Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.44881 | −1.41382 | −0.706910 | − | 0.707304i | \(-0.749911\pi\) | ||||
−0.706910 | + | 0.707304i | \(0.749911\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.87933 | 1.28768 | 0.643838 | − | 0.765162i | \(-0.277341\pi\) | ||||
0.643838 | + | 0.765162i | \(0.277341\pi\) | |||||||
\(6\) | −2.44881 | −0.999721 | ||||||||
\(7\) | −3.14262 | −1.18780 | −0.593899 | − | 0.804540i | \(-0.702412\pi\) | ||||
−0.593899 | + | 0.804540i | \(0.702412\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.99666 | 0.998886 | ||||||||
\(10\) | 2.87933 | 0.910524 | ||||||||
\(11\) | −3.58337 | −1.08043 | −0.540213 | − | 0.841528i | \(-0.681656\pi\) | ||||
−0.540213 | + | 0.841528i | \(0.681656\pi\) | |||||||
\(12\) | −2.44881 | −0.706910 | ||||||||
\(13\) | −2.44736 | −0.678776 | −0.339388 | − | 0.940647i | \(-0.610220\pi\) | ||||
−0.339388 | + | 0.940647i | \(0.610220\pi\) | |||||||
\(14\) | −3.14262 | −0.839900 | ||||||||
\(15\) | −7.05093 | −1.82054 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.485959 | −0.117862 | −0.0589312 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589312 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(18\) | 2.99666 | 0.706319 | ||||||||
\(19\) | −1.70933 | −0.392148 | −0.196074 | − | 0.980589i | \(-0.562819\pi\) | ||||
−0.196074 | + | 0.980589i | \(0.562819\pi\) | |||||||
\(20\) | 2.87933 | 0.643838 | ||||||||
\(21\) | 7.69566 | 1.67933 | ||||||||
\(22\) | −3.58337 | −0.763977 | ||||||||
\(23\) | 6.28484 | 1.31048 | 0.655239 | − | 0.755421i | \(-0.272568\pi\) | ||||
0.655239 | + | 0.755421i | \(0.272568\pi\) | |||||||
\(24\) | −2.44881 | −0.499861 | ||||||||
\(25\) | 3.29054 | 0.658109 | ||||||||
\(26\) | −2.44736 | −0.479967 | ||||||||
\(27\) | 0.00818672 | 0.00157554 | ||||||||
\(28\) | −3.14262 | −0.593899 | ||||||||
\(29\) | 5.84498 | 1.08539 | 0.542693 | − | 0.839931i | \(-0.317405\pi\) | ||||
0.542693 | + | 0.839931i | \(0.317405\pi\) | |||||||
\(30\) | −7.05093 | −1.28732 | ||||||||
\(31\) | 8.31794 | 1.49395 | 0.746973 | − | 0.664854i | \(-0.231506\pi\) | ||||
0.746973 | + | 0.664854i | \(0.231506\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.77498 | 1.52753 | ||||||||
\(34\) | −0.485959 | −0.0833413 | ||||||||
\(35\) | −9.04863 | −1.52950 | ||||||||
\(36\) | 2.99666 | 0.499443 | ||||||||
\(37\) | 6.89647 | 1.13377 | 0.566886 | − | 0.823796i | \(-0.308148\pi\) | ||||
0.566886 | + | 0.823796i | \(0.308148\pi\) | |||||||
\(38\) | −1.70933 | −0.277291 | ||||||||
\(39\) | 5.99312 | 0.959666 | ||||||||
\(40\) | 2.87933 | 0.455262 | ||||||||
\(41\) | −0.133244 | −0.0208092 | −0.0104046 | − | 0.999946i | \(-0.503312\pi\) | ||||
−0.0104046 | + | 0.999946i | \(0.503312\pi\) | |||||||
\(42\) | 7.69566 | 1.18747 | ||||||||
\(43\) | 3.40114 | 0.518670 | 0.259335 | − | 0.965787i | \(-0.416497\pi\) | ||||
0.259335 | + | 0.965787i | \(0.416497\pi\) | |||||||
\(44\) | −3.58337 | −0.540213 | ||||||||
\(45\) | 8.62837 | 1.28624 | ||||||||
\(46\) | 6.28484 | 0.926648 | ||||||||
\(47\) | −7.79529 | −1.13706 | −0.568530 | − | 0.822663i | \(-0.692488\pi\) | ||||
−0.568530 | + | 0.822663i | \(0.692488\pi\) | |||||||
\(48\) | −2.44881 | −0.353455 | ||||||||
\(49\) | 2.87604 | 0.410864 | ||||||||
\(50\) | 3.29054 | 0.465353 | ||||||||
\(51\) | 1.19002 | 0.166636 | ||||||||
\(52\) | −2.44736 | −0.339388 | ||||||||
\(53\) | −10.3214 | −1.41776 | −0.708879 | − | 0.705331i | \(-0.750799\pi\) | ||||
−0.708879 | + | 0.705331i | \(0.750799\pi\) | |||||||
\(54\) | 0.00818672 | 0.00111407 | ||||||||
\(55\) | −10.3177 | −1.39124 | ||||||||
\(56\) | −3.14262 | −0.419950 | ||||||||
\(57\) | 4.18583 | 0.554427 | ||||||||
\(58\) | 5.84498 | 0.767484 | ||||||||
\(59\) | −12.2561 | −1.59561 | −0.797804 | − | 0.602916i | \(-0.794005\pi\) | ||||
−0.797804 | + | 0.602916i | \(0.794005\pi\) | |||||||
\(60\) | −7.05093 | −0.910271 | ||||||||
\(61\) | 11.8468 | 1.51682 | 0.758411 | − | 0.651777i | \(-0.225976\pi\) | ||||
0.758411 | + | 0.651777i | \(0.225976\pi\) | |||||||
\(62\) | 8.31794 | 1.05638 | ||||||||
\(63\) | −9.41735 | −1.18647 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.04676 | −0.874043 | ||||||||
\(66\) | 8.77498 | 1.08012 | ||||||||
\(67\) | −3.32337 | −0.406014 | −0.203007 | − | 0.979177i | \(-0.565071\pi\) | ||||
−0.203007 | + | 0.979177i | \(0.565071\pi\) | |||||||
\(68\) | −0.485959 | −0.0589312 | ||||||||
\(69\) | −15.3904 | −1.85278 | ||||||||
\(70\) | −9.04863 | −1.08152 | ||||||||
\(71\) | −13.8090 | −1.63883 | −0.819413 | − | 0.573203i | \(-0.805701\pi\) | ||||
−0.819413 | + | 0.573203i | \(0.805701\pi\) | |||||||
\(72\) | 2.99666 | 0.353159 | ||||||||
\(73\) | −0.396742 | −0.0464352 | −0.0232176 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232176 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(74\) | 6.89647 | 0.801698 | ||||||||
\(75\) | −8.05791 | −0.930447 | ||||||||
\(76\) | −1.70933 | −0.196074 | ||||||||
\(77\) | 11.2612 | 1.28333 | ||||||||
\(78\) | 5.99312 | 0.678587 | ||||||||
\(79\) | −12.4145 | −1.39674 | −0.698370 | − | 0.715737i | \(-0.746091\pi\) | ||||
−0.698370 | + | 0.715737i | \(0.746091\pi\) | |||||||
\(80\) | 2.87933 | 0.321919 | ||||||||
\(81\) | −9.01002 | −1.00111 | ||||||||
\(82\) | −0.133244 | −0.0147143 | ||||||||
\(83\) | 1.89872 | 0.208412 | 0.104206 | − | 0.994556i | \(-0.466770\pi\) | ||||
0.104206 | + | 0.994556i | \(0.466770\pi\) | |||||||
\(84\) | 7.69566 | 0.839666 | ||||||||
\(85\) | −1.39924 | −0.151769 | ||||||||
\(86\) | 3.40114 | 0.366755 | ||||||||
\(87\) | −14.3132 | −1.53454 | ||||||||
\(88\) | −3.58337 | −0.381988 | ||||||||
\(89\) | −9.24598 | −0.980072 | −0.490036 | − | 0.871702i | \(-0.663016\pi\) | ||||
−0.490036 | + | 0.871702i | \(0.663016\pi\) | |||||||
\(90\) | 8.62837 | 0.909510 | ||||||||
\(91\) | 7.69112 | 0.806248 | ||||||||
\(92\) | 6.28484 | 0.655239 | ||||||||
\(93\) | −20.3690 | −2.11217 | ||||||||
\(94\) | −7.79529 | −0.804022 | ||||||||
\(95\) | −4.92174 | −0.504960 | ||||||||
\(96\) | −2.44881 | −0.249930 | ||||||||
\(97\) | 8.08104 | 0.820505 | 0.410253 | − | 0.911972i | \(-0.365440\pi\) | ||||
0.410253 | + | 0.911972i | \(0.365440\pi\) | |||||||
\(98\) | 2.87604 | 0.290524 | ||||||||
\(99\) | −10.7381 | −1.07922 | ||||||||
\(100\) | 3.29054 | 0.329054 | ||||||||
\(101\) | −6.11390 | −0.608356 | −0.304178 | − | 0.952615i | \(-0.598382\pi\) | ||||
−0.304178 | + | 0.952615i | \(0.598382\pi\) | |||||||
\(102\) | 1.19002 | 0.117830 | ||||||||
\(103\) | −18.7681 | −1.84928 | −0.924638 | − | 0.380847i | \(-0.875632\pi\) | ||||
−0.924638 | + | 0.380847i | \(0.875632\pi\) | |||||||
\(104\) | −2.44736 | −0.239983 | ||||||||
\(105\) | 22.1584 | 2.16243 | ||||||||
\(106\) | −10.3214 | −1.00251 | ||||||||
\(107\) | −11.9793 | −1.15808 | −0.579042 | − | 0.815298i | \(-0.696573\pi\) | ||||
−0.579042 | + | 0.815298i | \(0.696573\pi\) | |||||||
\(108\) | 0.00818672 | 0.000787768 0 | ||||||||
\(109\) | −3.08904 | −0.295876 | −0.147938 | − | 0.988997i | \(-0.547264\pi\) | ||||
−0.147938 | + | 0.988997i | \(0.547264\pi\) | |||||||
\(110\) | −10.3177 | −0.983754 | ||||||||
\(111\) | −16.8881 | −1.60295 | ||||||||
\(112\) | −3.14262 | −0.296949 | ||||||||
\(113\) | 16.3673 | 1.53970 | 0.769852 | − | 0.638222i | \(-0.220330\pi\) | ||||
0.769852 | + | 0.638222i | \(0.220330\pi\) | |||||||
\(114\) | 4.18583 | 0.392039 | ||||||||
\(115\) | 18.0961 | 1.68747 | ||||||||
\(116\) | 5.84498 | 0.542693 | ||||||||
\(117\) | −7.33390 | −0.678019 | ||||||||
\(118\) | −12.2561 | −1.12827 | ||||||||
\(119\) | 1.52718 | 0.139997 | ||||||||
\(120\) | −7.05093 | −0.643659 | ||||||||
\(121\) | 1.84052 | 0.167320 | ||||||||
\(122\) | 11.8468 | 1.07255 | ||||||||
\(123\) | 0.326288 | 0.0294204 | ||||||||
\(124\) | 8.31794 | 0.746973 | ||||||||
\(125\) | −4.92209 | −0.440245 | ||||||||
\(126\) | −9.41735 | −0.838964 | ||||||||
\(127\) | −10.3216 | −0.915895 | −0.457948 | − | 0.888979i | \(-0.651415\pi\) | ||||
−0.457948 | + | 0.888979i | \(0.651415\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.32875 | −0.733305 | ||||||||
\(130\) | −7.04676 | −0.618042 | ||||||||
\(131\) | 11.8612 | 1.03632 | 0.518158 | − | 0.855285i | \(-0.326618\pi\) | ||||
0.518158 | + | 0.855285i | \(0.326618\pi\) | |||||||
\(132\) | 8.77498 | 0.763764 | ||||||||
\(133\) | 5.37178 | 0.465793 | ||||||||
\(134\) | −3.32337 | −0.287095 | ||||||||
\(135\) | 0.0235723 | 0.00202878 | ||||||||
\(136\) | −0.485959 | −0.0416707 | ||||||||
\(137\) | −1.10912 | −0.0947589 | −0.0473795 | − | 0.998877i | \(-0.515087\pi\) | ||||
−0.0473795 | + | 0.998877i | \(0.515087\pi\) | |||||||
\(138\) | −15.3904 | −1.31011 | ||||||||
\(139\) | −1.19293 | −0.101183 | −0.0505915 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505915 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(140\) | −9.04863 | −0.764749 | ||||||||
\(141\) | 19.0892 | 1.60760 | ||||||||
\(142\) | −13.8090 | −1.15883 | ||||||||
\(143\) | 8.76979 | 0.733367 | ||||||||
\(144\) | 2.99666 | 0.249721 | ||||||||
\(145\) | 16.8296 | 1.39763 | ||||||||
\(146\) | −0.396742 | −0.0328346 | ||||||||
\(147\) | −7.04288 | −0.580887 | ||||||||
\(148\) | 6.89647 | 0.566886 | ||||||||
\(149\) | −20.0727 | −1.64442 | −0.822209 | − | 0.569186i | \(-0.807259\pi\) | ||||
−0.822209 | + | 0.569186i | \(0.807259\pi\) | |||||||
\(150\) | −8.05791 | −0.657926 | ||||||||
\(151\) | −8.77777 | −0.714325 | −0.357162 | − | 0.934042i | \(-0.616256\pi\) | ||||
−0.357162 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(152\) | −1.70933 | −0.138645 | ||||||||
\(153\) | −1.45625 | −0.117731 | ||||||||
\(154\) | 11.2612 | 0.907450 | ||||||||
\(155\) | 23.9501 | 1.92372 | ||||||||
\(156\) | 5.99312 | 0.479833 | ||||||||
\(157\) | 4.93727 | 0.394037 | 0.197019 | − | 0.980400i | \(-0.436874\pi\) | ||||
0.197019 | + | 0.980400i | \(0.436874\pi\) | |||||||
\(158\) | −12.4145 | −0.987645 | ||||||||
\(159\) | 25.2752 | 2.00445 | ||||||||
\(160\) | 2.87933 | 0.227631 | ||||||||
\(161\) | −19.7508 | −1.55658 | ||||||||
\(162\) | −9.01002 | −0.707894 | ||||||||
\(163\) | 2.93231 | 0.229677 | 0.114838 | − | 0.993384i | \(-0.463365\pi\) | ||||
0.114838 | + | 0.993384i | \(0.463365\pi\) | |||||||
\(164\) | −0.133244 | −0.0104046 | ||||||||
\(165\) | 25.2661 | 1.96696 | ||||||||
\(166\) | 1.89872 | 0.147369 | ||||||||
\(167\) | 14.6497 | 1.13362 | 0.566812 | − | 0.823847i | \(-0.308176\pi\) | ||||
0.566812 | + | 0.823847i | \(0.308176\pi\) | |||||||
\(168\) | 7.69566 | 0.593733 | ||||||||
\(169\) | −7.01042 | −0.539263 | ||||||||
\(170\) | −1.39924 | −0.107317 | ||||||||
\(171\) | −5.12229 | −0.391711 | ||||||||
\(172\) | 3.40114 | 0.259335 | ||||||||
\(173\) | −11.9772 | −0.910608 | −0.455304 | − | 0.890336i | \(-0.650469\pi\) | ||||
−0.455304 | + | 0.890336i | \(0.650469\pi\) | |||||||
\(174\) | −14.3132 | −1.08508 | ||||||||
\(175\) | −10.3409 | −0.781700 | ||||||||
\(176\) | −3.58337 | −0.270106 | ||||||||
\(177\) | 30.0128 | 2.25590 | ||||||||
\(178\) | −9.24598 | −0.693015 | ||||||||
\(179\) | −13.4935 | −1.00855 | −0.504274 | − | 0.863544i | \(-0.668240\pi\) | ||||
−0.504274 | + | 0.863544i | \(0.668240\pi\) | |||||||
\(180\) | 8.62837 | 0.643120 | ||||||||
\(181\) | −3.92575 | −0.291799 | −0.145899 | − | 0.989299i | \(-0.546608\pi\) | ||||
−0.145899 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(182\) | 7.69112 | 0.570104 | ||||||||
\(183\) | −29.0104 | −2.14451 | ||||||||
\(184\) | 6.28484 | 0.463324 | ||||||||
\(185\) | 19.8572 | 1.45993 | ||||||||
\(186\) | −20.3690 | −1.49353 | ||||||||
\(187\) | 1.74137 | 0.127342 | ||||||||
\(188\) | −7.79529 | −0.568530 | ||||||||
\(189\) | −0.0257277 | −0.00187142 | ||||||||
\(190\) | −4.92174 | −0.357060 | ||||||||
\(191\) | 21.5097 | 1.55639 | 0.778194 | − | 0.628024i | \(-0.216136\pi\) | ||||
0.778194 | + | 0.628024i | \(0.216136\pi\) | |||||||
\(192\) | −2.44881 | −0.176727 | ||||||||
\(193\) | −9.74815 | −0.701687 | −0.350844 | − | 0.936434i | \(-0.614105\pi\) | ||||
−0.350844 | + | 0.936434i | \(0.614105\pi\) | |||||||
\(194\) | 8.08104 | 0.580185 | ||||||||
\(195\) | 17.2562 | 1.23574 | ||||||||
\(196\) | 2.87604 | 0.205432 | ||||||||
\(197\) | −19.4759 | −1.38760 | −0.693801 | − | 0.720167i | \(-0.744065\pi\) | ||||
−0.693801 | + | 0.720167i | \(0.744065\pi\) | |||||||
\(198\) | −10.7381 | −0.763125 | ||||||||
\(199\) | −2.37529 | −0.168380 | −0.0841900 | − | 0.996450i | \(-0.526830\pi\) | ||||
−0.0841900 | + | 0.996450i | \(0.526830\pi\) | |||||||
\(200\) | 3.29054 | 0.232677 | ||||||||
\(201\) | 8.13829 | 0.574031 | ||||||||
\(202\) | −6.11390 | −0.430173 | ||||||||
\(203\) | −18.3685 | −1.28922 | ||||||||
\(204\) | 1.19002 | 0.0833181 | ||||||||
\(205\) | −0.383653 | −0.0267955 | ||||||||
\(206\) | −18.7681 | −1.30764 | ||||||||
\(207\) | 18.8335 | 1.30902 | ||||||||
\(208\) | −2.44736 | −0.169694 | ||||||||
\(209\) | 6.12517 | 0.423687 | ||||||||
\(210\) | 22.1584 | 1.52907 | ||||||||
\(211\) | −23.3913 | −1.61032 | −0.805162 | − | 0.593055i | \(-0.797921\pi\) | ||||
−0.805162 | + | 0.593055i | \(0.797921\pi\) | |||||||
\(212\) | −10.3214 | −0.708879 | ||||||||
\(213\) | 33.8156 | 2.31701 | ||||||||
\(214\) | −11.9793 | −0.818888 | ||||||||
\(215\) | 9.79302 | 0.667878 | ||||||||
\(216\) | 0.00818672 | 0.000557036 0 | ||||||||
\(217\) | −26.1401 | −1.77451 | ||||||||
\(218\) | −3.08904 | −0.209216 | ||||||||
\(219\) | 0.971546 | 0.0656510 | ||||||||
\(220\) | −10.3177 | −0.695619 | ||||||||
\(221\) | 1.18932 | 0.0800022 | ||||||||
\(222\) | −16.8881 | −1.13346 | ||||||||
\(223\) | −12.5669 | −0.841545 | −0.420772 | − | 0.907166i | \(-0.638241\pi\) | ||||
−0.420772 | + | 0.907166i | \(0.638241\pi\) | |||||||
\(224\) | −3.14262 | −0.209975 | ||||||||
\(225\) | 9.86063 | 0.657376 | ||||||||
\(226\) | 16.3673 | 1.08874 | ||||||||
\(227\) | −12.9012 | −0.856280 | −0.428140 | − | 0.903712i | \(-0.640831\pi\) | ||||
−0.428140 | + | 0.903712i | \(0.640831\pi\) | |||||||
\(228\) | 4.18583 | 0.277213 | ||||||||
\(229\) | 14.2920 | 0.944439 | 0.472219 | − | 0.881481i | \(-0.343453\pi\) | ||||
0.472219 | + | 0.881481i | \(0.343453\pi\) | |||||||
\(230\) | 18.0961 | 1.19322 | ||||||||
\(231\) | −27.5764 | −1.81439 | ||||||||
\(232\) | 5.84498 | 0.383742 | ||||||||
\(233\) | 21.9100 | 1.43537 | 0.717687 | − | 0.696366i | \(-0.245201\pi\) | ||||
0.717687 | + | 0.696366i | \(0.245201\pi\) | |||||||
\(234\) | −7.33390 | −0.479432 | ||||||||
\(235\) | −22.4452 | −1.46416 | ||||||||
\(236\) | −12.2561 | −0.797804 | ||||||||
\(237\) | 30.4007 | 1.97474 | ||||||||
\(238\) | 1.52718 | 0.0989926 | ||||||||
\(239\) | 22.6295 | 1.46378 | 0.731890 | − | 0.681422i | \(-0.238638\pi\) | ||||
0.731890 | + | 0.681422i | \(0.238638\pi\) | |||||||
\(240\) | −7.05093 | −0.455135 | ||||||||
\(241\) | 9.79992 | 0.631268 | 0.315634 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315634 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(242\) | 1.84052 | 0.118313 | ||||||||
\(243\) | 22.0392 | 1.41382 | ||||||||
\(244\) | 11.8468 | 0.758411 | ||||||||
\(245\) | 8.28108 | 0.529059 | ||||||||
\(246\) | 0.326288 | 0.0208034 | ||||||||
\(247\) | 4.18336 | 0.266181 | ||||||||
\(248\) | 8.31794 | 0.528190 | ||||||||
\(249\) | −4.64961 | −0.294657 | ||||||||
\(250\) | −4.92209 | −0.311300 | ||||||||
\(251\) | −25.4567 | −1.60681 | −0.803406 | − | 0.595432i | \(-0.796981\pi\) | ||||
−0.803406 | + | 0.595432i | \(0.796981\pi\) | |||||||
\(252\) | −9.41735 | −0.593237 | ||||||||
\(253\) | −22.5209 | −1.41588 | ||||||||
\(254\) | −10.3216 | −0.647636 | ||||||||
\(255\) | 3.42646 | 0.214573 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.42569 | −0.463202 | −0.231601 | − | 0.972811i | \(-0.574396\pi\) | ||||
−0.231601 | + | 0.972811i | \(0.574396\pi\) | |||||||
\(258\) | −8.32875 | −0.518525 | ||||||||
\(259\) | −21.6730 | −1.34669 | ||||||||
\(260\) | −7.04676 | −0.437022 | ||||||||
\(261\) | 17.5154 | 1.08418 | ||||||||
\(262\) | 11.8612 | 0.732785 | ||||||||
\(263\) | 10.1421 | 0.625388 | 0.312694 | − | 0.949854i | \(-0.398768\pi\) | ||||
0.312694 | + | 0.949854i | \(0.398768\pi\) | |||||||
\(264\) | 8.77498 | 0.540062 | ||||||||
\(265\) | −29.7188 | −1.82561 | ||||||||
\(266\) | 5.37178 | 0.329365 | ||||||||
\(267\) | 22.6416 | 1.38564 | ||||||||
\(268\) | −3.32337 | −0.203007 | ||||||||
\(269\) | 0.384096 | 0.0234187 | 0.0117094 | − | 0.999931i | \(-0.496273\pi\) | ||||
0.0117094 | + | 0.999931i | \(0.496273\pi\) | |||||||
\(270\) | 0.0235723 | 0.00143456 | ||||||||
\(271\) | −9.22397 | −0.560316 | −0.280158 | − | 0.959954i | \(-0.590387\pi\) | ||||
−0.280158 | + | 0.959954i | \(0.590387\pi\) | |||||||
\(272\) | −0.485959 | −0.0294656 | ||||||||
\(273\) | −18.8341 | −1.13989 | ||||||||
\(274\) | −1.10912 | −0.0670047 | ||||||||
\(275\) | −11.7912 | −0.711038 | ||||||||
\(276\) | −15.3904 | −0.926390 | ||||||||
\(277\) | 15.3135 | 0.920096 | 0.460048 | − | 0.887894i | \(-0.347832\pi\) | ||||
0.460048 | + | 0.887894i | \(0.347832\pi\) | |||||||
\(278\) | −1.19293 | −0.0715472 | ||||||||
\(279\) | 24.9260 | 1.49228 | ||||||||
\(280\) | −9.04863 | −0.540759 | ||||||||
\(281\) | 11.6450 | 0.694684 | 0.347342 | − | 0.937739i | \(-0.387084\pi\) | ||||
0.347342 | + | 0.937739i | \(0.387084\pi\) | |||||||
\(282\) | 19.0892 | 1.13674 | ||||||||
\(283\) | 28.2293 | 1.67806 | 0.839029 | − | 0.544086i | \(-0.183123\pi\) | ||||
0.839029 | + | 0.544086i | \(0.183123\pi\) | |||||||
\(284\) | −13.8090 | −0.819413 | ||||||||
\(285\) | 12.0524 | 0.713922 | ||||||||
\(286\) | 8.76979 | 0.518569 | ||||||||
\(287\) | 0.418734 | 0.0247171 | ||||||||
\(288\) | 2.99666 | 0.176580 | ||||||||
\(289\) | −16.7638 | −0.986108 | ||||||||
\(290\) | 16.8296 | 0.988270 | ||||||||
\(291\) | −19.7889 | −1.16005 | ||||||||
\(292\) | −0.396742 | −0.0232176 | ||||||||
\(293\) | 8.49844 | 0.496484 | 0.248242 | − | 0.968698i | \(-0.420147\pi\) | ||||
0.248242 | + | 0.968698i | \(0.420147\pi\) | |||||||
\(294\) | −7.04288 | −0.410749 | ||||||||
\(295\) | −35.2894 | −2.05463 | ||||||||
\(296\) | 6.89647 | 0.400849 | ||||||||
\(297\) | −0.0293360 | −0.00170225 | ||||||||
\(298\) | −20.0727 | −1.16278 | ||||||||
\(299\) | −15.3813 | −0.889521 | ||||||||
\(300\) | −8.05791 | −0.465224 | ||||||||
\(301\) | −10.6885 | −0.616075 | ||||||||
\(302\) | −8.77777 | −0.505104 | ||||||||
\(303\) | 14.9718 | 0.860106 | ||||||||
\(304\) | −1.70933 | −0.0980370 | ||||||||
\(305\) | 34.1107 | 1.95317 | ||||||||
\(306\) | −1.45625 | −0.0832485 | ||||||||
\(307\) | −17.6193 | −1.00559 | −0.502793 | − | 0.864407i | \(-0.667694\pi\) | ||||
−0.502793 | + | 0.864407i | \(0.667694\pi\) | |||||||
\(308\) | 11.2612 | 0.641664 | ||||||||
\(309\) | 45.9595 | 2.61454 | ||||||||
\(310\) | 23.9501 | 1.36027 | ||||||||
\(311\) | 13.7349 | 0.778833 | 0.389416 | − | 0.921062i | \(-0.372677\pi\) | ||||
0.389416 | + | 0.921062i | \(0.372677\pi\) | |||||||
\(312\) | 5.99312 | 0.339293 | ||||||||
\(313\) | −23.1094 | −1.30622 | −0.653110 | − | 0.757263i | \(-0.726536\pi\) | ||||
−0.653110 | + | 0.757263i | \(0.726536\pi\) | |||||||
\(314\) | 4.93727 | 0.278626 | ||||||||
\(315\) | −27.1157 | −1.52779 | ||||||||
\(316\) | −12.4145 | −0.698370 | ||||||||
\(317\) | 31.7713 | 1.78445 | 0.892226 | − | 0.451590i | \(-0.149143\pi\) | ||||
0.892226 | + | 0.451590i | \(0.149143\pi\) | |||||||
\(318\) | 25.2752 | 1.41736 | ||||||||
\(319\) | −20.9447 | −1.17268 | ||||||||
\(320\) | 2.87933 | 0.160959 | ||||||||
\(321\) | 29.3350 | 1.63732 | ||||||||
\(322\) | −19.7508 | −1.10067 | ||||||||
\(323\) | 0.830667 | 0.0462195 | ||||||||
\(324\) | −9.01002 | −0.500557 | ||||||||
\(325\) | −8.05315 | −0.446708 | ||||||||
\(326\) | 2.93231 | 0.162406 | ||||||||
\(327\) | 7.56446 | 0.418315 | ||||||||
\(328\) | −0.133244 | −0.00735716 | ||||||||
\(329\) | 24.4976 | 1.35060 | ||||||||
\(330\) | 25.2661 | 1.39085 | ||||||||
\(331\) | 9.12619 | 0.501621 | 0.250810 | − | 0.968036i | \(-0.419303\pi\) | ||||
0.250810 | + | 0.968036i | \(0.419303\pi\) | |||||||
\(332\) | 1.89872 | 0.104206 | ||||||||
\(333\) | 20.6663 | 1.13251 | ||||||||
\(334\) | 14.6497 | 0.801594 | ||||||||
\(335\) | −9.56908 | −0.522815 | ||||||||
\(336\) | 7.69566 | 0.419833 | ||||||||
\(337\) | 2.44560 | 0.133220 | 0.0666101 | − | 0.997779i | \(-0.478782\pi\) | ||||
0.0666101 | + | 0.997779i | \(0.478782\pi\) | |||||||
\(338\) | −7.01042 | −0.381317 | ||||||||
\(339\) | −40.0803 | −2.17686 | ||||||||
\(340\) | −1.39924 | −0.0758843 | ||||||||
\(341\) | −29.8062 | −1.61410 | ||||||||
\(342\) | −5.12229 | −0.276982 | ||||||||
\(343\) | 12.9600 | 0.699775 | ||||||||
\(344\) | 3.40114 | 0.183377 | ||||||||
\(345\) | −44.3139 | −2.38578 | ||||||||
\(346\) | −11.9772 | −0.643897 | ||||||||
\(347\) | −19.9586 | −1.07144 | −0.535718 | − | 0.844397i | \(-0.679959\pi\) | ||||
−0.535718 | + | 0.844397i | \(0.679959\pi\) | |||||||
\(348\) | −14.3132 | −0.767270 | ||||||||
\(349\) | −12.3000 | −0.658405 | −0.329203 | − | 0.944259i | \(-0.606780\pi\) | ||||
−0.329203 | + | 0.944259i | \(0.606780\pi\) | |||||||
\(350\) | −10.3409 | −0.552746 | ||||||||
\(351\) | −0.0200359 | −0.00106944 | ||||||||
\(352\) | −3.58337 | −0.190994 | ||||||||
\(353\) | −23.8380 | −1.26877 | −0.634385 | − | 0.773018i | \(-0.718746\pi\) | ||||
−0.634385 | + | 0.773018i | \(0.718746\pi\) | |||||||
\(354\) | 30.0128 | 1.59516 | ||||||||
\(355\) | −39.7607 | −2.11028 | ||||||||
\(356\) | −9.24598 | −0.490036 | ||||||||
\(357\) | −3.73978 | −0.197930 | ||||||||
\(358\) | −13.4935 | −0.713151 | ||||||||
\(359\) | −17.3091 | −0.913537 | −0.456769 | − | 0.889585i | \(-0.650993\pi\) | ||||
−0.456769 | + | 0.889585i | \(0.650993\pi\) | |||||||
\(360\) | 8.62837 | 0.454755 | ||||||||
\(361\) | −16.0782 | −0.846220 | ||||||||
\(362\) | −3.92575 | −0.206333 | ||||||||
\(363\) | −4.50708 | −0.236561 | ||||||||
\(364\) | 7.69112 | 0.403124 | ||||||||
\(365\) | −1.14235 | −0.0597935 | ||||||||
\(366\) | −29.0104 | −1.51640 | ||||||||
\(367\) | −17.4035 | −0.908453 | −0.454227 | − | 0.890886i | \(-0.650084\pi\) | ||||
−0.454227 | + | 0.890886i | \(0.650084\pi\) | |||||||
\(368\) | 6.28484 | 0.327620 | ||||||||
\(369\) | −0.399286 | −0.0207860 | ||||||||
\(370\) | 19.8572 | 1.03233 | ||||||||
\(371\) | 32.4363 | 1.68401 | ||||||||
\(372\) | −20.3690 | −1.05608 | ||||||||
\(373\) | −9.64782 | −0.499545 | −0.249773 | − | 0.968305i | \(-0.580356\pi\) | ||||
−0.249773 | + | 0.968305i | \(0.580356\pi\) | |||||||
\(374\) | 1.74137 | 0.0900441 | ||||||||
\(375\) | 12.0532 | 0.622427 | ||||||||
\(376\) | −7.79529 | −0.402011 | ||||||||
\(377\) | −14.3048 | −0.736734 | ||||||||
\(378\) | −0.0257277 | −0.00132329 | ||||||||
\(379\) | 19.2178 | 0.987153 | 0.493576 | − | 0.869702i | \(-0.335689\pi\) | ||||
0.493576 | + | 0.869702i | \(0.335689\pi\) | |||||||
\(380\) | −4.92174 | −0.252480 | ||||||||
\(381\) | 25.2757 | 1.29491 | ||||||||
\(382\) | 21.5097 | 1.10053 | ||||||||
\(383\) | 11.8519 | 0.605602 | 0.302801 | − | 0.953054i | \(-0.402078\pi\) | ||||
0.302801 | + | 0.953054i | \(0.402078\pi\) | |||||||
\(384\) | −2.44881 | −0.124965 | ||||||||
\(385\) | 32.4246 | 1.65251 | ||||||||
\(386\) | −9.74815 | −0.496168 | ||||||||
\(387\) | 10.1921 | 0.518092 | ||||||||
\(388\) | 8.08104 | 0.410253 | ||||||||
\(389\) | −0.831830 | −0.0421754 | −0.0210877 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210877 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(390\) | 17.2562 | 0.873800 | ||||||||
\(391\) | −3.05417 | −0.154456 | ||||||||
\(392\) | 2.87604 | 0.145262 | ||||||||
\(393\) | −29.0457 | −1.46516 | ||||||||
\(394\) | −19.4759 | −0.981183 | ||||||||
\(395\) | −35.7454 | −1.79855 | ||||||||
\(396\) | −10.7381 | −0.539611 | ||||||||
\(397\) | 19.3691 | 0.972106 | 0.486053 | − | 0.873929i | \(-0.338436\pi\) | ||||
0.486053 | + | 0.873929i | \(0.338436\pi\) | |||||||
\(398\) | −2.37529 | −0.119063 | ||||||||
\(399\) | −13.1545 | −0.658547 | ||||||||
\(400\) | 3.29054 | 0.164527 | ||||||||
\(401\) | −31.8319 | −1.58961 | −0.794805 | − | 0.606864i | \(-0.792427\pi\) | ||||
−0.794805 | + | 0.606864i | \(0.792427\pi\) | |||||||
\(402\) | 8.13829 | 0.405901 | ||||||||
\(403\) | −20.3570 | −1.01405 | ||||||||
\(404\) | −6.11390 | −0.304178 | ||||||||
\(405\) | −25.9428 | −1.28911 | ||||||||
\(406\) | −18.3685 | −0.911615 | ||||||||
\(407\) | −24.7126 | −1.22496 | ||||||||
\(408\) | 1.19002 | 0.0589148 | ||||||||
\(409\) | 35.5846 | 1.75955 | 0.879773 | − | 0.475394i | \(-0.157694\pi\) | ||||
0.879773 | + | 0.475394i | \(0.157694\pi\) | |||||||
\(410\) | −0.383653 | −0.0189473 | ||||||||
\(411\) | 2.71603 | 0.133972 | ||||||||
\(412\) | −18.7681 | −0.924638 | ||||||||
\(413\) | 38.5162 | 1.89526 | ||||||||
\(414\) | 18.8335 | 0.925616 | ||||||||
\(415\) | 5.46705 | 0.268367 | ||||||||
\(416\) | −2.44736 | −0.119992 | ||||||||
\(417\) | 2.92126 | 0.143054 | ||||||||
\(418\) | 6.12517 | 0.299592 | ||||||||
\(419\) | −32.5011 | −1.58778 | −0.793892 | − | 0.608059i | \(-0.791949\pi\) | ||||
−0.793892 | + | 0.608059i | \(0.791949\pi\) | |||||||
\(420\) | 22.1584 | 1.08122 | ||||||||
\(421\) | −29.8065 | −1.45268 | −0.726339 | − | 0.687337i | \(-0.758780\pi\) | ||||
−0.726339 | + | 0.687337i | \(0.758780\pi\) | |||||||
\(422\) | −23.3913 | −1.13867 | ||||||||
\(423\) | −23.3598 | −1.13579 | ||||||||
\(424\) | −10.3214 | −0.501253 | ||||||||
\(425\) | −1.59907 | −0.0775663 | ||||||||
\(426\) | 33.8156 | 1.63837 | ||||||||
\(427\) | −37.2298 | −1.80168 | ||||||||
\(428\) | −11.9793 | −0.579042 | ||||||||
\(429\) | −21.4755 | −1.03685 | ||||||||
\(430\) | 9.79302 | 0.472261 | ||||||||
\(431\) | −36.9293 | −1.77882 | −0.889410 | − | 0.457110i | \(-0.848884\pi\) | ||||
−0.889410 | + | 0.457110i | \(0.848884\pi\) | |||||||
\(432\) | 0.00818672 | 0.000393884 0 | ||||||||
\(433\) | 5.93862 | 0.285392 | 0.142696 | − | 0.989767i | \(-0.454423\pi\) | ||||
0.142696 | + | 0.989767i | \(0.454423\pi\) | |||||||
\(434\) | −26.1401 | −1.25476 | ||||||||
\(435\) | −41.2125 | −1.97599 | ||||||||
\(436\) | −3.08904 | −0.147938 | ||||||||
\(437\) | −10.7429 | −0.513902 | ||||||||
\(438\) | 0.971546 | 0.0464222 | ||||||||
\(439\) | 33.4671 | 1.59730 | 0.798649 | − | 0.601796i | \(-0.205548\pi\) | ||||
0.798649 | + | 0.601796i | \(0.205548\pi\) | |||||||
\(440\) | −10.3177 | −0.491877 | ||||||||
\(441\) | 8.61852 | 0.410406 | ||||||||
\(442\) | 1.18932 | 0.0565701 | ||||||||
\(443\) | 13.5506 | 0.643809 | 0.321904 | − | 0.946772i | \(-0.395677\pi\) | ||||
0.321904 | + | 0.946772i | \(0.395677\pi\) | |||||||
\(444\) | −16.8881 | −0.801475 | ||||||||
\(445\) | −26.6222 | −1.26201 | ||||||||
\(446\) | −12.5669 | −0.595062 | ||||||||
\(447\) | 49.1541 | 2.32491 | ||||||||
\(448\) | −3.14262 | −0.148475 | ||||||||
\(449\) | 7.87634 | 0.371708 | 0.185854 | − | 0.982577i | \(-0.440495\pi\) | ||||
0.185854 | + | 0.982577i | \(0.440495\pi\) | |||||||
\(450\) | 9.86063 | 0.464835 | ||||||||
\(451\) | 0.477461 | 0.0224828 | ||||||||
\(452\) | 16.3673 | 0.769852 | ||||||||
\(453\) | 21.4951 | 1.00993 | ||||||||
\(454\) | −12.9012 | −0.605481 | ||||||||
\(455\) | 22.1453 | 1.03819 | ||||||||
\(456\) | 4.18583 | 0.196019 | ||||||||
\(457\) | 15.4315 | 0.721857 | 0.360929 | − | 0.932593i | \(-0.382460\pi\) | ||||
0.360929 | + | 0.932593i | \(0.382460\pi\) | |||||||
\(458\) | 14.2920 | 0.667819 | ||||||||
\(459\) | −0.00397841 | −0.000185696 0 | ||||||||
\(460\) | 18.0961 | 0.843736 | ||||||||
\(461\) | 5.42936 | 0.252871 | 0.126435 | − | 0.991975i | \(-0.459646\pi\) | ||||
0.126435 | + | 0.991975i | \(0.459646\pi\) | |||||||
\(462\) | −27.5764 | −1.28297 | ||||||||
\(463\) | 35.6688 | 1.65767 | 0.828834 | − | 0.559495i | \(-0.189005\pi\) | ||||
0.828834 | + | 0.559495i | \(0.189005\pi\) | |||||||
\(464\) | 5.84498 | 0.271346 | ||||||||
\(465\) | −58.6492 | −2.71979 | ||||||||
\(466\) | 21.9100 | 1.01496 | ||||||||
\(467\) | −6.75140 | −0.312418 | −0.156209 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156209 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(468\) | −7.33390 | −0.339010 | ||||||||
\(469\) | 10.4441 | 0.482263 | ||||||||
\(470\) | −22.4452 | −1.03532 | ||||||||
\(471\) | −12.0904 | −0.557097 | ||||||||
\(472\) | −12.2561 | −0.564133 | ||||||||
\(473\) | −12.1876 | −0.560384 | ||||||||
\(474\) | 30.4007 | 1.39635 | ||||||||
\(475\) | −5.62464 | −0.258076 | ||||||||
\(476\) | 1.52718 | 0.0699984 | ||||||||
\(477\) | −30.9298 | −1.41618 | ||||||||
\(478\) | 22.6295 | 1.03505 | ||||||||
\(479\) | −0.150715 | −0.00688636 | −0.00344318 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344318 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(480\) | −7.05093 | −0.321829 | ||||||||
\(481\) | −16.8781 | −0.769577 | ||||||||
\(482\) | 9.79992 | 0.446374 | ||||||||
\(483\) | 48.3660 | 2.20073 | ||||||||
\(484\) | 1.84052 | 0.0836601 | ||||||||
\(485\) | 23.2680 | 1.05655 | ||||||||
\(486\) | 22.0392 | 0.999720 | ||||||||
\(487\) | −29.0724 | −1.31740 | −0.658698 | − | 0.752407i | \(-0.728892\pi\) | ||||
−0.658698 | + | 0.752407i | \(0.728892\pi\) | |||||||
\(488\) | 11.8468 | 0.536277 | ||||||||
\(489\) | −7.18067 | −0.324721 | ||||||||
\(490\) | 8.28108 | 0.374101 | ||||||||
\(491\) | −12.1907 | −0.550157 | −0.275079 | − | 0.961422i | \(-0.588704\pi\) | ||||
−0.275079 | + | 0.961422i | \(0.588704\pi\) | |||||||
\(492\) | 0.326288 | 0.0147102 | ||||||||
\(493\) | −2.84042 | −0.127926 | ||||||||
\(494\) | 4.18336 | 0.188218 | ||||||||
\(495\) | −30.9186 | −1.38969 | ||||||||
\(496\) | 8.31794 | 0.373486 | ||||||||
\(497\) | 43.3964 | 1.94659 | ||||||||
\(498\) | −4.64961 | −0.208354 | ||||||||
\(499\) | −37.7053 | −1.68792 | −0.843960 | − | 0.536406i | \(-0.819782\pi\) | ||||
−0.843960 | + | 0.536406i | \(0.819782\pi\) | |||||||
\(500\) | −4.92209 | −0.220122 | ||||||||
\(501\) | −35.8742 | −1.60274 | ||||||||
\(502\) | −25.4567 | −1.13619 | ||||||||
\(503\) | 1.90186 | 0.0847997 | 0.0423999 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0423999 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(504\) | −9.41735 | −0.419482 | ||||||||
\(505\) | −17.6040 | −0.783366 | ||||||||
\(506\) | −22.5209 | −1.00118 | ||||||||
\(507\) | 17.1672 | 0.762421 | ||||||||
\(508\) | −10.3216 | −0.457948 | ||||||||
\(509\) | 6.34495 | 0.281235 | 0.140617 | − | 0.990064i | \(-0.455091\pi\) | ||||
0.140617 | + | 0.990064i | \(0.455091\pi\) | |||||||
\(510\) | 3.42646 | 0.151726 | ||||||||
\(511\) | 1.24681 | 0.0551556 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.0139938 | −0.000617843 0 | ||||||||
\(514\) | −7.42569 | −0.327533 | ||||||||
\(515\) | −54.0396 | −2.38127 | ||||||||
\(516\) | −8.32875 | −0.366653 | ||||||||
\(517\) | 27.9334 | 1.22851 | ||||||||
\(518\) | −21.6730 | −0.952255 | ||||||||
\(519\) | 29.3298 | 1.28744 | ||||||||
\(520\) | −7.04676 | −0.309021 | ||||||||
\(521\) | 17.0393 | 0.746507 | 0.373254 | − | 0.927729i | \(-0.378242\pi\) | ||||
0.373254 | + | 0.927729i | \(0.378242\pi\) | |||||||
\(522\) | 17.5154 | 0.766628 | ||||||||
\(523\) | 5.20687 | 0.227680 | 0.113840 | − | 0.993499i | \(-0.463685\pi\) | ||||
0.113840 | + | 0.993499i | \(0.463685\pi\) | |||||||
\(524\) | 11.8612 | 0.518158 | ||||||||
\(525\) | 25.3229 | 1.10518 | ||||||||
\(526\) | 10.1421 | 0.442216 | ||||||||
\(527\) | −4.04218 | −0.176080 | ||||||||
\(528\) | 8.77498 | 0.381882 | ||||||||
\(529\) | 16.4992 | 0.717355 | ||||||||
\(530\) | −29.7188 | −1.29090 | ||||||||
\(531\) | −36.7273 | −1.59383 | ||||||||
\(532\) | 5.37178 | 0.232896 | ||||||||
\(533\) | 0.326096 | 0.0141248 | ||||||||
\(534\) | 22.6416 | 0.979799 | ||||||||
\(535\) | −34.4924 | −1.49124 | ||||||||
\(536\) | −3.32337 | −0.143548 | ||||||||
\(537\) | 33.0429 | 1.42590 | ||||||||
\(538\) | 0.384096 | 0.0165595 | ||||||||
\(539\) | −10.3059 | −0.443908 | ||||||||
\(540\) | 0.0235723 | 0.00101439 | ||||||||
\(541\) | −21.5657 | −0.927183 | −0.463592 | − | 0.886049i | \(-0.653440\pi\) | ||||
−0.463592 | + | 0.886049i | \(0.653440\pi\) | |||||||
\(542\) | −9.22397 | −0.396204 | ||||||||
\(543\) | 9.61341 | 0.412551 | ||||||||
\(544\) | −0.485959 | −0.0208353 | ||||||||
\(545\) | −8.89436 | −0.380993 | ||||||||
\(546\) | −18.8341 | −0.806024 | ||||||||
\(547\) | 19.5179 | 0.834526 | 0.417263 | − | 0.908786i | \(-0.362989\pi\) | ||||
0.417263 | + | 0.908786i | \(0.362989\pi\) | |||||||
\(548\) | −1.10912 | −0.0473795 | ||||||||
\(549\) | 35.5007 | 1.51513 | ||||||||
\(550\) | −11.7912 | −0.502780 | ||||||||
\(551\) | −9.99103 | −0.425632 | ||||||||
\(552\) | −15.3904 | −0.655057 | ||||||||
\(553\) | 39.0140 | 1.65905 | ||||||||
\(554\) | 15.3135 | 0.650606 | ||||||||
\(555\) | −48.6265 | −2.06408 | ||||||||
\(556\) | −1.19293 | −0.0505915 | ||||||||
\(557\) | 39.8651 | 1.68914 | 0.844569 | − | 0.535447i | \(-0.179857\pi\) | ||||
0.844569 | + | 0.535447i | \(0.179857\pi\) | |||||||
\(558\) | 24.9260 | 1.05520 | ||||||||
\(559\) | −8.32383 | −0.352060 | ||||||||
\(560\) | −9.04863 | −0.382375 | ||||||||
\(561\) | −4.26428 | −0.180038 | ||||||||
\(562\) | 11.6450 | 0.491216 | ||||||||
\(563\) | 33.1303 | 1.39628 | 0.698138 | − | 0.715963i | \(-0.254012\pi\) | ||||
0.698138 | + | 0.715963i | \(0.254012\pi\) | |||||||
\(564\) | 19.0892 | 0.803798 | ||||||||
\(565\) | 47.1268 | 1.98264 | ||||||||
\(566\) | 28.2293 | 1.18657 | ||||||||
\(567\) | 28.3150 | 1.18912 | ||||||||
\(568\) | −13.8090 | −0.579413 | ||||||||
\(569\) | 6.31591 | 0.264777 | 0.132388 | − | 0.991198i | \(-0.457735\pi\) | ||||
0.132388 | + | 0.991198i | \(0.457735\pi\) | |||||||
\(570\) | 12.0524 | 0.504819 | ||||||||
\(571\) | 32.5756 | 1.36325 | 0.681624 | − | 0.731703i | \(-0.261274\pi\) | ||||
0.681624 | + | 0.731703i | \(0.261274\pi\) | |||||||
\(572\) | 8.76979 | 0.366683 | ||||||||
\(573\) | −52.6731 | −2.20045 | ||||||||
\(574\) | 0.418734 | 0.0174776 | ||||||||
\(575\) | 20.6805 | 0.862438 | ||||||||
\(576\) | 2.99666 | 0.124861 | ||||||||
\(577\) | −15.4153 | −0.641748 | −0.320874 | − | 0.947122i | \(-0.603977\pi\) | ||||
−0.320874 | + | 0.947122i | \(0.603977\pi\) | |||||||
\(578\) | −16.7638 | −0.697284 | ||||||||
\(579\) | 23.8713 | 0.992059 | ||||||||
\(580\) | 16.8296 | 0.698813 | ||||||||
\(581\) | −5.96696 | −0.247551 | ||||||||
\(582\) | −19.7889 | −0.820277 | ||||||||
\(583\) | 36.9855 | 1.53178 | ||||||||
\(584\) | −0.396742 | −0.0164173 | ||||||||
\(585\) | −21.1167 | −0.873069 | ||||||||
\(586\) | 8.49844 | 0.351067 | ||||||||
\(587\) | −3.74564 | −0.154599 | −0.0772995 | − | 0.997008i | \(-0.524630\pi\) | ||||
−0.0772995 | + | 0.997008i | \(0.524630\pi\) | |||||||
\(588\) | −7.04288 | −0.290443 | ||||||||
\(589\) | −14.2181 | −0.585848 | ||||||||
\(590\) | −35.2894 | −1.45284 | ||||||||
\(591\) | 47.6928 | 1.96182 | ||||||||
\(592\) | 6.89647 | 0.283443 | ||||||||
\(593\) | −30.6555 | −1.25887 | −0.629434 | − | 0.777054i | \(-0.716713\pi\) | ||||
−0.629434 | + | 0.777054i | \(0.716713\pi\) | |||||||
\(594\) | −0.0293360 | −0.00120367 | ||||||||
\(595\) | 4.39727 | 0.180270 | ||||||||
\(596\) | −20.0727 | −0.822209 | ||||||||
\(597\) | 5.81663 | 0.238059 | ||||||||
\(598\) | −15.3813 | −0.628987 | ||||||||
\(599\) | 24.2752 | 0.991857 | 0.495929 | − | 0.868363i | \(-0.334828\pi\) | ||||
0.495929 | + | 0.868363i | \(0.334828\pi\) | |||||||
\(600\) | −8.05791 | −0.328963 | ||||||||
\(601\) | −32.7233 | −1.33481 | −0.667406 | − | 0.744694i | \(-0.732595\pi\) | ||||
−0.667406 | + | 0.744694i | \(0.732595\pi\) | |||||||
\(602\) | −10.6885 | −0.435631 | ||||||||
\(603\) | −9.95900 | −0.405562 | ||||||||
\(604\) | −8.77777 | −0.357162 | ||||||||
\(605\) | 5.29947 | 0.215454 | ||||||||
\(606\) | 14.9718 | 0.608187 | ||||||||
\(607\) | −6.93012 | −0.281285 | −0.140642 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140642 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(608\) | −1.70933 | −0.0693226 | ||||||||
\(609\) | 44.9810 | 1.82272 | ||||||||
\(610\) | 34.1107 | 1.38110 | ||||||||
\(611\) | 19.0779 | 0.771808 | ||||||||
\(612\) | −1.45625 | −0.0588655 | ||||||||
\(613\) | 32.3542 | 1.30677 | 0.653387 | − | 0.757024i | \(-0.273348\pi\) | ||||
0.653387 | + | 0.757024i | \(0.273348\pi\) | |||||||
\(614\) | −17.6193 | −0.711057 | ||||||||
\(615\) | 0.939492 | 0.0378840 | ||||||||
\(616\) | 11.2612 | 0.453725 | ||||||||
\(617\) | 27.3309 | 1.10030 | 0.550150 | − | 0.835066i | \(-0.314571\pi\) | ||||
0.550150 | + | 0.835066i | \(0.314571\pi\) | |||||||
\(618\) | 45.9595 | 1.84876 | ||||||||
\(619\) | 22.0584 | 0.886601 | 0.443300 | − | 0.896373i | \(-0.353808\pi\) | ||||
0.443300 | + | 0.896373i | \(0.353808\pi\) | |||||||
\(620\) | 23.9501 | 0.961859 | ||||||||
\(621\) | 0.0514522 | 0.00206471 | ||||||||
\(622\) | 13.7349 | 0.550718 | ||||||||
\(623\) | 29.0566 | 1.16413 | ||||||||
\(624\) | 5.99312 | 0.239917 | ||||||||
\(625\) | −30.6250 | −1.22500 | ||||||||
\(626\) | −23.1094 | −0.923636 | ||||||||
\(627\) | −14.9994 | −0.599017 | ||||||||
\(628\) | 4.93727 | 0.197019 | ||||||||
\(629\) | −3.35140 | −0.133629 | ||||||||
\(630\) | −27.1157 | −1.08031 | ||||||||
\(631\) | −5.62806 | −0.224050 | −0.112025 | − | 0.993705i | \(-0.535734\pi\) | ||||
−0.112025 | + | 0.993705i | \(0.535734\pi\) | |||||||
\(632\) | −12.4145 | −0.493822 | ||||||||
\(633\) | 57.2808 | 2.27671 | ||||||||
\(634\) | 31.7713 | 1.26180 | ||||||||
\(635\) | −29.7193 | −1.17938 | ||||||||
\(636\) | 25.2752 | 1.00223 | ||||||||
\(637\) | −7.03872 | −0.278884 | ||||||||
\(638\) | −20.9447 | −0.829209 | ||||||||
\(639\) | −41.3808 | −1.63700 | ||||||||
\(640\) | 2.87933 | 0.113816 | ||||||||
\(641\) | −12.0548 | −0.476134 | −0.238067 | − | 0.971249i | \(-0.576514\pi\) | ||||
−0.238067 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(642\) | 29.3350 | 1.15776 | ||||||||
\(643\) | −15.8632 | −0.625582 | −0.312791 | − | 0.949822i | \(-0.601264\pi\) | ||||
−0.312791 | + | 0.949822i | \(0.601264\pi\) | |||||||
\(644\) | −19.7508 | −0.778292 | ||||||||
\(645\) | −23.9812 | −0.944260 | ||||||||
\(646\) | 0.830667 | 0.0326821 | ||||||||
\(647\) | 18.1598 | 0.713934 | 0.356967 | − | 0.934117i | \(-0.383811\pi\) | ||||
0.356967 | + | 0.934117i | \(0.383811\pi\) | |||||||
\(648\) | −9.01002 | −0.353947 | ||||||||
\(649\) | 43.9181 | 1.72394 | ||||||||
\(650\) | −8.05315 | −0.315871 | ||||||||
\(651\) | 64.0121 | 2.50883 | ||||||||
\(652\) | 2.93231 | 0.114838 | ||||||||
\(653\) | −8.69811 | −0.340383 | −0.170192 | − | 0.985411i | \(-0.554439\pi\) | ||||
−0.170192 | + | 0.985411i | \(0.554439\pi\) | |||||||
\(654\) | 7.56446 | 0.295794 | ||||||||
\(655\) | 34.1522 | 1.33444 | ||||||||
\(656\) | −0.133244 | −0.00520229 | ||||||||
\(657\) | −1.18890 | −0.0463834 | ||||||||
\(658\) | 24.4976 | 0.955016 | ||||||||
\(659\) | −40.5063 | −1.57790 | −0.788950 | − | 0.614458i | \(-0.789375\pi\) | ||||
−0.788950 | + | 0.614458i | \(0.789375\pi\) | |||||||
\(660\) | 25.2661 | 0.983480 | ||||||||
\(661\) | 45.8004 | 1.78143 | 0.890714 | − | 0.454565i | \(-0.150205\pi\) | ||||
0.890714 | + | 0.454565i | \(0.150205\pi\) | |||||||
\(662\) | 9.12619 | 0.354700 | ||||||||
\(663\) | −2.91241 | −0.113109 | ||||||||
\(664\) | 1.89872 | 0.0736847 | ||||||||
\(665\) | 15.4671 | 0.599790 | ||||||||
\(666\) | 20.6663 | 0.800805 | ||||||||
\(667\) | 36.7348 | 1.42238 | ||||||||
\(668\) | 14.6497 | 0.566812 | ||||||||
\(669\) | 30.7740 | 1.18979 | ||||||||
\(670\) | −9.56908 | −0.369686 | ||||||||
\(671\) | −42.4513 | −1.63881 | ||||||||
\(672\) | 7.69566 | 0.296867 | ||||||||
\(673\) | −27.2223 | −1.04934 | −0.524671 | − | 0.851305i | \(-0.675812\pi\) | ||||
−0.524671 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(674\) | 2.44560 | 0.0942009 | ||||||||
\(675\) | 0.0269388 | 0.00103687 | ||||||||
\(676\) | −7.01042 | −0.269632 | ||||||||
\(677\) | 28.0462 | 1.07790 | 0.538952 | − | 0.842336i | \(-0.318820\pi\) | ||||
0.538952 | + | 0.842336i | \(0.318820\pi\) | |||||||
\(678\) | −40.0803 | −1.53928 | ||||||||
\(679\) | −25.3956 | −0.974595 | ||||||||
\(680\) | −1.39924 | −0.0536583 | ||||||||
\(681\) | 31.5925 | 1.21063 | ||||||||
\(682\) | −29.8062 | −1.14134 | ||||||||
\(683\) | −1.34359 | −0.0514112 | −0.0257056 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257056 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(684\) | −5.12229 | −0.195856 | ||||||||
\(685\) | −3.19354 | −0.122019 | ||||||||
\(686\) | 12.9600 | 0.494816 | ||||||||
\(687\) | −34.9982 | −1.33527 | ||||||||
\(688\) | 3.40114 | 0.129667 | ||||||||
\(689\) | 25.2603 | 0.962339 | ||||||||
\(690\) | −44.3139 | −1.68700 | ||||||||
\(691\) | 12.7226 | 0.483991 | 0.241996 | − | 0.970277i | \(-0.422198\pi\) | ||||
0.241996 | + | 0.970277i | \(0.422198\pi\) | |||||||
\(692\) | −11.9772 | −0.455304 | ||||||||
\(693\) | 33.7458 | 1.28190 | ||||||||
\(694\) | −19.9586 | −0.757620 | ||||||||
\(695\) | −3.43484 | −0.130291 | ||||||||
\(696\) | −14.3132 | −0.542542 | ||||||||
\(697\) | 0.0647510 | 0.00245262 | ||||||||
\(698\) | −12.3000 | −0.465563 | ||||||||
\(699\) | −53.6535 | −2.02936 | ||||||||
\(700\) | −10.3409 | −0.390850 | ||||||||
\(701\) | −39.9746 | −1.50982 | −0.754910 | − | 0.655828i | \(-0.772320\pi\) | ||||
−0.754910 | + | 0.655828i | \(0.772320\pi\) | |||||||
\(702\) | −0.0200359 | −0.000756205 0 | ||||||||
\(703\) | −11.7884 | −0.444607 | ||||||||
\(704\) | −3.58337 | −0.135053 | ||||||||
\(705\) | 54.9640 | 2.07006 | ||||||||
\(706\) | −23.8380 | −0.897155 | ||||||||
\(707\) | 19.2137 | 0.722604 | ||||||||
\(708\) | 30.0128 | 1.12795 | ||||||||
\(709\) | 36.5380 | 1.37221 | 0.686106 | − | 0.727502i | \(-0.259319\pi\) | ||||
0.686106 | + | 0.727502i | \(0.259319\pi\) | |||||||
\(710\) | −39.7607 | −1.49219 | ||||||||
\(711\) | −37.2020 | −1.39518 | ||||||||
\(712\) | −9.24598 | −0.346508 | ||||||||
\(713\) | 52.2769 | 1.95778 | ||||||||
\(714\) | −3.73978 | −0.139958 | ||||||||
\(715\) | 25.2511 | 0.944339 | ||||||||
\(716\) | −13.4935 | −0.504274 | ||||||||
\(717\) | −55.4153 | −2.06952 | ||||||||
\(718\) | −17.3091 | −0.645969 | ||||||||
\(719\) | −14.8536 | −0.553945 | −0.276972 | − | 0.960878i | \(-0.589331\pi\) | ||||
−0.276972 | + | 0.960878i | \(0.589331\pi\) | |||||||
\(720\) | 8.62837 | 0.321560 | ||||||||
\(721\) | 58.9810 | 2.19657 | ||||||||
\(722\) | −16.0782 | −0.598368 | ||||||||
\(723\) | −23.9981 | −0.892499 | ||||||||
\(724\) | −3.92575 | −0.145899 | ||||||||
\(725\) | 19.2332 | 0.714302 | ||||||||
\(726\) | −4.50708 | −0.167274 | ||||||||
\(727\) | 28.0932 | 1.04192 | 0.520959 | − | 0.853582i | \(-0.325574\pi\) | ||||
0.520959 | + | 0.853582i | \(0.325574\pi\) | |||||||
\(728\) | 7.69112 | 0.285052 | ||||||||
\(729\) | −26.9398 | −0.997770 | ||||||||
\(730\) | −1.14235 | −0.0422804 | ||||||||
\(731\) | −1.65282 | −0.0611317 | ||||||||
\(732\) | −29.0104 | −1.07226 | ||||||||
\(733\) | −26.1129 | −0.964501 | −0.482250 | − | 0.876033i | \(-0.660180\pi\) | ||||
−0.482250 | + | 0.876033i | \(0.660180\pi\) | |||||||
\(734\) | −17.4035 | −0.642373 | ||||||||
\(735\) | −20.2788 | −0.747994 | ||||||||
\(736\) | 6.28484 | 0.231662 | ||||||||
\(737\) | 11.9089 | 0.438668 | ||||||||
\(738\) | −0.399286 | −0.0146979 | ||||||||
\(739\) | 2.40948 | 0.0886342 | 0.0443171 | − | 0.999018i | \(-0.485889\pi\) | ||||
0.0443171 | + | 0.999018i | \(0.485889\pi\) | |||||||
\(740\) | 19.8572 | 0.729966 | ||||||||
\(741\) | −10.2442 | −0.376331 | ||||||||
\(742\) | 32.4363 | 1.19077 | ||||||||
\(743\) | 9.25783 | 0.339637 | 0.169818 | − | 0.985475i | \(-0.445682\pi\) | ||||
0.169818 | + | 0.985475i | \(0.445682\pi\) | |||||||
\(744\) | −20.3690 | −0.746765 | ||||||||
\(745\) | −57.7959 | −2.11748 | ||||||||
\(746\) | −9.64782 | −0.353232 | ||||||||
\(747\) | 5.68982 | 0.208180 | ||||||||
\(748\) | 1.74137 | 0.0636708 | ||||||||
\(749\) | 37.6464 | 1.37557 | ||||||||
\(750\) | 12.0532 | 0.440122 | ||||||||
\(751\) | −43.7889 | −1.59788 | −0.798940 | − | 0.601411i | \(-0.794605\pi\) | ||||
−0.798940 | + | 0.601411i | \(0.794605\pi\) | |||||||
\(752\) | −7.79529 | −0.284265 | ||||||||
\(753\) | 62.3385 | 2.27174 | ||||||||
\(754\) | −14.3048 | −0.520949 | ||||||||
\(755\) | −25.2741 | −0.919819 | ||||||||
\(756\) | −0.0257277 | −0.000935709 0 | ||||||||
\(757\) | −51.5182 | −1.87246 | −0.936231 | − | 0.351386i | \(-0.885710\pi\) | ||||
−0.936231 | + | 0.351386i | \(0.885710\pi\) | |||||||
\(758\) | 19.2178 | 0.698022 | ||||||||
\(759\) | 55.1493 | 2.00179 | ||||||||
\(760\) | −4.92174 | −0.178530 | ||||||||
\(761\) | 13.4157 | 0.486317 | 0.243159 | − | 0.969987i | \(-0.421816\pi\) | ||||
0.243159 | + | 0.969987i | \(0.421816\pi\) | |||||||
\(762\) | 25.2757 | 0.915640 | ||||||||
\(763\) | 9.70766 | 0.351441 | ||||||||
\(764\) | 21.5097 | 0.778194 | ||||||||
\(765\) | −4.19303 | −0.151599 | ||||||||
\(766\) | 11.8519 | 0.428225 | ||||||||
\(767\) | 29.9951 | 1.08306 | ||||||||
\(768\) | −2.44881 | −0.0883637 | ||||||||
\(769\) | −6.93637 | −0.250132 | −0.125066 | − | 0.992148i | \(-0.539914\pi\) | ||||
−0.125066 | + | 0.992148i | \(0.539914\pi\) | |||||||
\(770\) | 32.4246 | 1.16850 | ||||||||
\(771\) | 18.1841 | 0.654884 | ||||||||
\(772\) | −9.74815 | −0.350844 | ||||||||
\(773\) | −11.8596 | −0.426561 | −0.213280 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213280 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(774\) | 10.1921 | 0.366346 | ||||||||
\(775\) | 27.3706 | 0.983179 | ||||||||
\(776\) | 8.08104 | 0.290092 | ||||||||
\(777\) | 53.0729 | 1.90398 | ||||||||
\(778\) | −0.831830 | −0.0298225 | ||||||||
\(779\) | 0.227758 | 0.00816028 | ||||||||
\(780\) | 17.2562 | 0.617870 | ||||||||
\(781\) | 49.4827 | 1.77063 | ||||||||
\(782\) | −3.05417 | −0.109217 | ||||||||
\(783\) | 0.0478513 | 0.00171006 | ||||||||
\(784\) | 2.87604 | 0.102716 | ||||||||
\(785\) | 14.2160 | 0.507392 | ||||||||
\(786\) | −29.0457 | −1.03603 | ||||||||
\(787\) | 23.4528 | 0.836001 | 0.418001 | − | 0.908447i | \(-0.362731\pi\) | ||||
0.418001 | + | 0.908447i | \(0.362731\pi\) | |||||||
\(788\) | −19.4759 | −0.693801 | ||||||||
\(789\) | −24.8360 | −0.884186 | ||||||||
\(790\) | −35.7454 | −1.27177 | ||||||||
\(791\) | −51.4361 | −1.82886 | ||||||||
\(792\) | −10.7381 | −0.381563 | ||||||||
\(793\) | −28.9933 | −1.02958 | ||||||||
\(794\) | 19.3691 | 0.687383 | ||||||||
\(795\) | 72.7756 | 2.58109 | ||||||||
\(796\) | −2.37529 | −0.0841900 | ||||||||
\(797\) | −31.2693 | −1.10762 | −0.553808 | − | 0.832645i | \(-0.686826\pi\) | ||||
−0.553808 | + | 0.832645i | \(0.686826\pi\) | |||||||
\(798\) | −13.1545 | −0.465663 | ||||||||
\(799\) | 3.78819 | 0.134017 | ||||||||
\(800\) | 3.29054 | 0.116338 | ||||||||
\(801\) | −27.7070 | −0.978980 | ||||||||
\(802\) | −31.8319 | −1.12402 | ||||||||
\(803\) | 1.42167 | 0.0501698 | ||||||||
\(804\) | 8.13829 | 0.287015 | ||||||||
\(805\) | −56.8692 | −2.00438 | ||||||||
\(806\) | −20.3570 | −0.717045 | ||||||||
\(807\) | −0.940576 | −0.0331098 | ||||||||
\(808\) | −6.11390 | −0.215086 | ||||||||
\(809\) | 43.3858 | 1.52536 | 0.762681 | − | 0.646775i | \(-0.223883\pi\) | ||||
0.762681 | + | 0.646775i | \(0.223883\pi\) | |||||||
\(810\) | −25.9428 | −0.911538 | ||||||||
\(811\) | 6.99831 | 0.245744 | 0.122872 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122872 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(812\) | −18.3685 | −0.644609 | ||||||||
\(813\) | 22.5877 | 0.792186 | ||||||||
\(814\) | −24.7126 | −0.866175 | ||||||||
\(815\) | 8.44310 | 0.295749 | ||||||||
\(816\) | 1.19002 | 0.0416591 | ||||||||
\(817\) | −5.81369 | −0.203395 | ||||||||
\(818\) | 35.5846 | 1.24419 | ||||||||
\(819\) | 23.0476 | 0.805350 | ||||||||
\(820\) | −0.383653 | −0.0133977 | ||||||||
\(821\) | −33.5593 | −1.17123 | −0.585613 | − | 0.810590i | \(-0.699146\pi\) | ||||
−0.585613 | + | 0.810590i | \(0.699146\pi\) | |||||||
\(822\) | 2.71603 | 0.0947325 | ||||||||
\(823\) | 18.1419 | 0.632387 | 0.316194 | − | 0.948695i | \(-0.397595\pi\) | ||||
0.316194 | + | 0.948695i | \(0.397595\pi\) | |||||||
\(824\) | −18.7681 | −0.653818 | ||||||||
\(825\) | 28.8745 | 1.00528 | ||||||||
\(826\) | 38.5162 | 1.34015 | ||||||||
\(827\) | −41.2866 | −1.43568 | −0.717839 | − | 0.696210i | \(-0.754868\pi\) | ||||
−0.717839 | + | 0.696210i | \(0.754868\pi\) | |||||||
\(828\) | 18.8335 | 0.654509 | ||||||||
\(829\) | −29.5190 | −1.02524 | −0.512619 | − | 0.858616i | \(-0.671325\pi\) | ||||
−0.512619 | + | 0.858616i | \(0.671325\pi\) | |||||||
\(830\) | 5.46705 | 0.189764 | ||||||||
\(831\) | −37.4997 | −1.30085 | ||||||||
\(832\) | −2.44736 | −0.0848470 | ||||||||
\(833\) | −1.39764 | −0.0484254 | ||||||||
\(834\) | 2.92126 | 0.101155 | ||||||||
\(835\) | 42.1812 | 1.45974 | ||||||||
\(836\) | 6.12517 | 0.211843 | ||||||||
\(837\) | 0.0680967 | 0.00235377 | ||||||||
\(838\) | −32.5011 | −1.12273 | ||||||||
\(839\) | −0.262035 | −0.00904644 | −0.00452322 | − | 0.999990i | \(-0.501440\pi\) | ||||
−0.00452322 | + | 0.999990i | \(0.501440\pi\) | |||||||
\(840\) | 22.1584 | 0.764536 | ||||||||
\(841\) | 5.16381 | 0.178063 | ||||||||
\(842\) | −29.8065 | −1.02720 | ||||||||
\(843\) | −28.5164 | −0.982157 | ||||||||
\(844\) | −23.3913 | −0.805162 | ||||||||
\(845\) | −20.1853 | −0.694396 | ||||||||
\(846\) | −23.3598 | −0.803126 | ||||||||
\(847\) | −5.78406 | −0.198743 | ||||||||
\(848\) | −10.3214 | −0.354439 | ||||||||
\(849\) | −69.1282 | −2.37247 | ||||||||
\(850\) | −1.59907 | −0.0548477 | ||||||||
\(851\) | 43.3432 | 1.48578 | ||||||||
\(852\) | 33.8156 | 1.15850 | ||||||||
\(853\) | −13.8837 | −0.475367 | −0.237684 | − | 0.971343i | \(-0.576388\pi\) | ||||
−0.237684 | + | 0.971343i | \(0.576388\pi\) | |||||||
\(854\) | −37.2298 | −1.27398 | ||||||||
\(855\) | −14.7488 | −0.504397 | ||||||||
\(856\) | −11.9793 | −0.409444 | ||||||||
\(857\) | −19.6350 | −0.670718 | −0.335359 | − | 0.942090i | \(-0.608858\pi\) | ||||
−0.335359 | + | 0.942090i | \(0.608858\pi\) | |||||||
\(858\) | −21.4755 | −0.733163 | ||||||||
\(859\) | 34.4969 | 1.17702 | 0.588509 | − | 0.808491i | \(-0.299715\pi\) | ||||
0.588509 | + | 0.808491i | \(0.299715\pi\) | |||||||
\(860\) | 9.79302 | 0.333939 | ||||||||
\(861\) | −1.02540 | −0.0349455 | ||||||||
\(862\) | −36.9293 | −1.25782 | ||||||||
\(863\) | 34.0025 | 1.15746 | 0.578729 | − | 0.815520i | \(-0.303549\pi\) | ||||
0.578729 | + | 0.815520i | \(0.303549\pi\) | |||||||
\(864\) | 0.00818672 | 0.000278518 0 | ||||||||
\(865\) | −34.4863 | −1.17257 | ||||||||
\(866\) | 5.93862 | 0.201803 | ||||||||
\(867\) | 41.0514 | 1.39418 | ||||||||
\(868\) | −26.1401 | −0.887253 | ||||||||
\(869\) | 44.4857 | 1.50907 | ||||||||
\(870\) | −41.2125 | −1.39724 | ||||||||
\(871\) | 8.13348 | 0.275593 | ||||||||
\(872\) | −3.08904 | −0.104608 | ||||||||
\(873\) | 24.2161 | 0.819591 | ||||||||
\(874\) | −10.7429 | −0.363383 | ||||||||
\(875\) | 15.4682 | 0.522922 | ||||||||
\(876\) | 0.971546 | 0.0328255 | ||||||||
\(877\) | −1.05388 | −0.0355870 | −0.0177935 | − | 0.999842i | \(-0.505664\pi\) | ||||
−0.0177935 | + | 0.999842i | \(0.505664\pi\) | |||||||
\(878\) | 33.4671 | 1.12946 | ||||||||
\(879\) | −20.8110 | −0.701939 | ||||||||
\(880\) | −10.3177 | −0.347810 | ||||||||
\(881\) | −23.0539 | −0.776706 | −0.388353 | − | 0.921511i | \(-0.626956\pi\) | ||||
−0.388353 | + | 0.921511i | \(0.626956\pi\) | |||||||
\(882\) | 8.61852 | 0.290201 | ||||||||
\(883\) | −47.2837 | −1.59122 | −0.795612 | − | 0.605806i | \(-0.792851\pi\) | ||||
−0.795612 | + | 0.605806i | \(0.792851\pi\) | |||||||
\(884\) | 1.18932 | 0.0400011 | ||||||||
\(885\) | 86.4169 | 2.90487 | ||||||||
\(886\) | 13.5506 | 0.455241 | ||||||||
\(887\) | 37.4219 | 1.25650 | 0.628252 | − | 0.778010i | \(-0.283771\pi\) | ||||
0.628252 | + | 0.778010i | \(0.283771\pi\) | |||||||
\(888\) | −16.8881 | −0.566728 | ||||||||
\(889\) | 32.4369 | 1.08790 | ||||||||
\(890\) | −26.6222 | −0.892379 | ||||||||
\(891\) | 32.2862 | 1.08163 | ||||||||
\(892\) | −12.5669 | −0.420772 | ||||||||
\(893\) | 13.3247 | 0.445896 | ||||||||
\(894\) | 49.1541 | 1.64396 | ||||||||
\(895\) | −38.8521 | −1.29868 | ||||||||
\(896\) | −3.14262 | −0.104987 | ||||||||
\(897\) | 37.6657 | 1.25762 | ||||||||
\(898\) | 7.87634 | 0.262837 | ||||||||
\(899\) | 48.6182 | 1.62151 | ||||||||
\(900\) | 9.86063 | 0.328688 | ||||||||
\(901\) | 5.01579 | 0.167100 | ||||||||
\(902\) | 0.477461 | 0.0158977 | ||||||||
\(903\) | 26.1741 | 0.871018 | ||||||||
\(904\) | 16.3673 | 0.544368 | ||||||||
\(905\) | −11.3035 | −0.375742 | ||||||||
\(906\) | 21.4951 | 0.714126 | ||||||||
\(907\) | −27.7373 | −0.921001 | −0.460500 | − | 0.887659i | \(-0.652330\pi\) | ||||
−0.460500 | + | 0.887659i | \(0.652330\pi\) | |||||||
\(908\) | −12.9012 | −0.428140 | ||||||||
\(909\) | −18.3213 | −0.607678 | ||||||||
\(910\) | 22.1453 | 0.734109 | ||||||||
\(911\) | 36.6037 | 1.21273 | 0.606367 | − | 0.795185i | \(-0.292626\pi\) | ||||
0.606367 | + | 0.795185i | \(0.292626\pi\) | |||||||
\(912\) | 4.18583 | 0.138607 | ||||||||
\(913\) | −6.80382 | −0.225174 | ||||||||
\(914\) | 15.4315 | 0.510430 | ||||||||
\(915\) | −83.5306 | −2.76144 | ||||||||
\(916\) | 14.2920 | 0.472219 | ||||||||
\(917\) | −37.2751 | −1.23093 | ||||||||
\(918\) | −0.00397841 | −0.000131307 0 | ||||||||
\(919\) | −1.93409 | −0.0637996 | −0.0318998 | − | 0.999491i | \(-0.510156\pi\) | ||||
−0.0318998 | + | 0.999491i | \(0.510156\pi\) | |||||||
\(920\) | 18.0961 | 0.596611 | ||||||||
\(921\) | 43.1463 | 1.42172 | ||||||||
\(922\) | 5.42936 | 0.178807 | ||||||||
\(923\) | 33.7956 | 1.11240 | ||||||||
\(924\) | −27.5764 | −0.907197 | ||||||||
\(925\) | 22.6931 | 0.746146 | ||||||||
\(926\) | 35.6688 | 1.17215 | ||||||||
\(927\) | −56.2416 | −1.84722 | ||||||||
\(928\) | 5.84498 | 0.191871 | ||||||||
\(929\) | −46.5848 | −1.52840 | −0.764199 | − | 0.644981i | \(-0.776865\pi\) | ||||
−0.764199 | + | 0.644981i | \(0.776865\pi\) | |||||||
\(930\) | −58.6492 | −1.92318 | ||||||||
\(931\) | −4.91612 | −0.161119 | ||||||||
\(932\) | 21.9100 | 0.717687 | ||||||||
\(933\) | −33.6340 | −1.10113 | ||||||||
\(934\) | −6.75140 | −0.220913 | ||||||||
\(935\) | 5.01398 | 0.163975 | ||||||||
\(936\) | −7.33390 | −0.239716 | ||||||||
\(937\) | −20.6247 | −0.673779 | −0.336889 | − | 0.941544i | \(-0.609375\pi\) | ||||
−0.336889 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(938\) | 10.4441 | 0.341011 | ||||||||
\(939\) | 56.5904 | 1.84676 | ||||||||
\(940\) | −22.4452 | −0.732082 | ||||||||
\(941\) | 13.3231 | 0.434321 | 0.217160 | − | 0.976136i | \(-0.430321\pi\) | ||||
0.217160 | + | 0.976136i | \(0.430321\pi\) | |||||||
\(942\) | −12.0904 | −0.393927 | ||||||||
\(943\) | −0.837415 | −0.0272700 | ||||||||
\(944\) | −12.2561 | −0.398902 | ||||||||
\(945\) | −0.0740787 | −0.00240978 | ||||||||
\(946\) | −12.1876 | −0.396251 | ||||||||
\(947\) | −48.2110 | −1.56665 | −0.783323 | − | 0.621615i | \(-0.786477\pi\) | ||||
−0.783323 | + | 0.621615i | \(0.786477\pi\) | |||||||
\(948\) | 30.4007 | 0.987369 | ||||||||
\(949\) | 0.970972 | 0.0315191 | ||||||||
\(950\) | −5.62464 | −0.182487 | ||||||||
\(951\) | −77.8017 | −2.52289 | ||||||||
\(952\) | 1.52718 | 0.0494963 | ||||||||
\(953\) | −34.7386 | −1.12529 | −0.562647 | − | 0.826697i | \(-0.690217\pi\) | ||||
−0.562647 | + | 0.826697i | \(0.690217\pi\) | |||||||
\(954\) | −30.9298 | −1.00139 | ||||||||
\(955\) | 61.9336 | 2.00412 | ||||||||
\(956\) | 22.6295 | 0.731890 | ||||||||
\(957\) | 51.2896 | 1.65796 | ||||||||
\(958\) | −0.150715 | −0.00486939 | ||||||||
\(959\) | 3.48556 | 0.112554 | ||||||||
\(960\) | −7.05093 | −0.227568 | ||||||||
\(961\) | 38.1881 | 1.23187 | ||||||||
\(962\) | −16.8781 | −0.544173 | ||||||||
\(963\) | −35.8979 | −1.15679 | ||||||||
\(964\) | 9.79992 | 0.315634 | ||||||||
\(965\) | −28.0682 | −0.903546 | ||||||||
\(966\) | 48.3660 | 1.55615 | ||||||||
\(967\) | −18.9220 | −0.608491 | −0.304246 | − | 0.952594i | \(-0.598404\pi\) | ||||
−0.304246 | + | 0.952594i | \(0.598404\pi\) | |||||||
\(968\) | 1.84052 | 0.0591566 | ||||||||
\(969\) | −2.03414 | −0.0653461 | ||||||||
\(970\) | 23.2680 | 0.747090 | ||||||||
\(971\) | −57.6709 | −1.85075 | −0.925374 | − | 0.379056i | \(-0.876249\pi\) | ||||
−0.925374 | + | 0.379056i | \(0.876249\pi\) | |||||||
\(972\) | 22.0392 | 0.706909 | ||||||||
\(973\) | 3.74892 | 0.120185 | ||||||||
\(974\) | −29.0724 | −0.931540 | ||||||||
\(975\) | 19.7206 | 0.631565 | ||||||||
\(976\) | 11.8468 | 0.379205 | ||||||||
\(977\) | −13.7527 | −0.439988 | −0.219994 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219994 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(978\) | −7.18067 | −0.229613 | ||||||||
\(979\) | 33.1317 | 1.05889 | ||||||||
\(980\) | 8.28108 | 0.264530 | ||||||||
\(981\) | −9.25678 | −0.295546 | ||||||||
\(982\) | −12.1907 | −0.389020 | ||||||||
\(983\) | 17.3874 | 0.554573 | 0.277287 | − | 0.960787i | \(-0.410565\pi\) | ||||
0.277287 | + | 0.960787i | \(0.410565\pi\) | |||||||
\(984\) | 0.326288 | 0.0104017 | ||||||||
\(985\) | −56.0776 | −1.78678 | ||||||||
\(986\) | −2.84042 | −0.0904575 | ||||||||
\(987\) | −59.9899 | −1.90950 | ||||||||
\(988\) | 4.18336 | 0.133090 | ||||||||
\(989\) | 21.3756 | 0.679706 | ||||||||
\(990\) | −30.9186 | −0.982658 | ||||||||
\(991\) | −5.48961 | −0.174383 | −0.0871916 | − | 0.996192i | \(-0.527789\pi\) | ||||
−0.0871916 | + | 0.996192i | \(0.527789\pi\) | |||||||
\(992\) | 8.31794 | 0.264095 | ||||||||
\(993\) | −22.3483 | −0.709201 | ||||||||
\(994\) | 43.3964 | 1.37645 | ||||||||
\(995\) | −6.83925 | −0.216819 | ||||||||
\(996\) | −4.64961 | −0.147328 | ||||||||
\(997\) | −33.0473 | −1.04662 | −0.523310 | − | 0.852142i | \(-0.675303\pi\) | ||||
−0.523310 | + | 0.852142i | \(0.675303\pi\) | |||||||
\(998\) | −37.7053 | −1.19354 | ||||||||
\(999\) | 0.0564595 | 0.00178630 |
(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 | 6046.2.a.e.1.9 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.e.1.9 | ✓ | 56 | 1.1 | even | 1 | trivial |