Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(89,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bo (of order \(6\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.8 | ||
Root | \(-2.11940 - 0.712845i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.89 |
Dual form | 630.2.bo.a.269.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.11940 | − | 0.712845i | 0.947824 | − | 0.318794i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63937 | + | 2.07665i | 0.619624 | + | 0.784899i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.442358 | + | 2.19188i | −0.139886 | + | 0.693132i | ||||
\(11\) | −5.48223 | + | 3.16517i | −1.65295 | + | 0.954334i | −0.677106 | + | 0.735886i | \(0.736766\pi\) |
−0.975849 | + | 0.218448i | \(0.929901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.05290 | 0.292021 | 0.146011 | − | 0.989283i | \(-0.453357\pi\) | ||||
0.146011 | + | 0.989283i | \(0.453357\pi\) | |||||||
\(14\) | −2.61811 | + | 0.381412i | −0.699721 | + | 0.101937i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.01562 | − | 2.31842i | 0.973931 | − | 0.562299i | 0.0734985 | − | 0.997295i | \(-0.476584\pi\) |
0.900432 | + | 0.434996i | \(0.143250\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.35129 | + | 3.08957i | 1.22767 | + | 0.708795i | 0.966542 | − | 0.256509i | \(-0.0825723\pi\) |
0.261128 | + | 0.965304i | \(0.415906\pi\) | |||||||
\(20\) | −1.67704 | − | 1.47903i | −0.374998 | − | 0.330721i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.33033i | − | 1.34963i | ||||||
\(23\) | −3.52236 | + | 6.10091i | −0.734463 | + | 1.27213i | 0.220496 | + | 0.975388i | \(0.429232\pi\) |
−0.954959 | + | 0.296739i | \(0.904101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.98371 | − | 3.02160i | 0.796741 | − | 0.604321i | ||||
\(26\) | −0.526449 | + | 0.911836i | −0.103245 | + | 0.178826i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.978745 | − | 2.45806i | 0.184965 | − | 0.464530i | ||||
\(29\) | − | 2.98101i | − | 0.553560i | −0.960933 | − | 0.276780i | \(-0.910733\pi\) | ||
0.960933 | − | 0.276780i | \(-0.0892674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46948 | − | 3.15781i | 0.982348 | − | 0.567159i | 0.0793697 | − | 0.996845i | \(-0.474709\pi\) |
0.902978 | + | 0.429686i | \(0.141376\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.63684i | 0.795211i | ||||||||
\(35\) | 4.95481 | + | 3.23263i | 0.837515 | + | 0.546414i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.01361 | + | 1.73991i | 0.495434 | + | 0.286039i | 0.726826 | − | 0.686821i | \(-0.240995\pi\) |
−0.231392 | + | 0.972861i | \(0.574328\pi\) | |||||||
\(38\) | −5.35129 | + | 3.08957i | −0.868094 | + | 0.501194i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.11940 | − | 0.712845i | 0.335106 | − | 0.112711i | ||||
\(41\) | −6.97007 | −1.08854 | −0.544271 | − | 0.838909i | \(-0.683194\pi\) | ||||
−0.544271 | + | 0.838909i | \(0.683194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.58650i | 0.394437i | 0.980360 | + | 0.197218i | \(0.0631908\pi\) | ||||
−0.980360 | + | 0.197218i | \(0.936809\pi\) | |||||||
\(44\) | 5.48223 | + | 3.16517i | 0.826477 | + | 0.477167i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.52236 | − | 6.10091i | −0.519344 | − | 0.899529i | ||||
\(47\) | 7.06176 | + | 4.07711i | 1.03006 | + | 0.594707i | 0.917003 | − | 0.398881i | \(-0.130601\pi\) |
0.113060 | + | 0.993588i | \(0.463935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.62493 | + | 6.80879i | −0.232133 | + | 0.972684i | ||||
\(50\) | 0.624933 | + | 4.96079i | 0.0883789 | + | 0.701562i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.526449 | − | 0.911836i | −0.0730053 | − | 0.126449i | ||||
\(53\) | 4.43682 | + | 7.68480i | 0.609445 | + | 1.05559i | 0.991332 | + | 0.131380i | \(0.0419409\pi\) |
−0.381887 | + | 0.924209i | \(0.624726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.36276 | + | 10.6162i | −1.26247 | + | 1.43149i | ||||
\(56\) | 1.63937 | + | 2.07665i | 0.219070 | + | 0.277504i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.58163 | + | 1.49051i | 0.338985 | + | 0.195713i | ||||
\(59\) | 0.452296 | + | 0.783400i | 0.0588839 | + | 0.101990i | 0.893965 | − | 0.448137i | \(-0.147912\pi\) |
−0.835081 | + | 0.550127i | \(0.814579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.81047 | − | 5.08673i | −1.12807 | − | 0.651289i | −0.184618 | − | 0.982810i | \(-0.559105\pi\) |
−0.943448 | + | 0.331522i | \(0.892438\pi\) | |||||||
\(62\) | 6.31561i | 0.802084i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.23151 | − | 0.750552i | 0.276785 | − | 0.0930946i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.51497 | + | 4.91612i | −1.04027 | + | 0.600600i | −0.919909 | − | 0.392131i | \(-0.871738\pi\) |
−0.120360 | + | 0.992730i | \(0.538405\pi\) | |||||||
\(68\) | −4.01562 | − | 2.31842i | −0.486965 | − | 0.281150i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.27694 | + | 2.67467i | −0.630715 | + | 0.319685i | ||||
\(71\) | − | 14.4282i | − | 1.71232i | −0.516713 | − | 0.856159i | \(-0.672844\pi\) | ||
0.516713 | − | 0.856159i | \(-0.327156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.18333 | + | 7.24574i | 0.489622 | + | 0.848050i | 0.999929 | − | 0.0119423i | \(-0.00380146\pi\) |
−0.510307 | + | 0.859992i | \(0.670468\pi\) | |||||||
\(74\) | −3.01361 | + | 1.73991i | −0.350325 | + | 0.202260i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.17914i | − | 0.708795i | ||||||
\(77\) | −15.5603 | − | 6.19578i | −1.77327 | − | 0.706075i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.73283 | − | 4.73340i | 0.307467 | − | 0.532549i | −0.670340 | − | 0.742054i | \(-0.733852\pi\) |
0.977808 | + | 0.209505i | \(0.0671852\pi\) | |||||||
\(80\) | −0.442358 | + | 2.19188i | −0.0494571 | + | 0.245059i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.48504 | − | 6.03626i | 0.384858 | − | 0.666593i | ||||
\(83\) | − | 14.6297i | − | 1.60581i | −0.596105 | − | 0.802907i | \(-0.703286\pi\) | ||
0.596105 | − | 0.802907i | \(-0.296714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.85803 | − | 7.77617i | 0.743858 | − | 0.843444i | ||||
\(86\) | −2.23997 | − | 1.29325i | −0.241542 | − | 0.139455i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.48223 | + | 3.16517i | −0.584408 | + | 0.337408i | ||||
\(89\) | 1.91982 | − | 3.32522i | 0.203500 | − | 0.352473i | −0.746154 | − | 0.665774i | \(-0.768102\pi\) |
0.949654 | + | 0.313301i | \(0.101435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72609 | + | 2.18650i | 0.180943 | + | 0.229207i | ||||
\(92\) | 7.04472 | 0.734463 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.06176 | + | 4.07711i | −0.728365 | + | 0.420522i | ||||
\(95\) | 13.5439 | + | 2.73339i | 1.38957 | + | 0.280440i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.87891 | −0.596913 | −0.298457 | − | 0.954423i | \(-0.596472\pi\) | ||||
−0.298457 | + | 0.954423i | \(0.596472\pi\) | |||||||
\(98\) | −5.08412 | − | 4.81163i | −0.513573 | − | 0.486048i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.60864 | − | 1.93919i | −0.460864 | − | 0.193919i | ||||
\(101\) | 3.35408 | + | 5.80944i | 0.333744 | + | 0.578061i | 0.983243 | − | 0.182301i | \(-0.0583547\pi\) |
−0.649499 | + | 0.760362i | \(0.725021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.48716 | − | 4.30789i | 0.245067 | − | 0.424469i | −0.717083 | − | 0.696988i | \(-0.754523\pi\) |
0.962151 | + | 0.272519i | \(0.0878566\pi\) | |||||||
\(104\) | 1.05290 | 0.103245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.87365 | −0.861885 | ||||||||
\(107\) | −3.66965 | + | 6.35602i | −0.354759 | + | 0.614460i | −0.987077 | − | 0.160249i | \(-0.948770\pi\) |
0.632318 | + | 0.774709i | \(0.282104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | −4.51254 | − | 13.4165i | −0.430254 | − | 1.27921i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.61811 | + | 0.381412i | −0.247389 | + | 0.0360400i | ||||
\(113\) | 0.184551 | 0.0173611 | 0.00868054 | − | 0.999962i | \(-0.497237\pi\) | ||||
0.00868054 | + | 0.999962i | \(0.497237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.11629 | + | 15.4411i | −0.290595 | + | 1.43989i | ||||
\(116\) | −2.58163 | + | 1.49051i | −0.239699 | + | 0.138390i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.904592 | −0.0832745 | ||||||||
\(119\) | 11.3976 | + | 4.53828i | 1.04482 | + | 0.416024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.5366 | − | 25.1781i | 1.32151 | − | 2.28891i | ||||
\(122\) | 8.81047 | − | 5.08673i | 0.797663 | − | 0.460531i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.46948 | − | 3.15781i | −0.491174 | − | 0.283579i | ||||
\(125\) | 6.28913 | − | 9.24375i | 0.562517 | − | 0.826786i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.70276i | − | 0.594774i | −0.954757 | − | 0.297387i | \(-0.903885\pi\) | ||
0.954757 | − | 0.297387i | \(-0.0961151\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.465758 | + | 2.30782i | −0.0408497 | + | 0.202409i | ||||
\(131\) | −2.24116 | + | 3.88180i | −0.195811 | + | 0.339155i | −0.947166 | − | 0.320743i | \(-0.896067\pi\) |
0.751355 | + | 0.659898i | \(0.229401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.35680 | + | 16.1777i | 0.204360 | + | 1.40278i | ||||
\(134\) | − | 9.83224i | − | 0.849376i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.01562 | − | 2.31842i | 0.344337 | − | 0.198803i | ||||
\(137\) | −8.78137 | − | 15.2098i | −0.750243 | − | 1.29946i | −0.947705 | − | 0.319149i | \(-0.896603\pi\) |
0.197461 | − | 0.980311i | \(-0.436730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.02268i | 0.510837i | 0.966831 | + | 0.255418i | \(0.0822132\pi\) | ||||
−0.966831 | + | 0.255418i | \(0.917787\pi\) | |||||||
\(140\) | 0.322137 | − | 5.90730i | 0.0272255 | − | 0.499258i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.4952 | + | 7.21412i | 1.04858 | + | 0.605396i | ||||
\(143\) | −5.77223 | + | 3.33260i | −0.482698 | + | 0.278686i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.12500 | − | 6.31796i | −0.176472 | − | 0.524678i | ||||
\(146\) | −8.36666 | −0.692430 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 3.47982i | − | 0.286039i | ||||||
\(149\) | 6.06548 | + | 3.50191i | 0.496903 | + | 0.286887i | 0.727434 | − | 0.686178i | \(-0.240713\pi\) |
−0.230530 | + | 0.973065i | \(0.574046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.43540 | − | 11.1464i | −0.523706 | − | 0.907085i | −0.999619 | − | 0.0275929i | \(-0.991216\pi\) |
0.475913 | − | 0.879492i | \(-0.342118\pi\) | |||||||
\(152\) | 5.35129 | + | 3.08957i | 0.434047 | + | 0.250597i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.1459 | − | 10.3778i | 1.05932 | − | 0.836263i | ||||
\(155\) | 9.34099 | − | 10.5915i | 0.750286 | − | 0.850733i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.52193 | − | 9.56427i | −0.440698 | − | 0.763312i | 0.557043 | − | 0.830484i | \(-0.311936\pi\) |
−0.997741 | + | 0.0671718i | \(0.978602\pi\) | |||||||
\(158\) | 2.73283 | + | 4.73340i | 0.217412 | + | 0.376569i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.67704 | − | 1.47903i | −0.132582 | − | 0.116928i | ||||
\(161\) | −18.4439 | + | 2.68694i | −1.45358 | + | 0.211760i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27500 | − | 3.62287i | −0.491496 | − | 0.283765i | 0.233699 | − | 0.972309i | \(-0.424917\pi\) |
−0.725195 | + | 0.688544i | \(0.758250\pi\) | |||||||
\(164\) | 3.48504 | + | 6.03626i | 0.272136 | + | 0.471353i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6697 | + | 7.31483i | 0.983356 | + | 0.567741i | ||||
\(167\) | − | 13.8606i | − | 1.07257i | −0.844038 | − | 0.536283i | \(-0.819828\pi\) | ||
0.844038 | − | 0.536283i | \(-0.180172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8914 | −0.914724 | ||||||||
\(170\) | 3.30534 | + | 9.82731i | 0.253508 | + | 0.753720i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.23997 | − | 1.29325i | 0.170796 | − | 0.0986092i | ||||
\(173\) | −0.830348 | − | 0.479402i | −0.0631302 | − | 0.0364482i | 0.468103 | − | 0.883674i | \(-0.344938\pi\) |
−0.531233 | + | 0.847226i | \(0.678271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.8056 | + | 3.31923i | 0.968010 | + | 0.250910i | ||||
\(176\) | − | 6.33033i | − | 0.477167i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.91982 | + | 3.32522i | 0.143896 | + | 0.249236i | ||||
\(179\) | 20.2531 | − | 11.6931i | 1.51379 | − | 0.873984i | 0.513916 | − | 0.857841i | \(-0.328194\pi\) |
0.999870 | − | 0.0161436i | \(-0.00513888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.2865i | − | 1.43355i | −0.697303 | − | 0.716776i | \(-0.745617\pi\) | ||
0.697303 | − | 0.716776i | \(-0.254383\pi\) | |||||||
\(182\) | −2.75661 | + | 0.401588i | −0.204333 | + | 0.0297677i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.52236 | + | 6.10091i | −0.259672 | + | 0.449765i | ||||
\(185\) | 7.62733 | + | 1.53933i | 0.560772 | + | 0.113173i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.6764 | + | 25.4202i | −1.07324 | + | 1.85891i | ||||
\(188\) | − | 8.15421i | − | 0.594707i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.13913 | + | 10.3627i | −0.663022 | + | 0.751787i | ||||
\(191\) | −2.44949 | − | 1.41421i | −0.177239 | − | 0.102329i | 0.408756 | − | 0.912644i | \(-0.365963\pi\) |
−0.585995 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.11634 | − | 4.10862i | 0.512246 | − | 0.295745i | −0.221511 | − | 0.975158i | \(-0.571099\pi\) |
0.733756 | + | 0.679413i | \(0.237765\pi\) | |||||||
\(194\) | 2.93946 | − | 5.09129i | 0.211041 | − | 0.365533i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70905 | − | 1.99716i | 0.479218 | − | 0.142654i | ||||
\(197\) | 3.51321 | 0.250306 | 0.125153 | − | 0.992137i | \(-0.460058\pi\) | ||||
0.125153 | + | 0.992137i | \(0.460058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | + | 1.73205i | −0.212664 | + | 0.122782i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | 3.98371 | − | 3.02160i | 0.281690 | − | 0.213660i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.70816 | −0.471985 | ||||||||
\(203\) | 6.19052 | − | 4.88698i | 0.434489 | − | 0.342999i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.7724 | + | 4.96858i | −1.03175 | + | 0.347021i | ||||
\(206\) | 2.48716 | + | 4.30789i | 0.173289 | + | 0.300145i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.526449 | + | 0.911836i | −0.0365027 | + | 0.0632245i | ||||
\(209\) | −39.1160 | −2.70571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.96592 | −0.686082 | −0.343041 | − | 0.939320i | \(-0.611457\pi\) | ||||
−0.343041 | + | 0.939320i | \(0.611457\pi\) | |||||||
\(212\) | 4.43682 | − | 7.68480i | 0.304722 | − | 0.527795i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.66965 | − | 6.35602i | −0.250852 | − | 0.434489i | ||||
\(215\) | 1.84377 | + | 5.48182i | 0.125744 | + | 0.373857i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5242 | + | 6.18138i | 1.05385 | + | 0.419619i | ||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.8753 | + | 2.80027i | 0.935473 | + | 0.188794i | ||||
\(221\) | 4.22804 | − | 2.44106i | 0.284408 | − | 0.164203i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.1087 | −0.743894 | −0.371947 | − | 0.928254i | \(-0.621310\pi\) | ||||
−0.371947 | + | 0.928254i | \(0.621310\pi\) | |||||||
\(224\) | 0.978745 | − | 2.45806i | 0.0653952 | − | 0.164236i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0922754 | + | 0.159826i | −0.00613807 | + | 0.0106314i | ||||
\(227\) | −20.3722 | + | 11.7619i | −1.35215 | + | 0.780665i | −0.988551 | − | 0.150889i | \(-0.951786\pi\) |
−0.363602 | + | 0.931555i | \(0.618453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.21579 | − | 4.74339i | −0.542915 | − | 0.313452i | 0.203345 | − | 0.979107i | \(-0.434819\pi\) |
−0.746259 | + | 0.665655i | \(0.768152\pi\) | |||||||
\(230\) | −11.8143 | − | 10.4194i | −0.779011 | − | 0.687032i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.98101i | − | 0.195713i | ||||||
\(233\) | −5.18669 | + | 8.98361i | −0.339791 | + | 0.588536i | −0.984393 | − | 0.175982i | \(-0.943690\pi\) |
0.644602 | + | 0.764518i | \(0.277023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8730 | + | 3.60708i | 1.16591 | + | 0.235300i | ||||
\(236\) | 0.452296 | − | 0.783400i | 0.0294420 | − | 0.0509950i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.62908 | + | 7.60149i | −0.624161 | + | 0.492732i | ||||
\(239\) | 12.3746i | 0.800444i | 0.916418 | + | 0.400222i | \(0.131067\pi\) | ||||
−0.916418 | + | 0.400222i | \(0.868933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8208 | + | 6.24737i | −0.697027 | + | 0.402429i | −0.806239 | − | 0.591590i | \(-0.798501\pi\) |
0.109212 | + | 0.994018i | \(0.465167\pi\) | |||||||
\(242\) | 14.5366 | + | 25.1781i | 0.934445 | + | 1.61851i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.1735i | 0.651289i | ||||||||
\(245\) | 1.40972 | + | 15.5889i | 0.0900640 | + | 0.995936i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.63436 | + | 3.25300i | 0.358506 | + | 0.206983i | ||||
\(248\) | 5.46948 | − | 3.15781i | 0.347312 | − | 0.200521i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.86076 | + | 10.0684i | 0.307421 | + | 0.636783i | ||||
\(251\) | 13.5304 | 0.854034 | 0.427017 | − | 0.904244i | \(-0.359564\pi\) | ||||
0.427017 | + | 0.904244i | \(0.359564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 44.5954i | − | 2.80369i | ||||||
\(254\) | 5.80476 | + | 3.35138i | 0.364223 | + | 0.210284i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.82609 | − | 2.20899i | −0.238665 | − | 0.137793i | 0.375898 | − | 0.926661i | \(-0.377334\pi\) |
−0.614563 | + | 0.788868i | \(0.710668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.32724 | + | 9.11056i | 0.0824709 | + | 0.566103i | ||||
\(260\) | −1.76575 | − | 1.55727i | −0.109507 | − | 0.0965777i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.24116 | − | 3.88180i | −0.138459 | − | 0.239819i | ||||
\(263\) | 3.06318 | + | 5.30558i | 0.188884 | + | 0.327156i | 0.944878 | − | 0.327422i | \(-0.106180\pi\) |
−0.755995 | + | 0.654578i | \(0.772846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.8815 | + | 13.1244i | 0.914162 | + | 0.806226i | ||||
\(266\) | −15.1887 | − | 6.04780i | −0.931278 | − | 0.370814i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.51497 | + | 4.91612i | 0.520135 | + | 0.300300i | ||||
\(269\) | 2.09370 | + | 3.62639i | 0.127655 | + | 0.221105i | 0.922768 | − | 0.385357i | \(-0.125922\pi\) |
−0.795113 | + | 0.606462i | \(0.792588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.253692 | + | 0.146469i | 0.0154107 | + | 0.00889737i | 0.507686 | − | 0.861542i | \(-0.330501\pi\) |
−0.492275 | + | 0.870440i | \(0.663835\pi\) | |||||||
\(272\) | 4.63684i | 0.281150i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.5627 | 1.06100 | ||||||||
\(275\) | −12.2757 | + | 29.1742i | −0.740253 | + | 1.75927i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6630 | − | 7.31099i | 0.760847 | − | 0.439275i | −0.0687531 | − | 0.997634i | \(-0.521902\pi\) |
0.829600 | + | 0.558359i | \(0.188569\pi\) | |||||||
\(278\) | −5.21579 | − | 3.01134i | −0.312822 | − | 0.180608i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.95481 | + | 3.23263i | 0.296106 | + | 0.193187i | ||||
\(281\) | − | 18.1691i | − | 1.08388i | −0.840419 | − | 0.541938i | \(-0.817691\pi\) | ||
0.840419 | − | 0.541938i | \(-0.182309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6066 | − | 18.3712i | −0.630499 | − | 1.09206i | −0.987450 | − | 0.157933i | \(-0.949517\pi\) |
0.356951 | − | 0.934123i | \(-0.383816\pi\) | |||||||
\(284\) | −12.4952 | + | 7.21412i | −0.741455 | + | 0.428079i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.66519i | − | 0.394121i | ||||||
\(287\) | −11.4265 | − | 14.4744i | −0.674486 | − | 0.854396i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.25013 | − | 3.89734i | 0.132361 | − | 0.229256i | ||||
\(290\) | 6.53401 | + | 1.31868i | 0.383690 | + | 0.0774353i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.18333 | − | 7.24574i | 0.244811 | − | 0.424025i | ||||
\(293\) | 7.64481i | 0.446615i | 0.974748 | + | 0.223307i | \(0.0716853\pi\) | ||||
−0.974748 | + | 0.223307i | \(0.928315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51704 | + | 1.33792i | 0.0883254 | + | 0.0778967i | ||||
\(296\) | 3.01361 | + | 1.73991i | 0.175163 | + | 0.101130i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.06548 | + | 3.50191i | −0.351364 | + | 0.202860i | ||||
\(299\) | −3.70868 | + | 6.42363i | −0.214479 | + | 0.371488i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.37124 | + | 4.24022i | −0.309593 | + | 0.244402i | ||||
\(302\) | 12.8708 | 0.740632 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.35129 | + | 3.08957i | −0.306917 | + | 0.177199i | ||||
\(305\) | −22.2990 | − | 4.50031i | −1.27683 | − | 0.257687i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1561 | −0.750859 | −0.375429 | − | 0.926851i | \(-0.622505\pi\) | ||||
−0.375429 | + | 0.926851i | \(0.622505\pi\) | |||||||
\(308\) | 2.41446 | + | 16.5735i | 0.137577 | + | 0.944365i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.50205 | + | 13.3853i | 0.255699 | + | 0.760234i | ||||
\(311\) | −3.13043 | − | 5.42207i | −0.177511 | − | 0.307457i | 0.763517 | − | 0.645788i | \(-0.223471\pi\) |
−0.941027 | + | 0.338331i | \(0.890138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.74065 | − | 15.1392i | 0.494051 | − | 0.855721i | −0.505926 | − | 0.862577i | \(-0.668849\pi\) |
0.999976 | + | 0.00685609i | \(0.00218238\pi\) | |||||||
\(314\) | 11.0439 | 0.623241 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.46566 | −0.307467 | ||||||||
\(317\) | 0.766906 | − | 1.32832i | 0.0430737 | − | 0.0746058i | −0.843685 | − | 0.536839i | \(-0.819618\pi\) |
0.886758 | + | 0.462233i | \(0.152952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.43540 | + | 16.3426i | 0.528281 | + | 0.915010i | ||||
\(320\) | 2.11940 | − | 0.712845i | 0.118478 | − | 0.0398492i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.89498 | − | 17.3163i | 0.384242 | − | 0.965002i | ||||
\(323\) | 28.6516 | 1.59422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.19443 | − | 3.18144i | 0.232665 | − | 0.176475i | ||||
\(326\) | 6.27500 | − | 3.62287i | 0.347540 | − | 0.200652i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.97007 | −0.384858 | ||||||||
\(329\) | 3.11011 | + | 21.3487i | 0.171466 | + | 1.17699i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.756607 | − | 1.31048i | 0.0415869 | − | 0.0720306i | −0.844483 | − | 0.535583i | \(-0.820092\pi\) |
0.886070 | + | 0.463552i | \(0.153425\pi\) | |||||||
\(332\) | −12.6697 | + | 7.31483i | −0.695337 | + | 0.401453i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0036 | + | 6.93030i | 0.656810 | + | 0.379209i | ||||
\(335\) | −14.5422 | + | 16.4891i | −0.794525 | + | 0.900894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.14064i | − | 0.171082i | −0.996335 | − | 0.0855408i | \(-0.972738\pi\) | ||
0.996335 | − | 0.0855408i | \(-0.0272618\pi\) | |||||||
\(338\) | 5.94570 | − | 10.2983i | 0.323404 | − | 0.560152i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.1634 | − | 2.05114i | −0.551186 | − | 0.111239i | ||||
\(341\) | −19.9900 | + | 34.6236i | −1.08252 | + | 1.87498i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8033 | + | 7.78771i | −0.907294 | + | 0.420497i | ||||
\(344\) | 2.58650i | 0.139455i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.830348 | − | 0.479402i | 0.0446398 | − | 0.0257728i | ||||
\(347\) | 13.7026 | + | 23.7336i | 0.735593 | + | 1.27408i | 0.954463 | + | 0.298330i | \(0.0964296\pi\) |
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5594i | 1.04699i | 0.852028 | + | 0.523496i | \(0.175373\pi\) | ||||
−0.852028 | + | 0.523496i | \(0.824627\pi\) | |||||||
\(350\) | −9.27732 | + | 9.43034i | −0.495894 | + | 0.504073i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.48223 | + | 3.16517i | 0.292204 | + | 0.168704i | ||||
\(353\) | 12.8261 | − | 7.40515i | 0.682664 | − | 0.394136i | −0.118194 | − | 0.992991i | \(-0.537710\pi\) |
0.800858 | + | 0.598854i | \(0.204377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2851 | − | 30.5792i | −0.545876 | − | 1.62298i | ||||
\(356\) | −3.83964 | −0.203500 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.3862i | 1.23600i | ||||||||
\(359\) | −14.3492 | − | 8.28450i | −0.757321 | − | 0.437239i | 0.0710122 | − | 0.997475i | \(-0.477377\pi\) |
−0.828333 | + | 0.560236i | \(0.810710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.59086 | + | 16.6119i | 0.504782 | + | 0.874308i | ||||
\(362\) | 16.7026 | + | 9.64324i | 0.877868 | + | 0.506837i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.03052 | − | 2.58809i | 0.0540138 | − | 0.135653i | ||||
\(365\) | 14.0312 | + | 12.3746i | 0.734429 | + | 0.647714i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00655 | + | 12.1357i | 0.365739 | + | 0.633479i | 0.988894 | − | 0.148619i | \(-0.0474829\pi\) |
−0.623155 | + | 0.782098i | \(0.714150\pi\) | |||||||
\(368\) | −3.52236 | − | 6.10091i | −0.183616 | − | 0.318032i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.14676 | + | 5.83580i | −0.267567 | + | 0.303389i | ||||
\(371\) | −8.68504 | + | 21.8120i | −0.450905 | + | 1.13242i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6630 | + | 7.31099i | 0.655666 | + | 0.378549i | 0.790624 | − | 0.612303i | \(-0.209757\pi\) |
−0.134958 | + | 0.990851i | \(0.543090\pi\) | |||||||
\(374\) | −14.6764 | − | 25.4202i | −0.758897 | − | 1.31445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.06176 | + | 4.07711i | 0.364182 | + | 0.210261i | ||||
\(377\) | − | 3.13870i | − | 0.161651i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.68145 | −0.240470 | −0.120235 | − | 0.992745i | \(-0.538365\pi\) | ||||
−0.120235 | + | 0.992745i | \(0.538365\pi\) | |||||||
\(380\) | −4.40476 | − | 13.0961i | −0.225960 | − | 0.671813i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.44949 | − | 1.41421i | 0.125327 | − | 0.0723575i | ||||
\(383\) | 10.1086 | + | 5.83621i | 0.516526 | + | 0.298216i | 0.735512 | − | 0.677511i | \(-0.236942\pi\) |
−0.218986 | + | 0.975728i | \(0.570275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −37.3952 | − | 2.03923i | −1.90584 | − | 0.103929i | ||||
\(386\) | 8.21725i | 0.418247i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.93946 | + | 5.09129i | 0.149228 | + | 0.258471i | ||||
\(389\) | 11.3452 | − | 6.55018i | 0.575226 | − | 0.332107i | −0.184008 | − | 0.982925i | \(-0.558907\pi\) |
0.759234 | + | 0.650818i | \(0.225574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.6652i | 1.65195i | ||||||||
\(392\) | −1.62493 | + | 6.80879i | −0.0820715 | + | 0.343896i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.75661 | + | 3.04253i | −0.0884966 | + | 0.153281i | ||||
\(395\) | 2.41778 | − | 11.9800i | 0.121652 | − | 0.602781i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3402 | + | 26.5700i | −0.769903 | + | 1.33351i | 0.167712 | + | 0.985836i | \(0.446362\pi\) |
−0.937615 | + | 0.347675i | \(0.886971\pi\) | |||||||
\(398\) | − | 3.46410i | − | 0.173640i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.624933 | + | 4.96079i | 0.0312467 | + | 0.248040i | ||||
\(401\) | 6.88085 | + | 3.97266i | 0.343613 | + | 0.198385i | 0.661869 | − | 0.749620i | \(-0.269764\pi\) |
−0.318255 | + | 0.948005i | \(0.603097\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.75880 | − | 3.32485i | 0.286866 | − | 0.165622i | ||||
\(404\) | 3.35408 | − | 5.80944i | 0.166872 | − | 0.289030i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.13699 | + | 7.80464i | 0.0564281 | + | 0.387338i | ||||
\(407\) | −22.0284 | −1.09191 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4957 | − | 19.9161i | 1.70570 | − | 0.984789i | 0.765975 | − | 0.642870i | \(-0.222256\pi\) |
0.939729 | − | 0.341919i | \(-0.111077\pi\) | |||||||
\(410\) | 3.08327 | − | 15.2775i | 0.152272 | − | 0.754503i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.97432 | −0.245067 | ||||||||
\(413\) | −0.885365 | + | 2.22354i | −0.0435660 | + | 0.109413i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4287 | − | 31.0061i | −0.511923 | − | 1.52203i | ||||
\(416\) | −0.526449 | − | 0.911836i | −0.0258113 | − | 0.0447064i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.5580 | − | 33.8754i | 0.956613 | − | 1.65690i | ||||
\(419\) | 11.0357 | 0.539131 | 0.269566 | − | 0.962982i | \(-0.413120\pi\) | ||||
0.269566 | + | 0.962982i | \(0.413120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.78421 | −0.379379 | −0.189690 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189690 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(422\) | 4.98296 | − | 8.63074i | 0.242567 | − | 0.420138i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.43682 | + | 7.68480i | 0.215471 | + | 0.373207i | ||||
\(425\) | 8.99170 | − | 21.3695i | 0.436161 | − | 1.03657i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.88028 | − | 26.6353i | −0.187780 | − | 1.28897i | ||||
\(428\) | 7.33930 | 0.354759 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.66928 | − | 1.14416i | −0.273397 | − | 0.0551762i | ||||
\(431\) | −8.86273 | + | 5.11690i | −0.426903 | + | 0.246472i | −0.698026 | − | 0.716072i | \(-0.745938\pi\) |
0.271124 | + | 0.962545i | \(0.412605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.3902 | 1.94103 | 0.970513 | − | 0.241047i | \(-0.0774909\pi\) | ||||
0.970513 | + | 0.241047i | \(0.0774909\pi\) | |||||||
\(434\) | −13.1153 | + | 10.3536i | −0.629555 | + | 0.496990i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | −37.6983 | + | 21.7651i | −1.80336 | + | 1.04117i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2331 | − | 6.48543i | −0.536126 | − | 0.309533i | 0.207381 | − | 0.978260i | \(-0.433506\pi\) |
−0.743508 | + | 0.668728i | \(0.766839\pi\) | |||||||
\(440\) | −9.36276 | + | 10.6162i | −0.446352 | + | 0.506109i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.88212i | 0.232219i | ||||||||
\(443\) | 4.32751 | − | 7.49547i | 0.205606 | − | 0.356120i | −0.744720 | − | 0.667378i | \(-0.767417\pi\) |
0.950326 | + | 0.311257i | \(0.100750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.69849 | − | 8.41601i | 0.0805164 | − | 0.398957i | ||||
\(446\) | 5.55435 | − | 9.62042i | 0.263006 | − | 0.455540i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.63937 | + | 2.07665i | 0.0774529 | + | 0.0981124i | ||||
\(449\) | − | 25.4407i | − | 1.20062i | −0.799768 | − | 0.600310i | \(-0.795044\pi\) | ||
0.799768 | − | 0.600310i | \(-0.204956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.2115 | − | 22.0614i | 1.79931 | − | 1.03883i | ||||
\(452\) | −0.0922754 | − | 0.159826i | −0.00434027 | − | 0.00751757i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.5238i | − | 1.10403i | ||||||
\(455\) | 5.21690 | + | 3.40363i | 0.244572 | + | 0.159565i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.4480 | + | 15.2697i | 1.23718 | + | 0.714289i | 0.968518 | − | 0.248945i | \(-0.0800837\pi\) |
0.268666 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(458\) | 8.21579 | − | 4.74339i | 0.383899 | − | 0.221644i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.9306 | − | 5.02179i | 0.696141 | − | 0.234142i | ||||
\(461\) | 15.6680 | 0.729734 | 0.364867 | − | 0.931060i | \(-0.381114\pi\) | ||||
0.364867 | + | 0.931060i | \(0.381114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0462i | 1.48931i | 0.667448 | + | 0.744656i | \(0.267387\pi\) | ||||
−0.667448 | + | 0.744656i | \(0.732613\pi\) | |||||||
\(464\) | 2.58163 | + | 1.49051i | 0.119849 | + | 0.0691950i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.18669 | − | 8.98361i | −0.240269 | − | 0.416158i | ||||
\(467\) | 0.605489 | + | 0.349579i | 0.0280187 | + | 0.0161766i | 0.513944 | − | 0.857824i | \(-0.328184\pi\) |
−0.485925 | + | 0.874000i | \(0.661517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.1682 | − | 9.62326i | −1.11599 | − | 0.444361i | ||||
\(470\) | −12.0603 | + | 13.6750i | −0.556302 | + | 0.630779i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.452296 | + | 0.783400i | 0.0208186 | + | 0.0360589i | ||||
\(473\) | −8.18669 | − | 14.1798i | −0.376424 | − | 0.651986i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.6534 | − | 3.86155i | 1.40647 | − | 0.177180i | ||||
\(476\) | −1.76855 | − | 12.1398i | −0.0810611 | − | 0.556426i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.7167 | − | 6.18728i | −0.490170 | − | 0.283000i | ||||
\(479\) | 4.27280 | + | 7.40071i | 0.195229 | + | 0.338147i | 0.946976 | − | 0.321305i | \(-0.104122\pi\) |
−0.751746 | + | 0.659452i | \(0.770788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.17302 | + | 1.83195i | 0.144677 | + | 0.0835295i | ||||
\(482\) | − | 12.4947i | − | 0.569120i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −29.0731 | −1.32151 | ||||||||
\(485\) | −12.4598 | + | 4.19075i | −0.565769 | + | 0.190292i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6268 | − | 11.9089i | 0.934689 | − | 0.539643i | 0.0463978 | − | 0.998923i | \(-0.485226\pi\) |
0.888292 | + | 0.459280i | \(0.151892\pi\) | |||||||
\(488\) | −8.81047 | − | 5.08673i | −0.398831 | − | 0.230265i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.2052 | − | 6.57357i | −0.641726 | − | 0.296964i | ||||
\(491\) | − | 12.9104i | − | 0.582638i | −0.956626 | − | 0.291319i | \(-0.905906\pi\) | ||
0.956626 | − | 0.291319i | \(-0.0940941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.91124 | − | 11.9706i | −0.311267 | − | 0.539129i | ||||
\(494\) | −5.63436 | + | 3.25300i | −0.253502 | + | 0.146359i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.31561i | 0.283579i | ||||||||
\(497\) | 29.9624 | − | 23.6532i | 1.34400 | − | 1.06099i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.16823 | − | 14.1478i | 0.365660 | − | 0.633342i | −0.623222 | − | 0.782045i | \(-0.714177\pi\) |
0.988882 | + | 0.148703i | \(0.0475099\pi\) | |||||||
\(500\) | −11.1499 | − | 0.824670i | −0.498638 | − | 0.0368804i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.76522 | + | 11.7177i | −0.301947 | + | 0.522987i | ||||
\(503\) | − | 28.3413i | − | 1.26368i | −0.775100 | − | 0.631838i | \(-0.782301\pi\) | ||
0.775100 | − | 0.631838i | \(-0.217699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2499 | + | 9.92158i | 0.500613 | + | 0.441505i | ||||
\(506\) | 38.6208 | + | 22.2977i | 1.71690 | + | 0.991254i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.80476 | + | 3.35138i | −0.257545 | + | 0.148693i | ||||
\(509\) | 1.18911 | − | 2.05959i | 0.0527062 | − | 0.0912898i | −0.838469 | − | 0.544950i | \(-0.816549\pi\) |
0.891175 | + | 0.453660i | \(0.149882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.18883 | + | 20.5658i | −0.362253 | + | 0.909776i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.82609 | − | 2.20899i | 0.168762 | − | 0.0974346i | ||||
\(515\) | 2.20043 | − | 10.9031i | 0.0969626 | − | 0.480448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.6189 | −2.27020 | ||||||||
\(518\) | −8.55360 | − | 3.40585i | −0.375824 | − | 0.149645i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.23151 | − | 0.750552i | 0.0978582 | − | 0.0329139i | ||||
\(521\) | −4.14185 | − | 7.17389i | −0.181458 | − | 0.314294i | 0.760919 | − | 0.648846i | \(-0.224748\pi\) |
−0.942377 | + | 0.334552i | \(0.891415\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.9308 | + | 36.2532i | −0.915239 | + | 1.58524i | −0.108689 | + | 0.994076i | \(0.534665\pi\) |
−0.806550 | + | 0.591166i | \(0.798668\pi\) | |||||||
\(524\) | 4.48232 | 0.195811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.12635 | −0.267122 | ||||||||
\(527\) | 14.6422 | − | 25.3611i | 0.637826 | − | 1.10475i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.3140 | − | 23.0606i | −0.578871 | − | 1.00263i | ||||
\(530\) | −18.8068 | + | 6.32553i | −0.816915 | + | 0.274764i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.8319 | − | 10.1299i | 0.556333 | − | 0.439186i | ||||
\(533\) | −7.33877 | −0.317877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.24660 | + | 16.0868i | −0.140363 | + | 0.695495i | ||||
\(536\) | −8.51497 | + | 4.91612i | −0.367791 | + | 0.212344i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.18740 | −0.180531 | ||||||||
\(539\) | −12.6427 | − | 42.4705i | −0.544559 | − | 1.82933i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9652 | + | 39.7769i | −0.987352 | + | 1.71014i | −0.356374 | + | 0.934343i | \(0.615987\pi\) |
−0.630978 | + | 0.775801i | \(0.717346\pi\) | |||||||
\(542\) | −0.253692 | + | 0.146469i | −0.0108970 | + | 0.00629139i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.01562 | − | 2.31842i | −0.172168 | − | 0.0994014i | ||||
\(545\) | −3.35408 | − | 2.95806i | −0.143673 | − | 0.126709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.88688i | − | 0.208948i | −0.994528 | − | 0.104474i | \(-0.966684\pi\) | ||
0.994528 | − | 0.104474i | \(-0.0333159\pi\) | |||||||
\(548\) | −8.78137 | + | 15.2098i | −0.375122 | + | 0.649730i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.1278 | − | 25.2182i | −0.815611 | − | 1.07531i | ||||
\(551\) | 9.21004 | − | 15.9523i | 0.392361 | − | 0.679589i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3097 | − | 2.08467i | 0.608511 | − | 0.0886490i | ||||
\(554\) | 14.6220i | 0.621229i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.21579 | − | 3.01134i | 0.221199 | − | 0.127709i | ||||
\(557\) | −14.6839 | − | 25.4332i | −0.622175 | − | 1.07764i | −0.989080 | − | 0.147380i | \(-0.952916\pi\) |
0.366905 | − | 0.930258i | \(-0.380417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.72332i | 0.115184i | ||||||||
\(560\) | −5.27694 | + | 2.67467i | −0.222992 | + | 0.113026i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.7349 | + | 9.08453i | 0.663735 | + | 0.383208i | ||||
\(563\) | −2.37223 | + | 1.36961i | −0.0999775 | + | 0.0577220i | −0.549155 | − | 0.835720i | \(-0.685050\pi\) |
0.449178 | + | 0.893442i | \(0.351717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.391137 | − | 0.131556i | 0.0164553 | − | 0.00553461i | ||||
\(566\) | 21.2133 | 0.891660 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 14.4282i | − | 0.605396i | ||||||
\(569\) | −0.798865 | − | 0.461225i | −0.0334902 | − | 0.0193356i | 0.483161 | − | 0.875531i | \(-0.339488\pi\) |
−0.516652 | + | 0.856196i | \(0.672822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2761 | + | 21.2629i | 0.513740 | + | 0.889824i | 0.999873 | + | 0.0159389i | \(0.00507372\pi\) |
−0.486133 | + | 0.873885i | \(0.661593\pi\) | |||||||
\(572\) | 5.77223 | + | 3.33260i | 0.241349 | + | 0.139343i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.2484 | − | 2.65847i | 0.761675 | − | 0.110962i | ||||
\(575\) | 4.40248 | + | 34.9474i | 0.183596 | + | 1.45741i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5667 | − | 23.4982i | −0.564788 | − | 0.978241i | −0.997069 | − | 0.0765024i | \(-0.975625\pi\) |
0.432282 | − | 0.901739i | \(-0.357709\pi\) | |||||||
\(578\) | 2.25013 | + | 3.89734i | 0.0935932 | + | 0.162108i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.40901 | + | 4.99928i | −0.183074 | + | 0.207584i | ||||
\(581\) | 30.3806 | − | 23.9834i | 1.26040 | − | 0.995000i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −48.6474 | − | 28.0866i | −2.01477 | − | 1.16323i | ||||
\(584\) | 4.18333 | + | 7.24574i | 0.173108 | + | 0.299831i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.62060 | − | 3.82240i | −0.273494 | − | 0.157902i | ||||
\(587\) | 8.71353i | 0.359646i | 0.983699 | + | 0.179823i | \(0.0575525\pi\) | ||||
−0.983699 | + | 0.179823i | \(0.942448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.0250 | 1.60800 | ||||||||
\(590\) | −1.91719 | + | 0.644834i | −0.0789296 | + | 0.0265474i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.01361 | + | 1.73991i | −0.123859 | + | 0.0715098i | ||||
\(593\) | 15.8211 | + | 9.13432i | 0.649695 | + | 0.375102i | 0.788339 | − | 0.615241i | \(-0.210941\pi\) |
−0.138644 | + | 0.990342i | \(0.544274\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.3912 | + | 1.49370i | 1.12293 | + | 0.0612355i | ||||
\(596\) | − | 7.00381i | − | 0.286887i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.70868 | − | 6.42363i | −0.151659 | − | 0.262682i | ||||
\(599\) | −9.94576 | + | 5.74219i | −0.406373 | + | 0.234619i | −0.689230 | − | 0.724543i | \(-0.742051\pi\) |
0.282857 | + | 0.959162i | \(0.408718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.4022i | − | 1.40329i | −0.712525 | − | 0.701647i | \(-0.752448\pi\) | ||
0.712525 | − | 0.701647i | \(-0.247552\pi\) | |||||||
\(602\) | −0.986520 | − | 6.77174i | −0.0402076 | − | 0.275996i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.43540 | + | 11.1464i | −0.261853 | + | 0.453543i | ||||
\(605\) | 12.8607 | − | 63.7247i | 0.522863 | − | 2.59078i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7564 | + | 39.4152i | −0.923653 | + | 1.59981i | −0.129941 | + | 0.991522i | \(0.541479\pi\) |
−0.793713 | + | 0.608293i | \(0.791855\pi\) | |||||||
\(608\) | − | 6.17914i | − | 0.250597i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0469 | − | 17.0613i | 0.609229 | − | 0.690792i | ||||
\(611\) | 7.43531 | + | 4.29278i | 0.300800 | + | 0.173667i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1361 | + | 5.85205i | −0.409391 | + | 0.236362i | −0.690528 | − | 0.723306i | \(-0.742622\pi\) |
0.281137 | + | 0.959668i | \(0.409289\pi\) | |||||||
\(614\) | 6.57805 | − | 11.3935i | 0.265469 | − | 0.459805i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.5603 | − | 6.19578i | −0.626944 | − | 0.249635i | ||||
\(617\) | −24.0582 | −0.968547 | −0.484273 | − | 0.874917i | \(-0.660916\pi\) | ||||
−0.484273 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.32794 | − | 1.92139i | 0.133761 | − | 0.0772271i | −0.431626 | − | 0.902053i | \(-0.642060\pi\) |
0.565387 | + | 0.824825i | \(0.308727\pi\) | |||||||
\(620\) | −13.8430 | − | 2.79376i | −0.555950 | − | 0.112200i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.26087 | 0.251038 | ||||||||
\(623\) | 10.0526 | − | 1.46448i | 0.402749 | − | 0.0586733i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.73981 | − | 24.0744i | 0.269593 | − | 0.962974i | ||||
\(626\) | 8.74065 | + | 15.1392i | 0.349347 | + | 0.605086i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.52193 | + | 9.56427i | −0.220349 | + | 0.381656i | ||||
\(629\) | 16.1353 | 0.643358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4387 | −1.01270 | −0.506349 | − | 0.862328i | \(-0.669005\pi\) | ||||
−0.506349 | + | 0.862328i | \(0.669005\pi\) | |||||||
\(632\) | 2.73283 | − | 4.73340i | 0.108706 | − | 0.188284i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.766906 | + | 1.32832i | 0.0304577 | + | 0.0527543i | ||||
\(635\) | −4.77803 | − | 14.2058i | −0.189610 | − | 0.563741i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.71089 | + | 7.16896i | −0.0677879 | + | 0.284044i | ||||
\(638\) | −18.8708 | −0.747102 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.442358 | + | 2.19188i | −0.0174857 | + | 0.0866415i | ||||
\(641\) | 34.2380 | − | 19.7673i | 1.35232 | − | 0.780762i | 0.363745 | − | 0.931499i | \(-0.381498\pi\) |
0.988574 | + | 0.150737i | \(0.0481647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2816 | 0.484341 | 0.242170 | − | 0.970234i | \(-0.422141\pi\) | ||||
0.242170 | + | 0.970234i | \(0.422141\pi\) | |||||||
\(644\) | 11.5489 | + | 14.6294i | 0.455090 | + | 0.576479i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.3258 | + | 24.8131i | −0.563642 | + | 0.976257i | ||||
\(647\) | −11.5956 | + | 6.69470i | −0.455869 | + | 0.263196i | −0.710306 | − | 0.703893i | \(-0.751443\pi\) |
0.254437 | + | 0.967089i | \(0.418110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.95918 | − | 2.86319i | −0.194665 | − | 0.112390i | ||||
\(650\) | 0.657991 | + | 5.22321i | 0.0258085 | + | 0.204871i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.24574i | 0.283765i | ||||||||
\(653\) | −24.7888 | + | 42.9355i | −0.970062 | + | 1.68020i | −0.274710 | + | 0.961527i | \(0.588582\pi\) |
−0.695352 | + | 0.718670i | \(0.744751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.98279 | + | 9.82469i | −0.0774741 | + | 0.383883i | ||||
\(656\) | 3.48504 | − | 6.03626i | 0.136068 | − | 0.235676i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.0435 | − | 7.98090i | −0.781379 | − | 0.311128i | ||||
\(659\) | 40.7622i | 1.58787i | 0.608002 | + | 0.793936i | \(0.291971\pi\) | ||||
−0.608002 | + | 0.793936i | \(0.708029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9652 | + | 17.8778i | −1.20441 | + | 0.695365i | −0.961532 | − | 0.274692i | \(-0.911424\pi\) |
−0.242875 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(662\) | 0.756607 | + | 1.31048i | 0.0294064 | + | 0.0509333i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.6297i | − | 0.567741i | ||||||
\(665\) | 16.5272 | + | 32.6069i | 0.640896 | + | 1.26444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1869 | + | 10.5002i | 0.704199 | + | 0.406569i | ||||
\(668\) | −12.0036 | + | 6.93030i | −0.464435 | + | 0.268141i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.00886 | − | 20.8384i | −0.270776 | − | 0.805059i | ||||
\(671\) | 64.4014 | 2.48619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1987i | 1.35681i | 0.734687 | + | 0.678406i | \(0.237329\pi\) | ||||
−0.734687 | + | 0.678406i | \(0.762671\pi\) | |||||||
\(674\) | 2.71987 | + | 1.57032i | 0.104766 | + | 0.0604865i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.94570 | + | 10.2983i | 0.228681 | + | 0.396087i | ||||
\(677\) | 33.2919 | + | 19.2211i | 1.27951 | + | 0.738727i | 0.976759 | − | 0.214341i | \(-0.0687605\pi\) |
0.302754 | + | 0.953069i | \(0.402094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.63771 | − | 12.2084i | −0.369862 | − | 0.468517i | ||||
\(680\) | 6.85803 | − | 7.77617i | 0.262993 | − | 0.298202i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.9900 | − | 34.6236i | −0.765455 | − | 1.32581i | ||||
\(683\) | −19.2012 | − | 33.2574i | −0.734712 | − | 1.27256i | −0.954850 | − | 0.297089i | \(-0.903984\pi\) |
0.220138 | − | 0.975469i | \(-0.429349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.4534 | − | 25.9758i | −1.12536 | − | 0.992486i | ||||
\(686\) | 1.65731 | − | 18.4460i | 0.0632764 | − | 0.704270i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.23997 | − | 1.29325i | −0.0853981 | − | 0.0493046i | ||||
\(689\) | 4.67152 | + | 8.09131i | 0.177971 | + | 0.308254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6209 | + | 10.1735i | 0.670332 | + | 0.387016i | 0.796203 | − | 0.605030i | \(-0.206839\pi\) |
−0.125870 | + | 0.992047i | \(0.540172\pi\) | |||||||
\(692\) | 0.958803i | 0.0364482i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.4052 | −1.04029 | ||||||||
\(695\) | 4.29323 | + | 12.7645i | 0.162852 | + | 0.484183i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.9892 | + | 16.1595i | −1.06016 | + | 0.612086i | ||||
\(698\) | −16.9390 | − | 9.77972i | −0.641149 | − | 0.370168i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.52825 | − | 12.7496i | −0.133355 | − | 0.481888i | ||||
\(701\) | − | 6.98574i | − | 0.263848i | −0.991260 | − | 0.131924i | \(-0.957885\pi\) | ||
0.991260 | − | 0.131924i | \(-0.0421154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7511 | + | 18.6215i | 0.405487 | + | 0.702323i | ||||
\(704\) | −5.48223 | + | 3.16517i | −0.206619 | + | 0.119292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8103i | 0.557393i | ||||||||
\(707\) | −6.56558 | + | 16.4891i | −0.246924 | + | 0.620135i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.01348 | + | 10.4157i | −0.225841 | + | 0.391168i | −0.956571 | − | 0.291498i | \(-0.905846\pi\) |
0.730730 | + | 0.682666i | \(0.239180\pi\) | |||||||
\(710\) | 31.6249 | + | 6.38245i | 1.18686 | + | 0.239529i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.91982 | − | 3.32522i | 0.0719482 | − | 0.124618i | ||||
\(713\) | 44.4917i | 1.66623i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.85803 | + | 11.1778i | −0.368669 | + | 0.418026i | ||||
\(716\) | −20.2531 | − | 11.6931i | −0.756893 | − | 0.436992i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.3492 | − | 8.28450i | 0.535507 | − | 0.309175i | ||||
\(719\) | −0.835694 | + | 1.44746i | −0.0311661 | + | 0.0539813i | −0.881188 | − | 0.472766i | \(-0.843255\pi\) |
0.850022 | + | 0.526748i | \(0.176589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0233 | − | 1.89727i | 0.485015 | − | 0.0706579i | ||||
\(722\) | −19.1817 | −0.713869 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.7026 | + | 9.64324i | −0.620746 | + | 0.358388i | ||||
\(725\) | −9.00744 | − | 11.8755i | −0.334528 | − | 0.441044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.5043 | 1.57640 | 0.788198 | − | 0.615422i | \(-0.211014\pi\) | ||||
0.788198 | + | 0.615422i | \(0.211014\pi\) | |||||||
\(728\) | 1.72609 | + | 2.18650i | 0.0639731 | + | 0.0810370i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7323 | + | 5.96413i | −0.656302 | + | 0.220742i | ||||
\(731\) | 5.99658 | + | 10.3864i | 0.221792 | + | 0.384154i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.9379 | − | 27.6053i | 0.588681 | − | 1.01963i | −0.405724 | − | 0.913996i | \(-0.632981\pi\) |
0.994405 | − | 0.105630i | \(-0.0336860\pi\) | |||||||
\(734\) | −14.0131 | −0.517233 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.04472 | 0.259672 | ||||||||
\(737\) | 31.1207 | − | 53.9026i | 1.14634 | − | 1.98553i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.20932 | − | 14.2190i | −0.301985 | − | 0.523053i | 0.674601 | − | 0.738183i | \(-0.264316\pi\) |
−0.976585 | + | 0.215130i | \(0.930982\pi\) | |||||||
\(740\) | −2.48057 | − | 7.37512i | −0.0911875 | − | 0.271115i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.5472 | − | 18.4274i | −0.534044 | − | 0.676493i | ||||
\(743\) | −4.52385 | −0.165964 | −0.0829821 | − | 0.996551i | \(-0.526444\pi\) | ||||
−0.0829821 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3515 | + | 3.09819i | 0.562435 | + | 0.113509i | ||||
\(746\) | −12.6630 | + | 7.31099i | −0.463626 | + | 0.267674i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29.3527 | 1.07324 | ||||||||
\(749\) | −19.2151 | + | 2.79930i | −0.702106 | + | 0.102284i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.69875 | − | 15.0667i | 0.317422 | − | 0.549791i | −0.662527 | − | 0.749038i | \(-0.730516\pi\) |
0.979949 | + | 0.199247i | \(0.0638495\pi\) | |||||||
\(752\) | −7.06176 | + | 4.07711i | −0.257516 | + | 0.148677i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.71820 | + | 1.56935i | 0.0989908 | + | 0.0571524i | ||||
\(755\) | −21.5849 | − | 19.0363i | −0.785554 | − | 0.692803i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.25454i | − | 0.190980i | −0.995430 | − | 0.0954898i | \(-0.969558\pi\) | ||
0.995430 | − | 0.0954898i | \(-0.0304417\pi\) | |||||||
\(758\) | 2.34072 | − | 4.05425i | 0.0850189 | − | 0.147257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.5439 | + | 2.73339i | 0.491289 | + | 0.0991505i | ||||
\(761\) | −7.31402 | + | 12.6683i | −0.265133 | + | 0.459224i | −0.967598 | − | 0.252494i | \(-0.918749\pi\) |
0.702465 | + | 0.711718i | \(0.252083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.95749 | − | 4.91612i | 0.0708659 | − | 0.177975i | ||||
\(764\) | 2.82843i | 0.102329i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1086 | + | 5.83621i | −0.365239 | + | 0.210871i | ||||
\(767\) | 0.476222 | + | 0.824840i | 0.0171954 | + | 0.0297832i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.4548i | − | 0.449131i | −0.974459 | − | 0.224566i | \(-0.927904\pi\) | ||
0.974459 | − | 0.224566i | \(-0.0720963\pi\) | |||||||
\(770\) | 20.4636 | − | 31.3656i | 0.737458 | − | 1.13034i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.11634 | − | 4.10862i | −0.256123 | − | 0.147873i | ||||
\(773\) | −7.19300 | + | 4.15288i | −0.258714 | + | 0.149369i | −0.623748 | − | 0.781626i | \(-0.714391\pi\) |
0.365034 | + | 0.930994i | \(0.381057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.2472 | − | 29.1064i | 0.439931 | − | 1.04553i | ||||
\(776\) | −5.87891 | −0.211041 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1004i | 0.469670i | ||||||||
\(779\) | −37.2989 | − | 21.5345i | −1.33637 | − | 0.771554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.6678 | + | 79.0990i | 1.63412 | + | 2.83038i | ||||
\(782\) | −28.2889 | − | 16.3326i | −1.01161 | − | 0.584053i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.08412 | − | 4.81163i | −0.181576 | − | 0.171844i | ||||
\(785\) | −18.5210 | − | 16.3342i | −0.661043 | − | 0.582993i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.3036 | − | 43.8271i | −0.901975 | − | 1.56227i | −0.824927 | − | 0.565239i | \(-0.808784\pi\) |
−0.0770479 | − | 0.997027i | \(-0.524549\pi\) | |||||||
\(788\) | −1.75661 | − | 3.04253i | −0.0625765 | − | 0.108386i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.16613 | + | 8.08388i | 0.326116 | + | 0.287611i | ||||
\(791\) | 0.302547 | + | 0.383247i | 0.0107573 | + | 0.0136267i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.27652 | − | 5.35580i | −0.329419 | − | 0.190190i | ||||
\(794\) | −15.3402 | − | 26.5700i | −0.544404 | − | 0.942935i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | + | 1.73205i | 0.106332 | + | 0.0613909i | ||||
\(797\) | 36.6354i | 1.29769i | 0.760920 | + | 0.648846i | \(0.224748\pi\) | ||||
−0.760920 | + | 0.648846i | \(0.775252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.8098 | 1.33761 | ||||||||
\(800\) | −4.60864 | − | 1.93919i | −0.162940 | − | 0.0685606i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.88085 | + | 3.97266i | −0.242971 | + | 0.140280i | ||||
\(803\) | −45.8680 | − | 26.4819i | −1.61865 | − | 0.934525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.1746 | + | 18.8423i | −1.31023 | + | 0.664104i | ||||
\(806\) | 6.64969i | 0.234225i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.35408 | + | 5.80944i | 0.117996 | + | 0.204375i | ||||
\(809\) | 37.7055 | − | 21.7693i | 1.32566 | − | 0.765368i | 0.341031 | − | 0.940052i | \(-0.389224\pi\) |
0.984624 | + | 0.174685i | \(0.0558906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8915i | 0.487795i | 0.969801 | + | 0.243897i | \(0.0784260\pi\) | ||||
−0.969801 | + | 0.243897i | \(0.921574\pi\) | |||||||
\(812\) | −7.32751 | − | 2.91765i | −0.257145 | − | 0.102390i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.0142 | − | 19.0772i | 0.386048 | − | 0.668654i | ||||
\(815\) | −15.8818 | − | 3.20521i | −0.556314 | − | 0.112274i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.99115 | + | 13.8411i | −0.279575 | + | 0.484238i | ||||
\(818\) | 39.8323i | 1.39270i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.6891 | + | 10.3090i | 0.408201 | + | 0.360004i | ||||
\(821\) | −8.26634 | − | 4.77257i | −0.288497 | − | 0.166564i | 0.348767 | − | 0.937210i | \(-0.386601\pi\) |
−0.637264 | + | 0.770646i | \(0.719934\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.34957 | + | 5.39798i | −0.325905 | + | 0.188162i | −0.654022 | − | 0.756476i | \(-0.726920\pi\) |
0.328116 | + | 0.944637i | \(0.393586\pi\) | |||||||
\(824\) | 2.48716 | − | 4.30789i | 0.0866444 | − | 0.150072i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.48296 | − | 1.87852i | −0.0515988 | − | 0.0653621i | ||||
\(827\) | 10.5599 | 0.367204 | 0.183602 | − | 0.983001i | \(-0.441224\pi\) | ||||
0.183602 | + | 0.983001i | \(0.441224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.7288 | + | 17.7413i | −1.06726 | + | 0.616181i | −0.927431 | − | 0.373995i | \(-0.877988\pi\) |
−0.139826 | + | 0.990176i | \(0.544654\pi\) | |||||||
\(830\) | 32.0664 | + | 6.47155i | 1.11304 | + | 0.224631i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.05290 | 0.0365027 | ||||||||
\(833\) | 9.26051 | + | 31.1088i | 0.320858 | + | 1.07786i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.88046 | − | 29.3762i | −0.341927 | − | 1.01660i | ||||
\(836\) | 19.5580 | + | 33.8754i | 0.676427 | + | 1.17161i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.51787 | + | 9.55723i | −0.190612 | + | 0.330149i | ||||
\(839\) | −32.5932 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.1136 | 0.693571 | ||||||||
\(842\) | 3.89211 | − | 6.74132i | 0.134131 | − | 0.232321i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.98296 | + | 8.63074i | 0.171521 | + | 0.297082i | ||||
\(845\) | −25.2026 | + | 8.47672i | −0.866997 | + | 0.291608i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 76.1168 | − | 11.0888i | 2.61540 | − | 0.381017i | ||||
\(848\) | −8.87365 | −0.304722 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.0107 | + | 18.4718i | 0.480563 | + | 0.633577i | ||||
\(851\) | −21.2300 | + | 12.2572i | −0.727756 | + | 0.420170i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.2310 | −0.692695 | −0.346347 | − | 0.938106i | \(-0.612578\pi\) | ||||
−0.346347 | + | 0.938106i | \(0.612578\pi\) | |||||||
\(854\) | 25.0070 | + | 9.95722i | 0.855721 | + | 0.340729i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.66965 | + | 6.35602i | −0.125426 | + | 0.217244i | ||||
\(857\) | 38.9461 | − | 22.4855i | 1.33037 | − | 0.768091i | 0.345016 | − | 0.938597i | \(-0.387874\pi\) |
0.985357 | + | 0.170506i | \(0.0545402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.8490 | − | 21.8521i | −1.29139 | − | 0.745585i | −0.312490 | − | 0.949921i | \(-0.601163\pi\) |
−0.978901 | + | 0.204336i | \(0.934496\pi\) | |||||||
\(860\) | 3.82551 | − | 4.33766i | 0.130449 | − | 0.147913i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 10.2338i | − | 0.348565i | ||||||
\(863\) | 17.8191 | − | 30.8636i | 0.606569 | − | 1.05061i | −0.385233 | − | 0.922819i | \(-0.625879\pi\) |
0.991801 | − | 0.127788i | \(-0.0407878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.10158 | − | 0.424134i | −0.0714558 | − | 0.0144210i | ||||
\(866\) | −20.1951 | + | 34.9789i | −0.686257 | + | 1.18863i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.40885 | − | 16.5350i | −0.0817617 | − | 0.561235i | ||||
\(869\) | 34.5994i | 1.17371i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.96539 | + | 5.17617i | −0.303781 | + | 0.175388i | ||||
\(872\) | −1.00000 | − | 1.73205i | −0.0338643 | − | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 43.5303i | − | 1.47243i | ||||||
\(875\) | 29.5062 | − | 2.09362i | 0.997492 | − | 0.0707772i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.6018 | + | 18.2453i | 1.06712 | + | 0.616100i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(878\) | 11.2331 | − | 6.48543i | 0.379099 | − | 0.218873i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.51254 | − | 13.4165i | −0.152118 | − | 0.452270i | ||||
\(881\) | 0.487935 | 0.0164390 | 0.00821948 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821948 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.26720i | 0.210908i | 0.994424 | + | 0.105454i | \(0.0336296\pi\) | ||||
−0.994424 | + | 0.105454i | \(0.966370\pi\) | |||||||
\(884\) | −4.22804 | − | 2.44106i | −0.142204 | − | 0.0821017i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.32751 | + | 7.49547i | 0.145386 | + | 0.251815i | ||||
\(887\) | 49.2939 | + | 28.4598i | 1.65513 | + | 0.955588i | 0.974917 | + | 0.222571i | \(0.0714448\pi\) |
0.680210 | + | 0.733017i | \(0.261888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.9193 | − | 10.9883i | 0.466838 | − | 0.368536i | ||||
\(890\) | 6.43923 | + | 5.67894i | 0.215843 | + | 0.190359i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.55435 | + | 9.62042i | 0.185973 | + | 0.322115i | ||||
\(893\) | 25.1930 | + | 43.6356i | 0.843052 | + | 1.46021i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.5890 | − | 39.2197i | 1.15618 | − | 1.31097i | ||||
\(896\) | −2.61811 | + | 0.381412i | −0.0874651 | + | 0.0127421i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.0323 | + | 12.7203i | 0.735226 | + | 0.424483i | ||||
\(899\) | −9.41346 | − | 16.3046i | −0.313957 | − | 0.543789i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.6332 | + | 20.5728i | 1.18711 | + | 0.685380i | ||||
\(902\) | 44.1229i | 1.46913i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.184551 | 0.00613807 | ||||||||
\(905\) | −13.7483 | − | 40.8757i | −0.457008 | − | 1.35876i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.4285 | + | 8.33031i | −0.479091 | + | 0.276603i | −0.720038 | − | 0.693935i | \(-0.755876\pi\) |
0.240946 | + | 0.970538i | \(0.422542\pi\) | |||||||
\(908\) | 20.3722 | + | 11.7619i | 0.676076 | + | 0.390333i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.55608 | + | 2.81616i | −0.184182 | + | 0.0933547i | ||||
\(911\) | 8.02653i | 0.265931i | 0.991121 | + | 0.132965i | \(0.0424499\pi\) | ||||
−0.991121 | + | 0.132965i | \(0.957550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.3053 | + | 80.2031i | 1.53248 | + | 2.65434i | ||||
\(914\) | −26.4480 | + | 15.2697i | −0.874821 | + | 0.505078i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.48678i | 0.313452i | ||||||||
\(917\) | −11.7352 | + | 1.70961i | −0.387532 | + | 0.0564563i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.85733 | + | 11.8772i | −0.226202 | + | 0.391794i | −0.956680 | − | 0.291143i | \(-0.905964\pi\) |
0.730477 | + | 0.682937i | \(0.239298\pi\) | |||||||
\(920\) | −3.11629 | + | 15.4411i | −0.102741 | + | 0.509080i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.83402 | + | 13.5689i | −0.258000 | + | 0.446869i | ||||
\(923\) | − | 15.1915i | − | 0.500033i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.2626 | − | 2.17465i | 0.567592 | − | 0.0715022i | ||||
\(926\) | −27.7528 | − | 16.0231i | −0.912014 | − | 0.526551i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.58163 | + | 1.49051i | −0.0847463 | + | 0.0489283i | ||||
\(929\) | −22.9480 | + | 39.7470i | −0.752898 | + | 1.30406i | 0.193515 | + | 0.981097i | \(0.438011\pi\) |
−0.946413 | + | 0.322960i | \(0.895322\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.7317 | + | 31.4154i | −0.974417 | + | 1.02960i | ||||
\(932\) | 10.3734 | 0.339791 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.605489 | + | 0.349579i | −0.0198122 | + | 0.0114386i | ||||
\(935\) | −12.9844 | + | 64.3375i | −0.424636 | + | 2.10406i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.17552 | 0.201746 | 0.100873 | − | 0.994899i | \(-0.467836\pi\) | ||||
0.100873 | + | 0.994899i | \(0.467836\pi\) | |||||||
\(938\) | 20.4181 | − | 16.1187i | 0.666675 | − | 0.526293i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.81269 | − | 17.2820i | −0.189589 | − | 0.563678i | ||||
\(941\) | 16.7048 | + | 28.9335i | 0.544560 | + | 0.943206i | 0.998634 | + | 0.0522424i | \(0.0166368\pi\) |
−0.454074 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5511 | − | 42.5237i | 0.799494 | − | 1.38476i | ||||
\(944\) | −0.904592 | −0.0294420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3734 | 0.532345 | ||||||||
\(947\) | 3.27683 | − | 5.67563i | 0.106483 | − | 0.184433i | −0.807860 | − | 0.589374i | \(-0.799375\pi\) |
0.914343 | + | 0.404941i | \(0.132708\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.40462 | + | 7.62903i | 0.142980 | + | 0.247649i | ||||
\(950\) | −11.9825 | + | 28.4774i | −0.388764 | + | 0.923929i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.3976 | + | 4.53828i | 0.369399 | + | 0.147087i | ||||
\(953\) | −46.5253 | −1.50710 | −0.753551 | − | 0.657389i | \(-0.771661\pi\) | ||||
−0.753551 | + | 0.657389i | \(0.771661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.19956 | − | 1.25118i | −0.200613 | − | 0.0404872i | ||||
\(956\) | 10.7167 | − | 6.18728i | 0.346602 | − | 0.200111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.54561 | −0.276096 | ||||||||
\(959\) | 17.1894 | − | 43.1703i | 0.555076 | − | 1.39404i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.44349 | − | 7.69635i | 0.143338 | − | 0.248269i | ||||
\(962\) | −3.17302 | + | 1.83195i | −0.102302 | + | 0.0590643i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8208 | + | 6.24737i | 0.348514 | + | 0.201214i | ||||
\(965\) | 12.1536 | − | 13.7807i | 0.391237 | − | 0.443615i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.93169i | − | 0.190750i | −0.995441 | − | 0.0953752i | \(-0.969595\pi\) | ||
0.995441 | − | 0.0953752i | \(-0.0304051\pi\) | |||||||
\(968\) | 14.5366 | − | 25.1781i | 0.467223 | − | 0.809253i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.60059 | − | 12.8859i | 0.0834998 | − | 0.413740i | ||||
\(971\) | 0.170069 | − | 0.294568i | 0.00545777 | − | 0.00945314i | −0.863284 | − | 0.504719i | \(-0.831596\pi\) |
0.868741 | + | 0.495266i | \(0.164929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5070 | + | 9.87339i | −0.400955 | + | 0.316526i | ||||
\(974\) | 23.8178i | 0.763171i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.81047 | − | 5.08673i | 0.282016 | − | 0.162822i | ||||
\(977\) | 10.3443 | + | 17.9168i | 0.330943 | + | 0.573210i | 0.982697 | − | 0.185220i | \(-0.0592999\pi\) |
−0.651754 | + | 0.758430i | \(0.725967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3062i | 0.776829i | ||||||||
\(980\) | 12.7955 | − | 9.01529i | 0.408737 | − | 0.287983i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.1807 | + | 6.45520i | 0.356791 | + | 0.205994i | ||||
\(983\) | 18.3821 | − | 10.6129i | 0.586297 | − | 0.338499i | −0.177335 | − | 0.984151i | \(-0.556748\pi\) |
0.763632 | + | 0.645652i | \(0.223414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.44590 | − | 2.50438i | 0.237246 | − | 0.0797960i | ||||
\(986\) | 13.8225 | 0.440197 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 6.50600i | − | 0.206983i | ||||||
\(989\) | −15.7800 | − | 9.11057i | −0.501774 | − | 0.289699i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1034 | − | 50.4085i | −0.924499 | − | 1.60128i | −0.792365 | − | 0.610048i | \(-0.791150\pi\) |
−0.132134 | − | 0.991232i | \(-0.542183\pi\) | |||||||
\(992\) | −5.46948 | − | 3.15781i | −0.173656 | − | 0.100260i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.50310 | + | 37.7748i | 0.174548 | + | 1.19814i | ||||
\(995\) | −5.12351 | + | 5.80944i | −0.162426 | + | 0.184172i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.1416 | − | 33.1542i | −0.606220 | − | 1.05000i | −0.991857 | − | 0.127354i | \(-0.959352\pi\) |
0.385637 | − | 0.922651i | \(-0.373982\pi\) | |||||||
\(998\) | 8.16823 | + | 14.1478i | 0.258561 | + | 0.447841i | ||||
\(999\) | 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 | 630.2.bo.a.89.8 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.b.89.1 | yes | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1601.3 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1601.16 | 32 | |||
5.4 | even | 2 | 630.2.bo.b.89.3 | yes | 16 | ||
7.2 | even | 3 | 4410.2.d.b.4409.5 | 16 | |||
7.3 | odd | 6 | inner | 630.2.bo.a.269.6 | yes | 16 | |
7.5 | odd | 6 | 4410.2.d.b.4409.12 | 16 | |||
15.2 | even | 4 | 3150.2.bf.f.1601.15 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1601.4 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.a.89.6 | ✓ | 16 | |
21.2 | odd | 6 | 4410.2.d.a.4409.12 | 16 | |||
21.5 | even | 6 | 4410.2.d.a.4409.5 | 16 | |||
21.17 | even | 6 | 630.2.bo.b.269.3 | yes | 16 | ||
35.3 | even | 12 | 3150.2.bf.f.1151.4 | 32 | |||
35.9 | even | 6 | 4410.2.d.a.4409.6 | 16 | |||
35.17 | even | 12 | 3150.2.bf.f.1151.13 | 32 | |||
35.19 | odd | 6 | 4410.2.d.a.4409.11 | 16 | |||
35.24 | odd | 6 | 630.2.bo.b.269.1 | yes | 16 | ||
105.17 | odd | 12 | 3150.2.bf.f.1151.3 | 32 | |||
105.38 | odd | 12 | 3150.2.bf.f.1151.14 | 32 | |||
105.44 | odd | 6 | 4410.2.d.b.4409.11 | 16 | |||
105.59 | even | 6 | inner | 630.2.bo.a.269.8 | yes | 16 | |
105.89 | even | 6 | 4410.2.d.b.4409.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.6 | ✓ | 16 | 15.14 | odd | 2 | inner | |
630.2.bo.a.89.8 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.a.269.6 | yes | 16 | 7.3 | odd | 6 | inner | |
630.2.bo.a.269.8 | yes | 16 | 105.59 | even | 6 | inner | |
630.2.bo.b.89.1 | yes | 16 | 3.2 | odd | 2 | ||
630.2.bo.b.89.3 | yes | 16 | 5.4 | even | 2 | ||
630.2.bo.b.269.1 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bo.b.269.3 | yes | 16 | 21.17 | even | 6 | ||
3150.2.bf.f.1151.3 | 32 | 105.17 | odd | 12 | |||
3150.2.bf.f.1151.4 | 32 | 35.3 | even | 12 | |||
3150.2.bf.f.1151.13 | 32 | 35.17 | even | 12 | |||
3150.2.bf.f.1151.14 | 32 | 105.38 | odd | 12 | |||
3150.2.bf.f.1601.3 | 32 | 5.2 | odd | 4 | |||
3150.2.bf.f.1601.4 | 32 | 15.8 | even | 4 | |||
3150.2.bf.f.1601.15 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1601.16 | 32 | 5.3 | odd | 4 | |||
4410.2.d.a.4409.5 | 16 | 21.5 | even | 6 | |||
4410.2.d.a.4409.6 | 16 | 35.9 | even | 6 | |||
4410.2.d.a.4409.11 | 16 | 35.19 | odd | 6 | |||
4410.2.d.a.4409.12 | 16 | 21.2 | odd | 6 | |||
4410.2.d.b.4409.5 | 16 | 7.2 | even | 3 | |||
4410.2.d.b.4409.6 | 16 | 105.89 | even | 6 | |||
4410.2.d.b.4409.11 | 16 | 105.44 | odd | 6 | |||
4410.2.d.b.4409.12 | 16 | 7.5 | odd | 6 |