Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(99,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.76519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.6053445140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(0.473442 - 0.397265i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.99 |
Dual form | 722.2.e.p.423.2 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.939693 | − | 0.342020i | −0.664463 | − | 0.241845i | ||||
\(3\) | 0.214641 | + | 1.21729i | 0.123923 | + | 0.702802i | 0.981942 | + | 0.189184i | \(0.0605842\pi\) |
−0.858019 | + | 0.513618i | \(0.828305\pi\) | |||||||
\(4\) | 0.766044 | + | 0.642788i | 0.383022 | + | 0.321394i | ||||
\(5\) | −2.77157 | + | 2.32563i | −1.23949 | + | 1.04005i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(6\) | 0.214641 | − | 1.21729i | 0.0876268 | − | 0.496956i | ||||
\(7\) | 1.61803 | − | 2.80252i | 0.611559 | − | 1.05925i | −0.379418 | − | 0.925225i | \(-0.623876\pi\) |
0.990978 | − | 0.134027i | \(-0.0427908\pi\) | |||||||
\(8\) | −0.500000 | − | 0.866025i | −0.176777 | − | 0.306186i | ||||
\(9\) | 1.38336 | − | 0.503500i | 0.461118 | − | 0.167833i | ||||
\(10\) | 3.39984 | − | 1.23744i | 1.07512 | − | 0.391313i | ||||
\(11\) | 1.61803 | + | 2.80252i | 0.487856 | + | 0.844991i | 0.999902 | − | 0.0139668i | \(-0.00444592\pi\) |
−0.512047 | + | 0.858958i | \(0.671113\pi\) | |||||||
\(12\) | −0.618034 | + | 1.07047i | −0.178411 | + | 0.309017i | ||||
\(13\) | −0.239976 | + | 1.36097i | −0.0665573 | + | 0.377465i | 0.933275 | + | 0.359162i | \(0.116938\pi\) |
−0.999832 | + | 0.0183032i | \(0.994174\pi\) | |||||||
\(14\) | −2.47897 | + | 2.08010i | −0.662533 | + | 0.555931i | ||||
\(15\) | −3.42585 | − | 2.87463i | −0.884552 | − | 0.742227i | ||||
\(16\) | 0.173648 | + | 0.984808i | 0.0434120 | + | 0.246202i | ||||
\(17\) | 3.17801 | + | 1.15670i | 0.770780 | + | 0.280541i | 0.697323 | − | 0.716757i | \(-0.254374\pi\) |
0.0734575 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(18\) | −1.47214 | −0.346986 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.61803 | −0.809017 | ||||||||
\(21\) | 3.75877 | + | 1.36808i | 0.820231 | + | 0.298540i | ||||
\(22\) | −0.561937 | − | 3.18690i | −0.119805 | − | 0.679450i | ||||
\(23\) | 4.01106 | + | 3.36568i | 0.836364 | + | 0.701793i | 0.956743 | − | 0.290935i | \(-0.0939664\pi\) |
−0.120379 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(24\) | 0.946883 | − | 0.794529i | 0.193282 | − | 0.162183i | ||||
\(25\) | 1.40484 | − | 7.96726i | 0.280969 | − | 1.59345i | ||||
\(26\) | 0.690983 | − | 1.19682i | 0.135513 | − | 0.234715i | ||||
\(27\) | 2.76393 | + | 4.78727i | 0.531919 | + | 0.921311i | ||||
\(28\) | 3.04091 | − | 1.10680i | 0.574678 | − | 0.209166i | ||||
\(29\) | −8.54197 | + | 3.10902i | −1.58620 | + | 0.577331i | −0.976541 | − | 0.215331i | \(-0.930917\pi\) |
−0.609662 | + | 0.792661i | \(0.708695\pi\) | |||||||
\(30\) | 2.23607 | + | 3.87298i | 0.408248 | + | 0.707107i | ||||
\(31\) | −0.618034 | + | 1.07047i | −0.111002 | + | 0.192261i | −0.916175 | − | 0.400779i | \(-0.868739\pi\) |
0.805172 | + | 0.593041i | \(0.202073\pi\) | |||||||
\(32\) | 0.173648 | − | 0.984808i | 0.0306970 | − | 0.174091i | ||||
\(33\) | −3.06418 | + | 2.57115i | −0.533405 | + | 0.447580i | ||||
\(34\) | −2.59074 | − | 2.17389i | −0.444308 | − | 0.372818i | ||||
\(35\) | 2.03311 | + | 11.5303i | 0.343658 | + | 1.94898i | ||||
\(36\) | 1.38336 | + | 0.503500i | 0.230559 | + | 0.0839167i | ||||
\(37\) | −8.38197 | −1.37799 | −0.688993 | − | 0.724768i | \(-0.741947\pi\) | ||||
−0.688993 | + | 0.724768i | \(0.741947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.70820 | −0.273532 | ||||||||
\(40\) | 3.39984 | + | 1.23744i | 0.537562 | + | 0.195657i | ||||
\(41\) | −0.148313 | − | 0.841126i | −0.0231626 | − | 0.131362i | 0.971034 | − | 0.238942i | \(-0.0768007\pi\) |
−0.994196 | + | 0.107581i | \(0.965690\pi\) | |||||||
\(42\) | −3.06418 | − | 2.57115i | −0.472813 | − | 0.396737i | ||||
\(43\) | −7.07524 | + | 5.93683i | −1.07896 | + | 0.905358i | −0.995834 | − | 0.0911807i | \(-0.970936\pi\) |
−0.0831294 | + | 0.996539i | \(0.526491\pi\) | |||||||
\(44\) | −0.561937 | + | 3.18690i | −0.0847152 | + | 0.480444i | ||||
\(45\) | −2.66312 | + | 4.61266i | −0.396994 | + | 0.687614i | ||||
\(46\) | −2.61803 | − | 4.53457i | −0.386008 | − | 0.668586i | ||||
\(47\) | −4.20243 | + | 1.52956i | −0.612988 | + | 0.223109i | −0.629810 | − | 0.776749i | \(-0.716867\pi\) |
0.0168222 | + | 0.999858i | \(0.494645\pi\) | |||||||
\(48\) | −1.16152 | + | 0.422760i | −0.167652 | + | 0.0610202i | ||||
\(49\) | −1.73607 | − | 3.00696i | −0.248010 | − | 0.429565i | ||||
\(50\) | −4.04508 | + | 7.00629i | −0.572061 | + | 0.990839i | ||||
\(51\) | −0.725908 | + | 4.11683i | −0.101648 | + | 0.576472i | ||||
\(52\) | −1.05865 | + | 0.888311i | −0.146808 | + | 0.123187i | ||||
\(53\) | 4.66534 | + | 3.91469i | 0.640834 | + | 0.537723i | 0.904274 | − | 0.426952i | \(-0.140413\pi\) |
−0.263440 | + | 0.964676i | \(0.584857\pi\) | |||||||
\(54\) | −0.959904 | − | 5.44388i | −0.130626 | − | 0.740819i | ||||
\(55\) | −11.0021 | − | 4.00444i | −1.48352 | − | 0.539959i | ||||
\(56\) | −3.23607 | −0.432438 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.09017 | 1.19360 | ||||||||
\(59\) | −0.443663 | − | 0.161480i | −0.0577600 | − | 0.0210229i | 0.312979 | − | 0.949760i | \(-0.398673\pi\) |
−0.370739 | + | 0.928737i | \(0.620895\pi\) | |||||||
\(60\) | −0.776578 | − | 4.40419i | −0.100256 | − | 0.568579i | ||||
\(61\) | 1.05865 | + | 0.888311i | 0.135546 | + | 0.113737i | 0.708040 | − | 0.706172i | \(-0.249580\pi\) |
−0.572494 | + | 0.819909i | \(0.694024\pi\) | |||||||
\(62\) | 0.946883 | − | 0.794529i | 0.120254 | − | 0.100905i | ||||
\(63\) | 0.827248 | − | 4.69156i | 0.104223 | − | 0.591081i | ||||
\(64\) | −0.500000 | + | 0.866025i | −0.0625000 | + | 0.108253i | ||||
\(65\) | −2.50000 | − | 4.33013i | −0.310087 | − | 0.537086i | ||||
\(66\) | 3.75877 | − | 1.36808i | 0.462673 | − | 0.168399i | ||||
\(67\) | 11.0021 | − | 4.00444i | 1.34412 | − | 0.489220i | 0.433014 | − | 0.901387i | \(-0.357450\pi\) |
0.911108 | + | 0.412167i | \(0.135228\pi\) | |||||||
\(68\) | 1.69098 | + | 2.92887i | 0.205062 | + | 0.355177i | ||||
\(69\) | −3.23607 | + | 5.60503i | −0.389577 | + | 0.674767i | ||||
\(70\) | 2.03311 | − | 11.5303i | 0.243003 | − | 1.37814i | ||||
\(71\) | −2.25544 | + | 1.89254i | −0.267672 | + | 0.224603i | −0.766737 | − | 0.641961i | \(-0.778121\pi\) |
0.499066 | + | 0.866564i | \(0.333677\pi\) | |||||||
\(72\) | −1.12772 | − | 0.946271i | −0.132903 | − | 0.111519i | ||||
\(73\) | −0.975561 | − | 5.53268i | −0.114181 | − | 0.647552i | −0.987153 | − | 0.159781i | \(-0.948921\pi\) |
0.872972 | − | 0.487771i | \(-0.162190\pi\) | |||||||
\(74\) | 7.87647 | + | 2.86680i | 0.915621 | + | 0.333259i | ||||
\(75\) | 10.0000 | 1.15470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.4721 | 1.19341 | ||||||||
\(78\) | 1.60519 | + | 0.584240i | 0.181752 | + | 0.0661522i | ||||
\(79\) | 0.479952 | + | 2.72194i | 0.0539988 | + | 0.306242i | 0.999830 | − | 0.0184152i | \(-0.00586206\pi\) |
−0.945832 | + | 0.324658i | \(0.894751\pi\) | |||||||
\(80\) | −2.77157 | − | 2.32563i | −0.309871 | − | 0.260013i | ||||
\(81\) | −1.85108 | + | 1.55324i | −0.205675 | + | 0.172582i | ||||
\(82\) | −0.148313 | + | 0.841126i | −0.0163785 | + | 0.0928869i | ||||
\(83\) | 0.236068 | − | 0.408882i | 0.0259118 | − | 0.0448806i | −0.852779 | − | 0.522272i | \(-0.825084\pi\) |
0.878691 | + | 0.477392i | \(0.158418\pi\) | |||||||
\(84\) | 2.00000 | + | 3.46410i | 0.218218 | + | 0.377964i | ||||
\(85\) | −11.4981 | + | 4.18498i | −1.24715 | + | 0.453925i | ||||
\(86\) | 8.67906 | − | 3.15892i | 0.935888 | − | 0.340635i | ||||
\(87\) | −5.61803 | − | 9.73072i | −0.602316 | − | 1.04324i | ||||
\(88\) | 1.61803 | − | 2.80252i | 0.172483 | − | 0.298749i | ||||
\(89\) | −1.53750 | + | 8.71959i | −0.162975 | + | 0.924275i | 0.788154 | + | 0.615478i | \(0.211037\pi\) |
−0.951128 | + | 0.308796i | \(0.900074\pi\) | |||||||
\(90\) | 4.08013 | − | 3.42364i | 0.430084 | − | 0.360883i | ||||
\(91\) | 3.42585 | + | 2.87463i | 0.359127 | + | 0.301343i | ||||
\(92\) | 0.909234 | + | 5.15652i | 0.0947942 | + | 0.537604i | ||||
\(93\) | −1.43572 | − | 0.522560i | −0.148877 | − | 0.0541870i | ||||
\(94\) | 4.47214 | 0.461266 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.23607 | 0.126156 | ||||||||
\(97\) | 8.09830 | + | 2.94754i | 0.822258 | + | 0.299277i | 0.718677 | − | 0.695344i | \(-0.244748\pi\) |
0.103581 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(98\) | 0.602930 | + | 3.41939i | 0.0609051 | + | 0.345410i | ||||
\(99\) | 3.64938 | + | 3.06220i | 0.366777 | + | 0.307762i | ||||
\(100\) | 6.19743 | − | 5.20026i | 0.619743 | − | 0.520026i | ||||
\(101\) | −2.71204 | + | 15.3808i | −0.269858 | + | 1.53044i | 0.484976 | + | 0.874527i | \(0.338828\pi\) |
−0.754834 | + | 0.655915i | \(0.772283\pi\) | |||||||
\(102\) | 2.09017 | − | 3.62028i | 0.206958 | − | 0.358461i | ||||
\(103\) | 7.32624 | + | 12.6894i | 0.721876 | + | 1.25033i | 0.960247 | + | 0.279151i | \(0.0900531\pi\) |
−0.238371 | + | 0.971174i | \(0.576614\pi\) | |||||||
\(104\) | 1.29862 | − | 0.472660i | 0.127340 | − | 0.0463481i | ||||
\(105\) | −13.5994 | + | 4.94976i | −1.32716 | + | 0.483047i | ||||
\(106\) | −3.04508 | − | 5.27424i | −0.295765 | − | 0.512280i | ||||
\(107\) | 4.70820 | − | 8.15485i | 0.455159 | − | 0.788359i | −0.543538 | − | 0.839385i | \(-0.682916\pi\) |
0.998697 | + | 0.0510255i | \(0.0162490\pi\) | |||||||
\(108\) | −0.959904 | + | 5.44388i | −0.0923668 | + | 0.523838i | ||||
\(109\) | 8.45287 | − | 7.09280i | 0.809638 | − | 0.679367i | −0.140883 | − | 0.990026i | \(-0.544994\pi\) |
0.950521 | + | 0.310659i | \(0.100550\pi\) | |||||||
\(110\) | 8.96900 | + | 7.52589i | 0.855161 | + | 0.717565i | ||||
\(111\) | −1.79911 | − | 10.2033i | −0.170764 | − | 0.968452i | ||||
\(112\) | 3.04091 | + | 1.10680i | 0.287339 | + | 0.104583i | ||||
\(113\) | 9.85410 | 0.926996 | 0.463498 | − | 0.886098i | \(-0.346594\pi\) | ||||
0.463498 | + | 0.886098i | \(0.346594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9443 | −1.76656 | ||||||||
\(116\) | −8.54197 | − | 3.10902i | −0.793102 | − | 0.288665i | ||||
\(117\) | 0.353277 | + | 2.00353i | 0.0326605 | + | 0.185227i | ||||
\(118\) | 0.361677 | + | 0.303483i | 0.0332951 | + | 0.0279379i | ||||
\(119\) | 8.38380 | − | 7.03484i | 0.768542 | − | 0.644883i | ||||
\(120\) | −0.776578 | + | 4.40419i | −0.0708916 | + | 0.402046i | ||||
\(121\) | 0.263932 | − | 0.457144i | 0.0239938 | − | 0.0415585i | ||||
\(122\) | −0.690983 | − | 1.19682i | −0.0625587 | − | 0.108355i | ||||
\(123\) | 0.992060 | − | 0.361080i | 0.0894510 | − | 0.0325575i | ||||
\(124\) | −1.16152 | + | 0.422760i | −0.104308 | + | 0.0379650i | ||||
\(125\) | 5.59017 | + | 9.68246i | 0.500000 | + | 0.866025i | ||||
\(126\) | −2.38197 | + | 4.12569i | −0.212202 | + | 0.367545i | ||||
\(127\) | 1.98244 | − | 11.2430i | 0.175913 | − | 0.997652i | −0.761172 | − | 0.648550i | \(-0.775376\pi\) |
0.937085 | − | 0.349102i | \(-0.113513\pi\) | |||||||
\(128\) | 0.766044 | − | 0.642788i | 0.0677094 | − | 0.0568149i | ||||
\(129\) | −8.74548 | − | 7.33833i | −0.769996 | − | 0.646104i | ||||
\(130\) | 0.868241 | + | 4.92404i | 0.0761498 | + | 0.431867i | ||||
\(131\) | −4.20243 | − | 1.52956i | −0.367168 | − | 0.133638i | 0.151845 | − | 0.988404i | \(-0.451478\pi\) |
−0.519014 | + | 0.854766i | \(0.673701\pi\) | |||||||
\(132\) | −4.00000 | −0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.7082 | −1.01143 | ||||||||
\(135\) | −18.7939 | − | 6.84040i | −1.61752 | − | 0.588728i | ||||
\(136\) | −0.587272 | − | 3.33059i | −0.0503582 | − | 0.285595i | ||||
\(137\) | 1.82469 | + | 1.53110i | 0.155894 | + | 0.130811i | 0.717398 | − | 0.696663i | \(-0.245333\pi\) |
−0.561504 | + | 0.827474i | \(0.689777\pi\) | |||||||
\(138\) | 4.95794 | − | 4.16021i | 0.422048 | − | 0.354140i | ||||
\(139\) | −2.43107 | + | 13.7873i | −0.206201 | + | 1.16942i | 0.689338 | + | 0.724440i | \(0.257902\pi\) |
−0.895539 | + | 0.444984i | \(0.853209\pi\) | |||||||
\(140\) | −5.85410 | + | 10.1396i | −0.494762 | + | 0.856953i | ||||
\(141\) | −2.76393 | − | 4.78727i | −0.232765 | − | 0.403161i | ||||
\(142\) | 2.76671 | − | 1.00700i | 0.232177 | − | 0.0845056i | ||||
\(143\) | −4.20243 | + | 1.52956i | −0.351425 | + | 0.127908i | ||||
\(144\) | 0.736068 | + | 1.27491i | 0.0613390 | + | 0.106242i | ||||
\(145\) | 16.4443 | − | 28.4823i | 1.36562 | − | 2.36533i | ||||
\(146\) | −0.975561 | + | 5.53268i | −0.0807380 | + | 0.457888i | ||||
\(147\) | 3.28771 | − | 2.75871i | 0.271165 | − | 0.227535i | ||||
\(148\) | −6.42096 | − | 5.38782i | −0.527800 | − | 0.442876i | ||||
\(149\) | −2.27308 | − | 12.8913i | −0.186218 | − | 1.05610i | −0.924380 | − | 0.381473i | \(-0.875417\pi\) |
0.738162 | − | 0.674624i | \(-0.235694\pi\) | |||||||
\(150\) | −9.39693 | − | 3.42020i | −0.767256 | − | 0.279258i | ||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.97871 | 0.402505 | ||||||||
\(154\) | −9.84059 | − | 3.58168i | −0.792977 | − | 0.288620i | ||||
\(155\) | −0.776578 | − | 4.40419i | −0.0623763 | − | 0.353753i | ||||
\(156\) | −1.30856 | − | 1.09801i | −0.104769 | − | 0.0879113i | ||||
\(157\) | 7.18700 | − | 6.03061i | 0.573585 | − | 0.481295i | −0.309248 | − | 0.950981i | \(-0.600077\pi\) |
0.882833 | + | 0.469686i | \(0.155633\pi\) | |||||||
\(158\) | 0.479952 | − | 2.72194i | 0.0381829 | − | 0.216546i | ||||
\(159\) | −3.76393 | + | 6.51932i | −0.298499 | + | 0.517016i | ||||
\(160\) | 1.80902 | + | 3.13331i | 0.143015 | + | 0.247710i | ||||
\(161\) | 15.9224 | − | 5.79528i | 1.25486 | − | 0.456732i | ||||
\(162\) | 2.27068 | − | 0.826460i | 0.178402 | − | 0.0649328i | ||||
\(163\) | −5.32624 | − | 9.22531i | −0.417183 | − | 0.722582i | 0.578472 | − | 0.815702i | \(-0.303649\pi\) |
−0.995655 | + | 0.0931200i | \(0.970316\pi\) | |||||||
\(164\) | 0.427051 | − | 0.739674i | 0.0333471 | − | 0.0577588i | ||||
\(165\) | 2.51306 | − | 14.2523i | 0.195641 | − | 1.10954i | ||||
\(166\) | −0.361677 | + | 0.303483i | −0.0280716 | + | 0.0235549i | ||||
\(167\) | 9.55421 | + | 8.01693i | 0.739327 | + | 0.620369i | 0.932657 | − | 0.360765i | \(-0.117484\pi\) |
−0.193330 | + | 0.981134i | \(0.561929\pi\) | |||||||
\(168\) | −0.694593 | − | 3.93923i | −0.0535890 | − | 0.303918i | ||||
\(169\) | 10.4214 | + | 3.79306i | 0.801642 | + | 0.291774i | ||||
\(170\) | 12.2361 | 0.938464 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.23607 | −0.704244 | ||||||||
\(173\) | 1.24626 | + | 0.453600i | 0.0947511 | + | 0.0344866i | 0.388961 | − | 0.921254i | \(-0.372834\pi\) |
−0.294210 | + | 0.955741i | \(0.595056\pi\) | |||||||
\(174\) | 1.95112 | + | 11.0654i | 0.147914 | + | 0.838863i | ||||
\(175\) | −20.0553 | − | 16.8284i | −1.51604 | − | 1.27211i | ||||
\(176\) | −2.47897 | + | 2.08010i | −0.186860 | + | 0.156794i | ||||
\(177\) | 0.101340 | − | 0.574726i | 0.00761716 | − | 0.0431991i | ||||
\(178\) | 4.42705 | − | 7.66788i | 0.331822 | − | 0.574732i | ||||
\(179\) | −11.7082 | − | 20.2792i | −0.875112 | − | 1.51574i | −0.856643 | − | 0.515909i | \(-0.827454\pi\) |
−0.0184691 | − | 0.999829i | \(-0.505879\pi\) | |||||||
\(180\) | −5.00503 | + | 1.82168i | −0.373053 | + | 0.135780i | ||||
\(181\) | 5.08976 | − | 1.85252i | 0.378319 | − | 0.137697i | −0.145860 | − | 0.989305i | \(-0.546595\pi\) |
0.524178 | + | 0.851609i | \(0.324373\pi\) | |||||||
\(182\) | −2.23607 | − | 3.87298i | −0.165748 | − | 0.287085i | ||||
\(183\) | −0.854102 | + | 1.47935i | −0.0631370 | + | 0.109357i | ||||
\(184\) | 0.909234 | − | 5.15652i | 0.0670296 | − | 0.380144i | ||||
\(185\) | 23.2312 | − | 19.4933i | 1.70800 | − | 1.43318i | ||||
\(186\) | 1.17041 | + | 0.982092i | 0.0858188 | + | 0.0720105i | ||||
\(187\) | 1.90045 | + | 10.7780i | 0.138975 | + | 0.788166i | ||||
\(188\) | −4.20243 | − | 1.52956i | −0.306494 | − | 0.111555i | ||||
\(189\) | 17.8885 | 1.30120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52786 | 0.255267 | 0.127634 | − | 0.991821i | \(-0.459262\pi\) | ||||
0.127634 | + | 0.991821i | \(0.459262\pi\) | |||||||
\(192\) | −1.16152 | − | 0.422760i | −0.0838258 | − | 0.0305101i | ||||
\(193\) | 2.00179 | + | 11.3527i | 0.144092 | + | 0.817187i | 0.968092 | + | 0.250597i | \(0.0806268\pi\) |
−0.823999 | + | 0.566591i | \(0.808262\pi\) | |||||||
\(194\) | −6.60180 | − | 5.53957i | −0.473981 | − | 0.397718i | ||||
\(195\) | 4.73442 | − | 3.97265i | 0.339039 | − | 0.284487i | ||||
\(196\) | 0.602930 | − | 3.41939i | 0.0430664 | − | 0.244242i | ||||
\(197\) | 2.07295 | − | 3.59045i | 0.147692 | − | 0.255809i | −0.782682 | − | 0.622421i | \(-0.786149\pi\) |
0.930374 | + | 0.366612i | \(0.119482\pi\) | |||||||
\(198\) | −2.38197 | − | 4.12569i | −0.169279 | − | 0.293200i | ||||
\(199\) | −9.84059 | + | 3.58168i | −0.697581 | + | 0.253899i | −0.666378 | − | 0.745614i | \(-0.732156\pi\) |
−0.0312032 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(200\) | −7.60227 | + | 2.76700i | −0.537562 | + | 0.195657i | ||||
\(201\) | 7.23607 | + | 12.5332i | 0.510393 | + | 0.884026i | ||||
\(202\) | 7.80902 | − | 13.5256i | 0.549441 | − | 0.951659i | ||||
\(203\) | −5.10811 | + | 28.9695i | −0.358519 | + | 2.03326i | ||||
\(204\) | −3.20233 | + | 2.68707i | −0.224208 | + | 0.188133i | ||||
\(205\) | 2.36721 | + | 1.98632i | 0.165333 | + | 0.138731i | ||||
\(206\) | −2.54438 | − | 14.4299i | −0.177275 | − | 1.00538i | ||||
\(207\) | 7.24334 | + | 2.63636i | 0.503447 | + | 0.183240i | ||||
\(208\) | −1.38197 | −0.0958221 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 14.4721 | 0.998672 | ||||||||
\(211\) | −6.79968 | − | 2.47488i | −0.468109 | − | 0.170378i | 0.0971864 | − | 0.995266i | \(-0.469016\pi\) |
−0.565296 | + | 0.824888i | \(0.691238\pi\) | |||||||
\(212\) | 1.05755 | + | 5.99765i | 0.0726326 | + | 0.411920i | ||||
\(213\) | −2.78788 | − | 2.33931i | −0.191022 | − | 0.160287i | ||||
\(214\) | −7.21339 | + | 6.05275i | −0.493097 | + | 0.413757i | ||||
\(215\) | 5.80270 | − | 32.9087i | 0.395741 | − | 2.24436i | ||||
\(216\) | 2.76393 | − | 4.78727i | 0.188062 | − | 0.325733i | ||||
\(217\) | 2.00000 | + | 3.46410i | 0.135769 | + | 0.235159i | ||||
\(218\) | −10.3690 | + | 3.77400i | −0.702276 | + | 0.255608i | ||||
\(219\) | 6.52548 | − | 2.37508i | 0.440951 | − | 0.160493i | ||||
\(220\) | −5.85410 | − | 10.1396i | −0.394683 | − | 0.683612i | ||||
\(221\) | −2.33688 | + | 4.04760i | −0.157196 | + | 0.272271i | ||||
\(222\) | −1.79911 | + | 10.2033i | −0.120749 | + | 0.684799i | ||||
\(223\) | −21.2257 | + | 17.8105i | −1.42138 | + | 1.19268i | −0.470783 | + | 0.882249i | \(0.656028\pi\) |
−0.950596 | + | 0.310429i | \(0.899527\pi\) | |||||||
\(224\) | −2.47897 | − | 2.08010i | −0.165633 | − | 0.138983i | ||||
\(225\) | −2.06812 | − | 11.7289i | −0.137875 | − | 0.781926i | ||||
\(226\) | −9.25983 | − | 3.37030i | −0.615955 | − | 0.224189i | ||||
\(227\) | 8.94427 | 0.593652 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.38197 | 0.289568 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(230\) | 17.8018 | + | 6.47932i | 1.17382 | + | 0.427234i | ||||
\(231\) | 2.24775 | + | 12.7476i | 0.147891 | + | 0.838732i | ||||
\(232\) | 6.96347 | + | 5.84305i | 0.457174 | + | 0.383615i | ||||
\(233\) | 1.19680 | − | 1.00423i | 0.0784047 | − | 0.0657894i | −0.602743 | − | 0.797935i | \(-0.705926\pi\) |
0.681148 | + | 0.732146i | \(0.261481\pi\) | |||||||
\(234\) | 0.353277 | − | 2.00353i | 0.0230944 | − | 0.130975i | ||||
\(235\) | 8.09017 | − | 14.0126i | 0.527744 | − | 0.914080i | ||||
\(236\) | −0.236068 | − | 0.408882i | −0.0153667 | − | 0.0266159i | ||||
\(237\) | −3.21037 | + | 1.16848i | −0.208536 | + | 0.0759010i | ||||
\(238\) | −10.2843 | + | 3.74316i | −0.666629 | + | 0.242633i | ||||
\(239\) | −15.0902 | − | 26.1369i | −0.976102 | − | 1.69066i | −0.676250 | − | 0.736673i | \(-0.736396\pi\) |
−0.299852 | − | 0.953986i | \(-0.596937\pi\) | |||||||
\(240\) | 2.23607 | − | 3.87298i | 0.144338 | − | 0.250000i | ||||
\(241\) | 4.41351 | − | 25.0303i | 0.284299 | − | 1.61234i | −0.423478 | − | 0.905906i | \(-0.639191\pi\) |
0.707777 | − | 0.706435i | \(-0.249698\pi\) | |||||||
\(242\) | −0.404367 | + | 0.339304i | −0.0259937 | + | 0.0218113i | ||||
\(243\) | 10.4157 | + | 8.73982i | 0.668168 | + | 0.560660i | ||||
\(244\) | 0.239976 | + | 1.36097i | 0.0153629 | + | 0.0871272i | ||||
\(245\) | 11.8047 | + | 4.29656i | 0.754175 | + | 0.274497i | ||||
\(246\) | −1.05573 | −0.0673108 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.23607 | 0.0784904 | ||||||||
\(249\) | 0.548397 | + | 0.199600i | 0.0347533 | + | 0.0126492i | ||||
\(250\) | −1.94145 | − | 11.0105i | −0.122788 | − | 0.696364i | ||||
\(251\) | −1.75562 | − | 1.47314i | −0.110814 | − | 0.0929837i | 0.585697 | − | 0.810530i | \(-0.300821\pi\) |
−0.696511 | + | 0.717546i | \(0.745265\pi\) | |||||||
\(252\) | 3.64938 | − | 3.06220i | 0.229890 | − | 0.192900i | ||||
\(253\) | −2.94234 | + | 16.6869i | −0.184983 | + | 1.04909i | ||||
\(254\) | −5.70820 | + | 9.88690i | −0.358165 | + | 0.620359i | ||||
\(255\) | −7.56231 | − | 13.0983i | −0.473570 | − | 0.820247i | ||||
\(256\) | −0.939693 | + | 0.342020i | −0.0587308 | + | 0.0213763i | ||||
\(257\) | 17.2734 | − | 6.28700i | 1.07748 | − | 0.392172i | 0.258514 | − | 0.966007i | \(-0.416767\pi\) |
0.818971 | + | 0.573835i | \(0.194545\pi\) | |||||||
\(258\) | 5.70820 | + | 9.88690i | 0.355377 | + | 0.615531i | ||||
\(259\) | −13.5623 | + | 23.4906i | −0.842721 | + | 1.45964i | ||||
\(260\) | 0.868241 | − | 4.92404i | 0.0538460 | − | 0.305376i | ||||
\(261\) | −10.2512 | + | 8.60176i | −0.634532 | + | 0.532436i | ||||
\(262\) | 3.42585 | + | 2.87463i | 0.211650 | + | 0.177595i | ||||
\(263\) | 0.511267 | + | 2.89954i | 0.0315261 | + | 0.178793i | 0.996505 | − | 0.0835345i | \(-0.0266209\pi\) |
−0.964979 | + | 0.262328i | \(0.915510\pi\) | |||||||
\(264\) | 3.75877 | + | 1.36808i | 0.231336 | + | 0.0841995i | ||||
\(265\) | −22.0344 | −1.35357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9443 | −0.669779 | ||||||||
\(268\) | 11.0021 | + | 4.00444i | 0.672061 | + | 0.244610i | ||||
\(269\) | −2.48773 | − | 14.1086i | −0.151679 | − | 0.860216i | −0.961759 | − | 0.273896i | \(-0.911687\pi\) |
0.810080 | − | 0.586319i | \(-0.199424\pi\) | |||||||
\(270\) | 15.3209 | + | 12.8558i | 0.932400 | + | 0.782376i | ||||
\(271\) | 19.9172 | − | 16.7125i | 1.20988 | − | 1.01521i | 0.210590 | − | 0.977575i | \(-0.432462\pi\) |
0.999292 | − | 0.0376362i | \(-0.0119828\pi\) | |||||||
\(272\) | −0.587272 | + | 3.33059i | −0.0356086 | + | 0.201946i | ||||
\(273\) | −2.76393 | + | 4.78727i | −0.167281 | + | 0.289739i | ||||
\(274\) | −1.19098 | − | 2.06284i | −0.0719499 | − | 0.124621i | ||||
\(275\) | 24.6015 | − | 8.95420i | 1.48352 | − | 0.539959i | ||||
\(276\) | −6.08182 | + | 2.21360i | −0.366082 | + | 0.133243i | ||||
\(277\) | 5.04508 | + | 8.73834i | 0.303130 | + | 0.525036i | 0.976843 | − | 0.213957i | \(-0.0686351\pi\) |
−0.673713 | + | 0.738993i | \(0.735302\pi\) | |||||||
\(278\) | 7.00000 | − | 12.1244i | 0.419832 | − | 0.727171i | ||||
\(279\) | −0.315981 | + | 1.79202i | −0.0189173 | + | 0.107285i | ||||
\(280\) | 8.96900 | − | 7.52589i | 0.536001 | − | 0.449758i | ||||
\(281\) | −16.0706 | − | 13.4849i | −0.958693 | − | 0.804439i | 0.0220468 | − | 0.999757i | \(-0.492982\pi\) |
−0.980740 | + | 0.195318i | \(0.937426\pi\) | |||||||
\(282\) | 0.959904 | + | 5.44388i | 0.0571614 | + | 0.324179i | ||||
\(283\) | −21.1169 | − | 7.68592i | −1.25527 | − | 0.456881i | −0.373090 | − | 0.927795i | \(-0.621702\pi\) |
−0.882179 | + | 0.470914i | \(0.843924\pi\) | |||||||
\(284\) | −2.94427 | −0.174710 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.47214 | 0.264443 | ||||||||
\(287\) | −2.59725 | − | 0.945320i | −0.153311 | − | 0.0558005i | ||||
\(288\) | −0.255634 | − | 1.44977i | −0.0150634 | − | 0.0854286i | ||||
\(289\) | −4.26097 | − | 3.57538i | −0.250646 | − | 0.210317i | ||||
\(290\) | −25.1941 | + | 21.1403i | −1.47945 | + | 1.24140i | ||||
\(291\) | −1.84978 | + | 10.4906i | −0.108436 | + | 0.614972i | ||||
\(292\) | 2.80902 | − | 4.86536i | 0.164385 | − | 0.284724i | ||||
\(293\) | 11.4721 | + | 19.8703i | 0.670209 | + | 1.16084i | 0.977845 | + | 0.209332i | \(0.0671290\pi\) |
−0.307635 | + | 0.951504i | \(0.599538\pi\) | |||||||
\(294\) | −4.03297 | + | 1.46788i | −0.235208 | + | 0.0856085i | ||||
\(295\) | 1.60519 | − | 0.584240i | 0.0934576 | − | 0.0340158i | ||||
\(296\) | 4.19098 | + | 7.25900i | 0.243596 | + | 0.421921i | ||||
\(297\) | −8.94427 | + | 15.4919i | −0.518999 | + | 0.898933i | ||||
\(298\) | −2.27308 | + | 12.8913i | −0.131676 | + | 0.746773i | ||||
\(299\) | −5.54315 | + | 4.65125i | −0.320569 | + | 0.268989i | ||||
\(300\) | 7.66044 | + | 6.42788i | 0.442276 | + | 0.371114i | ||||
\(301\) | 5.19009 | + | 29.4345i | 0.299152 | + | 1.69657i | ||||
\(302\) | 13.5994 | + | 4.94976i | 0.782555 | + | 0.284827i | ||||
\(303\) | −19.3050 | −1.10904 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.00000 | −0.286299 | ||||||||
\(306\) | −4.67846 | − | 1.70282i | −0.267450 | − | 0.0973438i | ||||
\(307\) | −2.03311 | − | 11.5303i | −0.116036 | − | 0.658071i | −0.986232 | − | 0.165366i | \(-0.947119\pi\) |
0.870197 | − | 0.492705i | \(-0.163992\pi\) | |||||||
\(308\) | 8.02212 | + | 6.73136i | 0.457103 | + | 0.383555i | ||||
\(309\) | −13.8742 | + | 11.6418i | −0.789275 | + | 0.662280i | ||||
\(310\) | −0.776578 | + | 4.40419i | −0.0441067 | + | 0.250141i | ||||
\(311\) | −15.6180 | + | 27.0512i | −0.885617 | + | 1.53393i | −0.0406131 | + | 0.999175i | \(0.512931\pi\) |
−0.845004 | + | 0.534759i | \(0.820402\pi\) | |||||||
\(312\) | 0.854102 | + | 1.47935i | 0.0483540 | + | 0.0837516i | ||||
\(313\) | 14.5714 | − | 5.30356i | 0.823625 | − | 0.299775i | 0.104385 | − | 0.994537i | \(-0.466712\pi\) |
0.719240 | + | 0.694762i | \(0.244490\pi\) | |||||||
\(314\) | −8.81616 | + | 3.20882i | −0.497525 | + | 0.181084i | ||||
\(315\) | 8.61803 | + | 14.9269i | 0.485571 | + | 0.841034i | ||||
\(316\) | −1.38197 | + | 2.39364i | −0.0777417 | + | 0.134653i | ||||
\(317\) | −0.230299 | + | 1.30609i | −0.0129349 | + | 0.0733573i | −0.990592 | − | 0.136849i | \(-0.956302\pi\) |
0.977657 | + | 0.210206i | \(0.0674136\pi\) | |||||||
\(318\) | 5.76668 | − | 4.83882i | 0.323379 | − | 0.271347i | ||||
\(319\) | −22.5343 | − | 18.9085i | −1.26168 | − | 1.05867i | ||||
\(320\) | −0.628265 | − | 3.56307i | −0.0351211 | − | 0.199182i | ||||
\(321\) | 10.9374 | + | 3.98088i | 0.610465 | + | 0.222191i | ||||
\(322\) | −16.9443 | −0.944267 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.41641 | −0.134245 | ||||||||
\(325\) | 10.5061 | + | 3.82390i | 0.582773 | + | 0.212112i | ||||
\(326\) | 1.84978 | + | 10.4906i | 0.102450 | + | 0.581023i | ||||
\(327\) | 10.4483 | + | 8.76719i | 0.577794 | + | 0.484826i | ||||
\(328\) | −0.654280 | + | 0.549006i | −0.0361266 | + | 0.0303138i | ||||
\(329\) | −2.51306 | + | 14.2523i | −0.138549 | + | 0.785753i | ||||
\(330\) | −7.23607 | + | 12.5332i | −0.398332 | + | 0.689932i | ||||
\(331\) | 12.8541 | + | 22.2640i | 0.706525 | + | 1.22374i | 0.966138 | + | 0.258025i | \(0.0830717\pi\) |
−0.259613 | + | 0.965713i | \(0.583595\pi\) | |||||||
\(332\) | 0.443663 | − | 0.161480i | 0.0243492 | − | 0.00886237i | ||||
\(333\) | −11.5952 | + | 4.22032i | −0.635415 | + | 0.231272i | ||||
\(334\) | −6.23607 | − | 10.8012i | −0.341222 | − | 0.591015i | ||||
\(335\) | −21.1803 | + | 36.6854i | −1.15721 | + | 2.00434i | ||||
\(336\) | −0.694593 | + | 3.93923i | −0.0378931 | + | 0.214903i | ||||
\(337\) | −1.82469 | + | 1.53110i | −0.0993973 | + | 0.0834042i | −0.691132 | − | 0.722728i | \(-0.742888\pi\) |
0.591735 | + | 0.806133i | \(0.298443\pi\) | |||||||
\(338\) | −8.49556 | − | 7.12862i | −0.462098 | − | 0.387746i | ||||
\(339\) | 2.11509 | + | 11.9953i | 0.114876 | + | 0.651495i | ||||
\(340\) | −11.4981 | − | 4.18498i | −0.623574 | − | 0.226963i | ||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 8.67906 | + | 3.15892i | 0.467944 | + | 0.170318i | ||||
\(345\) | −4.06622 | − | 23.0607i | −0.218918 | − | 1.24154i | ||||
\(346\) | −1.01596 | − | 0.852489i | −0.0546182 | − | 0.0458301i | ||||
\(347\) | −2.03191 | + | 1.70498i | −0.109079 | + | 0.0915280i | −0.695696 | − | 0.718336i | \(-0.744904\pi\) |
0.586617 | + | 0.809865i | \(0.300459\pi\) | |||||||
\(348\) | 1.95112 | − | 11.0654i | 0.104591 | − | 0.593166i | ||||
\(349\) | 16.5451 | − | 28.6569i | 0.885638 | − | 1.53397i | 0.0406575 | − | 0.999173i | \(-0.487055\pi\) |
0.844981 | − | 0.534797i | \(-0.179612\pi\) | |||||||
\(350\) | 13.0902 | + | 22.6728i | 0.699699 | + | 1.21191i | ||||
\(351\) | −7.17861 | + | 2.61280i | −0.383166 | + | 0.139461i | ||||
\(352\) | 3.04091 | − | 1.10680i | 0.162081 | − | 0.0589927i | ||||
\(353\) | 11.8713 | + | 20.5617i | 0.631847 | + | 1.09439i | 0.987174 | + | 0.159649i | \(0.0510361\pi\) |
−0.355327 | + | 0.934742i | \(0.615631\pi\) | |||||||
\(354\) | −0.291796 | + | 0.505406i | −0.0155088 | + | 0.0268620i | ||||
\(355\) | 1.84978 | − | 10.4906i | 0.0981763 | − | 0.556785i | ||||
\(356\) | −6.78264 | + | 5.69131i | −0.359479 | + | 0.301639i | ||||
\(357\) | 10.3629 | + | 8.69554i | 0.548465 | + | 0.460217i | ||||
\(358\) | 4.06622 | + | 23.0607i | 0.214906 | + | 1.21879i | ||||
\(359\) | −10.8326 | − | 3.94276i | −0.571725 | − | 0.208091i | 0.0399476 | − | 0.999202i | \(-0.487281\pi\) |
−0.611673 | + | 0.791111i | \(0.709503\pi\) | |||||||
\(360\) | 5.32624 | 0.280717 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.41641 | −0.284680 | ||||||||
\(363\) | 0.613127 | + | 0.223160i | 0.0321808 | + | 0.0117129i | ||||
\(364\) | 0.776578 | + | 4.40419i | 0.0407038 | + | 0.230842i | ||||
\(365\) | 15.5708 | + | 13.0655i | 0.815013 | + | 0.683877i | ||||
\(366\) | 1.30856 | − | 1.09801i | 0.0683995 | − | 0.0573940i | ||||
\(367\) | 3.27028 | − | 18.5467i | 0.170707 | − | 0.968130i | −0.772275 | − | 0.635288i | \(-0.780881\pi\) |
0.942983 | − | 0.332842i | \(-0.108008\pi\) | |||||||
\(368\) | −2.61803 | + | 4.53457i | −0.136474 | + | 0.236381i | ||||
\(369\) | −0.628677 | − | 1.08890i | −0.0327276 | − | 0.0566859i | ||||
\(370\) | −28.4973 | + | 10.3722i | −1.48151 | + | 0.539224i | ||||
\(371\) | 18.5197 | − | 6.74060i | 0.961493 | − | 0.349955i | ||||
\(372\) | −0.763932 | − | 1.32317i | −0.0396080 | − | 0.0686031i | ||||
\(373\) | 9.16312 | − | 15.8710i | 0.474448 | − | 0.821769i | −0.525124 | − | 0.851026i | \(-0.675981\pi\) |
0.999572 | + | 0.0292574i | \(0.00931424\pi\) | |||||||
\(374\) | 1.90045 | − | 10.7780i | 0.0982701 | − | 0.557317i | ||||
\(375\) | −10.5865 | + | 8.88311i | −0.546683 | + | 0.458722i | ||||
\(376\) | 3.42585 | + | 2.87463i | 0.176675 | + | 0.148248i | ||||
\(377\) | −2.18142 | − | 12.3715i | −0.112349 | − | 0.637162i | ||||
\(378\) | −16.8097 | − | 6.11824i | −0.864599 | − | 0.314688i | ||||
\(379\) | 35.4164 | 1.81922 | 0.909609 | − | 0.415465i | \(-0.136381\pi\) | ||||
0.909609 | + | 0.415465i | \(0.136381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1115 | 0.722952 | ||||||||
\(382\) | −3.31511 | − | 1.20660i | −0.169616 | − | 0.0617351i | ||||
\(383\) | −3.60562 | − | 20.4485i | −0.184239 | − | 1.04487i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) |
0.742691 | − | 0.669634i | \(-0.233549\pi\) | |||||||
\(384\) | 0.946883 | + | 0.794529i | 0.0483204 | + | 0.0405456i | ||||
\(385\) | −29.0243 | + | 24.3543i | −1.47922 | + | 1.24121i | ||||
\(386\) | 2.00179 | − | 11.3527i | 0.101889 | − | 0.577839i | ||||
\(387\) | −6.79837 | + | 11.7751i | −0.345581 | + | 0.598563i | ||||
\(388\) | 4.30902 | + | 7.46344i | 0.218757 | + | 0.378899i | ||||
\(389\) | −12.0265 | + | 4.37730i | −0.609770 | + | 0.221938i | −0.628402 | − | 0.777888i | \(-0.716291\pi\) |
0.0186328 | + | 0.999826i | \(0.494069\pi\) | |||||||
\(390\) | −5.80762 | + | 2.11380i | −0.294080 | + | 0.107036i | ||||
\(391\) | 8.85410 | + | 15.3358i | 0.447771 | + | 0.775562i | ||||
\(392\) | −1.73607 | + | 3.00696i | −0.0876847 | + | 0.151874i | ||||
\(393\) | 0.959904 | − | 5.44388i | 0.0484207 | − | 0.274608i | ||||
\(394\) | −3.17594 | + | 2.66493i | −0.160002 | + | 0.134257i | ||||
\(395\) | −7.66044 | − | 6.42788i | −0.385439 | − | 0.323422i | ||||
\(396\) | 0.827248 | + | 4.69156i | 0.0415708 | + | 0.235760i | ||||
\(397\) | 21.0122 | + | 7.64780i | 1.05457 | + | 0.383832i | 0.810386 | − | 0.585897i | \(-0.199258\pi\) |
0.244185 | + | 0.969729i | \(0.421480\pi\) | |||||||
\(398\) | 10.4721 | 0.524921 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.09017 | 0.404508 | ||||||||
\(401\) | 17.8018 | + | 6.47932i | 0.888979 | + | 0.323562i | 0.745828 | − | 0.666139i | \(-0.232054\pi\) |
0.143151 | + | 0.989701i | \(0.454276\pi\) | |||||||
\(402\) | −2.51306 | − | 14.2523i | −0.125340 | − | 0.710839i | ||||
\(403\) | −1.30856 | − | 1.09801i | −0.0651840 | − | 0.0546959i | ||||
\(404\) | −11.9641 | + | 10.0391i | −0.595237 | + | 0.499463i | ||||
\(405\) | 1.51814 | − | 8.60983i | 0.0754372 | − | 0.427826i | ||||
\(406\) | 14.7082 | − | 25.4754i | 0.729956 | − | 1.26432i | ||||
\(407\) | −13.5623 | − | 23.4906i | −0.672259 | − | 1.16439i | ||||
\(408\) | 3.92823 | − | 1.42976i | 0.194477 | − | 0.0707837i | ||||
\(409\) | 15.2893 | − | 5.56484i | 0.756006 | − | 0.275164i | 0.0648753 | − | 0.997893i | \(-0.479335\pi\) |
0.691131 | + | 0.722730i | \(0.257113\pi\) | |||||||
\(410\) | −1.54508 | − | 2.67617i | −0.0763063 | − | 0.132166i | ||||
\(411\) | −1.47214 | + | 2.54981i | −0.0726151 | + | 0.125773i | ||||
\(412\) | −2.54438 | + | 14.4299i | −0.125352 | + | 0.710909i | ||||
\(413\) | −1.17041 | + | 0.982092i | −0.0575922 | + | 0.0483256i | ||||
\(414\) | −5.90483 | − | 4.95474i | −0.290206 | − | 0.243512i | ||||
\(415\) | 0.296626 | + | 1.68225i | 0.0145608 | + | 0.0825785i | ||||
\(416\) | 1.29862 | + | 0.472660i | 0.0636702 | + | 0.0231741i | ||||
\(417\) | −17.3050 | −0.847427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.47214 | −0.316185 | −0.158092 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158092 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(420\) | −13.5994 | − | 4.94976i | −0.663581 | − | 0.241524i | ||||
\(421\) | −2.41542 | − | 13.6985i | −0.117720 | − | 0.667624i | −0.985367 | − | 0.170444i | \(-0.945480\pi\) |
0.867647 | − | 0.497180i | \(-0.165631\pi\) | |||||||
\(422\) | 5.54315 | + | 4.65125i | 0.269836 | + | 0.226420i | ||||
\(423\) | −5.04332 | + | 4.23185i | −0.245215 | + | 0.205760i | ||||
\(424\) | 1.05755 | − | 5.99765i | 0.0513590 | − | 0.291271i | ||||
\(425\) | 13.6803 | − | 23.6950i | 0.663594 | − | 1.14938i | ||||
\(426\) | 1.81966 | + | 3.15174i | 0.0881628 | + | 0.152702i | ||||
\(427\) | 4.20243 | − | 1.52956i | 0.203370 | − | 0.0740206i | ||||
\(428\) | 8.84853 | − | 3.22060i | 0.427710 | − | 0.155674i | ||||
\(429\) | −2.76393 | − | 4.78727i | −0.133444 | − | 0.231132i | ||||
\(430\) | −16.7082 | + | 28.9395i | −0.805741 | + | 1.39558i | ||||
\(431\) | −1.15519 | + | 6.55141i | −0.0556436 | + | 0.315570i | −0.999907 | − | 0.0136197i | \(-0.995665\pi\) |
0.944264 | + | 0.329190i | \(0.106776\pi\) | |||||||
\(432\) | −4.23459 | + | 3.55324i | −0.203737 | + | 0.170955i | ||||
\(433\) | 19.1775 | + | 16.0918i | 0.921612 | + | 0.773324i | 0.974292 | − | 0.225287i | \(-0.0723321\pi\) |
−0.0526807 | + | 0.998611i | \(0.516777\pi\) | |||||||
\(434\) | −0.694593 | − | 3.93923i | −0.0333415 | − | 0.189089i | ||||
\(435\) | 38.2008 | + | 13.9040i | 1.83159 | + | 0.666644i | ||||
\(436\) | 11.0344 | 0.528454 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.94427 | −0.331810 | ||||||||
\(439\) | 27.4729 | + | 9.99932i | 1.31121 | + | 0.477242i | 0.900632 | − | 0.434583i | \(-0.143104\pi\) |
0.410579 | + | 0.911825i | \(0.365327\pi\) | |||||||
\(440\) | 2.03311 | + | 11.5303i | 0.0969246 | + | 0.549687i | ||||
\(441\) | −3.91560 | − | 3.28558i | −0.186457 | − | 0.156456i | ||||
\(442\) | 3.58031 | − | 3.00424i | 0.170298 | − | 0.142897i | ||||
\(443\) | 1.60383 | − | 9.09575i | 0.0762001 | − | 0.432152i | −0.922711 | − | 0.385493i | \(-0.874031\pi\) |
0.998911 | − | 0.0466592i | \(-0.0148575\pi\) | |||||||
\(444\) | 5.18034 | − | 8.97261i | 0.245848 | − | 0.425821i | ||||
\(445\) | −16.0172 | − | 27.7426i | −0.759289 | − | 1.31513i | ||||
\(446\) | 26.0372 | − | 9.47676i | 1.23290 | − | 0.448738i | ||||
\(447\) | 15.2045 | − | 5.53400i | 0.719150 | − | 0.261749i | ||||
\(448\) | 1.61803 | + | 2.80252i | 0.0764449 | + | 0.132406i | ||||
\(449\) | −11.3992 | + | 19.7440i | −0.537961 | + | 0.931776i | 0.461053 | + | 0.887373i | \(0.347472\pi\) |
−0.999014 | + | 0.0444029i | \(0.985861\pi\) | |||||||
\(450\) | −2.06812 | + | 11.7289i | −0.0974921 | + | 0.552905i | ||||
\(451\) | 2.11729 | − | 1.77662i | 0.0996995 | − | 0.0836578i | ||||
\(452\) | 7.54868 | + | 6.33409i | 0.355060 | + | 0.297931i | ||||
\(453\) | −3.10631 | − | 17.6168i | −0.145947 | − | 0.827708i | ||||
\(454\) | −8.40487 | − | 3.05912i | −0.394460 | − | 0.143572i | ||||
\(455\) | −16.1803 | −0.758546 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2148 | 1.17950 | 0.589749 | − | 0.807587i | \(-0.299227\pi\) | ||||
0.589749 | + | 0.807587i | \(0.299227\pi\) | |||||||
\(458\) | −4.11770 | − | 1.49872i | −0.192408 | − | 0.0700306i | ||||
\(459\) | 3.24636 | + | 18.4110i | 0.151527 | + | 0.859353i | ||||
\(460\) | −14.5122 | − | 12.1771i | −0.676633 | − | 0.567762i | ||||
\(461\) | 16.4059 | − | 13.7662i | 0.764100 | − | 0.641156i | −0.175091 | − | 0.984552i | \(-0.556022\pi\) |
0.939191 | + | 0.343396i | \(0.111577\pi\) | |||||||
\(462\) | 2.24775 | − | 12.7476i | 0.104575 | − | 0.593073i | ||||
\(463\) | 2.52786 | − | 4.37839i | 0.117480 | − | 0.203481i | −0.801289 | − | 0.598278i | \(-0.795852\pi\) |
0.918768 | + | 0.394797i | \(0.129185\pi\) | |||||||
\(464\) | −4.54508 | − | 7.87232i | −0.211000 | − | 0.365463i | ||||
\(465\) | 5.19449 | − | 1.89064i | 0.240889 | − | 0.0876764i | ||||
\(466\) | −1.46809 | + | 0.534340i | −0.0680078 | + | 0.0247528i | ||||
\(467\) | 16.6525 | + | 28.8429i | 0.770585 | + | 1.33469i | 0.937243 | + | 0.348677i | \(0.113369\pi\) |
−0.166658 | + | 0.986015i | \(0.553298\pi\) | |||||||
\(468\) | −1.01722 | + | 1.76188i | −0.0470211 | + | 0.0814429i | ||||
\(469\) | 6.57928 | − | 37.3129i | 0.303803 | − | 1.72295i | ||||
\(470\) | −12.3949 | + | 10.4005i | −0.571732 | + | 0.479740i | ||||
\(471\) | 8.88362 | + | 7.45425i | 0.409336 | + | 0.343474i | ||||
\(472\) | 0.0819855 | + | 0.464963i | 0.00377369 | + | 0.0214017i | ||||
\(473\) | −28.0860 | − | 10.2225i | −1.29140 | − | 0.470030i | ||||
\(474\) | 3.41641 | 0.156921 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.9443 | 0.501630 | ||||||||
\(477\) | 8.42487 | + | 3.06640i | 0.385748 | + | 0.140401i | ||||
\(478\) | 5.24076 | + | 29.7218i | 0.239707 | + | 1.35944i | ||||
\(479\) | 5.90483 | + | 4.95474i | 0.269798 | + | 0.226388i | 0.767642 | − | 0.640879i | \(-0.221430\pi\) |
−0.497843 | + | 0.867267i | \(0.665875\pi\) | |||||||
\(480\) | −3.42585 | + | 2.87463i | −0.156368 | + | 0.131208i | ||||
\(481\) | 2.01147 | − | 11.4076i | 0.0917151 | − | 0.520142i | ||||
\(482\) | −12.7082 | + | 22.0113i | −0.578843 | + | 1.00259i | ||||
\(483\) | 10.4721 | + | 18.1383i | 0.476499 | + | 0.825320i | ||||
\(484\) | 0.496030 | − | 0.180540i | 0.0225468 | − | 0.00820637i | ||||
\(485\) | −29.2999 | + | 10.6643i | −1.33044 | + | 0.484241i | ||||
\(486\) | −6.79837 | − | 11.7751i | −0.308381 | − | 0.534131i | ||||
\(487\) | 9.61803 | − | 16.6589i | 0.435835 | − | 0.754888i | −0.561529 | − | 0.827457i | \(-0.689787\pi\) |
0.997363 | + | 0.0725694i | \(0.0231199\pi\) | |||||||
\(488\) | 0.239976 | − | 1.36097i | 0.0108632 | − | 0.0616083i | ||||
\(489\) | 10.0866 | − | 8.46370i | 0.456134 | − | 0.382742i | ||||
\(490\) | −9.62328 | − | 8.07489i | −0.434736 | − | 0.364787i | ||||
\(491\) | −0.265311 | − | 1.50465i | −0.0119733 | − | 0.0679040i | 0.978236 | − | 0.207497i | \(-0.0665317\pi\) |
−0.990209 | + | 0.139593i | \(0.955421\pi\) | |||||||
\(492\) | 0.992060 | + | 0.361080i | 0.0447255 | + | 0.0162788i | ||||
\(493\) | −30.7426 | −1.38458 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.2361 | −0.774704 | ||||||||
\(496\) | −1.16152 | − | 0.422760i | −0.0521540 | − | 0.0189825i | ||||
\(497\) | 1.65450 | + | 9.38311i | 0.0742143 | + | 0.420890i | ||||
\(498\) | −0.447058 | − | 0.375126i | −0.0200331 | − | 0.0168098i | ||||
\(499\) | −27.0452 | + | 22.6936i | −1.21071 | + | 1.01590i | −0.211450 | + | 0.977389i | \(0.567818\pi\) |
−0.999258 | + | 0.0385155i | \(0.987737\pi\) | |||||||
\(500\) | −1.94145 | + | 11.0105i | −0.0868241 | + | 0.492404i | ||||
\(501\) | −7.70820 | + | 13.3510i | −0.344377 | + | 0.596479i | ||||
\(502\) | 1.14590 | + | 1.98475i | 0.0511439 | + | 0.0885839i | ||||
\(503\) | −6.35602 | + | 2.31340i | −0.283401 | + | 0.103149i | −0.479810 | − | 0.877373i | \(-0.659294\pi\) |
0.196409 | + | 0.980522i | \(0.437072\pi\) | |||||||
\(504\) | −4.47663 | + | 1.62936i | −0.199405 | + | 0.0725775i | ||||
\(505\) | −28.2533 | − | 48.9361i | −1.25725 | − | 2.17763i | ||||
\(506\) | 8.47214 | − | 14.6742i | 0.376632 | − | 0.652346i | ||||
\(507\) | −2.38040 | + | 13.4999i | −0.105717 | + | 0.599554i | ||||
\(508\) | 8.74548 | − | 7.33833i | 0.388018 | − | 0.325586i | ||||
\(509\) | −32.7001 | − | 27.4386i | −1.44941 | − | 1.21620i | −0.933013 | − | 0.359844i | \(-0.882830\pi\) |
−0.516393 | − | 0.856352i | \(-0.672726\pi\) | |||||||
\(510\) | 2.62636 | + | 14.8948i | 0.116297 | + | 0.659554i | ||||
\(511\) | −17.0839 | − | 6.21804i | −0.755749 | − | 0.275070i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.3820 | −0.810794 | ||||||||
\(515\) | −49.8161 | − | 18.1316i | −2.19516 | − | 0.798972i | ||||
\(516\) | −1.98244 | − | 11.2430i | −0.0872720 | − | 0.494944i | ||||
\(517\) | −11.0863 | − | 9.30251i | −0.487575 | − | 0.409124i | ||||
\(518\) | 20.7787 | − | 17.4354i | 0.912962 | − | 0.766066i | ||||
\(519\) | −0.284665 | + | 1.61442i | −0.0124954 | + | 0.0708650i | ||||
\(520\) | −2.50000 | + | 4.33013i | −0.109632 | + | 0.189889i | ||||
\(521\) | −2.63525 | − | 4.56440i | −0.115453 | − | 0.199970i | 0.802508 | − | 0.596641i | \(-0.203499\pi\) |
−0.917961 | + | 0.396672i | \(0.870165\pi\) | |||||||
\(522\) | 12.5749 | − | 4.57690i | 0.550390 | − | 0.200326i | ||||
\(523\) | −3.75877 | + | 1.36808i | −0.164360 | + | 0.0598220i | −0.422889 | − | 0.906181i | \(-0.638984\pi\) |
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(524\) | −2.23607 | − | 3.87298i | −0.0976831 | − | 0.169192i | ||||
\(525\) | 16.1803 | − | 28.0252i | 0.706168 | − | 1.22312i | ||||
\(526\) | 0.511267 | − | 2.89954i | 0.0222923 | − | 0.126426i | ||||
\(527\) | −3.20233 | + | 2.68707i | −0.139496 | + | 0.117051i | ||||
\(528\) | −3.06418 | − | 2.57115i | −0.133351 | − | 0.111895i | ||||
\(529\) | 0.766901 | + | 4.34931i | 0.0333435 | + | 0.189101i | ||||
\(530\) | 20.7056 | + | 7.53622i | 0.899394 | + | 0.327353i | ||||
\(531\) | −0.695048 | −0.0301625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.18034 | 0.0511262 | ||||||||
\(534\) | 10.2843 | + | 3.74316i | 0.445043 | + | 0.161982i | ||||
\(535\) | 5.91600 | + | 33.5513i | 0.255771 | + | 1.45055i | ||||
\(536\) | −8.96900 | − | 7.52589i | −0.387402 | − | 0.325069i | ||||
\(537\) | 22.1726 | − | 18.6050i | 0.956818 | − | 0.802866i | ||||
\(538\) | −2.48773 | + | 14.1086i | −0.107253 | + | 0.608265i | ||||
\(539\) | 5.61803 | − | 9.73072i | 0.241986 | − | 0.419132i | ||||
\(540\) | −10.0000 | − | 17.3205i | −0.430331 | − | 0.745356i | ||||
\(541\) | 25.0128 | − | 9.10390i | 1.07538 | − | 0.391407i | 0.257196 | − | 0.966359i | \(-0.417201\pi\) |
0.818187 | + | 0.574952i | \(0.194979\pi\) | |||||||
\(542\) | −24.4320 | + | 8.89252i | −1.04944 | + | 0.381967i | ||||
\(543\) | 3.34752 | + | 5.79808i | 0.143656 | + | 0.248820i | ||||
\(544\) | 1.69098 | − | 2.92887i | 0.0725003 | − | 0.125574i | ||||
\(545\) | −6.93255 | + | 39.3165i | −0.296958 | + | 1.68413i | ||||
\(546\) | 4.23459 | − | 3.55324i | 0.181224 | − | 0.152065i | ||||
\(547\) | −3.87291 | − | 3.24976i | −0.165594 | − | 0.138950i | 0.556225 | − | 0.831032i | \(-0.312249\pi\) |
−0.721819 | + | 0.692082i | \(0.756694\pi\) | |||||||
\(548\) | 0.413624 | + | 2.34578i | 0.0176691 | + | 0.100207i | ||||
\(549\) | 1.91175 | + | 0.695820i | 0.0815915 | + | 0.0296969i | ||||
\(550\) | −26.1803 | −1.11633 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.47214 | 0.275472 | ||||||||
\(553\) | 8.40487 | + | 3.05912i | 0.357411 | + | 0.130087i | ||||
\(554\) | −1.75214 | − | 9.93688i | −0.0744413 | − | 0.422177i | ||||
\(555\) | 28.7154 | + | 24.0951i | 1.21890 | + | 1.02278i | ||||
\(556\) | −10.7246 | + | 8.99903i | −0.454825 | + | 0.381644i | ||||
\(557\) | 0.877918 | − | 4.97892i | 0.0371986 | − | 0.210964i | −0.960543 | − | 0.278131i | \(-0.910285\pi\) |
0.997742 | + | 0.0671674i | \(0.0213962\pi\) | |||||||
\(558\) | 0.909830 | − | 1.57587i | 0.0385162 | − | 0.0667120i | ||||
\(559\) | −6.38197 | − | 11.0539i | −0.269928 | − | 0.467530i | ||||
\(560\) | −11.0021 | + | 4.00444i | −0.464924 | + | 0.169219i | ||||
\(561\) | −12.7120 | + | 4.62680i | −0.536702 | + | 0.195344i | ||||
\(562\) | 10.4894 | + | 18.1681i | 0.442467 | + | 0.766375i | ||||
\(563\) | 13.1459 | − | 22.7694i | 0.554034 | − | 0.959614i | −0.443944 | − | 0.896054i | \(-0.646421\pi\) |
0.997978 | − | 0.0635600i | \(-0.0202454\pi\) | |||||||
\(564\) | 0.959904 | − | 5.44388i | 0.0404192 | − | 0.229229i | ||||
\(565\) | −27.3114 | + | 22.9170i | −1.14900 | + | 0.964124i | ||||
\(566\) | 17.2147 | + | 14.4448i | 0.723586 | + | 0.607161i | ||||
\(567\) | 1.35787 | + | 7.70086i | 0.0570252 | + | 0.323406i | ||||
\(568\) | 2.76671 | + | 1.00700i | 0.116089 | + | 0.0422528i | ||||
\(569\) | −7.90983 | −0.331597 | −0.165799 | − | 0.986160i | \(-0.553020\pi\) | ||||
−0.165799 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.5410 | −1.36180 | −0.680900 | − | 0.732377i | \(-0.738411\pi\) | ||||
−0.680900 | + | 0.732377i | \(0.738411\pi\) | |||||||
\(572\) | −4.20243 | − | 1.52956i | −0.175713 | − | 0.0639541i | ||||
\(573\) | 0.757224 | + | 4.29443i | 0.0316335 | + | 0.179402i | ||||
\(574\) | 2.11729 | + | 1.77662i | 0.0883742 | + | 0.0741547i | ||||
\(575\) | 32.4502 | − | 27.2289i | 1.35327 | − | 1.13552i | ||||
\(576\) | −0.255634 | + | 1.44977i | −0.0106514 | + | 0.0604071i | ||||
\(577\) | −22.9615 | + | 39.7705i | −0.955899 | + | 1.65567i | −0.223603 | + | 0.974680i | \(0.571782\pi\) |
−0.732296 | + | 0.680986i | \(0.761551\pi\) | |||||||
\(578\) | 2.78115 | + | 4.81710i | 0.115681 | + | 0.200365i | ||||
\(579\) | −13.3899 | + | 4.87352i | −0.556465 | + | 0.202537i | ||||
\(580\) | 30.9051 | − | 11.2485i | 1.28327 | − | 0.467070i | ||||
\(581\) | −0.763932 | − | 1.32317i | −0.0316932 | − | 0.0548943i | ||||
\(582\) | 5.32624 | − | 9.22531i | 0.220780 | − | 0.382402i | ||||
\(583\) | −3.42229 | + | 19.4088i | −0.141737 | + | 0.803830i | ||||
\(584\) | −4.30366 | + | 3.61120i | −0.178087 | + | 0.149433i | ||||
\(585\) | −5.63861 | − | 4.73135i | −0.233128 | − | 0.195617i | ||||
\(586\) | −3.98423 | − | 22.5957i | −0.164587 | − | 0.933420i | ||||
\(587\) | −2.70198 | − | 0.983441i | −0.111523 | − | 0.0405909i | 0.285656 | − | 0.958332i | \(-0.407788\pi\) |
−0.397179 | + | 0.917741i | \(0.630011\pi\) | |||||||
\(588\) | 4.29180 | 0.176991 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.70820 | −0.0703256 | ||||||||
\(591\) | 4.81556 | + | 1.75272i | 0.198086 | + | 0.0720973i | ||||
\(592\) | −1.45551 | − | 8.25463i | −0.0598212 | − | 0.339263i | ||||
\(593\) | −26.7526 | − | 22.4481i | −1.09860 | − | 0.921831i | −0.101266 | − | 0.994859i | \(-0.532289\pi\) |
−0.997330 | + | 0.0730279i | \(0.976734\pi\) | |||||||
\(594\) | 13.7034 | − | 11.4985i | 0.562258 | − | 0.471791i | ||||
\(595\) | −6.87590 | + | 38.9952i | −0.281885 | + | 1.59865i | ||||
\(596\) | 6.54508 | − | 11.3364i | 0.268097 | − | 0.464358i | ||||
\(597\) | −6.47214 | − | 11.2101i | −0.264887 | − | 0.458798i | ||||
\(598\) | 6.79968 | − | 2.47488i | 0.278060 | − | 0.101205i | ||||
\(599\) | −36.7651 | + | 13.3814i | −1.50218 | + | 0.546749i | −0.956624 | − | 0.291324i | \(-0.905904\pi\) |
−0.545557 | + | 0.838074i | \(0.683682\pi\) | |||||||
\(600\) | −5.00000 | − | 8.66025i | −0.204124 | − | 0.353553i | ||||
\(601\) | 8.23607 | − | 14.2653i | 0.335956 | − | 0.581893i | −0.647712 | − | 0.761885i | \(-0.724274\pi\) |
0.983668 | + | 0.179992i | \(0.0576072\pi\) | |||||||
\(602\) | 5.19009 | − | 29.4345i | 0.211532 | − | 1.19966i | ||||
\(603\) | 13.2036 | − | 11.0791i | 0.537692 | − | 0.451177i | ||||
\(604\) | −11.0863 | − | 9.30251i | −0.451095 | − | 0.378514i | ||||
\(605\) | 0.331639 | + | 1.88082i | 0.0134830 | + | 0.0764660i | ||||
\(606\) | 18.1407 | + | 6.60268i | 0.736916 | + | 0.268216i | ||||
\(607\) | 47.7771 | 1.93921 | 0.969606 | − | 0.244671i | \(-0.0786801\pi\) | ||||
0.969606 | + | 0.244671i | \(0.0786801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.3607 | −1.47341 | ||||||||
\(610\) | 4.69846 | + | 1.71010i | 0.190235 | + | 0.0692400i | ||||
\(611\) | −1.07320 | − | 6.08645i | −0.0434172 | − | 0.246231i | ||||
\(612\) | 3.81392 | + | 3.20026i | 0.154168 | + | 0.129363i | ||||
\(613\) | 6.42096 | − | 5.38782i | 0.259340 | − | 0.217612i | −0.503842 | − | 0.863796i | \(-0.668081\pi\) |
0.763182 | + | 0.646184i | \(0.223636\pi\) | |||||||
\(614\) | −2.03311 | + | 11.5303i | −0.0820496 | + | 0.465326i | ||||
\(615\) | −1.90983 | + | 3.30792i | −0.0770118 | + | 0.133388i | ||||
\(616\) | −5.23607 | − | 9.06914i | −0.210967 | − | 0.365406i | ||||
\(617\) | −40.3544 | + | 14.6878i | −1.62461 | + | 0.591309i | −0.984252 | − | 0.176770i | \(-0.943435\pi\) |
−0.640355 | + | 0.768079i | \(0.721213\pi\) | |||||||
\(618\) | 17.0192 | − | 6.19448i | 0.684613 | − | 0.249179i | ||||
\(619\) | −11.1803 | − | 19.3649i | −0.449376 | − | 0.778342i | 0.548970 | − | 0.835842i | \(-0.315020\pi\) |
−0.998345 | + | 0.0575005i | \(0.981687\pi\) | |||||||
\(620\) | 2.23607 | − | 3.87298i | 0.0898027 | − | 0.155543i | ||||
\(621\) | −5.02612 | + | 28.5045i | −0.201691 | + | 1.14385i | ||||
\(622\) | 23.9282 | − | 20.0782i | 0.959434 | − | 0.805061i | ||||
\(623\) | 21.9491 | + | 18.4175i | 0.879371 | + | 0.737880i | ||||
\(624\) | −0.296626 | − | 1.68225i | −0.0118746 | − | 0.0673440i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5066 | −0.619767 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.38197 | 0.374381 | ||||||||
\(629\) | −26.6380 | − | 9.69542i | −1.06212 | − | 0.386582i | ||||
\(630\) | −2.99301 | − | 16.9742i | −0.119244 | − | 0.676269i | ||||
\(631\) | −23.8428 | − | 20.0065i | −0.949168 | − | 0.796447i | 0.0299890 | − | 0.999550i | \(-0.490453\pi\) |
−0.979157 | + | 0.203103i | \(0.934897\pi\) | |||||||
\(632\) | 2.11729 | − | 1.77662i | 0.0842215 | − | 0.0706702i | ||||
\(633\) | 1.55316 | − | 8.80839i | 0.0617324 | − | 0.350102i | ||||
\(634\) | 0.663119 | − | 1.14856i | 0.0263358 | − | 0.0456150i | ||||
\(635\) | 20.6525 | + | 35.7711i | 0.819569 | + | 1.41953i | ||||
\(636\) | −7.07388 | + | 2.57468i | −0.280498 | + | 0.102093i | ||||
\(637\) | 4.50900 | − | 1.64114i | 0.178653 | − | 0.0650244i | ||||
\(638\) | 14.7082 | + | 25.4754i | 0.582303 | + | 1.00858i | ||||
\(639\) | −2.16718 | + | 3.75367i | −0.0857325 | + | 0.148493i | ||||
\(640\) | −0.628265 | + | 3.56307i | −0.0248344 | + | 0.140843i | ||||
\(641\) | 10.1658 | − | 8.53012i | 0.401525 | − | 0.336919i | −0.419558 | − | 0.907729i | \(-0.637815\pi\) |
0.821083 | + | 0.570809i | \(0.193370\pi\) | |||||||
\(642\) | −8.91624 | − | 7.48161i | −0.351896 | − | 0.295276i | ||||
\(643\) | −6.74325 | − | 38.2429i | −0.265928 | − | 1.50815i | −0.766380 | − | 0.642387i | \(-0.777944\pi\) |
0.500453 | − | 0.865764i | \(-0.333167\pi\) | |||||||
\(644\) | 15.9224 | + | 5.79528i | 0.627431 | + | 0.228366i | ||||
\(645\) | 41.3050 | 1.62638 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.0689 | 1.02487 | 0.512437 | − | 0.858725i | \(-0.328743\pi\) | ||||
0.512437 | + | 0.858725i | \(0.328743\pi\) | |||||||
\(648\) | 2.27068 | + | 0.826460i | 0.0892008 | + | 0.0324664i | ||||
\(649\) | −0.265311 | − | 1.50465i | −0.0104144 | − | 0.0590628i | ||||
\(650\) | −8.56464 | − | 7.18658i | −0.335933 | − | 0.281881i | ||||
\(651\) | −3.78753 | + | 3.17812i | −0.148445 | + | 0.124560i | ||||
\(652\) | 1.84978 | − | 10.4906i | 0.0724431 | − | 0.410845i | ||||
\(653\) | 17.6976 | − | 30.6531i | 0.692559 | − | 1.19955i | −0.278438 | − | 0.960454i | \(-0.589817\pi\) |
0.970997 | − | 0.239093i | \(-0.0768501\pi\) | |||||||
\(654\) | −6.81966 | − | 11.8120i | −0.266670 | − | 0.461886i | ||||
\(655\) | 15.2045 | − | 5.53400i | 0.594091 | − | 0.216231i | ||||
\(656\) | 0.802593 | − | 0.292120i | 0.0313360 | − | 0.0114054i | ||||
\(657\) | −4.13525 | − | 7.16247i | −0.161332 | − | 0.279435i | ||||
\(658\) | 7.23607 | − | 12.5332i | 0.282091 | − | 0.488596i | ||||
\(659\) | 8.42906 | − | 47.8036i | 0.328350 | − | 1.86216i | −0.156658 | − | 0.987653i | \(-0.550072\pi\) |
0.485008 | − | 0.874510i | \(-0.338817\pi\) | |||||||
\(660\) | 11.0863 | − | 9.30251i | 0.431534 | − | 0.362100i | ||||
\(661\) | 16.4059 | + | 13.7662i | 0.638116 | + | 0.535443i | 0.903439 | − | 0.428716i | \(-0.141034\pi\) |
−0.265323 | + | 0.964160i | \(0.585479\pi\) | |||||||
\(662\) | −4.46418 | − | 25.3176i | −0.173505 | − | 0.983998i | ||||
\(663\) | −5.42869 | − | 1.97588i | −0.210833 | − | 0.0767368i | ||||
\(664\) | −0.472136 | −0.0183224 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3394 | 0.478142 | ||||||||
\(667\) | −44.7263 | − | 16.2790i | −1.73181 | − | 0.630327i | ||||
\(668\) | 2.16576 | + | 12.2827i | 0.0837959 | + | 0.475230i | ||||
\(669\) | −26.2364 | − | 22.0150i | −1.01436 | − | 0.851148i | ||||
\(670\) | 32.4502 | − | 27.2289i | 1.25366 | − | 1.05194i | ||||
\(671\) | −0.776578 | + | 4.40419i | −0.0299795 | + | 0.170022i | ||||
\(672\) | 2.00000 | − | 3.46410i | 0.0771517 | − | 0.133631i | ||||
\(673\) | 15.1910 | + | 26.3116i | 0.585569 | + | 1.01424i | 0.994804 | + | 0.101807i | \(0.0324624\pi\) |
−0.409235 | + | 0.912429i | \(0.634204\pi\) | |||||||
\(674\) | 2.23832 | − | 0.814680i | 0.0862167 | − | 0.0313803i | ||||
\(675\) | 42.0243 | − | 15.2956i | 1.61752 | − | 0.588728i | ||||
\(676\) | 5.54508 | + | 9.60437i | 0.213272 | + | 0.369399i | ||||
\(677\) | −3.30902 | + | 5.73139i | −0.127176 | + | 0.220275i | −0.922581 | − | 0.385803i | \(-0.873925\pi\) |
0.795406 | + | 0.606078i | \(0.207258\pi\) | |||||||
\(678\) | 2.11509 | − | 11.9953i | 0.0812297 | − | 0.460676i | ||||
\(679\) | 21.3639 | − | 17.9264i | 0.819870 | − | 0.687952i | ||||
\(680\) | 9.37337 | + | 7.86519i | 0.359452 | + | 0.301616i | ||||
\(681\) | 1.91981 | + | 10.8878i | 0.0735672 | + | 0.417220i | ||||
\(682\) | 3.75877 | + | 1.36808i | 0.143931 | + | 0.0523865i | ||||
\(683\) | 20.1803 | 0.772179 | 0.386090 | − | 0.922461i | \(-0.373826\pi\) | ||||
0.386090 | + | 0.922461i | \(0.373826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.61803 | −0.329278 | ||||||||
\(686\) | −10.7279 | − | 3.90464i | −0.409594 | − | 0.149080i | ||||
\(687\) | 0.940549 | + | 5.33412i | 0.0358842 | + | 0.203509i | ||||
\(688\) | −7.07524 | − | 5.93683i | −0.269741 | − | 0.226340i | ||||
\(689\) | −6.44734 | + | 5.40996i | −0.245624 | + | 0.206103i | ||||
\(690\) | −4.06622 | + | 23.0607i | −0.154798 | + | 0.877904i | ||||
\(691\) | 11.1803 | − | 19.3649i | 0.425320 | − | 0.736676i | −0.571130 | − | 0.820860i | \(-0.693495\pi\) |
0.996450 | + | 0.0841834i | \(0.0268282\pi\) | |||||||
\(692\) | 0.663119 | + | 1.14856i | 0.0252080 | + | 0.0436615i | ||||
\(693\) | 14.4867 | − | 5.27272i | 0.550304 | − | 0.200294i | ||||
\(694\) | 2.49251 | − | 0.907200i | 0.0946145 | − | 0.0344368i | ||||
\(695\) | −25.3262 | − | 43.8663i | −0.960679 | − | 1.66394i | ||||
\(696\) | −5.61803 | + | 9.73072i | −0.212951 | + | 0.368842i | ||||
\(697\) | 0.501590 | − | 2.84466i | 0.0189991 | − | 0.107749i | ||||
\(698\) | −25.3485 | + | 21.2700i | −0.959456 | + | 0.805080i | ||||
\(699\) | 1.47932 | + | 1.24130i | 0.0559531 | + | 0.0469502i | ||||
\(700\) | −4.54617 | − | 25.7826i | −0.171829 | − | 0.974491i | ||||
\(701\) | −36.3014 | − | 13.2126i | −1.37109 | − | 0.499035i | −0.451623 | − | 0.892209i | \(-0.649155\pi\) |
−0.919464 | + | 0.393174i | \(0.871377\pi\) | |||||||
\(702\) | 7.63932 | 0.288328 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.23607 | −0.121964 | ||||||||
\(705\) | 18.7939 | + | 6.84040i | 0.707817 | + | 0.257624i | ||||
\(706\) | −4.12287 | − | 23.3819i | −0.155166 | − | 0.879991i | ||||
\(707\) | 38.7167 | + | 32.4871i | 1.45609 | + | 1.22180i | ||||
\(708\) | 0.447058 | − | 0.375126i | 0.0168015 | − | 0.0140981i | ||||
\(709\) | 1.19988 | − | 6.80485i | 0.0450624 | − | 0.255562i | −0.953951 | − | 0.299961i | \(-0.903026\pi\) |
0.999014 | + | 0.0443994i | \(0.0141374\pi\) | |||||||
\(710\) | −5.32624 | + | 9.22531i | −0.199890 | + | 0.346220i | ||||
\(711\) | 2.03444 | + | 3.52376i | 0.0762975 | + | 0.132151i | ||||
\(712\) | 8.32013 | − | 3.02828i | 0.311810 | − | 0.113490i | ||||
\(713\) | −6.08182 | + | 2.21360i | −0.227766 | + | 0.0829000i | ||||
\(714\) | −6.76393 | − | 11.7155i | −0.253134 | − | 0.438441i | ||||
\(715\) | 8.09017 | − | 14.0126i | 0.302555 | − | 0.524041i | ||||
\(716\) | 4.06622 | − | 23.0607i | 0.151962 | − | 0.861817i | ||||
\(717\) | 28.5773 | − | 23.9792i | 1.06724 | − | 0.895518i | ||||
\(718\) | 8.83086 | + | 7.40997i | 0.329565 | + | 0.276538i | ||||
\(719\) | 2.13445 | + | 12.1051i | 0.0796015 | + | 0.451442i | 0.998391 | + | 0.0566958i | \(0.0180565\pi\) |
−0.918790 | + | 0.394747i | \(0.870832\pi\) | |||||||
\(720\) | −5.00503 | − | 1.82168i | −0.186526 | − | 0.0678900i | ||||
\(721\) | 47.4164 | 1.76588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.4164 | 1.16839 | ||||||||
\(724\) | 5.08976 | + | 1.85252i | 0.189159 | + | 0.0688484i | ||||
\(725\) | 12.7703 | + | 72.4238i | 0.474276 | + | 2.68975i | ||||
\(726\) | −0.499825 | − | 0.419403i | −0.0185503 | − | 0.0155655i | ||||
\(727\) | −23.7047 | + | 19.8906i | −0.879158 | + | 0.737701i | −0.966006 | − | 0.258520i | \(-0.916765\pi\) |
0.0868476 | + | 0.996222i | \(0.472321\pi\) | |||||||
\(728\) | 0.776578 | − | 4.40419i | 0.0287819 | − | 0.163230i | ||||
\(729\) | −12.0279 | + | 20.8329i | −0.445476 | + | 0.771588i | ||||
\(730\) | −10.1631 | − | 17.6030i | −0.376154 | − | 0.651518i | ||||
\(731\) | −29.3523 | + | 10.6834i | −1.08563 | + | 0.395139i | ||||
\(732\) | −1.60519 | + | 0.584240i | −0.0593294 | + | 0.0215941i | ||||
\(733\) | 0.545085 | + | 0.944115i | 0.0201332 | + | 0.0348717i | 0.875916 | − | 0.482463i | \(-0.160258\pi\) |
−0.855783 | + | 0.517334i | \(0.826924\pi\) | |||||||
\(734\) | −9.41641 | + | 16.3097i | −0.347566 | + | 0.602002i | ||||
\(735\) | −2.69639 | + | 15.2920i | −0.0994577 | + | 0.564052i | ||||
\(736\) | 4.01106 | − | 3.36568i | 0.147850 | − | 0.124061i | ||||
\(737\) | 29.0243 | + | 24.3543i | 1.06912 | + | 0.897102i | ||||
\(738\) | 0.218337 | + | 1.23825i | 0.00803711 | + | 0.0455807i | ||||
\(739\) | −8.57433 | − | 3.12080i | −0.315412 | − | 0.114801i | 0.179463 | − | 0.983765i | \(-0.442564\pi\) |
−0.494875 | + | 0.868964i | \(0.664786\pi\) | |||||||
\(740\) | 30.3262 | 1.11481 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.7082 | −0.723511 | ||||||||
\(743\) | 5.74289 | + | 2.09024i | 0.210686 | + | 0.0766835i | 0.445207 | − | 0.895428i | \(-0.353130\pi\) |
−0.234521 | + | 0.972111i | \(0.575352\pi\) | |||||||
\(744\) | 0.265311 | + | 1.50465i | 0.00972677 | + | 0.0551632i | ||||
\(745\) | 36.2804 | + | 30.4429i | 1.32921 | + | 1.11534i | ||||
\(746\) | −14.0387 | + | 11.7799i | −0.513994 | + | 0.431292i | ||||
\(747\) | 0.120694 | − | 0.684489i | 0.00441596 | − | 0.0250441i | ||||
\(748\) | −5.47214 | + | 9.47802i | −0.200081 | + | 0.346551i | ||||
\(749\) | −15.2361 | − | 26.3896i | −0.556714 | − | 0.964257i | ||||
\(750\) | 12.9862 | − | 4.72660i | 0.474190 | − | 0.172591i | ||||
\(751\) | −22.6174 | + | 8.23204i | −0.825319 | + | 0.300392i | −0.719936 | − | 0.694040i | \(-0.755829\pi\) |
−0.105383 | + | 0.994432i | \(0.533607\pi\) | |||||||
\(752\) | −2.23607 | − | 3.87298i | −0.0815410 | − | 0.141233i | ||||
\(753\) | 1.41641 | − | 2.45329i | 0.0516168 | − | 0.0894029i | ||||
\(754\) | −2.18142 | + | 12.3715i | −0.0794427 | + | 0.450542i | ||||
\(755\) | 40.1106 | − | 33.6568i | 1.45977 | − | 1.22490i | ||||
\(756\) | 13.7034 | + | 11.4985i | 0.498389 | + | 0.418198i | ||||
\(757\) | 0.770597 | + | 4.37028i | 0.0280078 | + | 0.158840i | 0.995604 | − | 0.0936624i | \(-0.0298574\pi\) |
−0.967596 | + | 0.252503i | \(0.918746\pi\) | |||||||
\(758\) | −33.2805 | − | 12.1131i | −1.20880 | − | 0.439969i | ||||
\(759\) | −20.9443 | −0.760229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.3607 | 0.955574 | 0.477787 | − | 0.878476i | \(-0.341439\pi\) | ||||
0.477787 | + | 0.878476i | \(0.341439\pi\) | |||||||
\(762\) | −13.2604 | − | 4.82640i | −0.480375 | − | 0.174842i | ||||
\(763\) | −6.20066 | − | 35.1657i | −0.224479 | − | 1.27308i | ||||
\(764\) | 2.70250 | + | 2.26767i | 0.0977730 | + | 0.0820413i | ||||
\(765\) | −13.7989 | + | 11.5786i | −0.498899 | + | 0.418626i | ||||
\(766\) | −3.60562 | + | 20.4485i | −0.130276 | + | 0.738834i | ||||
\(767\) | 0.326238 | − | 0.565061i | 0.0117798 | − | 0.0204032i | ||||
\(768\) | −0.618034 | − | 1.07047i | −0.0223014 | − | 0.0386271i | ||||
\(769\) | −36.4062 | + | 13.2508i | −1.31284 | + | 0.477835i | −0.901157 | − | 0.433492i | \(-0.857281\pi\) |
−0.411683 | + | 0.911327i | \(0.635059\pi\) | |||||||
\(770\) | 35.6036 | − | 12.9586i | 1.28306 | − | 0.466997i | ||||
\(771\) | 11.3607 | + | 19.6773i | 0.409145 | + | 0.708660i | ||||
\(772\) | −5.76393 | + | 9.98342i | −0.207448 | + | 0.359311i | ||||
\(773\) | 1.41452 | − | 8.02214i | 0.0508768 | − | 0.288536i | −0.948745 | − | 0.316043i | \(-0.897646\pi\) |
0.999622 | + | 0.0275066i | \(0.00875672\pi\) | |||||||
\(774\) | 10.4157 | − | 8.73982i | 0.374385 | − | 0.314146i | ||||
\(775\) | 7.66044 | + | 6.42788i | 0.275171 | + | 0.230896i | ||||
\(776\) | −1.49651 | − | 8.48711i | −0.0537214 | − | 0.304669i | ||||
\(777\) | −31.5059 | − | 11.4672i | −1.13027 | − | 0.411384i | ||||
\(778\) | 12.7984 | 0.458844 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.18034 | 0.221292 | ||||||||
\(781\) | −8.95326 | − | 3.25872i | −0.320373 | − | 0.116606i | ||||
\(782\) | −3.07500 | − | 17.4392i | −0.109962 | − | 0.623624i | ||||
\(783\) | −38.4931 | − | 32.2996i | −1.37563 | − | 1.15429i | ||||
\(784\) | 2.65981 | − | 2.23185i | 0.0949932 | − | 0.0797088i | ||||
\(785\) | −5.89436 | + | 33.4286i | −0.210379 | + | 1.19312i | ||||
\(786\) | −2.76393 | + | 4.78727i | −0.0985862 | + | 0.170756i | ||||
\(787\) | 14.2361 | + | 24.6576i | 0.507461 | + | 0.878948i | 0.999963 | + | 0.00863678i | \(0.00274921\pi\) |
−0.492502 | + | 0.870311i | \(0.663917\pi\) | |||||||
\(788\) | 3.89587 | − | 1.41798i | 0.138785 | − | 0.0505135i | ||||
\(789\) | −3.41984 | + | 1.24472i | −0.121750 | + | 0.0443132i | ||||
\(790\) | 5.00000 | + | 8.66025i | 0.177892 | + | 0.308118i | ||||
\(791\) | 15.9443 | − | 27.6163i | 0.566913 | − | 0.981922i | ||||
\(792\) | 0.827248 | − | 4.69156i | 0.0293950 | − | 0.166707i | ||||
\(793\) | −1.46301 | + | 1.22762i | −0.0519532 | + | 0.0435939i | ||||
\(794\) | −17.1293 | − | 14.3732i | −0.607895 | − | 0.510085i | ||||
\(795\) | −4.72949 | − | 26.8223i | −0.167738 | − | 0.951289i | ||||
\(796\) | −9.84059 | − | 3.58168i | −0.348790 | − | 0.126949i | ||||
\(797\) | −28.4377 | −1.00731 | −0.503657 | − | 0.863903i | \(-0.668013\pi\) | ||||
−0.503657 | + | 0.863903i | \(0.668013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.1246 | −0.535070 | ||||||||
\(800\) | −7.60227 | − | 2.76700i | −0.268781 | − | 0.0978283i | ||||
\(801\) | 2.26341 | + | 12.8364i | 0.0799736 | + | 0.453553i | ||||
\(802\) | −14.5122 | − | 12.1771i | −0.512442 | − | 0.429990i | ||||
\(803\) | 13.9269 | − | 11.6861i | 0.491471 | − | 0.412393i | ||||
\(804\) | −2.51306 | + | 14.2523i | −0.0886288 | + | 0.502639i | ||||
\(805\) | −30.6525 | + | 53.0916i | −1.08036 | + | 1.87123i | ||||
\(806\) | 0.854102 | + | 1.47935i | 0.0300845 | + | 0.0521078i | ||||
\(807\) | 16.6403 | − | 6.05656i | 0.585765 | − | 0.213201i | ||||
\(808\) | 14.6762 | − | 5.34168i | 0.516305 | − | 0.187920i | ||||
\(809\) | −1.37132 | − | 2.37520i | −0.0482131 | − | 0.0835076i | 0.840912 | − | 0.541172i | \(-0.182019\pi\) |
−0.889125 | + | 0.457665i | \(0.848686\pi\) | |||||||
\(810\) | −4.37132 | + | 7.57135i | −0.153593 | + | 0.266030i | ||||
\(811\) | −0.971865 | + | 5.51172i | −0.0341268 | + | 0.193543i | −0.997105 | − | 0.0760364i | \(-0.975773\pi\) |
0.962978 | + | 0.269579i | \(0.0868846\pi\) | |||||||
\(812\) | −22.5343 | + | 18.9085i | −0.790798 | + | 0.663558i | ||||
\(813\) | 24.6190 | + | 20.6578i | 0.863425 | + | 0.724499i | ||||
\(814\) | 4.71014 | + | 26.7125i | 0.165090 | + | 0.936274i | ||||
\(815\) | 36.2167 | + | 13.1818i | 1.26862 | + | 0.461738i | ||||
\(816\) | −4.18034 | −0.146341 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16.2705 | −0.568885 | ||||||||
\(819\) | 6.18655 | + | 2.25172i | 0.216176 | + | 0.0786815i | ||||
\(820\) | 0.536602 | + | 3.04322i | 0.0187390 | + | 0.106274i | ||||
\(821\) | 14.7621 | + | 12.3868i | 0.515200 | + | 0.432304i | 0.862954 | − | 0.505282i | \(-0.168611\pi\) |
−0.347755 | + | 0.937586i | \(0.613056\pi\) | |||||||
\(822\) | 2.25544 | − | 1.89254i | 0.0786676 | − | 0.0660100i | ||||
\(823\) | −3.61758 | + | 20.5163i | −0.126101 | + | 0.715154i | 0.854547 | + | 0.519374i | \(0.173835\pi\) |
−0.980648 | + | 0.195780i | \(0.937276\pi\) | |||||||
\(824\) | 7.32624 | − | 12.6894i | 0.255222 | − | 0.442057i | ||||
\(825\) | 16.1803 | + | 28.0252i | 0.563327 | + | 0.975711i | ||||
\(826\) | 1.43572 | − | 0.522560i | 0.0499552 | − | 0.0181822i | ||||
\(827\) | −28.6992 | + | 10.4456i | −0.997968 | + | 0.363231i | −0.788801 | − | 0.614649i | \(-0.789298\pi\) |
−0.209167 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(828\) | 3.85410 | + | 6.67550i | 0.133939 | + | 0.231990i | ||||
\(829\) | −4.86475 | + | 8.42599i | −0.168960 | + | 0.292647i | −0.938054 | − | 0.346488i | \(-0.887374\pi\) |
0.769095 | + | 0.639135i | \(0.220707\pi\) | |||||||
\(830\) | 0.296626 | − | 1.68225i | 0.0102961 | − | 0.0583918i | ||||
\(831\) | −9.55421 | + | 8.01693i | −0.331432 | + | 0.278104i | ||||
\(832\) | −1.05865 | − | 0.888311i | −0.0367020 | − | 0.0307966i | ||||
\(833\) | −2.03909 | − | 11.5642i | −0.0706502 | − | 0.400677i | ||||
\(834\) | 16.2613 | + | 5.91864i | 0.563084 | + | 0.204946i | ||||
\(835\) | −45.1246 | −1.56160 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.83282 | −0.236177 | ||||||||
\(838\) | 6.08182 | + | 2.21360i | 0.210093 | + | 0.0764676i | ||||
\(839\) | −3.82026 | − | 21.6658i | −0.131890 | − | 0.747985i | −0.976975 | − | 0.213354i | \(-0.931561\pi\) |
0.845085 | − | 0.534632i | \(-0.179550\pi\) | |||||||
\(840\) | 11.0863 | + | 9.30251i | 0.382514 | + | 0.320967i | ||||
\(841\) | 41.0839 | − | 34.4735i | 1.41669 | − | 1.18874i | ||||
\(842\) | −2.41542 | + | 13.6985i | −0.0832408 | + | 0.472082i | ||||
\(843\) | 12.9656 | − | 22.4570i | 0.446558 | − | 0.773460i | ||||
\(844\) | −3.61803 | − | 6.26662i | −0.124538 | − | 0.215706i | ||||
\(845\) | −37.7048 | + | 13.7234i | −1.29708 | + | 0.472100i | ||||
\(846\) | 6.18655 | − | 2.25172i | 0.212698 | − | 0.0774158i | ||||
\(847\) | −0.854102 | − | 1.47935i | −0.0293473 | − | 0.0508310i | ||||
\(848\) | −3.04508 | + | 5.27424i | −0.104569 | + | 0.181118i | ||||
\(849\) | 4.82344 | − | 27.3551i | 0.165540 | − | 0.938824i | ||||
\(850\) | −20.9595 | + | 17.5871i | −0.718905 | + | 0.603233i | ||||
\(851\) | −33.6206 | − | 28.2110i | −1.15250 | − | 0.967061i | ||||
\(852\) | −0.631961 | − | 3.58403i | −0.0216506 | − | 0.122787i | ||||
\(853\) | 27.3358 | + | 9.94942i | 0.935961 | + | 0.340662i | 0.764570 | − | 0.644541i | \(-0.222952\pi\) |
0.171391 | + | 0.985203i | \(0.445174\pi\) | |||||||
\(854\) | −4.47214 | −0.153033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.41641 | −0.321846 | ||||||||
\(857\) | 5.22686 | + | 1.90242i | 0.178546 | + | 0.0649855i | 0.429746 | − | 0.902950i | \(-0.358603\pi\) |
−0.251200 | + | 0.967935i | \(0.580825\pi\) | |||||||
\(858\) | 0.959904 | + | 5.44388i | 0.0327706 | + | 0.185851i | ||||
\(859\) | 21.5020 | + | 18.0423i | 0.733639 | + | 0.615596i | 0.931121 | − | 0.364710i | \(-0.118832\pi\) |
−0.197482 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(860\) | 25.5985 | − | 21.4797i | 0.872900 | − | 0.732450i | ||||
\(861\) | 0.593253 | − | 3.36450i | 0.0202180 | − | 0.114662i | ||||
\(862\) | 3.32624 | − | 5.76121i | 0.113292 | − | 0.196228i | ||||
\(863\) | −12.9443 | − | 22.4201i | −0.440628 | − | 0.763190i | 0.557108 | − | 0.830440i | \(-0.311911\pi\) |
−0.997736 | + | 0.0672497i | \(0.978578\pi\) | |||||||
\(864\) | 5.19449 | − | 1.89064i | 0.176720 | − | 0.0643209i | ||||
\(865\) | −4.50900 | + | 1.64114i | −0.153310 | + | 0.0558005i | ||||
\(866\) | −12.5172 | − | 21.6805i | −0.425352 | − | 0.736732i | ||||
\(867\) | 3.43769 | − | 5.95426i | 0.116750 | − | 0.202217i | ||||
\(868\) | −0.694593 | + | 3.93923i | −0.0235760 | + | 0.133706i | ||||
\(869\) | −6.85171 | + | 5.74927i | −0.232428 | + | 0.195031i | ||||
\(870\) | −31.1416 | − | 26.1309i | −1.05580 | − | 0.885921i | ||||
\(871\) | 2.80969 | + | 15.9345i | 0.0952026 | + | 0.539921i | ||||
\(872\) | −10.3690 | − | 3.77400i | −0.351138 | − | 0.127804i | ||||
\(873\) | 12.6869 | 0.429387 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.1803 | 1.22312 | ||||||||
\(876\) | 6.52548 | + | 2.37508i | 0.220476 | + | 0.0802465i | ||||
\(877\) | −0.302607 | − | 1.71617i | −0.0102183 | − | 0.0579510i | 0.979272 | − | 0.202548i | \(-0.0649224\pi\) |
−0.989491 | + | 0.144598i | \(0.953811\pi\) | |||||||
\(878\) | −22.3961 | − | 18.7926i | −0.755833 | − | 0.634219i | ||||
\(879\) | −21.7255 | + | 18.2299i | −0.732784 | + | 0.614879i | ||||
\(880\) | 2.03311 | − | 11.5303i | 0.0685361 | − | 0.388687i | ||||
\(881\) | −2.60739 | + | 4.51613i | −0.0878452 | + | 0.152152i | −0.906600 | − | 0.421991i | \(-0.861331\pi\) |
0.818755 | + | 0.574143i | \(0.194665\pi\) | |||||||
\(882\) | 2.55573 | + | 4.42665i | 0.0860558 | + | 0.149053i | ||||
\(883\) | 16.7450 | − | 6.09468i | 0.563514 | − | 0.205102i | −0.0445266 | − | 0.999008i | \(-0.514178\pi\) |
0.608041 | + | 0.793906i | \(0.291956\pi\) | |||||||
\(884\) | −4.39190 | + | 1.59852i | −0.147716 | + | 0.0537641i | ||||
\(885\) | 1.05573 | + | 1.82857i | 0.0354879 | + | 0.0614669i | ||||
\(886\) | −4.61803 | + | 7.99867i | −0.155146 | + | 0.268721i | ||||
\(887\) | −1.20586 | + | 6.83877i | −0.0404888 | + | 0.229624i | −0.998337 | − | 0.0576523i | \(-0.981639\pi\) |
0.957848 | + | 0.287276i | \(0.0927496\pi\) | |||||||
\(888\) | −7.93674 | + | 6.65972i | −0.266340 | + | 0.223485i | ||||
\(889\) | −28.3010 | − | 23.7473i | −0.949184 | − | 0.796460i | ||||
\(890\) | 5.56272 | + | 31.5478i | 0.186463 | + | 1.05748i | ||||
\(891\) | −7.34808 | − | 2.67448i | −0.246170 | − | 0.0895985i | ||||
\(892\) | −27.7082 | −0.927739 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −16.1803 | −0.541152 | ||||||||
\(895\) | 79.6120 | + | 28.9764i | 2.66114 | + | 0.968575i | ||||
\(896\) | −0.561937 | − | 3.18690i | −0.0187730 | − | 0.106467i | ||||
\(897\) | −6.85171 | − | 5.74927i | −0.228772 | − | 0.191962i | ||||
\(898\) | 17.4646 | − | 14.6545i | 0.582800 | − | 0.489027i | ||||
\(899\) | 1.95112 | − | 11.0654i | 0.0650736 | − | 0.369051i | ||||
\(900\) | 5.95492 | − | 10.3142i | 0.198497 | − | 0.343807i | ||||
\(901\) | 10.2984 | + | 17.8373i | 0.343089 | + | 0.594247i | ||||
\(902\) | −2.59725 | + | 0.945320i | −0.0864788 | + | 0.0314757i | ||||
\(903\) | −34.7163 | + | 12.6357i | −1.15528 | + | 0.420489i | ||||
\(904\) | −4.92705 | − | 8.53390i | −0.163871 | − | 0.283833i | ||||
\(905\) | −9.79837 | + | 16.9713i | −0.325709 | + | 0.564144i | ||||
\(906\) | −3.10631 | + | 17.6168i | −0.103200 | + | 0.585278i | ||||
\(907\) | 0.223529 | − | 0.187563i | 0.00742215 | − | 0.00622792i | −0.639069 | − | 0.769149i | \(-0.720680\pi\) |
0.646491 | + | 0.762921i | \(0.276236\pi\) | |||||||
\(908\) | 6.85171 | + | 5.74927i | 0.227382 | + | 0.190796i | ||||
\(909\) | 3.99250 | + | 22.6426i | 0.132423 | + | 0.751007i | ||||
\(910\) | 15.2045 | + | 5.53400i | 0.504026 | + | 0.183450i | ||||
\(911\) | −12.0689 | −0.399860 | −0.199930 | − | 0.979810i | \(-0.564071\pi\) | ||||
−0.199930 | + | 0.979810i | \(0.564071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52786 | 0.0505649 | ||||||||
\(914\) | −23.6941 | − | 8.62396i | −0.783733 | − | 0.285255i | ||||
\(915\) | −1.07320 | − | 6.08645i | −0.0354791 | − | 0.201212i | ||||
\(916\) | 3.35678 | + | 2.81667i | 0.110911 | + | 0.0930655i | ||||
\(917\) | −11.0863 | + | 9.30251i | −0.366102 | + | 0.307196i | ||||
\(918\) | 3.24636 | − | 18.4110i | 0.107146 | − | 0.607654i | ||||
\(919\) | −22.9443 | + | 39.7406i | −0.756862 | + | 1.31092i | 0.187582 | + | 0.982249i | \(0.439935\pi\) |
−0.944443 | + | 0.328674i | \(0.893398\pi\) | |||||||
\(920\) | 9.47214 | + | 16.4062i | 0.312287 | + | 0.540897i | ||||
\(921\) | 13.5994 | − | 4.94976i | 0.448114 | − | 0.163100i | ||||
\(922\) | −20.1248 | + | 7.32484i | −0.662776 | + | 0.241231i | ||||
\(923\) | −2.03444 | − | 3.52376i | −0.0669645 | − | 0.115986i | ||||
\(924\) | −6.47214 | + | 11.2101i | −0.212918 | + | 0.368784i | ||||
\(925\) | −11.7753 | + | 66.7813i | −0.387171 | + | 2.19576i | ||||
\(926\) | −3.87291 | + | 3.24976i | −0.127272 | + | 0.106794i | ||||
\(927\) | 16.5239 | + | 13.8652i | 0.542717 | + | 0.455393i | ||||
\(928\) | 1.57849 | + | 8.95207i | 0.0518165 | + | 0.293866i | ||||
\(929\) | 55.5913 | + | 20.2336i | 1.82389 | + | 0.663842i | 0.994445 | + | 0.105257i | \(0.0335667\pi\) |
0.829447 | + | 0.558585i | \(0.188656\pi\) | |||||||
\(930\) | −5.52786 | −0.181266 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.56231 | 0.0511750 | ||||||||
\(933\) | −36.2814 | − | 13.2054i | −1.18780 | − | 0.432324i | ||||
\(934\) | −5.78334 | − | 32.7990i | −0.189237 | − | 1.07322i | ||||
\(935\) | −30.3329 | − | 25.4523i | −0.991991 | − | 0.832379i | ||||
\(936\) | 1.55847 | − | 1.30771i | 0.0509403 | − | 0.0427440i | ||||
\(937\) | 2.75902 | − | 15.6472i | 0.0901331 | − | 0.511170i | −0.905997 | − | 0.423283i | \(-0.860877\pi\) |
0.996130 | − | 0.0878870i | \(-0.0280114\pi\) | |||||||
\(938\) | −18.9443 | + | 32.8124i | −0.618552 | + | 1.07136i | ||||
\(939\) | 9.58359 | + | 16.5993i | 0.312749 | + | 0.541697i | ||||
\(940\) | 15.2045 | − | 5.53400i | 0.495918 | − | 0.180499i | ||||
\(941\) | 24.4320 | − | 8.89252i | 0.796461 | − | 0.289888i | 0.0884417 | − | 0.996081i | \(-0.471811\pi\) |
0.708019 | + | 0.706193i | \(0.249589\pi\) | |||||||
\(942\) | −5.79837 | − | 10.0431i | −0.188921 | − | 0.327221i | ||||
\(943\) | 2.23607 | − | 3.87298i | 0.0728164 | − | 0.126122i | ||||
\(944\) | 0.0819855 | − | 0.464963i | 0.00266840 | − | 0.0151333i | ||||
\(945\) | −49.5794 | + | 41.6021i | −1.61282 | + | 1.35332i | ||||
\(946\) | 22.8960 | + | 19.2120i | 0.744412 | + | 0.624636i | ||||
\(947\) | 1.42050 | + | 8.05606i | 0.0461601 | + | 0.261787i | 0.999150 | − | 0.0412141i | \(-0.0131226\pi\) |
−0.952990 | + | 0.303001i | \(0.902011\pi\) | |||||||
\(948\) | −3.21037 | − | 1.16848i | −0.104268 | − | 0.0379505i | ||||
\(949\) | 7.76393 | 0.252028 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.63932 | −0.0531586 | ||||||||
\(952\) | −10.2843 | − | 3.74316i | −0.333315 | − | 0.121317i | ||||
\(953\) | −8.30238 | − | 47.0852i | −0.268941 | − | 1.52524i | −0.757574 | − | 0.652749i | \(-0.773616\pi\) |
0.488634 | − | 0.872489i | \(-0.337495\pi\) | |||||||
\(954\) | −6.86802 | − | 5.76295i | −0.222360 | − | 0.186582i | ||||
\(955\) | −9.77774 | + | 8.20450i | −0.316400 | + | 0.265491i | ||||
\(956\) | 5.24076 | − | 29.7218i | 0.169498 | − | 0.961273i | ||||
\(957\) | 18.1803 | − | 31.4893i | 0.587687 | − | 1.01790i | ||||
\(958\) | −3.85410 | − | 6.67550i | −0.124520 | − | 0.215676i | ||||
\(959\) | 7.24334 | − | 2.63636i | 0.233900 | − | 0.0851325i | ||||
\(960\) | 4.20243 | − | 1.52956i | 0.135633 | − | 0.0493664i | ||||
\(961\) | 14.7361 | + | 25.5236i | 0.475357 | + | 0.823343i | ||||
\(962\) | −5.79180 | + | 10.0317i | −0.186735 | + | 0.323435i | ||||
\(963\) | 2.40715 | − | 13.6516i | 0.0775694 | − | 0.439918i | ||||
\(964\) | 19.4701 | − | 16.3374i | 0.627090 | − | 0.526191i | ||||
\(965\) | −31.9503 | − | 26.8095i | −1.02852 | − | 0.863029i | ||||
\(966\) | −3.63693 | − | 20.6261i | −0.117016 | − | 0.663633i | ||||
\(967\) | −8.30013 | − | 3.02100i | −0.266914 | − | 0.0971488i | 0.205096 | − | 0.978742i | \(-0.434249\pi\) |
−0.472010 | + | 0.881593i | \(0.656472\pi\) | |||||||
\(968\) | −0.527864 | −0.0169662 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.1803 | 1.00114 | ||||||||
\(971\) | 56.8899 | + | 20.7062i | 1.82569 | + | 0.664495i | 0.994017 | + | 0.109222i | \(0.0348359\pi\) |
0.831668 | + | 0.555273i | \(0.187386\pi\) | |||||||
\(972\) | 2.36105 | + | 13.3902i | 0.0757307 | + | 0.429490i | ||||
\(973\) | 34.7056 | + | 29.1215i | 1.11261 | + | 0.933591i | ||||
\(974\) | −14.7357 | + | 12.3647i | −0.472162 | + | 0.396191i | ||||
\(975\) | −2.39976 | + | 13.6097i | −0.0768538 | + | 0.435859i | ||||
\(976\) | −0.690983 | + | 1.19682i | −0.0221178 | + | 0.0383092i | ||||
\(977\) | −4.51722 | − | 7.82406i | −0.144519 | − | 0.250314i | 0.784675 | − | 0.619908i | \(-0.212830\pi\) |
−0.929193 | + | 0.369594i | \(0.879497\pi\) | |||||||
\(978\) | −12.3731 | + | 4.50344i | −0.395648 | + | 0.144004i | ||||
\(979\) | −26.9245 | + | 9.79972i | −0.860511 | + | 0.313201i | ||||
\(980\) | 6.28115 | + | 10.8793i | 0.200644 | + | 0.347526i | ||||
\(981\) | 8.12210 | − | 14.0679i | 0.259319 | − | 0.449153i | ||||
\(982\) | −0.265311 | + | 1.50465i | −0.00846641 | + | 0.0480154i | ||||
\(983\) | −15.0120 | + | 12.5965i | −0.478808 | + | 0.401767i | −0.849995 | − | 0.526791i | \(-0.823395\pi\) |
0.371187 | + | 0.928558i | \(0.378951\pi\) | |||||||
\(984\) | −0.808735 | − | 0.678609i | −0.0257815 | − | 0.0216333i | ||||
\(985\) | 2.60472 | + | 14.7721i | 0.0829934 | + | 0.470679i | ||||
\(986\) | 28.8886 | + | 10.5146i | 0.920002 | + | 0.334853i | ||||
\(987\) | −17.8885 | −0.569399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.3607 | −1.53778 | ||||||||
\(990\) | 16.1966 | + | 5.89508i | 0.514762 | + | 0.187358i | ||||
\(991\) | 5.32275 | + | 30.1868i | 0.169083 | + | 0.958915i | 0.944754 | + | 0.327779i | \(0.106300\pi\) |
−0.775672 | + | 0.631136i | \(0.782589\pi\) | |||||||
\(992\) | 0.946883 | + | 0.794529i | 0.0300636 | + | 0.0252263i | ||||
\(993\) | −24.3427 | + | 20.4259i | −0.772491 | + | 0.648197i | ||||
\(994\) | 1.65450 | − | 9.38311i | 0.0524774 | − | 0.297614i | ||||
\(995\) | 18.9443 | − | 32.8124i | 0.600574 | − | 1.04022i | ||||
\(996\) | 0.291796 | + | 0.505406i | 0.00924591 | + | 0.0160144i | ||||
\(997\) | 12.6920 | − | 4.61952i | 0.401961 | − | 0.146302i | −0.133126 | − | 0.991099i | \(-0.542501\pi\) |
0.535086 | + | 0.844797i | \(0.320279\pi\) | |||||||
\(998\) | 33.1758 | − | 12.0750i | 1.05016 | − | 0.382228i | ||||
\(999\) | −23.1672 | − | 40.1267i | −0.732977 | − | 1.26955i |
(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 | 722.2.e.p.99.2 | 12 | ||
19.2 | odd | 18 | 722.2.e.q.415.2 | 12 | |||
19.3 | odd | 18 | 722.2.e.q.245.1 | 12 | |||
19.4 | even | 9 | 722.2.c.h.653.1 | 4 | |||
19.5 | even | 9 | inner | 722.2.e.p.423.2 | 12 | ||
19.6 | even | 9 | 722.2.c.h.429.1 | 4 | |||
19.7 | even | 3 | inner | 722.2.e.p.595.1 | 12 | ||
19.8 | odd | 6 | 722.2.e.q.389.1 | 12 | |||
19.9 | even | 9 | 722.2.a.i.1.2 | yes | 2 | ||
19.10 | odd | 18 | 722.2.a.h.1.1 | ✓ | 2 | ||
19.11 | even | 3 | inner | 722.2.e.p.389.2 | 12 | ||
19.12 | odd | 6 | 722.2.e.q.595.2 | 12 | |||
19.13 | odd | 18 | 722.2.c.i.429.2 | 4 | |||
19.14 | odd | 18 | 722.2.e.q.423.1 | 12 | |||
19.15 | odd | 18 | 722.2.c.i.653.2 | 4 | |||
19.16 | even | 9 | inner | 722.2.e.p.245.2 | 12 | ||
19.17 | even | 9 | inner | 722.2.e.p.415.1 | 12 | ||
19.18 | odd | 2 | 722.2.e.q.99.1 | 12 | |||
57.29 | even | 18 | 6498.2.a.bk.1.2 | 2 | |||
57.47 | odd | 18 | 6498.2.a.be.1.2 | 2 | |||
76.47 | odd | 18 | 5776.2.a.be.1.1 | 2 | |||
76.67 | even | 18 | 5776.2.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.h.1.1 | ✓ | 2 | 19.10 | odd | 18 | ||
722.2.a.i.1.2 | yes | 2 | 19.9 | even | 9 | ||
722.2.c.h.429.1 | 4 | 19.6 | even | 9 | |||
722.2.c.h.653.1 | 4 | 19.4 | even | 9 | |||
722.2.c.i.429.2 | 4 | 19.13 | odd | 18 | |||
722.2.c.i.653.2 | 4 | 19.15 | odd | 18 | |||
722.2.e.p.99.2 | 12 | 1.1 | even | 1 | trivial | ||
722.2.e.p.245.2 | 12 | 19.16 | even | 9 | inner | ||
722.2.e.p.389.2 | 12 | 19.11 | even | 3 | inner | ||
722.2.e.p.415.1 | 12 | 19.17 | even | 9 | inner | ||
722.2.e.p.423.2 | 12 | 19.5 | even | 9 | inner | ||
722.2.e.p.595.1 | 12 | 19.7 | even | 3 | inner | ||
722.2.e.q.99.1 | 12 | 19.18 | odd | 2 | |||
722.2.e.q.245.1 | 12 | 19.3 | odd | 18 | |||
722.2.e.q.389.1 | 12 | 19.8 | odd | 6 | |||
722.2.e.q.415.2 | 12 | 19.2 | odd | 18 | |||
722.2.e.q.423.1 | 12 | 19.14 | odd | 18 | |||
722.2.e.q.595.2 | 12 | 19.12 | odd | 6 | |||
5776.2.a.t.1.2 | 2 | 76.67 | even | 18 | |||
5776.2.a.be.1.1 | 2 | 76.47 | odd | 18 | |||
6498.2.a.be.1.2 | 2 | 57.47 | odd | 18 | |||
6498.2.a.bk.1.2 | 2 | 57.29 | even | 18 |