Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.38 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.663063 | 0.468856 | 0.234428 | − | 0.972133i | \(-0.424678\pi\) | ||||
0.234428 | + | 0.972133i | \(0.424678\pi\) | |||||||
\(3\) | −2.54639 | −1.47016 | −0.735081 | − | 0.677979i | \(-0.762856\pi\) | ||||
−0.735081 | + | 0.677979i | \(0.762856\pi\) | |||||||
\(4\) | −1.56035 | −0.780174 | ||||||||
\(5\) | −2.36647 | −1.05832 | −0.529159 | − | 0.848523i | \(-0.677492\pi\) | ||||
−0.529159 | + | 0.848523i | \(0.677492\pi\) | |||||||
\(6\) | −1.68842 | −0.689295 | ||||||||
\(7\) | −2.65587 | −1.00382 | −0.501912 | − | 0.864919i | \(-0.667370\pi\) | ||||
−0.501912 | + | 0.864919i | \(0.667370\pi\) | |||||||
\(8\) | −2.36073 | −0.834646 | ||||||||
\(9\) | 3.48413 | 1.16138 | ||||||||
\(10\) | −1.56912 | −0.496199 | ||||||||
\(11\) | −4.08058 | −1.23034 | −0.615171 | − | 0.788394i | \(-0.710913\pi\) | ||||
−0.615171 | + | 0.788394i | \(0.710913\pi\) | |||||||
\(12\) | 3.97326 | 1.14698 | ||||||||
\(13\) | 4.38872 | 1.21721 | 0.608606 | − | 0.793473i | \(-0.291729\pi\) | ||||
0.608606 | + | 0.793473i | \(0.291729\pi\) | |||||||
\(14\) | −1.76101 | −0.470649 | ||||||||
\(15\) | 6.02597 | 1.55590 | ||||||||
\(16\) | 1.55538 | 0.388845 | ||||||||
\(17\) | −3.17585 | −0.770257 | −0.385128 | − | 0.922863i | \(-0.625843\pi\) | ||||
−0.385128 | + | 0.922863i | \(0.625843\pi\) | |||||||
\(18\) | 2.31020 | 0.544518 | ||||||||
\(19\) | −2.20707 | −0.506337 | −0.253168 | − | 0.967422i | \(-0.581473\pi\) | ||||
−0.253168 | + | 0.967422i | \(0.581473\pi\) | |||||||
\(20\) | 3.69252 | 0.825672 | ||||||||
\(21\) | 6.76289 | 1.47578 | ||||||||
\(22\) | −2.70568 | −0.576853 | ||||||||
\(23\) | 4.41820 | 0.921259 | 0.460629 | − | 0.887593i | \(-0.347624\pi\) | ||||
0.460629 | + | 0.887593i | \(0.347624\pi\) | |||||||
\(24\) | 6.01136 | 1.22706 | ||||||||
\(25\) | 0.600182 | 0.120036 | ||||||||
\(26\) | 2.91000 | 0.570697 | ||||||||
\(27\) | −1.23278 | −0.237248 | ||||||||
\(28\) | 4.14408 | 0.783157 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.99560 | 0.729493 | ||||||||
\(31\) | 8.62167 | 1.54850 | 0.774249 | − | 0.632881i | \(-0.218128\pi\) | ||||
0.774249 | + | 0.632881i | \(0.218128\pi\) | |||||||
\(32\) | 5.75278 | 1.01696 | ||||||||
\(33\) | 10.3908 | 1.80880 | ||||||||
\(34\) | −2.10579 | −0.361140 | ||||||||
\(35\) | 6.28503 | 1.06236 | ||||||||
\(36\) | −5.43645 | −0.906075 | ||||||||
\(37\) | 3.48283 | 0.572574 | 0.286287 | − | 0.958144i | \(-0.407579\pi\) | ||||
0.286287 | + | 0.958144i | \(0.407579\pi\) | |||||||
\(38\) | −1.46343 | −0.237399 | ||||||||
\(39\) | −11.1754 | −1.78950 | ||||||||
\(40\) | 5.58661 | 0.883320 | ||||||||
\(41\) | −1.04873 | −0.163784 | −0.0818918 | − | 0.996641i | \(-0.526096\pi\) | ||||
−0.0818918 | + | 0.996641i | \(0.526096\pi\) | |||||||
\(42\) | 4.48422 | 0.691930 | ||||||||
\(43\) | −2.02748 | −0.309187 | −0.154594 | − | 0.987978i | \(-0.549407\pi\) | ||||
−0.154594 | + | 0.987978i | \(0.549407\pi\) | |||||||
\(44\) | 6.36712 | 0.959880 | ||||||||
\(45\) | −8.24508 | −1.22910 | ||||||||
\(46\) | 2.92955 | 0.431938 | ||||||||
\(47\) | −1.01270 | −0.147718 | −0.0738589 | − | 0.997269i | \(-0.523531\pi\) | ||||
−0.0738589 | + | 0.997269i | \(0.523531\pi\) | |||||||
\(48\) | −3.96061 | −0.571665 | ||||||||
\(49\) | 0.0536357 | 0.00766225 | ||||||||
\(50\) | 0.397958 | 0.0562798 | ||||||||
\(51\) | 8.08697 | 1.13240 | ||||||||
\(52\) | −6.84793 | −0.949637 | ||||||||
\(53\) | −3.40628 | −0.467888 | −0.233944 | − | 0.972250i | \(-0.575163\pi\) | ||||
−0.233944 | + | 0.972250i | \(0.575163\pi\) | |||||||
\(54\) | −0.817409 | −0.111235 | ||||||||
\(55\) | 9.65657 | 1.30209 | ||||||||
\(56\) | 6.26980 | 0.837837 | ||||||||
\(57\) | 5.62007 | 0.744397 | ||||||||
\(58\) | −0.663063 | −0.0870644 | ||||||||
\(59\) | 11.4130 | 1.48585 | 0.742924 | − | 0.669376i | \(-0.233439\pi\) | ||||
0.742924 | + | 0.669376i | \(0.233439\pi\) | |||||||
\(60\) | −9.40260 | −1.21387 | ||||||||
\(61\) | 3.09165 | 0.395845 | 0.197922 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197922 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(62\) | 5.71671 | 0.726023 | ||||||||
\(63\) | −9.25338 | −1.16582 | ||||||||
\(64\) | 0.703698 | 0.0879623 | ||||||||
\(65\) | −10.3858 | −1.28820 | ||||||||
\(66\) | 6.88973 | 0.848068 | ||||||||
\(67\) | 4.87423 | 0.595482 | 0.297741 | − | 0.954647i | \(-0.403767\pi\) | ||||
0.297741 | + | 0.954647i | \(0.403767\pi\) | |||||||
\(68\) | 4.95543 | 0.600934 | ||||||||
\(69\) | −11.2505 | −1.35440 | ||||||||
\(70\) | 4.16737 | 0.498096 | ||||||||
\(71\) | 8.87674 | 1.05347 | 0.526737 | − | 0.850028i | \(-0.323415\pi\) | ||||
0.526737 | + | 0.850028i | \(0.323415\pi\) | |||||||
\(72\) | −8.22510 | −0.969337 | ||||||||
\(73\) | −7.51540 | −0.879611 | −0.439806 | − | 0.898093i | \(-0.644953\pi\) | ||||
−0.439806 | + | 0.898093i | \(0.644953\pi\) | |||||||
\(74\) | 2.30934 | 0.268455 | ||||||||
\(75\) | −1.52830 | −0.176473 | ||||||||
\(76\) | 3.44380 | 0.395030 | ||||||||
\(77\) | 10.8375 | 1.23505 | ||||||||
\(78\) | −7.41000 | −0.839017 | ||||||||
\(79\) | −4.88878 | −0.550030 | −0.275015 | − | 0.961440i | \(-0.588683\pi\) | ||||
−0.275015 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(80\) | −3.68076 | −0.411521 | ||||||||
\(81\) | −7.31324 | −0.812582 | ||||||||
\(82\) | −0.695372 | −0.0767910 | ||||||||
\(83\) | −8.13823 | −0.893287 | −0.446644 | − | 0.894712i | \(-0.647381\pi\) | ||||
−0.446644 | + | 0.894712i | \(0.647381\pi\) | |||||||
\(84\) | −10.5525 | −1.15137 | ||||||||
\(85\) | 7.51556 | 0.815176 | ||||||||
\(86\) | −1.34434 | −0.144964 | ||||||||
\(87\) | 2.54639 | 0.273002 | ||||||||
\(88\) | 9.63317 | 1.02690 | ||||||||
\(89\) | 10.3070 | 1.09254 | 0.546269 | − | 0.837610i | \(-0.316048\pi\) | ||||
0.546269 | + | 0.837610i | \(0.316048\pi\) | |||||||
\(90\) | −5.46701 | −0.576273 | ||||||||
\(91\) | −11.6559 | −1.22187 | ||||||||
\(92\) | −6.89393 | −0.718742 | ||||||||
\(93\) | −21.9542 | −2.27654 | ||||||||
\(94\) | −0.671485 | −0.0692584 | ||||||||
\(95\) | 5.22297 | 0.535865 | ||||||||
\(96\) | −14.6489 | −1.49509 | ||||||||
\(97\) | −19.4873 | −1.97863 | −0.989317 | − | 0.145781i | \(-0.953431\pi\) | ||||
−0.989317 | + | 0.145781i | \(0.953431\pi\) | |||||||
\(98\) | 0.0355639 | 0.00359249 | ||||||||
\(99\) | −14.2173 | −1.42889 | ||||||||
\(100\) | −0.936492 | −0.0936492 | ||||||||
\(101\) | −2.76890 | −0.275516 | −0.137758 | − | 0.990466i | \(-0.543990\pi\) | ||||
−0.137758 | + | 0.990466i | \(0.543990\pi\) | |||||||
\(102\) | 5.36217 | 0.530934 | ||||||||
\(103\) | −4.29238 | −0.422941 | −0.211470 | − | 0.977384i | \(-0.567825\pi\) | ||||
−0.211470 | + | 0.977384i | \(0.567825\pi\) | |||||||
\(104\) | −10.3606 | −1.01594 | ||||||||
\(105\) | −16.0042 | −1.56185 | ||||||||
\(106\) | −2.25858 | −0.219372 | ||||||||
\(107\) | 16.5070 | 1.59579 | 0.797897 | − | 0.602794i | \(-0.205946\pi\) | ||||
0.797897 | + | 0.602794i | \(0.205946\pi\) | |||||||
\(108\) | 1.92356 | 0.185095 | ||||||||
\(109\) | −8.42699 | −0.807159 | −0.403579 | − | 0.914945i | \(-0.632234\pi\) | ||||
−0.403579 | + | 0.914945i | \(0.632234\pi\) | |||||||
\(110\) | 6.40292 | 0.610494 | ||||||||
\(111\) | −8.86866 | −0.841776 | ||||||||
\(112\) | −4.13088 | −0.390332 | ||||||||
\(113\) | 14.8571 | 1.39763 | 0.698817 | − | 0.715300i | \(-0.253710\pi\) | ||||
0.698817 | + | 0.715300i | \(0.253710\pi\) | |||||||
\(114\) | 3.72646 | 0.349015 | ||||||||
\(115\) | −10.4555 | −0.974985 | ||||||||
\(116\) | 1.56035 | 0.144875 | ||||||||
\(117\) | 15.2909 | 1.41364 | ||||||||
\(118\) | 7.56754 | 0.696649 | ||||||||
\(119\) | 8.43464 | 0.773202 | ||||||||
\(120\) | −14.2257 | −1.29862 | ||||||||
\(121\) | 5.65114 | 0.513740 | ||||||||
\(122\) | 2.04996 | 0.185594 | ||||||||
\(123\) | 2.67047 | 0.240788 | ||||||||
\(124\) | −13.4528 | −1.20810 | ||||||||
\(125\) | 10.4120 | 0.931281 | ||||||||
\(126\) | −6.13557 | −0.546600 | ||||||||
\(127\) | 20.5921 | 1.82725 | 0.913626 | − | 0.406556i | \(-0.133270\pi\) | ||||
0.913626 | + | 0.406556i | \(0.133270\pi\) | |||||||
\(128\) | −11.0390 | −0.975716 | ||||||||
\(129\) | 5.16276 | 0.454555 | ||||||||
\(130\) | −6.88642 | −0.603979 | ||||||||
\(131\) | 4.77071 | 0.416819 | 0.208410 | − | 0.978042i | \(-0.433171\pi\) | ||||
0.208410 | + | 0.978042i | \(0.433171\pi\) | |||||||
\(132\) | −16.2132 | −1.41118 | ||||||||
\(133\) | 5.86169 | 0.508273 | ||||||||
\(134\) | 3.23192 | 0.279195 | ||||||||
\(135\) | 2.91733 | 0.251084 | ||||||||
\(136\) | 7.49734 | 0.642892 | ||||||||
\(137\) | 4.90344 | 0.418929 | 0.209465 | − | 0.977816i | \(-0.432828\pi\) | ||||
0.209465 | + | 0.977816i | \(0.432828\pi\) | |||||||
\(138\) | −7.45978 | −0.635019 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | −9.80684 | −0.828829 | ||||||||
\(141\) | 2.57874 | 0.217169 | ||||||||
\(142\) | 5.88583 | 0.493928 | ||||||||
\(143\) | −17.9085 | −1.49759 | ||||||||
\(144\) | 5.41914 | 0.451595 | ||||||||
\(145\) | 2.36647 | 0.196525 | ||||||||
\(146\) | −4.98319 | −0.412411 | ||||||||
\(147\) | −0.136578 | −0.0112647 | ||||||||
\(148\) | −5.43442 | −0.446707 | ||||||||
\(149\) | −6.27975 | −0.514457 | −0.257229 | − | 0.966351i | \(-0.582809\pi\) | ||||
−0.257229 | + | 0.966351i | \(0.582809\pi\) | |||||||
\(150\) | −1.01336 | −0.0827404 | ||||||||
\(151\) | −18.0807 | −1.47138 | −0.735692 | − | 0.677316i | \(-0.763143\pi\) | ||||
−0.735692 | + | 0.677316i | \(0.763143\pi\) | |||||||
\(152\) | 5.21031 | 0.422612 | ||||||||
\(153\) | −11.0651 | −0.894558 | ||||||||
\(154\) | 7.18593 | 0.579059 | ||||||||
\(155\) | −20.4029 | −1.63880 | ||||||||
\(156\) | 17.4375 | 1.39612 | ||||||||
\(157\) | −18.8883 | −1.50745 | −0.753725 | − | 0.657191i | \(-0.771745\pi\) | ||||
−0.753725 | + | 0.657191i | \(0.771745\pi\) | |||||||
\(158\) | −3.24157 | −0.257885 | ||||||||
\(159\) | 8.67373 | 0.687872 | ||||||||
\(160\) | −13.6138 | −1.07626 | ||||||||
\(161\) | −11.7342 | −0.924782 | ||||||||
\(162\) | −4.84914 | −0.380984 | ||||||||
\(163\) | 7.52863 | 0.589688 | 0.294844 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294844 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(164\) | 1.63638 | 0.127780 | ||||||||
\(165\) | −24.5894 | −1.91429 | ||||||||
\(166\) | −5.39616 | −0.418823 | ||||||||
\(167\) | 1.85660 | 0.143668 | 0.0718342 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718342 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(168\) | −15.9654 | −1.23176 | ||||||||
\(169\) | 6.26086 | 0.481605 | ||||||||
\(170\) | 4.98329 | 0.382201 | ||||||||
\(171\) | −7.68971 | −0.588047 | ||||||||
\(172\) | 3.16357 | 0.241220 | ||||||||
\(173\) | 9.94817 | 0.756346 | 0.378173 | − | 0.925735i | \(-0.376553\pi\) | ||||
0.378173 | + | 0.925735i | \(0.376553\pi\) | |||||||
\(174\) | 1.68842 | 0.127999 | ||||||||
\(175\) | −1.59400 | −0.120495 | ||||||||
\(176\) | −6.34685 | −0.478412 | ||||||||
\(177\) | −29.0620 | −2.18444 | ||||||||
\(178\) | 6.83418 | 0.512244 | ||||||||
\(179\) | −0.550522 | −0.0411480 | −0.0205740 | − | 0.999788i | \(-0.506549\pi\) | ||||
−0.0205740 | + | 0.999788i | \(0.506549\pi\) | |||||||
\(180\) | 12.8652 | 0.958915 | ||||||||
\(181\) | −9.00173 | −0.669093 | −0.334547 | − | 0.942379i | \(-0.608583\pi\) | ||||
−0.334547 | + | 0.942379i | \(0.608583\pi\) | |||||||
\(182\) | −7.72857 | −0.572880 | ||||||||
\(183\) | −7.87255 | −0.581956 | ||||||||
\(184\) | −10.4302 | −0.768925 | ||||||||
\(185\) | −8.24201 | −0.605965 | ||||||||
\(186\) | −14.5570 | −1.06737 | ||||||||
\(187\) | 12.9593 | 0.947679 | ||||||||
\(188\) | 1.58017 | 0.115246 | ||||||||
\(189\) | 3.27409 | 0.238155 | ||||||||
\(190\) | 3.46315 | 0.251244 | ||||||||
\(191\) | −2.12697 | −0.153902 | −0.0769510 | − | 0.997035i | \(-0.524518\pi\) | ||||
−0.0769510 | + | 0.997035i | \(0.524518\pi\) | |||||||
\(192\) | −1.79189 | −0.129319 | ||||||||
\(193\) | 1.52641 | 0.109873 | 0.0549366 | − | 0.998490i | \(-0.482504\pi\) | ||||
0.0549366 | + | 0.998490i | \(0.482504\pi\) | |||||||
\(194\) | −12.9213 | −0.927695 | ||||||||
\(195\) | 26.4463 | 1.89386 | ||||||||
\(196\) | −0.0836904 | −0.00597788 | ||||||||
\(197\) | −8.93752 | −0.636772 | −0.318386 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318386 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(198\) | −9.42694 | −0.669943 | ||||||||
\(199\) | −8.85206 | −0.627506 | −0.313753 | − | 0.949505i | \(-0.601586\pi\) | ||||
−0.313753 | + | 0.949505i | \(0.601586\pi\) | |||||||
\(200\) | −1.41687 | −0.100188 | ||||||||
\(201\) | −12.4117 | −0.875454 | ||||||||
\(202\) | −1.83595 | −0.129177 | ||||||||
\(203\) | 2.65587 | 0.186405 | ||||||||
\(204\) | −12.6185 | −0.883471 | ||||||||
\(205\) | 2.48178 | 0.173335 | ||||||||
\(206\) | −2.84612 | −0.198299 | ||||||||
\(207\) | 15.3936 | 1.06993 | ||||||||
\(208\) | 6.82612 | 0.473307 | ||||||||
\(209\) | 9.00613 | 0.622967 | ||||||||
\(210\) | −10.6118 | −0.732282 | ||||||||
\(211\) | 20.0135 | 1.37778 | 0.688892 | − | 0.724864i | \(-0.258098\pi\) | ||||
0.688892 | + | 0.724864i | \(0.258098\pi\) | |||||||
\(212\) | 5.31498 | 0.365034 | ||||||||
\(213\) | −22.6037 | −1.54878 | ||||||||
\(214\) | 10.9452 | 0.748198 | ||||||||
\(215\) | 4.79796 | 0.327218 | ||||||||
\(216\) | 2.91026 | 0.198018 | ||||||||
\(217\) | −22.8980 | −1.55442 | ||||||||
\(218\) | −5.58762 | −0.378441 | ||||||||
\(219\) | 19.1372 | 1.29317 | ||||||||
\(220\) | −15.0676 | −1.01586 | ||||||||
\(221\) | −13.9379 | −0.937566 | ||||||||
\(222\) | −5.88048 | −0.394672 | ||||||||
\(223\) | −17.0648 | −1.14275 | −0.571373 | − | 0.820690i | \(-0.693589\pi\) | ||||
−0.571373 | + | 0.820690i | \(0.693589\pi\) | |||||||
\(224\) | −15.2786 | −1.02085 | ||||||||
\(225\) | 2.09111 | 0.139407 | ||||||||
\(226\) | 9.85116 | 0.655290 | ||||||||
\(227\) | 6.03701 | 0.400690 | 0.200345 | − | 0.979725i | \(-0.435794\pi\) | ||||
0.200345 | + | 0.979725i | \(0.435794\pi\) | |||||||
\(228\) | −8.76926 | −0.580759 | ||||||||
\(229\) | −10.0352 | −0.663147 | −0.331573 | − | 0.943429i | \(-0.607579\pi\) | ||||
−0.331573 | + | 0.943429i | \(0.607579\pi\) | |||||||
\(230\) | −6.93268 | −0.457128 | ||||||||
\(231\) | −27.5965 | −1.81572 | ||||||||
\(232\) | 2.36073 | 0.154990 | ||||||||
\(233\) | 2.41989 | 0.158532 | 0.0792661 | − | 0.996853i | \(-0.474742\pi\) | ||||
0.0792661 | + | 0.996853i | \(0.474742\pi\) | |||||||
\(234\) | 10.1388 | 0.662794 | ||||||||
\(235\) | 2.39653 | 0.156332 | ||||||||
\(236\) | −17.8083 | −1.15922 | ||||||||
\(237\) | 12.4488 | 0.808633 | ||||||||
\(238\) | 5.59270 | 0.362521 | ||||||||
\(239\) | −11.1870 | −0.723628 | −0.361814 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361814 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(240\) | 9.37267 | 0.605003 | ||||||||
\(241\) | −13.4475 | −0.866231 | −0.433116 | − | 0.901338i | \(-0.642586\pi\) | ||||
−0.433116 | + | 0.901338i | \(0.642586\pi\) | |||||||
\(242\) | 3.74706 | 0.240870 | ||||||||
\(243\) | 22.3207 | 1.43188 | ||||||||
\(244\) | −4.82404 | −0.308828 | ||||||||
\(245\) | −0.126927 | −0.00810909 | ||||||||
\(246\) | 1.77069 | 0.112895 | ||||||||
\(247\) | −9.68621 | −0.616319 | ||||||||
\(248\) | −20.3535 | −1.29245 | ||||||||
\(249\) | 20.7232 | 1.31328 | ||||||||
\(250\) | 6.90384 | 0.436637 | ||||||||
\(251\) | 25.7559 | 1.62570 | 0.812849 | − | 0.582475i | \(-0.197915\pi\) | ||||
0.812849 | + | 0.582475i | \(0.197915\pi\) | |||||||
\(252\) | 14.4385 | 0.909539 | ||||||||
\(253\) | −18.0288 | −1.13346 | ||||||||
\(254\) | 13.6538 | 0.856719 | ||||||||
\(255\) | −19.1376 | −1.19844 | ||||||||
\(256\) | −8.72693 | −0.545433 | ||||||||
\(257\) | 9.59008 | 0.598213 | 0.299106 | − | 0.954220i | \(-0.403311\pi\) | ||||
0.299106 | + | 0.954220i | \(0.403311\pi\) | |||||||
\(258\) | 3.42323 | 0.213121 | ||||||||
\(259\) | −9.24994 | −0.574763 | ||||||||
\(260\) | 16.2054 | 1.00502 | ||||||||
\(261\) | −3.48413 | −0.215662 | ||||||||
\(262\) | 3.16328 | 0.195428 | ||||||||
\(263\) | −3.65688 | −0.225493 | −0.112746 | − | 0.993624i | \(-0.535965\pi\) | ||||
−0.112746 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(264\) | −24.5298 | −1.50971 | ||||||||
\(265\) | 8.06086 | 0.495175 | ||||||||
\(266\) | 3.88667 | 0.238307 | ||||||||
\(267\) | −26.2457 | −1.60621 | ||||||||
\(268\) | −7.60549 | −0.464579 | ||||||||
\(269\) | 10.2364 | 0.624122 | 0.312061 | − | 0.950062i | \(-0.398981\pi\) | ||||
0.312061 | + | 0.950062i | \(0.398981\pi\) | |||||||
\(270\) | 1.93437 | 0.117722 | ||||||||
\(271\) | 20.5581 | 1.24881 | 0.624407 | − | 0.781099i | \(-0.285341\pi\) | ||||
0.624407 | + | 0.781099i | \(0.285341\pi\) | |||||||
\(272\) | −4.93965 | −0.299510 | ||||||||
\(273\) | 29.6804 | 1.79634 | ||||||||
\(274\) | 3.25129 | 0.196418 | ||||||||
\(275\) | −2.44909 | −0.147686 | ||||||||
\(276\) | 17.5547 | 1.05667 | ||||||||
\(277\) | −17.1215 | −1.02873 | −0.514364 | − | 0.857572i | \(-0.671972\pi\) | ||||
−0.514364 | + | 0.857572i | \(0.671972\pi\) | |||||||
\(278\) | −0.663063 | −0.0397679 | ||||||||
\(279\) | 30.0390 | 1.79839 | ||||||||
\(280\) | −14.8373 | −0.886698 | ||||||||
\(281\) | −15.2045 | −0.907025 | −0.453512 | − | 0.891250i | \(-0.649829\pi\) | ||||
−0.453512 | + | 0.891250i | \(0.649829\pi\) | |||||||
\(282\) | 1.70987 | 0.101821 | ||||||||
\(283\) | 13.6131 | 0.809214 | 0.404607 | − | 0.914491i | \(-0.367408\pi\) | ||||
0.404607 | + | 0.914491i | \(0.367408\pi\) | |||||||
\(284\) | −13.8508 | −0.821893 | ||||||||
\(285\) | −13.2997 | −0.787808 | ||||||||
\(286\) | −11.8745 | −0.702153 | ||||||||
\(287\) | 2.78528 | 0.164410 | ||||||||
\(288\) | 20.0434 | 1.18107 | ||||||||
\(289\) | −6.91397 | −0.406704 | ||||||||
\(290\) | 1.56912 | 0.0921418 | ||||||||
\(291\) | 49.6223 | 2.90891 | ||||||||
\(292\) | 11.7266 | 0.686250 | ||||||||
\(293\) | 22.2224 | 1.29825 | 0.649125 | − | 0.760682i | \(-0.275135\pi\) | ||||
0.649125 | + | 0.760682i | \(0.275135\pi\) | |||||||
\(294\) | −0.0905596 | −0.00528154 | ||||||||
\(295\) | −27.0085 | −1.57250 | ||||||||
\(296\) | −8.22204 | −0.477896 | ||||||||
\(297\) | 5.03045 | 0.291896 | ||||||||
\(298\) | −4.16387 | −0.241207 | ||||||||
\(299\) | 19.3903 | 1.12137 | ||||||||
\(300\) | 2.38468 | 0.137679 | ||||||||
\(301\) | 5.38471 | 0.310370 | ||||||||
\(302\) | −11.9886 | −0.689868 | ||||||||
\(303\) | 7.05071 | 0.405053 | ||||||||
\(304\) | −3.43283 | −0.196886 | ||||||||
\(305\) | −7.31629 | −0.418929 | ||||||||
\(306\) | −7.33683 | −0.419419 | ||||||||
\(307\) | 18.7197 | 1.06839 | 0.534194 | − | 0.845362i | \(-0.320615\pi\) | ||||
0.534194 | + | 0.845362i | \(0.320615\pi\) | |||||||
\(308\) | −16.9102 | −0.963551 | ||||||||
\(309\) | 10.9301 | 0.621792 | ||||||||
\(310\) | −13.5284 | −0.768363 | ||||||||
\(311\) | 24.2299 | 1.37395 | 0.686977 | − | 0.726679i | \(-0.258937\pi\) | ||||
0.686977 | + | 0.726679i | \(0.258937\pi\) | |||||||
\(312\) | 26.3822 | 1.49360 | ||||||||
\(313\) | −19.8799 | −1.12368 | −0.561838 | − | 0.827247i | \(-0.689906\pi\) | ||||
−0.561838 | + | 0.827247i | \(0.689906\pi\) | |||||||
\(314\) | −12.5241 | −0.706777 | ||||||||
\(315\) | 21.8979 | 1.23380 | ||||||||
\(316\) | 7.62819 | 0.429119 | ||||||||
\(317\) | 19.8499 | 1.11488 | 0.557439 | − | 0.830218i | \(-0.311784\pi\) | ||||
0.557439 | + | 0.830218i | \(0.311784\pi\) | |||||||
\(318\) | 5.75123 | 0.322513 | ||||||||
\(319\) | 4.08058 | 0.228469 | ||||||||
\(320\) | −1.66528 | −0.0930921 | ||||||||
\(321\) | −42.0334 | −2.34607 | ||||||||
\(322\) | −7.78049 | −0.433590 | ||||||||
\(323\) | 7.00932 | 0.390009 | ||||||||
\(324\) | 11.4112 | 0.633955 | ||||||||
\(325\) | 2.63403 | 0.146110 | ||||||||
\(326\) | 4.99195 | 0.276479 | ||||||||
\(327\) | 21.4584 | 1.18665 | ||||||||
\(328\) | 2.47577 | 0.136701 | ||||||||
\(329\) | 2.68960 | 0.148283 | ||||||||
\(330\) | −16.3044 | −0.897525 | ||||||||
\(331\) | 4.38849 | 0.241213 | 0.120607 | − | 0.992700i | \(-0.461516\pi\) | ||||
0.120607 | + | 0.992700i | \(0.461516\pi\) | |||||||
\(332\) | 12.6985 | 0.696919 | ||||||||
\(333\) | 12.1346 | 0.664973 | ||||||||
\(334\) | 1.23105 | 0.0673598 | ||||||||
\(335\) | −11.5347 | −0.630209 | ||||||||
\(336\) | 10.5189 | 0.573851 | ||||||||
\(337\) | −20.8314 | −1.13476 | −0.567381 | − | 0.823456i | \(-0.692043\pi\) | ||||
−0.567381 | + | 0.823456i | \(0.692043\pi\) | |||||||
\(338\) | 4.15134 | 0.225803 | ||||||||
\(339\) | −37.8319 | −2.05475 | ||||||||
\(340\) | −11.7269 | −0.635979 | ||||||||
\(341\) | −35.1814 | −1.90518 | ||||||||
\(342\) | −5.09876 | −0.275709 | ||||||||
\(343\) | 18.4486 | 0.996132 | ||||||||
\(344\) | 4.78633 | 0.258062 | ||||||||
\(345\) | 26.6239 | 1.43339 | ||||||||
\(346\) | 6.59627 | 0.354617 | ||||||||
\(347\) | −6.10675 | −0.327828 | −0.163914 | − | 0.986475i | \(-0.552412\pi\) | ||||
−0.163914 | + | 0.986475i | \(0.552412\pi\) | |||||||
\(348\) | −3.97326 | −0.212989 | ||||||||
\(349\) | 29.0866 | 1.55697 | 0.778484 | − | 0.627664i | \(-0.215989\pi\) | ||||
0.778484 | + | 0.627664i | \(0.215989\pi\) | |||||||
\(350\) | −1.05692 | −0.0564950 | ||||||||
\(351\) | −5.41031 | −0.288781 | ||||||||
\(352\) | −23.4747 | −1.25121 | ||||||||
\(353\) | −19.1357 | −1.01849 | −0.509246 | − | 0.860621i | \(-0.670076\pi\) | ||||
−0.509246 | + | 0.860621i | \(0.670076\pi\) | |||||||
\(354\) | −19.2700 | −1.02419 | ||||||||
\(355\) | −21.0065 | −1.11491 | ||||||||
\(356\) | −16.0825 | −0.852370 | ||||||||
\(357\) | −21.4779 | −1.13673 | ||||||||
\(358\) | −0.365031 | −0.0192925 | ||||||||
\(359\) | 11.8779 | 0.626890 | 0.313445 | − | 0.949606i | \(-0.398517\pi\) | ||||
0.313445 | + | 0.949606i | \(0.398517\pi\) | |||||||
\(360\) | 19.4644 | 1.02587 | ||||||||
\(361\) | −14.1288 | −0.743623 | ||||||||
\(362\) | −5.96871 | −0.313709 | ||||||||
\(363\) | −14.3900 | −0.755281 | ||||||||
\(364\) | 18.1872 | 0.953268 | ||||||||
\(365\) | 17.7850 | 0.930908 | ||||||||
\(366\) | −5.22000 | −0.272854 | ||||||||
\(367\) | −9.80599 | −0.511869 | −0.255934 | − | 0.966694i | \(-0.582383\pi\) | ||||
−0.255934 | + | 0.966694i | \(0.582383\pi\) | |||||||
\(368\) | 6.87198 | 0.358227 | ||||||||
\(369\) | −3.65390 | −0.190214 | ||||||||
\(370\) | −5.46497 | −0.284110 | ||||||||
\(371\) | 9.04663 | 0.469677 | ||||||||
\(372\) | 34.2562 | 1.77610 | ||||||||
\(373\) | 17.0149 | 0.880996 | 0.440498 | − | 0.897753i | \(-0.354802\pi\) | ||||
0.440498 | + | 0.897753i | \(0.354802\pi\) | |||||||
\(374\) | 8.59284 | 0.444325 | ||||||||
\(375\) | −26.5132 | −1.36913 | ||||||||
\(376\) | 2.39072 | 0.123292 | ||||||||
\(377\) | −4.38872 | −0.226031 | ||||||||
\(378\) | 2.17093 | 0.111661 | ||||||||
\(379\) | −10.7945 | −0.554478 | −0.277239 | − | 0.960801i | \(-0.589419\pi\) | ||||
−0.277239 | + | 0.960801i | \(0.589419\pi\) | |||||||
\(380\) | −8.14964 | −0.418068 | ||||||||
\(381\) | −52.4356 | −2.68636 | ||||||||
\(382\) | −1.41031 | −0.0721579 | ||||||||
\(383\) | 8.73640 | 0.446409 | 0.223205 | − | 0.974772i | \(-0.428348\pi\) | ||||
0.223205 | + | 0.974772i | \(0.428348\pi\) | |||||||
\(384\) | 28.1096 | 1.43446 | ||||||||
\(385\) | −25.6466 | −1.30707 | ||||||||
\(386\) | 1.01210 | 0.0515147 | ||||||||
\(387\) | −7.06399 | −0.359083 | ||||||||
\(388\) | 30.4069 | 1.54368 | ||||||||
\(389\) | 24.5119 | 1.24280 | 0.621402 | − | 0.783492i | \(-0.286563\pi\) | ||||
0.621402 | + | 0.783492i | \(0.286563\pi\) | |||||||
\(390\) | 17.5355 | 0.887947 | ||||||||
\(391\) | −14.0316 | −0.709606 | ||||||||
\(392\) | −0.126620 | −0.00639526 | ||||||||
\(393\) | −12.1481 | −0.612791 | ||||||||
\(394\) | −5.92614 | −0.298555 | ||||||||
\(395\) | 11.5691 | 0.582107 | ||||||||
\(396\) | 22.1839 | 1.11478 | ||||||||
\(397\) | −26.6509 | −1.33757 | −0.668785 | − | 0.743456i | \(-0.733185\pi\) | ||||
−0.668785 | + | 0.743456i | \(0.733185\pi\) | |||||||
\(398\) | −5.86947 | −0.294210 | ||||||||
\(399\) | −14.9262 | −0.747243 | ||||||||
\(400\) | 0.933510 | 0.0466755 | ||||||||
\(401\) | 16.0327 | 0.800634 | 0.400317 | − | 0.916377i | \(-0.368900\pi\) | ||||
0.400317 | + | 0.916377i | \(0.368900\pi\) | |||||||
\(402\) | −8.22974 | −0.410462 | ||||||||
\(403\) | 37.8381 | 1.88485 | ||||||||
\(404\) | 4.32044 | 0.214950 | ||||||||
\(405\) | 17.3066 | 0.859970 | ||||||||
\(406\) | 1.76101 | 0.0873973 | ||||||||
\(407\) | −14.2120 | −0.704461 | ||||||||
\(408\) | −19.0912 | −0.945155 | ||||||||
\(409\) | 17.8344 | 0.881855 | 0.440928 | − | 0.897543i | \(-0.354650\pi\) | ||||
0.440928 | + | 0.897543i | \(0.354650\pi\) | |||||||
\(410\) | 1.64558 | 0.0812692 | ||||||||
\(411\) | −12.4861 | −0.615894 | ||||||||
\(412\) | 6.69761 | 0.329967 | ||||||||
\(413\) | −30.3114 | −1.49153 | ||||||||
\(414\) | 10.2069 | 0.501642 | ||||||||
\(415\) | 19.2589 | 0.945382 | ||||||||
\(416\) | 25.2474 | 1.23785 | ||||||||
\(417\) | 2.54639 | 0.124697 | ||||||||
\(418\) | 5.97163 | 0.292082 | ||||||||
\(419\) | −13.7739 | −0.672898 | −0.336449 | − | 0.941702i | \(-0.609226\pi\) | ||||
−0.336449 | + | 0.941702i | \(0.609226\pi\) | |||||||
\(420\) | 24.9721 | 1.21851 | ||||||||
\(421\) | −27.9889 | −1.36409 | −0.682047 | − | 0.731308i | \(-0.738910\pi\) | ||||
−0.682047 | + | 0.731308i | \(0.738910\pi\) | |||||||
\(422\) | 13.2702 | 0.645982 | ||||||||
\(423\) | −3.52838 | −0.171556 | ||||||||
\(424\) | 8.04132 | 0.390521 | ||||||||
\(425\) | −1.90609 | −0.0924588 | ||||||||
\(426\) | −14.9877 | −0.726154 | ||||||||
\(427\) | −8.21100 | −0.397358 | ||||||||
\(428\) | −25.7567 | −1.24500 | ||||||||
\(429\) | 45.6022 | 2.20169 | ||||||||
\(430\) | 3.18135 | 0.153418 | ||||||||
\(431\) | 24.9272 | 1.20070 | 0.600350 | − | 0.799737i | \(-0.295028\pi\) | ||||
0.600350 | + | 0.799737i | \(0.295028\pi\) | |||||||
\(432\) | −1.91744 | −0.0922527 | ||||||||
\(433\) | 17.4130 | 0.836814 | 0.418407 | − | 0.908260i | \(-0.362589\pi\) | ||||
0.418407 | + | 0.908260i | \(0.362589\pi\) | |||||||
\(434\) | −15.1828 | −0.728799 | ||||||||
\(435\) | −6.02597 | −0.288923 | ||||||||
\(436\) | 13.1490 | 0.629724 | ||||||||
\(437\) | −9.75128 | −0.466467 | ||||||||
\(438\) | 12.6892 | 0.606311 | ||||||||
\(439\) | 7.70376 | 0.367680 | 0.183840 | − | 0.982956i | \(-0.441147\pi\) | ||||
0.183840 | + | 0.982956i | \(0.441147\pi\) | |||||||
\(440\) | −22.7966 | −1.08679 | ||||||||
\(441\) | 0.186874 | 0.00889874 | ||||||||
\(442\) | −9.24172 | −0.439584 | ||||||||
\(443\) | 6.02754 | 0.286377 | 0.143189 | − | 0.989695i | \(-0.454264\pi\) | ||||
0.143189 | + | 0.989695i | \(0.454264\pi\) | |||||||
\(444\) | 13.8382 | 0.656731 | ||||||||
\(445\) | −24.3912 | −1.15625 | ||||||||
\(446\) | −11.3151 | −0.535784 | ||||||||
\(447\) | 15.9907 | 0.756335 | ||||||||
\(448\) | −1.86893 | −0.0882987 | ||||||||
\(449\) | 8.54161 | 0.403104 | 0.201552 | − | 0.979478i | \(-0.435402\pi\) | ||||
0.201552 | + | 0.979478i | \(0.435402\pi\) | |||||||
\(450\) | 1.38654 | 0.0653620 | ||||||||
\(451\) | 4.27941 | 0.201510 | ||||||||
\(452\) | −23.1822 | −1.09040 | ||||||||
\(453\) | 46.0405 | 2.16317 | ||||||||
\(454\) | 4.00291 | 0.187866 | ||||||||
\(455\) | 27.5832 | 1.29312 | ||||||||
\(456\) | −13.2675 | −0.621307 | ||||||||
\(457\) | −1.29272 | −0.0604709 | −0.0302355 | − | 0.999543i | \(-0.509626\pi\) | ||||
−0.0302355 | + | 0.999543i | \(0.509626\pi\) | |||||||
\(458\) | −6.65399 | −0.310920 | ||||||||
\(459\) | 3.91512 | 0.182742 | ||||||||
\(460\) | 16.3143 | 0.760657 | ||||||||
\(461\) | −10.2785 | −0.478719 | −0.239359 | − | 0.970931i | \(-0.576937\pi\) | ||||
−0.239359 | + | 0.970931i | \(0.576937\pi\) | |||||||
\(462\) | −18.2982 | −0.851311 | ||||||||
\(463\) | −32.2980 | −1.50102 | −0.750508 | − | 0.660862i | \(-0.770191\pi\) | ||||
−0.750508 | + | 0.660862i | \(0.770191\pi\) | |||||||
\(464\) | −1.55538 | −0.0722067 | ||||||||
\(465\) | 51.9539 | 2.40931 | ||||||||
\(466\) | 1.60454 | 0.0743289 | ||||||||
\(467\) | −7.11434 | −0.329213 | −0.164606 | − | 0.986359i | \(-0.552635\pi\) | ||||
−0.164606 | + | 0.986359i | \(0.552635\pi\) | |||||||
\(468\) | −23.8590 | −1.10288 | ||||||||
\(469\) | −12.9453 | −0.597759 | ||||||||
\(470\) | 1.58905 | 0.0732974 | ||||||||
\(471\) | 48.0970 | 2.21619 | ||||||||
\(472\) | −26.9431 | −1.24016 | ||||||||
\(473\) | 8.27328 | 0.380406 | ||||||||
\(474\) | 8.25431 | 0.379133 | ||||||||
\(475\) | −1.32464 | −0.0607788 | ||||||||
\(476\) | −13.1610 | −0.603232 | ||||||||
\(477\) | −11.8679 | −0.543394 | ||||||||
\(478\) | −7.41770 | −0.339278 | ||||||||
\(479\) | −32.6050 | −1.48976 | −0.744880 | − | 0.667199i | \(-0.767493\pi\) | ||||
−0.744880 | + | 0.667199i | \(0.767493\pi\) | |||||||
\(480\) | 34.6661 | 1.58228 | ||||||||
\(481\) | 15.2852 | 0.696943 | ||||||||
\(482\) | −8.91655 | −0.406138 | ||||||||
\(483\) | 29.8798 | 1.35958 | ||||||||
\(484\) | −8.81774 | −0.400806 | ||||||||
\(485\) | 46.1161 | 2.09402 | ||||||||
\(486\) | 14.8001 | 0.671344 | ||||||||
\(487\) | 17.2987 | 0.783880 | 0.391940 | − | 0.919991i | \(-0.371804\pi\) | ||||
0.391940 | + | 0.919991i | \(0.371804\pi\) | |||||||
\(488\) | −7.29855 | −0.330390 | ||||||||
\(489\) | −19.1709 | −0.866936 | ||||||||
\(490\) | −0.0841608 | −0.00380200 | ||||||||
\(491\) | −25.0616 | −1.13101 | −0.565506 | − | 0.824744i | \(-0.691319\pi\) | ||||
−0.565506 | + | 0.824744i | \(0.691319\pi\) | |||||||
\(492\) | −4.16687 | −0.187857 | ||||||||
\(493\) | 3.17585 | 0.143033 | ||||||||
\(494\) | −6.42257 | −0.288965 | ||||||||
\(495\) | 33.6447 | 1.51222 | ||||||||
\(496\) | 13.4100 | 0.602126 | ||||||||
\(497\) | −23.5754 | −1.05750 | ||||||||
\(498\) | 13.7408 | 0.615738 | ||||||||
\(499\) | 0.857549 | 0.0383891 | 0.0191946 | − | 0.999816i | \(-0.493890\pi\) | ||||
0.0191946 | + | 0.999816i | \(0.493890\pi\) | |||||||
\(500\) | −16.2464 | −0.726561 | ||||||||
\(501\) | −4.72765 | −0.211216 | ||||||||
\(502\) | 17.0778 | 0.762219 | ||||||||
\(503\) | −28.9728 | −1.29183 | −0.645916 | − | 0.763408i | \(-0.723525\pi\) | ||||
−0.645916 | + | 0.763408i | \(0.723525\pi\) | |||||||
\(504\) | 21.8448 | 0.973044 | ||||||||
\(505\) | 6.55252 | 0.291583 | ||||||||
\(506\) | −11.9543 | −0.531431 | ||||||||
\(507\) | −15.9426 | −0.708037 | ||||||||
\(508\) | −32.1308 | −1.42557 | ||||||||
\(509\) | −19.6979 | −0.873096 | −0.436548 | − | 0.899681i | \(-0.643799\pi\) | ||||
−0.436548 | + | 0.899681i | \(0.643799\pi\) | |||||||
\(510\) | −12.6894 | −0.561897 | ||||||||
\(511\) | 19.9599 | 0.882975 | ||||||||
\(512\) | 16.2914 | 0.719987 | ||||||||
\(513\) | 2.72083 | 0.120127 | ||||||||
\(514\) | 6.35883 | 0.280476 | ||||||||
\(515\) | 10.1578 | 0.447606 | ||||||||
\(516\) | −8.05569 | −0.354632 | ||||||||
\(517\) | 4.13241 | 0.181743 | ||||||||
\(518\) | −6.13329 | −0.269481 | ||||||||
\(519\) | −25.3320 | −1.11195 | ||||||||
\(520\) | 24.5181 | 1.07519 | ||||||||
\(521\) | 27.3820 | 1.19963 | 0.599813 | − | 0.800140i | \(-0.295242\pi\) | ||||
0.599813 | + | 0.800140i | \(0.295242\pi\) | |||||||
\(522\) | −2.31020 | −0.101114 | ||||||||
\(523\) | −9.37070 | −0.409752 | −0.204876 | − | 0.978788i | \(-0.565679\pi\) | ||||
−0.204876 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(524\) | −7.44397 | −0.325191 | ||||||||
\(525\) | 4.05896 | 0.177148 | ||||||||
\(526\) | −2.42474 | −0.105724 | ||||||||
\(527\) | −27.3811 | −1.19274 | ||||||||
\(528\) | 16.1616 | 0.703343 | ||||||||
\(529\) | −3.47948 | −0.151282 | ||||||||
\(530\) | 5.34486 | 0.232166 | ||||||||
\(531\) | 39.7644 | 1.72563 | ||||||||
\(532\) | −9.14627 | −0.396541 | ||||||||
\(533\) | −4.60257 | −0.199359 | ||||||||
\(534\) | −17.4025 | −0.753081 | ||||||||
\(535\) | −39.0634 | −1.68886 | ||||||||
\(536\) | −11.5068 | −0.497016 | ||||||||
\(537\) | 1.40185 | 0.0604942 | ||||||||
\(538\) | 6.78736 | 0.292624 | ||||||||
\(539\) | −0.218865 | −0.00942718 | ||||||||
\(540\) | −4.55205 | −0.195889 | ||||||||
\(541\) | 42.1264 | 1.81115 | 0.905577 | − | 0.424181i | \(-0.139438\pi\) | ||||
0.905577 | + | 0.424181i | \(0.139438\pi\) | |||||||
\(542\) | 13.6313 | 0.585515 | ||||||||
\(543\) | 22.9220 | 0.983675 | ||||||||
\(544\) | −18.2700 | −0.783319 | ||||||||
\(545\) | 19.9422 | 0.854230 | ||||||||
\(546\) | 19.6800 | 0.842226 | ||||||||
\(547\) | −13.3623 | −0.571330 | −0.285665 | − | 0.958330i | \(-0.592214\pi\) | ||||
−0.285665 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(548\) | −7.65107 | −0.326838 | ||||||||
\(549\) | 10.7717 | 0.459724 | ||||||||
\(550\) | −1.62390 | −0.0692434 | ||||||||
\(551\) | 2.20707 | 0.0940243 | ||||||||
\(552\) | 26.5594 | 1.13044 | ||||||||
\(553\) | 12.9839 | 0.552133 | ||||||||
\(554\) | −11.3526 | −0.482326 | ||||||||
\(555\) | 20.9874 | 0.890866 | ||||||||
\(556\) | 1.56035 | 0.0661735 | ||||||||
\(557\) | 7.70532 | 0.326485 | 0.163242 | − | 0.986586i | \(-0.447805\pi\) | ||||
0.163242 | + | 0.986586i | \(0.447805\pi\) | |||||||
\(558\) | 19.9178 | 0.843186 | ||||||||
\(559\) | −8.89803 | −0.376346 | ||||||||
\(560\) | 9.77561 | 0.413095 | ||||||||
\(561\) | −32.9995 | −1.39324 | ||||||||
\(562\) | −10.0815 | −0.425264 | ||||||||
\(563\) | −12.5779 | −0.530094 | −0.265047 | − | 0.964235i | \(-0.585387\pi\) | ||||
−0.265047 | + | 0.964235i | \(0.585387\pi\) | |||||||
\(564\) | −4.02373 | −0.169430 | ||||||||
\(565\) | −35.1588 | −1.47914 | ||||||||
\(566\) | 9.02633 | 0.379405 | ||||||||
\(567\) | 19.4230 | 0.815690 | ||||||||
\(568\) | −20.9556 | −0.879278 | ||||||||
\(569\) | −16.4727 | −0.690573 | −0.345287 | − | 0.938497i | \(-0.612218\pi\) | ||||
−0.345287 | + | 0.938497i | \(0.612218\pi\) | |||||||
\(570\) | −8.81856 | −0.369369 | ||||||||
\(571\) | 7.09721 | 0.297009 | 0.148505 | − | 0.988912i | \(-0.452554\pi\) | ||||
0.148505 | + | 0.988912i | \(0.452554\pi\) | |||||||
\(572\) | 27.9435 | 1.16838 | ||||||||
\(573\) | 5.41610 | 0.226261 | ||||||||
\(574\) | 1.84682 | 0.0770846 | ||||||||
\(575\) | 2.65172 | 0.110585 | ||||||||
\(576\) | 2.45177 | 0.102157 | ||||||||
\(577\) | 4.04803 | 0.168522 | 0.0842609 | − | 0.996444i | \(-0.473147\pi\) | ||||
0.0842609 | + | 0.996444i | \(0.473147\pi\) | |||||||
\(578\) | −4.58440 | −0.190686 | ||||||||
\(579\) | −3.88684 | −0.161531 | ||||||||
\(580\) | −3.69252 | −0.153323 | ||||||||
\(581\) | 21.6141 | 0.896703 | ||||||||
\(582\) | 32.9027 | 1.36386 | ||||||||
\(583\) | 13.8996 | 0.575662 | ||||||||
\(584\) | 17.7419 | 0.734164 | ||||||||
\(585\) | −36.1854 | −1.49608 | ||||||||
\(586\) | 14.7349 | 0.608692 | ||||||||
\(587\) | −2.48820 | −0.102699 | −0.0513494 | − | 0.998681i | \(-0.516352\pi\) | ||||
−0.0513494 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(588\) | 0.213109 | 0.00878846 | ||||||||
\(589\) | −19.0286 | −0.784061 | ||||||||
\(590\) | −17.9084 | −0.737276 | ||||||||
\(591\) | 22.7585 | 0.936158 | ||||||||
\(592\) | 5.41712 | 0.222642 | ||||||||
\(593\) | 37.0980 | 1.52343 | 0.761717 | − | 0.647910i | \(-0.224357\pi\) | ||||
0.761717 | + | 0.647910i | \(0.224357\pi\) | |||||||
\(594\) | 3.33550 | 0.136857 | ||||||||
\(595\) | −19.9603 | −0.818294 | ||||||||
\(596\) | 9.79859 | 0.401366 | ||||||||
\(597\) | 22.5408 | 0.922535 | ||||||||
\(598\) | 12.8570 | 0.525760 | ||||||||
\(599\) | −29.8212 | −1.21846 | −0.609230 | − | 0.792993i | \(-0.708522\pi\) | ||||
−0.609230 | + | 0.792993i | \(0.708522\pi\) | |||||||
\(600\) | 3.60791 | 0.147292 | ||||||||
\(601\) | 39.2623 | 1.60154 | 0.800771 | − | 0.598971i | \(-0.204423\pi\) | ||||
0.800771 | + | 0.598971i | \(0.204423\pi\) | |||||||
\(602\) | 3.57040 | 0.145519 | ||||||||
\(603\) | 16.9824 | 0.691578 | ||||||||
\(604\) | 28.2121 | 1.14794 | ||||||||
\(605\) | −13.3733 | −0.543700 | ||||||||
\(606\) | 4.67506 | 0.189912 | ||||||||
\(607\) | 31.3026 | 1.27053 | 0.635267 | − | 0.772292i | \(-0.280890\pi\) | ||||
0.635267 | + | 0.772292i | \(0.280890\pi\) | |||||||
\(608\) | −12.6968 | −0.514923 | ||||||||
\(609\) | −6.76289 | −0.274046 | ||||||||
\(610\) | −4.85116 | −0.196418 | ||||||||
\(611\) | −4.44447 | −0.179804 | ||||||||
\(612\) | 17.2653 | 0.697910 | ||||||||
\(613\) | −29.6426 | −1.19725 | −0.598626 | − | 0.801029i | \(-0.704286\pi\) | ||||
−0.598626 | + | 0.801029i | \(0.704286\pi\) | |||||||
\(614\) | 12.4123 | 0.500921 | ||||||||
\(615\) | −6.31959 | −0.254831 | ||||||||
\(616\) | −25.5844 | −1.03083 | ||||||||
\(617\) | 18.2502 | 0.734727 | 0.367363 | − | 0.930078i | \(-0.380261\pi\) | ||||
0.367363 | + | 0.930078i | \(0.380261\pi\) | |||||||
\(618\) | 7.24734 | 0.291531 | ||||||||
\(619\) | 2.48820 | 0.100009 | 0.0500046 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500046 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(620\) | 31.8357 | 1.27855 | ||||||||
\(621\) | −5.44666 | −0.218567 | ||||||||
\(622\) | 16.0660 | 0.644187 | ||||||||
\(623\) | −27.3740 | −1.09672 | ||||||||
\(624\) | −17.3820 | −0.695837 | ||||||||
\(625\) | −27.6407 | −1.10563 | ||||||||
\(626\) | −13.1816 | −0.526842 | ||||||||
\(627\) | −22.9332 | −0.915862 | ||||||||
\(628\) | 29.4723 | 1.17607 | ||||||||
\(629\) | −11.0609 | −0.441029 | ||||||||
\(630\) | 14.5197 | 0.578477 | ||||||||
\(631\) | −41.1710 | −1.63899 | −0.819496 | − | 0.573085i | \(-0.805746\pi\) | ||||
−0.819496 | + | 0.573085i | \(0.805746\pi\) | |||||||
\(632\) | 11.5411 | 0.459080 | ||||||||
\(633\) | −50.9622 | −2.02556 | ||||||||
\(634\) | 13.1617 | 0.522718 | ||||||||
\(635\) | −48.7306 | −1.93381 | ||||||||
\(636\) | −13.5340 | −0.536659 | ||||||||
\(637\) | 0.235392 | 0.00932658 | ||||||||
\(638\) | 2.70568 | 0.107119 | ||||||||
\(639\) | 30.9277 | 1.22348 | ||||||||
\(640\) | 26.1234 | 1.03262 | ||||||||
\(641\) | −15.8374 | −0.625541 | −0.312770 | − | 0.949829i | \(-0.601257\pi\) | ||||
−0.312770 | + | 0.949829i | \(0.601257\pi\) | |||||||
\(642\) | −27.8708 | −1.09997 | ||||||||
\(643\) | 15.2114 | 0.599878 | 0.299939 | − | 0.953958i | \(-0.403034\pi\) | ||||
0.299939 | + | 0.953958i | \(0.403034\pi\) | |||||||
\(644\) | 18.3094 | 0.721490 | ||||||||
\(645\) | −12.2175 | −0.481064 | ||||||||
\(646\) | 4.64762 | 0.182858 | ||||||||
\(647\) | −28.2478 | −1.11053 | −0.555267 | − | 0.831672i | \(-0.687384\pi\) | ||||
−0.555267 | + | 0.831672i | \(0.687384\pi\) | |||||||
\(648\) | 17.2646 | 0.678218 | ||||||||
\(649\) | −46.5717 | −1.82810 | ||||||||
\(650\) | 1.74653 | 0.0685044 | ||||||||
\(651\) | 58.3074 | 2.28525 | ||||||||
\(652\) | −11.7473 | −0.460059 | ||||||||
\(653\) | −3.92079 | −0.153432 | −0.0767162 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767162 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(654\) | 14.2283 | 0.556370 | ||||||||
\(655\) | −11.2897 | −0.441127 | ||||||||
\(656\) | −1.63117 | −0.0636864 | ||||||||
\(657\) | −26.1846 | −1.02156 | ||||||||
\(658\) | 1.78338 | 0.0695233 | ||||||||
\(659\) | −38.9914 | −1.51889 | −0.759444 | − | 0.650573i | \(-0.774529\pi\) | ||||
−0.759444 | + | 0.650573i | \(0.774529\pi\) | |||||||
\(660\) | 38.3681 | 1.49348 | ||||||||
\(661\) | 15.0467 | 0.585249 | 0.292624 | − | 0.956227i | \(-0.405471\pi\) | ||||
0.292624 | + | 0.956227i | \(0.405471\pi\) | |||||||
\(662\) | 2.90984 | 0.113094 | ||||||||
\(663\) | 35.4914 | 1.37837 | ||||||||
\(664\) | 19.2122 | 0.745578 | ||||||||
\(665\) | −13.8715 | −0.537914 | ||||||||
\(666\) | 8.04602 | 0.311777 | ||||||||
\(667\) | −4.41820 | −0.171073 | ||||||||
\(668\) | −2.89695 | −0.112086 | ||||||||
\(669\) | 43.4538 | 1.68002 | ||||||||
\(670\) | −7.64824 | −0.295477 | ||||||||
\(671\) | −12.6157 | −0.487024 | ||||||||
\(672\) | 38.9054 | 1.50081 | ||||||||
\(673\) | 43.1013 | 1.66143 | 0.830717 | − | 0.556696i | \(-0.187931\pi\) | ||||
0.830717 | + | 0.556696i | \(0.187931\pi\) | |||||||
\(674\) | −13.8126 | −0.532040 | ||||||||
\(675\) | −0.739890 | −0.0284784 | ||||||||
\(676\) | −9.76912 | −0.375735 | ||||||||
\(677\) | 29.0666 | 1.11712 | 0.558559 | − | 0.829465i | \(-0.311354\pi\) | ||||
0.558559 | + | 0.829465i | \(0.311354\pi\) | |||||||
\(678\) | −25.0849 | −0.963382 | ||||||||
\(679\) | 51.7557 | 1.98620 | ||||||||
\(680\) | −17.7422 | −0.680384 | ||||||||
\(681\) | −15.3726 | −0.589079 | ||||||||
\(682\) | −23.3275 | −0.893256 | ||||||||
\(683\) | 29.1695 | 1.11614 | 0.558069 | − | 0.829794i | \(-0.311542\pi\) | ||||
0.558069 | + | 0.829794i | \(0.311542\pi\) | |||||||
\(684\) | 11.9986 | 0.458779 | ||||||||
\(685\) | −11.6038 | −0.443360 | ||||||||
\(686\) | 12.2326 | 0.467043 | ||||||||
\(687\) | 25.5537 | 0.974933 | ||||||||
\(688\) | −3.15350 | −0.120226 | ||||||||
\(689\) | −14.9492 | −0.569519 | ||||||||
\(690\) | 17.6534 | 0.672052 | ||||||||
\(691\) | 12.2564 | 0.466257 | 0.233128 | − | 0.972446i | \(-0.425104\pi\) | ||||
0.233128 | + | 0.972446i | \(0.425104\pi\) | |||||||
\(692\) | −15.5226 | −0.590081 | ||||||||
\(693\) | 37.7592 | 1.43435 | ||||||||
\(694\) | −4.04916 | −0.153704 | ||||||||
\(695\) | 2.36647 | 0.0897653 | ||||||||
\(696\) | −6.01136 | −0.227860 | ||||||||
\(697\) | 3.33060 | 0.126155 | ||||||||
\(698\) | 19.2862 | 0.729995 | ||||||||
\(699\) | −6.16200 | −0.233068 | ||||||||
\(700\) | 2.48720 | 0.0940073 | ||||||||
\(701\) | −31.2340 | −1.17969 | −0.589846 | − | 0.807516i | \(-0.700812\pi\) | ||||
−0.589846 | + | 0.807516i | \(0.700812\pi\) | |||||||
\(702\) | −3.58738 | −0.135397 | ||||||||
\(703\) | −7.68685 | −0.289915 | ||||||||
\(704\) | −2.87150 | −0.108224 | ||||||||
\(705\) | −6.10251 | −0.229834 | ||||||||
\(706\) | −12.6882 | −0.477526 | ||||||||
\(707\) | 7.35383 | 0.276569 | ||||||||
\(708\) | 45.3469 | 1.70424 | ||||||||
\(709\) | −40.7262 | −1.52951 | −0.764753 | − | 0.644324i | \(-0.777139\pi\) | ||||
−0.764753 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(710\) | −13.9287 | −0.522733 | ||||||||
\(711\) | −17.0331 | −0.638792 | ||||||||
\(712\) | −24.3321 | −0.911883 | ||||||||
\(713\) | 38.0923 | 1.42657 | ||||||||
\(714\) | −14.2412 | −0.532964 | ||||||||
\(715\) | 42.3800 | 1.58492 | ||||||||
\(716\) | 0.859006 | 0.0321026 | ||||||||
\(717\) | 28.4866 | 1.06385 | ||||||||
\(718\) | 7.87577 | 0.293921 | ||||||||
\(719\) | 27.3143 | 1.01865 | 0.509327 | − | 0.860573i | \(-0.329895\pi\) | ||||
0.509327 | + | 0.860573i | \(0.329895\pi\) | |||||||
\(720\) | −12.8242 | −0.477931 | ||||||||
\(721\) | 11.4000 | 0.424558 | ||||||||
\(722\) | −9.36831 | −0.348652 | ||||||||
\(723\) | 34.2427 | 1.27350 | ||||||||
\(724\) | 14.0458 | 0.522009 | ||||||||
\(725\) | −0.600182 | −0.0222902 | ||||||||
\(726\) | −9.54150 | −0.354118 | ||||||||
\(727\) | −2.45544 | −0.0910673 | −0.0455337 | − | 0.998963i | \(-0.514499\pi\) | ||||
−0.0455337 | + | 0.998963i | \(0.514499\pi\) | |||||||
\(728\) | 27.5164 | 1.01983 | ||||||||
\(729\) | −34.8977 | −1.29251 | ||||||||
\(730\) | 11.7926 | 0.436462 | ||||||||
\(731\) | 6.43896 | 0.238154 | ||||||||
\(732\) | 12.2839 | 0.454027 | ||||||||
\(733\) | 40.6914 | 1.50297 | 0.751486 | − | 0.659750i | \(-0.229338\pi\) | ||||
0.751486 | + | 0.659750i | \(0.229338\pi\) | |||||||
\(734\) | −6.50199 | −0.239993 | ||||||||
\(735\) | 0.323207 | 0.0119217 | ||||||||
\(736\) | 25.4170 | 0.936882 | ||||||||
\(737\) | −19.8897 | −0.732646 | ||||||||
\(738\) | −2.42276 | −0.0891832 | ||||||||
\(739\) | −6.18246 | −0.227426 | −0.113713 | − | 0.993514i | \(-0.536274\pi\) | ||||
−0.113713 | + | 0.993514i | \(0.536274\pi\) | |||||||
\(740\) | 12.8604 | 0.472758 | ||||||||
\(741\) | 24.6649 | 0.906088 | ||||||||
\(742\) | 5.99848 | 0.220211 | ||||||||
\(743\) | 1.18751 | 0.0435654 | 0.0217827 | − | 0.999763i | \(-0.493066\pi\) | ||||
0.0217827 | + | 0.999763i | \(0.493066\pi\) | |||||||
\(744\) | 51.8280 | 1.90011 | ||||||||
\(745\) | 14.8608 | 0.544459 | ||||||||
\(746\) | 11.2819 | 0.413061 | ||||||||
\(747\) | −28.3546 | −1.03744 | ||||||||
\(748\) | −20.2210 | −0.739354 | ||||||||
\(749\) | −43.8405 | −1.60190 | ||||||||
\(750\) | −17.5799 | −0.641927 | ||||||||
\(751\) | −50.8223 | −1.85453 | −0.927265 | − | 0.374405i | \(-0.877847\pi\) | ||||
−0.927265 | + | 0.374405i | \(0.877847\pi\) | |||||||
\(752\) | −1.57514 | −0.0574393 | ||||||||
\(753\) | −65.5847 | −2.39004 | ||||||||
\(754\) | −2.91000 | −0.105976 | ||||||||
\(755\) | 42.7874 | 1.55719 | ||||||||
\(756\) | −5.10873 | −0.185803 | ||||||||
\(757\) | −44.3162 | −1.61070 | −0.805350 | − | 0.592799i | \(-0.798023\pi\) | ||||
−0.805350 | + | 0.592799i | \(0.798023\pi\) | |||||||
\(758\) | −7.15745 | −0.259970 | ||||||||
\(759\) | 45.9085 | 1.66637 | ||||||||
\(760\) | −12.3300 | −0.447257 | ||||||||
\(761\) | 6.00843 | 0.217806 | 0.108903 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108903 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(762\) | −34.7681 | −1.25951 | ||||||||
\(763\) | 22.3810 | 0.810245 | ||||||||
\(764\) | 3.31881 | 0.120070 | ||||||||
\(765\) | 26.1851 | 0.946726 | ||||||||
\(766\) | 5.79278 | 0.209302 | ||||||||
\(767\) | 50.0885 | 1.80859 | ||||||||
\(768\) | 22.2222 | 0.801875 | ||||||||
\(769\) | −40.7642 | −1.46999 | −0.734997 | − | 0.678071i | \(-0.762816\pi\) | ||||
−0.734997 | + | 0.678071i | \(0.762816\pi\) | |||||||
\(770\) | −17.0053 | −0.612828 | ||||||||
\(771\) | −24.4201 | −0.879470 | ||||||||
\(772\) | −2.38173 | −0.0857202 | ||||||||
\(773\) | −1.98713 | −0.0714721 | −0.0357360 | − | 0.999361i | \(-0.511378\pi\) | ||||
−0.0357360 | + | 0.999361i | \(0.511378\pi\) | |||||||
\(774\) | −4.68387 | −0.168358 | ||||||||
\(775\) | 5.17457 | 0.185876 | ||||||||
\(776\) | 46.0043 | 1.65146 | ||||||||
\(777\) | 23.5540 | 0.844995 | ||||||||
\(778\) | 16.2530 | 0.582697 | ||||||||
\(779\) | 2.31461 | 0.0829296 | ||||||||
\(780\) | −41.2654 | −1.47754 | ||||||||
\(781\) | −36.2222 | −1.29613 | ||||||||
\(782\) | −9.30380 | −0.332703 | ||||||||
\(783\) | 1.23278 | 0.0440559 | ||||||||
\(784\) | 0.0834239 | 0.00297943 | ||||||||
\(785\) | 44.6986 | 1.59536 | ||||||||
\(786\) | −8.05497 | −0.287311 | ||||||||
\(787\) | −15.7847 | −0.562665 | −0.281332 | − | 0.959610i | \(-0.590776\pi\) | ||||
−0.281332 | + | 0.959610i | \(0.590776\pi\) | |||||||
\(788\) | 13.9456 | 0.496793 | ||||||||
\(789\) | 9.31186 | 0.331511 | ||||||||
\(790\) | 7.67107 | 0.272924 | ||||||||
\(791\) | −39.4584 | −1.40298 | ||||||||
\(792\) | 33.5632 | 1.19262 | ||||||||
\(793\) | 13.5684 | 0.481827 | ||||||||
\(794\) | −17.6712 | −0.627128 | ||||||||
\(795\) | −20.5261 | −0.727987 | ||||||||
\(796\) | 13.8123 | 0.489564 | ||||||||
\(797\) | 2.84443 | 0.100755 | 0.0503774 | − | 0.998730i | \(-0.483958\pi\) | ||||
0.0503774 | + | 0.998730i | \(0.483958\pi\) | |||||||
\(798\) | −9.89699 | −0.350350 | ||||||||
\(799\) | 3.21619 | 0.113781 | ||||||||
\(800\) | 3.45272 | 0.122072 | ||||||||
\(801\) | 35.9108 | 1.26885 | ||||||||
\(802\) | 10.6307 | 0.375383 | ||||||||
\(803\) | 30.6672 | 1.08222 | ||||||||
\(804\) | 19.3666 | 0.683007 | ||||||||
\(805\) | 27.7686 | 0.978713 | ||||||||
\(806\) | 25.0890 | 0.883724 | ||||||||
\(807\) | −26.0658 | −0.917561 | ||||||||
\(808\) | 6.53664 | 0.229958 | ||||||||
\(809\) | −23.9498 | −0.842031 | −0.421016 | − | 0.907053i | \(-0.638326\pi\) | ||||
−0.421016 | + | 0.907053i | \(0.638326\pi\) | |||||||
\(810\) | 11.4753 | 0.403203 | ||||||||
\(811\) | 46.9938 | 1.65017 | 0.825087 | − | 0.565006i | \(-0.191126\pi\) | ||||
0.825087 | + | 0.565006i | \(0.191126\pi\) | |||||||
\(812\) | −4.14408 | −0.145429 | ||||||||
\(813\) | −52.3490 | −1.83596 | ||||||||
\(814\) | −9.42343 | −0.330291 | ||||||||
\(815\) | −17.8163 | −0.624077 | ||||||||
\(816\) | 12.5783 | 0.440329 | ||||||||
\(817\) | 4.47478 | 0.156553 | ||||||||
\(818\) | 11.8253 | 0.413463 | ||||||||
\(819\) | −40.6105 | −1.41905 | ||||||||
\(820\) | −3.87244 | −0.135231 | ||||||||
\(821\) | −10.1990 | −0.355946 | −0.177973 | − | 0.984035i | \(-0.556954\pi\) | ||||
−0.177973 | + | 0.984035i | \(0.556954\pi\) | |||||||
\(822\) | −8.27907 | −0.288766 | ||||||||
\(823\) | 33.9216 | 1.18243 | 0.591216 | − | 0.806513i | \(-0.298648\pi\) | ||||
0.591216 | + | 0.806513i | \(0.298648\pi\) | |||||||
\(824\) | 10.1332 | 0.353006 | ||||||||
\(825\) | 6.23635 | 0.217122 | ||||||||
\(826\) | −20.0984 | −0.699313 | ||||||||
\(827\) | −38.7238 | −1.34656 | −0.673280 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673280 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(828\) | −24.0193 | −0.834729 | ||||||||
\(829\) | −30.1736 | −1.04797 | −0.523986 | − | 0.851727i | \(-0.675556\pi\) | ||||
−0.523986 | + | 0.851727i | \(0.675556\pi\) | |||||||
\(830\) | 12.7699 | 0.443248 | ||||||||
\(831\) | 43.5980 | 1.51240 | ||||||||
\(832\) | 3.08833 | 0.107069 | ||||||||
\(833\) | −0.170339 | −0.00590190 | ||||||||
\(834\) | 1.68842 | 0.0584652 | ||||||||
\(835\) | −4.39360 | −0.152047 | ||||||||
\(836\) | −14.0527 | −0.486022 | ||||||||
\(837\) | −10.6286 | −0.367378 | ||||||||
\(838\) | −9.13295 | −0.315493 | ||||||||
\(839\) | −36.5864 | −1.26310 | −0.631551 | − | 0.775335i | \(-0.717581\pi\) | ||||
−0.631551 | + | 0.775335i | \(0.717581\pi\) | |||||||
\(840\) | 37.7816 | 1.30359 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −18.5584 | −0.639564 | ||||||||
\(843\) | 38.7167 | 1.33347 | ||||||||
\(844\) | −31.2280 | −1.07491 | ||||||||
\(845\) | −14.8161 | −0.509691 | ||||||||
\(846\) | −2.33954 | −0.0804350 | ||||||||
\(847\) | −15.0087 | −0.515704 | ||||||||
\(848\) | −5.29806 | −0.181936 | ||||||||
\(849\) | −34.6643 | −1.18968 | ||||||||
\(850\) | −1.26386 | −0.0433499 | ||||||||
\(851\) | 15.3878 | 0.527489 | ||||||||
\(852\) | 35.2696 | 1.20832 | ||||||||
\(853\) | 21.4996 | 0.736131 | 0.368065 | − | 0.929800i | \(-0.380020\pi\) | ||||
0.368065 | + | 0.929800i | \(0.380020\pi\) | |||||||
\(854\) | −5.44441 | −0.186304 | ||||||||
\(855\) | 18.1975 | 0.622340 | ||||||||
\(856\) | −38.9687 | −1.33192 | ||||||||
\(857\) | −19.5159 | −0.666649 | −0.333325 | − | 0.942812i | \(-0.608171\pi\) | ||||
−0.333325 | + | 0.942812i | \(0.608171\pi\) | |||||||
\(858\) | 30.2371 | 1.03228 | ||||||||
\(859\) | 36.0006 | 1.22833 | 0.614163 | − | 0.789179i | \(-0.289494\pi\) | ||||
0.614163 | + | 0.789179i | \(0.289494\pi\) | |||||||
\(860\) | −7.48649 | −0.255287 | ||||||||
\(861\) | −7.09242 | −0.241709 | ||||||||
\(862\) | 16.5283 | 0.562956 | ||||||||
\(863\) | −6.68443 | −0.227541 | −0.113770 | − | 0.993507i | \(-0.536293\pi\) | ||||
−0.113770 | + | 0.993507i | \(0.536293\pi\) | |||||||
\(864\) | −7.09190 | −0.241271 | ||||||||
\(865\) | −23.5421 | −0.800454 | ||||||||
\(866\) | 11.5459 | 0.392345 | ||||||||
\(867\) | 17.6057 | 0.597921 | ||||||||
\(868\) | 35.7289 | 1.21272 | ||||||||
\(869\) | 19.9490 | 0.676725 | ||||||||
\(870\) | −3.99560 | −0.135463 | ||||||||
\(871\) | 21.3916 | 0.724827 | ||||||||
\(872\) | 19.8939 | 0.673692 | ||||||||
\(873\) | −67.8962 | −2.29794 | ||||||||
\(874\) | −6.46571 | −0.218706 | ||||||||
\(875\) | −27.6530 | −0.934842 | ||||||||
\(876\) | −29.8607 | −1.00890 | ||||||||
\(877\) | −0.430584 | −0.0145398 | −0.00726989 | − | 0.999974i | \(-0.502314\pi\) | ||||
−0.00726989 | + | 0.999974i | \(0.502314\pi\) | |||||||
\(878\) | 5.10808 | 0.172389 | ||||||||
\(879\) | −56.5871 | −1.90864 | ||||||||
\(880\) | 15.0196 | 0.506312 | ||||||||
\(881\) | −5.64082 | −0.190044 | −0.0950220 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950220 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(882\) | 0.123909 | 0.00417223 | ||||||||
\(883\) | −17.5655 | −0.591126 | −0.295563 | − | 0.955323i | \(-0.595507\pi\) | ||||
−0.295563 | + | 0.955323i | \(0.595507\pi\) | |||||||
\(884\) | 21.7480 | 0.731464 | ||||||||
\(885\) | 68.7744 | 2.31183 | ||||||||
\(886\) | 3.99664 | 0.134270 | ||||||||
\(887\) | −3.06399 | −0.102879 | −0.0514393 | − | 0.998676i | \(-0.516381\pi\) | ||||
−0.0514393 | + | 0.998676i | \(0.516381\pi\) | |||||||
\(888\) | 20.9365 | 0.702585 | ||||||||
\(889\) | −54.6899 | −1.83424 | ||||||||
\(890\) | −16.1729 | −0.542116 | ||||||||
\(891\) | 29.8423 | 0.999754 | ||||||||
\(892\) | 26.6271 | 0.891541 | ||||||||
\(893\) | 2.23510 | 0.0747949 | ||||||||
\(894\) | 10.6029 | 0.354613 | ||||||||
\(895\) | 1.30279 | 0.0435476 | ||||||||
\(896\) | 29.3181 | 0.979447 | ||||||||
\(897\) | −49.3752 | −1.64859 | ||||||||
\(898\) | 5.66363 | 0.188998 | ||||||||
\(899\) | −8.62167 | −0.287549 | ||||||||
\(900\) | −3.26286 | −0.108762 | ||||||||
\(901\) | 10.8178 | 0.360394 | ||||||||
\(902\) | 2.83752 | 0.0944791 | ||||||||
\(903\) | −13.7116 | −0.456293 | ||||||||
\(904\) | −35.0736 | −1.16653 | ||||||||
\(905\) | 21.3023 | 0.708113 | ||||||||
\(906\) | 30.5278 | 1.01422 | ||||||||
\(907\) | 27.7618 | 0.921815 | 0.460907 | − | 0.887448i | \(-0.347524\pi\) | ||||
0.460907 | + | 0.887448i | \(0.347524\pi\) | |||||||
\(908\) | −9.41983 | −0.312608 | ||||||||
\(909\) | −9.64720 | −0.319977 | ||||||||
\(910\) | 18.2894 | 0.606289 | ||||||||
\(911\) | −48.8713 | −1.61918 | −0.809590 | − | 0.586996i | \(-0.800310\pi\) | ||||
−0.809590 | + | 0.586996i | \(0.800310\pi\) | |||||||
\(912\) | 8.74134 | 0.289455 | ||||||||
\(913\) | 33.2087 | 1.09905 | ||||||||
\(914\) | −0.857155 | −0.0283522 | ||||||||
\(915\) | 18.6302 | 0.615894 | ||||||||
\(916\) | 15.6584 | 0.517370 | ||||||||
\(917\) | −12.6704 | −0.418413 | ||||||||
\(918\) | 2.59597 | 0.0856797 | ||||||||
\(919\) | −54.5708 | −1.80012 | −0.900062 | − | 0.435762i | \(-0.856479\pi\) | ||||
−0.900062 | + | 0.435762i | \(0.856479\pi\) | |||||||
\(920\) | 24.6828 | 0.813767 | ||||||||
\(921\) | −47.6677 | −1.57070 | ||||||||
\(922\) | −6.81531 | −0.224450 | ||||||||
\(923\) | 38.9575 | 1.28230 | ||||||||
\(924\) | 43.0602 | 1.41658 | ||||||||
\(925\) | 2.09033 | 0.0687296 | ||||||||
\(926\) | −21.4156 | −0.703760 | ||||||||
\(927\) | −14.9552 | −0.491193 | ||||||||
\(928\) | −5.75278 | −0.188844 | ||||||||
\(929\) | −46.0806 | −1.51186 | −0.755928 | − | 0.654655i | \(-0.772814\pi\) | ||||
−0.755928 | + | 0.654655i | \(0.772814\pi\) | |||||||
\(930\) | 34.4487 | 1.12962 | ||||||||
\(931\) | −0.118378 | −0.00387967 | ||||||||
\(932\) | −3.77587 | −0.123683 | ||||||||
\(933\) | −61.6990 | −2.01993 | ||||||||
\(934\) | −4.71726 | −0.154353 | ||||||||
\(935\) | −30.6678 | −1.00295 | ||||||||
\(936\) | −36.0976 | −1.17989 | ||||||||
\(937\) | 47.0754 | 1.53789 | 0.768944 | − | 0.639317i | \(-0.220783\pi\) | ||||
0.768944 | + | 0.639317i | \(0.220783\pi\) | |||||||
\(938\) | −8.58355 | −0.280263 | ||||||||
\(939\) | 50.6220 | 1.65198 | ||||||||
\(940\) | −3.73942 | −0.121966 | ||||||||
\(941\) | 47.5842 | 1.55120 | 0.775600 | − | 0.631224i | \(-0.217447\pi\) | ||||
0.775600 | + | 0.631224i | \(0.217447\pi\) | |||||||
\(942\) | 31.8914 | 1.03908 | ||||||||
\(943\) | −4.63349 | −0.150887 | ||||||||
\(944\) | 17.7516 | 0.577764 | ||||||||
\(945\) | −7.74805 | −0.252044 | ||||||||
\(946\) | 5.48571 | 0.178356 | ||||||||
\(947\) | −39.4413 | −1.28167 | −0.640835 | − | 0.767678i | \(-0.721412\pi\) | ||||
−0.640835 | + | 0.767678i | \(0.721412\pi\) | |||||||
\(948\) | −19.4244 | −0.630875 | ||||||||
\(949\) | −32.9830 | −1.07067 | ||||||||
\(950\) | −0.878322 | −0.0284965 | ||||||||
\(951\) | −50.5456 | −1.63905 | ||||||||
\(952\) | −19.9119 | −0.645350 | ||||||||
\(953\) | −25.0439 | −0.811250 | −0.405625 | − | 0.914039i | \(-0.632946\pi\) | ||||
−0.405625 | + | 0.914039i | \(0.632946\pi\) | |||||||
\(954\) | −7.86917 | −0.254774 | ||||||||
\(955\) | 5.03340 | 0.162877 | ||||||||
\(956\) | 17.4556 | 0.564556 | ||||||||
\(957\) | −10.3908 | −0.335886 | ||||||||
\(958\) | −21.6192 | −0.698483 | ||||||||
\(959\) | −13.0229 | −0.420531 | ||||||||
\(960\) | 4.24046 | 0.136860 | ||||||||
\(961\) | 43.3333 | 1.39785 | ||||||||
\(962\) | 10.1350 | 0.326766 | ||||||||
\(963\) | 57.5125 | 1.85332 | ||||||||
\(964\) | 20.9828 | 0.675811 | ||||||||
\(965\) | −3.61220 | −0.116281 | ||||||||
\(966\) | 19.8122 | 0.637447 | ||||||||
\(967\) | −10.8112 | −0.347665 | −0.173832 | − | 0.984775i | \(-0.555615\pi\) | ||||
−0.173832 | + | 0.984775i | \(0.555615\pi\) | |||||||
\(968\) | −13.3408 | −0.428791 | ||||||||
\(969\) | −17.8485 | −0.573377 | ||||||||
\(970\) | 30.5779 | 0.981796 | ||||||||
\(971\) | −54.2227 | −1.74009 | −0.870045 | − | 0.492973i | \(-0.835910\pi\) | ||||
−0.870045 | + | 0.492973i | \(0.835910\pi\) | |||||||
\(972\) | −34.8281 | −1.11711 | ||||||||
\(973\) | 2.65587 | 0.0851432 | ||||||||
\(974\) | 11.4701 | 0.367527 | ||||||||
\(975\) | −6.70728 | −0.214805 | ||||||||
\(976\) | 4.80868 | 0.153922 | ||||||||
\(977\) | 6.94094 | 0.222060 | 0.111030 | − | 0.993817i | \(-0.464585\pi\) | ||||
0.111030 | + | 0.993817i | \(0.464585\pi\) | |||||||
\(978\) | −12.7115 | −0.406468 | ||||||||
\(979\) | −42.0585 | −1.34420 | ||||||||
\(980\) | 0.198051 | 0.00632650 | ||||||||
\(981\) | −29.3607 | −0.937414 | ||||||||
\(982\) | −16.6174 | −0.530283 | ||||||||
\(983\) | −29.7102 | −0.947607 | −0.473804 | − | 0.880631i | \(-0.657119\pi\) | ||||
−0.473804 | + | 0.880631i | \(0.657119\pi\) | |||||||
\(984\) | −6.30428 | −0.200973 | ||||||||
\(985\) | 21.1504 | 0.673907 | ||||||||
\(986\) | 2.10579 | 0.0670620 | ||||||||
\(987\) | −6.84879 | −0.217999 | ||||||||
\(988\) | 15.1139 | 0.480836 | ||||||||
\(989\) | −8.95780 | −0.284842 | ||||||||
\(990\) | 22.3086 | 0.709013 | ||||||||
\(991\) | −6.54877 | −0.208028 | −0.104014 | − | 0.994576i | \(-0.533169\pi\) | ||||
−0.104014 | + | 0.994576i | \(0.533169\pi\) | |||||||
\(992\) | 49.5986 | 1.57476 | ||||||||
\(993\) | −11.1748 | −0.354622 | ||||||||
\(994\) | −15.6320 | −0.495817 | ||||||||
\(995\) | 20.9481 | 0.664101 | ||||||||
\(996\) | −32.3353 | −1.02458 | ||||||||
\(997\) | −7.99707 | −0.253270 | −0.126635 | − | 0.991949i | \(-0.540418\pi\) | ||||
−0.126635 | + | 0.991949i | \(0.540418\pi\) | |||||||
\(998\) | 0.568609 | 0.0179990 | ||||||||
\(999\) | −4.29355 | −0.135842 |
(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 | 4031.2.a.c.1.38 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.38 | ✓ | 61 | 1.1 | even | 1 | trivial |