.212376 | − | 0.583925i | ||||
\(553\) | − | 677.570i | − | 1.22526i | ||||||
\(554\) | 283.948 | 0.512542 | ||||||||
\(555\) | 233.486 | + | 37.5555i | 0.420696 | + | 0.0676675i | ||||
\(556\) | 151.403 | 0.272307 | ||||||||
\(557\) | 797.478 | 1.43174 | 0.715869 | − | 0.698234i | \(-0.246031\pi\) | ||||
0.715869 | + | 0.698234i | \(0.246031\pi\) | |||||||
\(558\) | 3.11081i | 0.00557493i | ||||||||
\(559\) | − | 527.092i | − | 0.942919i | ||||||
\(560\) | −57.2718 | + | 356.065i | −0.102271 | + | 0.635830i | ||||
\(561\) | −228.411 | −0.407151 | ||||||||
\(562\) | −470.107 | −0.836489 | ||||||||
\(563\) | −490.117 | −0.870545 | −0.435273 | − | 0.900299i | \(-0.643348\pi\) | ||||
−0.435273 | + | 0.900299i | \(0.643348\pi\) | |||||||
\(564\) | 200.412 | 0.355341 | ||||||||
\(565\) | 112.291 | − | 698.125i | 0.198745 | − | 1.23562i | ||||
\(566\) | 309.866i | 0.547467i | ||||||||
\(567\) | 114.451 | 0.201854 | ||||||||
\(568\) | − | 326.501i | − | 0.574826i | ||||||
\(569\) | 58.9176i | 0.103546i | 0.998659 | + | 0.0517729i | \(0.0164872\pi\) | ||||
−0.998659 | + | 0.0517729i | \(0.983513\pi\) | |||||||
\(570\) | −137.050 | − | 22.0440i | −0.240439 | − | 0.0386737i | ||||
\(571\) | − | 248.329i | − | 0.434903i | −0.976071 | − | 0.217451i | \(-0.930226\pi\) | ||
0.976071 | − | 0.217451i | \(-0.0697743\pi\) | |||||||
\(572\) | 117.818 | 0.205975 | ||||||||
\(573\) | 18.0459 | 0.0314937 | ||||||||
\(574\) | 1239.21i | 2.15890i | ||||||||
\(575\) | 356.071 | − | 451.484i | 0.619255 | − | 0.785190i | ||||
\(576\) | 184.132 | 0.319673 | ||||||||
\(577\) | − | 261.919i | − | 0.453933i | −0.973903 | − | 0.226966i | \(-0.927119\pi\) | ||
0.973903 | − | 0.226966i | \(-0.0728808\pi\) | |||||||
\(578\) | − | 985.840i | − | 1.70561i | ||||||
\(579\) | 607.011 | 1.04838 | ||||||||
\(580\) | −38.1041 | + | 236.897i | −0.0656967 | + | 0.408443i | ||||
\(581\) | 1081.64 | 1.86169 | ||||||||
\(582\) | −102.437 | −0.176008 | ||||||||
\(583\) | 153.552i | 0.263383i | ||||||||
\(584\) | −779.316 | −1.33445 | ||||||||
\(585\) | −228.607 | − | 36.7706i | −0.390780 | − | 0.0628557i | ||||
\(586\) | − | 47.3782i | − | 0.0808501i | ||||||
\(587\) | − | 346.649i | − | 0.590543i | −0.955413 | − | 0.295272i | \(-0.904590\pi\) | ||
0.955413 | − | 0.295272i | \(-0.0954101\pi\) | |||||||
\(588\) | − | 348.535i | − | 0.592747i | ||||||
\(589\) | 7.50451i | 0.0127411i | ||||||||
\(590\) | 193.234 | + | 31.0810i | 0.327515 | + | 0.0526797i | ||||
\(591\) | −229.725 | −0.388705 | ||||||||
\(592\) | 154.884 | 0.261628 | ||||||||
\(593\) | − | 27.2582i | − | 0.0459667i | −0.999736 | − | 0.0229833i | \(-0.992684\pi\) | ||
0.999736 | − | 0.0229833i | \(-0.00731647\pi\) | |||||||
\(594\) | − | 33.0607i | − | 0.0556577i | ||||||
\(595\) | 311.460 | − | 1936.38i | 0.523462 | − | 3.25442i | ||||
\(596\) | − | 250.560i | − | 0.420403i | ||||||
\(597\) | −587.227 | −0.983630 | ||||||||
\(598\) | −180.595 | + | 496.543i | −0.301999 | + | 0.830340i | ||||
\(599\) | −475.431 | −0.793707 | −0.396854 | − | 0.917882i | \(-0.629898\pi\) | ||||
−0.396854 | + | 0.917882i | \(0.629898\pi\) | |||||||
\(600\) | 354.004 | + | 116.905i | 0.590007 | + | 0.194842i | ||||
\(601\) | 65.9612 | 0.109752 | 0.0548762 | − | 0.998493i | \(-0.482524\pi\) | ||||
0.0548762 | + | 0.998493i | \(0.482524\pi\) | |||||||
\(602\) | 646.222i | 1.07346i | ||||||||
\(603\) | 18.0294 | 0.0298994 | ||||||||
\(604\) | −382.455 | −0.633203 | ||||||||
\(605\) | 81.5639 | − | 507.091i | 0.134816 | − | 0.838167i | ||||
\(606\) | 255.308 | 0.421300 | ||||||||
\(607\) | 660.549i | 1.08822i | 0.839014 | + | 0.544110i | \(0.183132\pi\) | ||||
−0.839014 | + | 0.544110i | \(0.816868\pi\) | |||||||
\(608\) | 280.005 | 0.460534 | ||||||||
\(609\) | 592.073i | 0.972205i | ||||||||
\(610\) | 96.4375 | − | 599.562i | 0.158094 | − | 0.982888i | ||||
\(611\) | −1000.48 | −1.63745 | ||||||||
\(612\) | −165.200 | −0.269934 | ||||||||
\(613\) | 408.810 | 0.666901 | 0.333450 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333450 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(614\) | −367.566 | −0.598642 | ||||||||
\(615\) | 559.873 | + | 90.0537i | 0.910362 | + | 0.146429i | ||||
\(616\) | −468.090 | −0.759886 | ||||||||
\(617\) | 721.912 | 1.17004 | 0.585018 | − | 0.811020i | \(-0.301087\pi\) | ||||
0.585018 | + | 0.811020i | \(0.301087\pi\) | |||||||
\(618\) | 75.9497 | 0.122896 | ||||||||
\(619\) | − | 1152.86i | − | 1.86245i | −0.364443 | − | 0.931226i | \(-0.618741\pi\) | ||
0.364443 | − | 0.931226i | \(-0.381259\pi\) | |||||||
\(620\) | 0.987698 | − | 6.14062i | 0.00159306 | − | 0.00990423i | ||||
\(621\) | −112.314 | − | 40.8490i | −0.180859 | − | 0.0657794i | ||||
\(622\) | 629.093i | 1.01140i | ||||||||
\(623\) | 73.8682i | 0.118569i | ||||||||
\(624\) | −151.647 | −0.243023 | ||||||||
\(625\) | 502.084 | + | 372.205i | 0.803335 | + | 0.595528i | ||||
\(626\) | − | 650.206i | − | 1.03867i | ||||||
\(627\) | − | 79.7555i | − | 0.127202i | ||||||
\(628\) | 388.705 | 0.618956 | ||||||||
\(629\) | −842.300 | −1.33911 | ||||||||
\(630\) | 280.275 | + | 45.0813i | 0.444881 | + | 0.0715576i | ||||
\(631\) | 242.746i | 0.384701i | 0.981326 | + | 0.192350i | \(0.0616110\pi\) | ||||
−0.981326 | + | 0.192350i | \(0.938389\pi\) | |||||||
\(632\) | −458.735 | −0.725846 | ||||||||
\(633\) | 245.036i | 0.387103i | ||||||||
\(634\) | −382.081 | −0.602652 | ||||||||
\(635\) | 884.593 | + | 142.284i | 1.39306 | + | 0.224069i | ||||
\(636\) | 111.057i | 0.174618i | ||||||||
\(637\) | 1739.93i | 2.73144i | ||||||||
\(638\) | 171.028 | 0.268069 | ||||||||
\(639\) | −113.768 | −0.178041 | ||||||||
\(640\) | −62.4394 | − | 10.0432i | −0.0975615 | − | 0.0156924i | ||||
\(641\) | 422.353i | 0.658897i | 0.944174 | + | 0.329448i | \(0.106863\pi\) | ||||
−0.944174 | + | 0.329448i | \(0.893137\pi\) | |||||||
\(642\) | −165.888 | −0.258393 | ||||||||
\(643\) | −746.759 | −1.16137 | −0.580683 | − | 0.814129i | \(-0.697215\pi\) | ||||
−0.580683 | + | 0.814129i | \(0.697215\pi\) | |||||||
\(644\) | −178.474 | + | 490.712i | −0.277134 | + | 0.761975i | ||||
\(645\) | 291.962 | + | 46.9611i | 0.452654 | + | 0.0728079i | ||||
\(646\) | 494.407 | 0.765336 | ||||||||
\(647\) | 813.975i | 1.25808i | 0.777375 | + | 0.629038i | \(0.216551\pi\) | ||||
−0.777375 | + | 0.629038i | \(0.783449\pi\) | |||||||
\(648\) | − | 77.4867i | − | 0.119578i | ||||||
\(649\) | 112.451i | 0.173269i | ||||||||
\(650\) | −545.343 | − | 180.092i | −0.838989 | − | 0.277065i | ||||
\(651\) | − | 15.3472i | − | 0.0235747i | ||||||
\(652\) | − | 172.599i | − | 0.264722i | ||||||
\(653\) | 1014.21i | 1.55316i | 0.630018 | + | 0.776580i | \(0.283047\pi\) | ||||
−0.630018 | + | 0.776580i | \(0.716953\pi\) | |||||||
\(654\) | − | 203.061i | − | 0.310491i | ||||||
\(655\) | −78.1551 | + | 485.899i | −0.119321 | + | 0.741830i | ||||
\(656\) | 371.393 | 0.566148 | ||||||||
\(657\) | 271.550i | 0.413319i | ||||||||
\(658\) | 1226.60 | 1.86414 | ||||||||
\(659\) | 364.372i | 0.552917i | 0.961026 | + | 0.276458i | \(0.0891608\pi\) | ||||
−0.961026 | + | 0.276458i | \(0.910839\pi\) | |||||||
\(660\) | −10.4969 | + | 65.2605i | −0.0159044 | + | 0.0988795i | ||||
\(661\) | − | 420.665i | − | 0.636408i | −0.948022 | − | 0.318204i | \(-0.896920\pi\) | ||
0.948022 | − | 0.318204i | \(-0.103080\pi\) | |||||||
\(662\) | − | 870.640i | − | 1.31517i | ||||||
\(663\) | 824.697 | 1.24389 | ||||||||
\(664\) | − | 732.305i | − | 1.10287i | ||||||
\(665\) | 676.134 | + | 108.754i | 1.01674 | + | 0.163540i | ||||
\(666\) | − | 121.916i | − | 0.183057i | ||||||
\(667\) | 211.318 | − | 581.016i | 0.316819 | − | 0.871088i | ||||
\(668\) | − | 261.839i | − | 0.391974i | ||||||
\(669\) | −650.222 | −0.971931 | ||||||||
\(670\) | 44.1515 | + | 7.10161i | 0.0658977 | + | 0.0105994i | ||||
\(671\) | 348.912 | 0.519987 | ||||||||
\(672\) | −572.626 | −0.852121 | ||||||||
\(673\) | − | 922.669i | − | 1.37098i | −0.728082 | − | 0.685490i | \(-0.759588\pi\) | ||
0.728082 | − | 0.685490i | \(-0.240412\pi\) | |||||||
\(674\) | − | 574.847i | − | 0.852889i | ||||||
\(675\) | 40.7353 | − | 123.352i | 0.0603486 | − | 0.182743i | ||||
\(676\) | −123.682 | −0.182962 | ||||||||
\(677\) | 401.668 | 0.593306 | 0.296653 | − | 0.954985i | \(-0.404129\pi\) | ||||
0.296653 | + | 0.954985i | \(0.404129\pi\) | |||||||
\(678\) | −364.530 | −0.537654 | ||||||||
\(679\) | 505.371 | 0.744287 | ||||||||
\(680\) | −1310.99 | − | 210.868i | −1.92792 | − | 0.310099i | ||||
\(681\) | 558.594i | 0.820256i | ||||||||
\(682\) | −4.43323 | −0.00650034 | ||||||||
\(683\) | − | 159.499i | − | 0.233527i | −0.993160 | − | 0.116763i | \(-0.962748\pi\) | ||
0.993160 | − | 0.116763i | \(-0.0372519\pi\) | |||||||
\(684\) | − | 57.6836i | − | 0.0843327i | ||||||
\(685\) | −83.4677 | + | 518.927i | −0.121851 | + | 0.757558i | ||||
\(686\) | − | 1205.84i | − | 1.75779i | ||||||
\(687\) | 35.8120 | 0.0521280 | ||||||||
\(688\) | 193.674 | 0.281502 | ||||||||
\(689\) | − | 554.411i | − | 0.804661i | ||||||
\(690\) | −258.951 | − | 144.273i | −0.375291 | − | 0.209092i | ||||
\(691\) | −936.445 | −1.35520 | −0.677601 | − | 0.735429i | \(-0.736981\pi\) | ||||
−0.677601 | + | 0.735429i | \(0.736981\pi\) | |||||||
\(692\) | − | 11.7224i | − | 0.0169400i | ||||||
\(693\) | 163.104i | 0.235360i | ||||||||
\(694\) | 363.519 | 0.523802 | ||||||||
\(695\) | 67.3397 | − | 418.658i | 0.0968916 | − | 0.602385i | ||||
\(696\) | 400.851 | 0.575935 | ||||||||
\(697\) | −2019.74 | −2.89776 | ||||||||
\(698\) | − | 461.045i | − | 0.660523i | ||||||
\(699\) | 305.453 | 0.436985 | ||||||||
\(700\) | −538.938 | − | 177.977i | −0.769912 | − | 0.254253i | ||||
\(701\) | 98.0933i | 0.139933i | 0.997549 | + | 0.0699667i | \(0.0222893\pi\) | ||||
−0.997549 | + | 0.0699667i | \(0.977711\pi\) | |||||||
\(702\) | 119.368i | 0.170040i | ||||||||
\(703\) | − | 294.110i | − | 0.418364i | ||||||
\(704\) | 262.407i | 0.372737i | ||||||||
\(705\) | 89.1376 | − | 554.178i | 0.126436 | − | 0.786068i | ||||
\(706\) | 814.393 | 1.15353 | ||||||||
\(707\) | −1259.56 | −1.78155 | ||||||||
\(708\) | 81.3311i | 0.114874i | ||||||||
\(709\) | 919.680i | 1.29715i | 0.761150 | + | 0.648576i | \(0.224635\pi\) | ||||
−0.761150 | + | 0.648576i | \(0.775365\pi\) | |||||||
\(710\) | −278.603 | − | 44.8124i | −0.392399 | − | 0.0631161i | ||||
\(711\) | 159.845i | 0.224817i | ||||||||
\(712\) | 50.0109 | 0.0702401 | ||||||||
\(713\) | −5.47760 | + | 15.0606i | −0.00768246 | + | 0.0211228i | ||||
\(714\) | −1011.09 | −1.41609 | ||||||||
\(715\) | 52.4019 | − | 325.788i | 0.0732893 | − | 0.455647i | ||||
\(716\) | 124.411 | 0.173759 | ||||||||
\(717\) | − | 552.266i | − | 0.770245i | ||||||
\(718\) | −751.588 | −1.04678 | ||||||||
\(719\) | 748.619 | 1.04119 | 0.520597 | − | 0.853802i | \(-0.325709\pi\) | ||||
0.520597 | + | 0.853802i | \(0.325709\pi\) | |||||||
\(720\) | 13.5109 | − | 83.9988i | 0.0187652 | − | 0.116665i | ||||
\(721\) | −374.697 | −0.519690 | ||||||||
\(722\) | − | 364.607i | − | 0.504996i | ||||||
\(723\) | −403.264 | −0.557765 | ||||||||
\(724\) | − | 217.834i | − | 0.300875i | ||||||
\(725\) | 638.117 | + | 210.730i | 0.880162 | + | 0.290662i | ||||
\(726\) | −264.780 | −0.364711 | ||||||||
\(727\) | 37.0930 | 0.0510220 | 0.0255110 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255110 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(728\) | 1690.07 | 2.32153 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −106.961 | + | 664.990i | −0.146522 | + | 0.910945i | ||||
\(731\) | −1053.25 | −1.44084 | ||||||||
\(732\) | 252.352 | 0.344743 | ||||||||
\(733\) | −1282.77 | −1.75003 | −0.875017 | − | 0.484093i | \(-0.839150\pi\) | ||||
−0.875017 | + | 0.484093i | \(0.839150\pi\) | |||||||
\(734\) | − | 59.9052i | − | 0.0816148i | ||||||
\(735\) | −963.765 | − | 155.018i | −1.31125 | − | 0.210909i | ||||
\(736\) | 561.932 | + | 204.377i | 0.763494 | + | 0.277687i | ||||
\(737\) | 25.6937i | 0.0348625i | ||||||||
\(738\) | − | 292.341i | − | 0.396125i | ||||||
\(739\) | 881.738 | 1.19315 | 0.596575 | − | 0.802557i | \(-0.296528\pi\) | ||||
0.596575 | + | 0.802557i | \(0.296528\pi\) | |||||||
\(740\) | −38.7089 | + | 240.657i | −0.0523094 | + | 0.325213i | ||||
\(741\) | 287.963i | 0.388614i | ||||||||
\(742\) | 679.716i | 0.916060i | ||||||||
\(743\) | −704.213 | −0.947797 | −0.473899 | − | 0.880579i | \(-0.657154\pi\) | ||||
−0.473899 | + | 0.880579i | \(0.657154\pi\) | |||||||
\(744\) | −10.3905 | −0.0139657 | ||||||||
\(745\) | −692.847 | − | 111.442i | −0.929995 | − | 0.149587i | ||||
\(746\) | 862.495i | 1.15616i | ||||||||
\(747\) | −255.169 | −0.341592 | ||||||||
\(748\) | − | 235.427i | − | 0.314742i | ||||||
\(749\) | 818.406 | 1.09267 | ||||||||
\(750\) | 148.342 | − | 286.026i | 0.197790 | − | 0.381368i | ||||
\(751\) | 705.883i | 0.939924i | 0.882687 | + | 0.469962i | \(0.155732\pi\) | ||||
−0.882687 | + | 0.469962i | \(0.844268\pi\) | |||||||
\(752\) | − | 367.615i | − | 0.488850i | ||||||
\(753\) | −673.163 | −0.893974 | ||||||||
\(754\) | −617.510 | −0.818978 | ||||||||
\(755\) | −170.105 | + | 1057.56i | −0.225304 | + | 1.40074i | ||||
\(756\) | 117.966i | 0.156040i | ||||||||
\(757\) | 1368.07 | 1.80722 | 0.903611 | − | 0.428355i | \(-0.140907\pi\) | ||||
0.903611 | + | 0.428355i | \(0.140907\pi\) | |||||||
\(758\) | −498.546 | −0.657712 | ||||||||
\(759\) | 58.2141 | − | 160.059i | 0.0766984 | − | 0.210881i | ||||
\(760\) | 73.6296 | − | 457.763i | 0.0968810 | − | 0.602319i | ||||
\(761\) | 698.938 | 0.918447 | 0.459223 | − | 0.888321i | \(-0.348128\pi\) | ||||
0.459223 | + | 0.888321i | \(0.348128\pi\) | |||||||
\(762\) | − | 461.895i | − | 0.606161i | ||||||
\(763\) | 1001.80i | 1.31297i | ||||||||
\(764\) | 18.6002i | 0.0243458i | ||||||||
\(765\) | −73.4762 | + | 456.809i | −0.0960473 | + | 0.597136i | ||||
\(766\) | − | 756.138i | − | 0.987125i | ||||||
\(767\) | − | 406.014i | − | 0.529354i | ||||||
\(768\) | 457.837i | 0.596142i | ||||||||
\(769\) | − | 299.988i | − | 0.390101i | −0.980793 | − | 0.195050i | \(-0.937513\pi\) | ||
0.980793 | − | 0.195050i | \(-0.0624871\pi\) | |||||||
\(770\) | −64.2455 | + | 399.421i | −0.0834357 | + | 0.518728i | ||||
\(771\) | −85.0126 | −0.110263 | ||||||||
\(772\) | 625.654i | 0.810433i | ||||||||
\(773\) | −1493.57 | −1.93217 | −0.966086 | − | 0.258219i | \(-0.916864\pi\) | ||||
−0.966086 | + | 0.258219i | \(0.916864\pi\) | |||||||
\(774\) | − | 152.449i | − | 0.196963i | ||||||
\(775\) | −16.5407 | − | 5.46235i | −0.0213428 | − | 0.00704819i | ||||
\(776\) | − | 342.151i | − | 0.440916i | ||||||
\(777\) | 601.471i | 0.774094i | ||||||||
\(778\) | 551.112 | 0.708370 | ||||||||
\(779\) | − | 705.241i | − | 0.905316i | ||||||
\(780\) | 37.8999 | − | 235.628i | 0.0485897 | − | 0.302087i | ||||
\(781\) | − | 162.132i | − | 0.207595i | ||||||
\(782\) | 992.209 | + | 360.871i | 1.26881 | + | 0.461472i | ||||
\(783\) | − | 139.675i | − | 0.178385i | ||||||
\(784\) | −639.316 | −0.815454 | ||||||||
\(785\) | 172.885 | − | 1074.84i | 0.220235 | − | 1.36923i | ||||
\(786\) | 253.714 | 0.322792 | ||||||||
\(787\) | 97.7533 | 0.124210 | 0.0621050 | − | 0.998070i | \(-0.480219\pi\) | ||||
0.0621050 | + | 0.998070i | \(0.480219\pi\) | |||||||
\(788\) | − | 236.781i | − | 0.300483i | ||||||
\(789\) | 586.554i | 0.743414i | ||||||||
\(790\) | −62.9615 | + | 391.438i | −0.0796981 | + | 0.495491i | ||||
\(791\) | 1798.40 | 2.27358 | ||||||||
\(792\) | 110.426 | 0.139427 | ||||||||
\(793\) | −1259.77 | −1.58861 | ||||||||
\(794\) | 360.855 | 0.454478 | ||||||||
\(795\) | 307.095 | + | 49.3951i | 0.386283 | + | 0.0621323i | ||||
\(796\) | − | 605.263i | − | 0.760381i | ||||||
\(797\) | 230.206 | 0.288841 | 0.144420 | − | 0.989516i | \(-0.453868\pi\) | ||||
0.144420 | + | 0.989516i | \(0.453868\pi\) | |||||||
\(798\) | − | 353.047i | − | 0.442415i | ||||||
\(799\) | 1999.19i | 2.50212i | ||||||||
\(800\) | −203.808 | + | 617.158i | −0.254760 | + | 0.771447i | ||||
\(801\) | − | 17.4262i | − | 0.0217555i | ||||||
\(802\) | 747.271 | 0.931759 | ||||||||
\(803\) | −386.987 | −0.481927 | ||||||||
\(804\) | 18.5831i | 0.0231133i | ||||||||
\(805\) | 1277.53 | + | 711.770i | 1.58699 | + | 0.884186i | ||||
\(806\) | 16.0065 | 0.0198592 | ||||||||
\(807\) | 271.220i | 0.336084i | ||||||||
\(808\) | 852.757i | 1.05539i | ||||||||
\(809\) | −573.439 | −0.708825 | −0.354412 | − | 0.935089i | \(-0.615319\pi\) | ||||
−0.354412 | + | 0.935089i | \(0.615319\pi\) | |||||||
\(810\) | −66.1193 | − | 10.6351i | −0.0816288 | − | 0.0131297i | ||||
\(811\) | −667.428 | −0.822969 | −0.411485 | − | 0.911417i | \(-0.634990\pi\) | ||||
−0.411485 | + | 0.911417i | \(0.634990\pi\) | |||||||
\(812\) | −610.257 | −0.751548 | ||||||||
\(813\) | − | 246.381i | − | 0.303052i | ||||||
\(814\) | 173.743 | 0.213443 | ||||||||
\(815\) | −477.268 | − | 76.7670i | −0.585605 | − | 0.0941926i | ||||
\(816\) | 303.025i | 0.371354i | ||||||||
\(817\) | − | 367.769i | − | 0.450145i | ||||||
\(818\) | 246.103i | 0.300859i | ||||||||
\(819\) | − | 588.901i | − | 0.719049i | ||||||
\(820\) | −92.8195 | + | 577.068i | −0.113195 | + | 0.703742i | ||||
\(821\) | 260.045 | 0.316742 | 0.158371 | − | 0.987380i | \(-0.449376\pi\) | ||||
0.158371 | + | 0.987380i | \(0.449376\pi\) | |||||||
\(822\) | 270.961 | 0.329636 | ||||||||
\(823\) | 1087.33i | 1.32118i | 0.750747 | + | 0.660590i | \(0.229694\pi\) | ||||
−0.750747 | + | 0.660590i | \(0.770306\pi\) | |||||||
\(824\) | 253.681i | 0.307865i | ||||||||
\(825\) | 175.789 | + | 58.0520i | 0.213077 | + | 0.0703660i | ||||
\(826\) | 497.780i | 0.602639i | ||||||||
\(827\) | 1253.20 | 1.51536 | 0.757681 | − | 0.652625i | \(-0.226332\pi\) | ||||
0.757681 | + | 0.652625i | \(0.226332\pi\) | |||||||
\(828\) | 42.1037 | − | 115.763i | 0.0508498 | − | 0.139811i | ||||
\(829\) | −512.397 | −0.618090 | −0.309045 | − | 0.951047i | \(-0.600009\pi\) | ||||
−0.309045 | + | 0.951047i | \(0.600009\pi\) | |||||||
\(830\) | −624.875 | − | 100.509i | −0.752862 | − | 0.121095i | ||||
\(831\) | 330.474 | 0.397682 | ||||||||
\(832\) | − | 947.440i | − | 1.13875i | ||||||
\(833\) | 3476.78 | 4.17380 | ||||||||
\(834\) | −218.604 | −0.262115 | ||||||||
\(835\) | −724.034 | − | 116.458i | −0.867107 | − | 0.139471i | ||||
\(836\) | 82.2050 | 0.0983314 | ||||||||
\(837\) | 3.62053i | 0.00432560i | ||||||||
\(838\) | 145.693 | 0.173857 | ||||||||
\(839\) | 781.458i | 0.931416i | 0.884938 | + | 0.465708i | \(0.154200\pi\) | ||||
−0.884938 | + | 0.465708i | \(0.845800\pi\) | |||||||
\(840\) | −150.577 | + | 936.151i | −0.179258 | + | 1.11446i | ||||
\(841\) | −118.439 | −0.140831 | ||||||||
\(842\) | 863.400 | 1.02542 | ||||||||
\(843\) | −547.135 | −0.649033 | ||||||||
\(844\) | −252.562 | −0.299244 | ||||||||
\(845\) | −55.0103 | + | 342.004i | −0.0651009 | + | 0.404739i | ||||
\(846\) | −289.367 | −0.342041 | ||||||||
\(847\) | 1306.29 | 1.54225 | ||||||||
\(848\) | 203.712 | 0.240226 | ||||||||
\(849\) | 360.639i | 0.424781i | ||||||||
\(850\) | −359.866 | + | 1089.72i | −0.423372 | + | 1.28203i | ||||
\(851\) | 214.673 | − | 590.239i | 0.252259 | − | 0.693582i | ||||
\(852\) | − | 117.263i | − | 0.137632i | ||||||
\(853\) | − | 45.5152i | − | 0.0533589i | −0.999644 | − | 0.0266795i | \(-0.991507\pi\) | ||
0.999644 | − | 0.0266795i | \(-0.00849335\pi\) | |||||||
\(854\) | 1544.50 | 1.80855 | ||||||||
\(855\) | −159.506 | − | 25.6560i | −0.186557 | − | 0.0300070i | ||||
\(856\) | − | 554.085i | − | 0.647296i | ||||||
\(857\) | − | 766.778i | − | 0.894724i | −0.894353 | − | 0.447362i | \(-0.852364\pi\) | ||
0.894353 | − | 0.447362i | \(-0.147636\pi\) | |||||||
\(858\) | −170.112 | −0.198266 | ||||||||
\(859\) | 1073.34 | 1.24952 | 0.624761 | − | 0.780816i | \(-0.285196\pi\) | ||||
0.624761 | + | 0.780816i | \(0.285196\pi\) | |||||||
\(860\) | −48.4035 | + | 300.929i | −0.0562831 | + | 0.349918i | ||||
\(861\) | 1442.26i | 1.67510i | ||||||||
\(862\) | −1067.75 | −1.23869 | ||||||||
\(863\) | − | 998.850i | − | 1.15742i | −0.815535 | − | 0.578708i | \(-0.803557\pi\) | ||
0.815535 | − | 0.578708i | \(-0.196443\pi\) | |||||||
\(864\) | 135.087 | 0.156351 | ||||||||
\(865\) | −32.4148 | − | 5.21381i | −0.0374737 | − | 0.00602753i | ||||
\(866\) | − | 606.887i | − | 0.700793i | ||||||
\(867\) | − | 1147.37i | − | 1.32338i | ||||||
\(868\) | 15.8185 | 0.0182241 | ||||||||
\(869\) | −227.795 | −0.262135 | ||||||||
\(870\) | 55.0169 | − | 342.046i | 0.0632378 | − | 0.393156i | ||||
\(871\) | − | 92.7690i | − | 0.106509i | ||||||
\(872\) | 678.246 | 0.777806 | ||||||||
\(873\) | −119.222 | −0.136565 | ||||||||
\(874\) | −126.007 | + | 346.454i | −0.144173 | + | 0.396400i | ||||
\(875\) | −731.845 | + | 1411.11i | −0.836395 | + | 1.61269i | ||||
\(876\) | −279.891 | −0.319510 | ||||||||
\(877\) | 147.510i | 0.168198i | 0.996457 | + | 0.0840991i | \(0.0268012\pi\) | ||||
−0.996457 | + | 0.0840991i | \(0.973199\pi\) | |||||||
\(878\) | 612.951i | 0.698122i | ||||||||
\(879\) | − | 55.1412i | − | 0.0627318i | ||||||
\(880\) | 119.707 | + | 19.2545i | 0.136031 | + | 0.0218801i | ||||
\(881\) | 1021.09i | 1.15902i | 0.814967 | + | 0.579508i | \(0.196755\pi\) | ||||
−0.814967 | + | 0.579508i | \(0.803245\pi\) | |||||||
\(882\) | 503.235i | 0.570561i | ||||||||
\(883\) | − | 1179.44i | − | 1.33572i | −0.744288 | − | 0.667858i | \(-0.767211\pi\) | ||
0.744288 | − | 0.667858i | \(-0.232789\pi\) | |||||||
\(884\) | 850.026i | 0.961568i | ||||||||
\(885\) | 224.896 | + | 36.1738i | 0.254120 | + | 0.0408743i | ||||
\(886\) | 641.967 | 0.724568 | ||||||||
\(887\) | 44.5648i | 0.0502421i | 0.999684 | + | 0.0251211i | \(0.00799713\pi\) | ||||
−0.999684 | + | 0.0251211i | \(0.992003\pi\) | |||||||
\(888\) | 407.213 | 0.458574 | ||||||||
\(889\) | 2278.75i | 2.56328i | ||||||||
\(890\) | 6.86402 | − | 42.6743i | 0.00771238 | − | 0.0479487i | ||||
\(891\) | − | 38.4778i | − | 0.0431849i | ||||||
\(892\) | − | 670.192i | − | 0.751336i | ||||||
\(893\) | −698.067 | −0.781710 | ||||||||
\(894\) | 361.774i | 0.404668i | ||||||||
\(895\) | 55.3347 | − | 344.021i | 0.0618264 | − | 0.384381i | ||||
\(896\) | − | 160.847i | − | 0.179516i | ||||||
\(897\) | −210.186 | + | 577.903i | −0.234321 | + | 0.644262i | ||||
\(898\) | 637.688i | 0.710120i | ||||||||
\(899\) | −18.7296 | −0.0208338 | ||||||||
\(900\) | 127.140 | + | 41.9864i | 0.141267 | + | 0.0466516i | ||||
\(901\) | −1107.84 | −1.22957 | ||||||||
\(902\) | 416.615 | 0.461880 | ||||||||
\(903\) | 752.108i | 0.832899i | ||||||||
\(904\) | − | 1217.57i | − | 1.34687i | ||||||
\(905\) | −602.352 | − | 96.8862i | −0.665582 | − | 0.107057i | ||||
\(906\) | 552.210 | 0.609503 | ||||||||
\(907\) | −909.225 | −1.00245 | −0.501227 | − | 0.865316i | \(-0.667118\pi\) | ||||
−0.501227 | + | 0.865316i | \(0.667118\pi\) | |||||||
\(908\) | −575.751 | −0.634087 | ||||||||
\(909\) | 297.141 | 0.326888 | ||||||||
\(910\) | 231.963 | − | 1442.14i | 0.254905 | − | 1.58477i | ||||
\(911\) | 875.406i | 0.960929i | 0.877014 | + | 0.480464i | \(0.159532\pi\) | ||||
−0.877014 | + | 0.480464i | \(0.840468\pi\) | |||||||
\(912\) | −105.809 | −0.116018 | ||||||||
\(913\) | − | 363.643i | − | 0.398294i | ||||||
\(914\) | − | 622.862i | − | 0.681468i | ||||||
\(915\) | 112.239 | − | 697.802i | 0.122666 | − | 0.762625i | ||||
\(916\) | 36.9119i | 0.0402968i | ||||||||
\(917\) | −1251.70 | −1.36499 | ||||||||
\(918\) | 238.525 | 0.259831 | ||||||||
\(919\) | − | 357.631i | − | 0.389152i | −0.980887 | − | 0.194576i | \(-0.937667\pi\) | ||
0.980887 | − | 0.194576i | \(-0.0623331\pi\) | |||||||
\(920\) | 481.889 | − | 864.925i | 0.523792 | − | 0.940136i | ||||
\(921\) | −427.793 | −0.464487 | ||||||||
\(922\) | − | 278.445i | − | 0.302001i | ||||||
\(923\) | 585.388i | 0.634224i | ||||||||
\(924\) | −168.114 | −0.181942 | ||||||||
\(925\) | 648.246 | + | 214.075i | 0.700807 | + | 0.231432i | ||||
\(926\) | −1364.15 | −1.47316 | ||||||||
\(927\) | 88.3942 | 0.0953552 | ||||||||
\(928\) | 698.828i | 0.753047i | ||||||||
\(929\) | −833.634 | −0.897346 | −0.448673 | − | 0.893696i | \(-0.648103\pi\) | ||||
−0.448673 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(930\) | −1.42610 | + | 8.86619i | −0.00153344 | + | 0.00953353i | ||||
\(931\) | 1214.00i | 1.30398i | ||||||||
\(932\) | 314.834i | 0.337805i | ||||||||
\(933\) | 732.172i | 0.784751i | ||||||||
\(934\) | 439.341i | 0.470386i | ||||||||
\(935\) | −651.000 | − | 104.711i | −0.696256 | − | 0.111990i | ||||
\(936\) | −398.703 | −0.425965 | ||||||||
\(937\) | 405.050 | 0.432284 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(938\) | 113.736i | 0.121254i | ||||||||
\(939\) | − | 756.744i | − | 0.805904i | ||||||
\(940\) | 571.198 | + | 91.8754i | 0.607658 | + | 0.0977397i | ||||
\(941\) | 95.5436i | 0.101534i | 0.998711 | + | 0.0507670i | \(0.0161666\pi\) | ||||
−0.998711 | + | 0.0507670i | \(0.983833\pi\) | |||||||
\(942\) | −561.234 | −0.595790 | ||||||||
\(943\) | 514.760 | − | 1415.32i | 0.545875 | − | 1.50087i | ||||
\(944\) | 149.185 | 0.158035 | ||||||||
\(945\) | 326.199 | + | 52.4680i | 0.345184 | + | 0.0555217i | ||||
\(946\) | 217.256 | 0.229658 | ||||||||
\(947\) | − | 1280.55i | − | 1.35222i | −0.736801 | − | 0.676109i | \(-0.763665\pi\) | ||
0.736801 | − | 0.676109i | \(-0.236335\pi\) | |||||||
\(948\) | −164.754 | −0.173791 | ||||||||
\(949\) | 1397.25 | 1.47234 | ||||||||
\(950\) | −380.503 | − | 125.656i | −0.400529 | − | 0.132270i | ||||
\(951\) | −444.687 | −0.467599 | ||||||||
\(952\) | − | 3377.16i | − | 3.54743i | ||||||
\(953\) | 1307.15 | 1.37162 | 0.685809 | − | 0.727782i | \(-0.259449\pi\) | ||||
0.685809 | + | 0.727782i | \(0.259449\pi\) | |||||||
\(954\) | − | 160.351i | − | 0.168083i | ||||||
\(955\) | 51.4330 | + | 8.27282i | 0.0538565 | + | 0.00866264i | ||||
\(956\) | 569.228 | 0.595426 | ||||||||
\(957\) | 199.051 | 0.207995 | ||||||||
\(958\) | 704.953 | 0.735860 | ||||||||
\(959\) | −1336.78 | −1.39393 | ||||||||
\(960\) | 524.798 | + | 84.4119i | 0.546664 | + | 0.0879291i | ||||
\(961\) | −960.515 | −0.999495 | ||||||||
\(962\) | −627.312 | −0.652091 | ||||||||
\(963\) | −193.069 | −0.200487 | ||||||||
\(964\) | − | 415.650i | − | 0.431172i | ||||||
\(965\) | 1730.05 | + | 278.273i | 1.79280 | + | 0.288366i | ||||
\(966\) | 257.692 | − | 708.518i | 0.266761 | − | 0.733455i | ||||
\(967\) | 599.640i | 0.620103i | 0.950720 | + | 0.310051i | \(0.100346\pi\) | ||||
−0.950720 | + | 0.310051i | \(0.899654\pi\) | |||||||
\(968\) | − | 884.396i | − | 0.913632i | ||||||
\(969\) | 575.417 | 0.593826 | ||||||||
\(970\) | −291.957 | − | 46.9604i | −0.300987 | − | 0.0484127i | ||||
\(971\) | 118.802i | 0.122350i | 0.998127 | + | 0.0611751i | \(0.0194848\pi\) | ||||
−0.998127 | + | 0.0611751i | \(0.980515\pi\) | |||||||
\(972\) | − | 27.8293i | − | 0.0286309i | ||||||
\(973\) | 1078.48 | 1.10841 | ||||||||
\(974\) | 137.089 | 0.140748 | ||||||||
\(975\) | −634.699 | − | 209.601i | −0.650973 | − | 0.214975i | ||||
\(976\) | − | 462.888i | − | 0.474271i | ||||||
\(977\) | −665.578 | −0.681247 | −0.340623 | − | 0.940200i | \(-0.610638\pi\) | ||||
−0.340623 | + | 0.940200i | \(0.610638\pi\) | |||||||
\(978\) | 249.208i | 0.254814i | ||||||||
\(979\) | 24.8341 | 0.0253668 | ||||||||
\(980\) | 159.780 | − | 993.366i | 0.163040 | − | 1.01364i | ||||
\(981\) | − | 236.333i | − | 0.240910i | ||||||
\(982\) | 294.297i | 0.299691i | ||||||||
\(983\) | 715.970 | 0.728352 | 0.364176 | − | 0.931330i | \(-0.381351\pi\) | ||||
0.364176 | + | 0.931330i | \(0.381351\pi\) | |||||||
\(984\) | 976.451 | 0.992328 | ||||||||
\(985\) | −654.743 | − | 105.313i | −0.664714 | − | 0.106917i | ||||
\(986\) | 1233.93i | 1.25145i | ||||||||
\(987\) | 1427.59 | 1.44639 | ||||||||
\(988\) | −296.807 | −0.300412 | ||||||||
\(989\) | 268.437 | − | 738.062i | 0.271423 | − | 0.746271i | ||||
\(990\) | 15.1561 | − | 94.2269i | 0.0153092 | − | 0.0951787i | ||||
\(991\) | 1839.35 | 1.85606 | 0.928029 | − | 0.372507i | \(-0.121502\pi\) | ||||
0.928029 | + | 0.372507i | \(0.121502\pi\) | |||||||
\(992\) | − | 18.1144i | − | 0.0182605i | ||||||
\(993\) | − | 1013.30i | − | 1.02044i | ||||||
\(994\) | − | 717.695i | − | 0.722027i | ||||||
\(995\) | −1673.67 | − | 269.204i | −1.68208 | − | 0.270556i | ||||
\(996\) | − | 263.007i | − | 0.264063i | ||||||
\(997\) | 1310.89i | 1.31483i | 0.753528 | + | 0.657416i | \(0.228350\pi\) | ||||
−0.753528 | + | 0.657416i | \(0.771650\pi\) | |||||||
\(998\) | 1298.38i | 1.30098i | ||||||||
\(999\) | − | 141.892i | − | 0.142034i |
(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 | 345.3.d.a.229.16 | yes | 48 | |
5.4 | even | 2 | inner | 345.3.d.a.229.33 | yes | 48 | |
23.22 | odd | 2 | inner | 345.3.d.a.229.15 | ✓ | 48 | |
115.114 | odd | 2 | inner | 345.3.d.a.229.34 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
345.3.d.a.229.15 | ✓ | 48 | 23.22 | odd | 2 | inner | |
345.3.d.a.229.16 | yes | 48 | 1.1 | even | 1 | trivial | |
345.3.d.a.229.33 | yes | 48 | 5.4 | even | 2 | inner | |
345.3.d.a.229.34 | yes | 48 | 115.114 | odd | 2 | inner |