Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(55,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.b (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.60771337450861625344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 11x^{8} - 26x^{6} + 44x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.9 | ||
Root | \(-1.15343 - 0.818285i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.55 |
Dual form | 756.2.b.c.55.10 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.15343 | − | 0.818285i | 0.815601 | − | 0.578615i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.660819 | − | 1.88768i | 0.330409 | − | 0.943838i | ||||
\(5\) | 2.16295i | 0.967302i | 0.875261 | + | 0.483651i | \(0.160690\pi\) | ||||
−0.875261 | + | 0.483651i | \(0.839310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.94827 | − | 1.79004i | 0.736379 | − | 0.676570i | ||||
\(8\) | −0.782447 | − | 2.71805i | −0.276637 | − | 0.960975i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.76991 | + | 2.49482i | 0.559695 | + | 0.788932i | ||||
\(11\) | − | 0.414503i | − | 0.124977i | −0.998046 | − | 0.0624886i | \(-0.980096\pi\) | ||
0.998046 | − | 0.0624886i | \(-0.0199037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.36578i | − | 0.656148i | −0.944652 | − | 0.328074i | \(-0.893600\pi\) | ||
0.944652 | − | 0.328074i | \(-0.106400\pi\) | |||||||
\(14\) | 0.782447 | − | 3.65893i | 0.209118 | − | 0.977890i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.12664 | − | 2.49482i | −0.781659 | − | 0.623706i | ||||
\(17\) | − | 0.695686i | − | 0.168729i | −0.996435 | − | 0.0843643i | \(-0.973114\pi\) | ||
0.996435 | − | 0.0843643i | \(-0.0268859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.21819 | 1.19713 | 0.598567 | − | 0.801073i | \(-0.295737\pi\) | ||||
0.598567 | + | 0.801073i | \(0.295737\pi\) | |||||||
\(20\) | 4.08295 | + | 1.42932i | 0.912976 | + | 0.319605i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.339181 | − | 0.478101i | −0.0723137 | − | 0.101932i | ||||
\(23\) | 0.414503i | 0.0864298i | 0.999066 | + | 0.0432149i | \(0.0137600\pi\) | ||||
−0.999066 | + | 0.0432149i | \(0.986240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.321637 | 0.0643274 | ||||||||
\(26\) | −1.93588 | − | 2.72877i | −0.379657 | − | 0.535155i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.09155 | − | 4.86060i | −0.395266 | − | 0.918567i | ||||
\(29\) | 9.73080 | 1.80696 | 0.903482 | − | 0.428626i | \(-0.141002\pi\) | ||||
0.903482 | + | 0.428626i | \(0.141002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.03509 | −0.365513 | −0.182756 | − | 0.983158i | \(-0.558502\pi\) | ||||
−0.182756 | + | 0.983158i | \(0.558502\pi\) | |||||||
\(32\) | −5.64785 | − | 0.319131i | −0.998407 | − | 0.0564148i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.569269 | − | 0.802428i | −0.0976289 | − | 0.137615i | ||||
\(35\) | 3.87176 | + | 4.21403i | 0.654447 | + | 0.712300i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.43637 | −1.22253 | −0.611266 | − | 0.791425i | \(-0.709339\pi\) | ||||
−0.611266 | + | 0.791425i | \(0.709339\pi\) | |||||||
\(38\) | 6.01883 | − | 4.26997i | 0.976384 | − | 0.692680i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.87901 | − | 1.69239i | 0.929552 | − | 0.267591i | ||||
\(41\) | 10.5910i | 1.65404i | 0.562175 | + | 0.827018i | \(0.309965\pi\) | ||||
−0.562175 | + | 0.827018i | \(0.690035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.76500i | − | 1.33665i | −0.743870 | − | 0.668325i | \(-0.767012\pi\) | ||
0.743870 | − | 0.668325i | \(-0.232988\pi\) | |||||||
\(44\) | −0.782447 | − | 0.273911i | −0.117958 | − | 0.0412936i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.339181 | + | 0.478101i | 0.0500096 | + | 0.0704922i | ||||
\(47\) | −5.11706 | −0.746400 | −0.373200 | − | 0.927751i | \(-0.621740\pi\) | ||||
−0.373200 | + | 0.927751i | \(0.621740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.591549 | − | 6.97496i | 0.0845070 | − | 0.996423i | ||||
\(50\) | 0.370987 | − | 0.263191i | 0.0524655 | − | 0.0372208i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.46582 | − | 1.56335i | −0.619298 | − | 0.216798i | ||||
\(53\) | 3.12979 | 0.429909 | 0.214955 | − | 0.976624i | \(-0.431040\pi\) | ||||
0.214955 | + | 0.976624i | \(0.431040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.896550 | 0.120891 | ||||||||
\(56\) | −6.38982 | − | 3.89489i | −0.853876 | − | 0.520477i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.2238 | − | 7.96257i | 1.47376 | − | 1.04554i | ||||
\(59\) | −11.2147 | −1.46004 | −0.730018 | − | 0.683428i | \(-0.760488\pi\) | ||||
−0.730018 | + | 0.683428i | \(0.760488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.97063i | 0.508387i | 0.967153 | + | 0.254194i | \(0.0818101\pi\) | ||||
−0.967153 | + | 0.254194i | \(0.918190\pi\) | |||||||
\(62\) | −2.34734 | + | 1.66528i | −0.298112 | + | 0.211491i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.77555 | + | 4.25345i | −0.846944 | + | 0.531682i | ||||
\(65\) | 5.11706 | 0.634693 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.36578i | − | 0.289026i | −0.989503 | − | 0.144513i | \(-0.953839\pi\) | ||
0.989503 | − | 0.144513i | \(-0.0461615\pi\) | |||||||
\(68\) | −1.31323 | − | 0.459722i | −0.159252 | − | 0.0557495i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.91409 | + | 1.69239i | 0.945915 | + | 0.202280i | ||||
\(71\) | 4.04472i | 0.480020i | 0.970770 | + | 0.240010i | \(0.0771507\pi\) | ||||
−0.970770 | + | 0.240010i | \(0.922849\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3451i | 1.44488i | 0.691433 | + | 0.722440i | \(0.256980\pi\) | ||||
−0.691433 | + | 0.722440i | \(0.743020\pi\) | |||||||
\(74\) | −8.57736 | + | 6.08507i | −0.997098 | + | 0.707376i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.44827 | − | 9.85024i | 0.395544 | − | 1.12990i | ||||
\(77\) | −0.741974 | − | 0.807565i | −0.0845558 | − | 0.0920306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.61351i | 0.856587i | 0.903640 | + | 0.428293i | \(0.140885\pi\) | ||||
−0.903640 | + | 0.428293i | \(0.859115\pi\) | |||||||
\(80\) | 5.39618 | − | 6.76277i | 0.603311 | − | 0.756100i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.66646 | + | 12.2160i | 0.957051 | + | 1.34903i | ||||
\(83\) | −12.8606 | −1.41163 | −0.705816 | − | 0.708395i | \(-0.749420\pi\) | ||||
−0.705816 | + | 0.708395i | \(0.749420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50474 | 0.163211 | ||||||||
\(86\) | −7.17227 | − | 10.1098i | −0.773405 | − | 1.09017i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.12664 | + | 0.324326i | −0.120100 | + | 0.0345733i | ||||
\(89\) | 14.6931i | 1.55747i | 0.627353 | + | 0.778735i | \(0.284139\pi\) | ||||
−0.627353 | + | 0.778735i | \(0.715861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.23482 | − | 4.60918i | −0.443930 | − | 0.483174i | ||||
\(92\) | 0.782447 | + | 0.273911i | 0.0815757 | + | 0.0285572i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.90219 | + | 4.18722i | −0.608765 | + | 0.431878i | ||||
\(95\) | 11.2867i | 1.15799i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.97063i | − | 0.403157i | −0.979472 | − | 0.201578i | \(-0.935393\pi\) | ||
0.979472 | − | 0.201578i | \(-0.0646070\pi\) | |||||||
\(98\) | −5.02519 | − | 8.52921i | −0.507621 | − | 0.861580i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.212544 | − | 0.607147i | 0.0212544 | − | 0.0607147i | ||||
\(101\) | − | 14.8410i | − | 1.47674i | −0.674398 | − | 0.738368i | \(-0.735597\pi\) | ||
0.674398 | − | 0.738368i | \(-0.264403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.42509 | 0.337484 | 0.168742 | − | 0.985660i | \(-0.446030\pi\) | ||||
0.168742 | + | 0.985660i | \(0.446030\pi\) | |||||||
\(104\) | −6.43029 | + | 1.85109i | −0.630542 | + | 0.181515i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.61000 | − | 2.56106i | 0.350634 | − | 0.248752i | ||||
\(107\) | 14.5024i | 1.40200i | 0.713161 | + | 0.701000i | \(0.247263\pi\) | ||||
−0.713161 | + | 0.701000i | \(0.752737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.40128 | −0.804697 | −0.402349 | − | 0.915487i | \(-0.631806\pi\) | ||||
−0.402349 | + | 0.915487i | \(0.631806\pi\) | |||||||
\(110\) | 1.03411 | − | 0.733633i | 0.0985986 | − | 0.0699492i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.5574 | + | 0.736192i | −0.997578 | + | 0.0695636i | ||||
\(113\) | −4.61373 | −0.434024 | −0.217012 | − | 0.976169i | \(-0.569631\pi\) | ||||
−0.217012 | + | 0.976169i | \(0.569631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.896550 | −0.0836037 | ||||||||
\(116\) | 6.43029 | − | 18.3686i | 0.597038 | − | 1.70548i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.9355 | + | 9.17686i | −1.19081 | + | 0.844799i | ||||
\(119\) | −1.24530 | − | 1.35539i | −0.114157 | − | 0.124248i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8282 | 0.984381 | ||||||||
\(122\) | 3.24911 | + | 4.57986i | 0.294161 | + | 0.414641i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.34482 | + | 3.84159i | −0.120769 | + | 0.344985i | ||||
\(125\) | 11.5104i | 1.02953i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.33641i | 0.562265i | 0.959669 | + | 0.281133i | \(0.0907101\pi\) | ||||
−0.959669 | + | 0.281133i | \(0.909290\pi\) | |||||||
\(128\) | −4.33462 | + | 10.4504i | −0.383130 | + | 0.923695i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.90219 | − | 4.18722i | 0.517657 | − | 0.367243i | ||||
\(131\) | 18.9583 | 1.65639 | 0.828196 | − | 0.560439i | \(-0.189368\pi\) | ||||
0.828196 | + | 0.560439i | \(0.189368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.1665 | − | 9.34074i | 0.881544 | − | 0.809945i | ||||
\(134\) | −1.93588 | − | 2.72877i | −0.167235 | − | 0.235730i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.89091 | + | 0.544337i | −0.162144 | + | 0.0466765i | ||||
\(137\) | 1.98728 | 0.169784 | 0.0848922 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848922 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.6195 | −1.15519 | −0.577594 | − | 0.816324i | \(-0.696008\pi\) | ||||
−0.577594 | + | 0.816324i | \(0.696008\pi\) | |||||||
\(140\) | 10.5132 | − | 4.52392i | 0.888531 | − | 0.382341i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.30974 | + | 4.66532i | 0.277747 | + | 0.391505i | ||||
\(143\) | −0.980621 | −0.0820036 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0473i | 1.74788i | ||||||||
\(146\) | 10.1018 | + | 14.2392i | 0.836030 | + | 1.17845i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.91409 | + | 14.0375i | −0.403936 | + | 1.15387i | ||||
\(149\) | 12.3573 | 1.01235 | 0.506173 | − | 0.862432i | \(-0.331060\pi\) | ||||
0.506173 | + | 0.862432i | \(0.331060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8623i | 1.29086i | 0.763820 | + | 0.645429i | \(0.223321\pi\) | ||||
−0.763820 | + | 0.645429i | \(0.776679\pi\) | |||||||
\(152\) | −4.08295 | − | 14.1833i | −0.331171 | − | 1.15042i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.51664 | − | 0.324326i | −0.122214 | − | 0.0261349i | ||||
\(155\) | − | 4.40180i | − | 0.353561i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.37443i | − | 0.668353i | −0.942511 | − | 0.334176i | \(-0.891542\pi\) | ||
0.942511 | − | 0.334176i | \(-0.108458\pi\) | |||||||
\(158\) | 6.23002 | + | 8.78168i | 0.495634 | + | 0.698633i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.690264 | − | 12.2160i | 0.0545702 | − | 0.965761i | ||||
\(161\) | 0.741974 | + | 0.807565i | 0.0584758 | + | 0.0636450i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0766i | 1.33754i | 0.743468 | + | 0.668772i | \(0.233180\pi\) | ||||
−0.743468 | + | 0.668772i | \(0.766820\pi\) | |||||||
\(164\) | 19.9924 | + | 6.99873i | 1.56114 | + | 0.546509i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.8338 | + | 10.5236i | −1.15133 | + | 0.816792i | ||||
\(167\) | −7.74352 | −0.599212 | −0.299606 | − | 0.954063i | \(-0.596855\pi\) | ||||
−0.299606 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.40310 | 0.569469 | ||||||||
\(170\) | 1.73561 | − | 1.23130i | 0.133115 | − | 0.0944366i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.5455 | − | 5.79207i | −1.26158 | − | 0.441641i | ||||
\(173\) | 4.25001i | 0.323122i | 0.986863 | + | 0.161561i | \(0.0516529\pi\) | ||||
−0.986863 | + | 0.161561i | \(0.948347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.626638 | − | 0.575742i | 0.0473693 | − | 0.0435220i | ||||
\(176\) | −1.03411 | + | 1.29600i | −0.0779490 | + | 0.0976896i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0232 | + | 16.9476i | 0.901176 | + | 1.27027i | ||||
\(179\) | − | 8.85710i | − | 0.662011i | −0.943629 | − | 0.331005i | \(-0.892612\pi\) | ||
0.943629 | − | 0.331005i | \(-0.107388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.9292i | − | 1.77864i | −0.457281 | − | 0.889322i | \(-0.651177\pi\) | ||
0.457281 | − | 0.889322i | \(-0.348823\pi\) | |||||||
\(182\) | −8.65621 | − | 1.85109i | −0.641641 | − | 0.137212i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.12664 | − | 0.324326i | 0.0830568 | − | 0.0239096i | ||||
\(185\) | − | 16.0845i | − | 1.18256i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.288364 | −0.0210872 | ||||||||
\(188\) | −3.38145 | + | 9.65935i | −0.246618 | + | 0.704481i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.23573 | + | 13.0184i | 0.670030 | + | 0.944457i | ||||
\(191\) | − | 25.9224i | − | 1.87568i | −0.347068 | − | 0.937840i | \(-0.612823\pi\) | ||
0.347068 | − | 0.937840i | \(-0.387177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6896 | 0.841439 | 0.420720 | − | 0.907191i | \(-0.361778\pi\) | ||||
0.420720 | + | 0.907191i | \(0.361778\pi\) | |||||||
\(194\) | −3.24911 | − | 4.57986i | −0.233272 | − | 0.328815i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.7756 | − | 5.72584i | −0.912540 | − | 0.408988i | ||||
\(197\) | −11.7181 | −0.834878 | −0.417439 | − | 0.908705i | \(-0.637072\pi\) | ||||
−0.417439 | + | 0.908705i | \(0.637072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.72292 | −0.476575 | −0.238288 | − | 0.971195i | \(-0.576586\pi\) | ||||
−0.238288 | + | 0.971195i | \(0.576586\pi\) | |||||||
\(200\) | −0.251664 | − | 0.874225i | −0.0177953 | − | 0.0618170i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1442 | − | 17.1181i | −0.854462 | − | 1.20443i | ||||
\(203\) | 18.9583 | − | 17.4185i | 1.33061 | − | 1.22254i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.9078 | −1.59995 | ||||||||
\(206\) | 3.95061 | − | 2.80270i | 0.275252 | − | 0.195273i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.90219 | + | 7.39693i | −0.409243 | + | 0.512885i | ||||
\(209\) | − | 2.16295i | − | 0.149615i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.39922i | 0.440540i | 0.975439 | + | 0.220270i | \(0.0706939\pi\) | ||||
−0.975439 | + | 0.220270i | \(0.929306\pi\) | |||||||
\(212\) | 2.06822 | − | 5.90802i | 0.142046 | − | 0.405765i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.8671 | + | 16.7276i | 0.811219 | + | 1.14347i | ||||
\(215\) | 18.9583 | 1.29294 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.96491 | + | 3.64288i | −0.269156 | + | 0.247295i | ||||
\(218\) | −9.69033 | + | 6.87465i | −0.656312 | + | 0.465610i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.592457 | − | 1.69239i | 0.0399434 | − | 0.114101i | ||||
\(221\) | −1.64584 | −0.110711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.82637 | −0.591058 | −0.295529 | − | 0.955334i | \(-0.595496\pi\) | ||||
−0.295529 | + | 0.955334i | \(0.595496\pi\) | |||||||
\(224\) | −11.5748 | + | 9.48809i | −0.773374 | + | 0.633949i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.32164 | + | 3.77535i | −0.353990 | + | 0.251133i | ||||
\(227\) | −21.5847 | −1.43263 | −0.716314 | − | 0.697778i | \(-0.754172\pi\) | ||||
−0.716314 | + | 0.697778i | \(0.754172\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6521i | 1.49689i | 0.663195 | + | 0.748447i | \(0.269200\pi\) | ||||
−0.663195 | + | 0.748447i | \(0.730800\pi\) | |||||||
\(230\) | −1.03411 | + | 0.733633i | −0.0681872 | + | 0.0483743i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.61383 | − | 26.4488i | −0.499872 | − | 1.73645i | ||||
\(233\) | −22.5914 | −1.48001 | −0.740005 | − | 0.672601i | \(-0.765177\pi\) | ||||
−0.740005 | + | 0.672601i | \(0.765177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11.0680i | − | 0.721994i | ||||||
\(236\) | −7.41091 | + | 21.1698i | −0.482409 | + | 1.37804i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.54547 | − | 0.544337i | −0.164998 | − | 0.0352841i | ||||
\(239\) | 4.68298i | 0.302917i | 0.988464 | + | 0.151458i | \(0.0483970\pi\) | ||||
−0.988464 | + | 0.151458i | \(0.951603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.36578i | 0.152393i | 0.997093 | + | 0.0761965i | \(0.0242776\pi\) | ||||
−0.997093 | + | 0.0761965i | \(0.975722\pi\) | |||||||
\(242\) | 12.4896 | − | 8.86055i | 0.802862 | − | 0.569577i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.49526 | + | 2.62387i | 0.479835 | + | 0.167976i | ||||
\(245\) | 15.0865 | + | 1.27949i | 0.963842 | + | 0.0817438i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.3451i | − | 0.785498i | ||||||
\(248\) | 1.59235 | + | 5.53147i | 0.101114 | + | 0.351248i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.41883 | + | 13.2765i | 0.595699 | + | 0.839682i | ||||
\(251\) | 10.2341 | 0.645972 | 0.322986 | − | 0.946404i | \(-0.395313\pi\) | ||||
0.322986 | + | 0.946404i | \(0.395313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.171812 | 0.0108018 | ||||||||
\(254\) | 5.18499 | + | 7.30863i | 0.325335 | + | 0.458584i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.55173 | + | 15.6008i | 0.221983 | + | 0.975051i | ||||
\(257\) | − | 0.0758947i | − | 0.00473418i | −0.999997 | − | 0.00236709i | \(-0.999247\pi\) | ||
0.999997 | − | 0.00236709i | \(-0.000753469\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4881 | + | 13.3114i | −0.900247 | + | 0.827128i | ||||
\(260\) | 3.38145 | − | 9.65935i | 0.209709 | − | 0.599048i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.8671 | − | 15.5133i | 1.35095 | − | 0.958413i | ||||
\(263\) | − | 15.2740i | − | 0.941834i | −0.882177 | − | 0.470917i | \(-0.843923\pi\) | ||
0.882177 | − | 0.470917i | \(-0.156077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.76958i | 0.415852i | ||||||||
\(266\) | 4.08295 | − | 19.0930i | 0.250342 | − | 1.17067i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.46582 | − | 1.56335i | −0.272793 | − | 0.0954968i | ||||
\(269\) | − | 17.0040i | − | 1.03675i | −0.855153 | − | 0.518375i | \(-0.826537\pi\) | ||
0.855153 | − | 0.518375i | \(-0.173463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.676548 | 0.0410974 | 0.0205487 | − | 0.999789i | \(-0.493459\pi\) | ||||
0.0205487 | + | 0.999789i | \(0.493459\pi\) | |||||||
\(272\) | −1.73561 | + | 2.17516i | −0.105237 | + | 0.131888i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.29219 | − | 1.62616i | 0.138476 | − | 0.0982399i | ||||
\(275\) | − | 0.133319i | − | 0.00803947i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.323452 | −0.0194344 | −0.00971718 | − | 0.999953i | \(-0.503093\pi\) | ||||
−0.00971718 | + | 0.999953i | \(0.503093\pi\) | |||||||
\(278\) | −15.7092 | + | 11.1446i | −0.942173 | + | 0.668409i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.42447 | − | 13.8209i | 0.503459 | − | 0.825955i | ||||
\(281\) | −3.63311 | −0.216733 | −0.108367 | − | 0.994111i | \(-0.534562\pi\) | ||||
−0.108367 | + | 0.994111i | \(0.534562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5862 | 1.63983 | 0.819915 | − | 0.572486i | \(-0.194021\pi\) | ||||
0.819915 | + | 0.572486i | \(0.194021\pi\) | |||||||
\(284\) | 7.63512 | + | 2.67283i | 0.453061 | + | 0.158603i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.13108 | + | 0.802428i | −0.0668822 | + | 0.0474485i | ||||
\(287\) | 18.9583 | + | 20.6342i | 1.11907 | + | 1.21800i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5160 | 0.971531 | ||||||||
\(290\) | 17.2227 | + | 24.2766i | 1.01135 | + | 1.42557i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 23.3035 | + | 8.15785i | 1.36373 | + | 0.477402i | ||||
\(293\) | − | 20.4863i | − | 1.19682i | −0.801189 | − | 0.598412i | \(-0.795799\pi\) | ||
0.801189 | − | 0.598412i | \(-0.204201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 24.2570i | − | 1.41229i | ||||||
\(296\) | 5.81856 | + | 20.2124i | 0.338197 | + | 1.17482i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.2533 | − | 10.1118i | 0.825670 | − | 0.585759i | ||||
\(299\) | 0.980621 | 0.0567108 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.6896 | − | 17.0766i | −0.904336 | − | 0.984280i | ||||
\(302\) | 12.9799 | + | 18.2961i | 0.746910 | + | 1.05282i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.3154 | − | 13.0184i | −0.935751 | − | 0.746659i | ||||
\(305\) | −8.58829 | −0.491764 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6308 | 1.17746 | 0.588730 | − | 0.808330i | \(-0.299628\pi\) | ||||
0.588730 | + | 0.808330i | \(0.299628\pi\) | |||||||
\(308\) | −2.01473 | + | 0.866953i | −0.114800 | + | 0.0493992i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.60193 | − | 5.07718i | −0.204576 | − | 0.288365i | ||||
\(311\) | −16.4677 | −0.933795 | −0.466898 | − | 0.884311i | \(-0.654628\pi\) | ||||
−0.466898 | + | 0.884311i | \(0.654628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0559i | 1.52929i | 0.644452 | + | 0.764645i | \(0.277086\pi\) | ||||
−0.644452 | + | 0.764645i | \(0.722914\pi\) | |||||||
\(314\) | −6.85268 | − | 9.65935i | −0.386719 | − | 0.545109i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.3718 | + | 5.03115i | 0.808479 | + | 0.283024i | ||||
\(317\) | −31.3155 | −1.75885 | −0.879427 | − | 0.476033i | \(-0.842074\pi\) | ||||
−0.879427 | + | 0.476033i | \(0.842074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.03344i | − | 0.225829i | ||||||
\(320\) | −9.20001 | − | 14.6552i | −0.514296 | − | 0.819251i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.51664 | + | 0.324326i | 0.0845189 | + | 0.0180740i | ||||
\(323\) | − | 3.63022i | − | 0.201991i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.760922i | − | 0.0422083i | ||||||
\(326\) | 13.9735 | + | 19.6967i | 0.773923 | + | 1.09090i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.7868 | − | 8.28689i | 1.58949 | − | 0.457567i | ||||
\(329\) | −9.96944 | + | 9.15972i | −0.549633 | + | 0.504992i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.1101i | − | 1.16031i | −0.814505 | − | 0.580157i | \(-0.802991\pi\) | ||
0.814505 | − | 0.580157i | \(-0.197009\pi\) | |||||||
\(332\) | −8.49851 | + | 24.2766i | −0.466416 | + | 1.33235i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.93164 | + | 6.33641i | −0.488717 | + | 0.346713i | ||||
\(335\) | 5.11706 | 0.279575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8727 | −0.646750 | −0.323375 | − | 0.946271i | \(-0.604817\pi\) | ||||
−0.323375 | + | 0.946271i | \(0.604817\pi\) | |||||||
\(338\) | 8.53898 | − | 6.05785i | 0.464460 | − | 0.329503i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.994357 | − | 2.84045i | 0.0539266 | − | 0.154045i | ||||
\(341\) | 0.843550i | 0.0456808i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.3329 | − | 14.6480i | −0.611920 | − | 0.790919i | ||||
\(344\) | −23.8237 | + | 6.85814i | −1.28449 | + | 0.369766i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.47772 | + | 4.90210i | 0.186963 | + | 0.263539i | ||||
\(347\) | 19.8052i | 1.06320i | 0.846996 | + | 0.531599i | \(0.178409\pi\) | ||||
−0.846996 | + | 0.531599i | \(0.821591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.4718i | − | 0.828185i | −0.910235 | − | 0.414092i | \(-0.864099\pi\) | ||
0.910235 | − | 0.414092i | \(-0.135901\pi\) | |||||||
\(350\) | 0.251664 | − | 1.17685i | 0.0134520 | − | 0.0629052i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.132280 | + | 2.34105i | −0.00705057 | + | 0.124778i | ||||
\(353\) | − | 27.4471i | − | 1.46086i | −0.682986 | − | 0.730431i | \(-0.739319\pi\) | ||
0.682986 | − | 0.730431i | \(-0.260681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.74854 | −0.464324 | ||||||||
\(356\) | 27.7359 | + | 9.70951i | 1.47000 | + | 0.514603i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.24763 | − | 10.2161i | −0.383049 | − | 0.539936i | ||||
\(359\) | 8.33761i | 0.440042i | 0.975495 | + | 0.220021i | \(0.0706126\pi\) | ||||
−0.975495 | + | 0.220021i | \(0.929387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.22947 | 0.433130 | ||||||||
\(362\) | −19.5809 | − | 27.6008i | −1.02915 | − | 1.45066i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.4991 | + | 4.94814i | −0.602716 | + | 0.259353i | ||||
\(365\) | −26.7018 | −1.39764 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3091 | 0.851329 | 0.425665 | − | 0.904881i | \(-0.360040\pi\) | ||||
0.425665 | + | 0.904881i | \(0.360040\pi\) | |||||||
\(368\) | 1.03411 | − | 1.29600i | 0.0539067 | − | 0.0675587i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.1617 | − | 18.5524i | −0.684246 | − | 0.964495i | ||||
\(371\) | 6.09768 | − | 5.60243i | 0.316576 | − | 0.290864i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.42509 | 0.0737882 | 0.0368941 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368941 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(374\) | −0.332608 | + | 0.235964i | −0.0171988 | + | 0.0122014i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00383 | + | 13.9084i | 0.206482 | + | 0.717272i | ||||
\(377\) | − | 23.0209i | − | 1.18564i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.4465i | 1.40983i | 0.709292 | + | 0.704915i | \(0.249015\pi\) | ||||
−0.709292 | + | 0.704915i | \(0.750985\pi\) | |||||||
\(380\) | 21.3056 | + | 7.45845i | 1.09295 | + | 0.382611i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.2119 | − | 29.8998i | −1.08530 | − | 1.52981i | ||||
\(383\) | 6.09768 | 0.311577 | 0.155789 | − | 0.987790i | \(-0.450208\pi\) | ||||
0.155789 | + | 0.987790i | \(0.450208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.74672 | − | 1.60486i | 0.0890213 | − | 0.0817910i | ||||
\(386\) | 13.4832 | − | 9.56547i | 0.686279 | − | 0.486869i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.49526 | − | 2.62387i | −0.380514 | − | 0.133207i | ||||
\(389\) | −4.61373 | −0.233926 | −0.116963 | − | 0.993136i | \(-0.537316\pi\) | ||||
−0.116963 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.288364 | 0.0145832 | ||||||||
\(392\) | −19.4211 | + | 3.84968i | −0.980915 | + | 0.194438i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.5160 | + | 9.58873i | −0.680927 | + | 0.483073i | ||||
\(395\) | −16.4677 | −0.828578 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.2120i | − | 1.31554i | −0.753218 | − | 0.657771i | \(-0.771500\pi\) | ||
0.753218 | − | 0.657771i | \(-0.228500\pi\) | |||||||
\(398\) | −7.75444 | + | 5.50127i | −0.388695 | + | 0.275754i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00564 | − | 0.802428i | −0.0502821 | − | 0.0401214i | ||||
\(401\) | 21.0814 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.81457i | 0.239831i | ||||||||
\(404\) | −28.0150 | − | 9.80722i | −1.39380 | − | 0.487927i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.61383 | − | 35.6043i | 0.377868 | − | 1.76701i | ||||
\(407\) | 3.08240i | 0.152789i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.843933i | − | 0.0417298i | −0.999782 | − | 0.0208649i | \(-0.993358\pi\) | ||
0.999782 | − | 0.0208649i | \(-0.00664199\pi\) | |||||||
\(410\) | −26.4227 | + | 18.7451i | −1.30492 | + | 0.925757i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.26336 | − | 6.46545i | 0.111508 | − | 0.318530i | ||||
\(413\) | −21.8494 | + | 20.0748i | −1.07514 | + | 0.987816i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.8168i | − | 1.36547i | ||||||
\(416\) | −0.754992 | + | 13.3615i | −0.0370165 | + | 0.655103i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.76991 | − | 2.49482i | −0.0865692 | − | 0.122026i | ||||
\(419\) | 1.64584 | 0.0804044 | 0.0402022 | − | 0.999192i | \(-0.487200\pi\) | ||||
0.0402022 | + | 0.999192i | \(0.487200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.8822 | −1.40763 | −0.703817 | − | 0.710382i | \(-0.748522\pi\) | ||||
−0.703817 | + | 0.710382i | \(0.748522\pi\) | |||||||
\(422\) | 5.23639 | + | 7.38107i | 0.254903 | + | 0.359305i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.44889 | − | 8.50690i | −0.118929 | − | 0.413132i | ||||
\(425\) | − | 0.223758i | − | 0.0108539i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.10757 | + | 7.73588i | 0.343959 | + | 0.374366i | ||||
\(428\) | 27.3758 | + | 9.58346i | 1.32326 | + | 0.463234i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.8671 | − | 15.5133i | 1.05453 | − | 0.748116i | ||||
\(431\) | − | 35.5181i | − | 1.71085i | −0.517930 | − | 0.855423i | \(-0.673297\pi\) | ||
0.517930 | − | 0.855423i | \(-0.326703\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.0473i | − | 1.01147i | −0.862690 | − | 0.505733i | \(-0.831222\pi\) | ||
0.862690 | − | 0.505733i | \(-0.168778\pi\) | |||||||
\(434\) | −1.59235 | + | 7.44625i | −0.0764351 | + | 0.357431i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.55173 | + | 15.8589i | −0.265879 | + | 0.759504i | ||||
\(437\) | 2.16295i | 0.103468i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.2295 | 1.44277 | 0.721387 | − | 0.692532i | \(-0.243505\pi\) | ||||
0.721387 | + | 0.692532i | \(0.243505\pi\) | |||||||
\(440\) | −0.701502 | − | 2.43686i | −0.0334428 | − | 0.116173i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.89836 | + | 1.34676i | −0.0902960 | + | 0.0640591i | ||||
\(443\) | − | 2.14448i | − | 0.101887i | −0.998702 | − | 0.0509437i | \(-0.983777\pi\) | ||
0.998702 | − | 0.0509437i | \(-0.0162229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7806 | −1.50654 | ||||||||
\(446\) | −10.1806 | + | 7.22249i | −0.482067 | + | 0.341995i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.58681 | + | 20.4154i | −0.263952 | + | 0.964536i | ||||
\(449\) | 27.2051 | 1.28389 | 0.641944 | − | 0.766751i | \(-0.278128\pi\) | ||||
0.641944 | + | 0.766751i | \(0.278128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.39000 | 0.206717 | ||||||||
\(452\) | −3.04884 | + | 8.70923i | −0.143405 | + | 0.409648i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.8965 | + | 17.6625i | −1.16845 | + | 0.828940i | ||||
\(455\) | 9.96944 | − | 9.15972i | 0.467375 | − | 0.429414i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.2057 | 1.50652 | 0.753259 | − | 0.657724i | \(-0.228481\pi\) | ||||
0.753259 | + | 0.657724i | \(0.228481\pi\) | |||||||
\(458\) | 18.5359 | + | 26.1277i | 0.866125 | + | 1.22087i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.592457 | + | 1.69239i | −0.0276234 | + | 0.0789083i | ||||
\(461\) | − | 23.8169i | − | 1.10926i | −0.832096 | − | 0.554631i | \(-0.812859\pi\) | ||
0.832096 | − | 0.554631i | \(-0.187141\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6815i | 0.868202i | 0.900864 | + | 0.434101i | \(0.142934\pi\) | ||||
−0.900864 | + | 0.434101i | \(0.857066\pi\) | |||||||
\(464\) | −30.4247 | − | 24.2766i | −1.41243 | − | 1.12701i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.0577 | + | 18.4862i | −1.20710 | + | 0.856356i | ||||
\(467\) | 26.7018 | 1.23561 | 0.617806 | − | 0.786331i | \(-0.288022\pi\) | ||||
0.617806 | + | 0.786331i | \(0.288022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.23482 | − | 4.60918i | −0.195546 | − | 0.212832i | ||||
\(470\) | −9.05675 | − | 12.7662i | −0.417757 | − | 0.588859i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.77494 | + | 30.4822i | 0.403899 | + | 1.40306i | ||||
\(473\) | −3.63311 | −0.167051 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.67836 | 0.0770086 | ||||||||
\(476\) | −3.38145 | + | 1.45506i | −0.154989 | + | 0.0666926i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.83202 | + | 5.40151i | 0.175272 | + | 0.247059i | ||||
\(479\) | −37.9165 | −1.73245 | −0.866225 | − | 0.499654i | \(-0.833461\pi\) | ||||
−0.866225 | + | 0.499654i | \(0.833461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.5928i | 0.802163i | ||||||||
\(482\) | 1.93588 | + | 2.72877i | 0.0881769 | + | 0.124292i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.15547 | − | 20.4401i | 0.325249 | − | 0.929096i | ||||
\(485\) | 8.58829 | 0.389974 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.6942i | − | 1.48152i | −0.671772 | − | 0.740758i | \(-0.734467\pi\) | ||
0.671772 | − | 0.740758i | \(-0.265533\pi\) | |||||||
\(488\) | 10.7924 | − | 3.10681i | 0.488547 | − | 0.140639i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.4483 | − | 10.8693i | 0.833408 | − | 0.491023i | ||||
\(491\) | − | 36.8850i | − | 1.66460i | −0.554327 | − | 0.832299i | \(-0.687024\pi\) | ||
0.554327 | − | 0.832299i | \(-0.312976\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.76958i | − | 0.304886i | ||||||
\(494\) | −10.1018 | − | 14.2392i | −0.454501 | − | 0.640653i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.36298 | + | 5.07718i | 0.285706 | + | 0.227972i | ||||
\(497\) | 7.24019 | + | 7.88023i | 0.324767 | + | 0.353477i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.24881i | 0.369268i | 0.982807 | + | 0.184634i | \(0.0591099\pi\) | ||||
−0.982807 | + | 0.184634i | \(0.940890\pi\) | |||||||
\(500\) | 21.7280 | + | 7.60632i | 0.971705 | + | 0.340165i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.8044 | − | 8.37443i | 0.526855 | − | 0.373769i | ||||
\(503\) | −11.2147 | −0.500041 | −0.250020 | − | 0.968241i | \(-0.580437\pi\) | ||||
−0.250020 | + | 0.968241i | \(0.580437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.1004 | 1.42845 | ||||||||
\(506\) | 0.198174 | − | 0.140592i | 0.00880992 | − | 0.00625006i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9611 | + | 4.18722i | 0.530687 | + | 0.185778i | ||||
\(509\) | 24.3647i | 1.07995i | 0.841682 | + | 0.539973i | \(0.181566\pi\) | ||||
−0.841682 | + | 0.539973i | \(0.818434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0981 | + | 24.0516i | 0.977562 | + | 1.06398i | ||||
\(512\) | 16.8626 | + | 15.0882i | 0.745228 | + | 0.666809i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.0621035 | − | 0.0875395i | −0.00273927 | − | 0.00386120i | ||||
\(515\) | 7.40830i | 0.326449i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.12104i | 0.0932831i | ||||||||
\(518\) | −5.81856 | + | 27.2092i | −0.255653 | + | 1.19550i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.00383 | − | 13.9084i | −0.175579 | − | 0.609924i | ||||
\(521\) | 3.52991i | 0.154648i | 0.997006 | + | 0.0773242i | \(0.0246376\pi\) | ||||
−0.997006 | + | 0.0773242i | \(0.975362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.28655 | −0.0999838 | −0.0499919 | − | 0.998750i | \(-0.515920\pi\) | ||||
−0.0499919 | + | 0.998750i | \(0.515920\pi\) | |||||||
\(524\) | 12.5280 | − | 35.7871i | 0.547287 | − | 1.56336i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4985 | − | 17.6175i | −0.544959 | − | 0.768161i | ||||
\(527\) | 1.41578i | 0.0616724i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8282 | 0.992530 | ||||||||
\(530\) | 5.53945 | + | 7.80826i | 0.240618 | + | 0.339169i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.9141 | − | 25.3635i | −0.473186 | − | 1.09965i | ||||
\(533\) | 25.0560 | 1.08529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.3680 | −1.35616 | ||||||||
\(536\) | −6.43029 | + | 1.85109i | −0.277746 | + | 0.0799551i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.9141 | − | 19.6129i | −0.599879 | − | 0.845574i | ||||
\(539\) | −2.89114 | − | 0.245199i | −0.124530 | − | 0.0105615i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.216372 | 0.00930255 | 0.00465127 | − | 0.999989i | \(-0.498519\pi\) | ||||
0.00465127 | + | 0.999989i | \(0.498519\pi\) | |||||||
\(542\) | 0.780353 | − | 0.553609i | 0.0335190 | − | 0.0237795i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.222015 | + | 3.92913i | −0.00951880 | + | 0.168460i | ||||
\(545\) | − | 18.1716i | − | 0.778385i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.8761i | − | 1.40568i | −0.711347 | − | 0.702841i | \(-0.751915\pi\) | ||
0.711347 | − | 0.702841i | \(-0.248085\pi\) | |||||||
\(548\) | 1.31323 | − | 3.75133i | 0.0560984 | − | 0.160249i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.109093 | − | 0.153775i | −0.00465176 | − | 0.00655700i | ||||
\(551\) | 50.7771 | 2.16318 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6285 | + | 14.8332i | 0.579541 | + | 0.630772i | ||||
\(554\) | −0.373081 | + | 0.264676i | −0.0158507 | + | 0.0112450i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.00000 | + | 25.7091i | −0.381685 | + | 1.09031i | ||||
\(557\) | −1.48395 | −0.0628769 | −0.0314385 | − | 0.999506i | \(-0.510009\pi\) | ||||
−0.0314385 | + | 0.999506i | \(0.510009\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.7360 | −0.877040 | ||||||||
\(560\) | −1.59235 | − | 22.8351i | −0.0672890 | − | 0.964958i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.19056 | + | 2.97292i | −0.176768 | + | 0.125405i | ||||
\(563\) | 7.60767 | 0.320625 | 0.160312 | − | 0.987066i | \(-0.448750\pi\) | ||||
0.160312 | + | 0.987066i | \(0.448750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 9.97929i | − | 0.419832i | ||||||
\(566\) | 31.8189 | − | 22.5734i | 1.33745 | − | 0.948830i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.9937 | − | 3.16478i | 0.461287 | − | 0.132791i | ||||
\(569\) | −0.477293 | −0.0200092 | −0.0100046 | − | 0.999950i | \(-0.503185\pi\) | ||||
−0.0100046 | + | 0.999950i | \(0.503185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.97063i | − | 0.166166i | −0.996543 | − | 0.0830829i | \(-0.973523\pi\) | ||
0.996543 | − | 0.0830829i | \(-0.0264766\pi\) | |||||||
\(572\) | −0.648012 | + | 1.85109i | −0.0270948 | + | 0.0773981i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 38.7518 | + | 8.28689i | 1.61747 | + | 0.345888i | ||||
\(575\) | 0.133319i | 0.00555981i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7402i | 0.447121i | 0.974690 | + | 0.223560i | \(0.0717680\pi\) | ||||
−0.974690 | + | 0.223560i | \(0.928232\pi\) | |||||||
\(578\) | 19.0501 | − | 13.5148i | 0.792381 | − | 0.562142i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 39.7304 | + | 13.9084i | 1.64971 | + | 0.577515i | ||||
\(581\) | −25.0560 | + | 23.0209i | −1.03950 | + | 0.955068i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.29730i | − | 0.0537289i | ||||||
\(584\) | 33.5545 | − | 9.65935i | 1.38849 | − | 0.399707i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.7637 | − | 23.6296i | −0.692500 | − | 0.976130i | ||||
\(587\) | 1.64584 | 0.0679310 | 0.0339655 | − | 0.999423i | \(-0.489186\pi\) | ||||
0.0339655 | + | 0.999423i | \(0.489186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.6195 | −0.437568 | ||||||||
\(590\) | −19.8491 | − | 27.9788i | −0.817175 | − | 1.15187i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.2508 | + | 18.5524i | 0.955604 | + | 0.762500i | ||||
\(593\) | − | 8.28019i | − | 0.340027i | −0.985442 | − | 0.170013i | \(-0.945619\pi\) | ||
0.985442 | − | 0.170013i | \(-0.0543811\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.93164 | − | 2.69353i | 0.120185 | − | 0.110424i | ||||
\(596\) | 8.16590 | − | 23.3265i | 0.334488 | − | 0.955490i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.13108 | − | 0.802428i | 0.0462533 | − | 0.0328137i | ||||
\(599\) | 19.0006i | 0.776343i | 0.921587 | + | 0.388171i | \(0.126893\pi\) | ||||
−0.921587 | + | 0.388171i | \(0.873107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8168i | 1.13467i | 0.823486 | + | 0.567336i | \(0.192026\pi\) | ||||
−0.823486 | + | 0.567336i | \(0.807974\pi\) | |||||||
\(602\) | −32.0705 | − | 6.85814i | −1.30710 | − | 0.279517i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.9429 | + | 10.4821i | 1.21836 | + | 0.426511i | ||||
\(605\) | 23.4209i | 0.952193i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1166 | 0.775917 | 0.387958 | − | 0.921677i | \(-0.373180\pi\) | ||||
0.387958 | + | 0.921677i | \(0.373180\pi\) | |||||||
\(608\) | −29.4715 | − | 1.66528i | −1.19523 | − | 0.0675361i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.90602 | + | 7.02767i | −0.401083 | + | 0.284542i | ||||
\(611\) | 12.1058i | 0.489749i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.345440 | −0.0139522 | −0.00697609 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697609 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(614\) | 23.7962 | − | 16.8818i | 0.960337 | − | 0.681296i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.61444 | + | 2.64860i | −0.0650478 | + | 0.106715i | ||||
\(617\) | −13.3379 | −0.536963 | −0.268481 | − | 0.963285i | \(-0.586522\pi\) | ||||
−0.268481 | + | 0.963285i | \(0.586522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.4589 | −0.862508 | −0.431254 | − | 0.902231i | \(-0.641929\pi\) | ||||
−0.431254 | + | 0.902231i | \(0.641929\pi\) | |||||||
\(620\) | −8.30917 | − | 2.90879i | −0.333704 | − | 0.116820i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.9944 | + | 13.4752i | −0.761604 | + | 0.540308i | ||||
\(623\) | 26.3013 | + | 28.6263i | 1.05374 | + | 1.14689i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2884 | −0.931535 | ||||||||
\(626\) | 22.1394 | + | 31.2072i | 0.884870 | + | 1.24729i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.8082 | − | 5.53398i | −0.630816 | − | 0.220830i | ||||
\(629\) | 5.17338i | 0.206276i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4753i | 1.33263i | 0.745670 | + | 0.666316i | \(0.232130\pi\) | ||||
−0.745670 | + | 0.666316i | \(0.767870\pi\) | |||||||
\(632\) | 20.6939 | − | 5.95717i | 0.823158 | − | 0.236963i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −36.1204 | + | 25.6250i | −1.43452 | + | 1.01770i | ||||
\(635\) | −13.7054 | −0.543880 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.5012 | − | 1.39947i | −0.653801 | − | 0.0554491i | ||||
\(638\) | −3.30051 | − | 4.65231i | −0.130668 | − | 0.184187i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.6037 | − | 9.37557i | −0.893491 | − | 0.370602i | ||||
\(641\) | 3.12979 | 0.123619 | 0.0618096 | − | 0.998088i | \(-0.480313\pi\) | ||||
0.0618096 | + | 0.998088i | \(0.480313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.40128 | −0.0946974 | −0.0473487 | − | 0.998878i | \(-0.515077\pi\) | ||||
−0.0473487 | + | 0.998878i | \(0.515077\pi\) | |||||||
\(644\) | 2.01473 | − | 0.866953i | 0.0793915 | − | 0.0341627i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.97055 | − | 4.18722i | −0.116875 | − | 0.164744i | ||||
\(647\) | −44.6794 | −1.75653 | −0.878265 | − | 0.478174i | \(-0.841299\pi\) | ||||
−0.878265 | + | 0.478174i | \(0.841299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.64854i | 0.182471i | ||||||||
\(650\) | −0.622651 | − | 0.877673i | −0.0244224 | − | 0.0344252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.2351 | + | 11.2845i | 1.26242 | + | 0.441937i | ||||
\(653\) | 37.4132 | 1.46409 | 0.732046 | − | 0.681255i | \(-0.238566\pi\) | ||||
0.732046 | + | 0.681255i | \(0.238566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.0058i | 1.60223i | ||||||||
\(656\) | 26.4227 | − | 33.1142i | 1.03163 | − | 1.29289i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.00383 | + | 18.7230i | −0.156085 | + | 0.729898i | ||||
\(659\) | 34.3505i | 1.33810i | 0.743216 | + | 0.669052i | \(0.233300\pi\) | ||||
−0.743216 | + | 0.669052i | \(0.766700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0766i | 0.664203i | 0.943244 | + | 0.332102i | \(0.107758\pi\) | ||||
−0.943244 | + | 0.332102i | \(0.892242\pi\) | |||||||
\(662\) | −17.2741 | − | 24.3491i | −0.671375 | − | 0.946353i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.0627 | + | 34.9557i | 0.390509 | + | 1.35654i | ||||
\(665\) | 20.2036 | + | 21.9896i | 0.783461 | + | 0.852719i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.03344i | 0.156175i | ||||||||
\(668\) | −5.11706 | + | 14.6173i | −0.197985 | + | 0.565559i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.90219 | − | 4.18722i | 0.228022 | − | 0.161766i | ||||
\(671\) | 1.64584 | 0.0635369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0333 | −0.849320 | −0.424660 | − | 0.905353i | \(-0.639606\pi\) | ||||
−0.424660 | + | 0.905353i | \(0.639606\pi\) | |||||||
\(674\) | −13.6944 | + | 9.71529i | −0.527490 | + | 0.374219i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.89211 | − | 13.9747i | 0.188158 | − | 0.537487i | ||||
\(677\) | 10.3672i | 0.398446i | 0.979954 | + | 0.199223i | \(0.0638417\pi\) | ||||
−0.979954 | + | 0.199223i | \(0.936158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.10757 | − | 7.73588i | −0.272764 | − | 0.296876i | ||||
\(680\) | −1.17738 | − | 4.08994i | −0.0451503 | − | 0.156842i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.690264 | + | 0.972979i | 0.0264316 | + | 0.0372573i | ||||
\(683\) | 11.8919i | 0.455032i | 0.973774 | + | 0.227516i | \(0.0730604\pi\) | ||||
−0.973774 | + | 0.227516i | \(0.926940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.29838i | 0.164233i | ||||||||
\(686\) | −25.0580 | − | 7.62197i | −0.956721 | − | 0.291008i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.8671 | + | 27.4050i | −0.833676 | + | 1.04480i | ||||
\(689\) | − | 7.40438i | − | 0.282084i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.2389 | −1.72097 | −0.860485 | − | 0.509475i | \(-0.829840\pi\) | ||||
−0.860485 | + | 0.509475i | \(0.829840\pi\) | |||||||
\(692\) | 8.02264 | + | 2.80849i | 0.304975 | + | 0.106763i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.2063 | + | 22.8440i | 0.615182 | + | 0.867145i | ||||
\(695\) | − | 29.4583i | − | 1.11742i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.36801 | 0.279083 | ||||||||
\(698\) | −12.6603 | − | 17.8457i | −0.479200 | − | 0.675468i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.672720 | − | 1.56335i | −0.0254264 | − | 0.0590891i | ||||
\(701\) | 18.3191 | 0.691902 | 0.345951 | − | 0.938253i | \(-0.387556\pi\) | ||||
0.345951 | + | 0.938253i | \(0.387556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.8044 | −1.46354 | ||||||||
\(704\) | 1.76307 | + | 2.80849i | 0.0664481 | + | 0.105849i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.4596 | − | 31.6584i | −0.845277 | − | 1.19148i | ||||
\(707\) | −26.5659 | − | 28.9144i | −0.999115 | − | 1.08744i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.79491 | 0.217633 | 0.108816 | − | 0.994062i | \(-0.465294\pi\) | ||||
0.108816 | + | 0.994062i | \(0.465294\pi\) | |||||||
\(710\) | −10.0909 | + | 7.15880i | −0.378703 | + | 0.268665i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 39.9367 | − | 11.4966i | 1.49669 | − | 0.430853i | ||||
\(713\) | − | 0.843550i | − | 0.0315912i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.12104i | − | 0.0793223i | ||||||
\(716\) | −16.7193 | − | 5.85293i | −0.624831 | − | 0.218734i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.82254 | + | 9.61688i | 0.254615 | + | 0.358899i | ||||
\(719\) | −7.60767 | −0.283718 | −0.141859 | − | 0.989887i | \(-0.545308\pi\) | ||||
−0.141859 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.67301 | − | 6.13103i | 0.248516 | − | 0.228331i | ||||
\(722\) | 9.49215 | − | 6.73406i | 0.353261 | − | 0.250616i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −45.1706 | − | 15.8129i | −1.67875 | − | 0.587681i | ||||
\(725\) | 3.12979 | 0.116237 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.366196 | 0.0135815 | 0.00679074 | − | 0.999977i | \(-0.497838\pi\) | ||||
0.00679074 | + | 0.999977i | \(0.497838\pi\) | |||||||
\(728\) | −9.21445 | + | 15.1169i | −0.341510 | + | 0.560269i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.7987 | + | 21.8497i | −1.13991 | + | 0.808693i | ||||
\(731\) | −6.09768 | −0.225531 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 41.5220i | − | 1.53365i | −0.641856 | − | 0.766825i | \(-0.721835\pi\) | ||
0.641856 | − | 0.766825i | \(-0.278165\pi\) | |||||||
\(734\) | 18.8115 | − | 13.3455i | 0.694345 | − | 0.492592i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.132280 | − | 2.34105i | 0.00487592 | − | 0.0862921i | ||||
\(737\) | −0.980621 | −0.0361216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.29142i | 0.305005i | 0.988303 | + | 0.152502i | \(0.0487332\pi\) | ||||
−0.988303 | + | 0.152502i | \(0.951267\pi\) | |||||||
\(740\) | −30.3624 | − | 10.6290i | −1.11614 | − | 0.390728i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.44889 | − | 11.4517i | 0.0899016 | − | 0.420404i | ||||
\(743\) | 16.4172i | 0.602288i | 0.953579 | + | 0.301144i | \(0.0973685\pi\) | ||||
−0.953579 | + | 0.301144i | \(0.902631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.7282i | 0.979244i | ||||||||
\(746\) | 1.64374 | − | 1.16613i | 0.0601817 | − | 0.0426950i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.190556 | + | 0.544337i | −0.00696742 | + | 0.0199029i | ||||
\(749\) | 25.9598 | + | 28.2547i | 0.948551 | + | 1.03240i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4119i | 0.744843i | 0.928064 | + | 0.372421i | \(0.121472\pi\) | ||||
−0.928064 | + | 0.372421i | \(0.878528\pi\) | |||||||
\(752\) | 15.9992 | + | 12.7662i | 0.583431 | + | 0.465534i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.8377 | − | 26.5531i | −0.686027 | − | 0.967006i | ||||
\(755\) | −34.3095 | −1.24865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.04637 | −0.110722 | −0.0553612 | − | 0.998466i | \(-0.517631\pi\) | ||||
−0.0553612 | + | 0.998466i | \(0.517631\pi\) | |||||||
\(758\) | 22.4590 | + | 31.6577i | 0.815749 | + | 1.14986i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30.6777 | − | 8.83123i | 1.11280 | − | 0.320342i | ||||
\(761\) | 23.2691i | 0.843503i | 0.906711 | + | 0.421751i | \(0.138585\pi\) | ||||
−0.906711 | + | 0.421751i | \(0.861415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.3680 | + | 15.0386i | −0.592562 | + | 0.544434i | ||||
\(764\) | −48.9331 | − | 17.1300i | −1.77034 | − | 0.619742i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.03327 | − | 4.98964i | 0.254123 | − | 0.180283i | ||||
\(767\) | 26.5316i | 0.958000i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.4810i | 1.24342i | 0.783249 | + | 0.621708i | \(0.213561\pi\) | ||||
−0.783249 | + | 0.621708i | \(0.786439\pi\) | |||||||
\(770\) | 0.701502 | − | 3.28041i | 0.0252804 | − | 0.118218i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.72474 | − | 22.0663i | 0.278019 | − | 0.794182i | ||||
\(773\) | − | 18.1472i | − | 0.652708i | −0.945248 | − | 0.326354i | \(-0.894180\pi\) | ||
0.945248 | − | 0.326354i | \(-0.105820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.654560 | −0.0235125 | ||||||||
\(776\) | −10.7924 | + | 3.10681i | −0.387423 | + | 0.111528i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.32164 | + | 3.77535i | −0.190790 | + | 0.135353i | ||||
\(779\) | 55.2658i | 1.98010i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.67655 | 0.0599916 | ||||||||
\(782\) | 0.332608 | − | 0.235964i | 0.0118941 | − | 0.00843805i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.2508 | + | 20.3324i | −0.687530 | + | 0.726156i | ||||
\(785\) | 18.1135 | 0.646499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.1831 | 0.755096 | 0.377548 | − | 0.925990i | \(-0.376767\pi\) | ||||
0.377548 | + | 0.925990i | \(0.376767\pi\) | |||||||
\(788\) | −7.74352 | + | 22.1199i | −0.275852 | + | 0.787990i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.9944 | + | 13.4752i | −0.675789 | + | 0.479428i | ||||
\(791\) | −8.98882 | + | 8.25875i | −0.319606 | + | 0.293647i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.39363 | 0.333578 | ||||||||
\(794\) | −21.4489 | − | 30.2338i | −0.761192 | − | 1.07296i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.44263 | + | 12.6907i | −0.157465 | + | 0.449810i | ||||
\(797\) | 1.93919i | 0.0686898i | 0.999410 | + | 0.0343449i | \(0.0109345\pi\) | ||||
−0.999410 | + | 0.0343449i | \(0.989066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55987i | 0.125939i | ||||||||
\(800\) | −1.81656 | − | 0.102644i | −0.0642250 | − | 0.00362902i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.3160 | − | 17.2506i | 0.858628 | − | 0.609140i | ||||
\(803\) | 5.11706 | 0.180577 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.74672 | + | 1.60486i | −0.0615640 | + | 0.0565637i | ||||
\(806\) | 3.93969 | + | 5.55328i | 0.138770 | + | 0.195606i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −40.3386 | + | 11.6123i | −1.41911 | + | 0.408519i | ||||
\(809\) | 30.1990 | 1.06174 | 0.530871 | − | 0.847453i | \(-0.321865\pi\) | ||||
0.530871 | + | 0.847453i | \(0.321865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.17363 | 0.111441 | 0.0557206 | − | 0.998446i | \(-0.482254\pi\) | ||||
0.0557206 | + | 0.998446i | \(0.482254\pi\) | |||||||
\(812\) | −20.3524 | − | 47.2975i | −0.714231 | − | 1.65982i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.52228 | + | 3.55534i | 0.0884059 | + | 0.124615i | ||||
\(815\) | −36.9359 | −1.29381 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 45.7374i | − | 1.60015i | ||||||
\(818\) | −0.690578 | − | 0.973421i | −0.0241455 | − | 0.0340349i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.1379 | + | 43.2426i | −0.528639 | + | 1.51010i | ||||
\(821\) | −42.8717 | −1.49623 | −0.748116 | − | 0.663567i | \(-0.769042\pi\) | ||||
−0.748116 | + | 0.663567i | \(0.769042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.21837i | 0.321332i | 0.987009 | + | 0.160666i | \(0.0513642\pi\) | ||||
−0.987009 | + | 0.160666i | \(0.948636\pi\) | |||||||
\(824\) | −2.67995 | − | 9.30955i | −0.0933604 | − | 0.324313i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.77494 | + | 41.0340i | −0.305319 | + | 1.42775i | ||||
\(827\) | − | 20.2956i | − | 0.705746i | −0.935671 | − | 0.352873i | \(-0.885205\pi\) | ||
0.935671 | − | 0.352873i | \(-0.114795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.7875i | − | 1.10402i | −0.833836 | − | 0.552012i | \(-0.813860\pi\) | ||
0.833836 | − | 0.552012i | \(-0.186140\pi\) | |||||||
\(830\) | −22.7621 | − | 32.0849i | −0.790084 | − | 1.11368i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.0627 | + | 16.0295i | 0.348862 | + | 0.555721i | ||||
\(833\) | −4.85238 | − | 0.411532i | −0.168125 | − | 0.0142588i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.7489i | − | 0.579618i | ||||||
\(836\) | −4.08295 | − | 1.42932i | −0.141212 | − | 0.0494340i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.89836 | − | 1.34676i | 0.0655779 | − | 0.0465232i | ||||
\(839\) | −19.8030 | −0.683677 | −0.341838 | − | 0.939759i | \(-0.611050\pi\) | ||||
−0.341838 | + | 0.939759i | \(0.611050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.6884 | 2.26512 | ||||||||
\(842\) | −33.3137 | + | 23.6339i | −1.14807 | + | 0.814478i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.0796 | + | 4.22872i | 0.415799 | + | 0.145559i | ||||
\(845\) | 16.0126i | 0.550849i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0963 | − | 19.3828i | 0.724877 | − | 0.666002i | ||||
\(848\) | −9.78571 | − | 7.80826i | −0.336043 | − | 0.268137i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.183098 | − | 0.258091i | −0.00628022 | − | 0.00885243i | ||||
\(851\) | − | 3.08240i | − | 0.105663i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.49248i | 0.188059i | 0.995569 | + | 0.0940294i | \(0.0299748\pi\) | ||||
−0.995569 | + | 0.0940294i | \(0.970025\pi\) | |||||||
\(854\) | 14.5283 | + | 3.10681i | 0.497147 | + | 0.106313i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.4182 | − | 11.3474i | 1.34729 | − | 0.387845i | ||||
\(857\) | 30.6774i | 1.04792i | 0.851743 | + | 0.523959i | \(0.175546\pi\) | ||||
−0.851743 | + | 0.523959i | \(0.824454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.07783 | −0.309732 | −0.154866 | − | 0.987936i | \(-0.549495\pi\) | ||||
−0.154866 | + | 0.987936i | \(0.549495\pi\) | |||||||
\(860\) | 12.5280 | − | 35.7871i | 0.427200 | − | 1.22033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.0639 | − | 40.9677i | −0.989921 | − | 1.39537i | ||||
\(863\) | − | 41.5535i | − | 1.41450i | −0.706965 | − | 0.707248i | \(-0.749936\pi\) | ||
0.706965 | − | 0.707248i | \(-0.250064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.19257 | −0.312557 | ||||||||
\(866\) | −17.2227 | − | 24.2766i | −0.585250 | − | 0.824953i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.25649 | + | 9.89175i | 0.144475 | + | 0.335748i | ||||
\(869\) | 3.15582 | 0.107054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.59690 | −0.189644 | ||||||||
\(872\) | 6.57356 | + | 22.8351i | 0.222609 | + | 0.773294i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.76991 | + | 2.49482i | 0.0598682 | + | 0.0843886i | ||||
\(875\) | 20.6041 | + | 22.4255i | 0.696546 | + | 0.758121i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.63257 | −0.291501 | −0.145751 | − | 0.989321i | \(-0.546560\pi\) | ||||
−0.145751 | + | 0.989321i | \(0.546560\pi\) | |||||||
\(878\) | 34.8677 | − | 24.7363i | 1.17673 | − | 0.834811i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.80319 | − | 2.23673i | −0.0944954 | − | 0.0754002i | ||||
\(881\) | − | 19.4666i | − | 0.655845i | −0.944705 | − | 0.327923i | \(-0.893651\pi\) | ||
0.944705 | − | 0.327923i | \(-0.106349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7540i | 0.933997i | 0.884258 | + | 0.466999i | \(0.154665\pi\) | ||||
−0.884258 | + | 0.466999i | \(0.845335\pi\) | |||||||
\(884\) | −1.08760 | + | 3.10681i | −0.0365799 | + | 0.104493i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.75480 | − | 2.47352i | −0.0589536 | − | 0.0830995i | ||||
\(887\) | 2.62646 | 0.0881878 | 0.0440939 | − | 0.999027i | \(-0.485960\pi\) | ||||
0.0440939 | + | 0.999027i | \(0.485960\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.3424 | + | 12.3451i | 0.380412 | + | 0.414040i | ||||
\(890\) | −36.6568 | + | 26.0056i | −1.22874 | + | 0.871709i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.83263 | + | 16.6613i | −0.195291 | + | 0.557862i | ||||
\(893\) | −26.7018 | −0.893541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.1575 | 0.640364 | ||||||||
\(896\) | 10.2616 | + | 28.1194i | 0.342815 | + | 0.939403i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3793 | − | 22.2615i | 1.04714 | − | 0.742877i | ||||
\(899\) | −19.8030 | −0.660468 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.17735i | − | 0.0725380i | ||||||
\(902\) | 5.06357 | − | 3.59227i | 0.168599 | − | 0.119610i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.61000 | + | 12.5403i | 0.120067 | + | 0.417086i | ||||
\(905\) | 51.7577 | 1.72049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.22753i | − | 0.173577i | −0.996227 | − | 0.0867887i | \(-0.972340\pi\) | ||
0.996227 | − | 0.0867887i | \(-0.0276605\pi\) | |||||||
\(908\) | −14.2636 | + | 40.7450i | −0.473354 | + | 1.35217i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.00383 | − | 18.7230i | 0.132726 | − | 0.620661i | ||||
\(911\) | 52.9940i | 1.75577i | 0.478873 | + | 0.877884i | \(0.341046\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.33075i | 0.176422i | ||||||||
\(914\) | 37.1471 | − | 26.3534i | 1.22872 | − | 0.871694i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42.7598 | + | 14.9689i | 1.41282 | + | 0.494587i | ||||
\(917\) | 36.9359 | − | 33.9360i | 1.21973 | − | 1.12066i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.9137i | 1.48156i | 0.671745 | + | 0.740782i | \(0.265545\pi\) | ||||
−0.671745 | + | 0.740782i | \(0.734455\pi\) | |||||||
\(920\) | 0.701502 | + | 2.43686i | 0.0231278 | + | 0.0803410i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.4890 | − | 27.4712i | −0.641836 | − | 0.904716i | ||||
\(923\) | 9.56891 | 0.314964 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.39181 | −0.0786424 | ||||||||
\(926\) | 15.2868 | + | 21.5478i | 0.502355 | + | 0.708106i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −54.9580 | − | 3.10539i | −1.80409 | − | 0.101940i | ||||
\(929\) | 32.2964i | 1.05961i | 0.848119 | + | 0.529806i | \(0.177735\pi\) | ||||
−0.848119 | + | 0.529806i | \(0.822265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.08681 | − | 36.3966i | 0.101166 | − | 1.19285i | ||||
\(932\) | −14.9288 | + | 42.6452i | −0.489009 | + | 1.39689i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.7987 | − | 21.8497i | 1.00777 | − | 0.714943i | ||||
\(935\) | − | 0.623717i | − | 0.0203977i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.6781i | 1.32889i | 0.747335 | + | 0.664447i | \(0.231333\pi\) | ||||
−0.747335 | + | 0.664447i | \(0.768667\pi\) | |||||||
\(938\) | −8.65621 | − | 1.85109i | −0.282635 | − | 0.0604404i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.8927 | − | 7.31392i | −0.681445 | − | 0.238554i | ||||
\(941\) | − | 8.52836i | − | 0.278016i | −0.990291 | − | 0.139008i | \(-0.955609\pi\) | ||
0.990291 | − | 0.139008i | \(-0.0443915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.39000 | −0.142958 | ||||||||
\(944\) | 35.0644 | + | 27.9788i | 1.14125 | + | 0.910632i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.19056 | + | 2.97292i | −0.136247 | + | 0.0966581i | ||||
\(947\) | 19.9998i | 0.649908i | 0.945730 | + | 0.324954i | \(0.105349\pi\) | ||||
−0.945730 | + | 0.324954i | \(0.894651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.2057 | 0.948056 | ||||||||
\(950\) | 1.93588 | − | 1.37338i | 0.0628082 | − | 0.0445583i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.70962 | + | 4.44531i | −0.0878194 | + | 0.144073i | ||||
\(953\) | −24.5787 | −0.796181 | −0.398090 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398090 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.0689 | 1.81435 | ||||||||
\(956\) | 8.83995 | + | 3.09460i | 0.285904 | + | 0.100087i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −43.7342 | + | 31.0265i | −1.41299 | + | 1.00242i | ||||
\(959\) | 3.87176 | − | 3.55729i | 0.125026 | − | 0.114871i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8584 | −0.866400 | ||||||||
\(962\) | 14.3959 | + | 20.2921i | 0.464143 | + | 0.654244i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.46582 | + | 1.56335i | 0.143834 | + | 0.0503521i | ||||
\(965\) | 25.2842i | 0.813926i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.1619i | − | 1.29152i | −0.763541 | − | 0.645760i | \(-0.776541\pi\) | ||
0.763541 | − | 0.645760i | \(-0.223459\pi\) | |||||||
\(968\) | −8.47248 | − | 29.4315i | −0.272316 | − | 0.945965i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.90602 | − | 7.02767i | 0.318063 | − | 0.225645i | ||||
\(971\) | −24.7405 | −0.793962 | −0.396981 | − | 0.917827i | \(-0.629942\pi\) | ||||
−0.396981 | + | 0.917827i | \(0.629942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.5345 | + | 24.3793i | −0.850656 | + | 0.781565i | ||||
\(974\) | −26.7532 | − | 37.7106i | −0.857227 | − | 1.20833i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.90602 | − | 12.4147i | 0.317084 | − | 0.397386i | ||||
\(977\) | 41.8911 | 1.34021 | 0.670107 | − | 0.742264i | \(-0.266248\pi\) | ||||
0.670107 | + | 0.742264i | \(0.266248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.09035 | 0.194648 | ||||||||
\(980\) | 12.3847 | − | 27.6329i | 0.395615 | − | 0.882701i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.1825 | − | 42.5444i | −0.963162 | − | 1.35765i | ||||
\(983\) | 24.7405 | 0.789101 | 0.394550 | − | 0.918874i | \(-0.370900\pi\) | ||||
0.394550 | + | 0.918874i | \(0.370900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25.3456i | − | 0.807579i | ||||||
\(986\) | −5.53945 | − | 7.80826i | −0.176412 | − | 0.248666i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.3035 | − | 8.15785i | −0.741382 | − | 0.259536i | ||||
\(989\) | 3.63311 | 0.115526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 30.8807i | − | 0.980958i | −0.871453 | − | 0.490479i | \(-0.836822\pi\) | ||
0.871453 | − | 0.490479i | \(-0.163178\pi\) | |||||||
\(992\) | 11.4939 | + | 0.649459i | 0.364931 | + | 0.0206203i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.7994 | + | 3.16478i | 0.469407 | + | 0.100381i | ||||
\(995\) | − | 14.5414i | − | 0.460992i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 32.6314i | − | 1.03345i | −0.856152 | − | 0.516723i | \(-0.827152\pi\) | ||
0.856152 | − | 0.516723i | \(-0.172848\pi\) | |||||||
\(998\) | 6.74988 | + | 9.51446i | 0.213664 | + | 0.301175i | ||||
\(999\) | 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 | 756.2.b.c.55.9 | yes | 12 | |
3.2 | odd | 2 | inner | 756.2.b.c.55.4 | yes | 12 | |
4.3 | odd | 2 | 756.2.b.d.55.10 | yes | 12 | ||
7.6 | odd | 2 | 756.2.b.d.55.9 | yes | 12 | ||
12.11 | even | 2 | 756.2.b.d.55.3 | yes | 12 | ||
21.20 | even | 2 | 756.2.b.d.55.4 | yes | 12 | ||
28.27 | even | 2 | inner | 756.2.b.c.55.10 | yes | 12 | |
84.83 | odd | 2 | inner | 756.2.b.c.55.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.b.c.55.3 | ✓ | 12 | 84.83 | odd | 2 | inner | |
756.2.b.c.55.4 | yes | 12 | 3.2 | odd | 2 | inner | |
756.2.b.c.55.9 | yes | 12 | 1.1 | even | 1 | trivial | |
756.2.b.c.55.10 | yes | 12 | 28.27 | even | 2 | inner | |
756.2.b.d.55.3 | yes | 12 | 12.11 | even | 2 | ||
756.2.b.d.55.4 | yes | 12 | 21.20 | even | 2 | ||
756.2.b.d.55.9 | yes | 12 | 7.6 | odd | 2 | ||
756.2.b.d.55.10 | yes | 12 | 4.3 | odd | 2 |