Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.7 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.8 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16953 | − | 0.795104i | −0.826986 | − | 0.562223i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.735620 | + | 1.85980i | 0.367810 | + | 0.929901i | ||||
\(5\) | 2.09311 | 0.936069 | 0.468035 | − | 0.883710i | \(-0.344962\pi\) | ||||
0.468035 | + | 0.883710i | \(0.344962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0.618402 | − | 2.76000i | 0.218638 | − | 0.975806i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.44797 | − | 1.66424i | −0.774116 | − | 0.526280i | ||||
\(11\) | 0.961211i | 0.289816i | 0.989445 | + | 0.144908i | \(0.0462886\pi\) | ||||
−0.989445 | + | 0.144908i | \(0.953711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60210i | 1.27639i | 0.769874 | + | 0.638196i | \(0.220319\pi\) | ||||
−0.769874 | + | 0.638196i | \(0.779681\pi\) | |||||||
\(14\) | −0.795104 | + | 1.16953i | −0.212500 | + | 0.312571i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.91773 | + | 2.73622i | −0.729431 | + | 0.684054i | ||||
\(17\) | − | 3.28066i | − | 0.795677i | −0.917455 | − | 0.397839i | \(-0.869760\pi\) | ||
0.917455 | − | 0.397839i | \(-0.130240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.66977 | 0.841904 | 0.420952 | − | 0.907083i | \(-0.361696\pi\) | ||||
0.420952 | + | 0.907083i | \(0.361696\pi\) | |||||||
\(20\) | 1.53974 | + | 3.89278i | 0.344296 | + | 0.870452i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.764262 | − | 1.12417i | 0.162941 | − | 0.239674i | ||||
\(23\) | 2.40322 | 0.501105 | 0.250553 | − | 0.968103i | \(-0.419388\pi\) | ||||
0.250553 | + | 0.968103i | \(0.419388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.618872 | −0.123774 | ||||||||
\(26\) | 3.65914 | − | 5.38231i | 0.717617 | − | 1.05556i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.85980 | − | 0.735620i | 0.351470 | − | 0.139019i | ||||
\(29\) | 9.31771 | 1.73026 | 0.865128 | − | 0.501552i | \(-0.167237\pi\) | ||||
0.865128 | + | 0.501552i | \(0.167237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84927i | 0.332138i | 0.986114 | + | 0.166069i | \(0.0531075\pi\) | ||||
−0.986114 | + | 0.166069i | \(0.946892\pi\) | |||||||
\(32\) | 5.58795 | − | 0.880204i | 0.987820 | − | 0.155600i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.60847 | + | 3.83684i | −0.447348 | + | 0.658013i | ||||
\(35\) | − | 2.09311i | − | 0.353801i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.29364i | 0.377072i | 0.982066 | + | 0.188536i | \(0.0603742\pi\) | ||||
−0.982066 | + | 0.188536i | \(0.939626\pi\) | |||||||
\(38\) | −4.29193 | − | 2.91785i | −0.696242 | − | 0.473338i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.29439 | − | 5.77699i | 0.204660 | − | 0.913422i | ||||
\(41\) | 0.314406i | 0.0491020i | 0.999699 | + | 0.0245510i | \(0.00781561\pi\) | ||||
−0.999699 | + | 0.0245510i | \(0.992184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.64261 | −1.31799 | −0.658993 | − | 0.752149i | \(-0.729017\pi\) | ||||
−0.658993 | + | 0.752149i | \(0.729017\pi\) | |||||||
\(44\) | −1.78766 | + | 0.707086i | −0.269500 | + | 0.106597i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.81064 | − | 1.91081i | −0.414407 | − | 0.281733i | ||||
\(47\) | 2.34305 | 0.341769 | 0.170884 | − | 0.985291i | \(-0.445338\pi\) | ||||
0.170884 | + | 0.985291i | \(0.445338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0.723792 | + | 0.492067i | 0.102360 | + | 0.0695888i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.55899 | + | 3.38540i | −1.18692 | + | 0.469470i | ||||
\(53\) | 7.73354 | 1.06228 | 0.531142 | − | 0.847283i | \(-0.321763\pi\) | ||||
0.531142 | + | 0.847283i | \(0.321763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.01192i | 0.271288i | ||||||||
\(56\) | −2.76000 | − | 0.618402i | −0.368820 | − | 0.0826374i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.8974 | − | 7.40855i | −1.43090 | − | 0.972790i | ||||
\(59\) | − | 7.99530i | − | 1.04090i | −0.853892 | − | 0.520450i | \(-0.825764\pi\) | ||
0.853892 | − | 0.520450i | \(-0.174236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6321i | 1.36130i | 0.732610 | + | 0.680649i | \(0.238302\pi\) | ||||
−0.732610 | + | 0.680649i | \(0.761698\pi\) | |||||||
\(62\) | 1.47036 | − | 2.16278i | 0.186736 | − | 0.274674i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.23516 | − | 3.41357i | −0.904395 | − | 0.426697i | ||||
\(65\) | 9.63272i | 1.19479i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.12203 | 0.503586 | 0.251793 | − | 0.967781i | \(-0.418980\pi\) | ||||
0.251793 | + | 0.967781i | \(0.418980\pi\) | |||||||
\(68\) | 6.10138 | − | 2.41332i | 0.739901 | − | 0.292658i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.66424 | + | 2.44797i | −0.198915 | + | 0.292588i | ||||
\(71\) | −6.79440 | −0.806347 | −0.403174 | − | 0.915124i | \(-0.632093\pi\) | ||||
−0.403174 | + | 0.915124i | \(0.632093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0267 | 1.87579 | 0.937894 | − | 0.346922i | \(-0.112773\pi\) | ||||
0.937894 | + | 0.346922i | \(0.112773\pi\) | |||||||
\(74\) | 1.82368 | − | 2.68249i | 0.211999 | − | 0.311833i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.69956 | + | 6.82505i | 0.309661 | + | 0.782887i | ||||
\(77\) | 0.961211 | 0.109540 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.26231i | 0.142021i | 0.997476 | + | 0.0710106i | \(0.0226224\pi\) | ||||
−0.997476 | + | 0.0710106i | \(0.977378\pi\) | |||||||
\(80\) | −6.10713 | + | 5.72721i | −0.682798 | + | 0.640322i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.249985 | − | 0.367709i | 0.0276063 | − | 0.0406066i | ||||
\(83\) | 2.99495i | 0.328738i | 0.986399 | + | 0.164369i | \(0.0525589\pi\) | ||||
−0.986399 | + | 0.164369i | \(0.947441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.86680i | − | 0.744809i | ||||||
\(86\) | 10.1078 | + | 6.87177i | 1.08995 | + | 0.741002i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.65294 | + | 0.594415i | 0.282804 | + | 0.0633648i | ||||
\(89\) | 12.8990i | 1.36729i | 0.729815 | + | 0.683645i | \(0.239606\pi\) | ||||
−0.729815 | + | 0.683645i | \(0.760394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.60210 | 0.482431 | ||||||||
\(92\) | 1.76785 | + | 4.46950i | 0.184312 | + | 0.465978i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.74028 | − | 1.86297i | −0.282638 | − | 0.192150i | ||||
\(95\) | 7.68126 | 0.788080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.98346 | 0.505994 | 0.252997 | − | 0.967467i | \(-0.418584\pi\) | ||||
0.252997 | + | 0.967467i | \(0.418584\pi\) | |||||||
\(98\) | 1.16953 | + | 0.795104i | 0.118141 | + | 0.0803176i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.455255 | − | 1.15098i | −0.0455255 | − | 0.115098i | ||||
\(101\) | −3.18764 | −0.317182 | −0.158591 | − | 0.987344i | \(-0.550695\pi\) | ||||
−0.158591 | + | 0.987344i | \(0.550695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.535425i | − | 0.0527570i | −0.999652 | − | 0.0263785i | \(-0.991602\pi\) | ||
0.999652 | − | 0.0263785i | \(-0.00839750\pi\) | |||||||
\(104\) | 12.7018 | + | 2.84595i | 1.24551 | + | 0.279068i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.04464 | − | 6.14897i | −0.878493 | − | 0.597240i | ||||
\(107\) | − | 9.70673i | − | 0.938385i | −0.883096 | − | 0.469193i | \(-0.844545\pi\) | ||
0.883096 | − | 0.469193i | \(-0.155455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.03576i | 0.769686i | 0.922982 | + | 0.384843i | \(0.125744\pi\) | ||||
−0.922982 | + | 0.384843i | \(0.874256\pi\) | |||||||
\(110\) | 1.59969 | − | 2.35301i | 0.152524 | − | 0.224351i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.73622 | + | 2.91773i | 0.258548 | + | 0.275699i | ||||
\(113\) | 12.7809i | 1.20233i | 0.799126 | + | 0.601163i | \(0.205296\pi\) | ||||
−0.799126 | + | 0.601163i | \(0.794704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.03021 | 0.469069 | ||||||||
\(116\) | 6.85430 | + | 17.3291i | 0.636406 | + | 1.60897i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.35709 | + | 9.35078i | −0.585218 | + | 0.860809i | ||||
\(119\) | −3.28066 | −0.300738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0761 | 0.916007 | ||||||||
\(122\) | 8.45360 | − | 12.4346i | 0.765353 | − | 1.12577i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.43927 | + | 1.36036i | −0.308856 | + | 0.122164i | ||||
\(125\) | −11.7609 | −1.05193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.6260i | − | 1.47532i | −0.675175 | − | 0.737658i | \(-0.735932\pi\) | ||
0.675175 | − | 0.737658i | \(-0.264068\pi\) | |||||||
\(128\) | 5.74762 | + | 9.74499i | 0.508023 | + | 0.861344i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.65901 | − | 11.2658i | 0.671739 | − | 0.988075i | ||||
\(131\) | − | 14.5603i | − | 1.27214i | −0.771632 | − | 0.636069i | \(-0.780560\pi\) | ||
0.771632 | − | 0.636069i | \(-0.219440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.66977i | − | 0.318210i | ||||||
\(134\) | −4.82086 | − | 3.27744i | −0.416459 | − | 0.283128i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.05461 | − | 2.02877i | −0.776426 | − | 0.173965i | ||||
\(137\) | − | 17.2672i | − | 1.47524i | −0.675216 | − | 0.737620i | \(-0.735950\pi\) | ||
0.675216 | − | 0.737620i | \(-0.264050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5580 | 1.23480 | 0.617398 | − | 0.786651i | \(-0.288187\pi\) | ||||
0.617398 | + | 0.786651i | \(0.288187\pi\) | |||||||
\(140\) | 3.89278 | − | 1.53974i | 0.329000 | − | 0.130132i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.94629 | + | 5.40225i | 0.666837 | + | 0.453347i | ||||
\(143\) | −4.42358 | −0.369919 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.5030 | 1.61964 | ||||||||
\(146\) | −18.7438 | − | 12.7429i | −1.55125 | − | 1.05461i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.26571 | + | 1.68725i | −0.350640 | + | 0.138691i | ||||
\(149\) | 20.1739 | 1.65271 | 0.826356 | − | 0.563148i | \(-0.190410\pi\) | ||||
0.826356 | + | 0.563148i | \(0.190410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9560i | 0.972966i | 0.873690 | + | 0.486483i | \(0.161720\pi\) | ||||
−0.873690 | + | 0.486483i | \(0.838280\pi\) | |||||||
\(152\) | 2.26940 | − | 10.1286i | 0.184072 | − | 0.821535i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.12417 | − | 0.764262i | −0.0905881 | − | 0.0615860i | ||||
\(155\) | 3.87073i | 0.310905i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.1011i | − | 1.76386i | −0.471381 | − | 0.881930i | \(-0.656244\pi\) | ||
0.471381 | − | 0.881930i | \(-0.343756\pi\) | |||||||
\(158\) | 1.00367 | − | 1.47632i | 0.0798476 | − | 0.117450i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.6962 | − | 1.84237i | 0.924668 | − | 0.145652i | ||||
\(161\) | − | 2.40322i | − | 0.189400i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2054 | 0.877674 | 0.438837 | − | 0.898567i | \(-0.355391\pi\) | ||||
0.438837 | + | 0.898567i | \(0.355391\pi\) | |||||||
\(164\) | −0.584733 | + | 0.231284i | −0.0456600 | + | 0.0180602i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.38130 | − | 3.50270i | 0.184824 | − | 0.271862i | ||||
\(167\) | −1.76628 | −0.136679 | −0.0683395 | − | 0.997662i | \(-0.521770\pi\) | ||||
−0.0683395 | + | 0.997662i | \(0.521770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.17930 | −0.629177 | ||||||||
\(170\) | −5.45982 | + | 8.03095i | −0.418749 | + | 0.615946i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.35768 | − | 16.0735i | −0.484768 | − | 1.22560i | ||||
\(173\) | −4.37240 | −0.332428 | −0.166214 | − | 0.986090i | \(-0.553154\pi\) | ||||
−0.166214 | + | 0.986090i | \(0.553154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.618872i | 0.0467823i | ||||||||
\(176\) | −2.63008 | − | 2.80455i | −0.198250 | − | 0.211401i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.2560 | − | 15.0858i | 0.768722 | − | 1.13073i | ||||
\(179\) | − | 17.0068i | − | 1.27115i | −0.772041 | − | 0.635573i | \(-0.780764\pi\) | ||
0.772041 | − | 0.635573i | \(-0.219236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.50624i | 0.632264i | 0.948715 | + | 0.316132i | \(0.102384\pi\) | ||||
−0.948715 | + | 0.316132i | \(0.897616\pi\) | |||||||
\(182\) | −5.38231 | − | 3.65914i | −0.398963 | − | 0.271234i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.48615 | − | 6.63287i | 0.109561 | − | 0.488981i | ||||
\(185\) | 4.80085i | 0.352965i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.15341 | 0.230600 | ||||||||
\(188\) | 1.72359 | + | 4.35761i | 0.125706 | + | 0.317811i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.98349 | − | 6.10739i | −0.651731 | − | 0.443077i | ||||
\(191\) | 0.725194 | 0.0524732 | 0.0262366 | − | 0.999656i | \(-0.491648\pi\) | ||||
0.0262366 | + | 0.999656i | \(0.491648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7648 | −1.13478 | −0.567388 | − | 0.823450i | \(-0.692046\pi\) | ||||
−0.567388 | + | 0.823450i | \(0.692046\pi\) | |||||||
\(194\) | −5.82833 | − | 3.96237i | −0.418450 | − | 0.284481i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.735620 | − | 1.85980i | −0.0525443 | − | 0.132843i | ||||
\(197\) | −5.76032 | −0.410406 | −0.205203 | − | 0.978719i | \(-0.565785\pi\) | ||||
−0.205203 | + | 0.978719i | \(0.565785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7773i | 0.834872i | 0.908706 | + | 0.417436i | \(0.137071\pi\) | ||||
−0.908706 | + | 0.417436i | \(0.862929\pi\) | |||||||
\(200\) | −0.382712 | + | 1.70808i | −0.0270618 | + | 0.120780i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.72805 | + | 2.53450i | 0.262305 | + | 0.178327i | ||||
\(203\) | − | 9.31771i | − | 0.653975i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.658088i | 0.0459629i | ||||||||
\(206\) | −0.425718 | + | 0.626197i | −0.0296612 | + | 0.0436292i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.5923 | − | 13.4277i | −0.873121 | − | 0.931040i | ||||
\(209\) | 3.52742i | 0.243997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9971 | 1.37666 | 0.688328 | − | 0.725399i | \(-0.258345\pi\) | ||||
0.688328 | + | 0.725399i | \(0.258345\pi\) | |||||||
\(212\) | 5.68895 | + | 14.3829i | 0.390719 | + | 0.987818i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.71786 | + | 11.3524i | −0.527582 | + | 0.776031i | ||||
\(215\) | −18.0900 | −1.23373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84927 | 0.125537 | ||||||||
\(218\) | 6.38926 | − | 9.39810i | 0.432735 | − | 0.636519i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.74178 | + | 1.48001i | −0.252271 | + | 0.0997824i | ||||
\(221\) | 15.0979 | 1.01560 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.84047i | − | 0.458071i | −0.973418 | − | 0.229036i | \(-0.926443\pi\) | ||
0.973418 | − | 0.229036i | \(-0.0735573\pi\) | |||||||
\(224\) | −0.880204 | − | 5.58795i | −0.0588111 | − | 0.373361i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1621 | − | 14.9477i | 0.675976 | − | 0.994307i | ||||
\(227\) | − | 13.9061i | − | 0.922981i | −0.887145 | − | 0.461490i | \(-0.847315\pi\) | ||
0.887145 | − | 0.461490i | \(-0.152685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.87934i | − | 0.256354i | −0.991751 | − | 0.128177i | \(-0.959087\pi\) | ||
0.991751 | − | 0.128177i | \(-0.0409126\pi\) | |||||||
\(230\) | −5.88300 | − | 3.99953i | −0.387913 | − | 0.263722i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.76209 | − | 25.7168i | 0.378300 | − | 1.68839i | ||||
\(233\) | 21.8307i | 1.43017i | 0.699035 | + | 0.715087i | \(0.253613\pi\) | ||||
−0.699035 | + | 0.715087i | \(0.746387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.90427 | 0.319919 | ||||||||
\(236\) | 14.8697 | − | 5.88151i | 0.967933 | − | 0.382853i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.83684 | + | 2.60847i | 0.248706 | + | 0.169082i | ||||
\(239\) | −27.8956 | −1.80441 | −0.902207 | − | 0.431303i | \(-0.858054\pi\) | ||||
−0.902207 | + | 0.431303i | \(0.858054\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.17606 | −0.397835 | −0.198918 | − | 0.980016i | \(-0.563743\pi\) | ||||
−0.198918 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(242\) | −11.7843 | − | 8.01152i | −0.757524 | − | 0.515000i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.7736 | + | 7.82117i | −1.26587 | + | 0.500699i | ||||
\(245\) | −2.09311 | −0.133724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8887i | 1.07460i | ||||||||
\(248\) | 5.10397 | + | 1.14359i | 0.324103 | + | 0.0726181i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.7548 | + | 9.35117i | 0.869931 | + | 0.591420i | ||||
\(251\) | 18.6366i | 1.17633i | 0.808740 | + | 0.588167i | \(0.200150\pi\) | ||||
−0.808740 | + | 0.588167i | \(0.799850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.31000i | 0.145228i | ||||||||
\(254\) | −13.2194 | + | 19.4446i | −0.829456 | + | 1.22006i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.02624 | − | 15.9671i | 0.0641402 | − | 0.997941i | ||||
\(257\) | 8.25845i | 0.515148i | 0.966259 | + | 0.257574i | \(0.0829231\pi\) | ||||
−0.966259 | + | 0.257574i | \(0.917077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.29364 | 0.142520 | ||||||||
\(260\) | −17.9149 | + | 7.08602i | −1.11104 | + | 0.439456i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.5769 | + | 17.0287i | −0.715225 | + | 1.05204i | ||||
\(263\) | −9.34158 | −0.576027 | −0.288013 | − | 0.957626i | \(-0.592995\pi\) | ||||
−0.288013 | + | 0.957626i | \(0.592995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1872 | 0.994371 | ||||||||
\(266\) | −2.91785 | + | 4.29193i | −0.178905 | + | 0.263155i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.03225 | + | 7.66616i | 0.185224 | + | 0.468286i | ||||
\(269\) | 11.9972 | 0.731484 | 0.365742 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365742 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7030i | 1.43986i | 0.694049 | + | 0.719928i | \(0.255825\pi\) | ||||
−0.694049 | + | 0.719928i | \(0.744175\pi\) | |||||||
\(272\) | 8.97660 | + | 9.57207i | 0.544286 | + | 0.580392i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.7292 | + | 20.1946i | −0.829414 | + | 1.22000i | ||||
\(275\) | − | 0.594866i | − | 0.0358718i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7688i | 0.827284i | 0.910440 | + | 0.413642i | \(0.135744\pi\) | ||||
−0.910440 | + | 0.413642i | \(0.864256\pi\) | |||||||
\(278\) | −17.0261 | − | 11.5751i | −1.02116 | − | 0.694230i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.77699 | − | 1.29439i | −0.345241 | − | 0.0773544i | ||||
\(281\) | 8.69078i | 0.518448i | 0.965817 | + | 0.259224i | \(0.0834669\pi\) | ||||
−0.965817 | + | 0.259224i | \(0.916533\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.7518 | −1.94689 | −0.973447 | − | 0.228913i | \(-0.926483\pi\) | ||||
−0.973447 | + | 0.228913i | \(0.926483\pi\) | |||||||
\(284\) | −4.99810 | − | 12.6362i | −0.296583 | − | 0.749823i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.17353 | + | 3.51721i | 0.305917 | + | 0.207977i | ||||
\(287\) | 0.314406 | 0.0185588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.23727 | 0.366898 | ||||||||
\(290\) | −22.8095 | − | 15.5069i | −1.33942 | − | 0.910599i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.7896 | + | 29.8066i | 0.689934 | + | 1.74430i | ||||
\(293\) | 12.3629 | 0.722249 | 0.361124 | − | 0.932518i | \(-0.382393\pi\) | ||||
0.361124 | + | 0.932518i | \(0.382393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 16.7351i | − | 0.974354i | ||||||
\(296\) | 6.33044 | + | 1.41839i | 0.367949 | + | 0.0824423i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.5941 | − | 16.0404i | −1.36677 | − | 0.929193i | ||||
\(299\) | 11.0598i | 0.639607i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.64261i | 0.498152i | ||||||||
\(302\) | 9.50627 | − | 13.9830i | 0.547024 | − | 0.804629i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.7074 | + | 10.0413i | −0.614111 | + | 0.575908i | ||||
\(305\) | 22.2542i | 1.27427i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.2600 | 0.870935 | 0.435468 | − | 0.900204i | \(-0.356583\pi\) | ||||
0.435468 | + | 0.900204i | \(0.356583\pi\) | |||||||
\(308\) | 0.707086 | + | 1.78766i | 0.0402900 | + | 0.101861i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.07763 | − | 4.52695i | 0.174798 | − | 0.257114i | ||||
\(311\) | −5.12076 | −0.290372 | −0.145186 | − | 0.989404i | \(-0.546378\pi\) | ||||
−0.145186 | + | 0.989404i | \(0.546378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7058 | −0.661649 | −0.330825 | − | 0.943692i | \(-0.607327\pi\) | ||||
−0.330825 | + | 0.943692i | \(0.607327\pi\) | |||||||
\(314\) | −17.5727 | + | 25.8480i | −0.991683 | + | 1.45869i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.34765 | + | 0.928583i | −0.132066 | + | 0.0522369i | ||||
\(317\) | −18.5302 | −1.04076 | −0.520379 | − | 0.853935i | \(-0.674209\pi\) | ||||
−0.520379 | + | 0.853935i | \(0.674209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.95628i | 0.501456i | ||||||||
\(320\) | −15.1440 | − | 7.14500i | −0.846576 | − | 0.399418i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.91081 | + | 2.81064i | −0.106485 | + | 0.156631i | ||||
\(323\) | − | 12.0393i | − | 0.669883i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.84811i | − | 0.157985i | ||||||
\(326\) | −13.1051 | − | 8.90945i | −0.725824 | − | 0.493449i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.867760 | + | 0.194429i | 0.0479140 | + | 0.0107356i | ||||
\(329\) | − | 2.34305i | − | 0.129176i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4688 | −1.12507 | −0.562534 | − | 0.826774i | \(-0.690174\pi\) | ||||
−0.562534 | + | 0.826774i | \(0.690174\pi\) | |||||||
\(332\) | −5.57001 | + | 2.20315i | −0.305694 | + | 0.120913i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.06573 | + | 1.40438i | 0.113032 | + | 0.0768442i | ||||
\(335\) | 8.62789 | 0.471392 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.9419 | −1.08631 | −0.543153 | − | 0.839634i | \(-0.682769\pi\) | ||||
−0.543153 | + | 0.839634i | \(0.682769\pi\) | |||||||
\(338\) | 9.56597 | + | 6.50339i | 0.520320 | + | 0.353738i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.7709 | − | 5.05136i | 0.692598 | − | 0.273948i | ||||
\(341\) | −1.77754 | −0.0962590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −5.34461 | + | 23.8536i | −0.288162 | + | 1.28610i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.11367 | + | 3.47651i | 0.274913 | + | 0.186898i | ||||
\(347\) | − | 10.1743i | − | 0.546187i | −0.961987 | − | 0.273094i | \(-0.911953\pi\) | ||
0.961987 | − | 0.273094i | \(-0.0880469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 31.9386i | − | 1.70963i | −0.518930 | − | 0.854817i | \(-0.673669\pi\) | ||
0.518930 | − | 0.854817i | \(-0.326331\pi\) | |||||||
\(350\) | 0.492067 | − | 0.723792i | 0.0263021 | − | 0.0386883i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.846062 | + | 5.37120i | 0.0450952 | + | 0.286286i | ||||
\(353\) | − | 24.3932i | − | 1.29832i | −0.760653 | − | 0.649159i | \(-0.775121\pi\) | ||
0.760653 | − | 0.649159i | \(-0.224879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2215 | −0.754797 | ||||||||
\(356\) | −23.9895 | + | 9.48875i | −1.27144 | + | 0.502903i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5222 | + | 19.8900i | −0.714668 | + | 1.05122i | ||||
\(359\) | −8.59571 | −0.453664 | −0.226832 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226832 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.53276 | −0.291198 | ||||||||
\(362\) | 6.76335 | − | 9.94834i | 0.355474 | − | 0.522873i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.38540 | + | 8.55899i | 0.177443 | + | 0.448613i | ||||
\(365\) | 33.5458 | 1.75587 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.1285i | − | 1.52050i | −0.649632 | − | 0.760249i | \(-0.725077\pi\) | ||
0.649632 | − | 0.760249i | \(-0.274923\pi\) | |||||||
\(368\) | −7.01192 | + | 6.57572i | −0.365522 | + | 0.342783i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.81717 | − | 5.61476i | 0.198445 | − | 0.291897i | ||||
\(371\) | − | 7.73354i | − | 0.401505i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.56533i | − | 0.236384i | −0.992991 | − | 0.118192i | \(-0.962290\pi\) | ||
0.992991 | − | 0.118192i | \(-0.0377098\pi\) | |||||||
\(374\) | −3.68802 | − | 2.50728i | −0.190703 | − | 0.129649i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.44895 | − | 6.46680i | 0.0747237 | − | 0.333500i | ||||
\(377\) | 42.8810i | 2.20848i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5673 | 0.799641 | 0.399820 | − | 0.916593i | \(-0.369072\pi\) | ||||
0.399820 | + | 0.916593i | \(0.369072\pi\) | |||||||
\(380\) | 5.65049 | + | 14.2856i | 0.289864 | + | 0.732836i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.848139 | − | 0.576604i | −0.0433946 | − | 0.0295016i | ||||
\(383\) | 3.08947 | 0.157865 | 0.0789323 | − | 0.996880i | \(-0.474849\pi\) | ||||
0.0789323 | + | 0.996880i | \(0.474849\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01192 | 0.102537 | ||||||||
\(386\) | 18.4375 | + | 12.5347i | 0.938444 | + | 0.637998i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.66594 | + | 9.26825i | 0.186110 | + | 0.470524i | ||||
\(389\) | −30.6022 | −1.55160 | −0.775798 | − | 0.630982i | \(-0.782652\pi\) | ||||
−0.775798 | + | 0.630982i | \(0.782652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.88413i | − | 0.398718i | ||||||
\(392\) | −0.618402 | + | 2.76000i | −0.0312340 | + | 0.139401i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.73689 | + | 4.58005i | 0.339400 | + | 0.230740i | ||||
\(395\) | 2.64216i | 0.132942i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.403742i | 0.0202632i | 0.999949 | + | 0.0101316i | \(0.00322505\pi\) | ||||
−0.999949 | + | 0.0101316i | \(0.996775\pi\) | |||||||
\(398\) | 9.36419 | − | 13.7740i | 0.469385 | − | 0.690427i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.80570 | − | 1.69337i | 0.0902849 | − | 0.0846684i | ||||
\(401\) | 30.3779i | 1.51700i | 0.651672 | + | 0.758501i | \(0.274068\pi\) | ||||
−0.651672 | + | 0.758501i | \(0.725932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.51051 | −0.423939 | ||||||||
\(404\) | −2.34489 | − | 5.92838i | −0.116663 | − | 0.294948i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.40855 | + | 10.8974i | −0.367680 | + | 0.540828i | ||||
\(407\) | −2.20467 | −0.109281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8549 | −0.882869 | −0.441434 | − | 0.897293i | \(-0.645530\pi\) | ||||
−0.441434 | + | 0.897293i | \(0.645530\pi\) | |||||||
\(410\) | 0.523248 | − | 0.769656i | 0.0258414 | − | 0.0380106i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.995784 | − | 0.393869i | 0.0490587 | − | 0.0194045i | ||||
\(413\) | −7.99530 | −0.393423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.26877i | 0.307722i | ||||||||
\(416\) | 4.05079 | + | 25.7163i | 0.198606 | + | 1.26085i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.80467 | − | 4.12544i | 0.137181 | − | 0.201782i | ||||
\(419\) | − | 31.1609i | − | 1.52231i | −0.648569 | − | 0.761156i | \(-0.724632\pi\) | ||
0.648569 | − | 0.761156i | \(-0.275368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7.19292i | − | 0.350562i | −0.984518 | − | 0.175281i | \(-0.943917\pi\) | ||
0.984518 | − | 0.175281i | \(-0.0560833\pi\) | |||||||
\(422\) | −23.3873 | − | 15.8998i | −1.13848 | − | 0.773988i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.78244 | − | 21.3445i | 0.232256 | − | 1.03658i | ||||
\(425\) | 2.03031i | 0.0984844i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6321 | 0.514522 | ||||||||
\(428\) | 18.0526 | − | 7.14047i | 0.872605 | − | 0.345148i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.1568 | + | 14.3834i | 1.02027 | + | 0.693629i | ||||
\(431\) | −25.7598 | −1.24081 | −0.620404 | − | 0.784283i | \(-0.713031\pi\) | ||||
−0.620404 | + | 0.784283i | \(0.713031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.66449 | −0.176104 | −0.0880521 | − | 0.996116i | \(-0.528064\pi\) | ||||
−0.0880521 | + | 0.996116i | \(0.528064\pi\) | |||||||
\(434\) | −2.16278 | − | 1.47036i | −0.103817 | − | 0.0705796i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.9449 | + | 5.91127i | −0.715732 | + | 0.283098i | ||||
\(437\) | 8.81926 | 0.421882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.4350i | 1.88213i | 0.338227 | + | 0.941064i | \(0.390173\pi\) | ||||
−0.338227 | + | 0.941064i | \(0.609827\pi\) | |||||||
\(440\) | 5.55290 | + | 1.24418i | 0.264724 | + | 0.0593138i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.6575 | − | 12.0044i | −0.839883 | − | 0.570992i | ||||
\(443\) | 36.1437i | 1.71724i | 0.512612 | + | 0.858620i | \(0.328678\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.9990i | 1.27988i | ||||||||
\(446\) | −5.43888 | + | 8.00016i | −0.257538 | + | 0.378819i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.41357 | + | 7.23516i | −0.161276 | + | 0.341829i | ||||
\(449\) | − | 24.9465i | − | 1.17730i | −0.808389 | − | 0.588649i | \(-0.799660\pi\) | ||
0.808389 | − | 0.588649i | \(-0.200340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.302210 | −0.0142305 | ||||||||
\(452\) | −23.7700 | + | 9.40190i | −1.11804 | + | 0.442228i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.0568 | + | 16.2637i | −0.518921 | + | 0.763292i | ||||
\(455\) | 9.63272 | 0.451589 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1856 | 0.710354 | 0.355177 | − | 0.934799i | \(-0.384421\pi\) | ||||
0.355177 | + | 0.934799i | \(0.384421\pi\) | |||||||
\(458\) | −3.08448 | + | 4.53702i | −0.144128 | + | 0.212001i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.70032 | + | 9.35518i | 0.172528 | + | 0.436188i | ||||
\(461\) | −9.29479 | −0.432902 | −0.216451 | − | 0.976294i | \(-0.569448\pi\) | ||||
−0.216451 | + | 0.976294i | \(0.569448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.13438i | − | 0.0991930i | −0.998769 | − | 0.0495965i | \(-0.984206\pi\) | ||
0.998769 | − | 0.0495965i | \(-0.0157935\pi\) | |||||||
\(464\) | −27.1865 | + | 25.4953i | −1.26210 | + | 1.18359i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.3576 | − | 25.5317i | 0.804077 | − | 1.18273i | ||||
\(467\) | − | 41.6077i | − | 1.92538i | −0.270612 | − | 0.962688i | \(-0.587226\pi\) | ||
0.270612 | − | 0.962688i | \(-0.412774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.12203i | − | 0.190338i | ||||||
\(470\) | −5.73571 | − | 3.89940i | −0.264569 | − | 0.179866i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.0670 | − | 4.94431i | −1.01572 | − | 0.227580i | ||||
\(473\) | − | 8.30736i | − | 0.381973i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.27112 | −0.104206 | ||||||||
\(476\) | −2.41332 | − | 6.10138i | −0.110614 | − | 0.279656i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.6248 | + | 22.1799i | 1.49222 | + | 1.01448i | ||||
\(479\) | −40.9442 | −1.87079 | −0.935394 | − | 0.353608i | \(-0.884955\pi\) | ||||
−0.935394 | + | 0.353608i | \(0.884955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5556 | −0.481292 | ||||||||
\(482\) | 7.22312 | + | 4.91061i | 0.329004 | + | 0.223672i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.41217 | + | 18.7395i | 0.336917 | + | 0.851795i | ||||
\(485\) | 10.4310 | 0.473645 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.2039i | 0.643639i | 0.946801 | + | 0.321820i | \(0.104294\pi\) | ||||
−0.946801 | + | 0.321820i | \(0.895706\pi\) | |||||||
\(488\) | 29.3445 | + | 6.57490i | 1.32836 | + | 0.297632i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.44797 | + | 1.66424i | 0.110588 | + | 0.0751828i | ||||
\(491\) | 39.3013i | 1.77364i | 0.462113 | + | 0.886821i | \(0.347091\pi\) | ||||
−0.462113 | + | 0.886821i | \(0.652909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 30.5682i | − | 1.37672i | ||||||
\(494\) | 13.4282 | − | 19.7519i | 0.604165 | − | 0.888678i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.06000 | − | 5.39566i | −0.227201 | − | 0.242272i | ||||
\(497\) | 6.79440i | 0.304771i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.3257 | −1.44710 | −0.723548 | − | 0.690274i | \(-0.757490\pi\) | ||||
−0.723548 | + | 0.690274i | \(0.757490\pi\) | |||||||
\(500\) | −8.65159 | − | 21.8730i | −0.386911 | − | 0.978191i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.8180 | − | 21.7962i | 0.661362 | − | 0.972810i | ||||
\(503\) | 19.7861 | 0.882217 | 0.441108 | − | 0.897454i | \(-0.354585\pi\) | ||||
0.441108 | + | 0.897454i | \(0.354585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.67210 | −0.296904 | ||||||||
\(506\) | 1.83669 | − | 2.70162i | 0.0816507 | − | 0.120102i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.9210 | − | 12.2304i | 1.37190 | − | 0.542636i | ||||
\(509\) | −33.7174 | −1.49450 | −0.747248 | − | 0.664545i | \(-0.768625\pi\) | ||||
−0.747248 | + | 0.664545i | \(0.768625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.0267i | − | 0.708981i | ||||||
\(512\) | −13.8957 | + | 17.8580i | −0.614109 | + | 0.789222i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.56632 | − | 9.65854i | 0.289628 | − | 0.426020i | ||||
\(515\) | − | 1.12070i | − | 0.0493842i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.25216i | 0.0990500i | ||||||||
\(518\) | −2.68249 | − | 1.82368i | −0.117862 | − | 0.0801279i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.5863 | + | 5.95689i | 1.16588 | + | 0.261227i | ||||
\(521\) | − | 28.4958i | − | 1.24842i | −0.781255 | − | 0.624212i | \(-0.785420\pi\) | ||
0.781255 | − | 0.624212i | \(-0.214580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.42637 | −0.193552 | −0.0967758 | − | 0.995306i | \(-0.530853\pi\) | ||||
−0.0967758 | + | 0.995306i | \(0.530853\pi\) | |||||||
\(524\) | 27.0792 | − | 10.7108i | 1.18296 | − | 0.467905i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9253 | + | 7.42753i | 0.476366 | + | 0.323855i | ||||
\(527\) | 6.06682 | 0.264275 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2246 | −0.748894 | ||||||||
\(530\) | −18.9315 | − | 12.8705i | −0.822330 | − | 0.559058i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.82505 | − | 2.69956i | 0.295903 | − | 0.117041i | ||||
\(533\) | −1.44693 | −0.0626734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 20.3173i | − | 0.878394i | ||||||
\(536\) | 2.54907 | − | 11.3768i | 0.110103 | − | 0.491403i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.0312 | − | 9.53905i | −0.604927 | − | 0.411258i | ||||
\(539\) | − | 0.961211i | − | 0.0414023i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7548i | 1.45123i | 0.688101 | + | 0.725615i | \(0.258445\pi\) | ||||
−0.688101 | + | 0.725615i | \(0.741555\pi\) | |||||||
\(542\) | 18.8464 | − | 27.7215i | 0.809520 | − | 1.19074i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.88765 | − | 18.3322i | −0.123807 | − | 0.785986i | ||||
\(545\) | 16.8198i | 0.720480i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6641 | −0.626992 | −0.313496 | − | 0.949589i | \(-0.601500\pi\) | ||||
−0.313496 | + | 0.949589i | \(0.601500\pi\) | |||||||
\(548\) | 32.1136 | − | 12.7021i | 1.37183 | − | 0.542608i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.472980 | + | 0.695716i | −0.0201680 | + | 0.0296654i | ||||
\(551\) | 34.1939 | 1.45671 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.26231 | 0.0536790 | ||||||||
\(554\) | 10.9476 | − | 16.1030i | 0.465118 | − | 0.684152i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.7092 | + | 27.0750i | 0.454170 | + | 1.14824i | ||||
\(557\) | 15.4373 | 0.654099 | 0.327050 | − | 0.945007i | \(-0.393946\pi\) | ||||
0.327050 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 39.7741i | − | 1.68227i | ||||||
\(560\) | 5.72721 | + | 6.10713i | 0.242019 | + | 0.258073i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.91007 | − | 10.1642i | 0.291484 | − | 0.428749i | ||||
\(563\) | − | 26.9472i | − | 1.13569i | −0.823135 | − | 0.567845i | \(-0.807777\pi\) | ||
0.823135 | − | 0.567845i | \(-0.192223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.7519i | 1.12546i | ||||||||
\(566\) | 38.3044 | + | 26.0411i | 1.61005 | + | 1.09459i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.20167 | + | 18.7525i | −0.176298 | + | 0.786838i | ||||
\(569\) | − | 3.63013i | − | 0.152183i | −0.997101 | − | 0.0760915i | \(-0.975756\pi\) | ||
0.997101 | − | 0.0760915i | \(-0.0242441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2293 | −0.679174 | −0.339587 | − | 0.940575i | \(-0.610287\pi\) | ||||
−0.339587 | + | 0.940575i | \(0.610287\pi\) | |||||||
\(572\) | −3.25408 | − | 8.22699i | −0.136060 | − | 0.343988i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.367709 | − | 0.249985i | −0.0153479 | − | 0.0104342i | ||||
\(575\) | −1.48728 | −0.0620240 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1511 | 1.75477 | 0.877386 | − | 0.479786i | \(-0.159286\pi\) | ||||
0.877386 | + | 0.479786i | \(0.159286\pi\) | |||||||
\(578\) | −7.29470 | − | 4.95927i | −0.303419 | − | 0.206279i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.3468 | + | 36.2718i | 0.595720 | + | 1.50610i | ||||
\(581\) | 2.99495 | 0.124251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.43356i | 0.307867i | ||||||||
\(584\) | 9.91097 | − | 44.2337i | 0.410119 | − | 1.83040i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.4588 | − | 9.82979i | −0.597289 | − | 0.406065i | ||||
\(587\) | − | 22.7097i | − | 0.937328i | −0.883377 | − | 0.468664i | \(-0.844736\pi\) | ||
0.883377 | − | 0.468664i | \(-0.155264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.78640i | 0.279629i | ||||||||
\(590\) | −13.3061 | + | 19.5722i | −0.547804 | + | 0.805777i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.27589 | − | 6.69221i | −0.257938 | − | 0.275048i | ||||
\(593\) | − | 22.8921i | − | 0.940068i | −0.882648 | − | 0.470034i | \(-0.844242\pi\) | ||
0.882648 | − | 0.470034i | \(-0.155758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.86680 | −0.281511 | ||||||||
\(596\) | 14.8404 | + | 37.5195i | 0.607885 | + | 1.53686i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.79371 | − | 12.9349i | 0.359602 | − | 0.528945i | ||||
\(599\) | −31.0216 | −1.26751 | −0.633755 | − | 0.773534i | \(-0.718487\pi\) | ||||
−0.633755 | + | 0.773534i | \(0.718487\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.3657 | −1.48339 | −0.741693 | − | 0.670739i | \(-0.765977\pi\) | ||||
−0.741693 | + | 0.670739i | \(0.765977\pi\) | |||||||
\(602\) | 6.87177 | − | 10.1078i | 0.280072 | − | 0.411964i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.2358 | + | 8.79508i | −0.904762 | + | 0.357867i | ||||
\(605\) | 21.0904 | 0.857446 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.1019i | − | 1.10003i | −0.835154 | − | 0.550016i | \(-0.814622\pi\) | ||
0.835154 | − | 0.550016i | \(-0.185378\pi\) | |||||||
\(608\) | 20.5065 | − | 3.23015i | 0.831649 | − | 0.131000i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.6944 | − | 26.0270i | 0.716424 | − | 1.05380i | ||||
\(611\) | 10.7829i | 0.436231i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.7164i | 0.877118i | 0.898702 | + | 0.438559i | \(0.144511\pi\) | ||||
−0.898702 | + | 0.438559i | \(0.855489\pi\) | |||||||
\(614\) | −17.8471 | − | 12.1333i | −0.720251 | − | 0.489660i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.594415 | − | 2.65294i | 0.0239496 | − | 0.106890i | ||||
\(617\) | 15.0335i | 0.605224i | 0.953114 | + | 0.302612i | \(0.0978587\pi\) | ||||
−0.953114 | + | 0.302612i | \(0.902141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.2249 | −0.491359 | −0.245680 | − | 0.969351i | \(-0.579011\pi\) | ||||
−0.245680 | + | 0.969351i | \(0.579011\pi\) | |||||||
\(620\) | −7.19879 | + | 2.84739i | −0.289110 | + | 0.114354i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.98891 | + | 4.07154i | 0.240133 | + | 0.163254i | ||||
\(623\) | 12.8990 | 0.516787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.5226 | −0.860906 | ||||||||
\(626\) | 13.6903 | + | 9.30730i | 0.547174 | + | 0.371995i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.1037 | − | 16.2580i | 1.64021 | − | 0.648765i | ||||
\(629\) | 7.52465 | 0.300028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 0.290118i | − | 0.0115494i | −0.999983 | − | 0.00577472i | \(-0.998162\pi\) | ||
0.999983 | − | 0.00577472i | \(-0.00183816\pi\) | |||||||
\(632\) | 3.48398 | + | 0.780617i | 0.138585 | + | 0.0310513i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.6717 | + | 14.7334i | 0.860692 | + | 0.585138i | ||||
\(635\) | − | 34.8000i | − | 1.38100i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.60210i | − | 0.182342i | ||||||
\(638\) | 7.12117 | − | 10.4747i | 0.281930 | − | 0.414696i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.0304 | + | 20.3974i | 0.475544 | + | 0.806277i | ||||
\(641\) | − | 32.2612i | − | 1.27424i | −0.770764 | − | 0.637120i | \(-0.780125\pi\) | ||
0.770764 | − | 0.637120i | \(-0.219875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2641 | −0.996317 | −0.498159 | − | 0.867086i | \(-0.665990\pi\) | ||||
−0.498159 | + | 0.867086i | \(0.665990\pi\) | |||||||
\(644\) | 4.46950 | − | 1.76785i | 0.176123 | − | 0.0696632i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.57248 | + | 14.0803i | −0.376624 | + | 0.553984i | ||||
\(647\) | −15.6735 | −0.616188 | −0.308094 | − | 0.951356i | \(-0.599691\pi\) | ||||
−0.308094 | + | 0.951356i | \(0.599691\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.68517 | 0.301669 | ||||||||
\(650\) | −2.26454 | + | 3.33096i | −0.0888226 | + | 0.130651i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.24291 | + | 20.8398i | 0.322817 | + | 0.816150i | ||||
\(653\) | −17.4580 | −0.683183 | −0.341591 | − | 0.939849i | \(-0.610966\pi\) | ||||
−0.341591 | + | 0.939849i | \(0.610966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 30.4763i | − | 1.19081i | ||||||
\(656\) | −0.860283 | − | 0.917351i | −0.0335884 | − | 0.0358165i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.86297 | + | 2.74028i | −0.0726260 | + | 0.106827i | ||||
\(659\) | 34.8692i | 1.35831i | 0.733995 | + | 0.679155i | \(0.237653\pi\) | ||||
−0.733995 | + | 0.679155i | \(0.762347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13.7607i | − | 0.535230i | −0.963526 | − | 0.267615i | \(-0.913765\pi\) | ||
0.963526 | − | 0.267615i | \(-0.0862355\pi\) | |||||||
\(662\) | 23.9390 | + | 16.2748i | 0.930415 | + | 0.632540i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.26605 | + | 1.85208i | 0.320785 | + | 0.0718748i | ||||
\(665\) | − | 7.68126i | − | 0.297866i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.3925 | 0.867040 | ||||||||
\(668\) | −1.29931 | − | 3.28494i | −0.0502720 | − | 0.127098i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0906 | − | 6.86006i | −0.389834 | − | 0.265027i | ||||
\(671\) | −10.2197 | −0.394526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.50938 | −0.328013 | −0.164006 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164006 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(674\) | 23.3227 | + | 15.8559i | 0.898359 | + | 0.610746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.01686 | − | 15.2119i | −0.231418 | − | 0.585072i | ||||
\(677\) | 3.14515 | 0.120878 | 0.0604390 | − | 0.998172i | \(-0.480750\pi\) | ||||
0.0604390 | + | 0.998172i | \(0.480750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.98346i | − | 0.191248i | ||||||
\(680\) | −18.9523 | − | 4.24644i | −0.726789 | − | 0.162844i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.07889 | + | 1.41333i | 0.0796048 | + | 0.0541190i | ||||
\(683\) | − | 9.12590i | − | 0.349193i | −0.984640 | − | 0.174596i | \(-0.944138\pi\) | ||
0.984640 | − | 0.174596i | \(-0.0558621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.1423i | − | 1.38093i | ||||||
\(686\) | 0.795104 | − | 1.16953i | 0.0303572 | − | 0.0446530i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.2168 | − | 23.6480i | 0.961380 | − | 0.901573i | ||||
\(689\) | 35.5905i | 1.35589i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6298 | −0.594586 | −0.297293 | − | 0.954786i | \(-0.596084\pi\) | ||||
−0.297293 | + | 0.954786i | \(0.596084\pi\) | |||||||
\(692\) | −3.21643 | − | 8.13180i | −0.122270 | − | 0.309125i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.08965 | + | 11.8992i | −0.307079 | + | 0.451689i | ||||
\(695\) | 30.4716 | 1.15585 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03146 | 0.0390693 | ||||||||
\(698\) | −25.3945 | + | 37.3533i | −0.961196 | + | 1.41384i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.15098 | + | 0.455255i | −0.0435029 | + | 0.0172070i | ||||
\(701\) | 50.4853 | 1.90680 | 0.953402 | − | 0.301701i | \(-0.0975546\pi\) | ||||
0.953402 | + | 0.301701i | \(0.0975546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.41714i | 0.317458i | ||||||||
\(704\) | 3.28116 | − | 6.95451i | 0.123664 | − | 0.262108i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.3951 | + | 28.5286i | −0.729944 | + | 1.07369i | ||||
\(707\) | 3.18764i | 0.119884i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.7706i | − | 1.08050i | −0.841504 | − | 0.540251i | \(-0.818329\pi\) | ||
0.841504 | − | 0.540251i | \(-0.181671\pi\) | |||||||
\(710\) | 16.6325 | + | 11.3075i | 0.624206 | + | 0.424364i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35.6011 | + | 7.97676i | 1.33421 | + | 0.298942i | ||||
\(713\) | 4.44419i | 0.166436i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.25907 | −0.346270 | ||||||||
\(716\) | 31.6292 | − | 12.5105i | 1.18204 | − | 0.467541i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.0530 | + | 6.83448i | 0.375174 | + | 0.255061i | ||||
\(719\) | −0.582170 | −0.0217113 | −0.0108556 | − | 0.999941i | \(-0.503456\pi\) | ||||
−0.0108556 | + | 0.999941i | \(0.503456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.535425 | −0.0199403 | ||||||||
\(722\) | 6.47076 | + | 4.39912i | 0.240817 | + | 0.163718i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.8199 | + | 6.25737i | −0.587943 | + | 0.232553i | ||||
\(725\) | −5.76647 | −0.214161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.92907i | − | 0.256985i | −0.991710 | − | 0.128492i | \(-0.958986\pi\) | ||
0.991710 | − | 0.128492i | \(-0.0410138\pi\) | |||||||
\(728\) | 2.84595 | − | 12.7018i | 0.105478 | − | 0.470759i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −39.2330 | − | 26.6724i | −1.45208 | − | 0.987189i | ||||
\(731\) | 28.3535i | 1.04869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.86770i | 0.0689850i | 0.999405 | + | 0.0344925i | \(0.0109815\pi\) | ||||
−0.999405 | + | 0.0344925i | \(0.989019\pi\) | |||||||
\(734\) | −23.1602 | + | 34.0668i | −0.854859 | + | 1.25743i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.4291 | − | 2.11532i | 0.495002 | − | 0.0779717i | ||||
\(737\) | 3.96214i | 0.145947i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.7036 | −1.42373 | −0.711867 | − | 0.702314i | \(-0.752150\pi\) | ||||
−0.711867 | + | 0.702314i | \(0.752150\pi\) | |||||||
\(740\) | −8.92863 | + | 3.53160i | −0.328223 | + | 0.129824i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.14897 | + | 9.04464i | −0.225736 | + | 0.332039i | ||||
\(743\) | −23.3088 | −0.855118 | −0.427559 | − | 0.903987i | \(-0.640626\pi\) | ||||
−0.427559 | + | 0.903987i | \(0.640626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.2263 | 1.54705 | ||||||||
\(746\) | −3.62991 | + | 5.33931i | −0.132900 | + | 0.195486i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.31971 | + | 5.86471i | 0.0848170 | + | 0.214435i | ||||
\(749\) | −9.70673 | −0.354676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.6345i | − | 0.971908i | −0.873984 | − | 0.485954i | \(-0.838472\pi\) | ||
0.873984 | − | 0.485954i | \(-0.161528\pi\) | |||||||
\(752\) | −6.83637 | + | 6.41109i | −0.249297 | + | 0.233788i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.0948 | − | 50.1508i | 1.24166 | − | 1.82638i | ||||
\(755\) | 25.0253i | 0.910764i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.4285i | − | 0.960562i | −0.877115 | − | 0.480281i | \(-0.840535\pi\) | ||
0.877115 | − | 0.480281i | \(-0.159465\pi\) | |||||||
\(758\) | −18.2065 | − | 12.3777i | −0.661292 | − | 0.449577i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.75010 | − | 21.2002i | 0.172304 | − | 0.769013i | ||||
\(761\) | − | 13.2617i | − | 0.480736i | −0.970682 | − | 0.240368i | \(-0.922732\pi\) | ||
0.970682 | − | 0.240368i | \(-0.0772681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.03576 | 0.290914 | ||||||||
\(764\) | 0.533467 | + | 1.34872i | 0.0193002 | + | 0.0487949i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.61324 | − | 2.45645i | −0.130552 | − | 0.0887552i | ||||
\(767\) | 36.7951 | 1.32860 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.34986 | −0.156860 | −0.0784300 | − | 0.996920i | \(-0.524991\pi\) | ||||
−0.0784300 | + | 0.996920i | \(0.524991\pi\) | |||||||
\(770\) | −2.35301 | − | 1.59969i | −0.0847967 | − | 0.0576488i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.5969 | − | 29.3194i | −0.417382 | − | 1.05523i | ||||
\(773\) | 34.8861 | 1.25477 | 0.627383 | − | 0.778711i | \(-0.284126\pi\) | ||||
0.627383 | + | 0.778711i | \(0.284126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.14446i | − | 0.0411102i | ||||||
\(776\) | 3.08178 | − | 13.7543i | 0.110630 | − | 0.493752i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.7904 | + | 24.3320i | 1.28315 | + | 0.872343i | ||||
\(779\) | 1.15380i | 0.0413391i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.53085i | − | 0.233692i | ||||||
\(782\) | −6.26870 | + | 9.22076i | −0.224168 | + | 0.329734i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.91773 | − | 2.73622i | 0.104204 | − | 0.0977220i | ||||
\(785\) | − | 46.2601i | − | 1.65109i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9317 | 0.460964 | 0.230482 | − | 0.973077i | \(-0.425970\pi\) | ||||
0.230482 | + | 0.973077i | \(0.425970\pi\) | |||||||
\(788\) | −4.23741 | − | 10.7131i | −0.150951 | − | 0.381637i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.10079 | − | 3.09010i | 0.0747429 | − | 0.109941i | ||||
\(791\) | 12.7809 | 0.454437 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.9299 | −1.73755 | ||||||||
\(794\) | 0.321017 | − | 0.472190i | 0.0113925 | − | 0.0167574i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.9035 | + | 8.66364i | −0.776349 | + | 0.307075i | ||||
\(797\) | 11.1981 | 0.396656 | 0.198328 | − | 0.980136i | \(-0.436449\pi\) | ||||
0.198328 | + | 0.980136i | \(0.436449\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.68675i | − | 0.271938i | ||||||
\(800\) | −3.45823 | + | 0.544734i | −0.122267 | + | 0.0192592i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.1536 | − | 35.5280i | 0.852894 | − | 1.25454i | ||||
\(803\) | 15.4051i | 0.543633i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 5.03021i | − | 0.177291i | ||||||
\(806\) | 9.95334 | + | 6.76674i | 0.350591 | + | 0.238348i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.97124 | + | 8.79788i | −0.0693481 | + | 0.309508i | ||||
\(809\) | 23.6434i | 0.831258i | 0.909534 | + | 0.415629i | \(0.136439\pi\) | ||||
−0.909534 | + | 0.415629i | \(0.863561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.8213 | 1.22274 | 0.611371 | − | 0.791344i | \(-0.290618\pi\) | ||||
0.611371 | + | 0.791344i | \(0.290618\pi\) | |||||||
\(812\) | 17.3291 | − | 6.85430i | 0.608132 | − | 0.240539i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.57844 | + | 1.75294i | 0.0903742 | + | 0.0614406i | ||||
\(815\) | 23.4542 | 0.821564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.7164 | −1.10962 | ||||||||
\(818\) | 20.8819 | + | 14.1965i | 0.730120 | + | 0.496369i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.22391 | + | 0.484103i | −0.0427409 | + | 0.0169056i | ||||
\(821\) | −0.361884 | −0.0126298 | −0.00631491 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631491 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.2033i | 1.71512i | 0.514386 | + | 0.857559i | \(0.328020\pi\) | ||||
−0.514386 | + | 0.857559i | \(0.671980\pi\) | |||||||
\(824\) | −1.47777 | − | 0.331108i | −0.0514806 | − | 0.0115347i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.35078 | + | 6.35709i | 0.325355 | + | 0.221192i | ||||
\(827\) | − | 16.2920i | − | 0.566529i | −0.959042 | − | 0.283264i | \(-0.908583\pi\) | ||
0.959042 | − | 0.283264i | \(-0.0914174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.40526i | − | 0.222464i | −0.993794 | − | 0.111232i | \(-0.964520\pi\) | ||
0.993794 | − | 0.111232i | \(-0.0354796\pi\) | |||||||
\(830\) | 4.98432 | − | 7.33154i | 0.173008 | − | 0.254482i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.7096 | − | 33.2969i | 0.544632 | − | 1.15436i | ||||
\(833\) | 3.28066i | 0.113668i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.69703 | −0.127941 | ||||||||
\(836\) | −6.56031 | + | 2.59485i | −0.226893 | + | 0.0897446i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.7762 | + | 36.4438i | −0.855879 | + | 1.25893i | ||||
\(839\) | 23.3877 | 0.807432 | 0.403716 | − | 0.914884i | \(-0.367718\pi\) | ||||
0.403716 | + | 0.914884i | \(0.367718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.8197 | 1.99378 | ||||||||
\(842\) | −5.71912 | + | 8.41237i | −0.197094 | + | 0.289909i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.7103 | + | 37.1906i | 0.506348 | + | 1.28015i | ||||
\(845\) | −17.1202 | −0.588953 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.0761i | − | 0.346218i | ||||||
\(848\) | −22.5643 | + | 21.1606i | −0.774863 | + | 0.726659i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.61431 | − | 2.37452i | 0.0553702 | − | 0.0814452i | ||||
\(851\) | 5.51211i | 0.188953i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3667i | 0.765821i | 0.923786 | + | 0.382910i | \(0.125078\pi\) | ||||
−0.923786 | + | 0.382910i | \(0.874922\pi\) | |||||||
\(854\) | −12.4346 | − | 8.45360i | −0.425502 | − | 0.289276i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.7906 | − | 6.00266i | −0.915682 | − | 0.205167i | ||||
\(857\) | − | 34.7703i | − | 1.18773i | −0.804564 | − | 0.593866i | \(-0.797601\pi\) | ||
0.804564 | − | 0.593866i | \(-0.202399\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1287 | 0.550305 | 0.275152 | − | 0.961401i | \(-0.411272\pi\) | ||||
0.275152 | + | 0.961401i | \(0.411272\pi\) | |||||||
\(860\) | −13.3073 | − | 33.6437i | −0.453777 | − | 1.14724i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.1270 | + | 20.4817i | 1.02613 | + | 0.697611i | ||||
\(863\) | 34.3951 | 1.17082 | 0.585412 | − | 0.810736i | \(-0.300933\pi\) | ||||
0.585412 | + | 0.810736i | \(0.300933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.15194 | −0.311175 | ||||||||
\(866\) | 4.28575 | + | 2.91365i | 0.145636 | + | 0.0990099i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.36036 | + | 3.43927i | 0.0461736 | + | 0.116737i | ||||
\(869\) | −1.21335 | −0.0411600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9700i | 0.642774i | ||||||||
\(872\) | 22.1787 | + | 4.96933i | 0.751064 | + | 0.168283i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.3144 | − | 7.01222i | −0.348891 | − | 0.237192i | ||||
\(875\) | 11.7609i | 0.397592i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0555i | 0.474620i | 0.971434 | + | 0.237310i | \(0.0762658\pi\) | ||||
−0.971434 | + | 0.237310i | \(0.923734\pi\) | |||||||
\(878\) | 31.3549 | − | 46.1206i | 1.05818 | − | 1.55649i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.50506 | − | 5.87024i | −0.185575 | − | 0.197886i | ||||
\(881\) | 41.1209i | 1.38540i | 0.721226 | + | 0.692700i | \(0.243579\pi\) | ||||
−0.721226 | + | 0.692700i | \(0.756421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.8276 | −0.633598 | −0.316799 | − | 0.948493i | \(-0.602608\pi\) | ||||
−0.316799 | + | 0.948493i | \(0.602608\pi\) | |||||||
\(884\) | 11.1063 | + | 28.0791i | 0.373547 | + | 0.944404i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.7380 | − | 42.2713i | 0.965473 | − | 1.42013i | ||||
\(887\) | 10.8728 | 0.365071 | 0.182536 | − | 0.983199i | \(-0.441570\pi\) | ||||
0.182536 | + | 0.983199i | \(0.441570\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6260 | −0.557617 | ||||||||
\(890\) | 21.4670 | − | 31.5763i | 0.719577 | − | 1.05844i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.7219 | − | 5.03199i | 0.425961 | − | 0.168483i | ||||
\(893\) | 8.59846 | 0.287736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 35.5971i | − | 1.18988i | ||||||
\(896\) | 9.74499 | − | 5.74762i | 0.325557 | − | 0.192014i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.8350 | + | 29.1758i | −0.661904 | + | 0.973608i | ||||
\(899\) | 17.2310i | 0.574684i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 25.3711i | − | 0.845235i | ||||||
\(902\) | 0.353446 | + | 0.240289i | 0.0117684 | + | 0.00800074i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.2753 | + | 7.90374i | 1.17324 | + | 0.262874i | ||||
\(905\) | 17.8045i | 0.591843i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4589 | 0.513304 | 0.256652 | − | 0.966504i | \(-0.417381\pi\) | ||||
0.256652 | + | 0.966504i | \(0.417381\pi\) | |||||||
\(908\) | 25.8626 | − | 10.2296i | 0.858281 | − | 0.339482i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.2658 | − | 7.65901i | −0.373457 | − | 0.253894i | ||||
\(911\) | 23.9492 | 0.793473 | 0.396737 | − | 0.917933i | \(-0.370143\pi\) | ||||
0.396737 | + | 0.917933i | \(0.370143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87878 | −0.0952736 | ||||||||
\(914\) | −17.7601 | − | 12.0741i | −0.587452 | − | 0.399377i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.21480 | − | 2.85372i | 0.238384 | − | 0.0942896i | ||||
\(917\) | −14.5603 | −0.480823 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4853i | 0.807694i | 0.914826 | + | 0.403847i | \(0.132327\pi\) | ||||
−0.914826 | + | 0.403847i | \(0.867673\pi\) | |||||||
\(920\) | 3.11069 | − | 13.8833i | 0.102556 | − | 0.457720i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.8706 | + | 7.39032i | 0.358003 | + | 0.243387i | ||||
\(923\) | − | 31.2685i | − | 1.02922i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.41947i | − | 0.0466719i | ||||||
\(926\) | −1.69705 | + | 2.49623i | −0.0557686 | + | 0.0820312i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 52.0669 | − | 8.20149i | 1.70918 | − | 0.269227i | ||||
\(929\) | − | 35.7122i | − | 1.17168i | −0.810428 | − | 0.585839i | \(-0.800765\pi\) | ||
0.810428 | − | 0.585839i | \(-0.199235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.66977 | −0.120272 | ||||||||
\(932\) | −40.6007 | + | 16.0591i | −1.32992 | + | 0.526033i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.0825 | + | 48.6617i | −1.08249 | + | 1.59226i | ||||
\(935\) | 6.60044 | 0.215857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.263959 | 0.00862315 | 0.00431157 | − | 0.999991i | \(-0.498628\pi\) | ||||
0.00431157 | + | 0.999991i | \(0.498628\pi\) | |||||||
\(938\) | −3.27744 | + | 4.82086i | −0.107012 | + | 0.157407i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.60768 | + | 9.12097i | 0.117670 | + | 0.297493i | ||||
\(941\) | −40.9124 | −1.33371 | −0.666853 | − | 0.745189i | \(-0.732359\pi\) | ||||
−0.666853 | + | 0.745189i | \(0.732359\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.755586i | 0.0246053i | ||||||||
\(944\) | 21.8769 | + | 23.3281i | 0.712031 | + | 0.759265i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.60522 | + | 9.71575i | −0.214754 | + | 0.315886i | ||||
\(947\) | 43.3236i | 1.40783i | 0.710286 | + | 0.703913i | \(0.248566\pi\) | ||||
−0.710286 | + | 0.703913i | \(0.751434\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 73.7566i | 2.39424i | ||||||||
\(950\) | 2.65615 | + | 1.80578i | 0.0861770 | + | 0.0585871i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.02877 | + | 9.05461i | −0.0657527 | + | 0.293462i | ||||
\(953\) | − | 52.0756i | − | 1.68690i | −0.537211 | − | 0.843448i | \(-0.680522\pi\) | ||
0.537211 | − | 0.843448i | \(-0.319478\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.51791 | 0.0491185 | ||||||||
\(956\) | −20.5205 | − | 51.8802i | −0.663682 | − | 1.67793i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47.8856 | + | 32.5549i | 1.54711 | + | 1.05180i | ||||
\(959\) | −17.2672 | −0.557588 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.5802 | 0.889684 | ||||||||
\(962\) | 12.3451 | + | 8.39276i | 0.398021 | + | 0.270593i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.54324 | − | 11.4863i | −0.146328 | − | 0.369947i | ||||
\(965\) | −32.9976 | −1.06223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3116i | 0.556705i | 0.960479 | + | 0.278352i | \(0.0897883\pi\) | ||||
−0.960479 | + | 0.278352i | \(0.910212\pi\) | |||||||
\(968\) | 6.23106 | − | 27.8099i | 0.200274 | − | 0.893845i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.1994 | − | 8.29369i | −0.391698 | − | 0.266294i | ||||
\(971\) | − | 8.86074i | − | 0.284355i | −0.989841 | − | 0.142177i | \(-0.954590\pi\) | ||
0.989841 | − | 0.142177i | \(-0.0454103\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.5580i | − | 0.466709i | ||||||
\(974\) | 11.2936 | − | 16.6119i | 0.361869 | − | 0.532280i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.0917 | − | 31.0215i | −0.931201 | − | 0.992973i | ||||
\(977\) | 8.48509i | 0.271462i | 0.990746 | + | 0.135731i | \(0.0433383\pi\) | ||||
−0.990746 | + | 0.135731i | \(0.956662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.3986 | −0.396262 | ||||||||
\(980\) | −1.53974 | − | 3.89278i | −0.0491851 | − | 0.124350i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.2486 | − | 45.9642i | 0.997183 | − | 1.46678i | ||||
\(983\) | 43.6181 | 1.39120 | 0.695600 | − | 0.718429i | \(-0.255138\pi\) | ||||
0.695600 | + | 0.718429i | \(0.255138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0570 | −0.384168 | ||||||||
\(986\) | −24.3049 | + | 35.7506i | −0.774026 | + | 1.13853i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.4095 | + | 12.4236i | −0.999271 | + | 0.395249i | ||||
\(989\) | −20.7700 | −0.660449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.0937i | 1.62304i | 0.584322 | + | 0.811522i | \(0.301361\pi\) | ||||
−0.584322 | + | 0.811522i | \(0.698639\pi\) | |||||||
\(992\) | 1.62773 | + | 10.3336i | 0.0516806 | + | 0.328093i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.40225 | − | 7.94629i | 0.171349 | − | 0.252041i | ||||
\(995\) | 24.6513i | 0.781498i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.59455i | − | 0.0504998i | −0.999681 | − | 0.0252499i | \(-0.991962\pi\) | ||
0.999681 | − | 0.0252499i | \(-0.00803815\pi\) | |||||||
\(998\) | 37.8060 | + | 25.7023i | 1.19673 | + | 0.813591i | ||||
\(999\) | 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 | 1512.2.j.c.323.7 | ✓ | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.26 | yes | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.26 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.25 | yes | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.8 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.7 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.25 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1512.2.j.c.323.8 | yes | 32 | 24.11 | even | 2 | inner | |
1512.2.j.c.323.25 | yes | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.26 | yes | 32 | 3.2 | odd | 2 | inner | |
6048.2.j.c.5615.7 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.8 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.25 | 32 | 24.5 | odd | 2 | |||
6048.2.j.c.5615.26 | 32 | 4.3 | odd | 2 |