Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.28894 | −0.744171 | −0.372086 | − | 0.928198i | \(-0.621357\pi\) | ||||
−0.372086 | + | 0.928198i | \(0.621357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0476003 | 0.0179912 | 0.00899562 | − | 0.999960i | \(-0.497137\pi\) | ||||
0.00899562 | + | 0.999960i | \(0.497137\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33863 | −0.446209 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50278 | 0.453104 | 0.226552 | − | 0.973999i | \(-0.427255\pi\) | ||||
0.226552 | + | 0.973999i | \(0.427255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.90785 | 1.08384 | 0.541921 | − | 0.840429i | \(-0.317697\pi\) | ||||
0.541921 | + | 0.840429i | \(0.317697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.28894 | 0.332804 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.09866 | −0.751535 | −0.375768 | − | 0.926714i | \(-0.622621\pi\) | ||||
−0.375768 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.32814 | 1.91061 | 0.955304 | − | 0.295627i | \(-0.0955284\pi\) | ||||
0.955304 | + | 0.295627i | \(0.0955284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0613541 | −0.0133886 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.22939 | 0.464861 | 0.232430 | − | 0.972613i | \(-0.425332\pi\) | ||||
0.232430 | + | 0.972613i | \(0.425332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.59224 | 1.07623 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.06407 | −0.940373 | −0.470187 | − | 0.882567i | \(-0.655813\pi\) | ||||
−0.470187 | + | 0.882567i | \(0.655813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.71810 | −1.74542 | −0.872711 | − | 0.488238i | \(-0.837640\pi\) | ||||
−0.872711 | + | 0.488238i | \(0.837640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.93699 | −0.337187 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0476003 | −0.00804592 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.69898 | 1.59450 | 0.797251 | − | 0.603648i | \(-0.206287\pi\) | ||||
0.797251 | + | 0.603648i | \(0.206287\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.03700 | −0.806565 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7165 | 1.67364 | 0.836820 | − | 0.547478i | \(-0.184412\pi\) | ||||
0.836820 | + | 0.547478i | \(0.184412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.420809 | −0.0641728 | −0.0320864 | − | 0.999485i | \(-0.510215\pi\) | ||||
−0.0320864 | + | 0.999485i | \(0.510215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.33863 | 0.199551 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.217932 | 0.0317886 | 0.0158943 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158943 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99773 | −0.999676 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.99399 | 0.559271 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.878938 | −0.120731 | −0.0603657 | − | 0.998176i | \(-0.519227\pi\) | ||||
−0.0603657 | + | 0.998176i | \(0.519227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50278 | −0.202634 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.7345 | −1.42182 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.11977 | −0.275970 | −0.137985 | − | 0.990434i | \(-0.544063\pi\) | ||||
−0.137985 | + | 0.990434i | \(0.544063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0739777 | −0.00947188 | −0.00473594 | − | 0.999989i | \(-0.501508\pi\) | ||||
−0.00473594 | + | 0.999989i | \(0.501508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0637191 | −0.00802785 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.90785 | −0.484709 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0155387 | 0.00189836 | 0.000949178 | − | 1.00000i | \(-0.499698\pi\) | ||||
0.000949178 | 1.00000i | \(0.499698\pi\) | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.87356 | −0.345936 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.21165 | −0.262475 | −0.131237 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131237 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0592 | −1.76254 | −0.881271 | − | 0.472611i | \(-0.843312\pi\) | ||||
−0.881271 | + | 0.472611i | \(0.843312\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.28894 | −0.148834 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0715327 | 0.00815191 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77866 | 0.312624 | 0.156312 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156312 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.19220 | −0.354689 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.20330 | −0.132079 | −0.0660395 | − | 0.997817i | \(-0.521036\pi\) | ||||
−0.0660395 | + | 0.997817i | \(0.521036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.09866 | 0.336097 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.52729 | 0.699799 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.10286 | 0.858902 | 0.429451 | − | 0.903090i | \(-0.358707\pi\) | ||||
0.429451 | + | 0.903090i | \(0.358707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.186015 | 0.0194997 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5261 | 1.29889 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.32814 | −0.854449 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3371 | −1.35418 | −0.677089 | − | 0.735901i | \(-0.736759\pi\) | ||||
−0.677089 | + | 0.735901i | \(0.736759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.01166 | −0.202179 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.34968 | 0.233802 | 0.116901 | − | 0.993144i | \(-0.462704\pi\) | ||||
0.116901 | + | 0.993144i | \(0.462704\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.31040 | −0.326184 | −0.163092 | − | 0.986611i | \(-0.552147\pi\) | ||||
−0.163092 | + | 0.986611i | \(0.552147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0613541 | 0.00598755 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.0806 | 1.84459 | 0.922297 | − | 0.386482i | \(-0.126310\pi\) | ||||
0.922297 | + | 0.386482i | \(0.126310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.70033 | −0.162862 | −0.0814308 | − | 0.996679i | \(-0.525949\pi\) | ||||
−0.0814308 | + | 0.996679i | \(0.525949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.5014 | −1.18658 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.05493 | 0.851816 | 0.425908 | − | 0.904766i | \(-0.359955\pi\) | ||||
0.425908 | + | 0.904766i | \(0.359955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.22939 | −0.207892 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.23115 | −0.483620 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.147497 | −0.0135210 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.74166 | −0.794696 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.8130 | −1.24548 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.979099 | 0.0868810 | 0.0434405 | − | 0.999056i | \(-0.486168\pi\) | ||||
0.0434405 | + | 0.999056i | \(0.486168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.542399 | 0.0477556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.11612 | 0.621738 | 0.310869 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310869 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.396422 | 0.0343742 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.59224 | −0.481304 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.3929 | −1.74229 | −0.871143 | − | 0.491029i | \(-0.836621\pi\) | ||||
−0.871143 | + | 0.491029i | \(0.836621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.04716 | 0.428095 | 0.214047 | − | 0.976823i | \(-0.431335\pi\) | ||||
0.214047 | + | 0.976823i | \(0.431335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.280902 | −0.0236562 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.87263 | 0.491094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.06407 | 0.420548 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.01968 | 0.743931 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.6839 | 1.85834 | 0.929168 | − | 0.369657i | \(-0.120525\pi\) | ||||
0.929168 | + | 0.369657i | \(0.120525\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.57148 | 0.372022 | 0.186011 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186011 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.14795 | 0.335342 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.71810 | 0.780576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.88672 | 0.469811 | 0.234906 | − | 0.972018i | \(-0.424522\pi\) | ||||
0.234906 | + | 0.972018i | \(0.424522\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.13290 | 0.0898449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.106120 | 0.00836342 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1654 | −0.796218 | −0.398109 | − | 0.917338i | \(-0.630333\pi\) | ||||
−0.398109 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.93699 | 0.150795 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.54352 | −0.506353 | −0.253176 | − | 0.967420i | \(-0.581475\pi\) | ||||
−0.253176 | + | 0.967420i | \(0.581475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.27129 | 0.174715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1483 | −0.852530 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8658 | 0.902140 | 0.451070 | − | 0.892489i | \(-0.351043\pi\) | ||||
0.451070 | + | 0.892489i | \(0.351043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0476003 | 0.00359825 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.73226 | 0.205369 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.47248 | −0.110059 | −0.0550293 | − | 0.998485i | \(-0.517525\pi\) | ||||
−0.0550293 | + | 0.998485i | \(0.517525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0925 | −0.750168 | −0.375084 | − | 0.926991i | \(-0.622386\pi\) | ||||
−0.375084 | + | 0.926991i | \(0.622386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0953530 | 0.00704870 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.69898 | −0.713083 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.65659 | −0.340524 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.266192 | 0.0193627 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6202 | 0.985526 | 0.492763 | − | 0.870164i | \(-0.335987\pi\) | ||||
0.492763 | + | 0.870164i | \(0.335987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.10873 | −0.655660 | −0.327830 | − | 0.944737i | \(-0.606317\pi\) | ||||
−0.327830 | + | 0.944737i | \(0.606317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.03700 | 0.360707 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.0669 | −1.21597 | −0.607984 | − | 0.793949i | \(-0.708022\pi\) | ||||
−0.607984 | + | 0.793949i | \(0.708022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.1476 | −1.71178 | −0.855891 | − | 0.517157i | \(-0.826990\pi\) | ||||
−0.855891 | + | 0.517157i | \(0.826990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0200285 | −0.00141270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.241051 | −0.0169185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7165 | −0.748475 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.98433 | −0.207425 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.5153 | 0.865704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5516 | 1.13946 | 0.569731 | − | 0.821831i | \(-0.307048\pi\) | ||||
0.569731 | + | 0.821831i | \(0.307048\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.85069 | 0.195326 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.420809 | 0.0286990 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.462584 | −0.0314023 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.4104 | 1.31163 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.1091 | −0.814546 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6361 | 0.913141 | 0.456570 | − | 0.889687i | \(-0.349078\pi\) | ||||
0.456570 | + | 0.889687i | \(0.349078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.33863 | −0.0892418 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2715 | 0.748115 | 0.374058 | − | 0.927405i | \(-0.377966\pi\) | ||||
0.374058 | + | 0.927405i | \(0.377966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0109 | 0.727623 | 0.363812 | − | 0.931473i | \(-0.381475\pi\) | ||||
0.363812 | + | 0.931473i | \(0.381475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0922015 | −0.00606642 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2749 | 1.06621 | 0.533103 | − | 0.846050i | \(-0.321026\pi\) | ||||
0.533103 | + | 0.846050i | \(0.321026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.217932 | −0.0142163 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.58154 | −0.232646 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0764 | 0.781160 | 0.390580 | − | 0.920569i | \(-0.372275\pi\) | ||||
0.390580 | + | 0.920569i | \(0.372275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9670 | 0.964107 | 0.482053 | − | 0.876142i | \(-0.339891\pi\) | ||||
0.482053 | + | 0.876142i | \(0.339891\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.6622 | −0.812278 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.99773 | 0.447069 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.5451 | 2.07080 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.55098 | 0.0982895 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.3956 | 1.91855 | 0.959277 | − | 0.282467i | \(-0.0911529\pi\) | ||||
0.959277 | + | 0.282467i | \(0.0911529\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35028 | 0.210630 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.99399 | −0.250114 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5631 | 1.03318 | 0.516590 | − | 0.856233i | \(-0.327201\pi\) | ||||
0.516590 | + | 0.856233i | \(0.327201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.461675 | 0.0286871 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.77889 | 0.419603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8184 | −0.728754 | −0.364377 | − | 0.931251i | \(-0.618718\pi\) | ||||
−0.364377 | + | 0.931251i | \(0.618718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.878938 | 0.0539927 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4441 | −0.639170 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.1949 | 1.29228 | 0.646138 | − | 0.763221i | \(-0.276383\pi\) | ||||
0.646138 | + | 0.763221i | \(0.276383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4661 | 0.757260 | 0.378630 | − | 0.925548i | \(-0.376395\pi\) | ||||
0.378630 | + | 0.925548i | \(0.376395\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.239763 | −0.0145111 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50278 | 0.0906209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.32731 | 0.380171 | 0.190086 | − | 0.981768i | \(-0.439123\pi\) | ||||
0.190086 | + | 0.981768i | \(0.439123\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.0089 | 0.778822 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4246 | 1.33774 | 0.668869 | − | 0.743380i | \(-0.266779\pi\) | ||||
0.668869 | + | 0.743380i | \(0.266779\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.1531 | −1.61409 | −0.807043 | − | 0.590493i | \(-0.798934\pi\) | ||||
−0.807043 | + | 0.590493i | \(0.798934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7345 | 0.635857 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.510110 | 0.0301108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.39832 | −0.435195 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.1908 | 1.00774 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4240 | 0.842660 | 0.421330 | − | 0.906907i | \(-0.361563\pi\) | ||||
0.421330 | + | 0.906907i | \(0.361563\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11977 | 0.123418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.40389 | 0.487643 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.71214 | 0.503836 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0200307 | −0.00115455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.02860 | −0.173989 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0739777 | 0.00423595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9377 | −1.08083 | −0.540415 | − | 0.841399i | \(-0.681733\pi\) | ||||
−0.540415 | + | 0.841399i | \(0.681733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.26692 | 0.242737 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9663 | 0.962069 | 0.481034 | − | 0.876702i | \(-0.340261\pi\) | ||||
0.481034 | + | 0.876702i | \(0.340261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.94453 | −0.562098 | −0.281049 | − | 0.959693i | \(-0.590682\pi\) | ||||
−0.281049 | + | 0.959693i | \(0.590682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0637191 | 0.00359016 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 35.3133 | 1.98339 | 0.991697 | − | 0.128597i | \(-0.0410475\pi\) | ||||
0.991697 | + | 0.128597i | \(0.0410475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.61016 | −0.426087 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.5938 | −1.37269 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.8061 | −1.43589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.90785 | 0.216769 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.19162 | 0.121197 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0103736 | 0.000571917 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.5395 | −1.95343 | −0.976714 | − | 0.214547i | \(-0.931173\pi\) | ||||
−0.976714 | + | 0.214547i | \(0.931173\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.9833 | −0.711481 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0155387 | −0.000848970 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.66197 | 0.308427 | 0.154214 | − | 0.988038i | \(-0.450716\pi\) | ||||
0.154214 | + | 0.988038i | \(0.450716\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.6713 | −0.633897 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6041 | −0.790858 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.666297 | −0.0359766 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.87356 | 0.154707 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.9896 | −1.87834 | −0.939170 | − | 0.343452i | \(-0.888404\pi\) | ||||
−0.939170 | + | 0.343452i | \(0.888404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8431 | 0.580417 | 0.290209 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290209 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8536 | 1.16646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.3595 | 1.50942 | 0.754711 | − | 0.656058i | \(-0.227777\pi\) | ||||
0.754711 | + | 0.656058i | \(0.227777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.21165 | 0.117382 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.190115 | 0.0100620 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.5352 | −1.34769 | −0.673847 | − | 0.738871i | \(-0.735359\pi\) | ||||
−0.673847 | + | 0.738871i | \(0.735359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.3580 | 2.65042 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2675 | 0.591390 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0592 | 0.788233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9598 | 1.35509 | 0.677545 | − | 0.735481i | \(-0.263044\pi\) | ||||
0.677545 | + | 0.735481i | \(0.263044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.3454 | −0.746793 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0418377 | −0.00217211 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.377898 | 0.0195668 | 0.00978341 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978341 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.28894 | 0.0665607 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.7896 | −1.01922 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1000 | 1.34067 | 0.670333 | − | 0.742061i | \(-0.266151\pi\) | ||||
0.670333 | + | 0.742061i | \(0.266151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.26200 | −0.0646544 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.9759 | −1.17402 | −0.587008 | − | 0.809581i | \(-0.699694\pi\) | ||||
−0.587008 | + | 0.809581i | \(0.699694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0715327 | −0.00364564 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.563306 | 0.0286345 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.3936 | 0.881888 | 0.440944 | − | 0.897535i | \(-0.354644\pi\) | ||||
0.440944 | + | 0.897535i | \(0.354644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.90813 | −0.349359 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.17227 | −0.462680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.77866 | −0.139810 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2948 | 1.21932 | 0.609659 | − | 0.792664i | \(-0.291306\pi\) | ||||
0.609659 | + | 0.792664i | \(0.291306\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.510966 | −0.0255803 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.9769 | −1.89176 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.19220 | 0.158622 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.5754 | 0.722476 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3013 | −1.10273 | −0.551364 | − | 0.834265i | \(-0.685893\pi\) | ||||
−0.551364 | + | 0.834265i | \(0.685893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.2853 | 1.29656 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.100902 | −0.00496504 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20330 | 0.0590676 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.50550 | −0.318576 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.99302 | −0.439338 | −0.219669 | − | 0.975575i | \(-0.570498\pi\) | ||||
−0.219669 | + | 0.975575i | \(0.570498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.3160 | 1.57499 | 0.787494 | − | 0.616323i | \(-0.211378\pi\) | ||||
0.787494 | + | 0.616323i | \(0.211378\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.291730 | −0.0141844 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.09866 | −0.150307 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.00352136 | −0.000170411 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.56948 | −0.365458 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.70614 | −0.323023 | −0.161512 | − | 0.986871i | \(-0.551637\pi\) | ||||
−0.161512 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6776 | −0.801476 | −0.400738 | − | 0.916193i | \(-0.631246\pi\) | ||||
−0.400738 | + | 0.916193i | \(0.631246\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.52729 | −0.312960 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.5667 | 0.888166 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.42878 | −0.0681917 | −0.0340959 | − | 0.999419i | \(-0.510855\pi\) | ||||
−0.0340959 | + | 0.999419i | \(0.510855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.36735 | 0.446064 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1945 | 0.816936 | 0.408468 | − | 0.912773i | \(-0.366063\pi\) | ||||
0.408468 | + | 0.912773i | \(0.366063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.10286 | −0.384113 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.2382 | −1.38292 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.03537 | −0.190441 | −0.0952204 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952204 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1045 | 0.758334 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.89238 | −0.276848 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.186015 | −0.00872051 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.9332 | 0.745325 | 0.372662 | − | 0.927967i | \(-0.378445\pi\) | ||||
0.372662 | + | 0.927967i | \(0.378445\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.3284 | −0.808823 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.1828 | 1.35918 | 0.679590 | − | 0.733592i | \(-0.262158\pi\) | ||||
0.679590 | + | 0.733592i | \(0.262158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4105 | −1.55272 | −0.776359 | − | 0.630290i | \(-0.782936\pi\) | ||||
−0.776359 | + | 0.630290i | \(0.782936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5261 | −0.580883 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.37186 | 0.109757 | 0.0548784 | − | 0.998493i | \(-0.482523\pi\) | ||||
0.0548784 | + | 0.998493i | \(0.482523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.000739648 0 | 3.41537e−5 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.58764 | −0.349620 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.632383 | −0.0290770 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.32814 | 0.382121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17657 | 0.0538714 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0198 | −1.09749 | −0.548745 | − | 0.835990i | \(-0.684894\pi\) | ||||
−0.548745 | + | 0.835990i | \(0.684894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.9022 | 1.72819 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.136782 | −0.00622382 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.3371 | 0.605607 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4570 | 0.473854 | 0.236927 | − | 0.971527i | \(-0.423860\pi\) | ||||
0.236927 | + | 0.971527i | \(0.423860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.1027 | 0.592522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.8963 | 0.672262 | 0.336131 | − | 0.941815i | \(-0.390881\pi\) | ||||
0.336131 | + | 0.941815i | \(0.390881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6918 | 0.706723 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.01166 | 0.0904173 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.105275 | −0.00472225 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.46705 | −0.155207 | −0.0776033 | − | 0.996984i | \(-0.524727\pi\) | ||||
−0.0776033 | + | 0.996984i | \(0.524727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.43422 | 0.376813 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.8262 | −0.884009 | −0.442004 | − | 0.897013i | \(-0.645732\pi\) | ||||
−0.442004 | + | 0.897013i | \(0.645732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.34968 | −0.104559 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.92757 | −0.130018 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3931 | 0.637964 | 0.318982 | − | 0.947761i | \(-0.396659\pi\) | ||||
0.318982 | + | 0.947761i | \(0.396659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.716821 | −0.0317103 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46.5730 | 2.05625 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.31040 | 0.145874 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.327503 | 0.0144036 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.2943 | −0.671347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1517 | 1.71527 | 0.857633 | − | 0.514262i | \(-0.171934\pi\) | ||||
0.857633 | + | 0.514262i | \(0.171934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2954 | −0.843728 | −0.421864 | − | 0.906659i | \(-0.638624\pi\) | ||||
−0.421864 | + | 0.906659i | \(0.638624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0613541 | −0.00267771 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.1131 | 1.31175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.0298 | −0.783904 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.83757 | 0.123140 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.8786 | 1.81396 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.0806 | −0.824927 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.89795 | 0.0819025 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.5160 | −0.452958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.3387 | −1.64831 | −0.824154 | − | 0.566365i | \(-0.808349\pi\) | ||||
−0.824154 | + | 0.566365i | \(0.808349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.0086 | 0.558253 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.70033 | 0.0728340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.2043 | 1.37695 | 0.688477 | − | 0.725258i | \(-0.258279\pi\) | ||||
0.688477 | + | 0.725258i | \(0.258279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0990285 | 0.00422643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.1743 | −1.79668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.132265 | 0.00562449 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.5014 | 0.530656 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.7424 | −0.497542 | −0.248771 | − | 0.968562i | \(-0.580027\pi\) | ||||
−0.248771 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.64446 | −0.0695532 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00208 | 0.253408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.9362 | 1.43024 | 0.715120 | − | 0.699002i | \(-0.246372\pi\) | ||||
0.715120 | + | 0.699002i | \(0.246372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.05493 | −0.380944 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.151950 | −0.00638129 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.2860 | 1.01812 | 0.509061 | − | 0.860730i | \(-0.329993\pi\) | ||||
0.509061 | + | 0.860730i | \(0.329993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.9144 | −0.665999 | −0.332999 | − | 0.942927i | \(-0.608061\pi\) | ||||
−0.332999 | + | 0.942927i | \(0.608061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.5557 | −0.733400 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.22939 | 0.0929721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.8834 | 1.86852 | 0.934260 | − | 0.356592i | \(-0.116061\pi\) | ||||
0.934260 | + | 0.356592i | \(0.116061\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7406 | 0.487924 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0572773 | −0.00237626 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.32085 | −0.0547039 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.23115 | 0.216281 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.4990 | −0.639711 | −0.319856 | − | 0.947466i | \(-0.603634\pi\) | ||||
−0.319856 | + | 0.947466i | \(0.603634\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −80.9337 | −3.33481 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.9983 | 0.904889 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9706 | 1.10755 | 0.553774 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553774 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.147497 | 0.00604679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.1249 | 1.27386 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4884 | 0.796274 | 0.398137 | − | 0.917326i | \(-0.369657\pi\) | ||||
0.398137 | + | 0.917326i | \(0.369657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6204 | 0.718751 | 0.359375 | − | 0.933193i | \(-0.382990\pi\) | ||||
0.359375 | + | 0.933193i | \(0.382990\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0208005 | −0.000847063 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.74166 | 0.355399 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5996 | 1.24200 | 0.621000 | − | 0.783811i | \(-0.286727\pi\) | ||||
0.621000 | + | 0.783811i | \(0.286727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.310701 | 0.0125902 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.851646 | 0.0344539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.2528 | 1.66618 | 0.833092 | − | 0.553134i | \(-0.186568\pi\) | ||||
0.833092 | + | 0.553134i | \(0.186568\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.8130 | 0.556993 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.809268 | −0.0325799 | −0.0162899 | − | 0.999867i | \(-0.505185\pi\) | ||||
−0.0162899 | + | 0.999867i | \(0.505185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.2725 | 1.25695 | 0.628474 | − | 0.777831i | \(-0.283680\pi\) | ||||
0.628474 | + | 0.777831i | \(0.283680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.4673 | 0.500296 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.385699 | 0.0154527 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.1316 | −0.644233 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.0538 | −1.19832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.03218 | 0.0410906 | 0.0205453 | − | 0.999789i | \(-0.493460\pi\) | ||||
0.0205453 | + | 0.999789i | \(0.493460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.3341 | −0.847955 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.979099 | −0.0388544 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.3461 | −1.08349 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.96058 | 0.117119 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9666 | 1.02562 | 0.512809 | − | 0.858503i | \(-0.328605\pi\) | ||||
0.512809 | + | 0.858503i | \(0.328605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.5143 | −1.87378 | −0.936890 | − | 0.349624i | \(-0.886309\pi\) | ||||
−0.936890 | + | 0.349624i | \(0.886309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.542399 | −0.0213569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0205 | −1.14092 | −0.570458 | − | 0.821327i | \(-0.693234\pi\) | ||||
−0.570458 | + | 0.821327i | \(0.693234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.18554 | −0.125043 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.596245 | 0.0233687 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.1424 | −1.68829 | −0.844146 | − | 0.536113i | \(-0.819892\pi\) | ||||
−0.844146 | + | 0.536113i | \(0.819892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.11612 | −0.278050 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.1586 | 0.786462 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3354 | −0.480521 | −0.240260 | − | 0.970708i | \(-0.577233\pi\) | ||||
−0.240260 | + | 0.970708i | \(0.577233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0098 | 0.583813 | 0.291907 | − | 0.956447i | \(-0.405710\pi\) | ||||
0.291907 | + | 0.956447i | \(0.405710\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.6079 | 0.606162 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.396422 | −0.0153726 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2898 | −0.437143 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.5762 | −0.679533 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.111172 | −0.00429175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2319 | 0.779883 | 0.389942 | − | 0.920840i | \(-0.372495\pi\) | ||||
0.389942 | + | 0.920840i | \(0.372495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.59224 | 0.215245 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.2715 | −0.971263 | −0.485631 | − | 0.874164i | \(-0.661410\pi\) | ||||
−0.485631 | + | 0.874164i | \(0.661410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.634851 | −0.0243633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5283 | −0.556726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.90956 | −0.149595 | −0.0747976 | − | 0.997199i | \(-0.523831\pi\) | ||||
−0.0747976 | + | 0.997199i | \(0.523831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3929 | 0.779174 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.1925 | −0.541476 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.43476 | −0.130854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.7344 | 1.66373 | 0.831867 | − | 0.554974i | \(-0.187272\pi\) | ||||
0.831867 | + | 0.554974i | \(0.187272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0957555 | −0.00363745 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.04716 | −0.191450 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.2068 | −1.25780 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.9775 | −0.793440 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.3707 | 1.41147 | 0.705735 | − | 0.708476i | \(-0.250617\pi\) | ||||
0.705735 | + | 0.708476i | \(0.250617\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.7745 | 3.04647 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.280902 | 0.0105794 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.111846 | 0.00420638 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.6858 | −1.03976 | −0.519882 | − | 0.854238i | \(-0.674024\pi\) | ||||
−0.519882 | + | 0.854238i | \(0.674024\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71959 | −0.139496 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.6655 | −0.811378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.87263 | −0.219624 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5658 | −0.581317 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6700 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.157576 | −0.00586844 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.2916 | −0.717461 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.06407 | −0.188075 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.3281 | 1.45860 | 0.729299 | − | 0.684196i | \(-0.239847\pi\) | ||||
0.729299 | + | 0.684196i | \(0.239847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8974 | 0.959163 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.30394 | 0.0482281 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.9086 | 1.58487 | 0.792433 | − | 0.609959i | \(-0.208814\pi\) | ||||
0.792433 | + | 0.609959i | \(0.208814\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.01968 | −0.332696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0233512 | 0.000860153 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.75612 | 0.358885 | 0.179442 | − | 0.983768i | \(-0.442571\pi\) | ||||
0.179442 | + | 0.983768i | \(0.442571\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.9488 | −1.54103 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.7509 | 1.34826 | 0.674130 | − | 0.738613i | \(-0.264519\pi\) | ||||
0.674130 | + | 0.738613i | \(0.264519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6839 | −0.831073 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.61077 | 0.0589348 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.908244 | 0.0331865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.7414 | 1.63264 | 0.816318 | − | 0.577602i | \(-0.196011\pi\) | ||||
0.816318 | + | 0.577602i | \(0.196011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39.1782 | −1.42773 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.57148 | −0.166373 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.4818 | −0.853461 | −0.426730 | − | 0.904379i | \(-0.640335\pi\) | ||||
−0.426730 | + | 0.904379i | \(0.640335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.31832 | −0.156745 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3747 | −0.956082 | −0.478041 | − | 0.878337i | \(-0.658653\pi\) | ||||
−0.478041 | + | 0.878337i | \(0.658653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0809361 | −0.00293008 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.14795 | −0.149969 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.28373 | −0.299108 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.4834 | −1.56805 | −0.784025 | − | 0.620729i | \(-0.786837\pi\) | ||||
−0.784025 | + | 0.620729i | \(0.786837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3489 | −0.768863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.2137 | 1.26655 | 0.633275 | − | 0.773927i | \(-0.281710\pi\) | ||||
0.633275 | + | 0.773927i | \(0.281710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.71810 | −0.349084 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.595072 | −0.0213481 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 89.2488 | 3.19767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.32362 | −0.118929 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.3195 | −1.01206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.88672 | −0.210106 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.3793 | −1.33243 | −0.666215 | − | 0.745760i | \(-0.732087\pi\) | ||||
−0.666215 | + | 0.745760i | \(0.732087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.2333 | 0.542318 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.431018 | 0.0153252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.289094 | −0.0102660 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.13290 | −0.0401799 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6706 | −1.05099 | −0.525493 | − | 0.850798i | \(-0.676119\pi\) | ||||
−0.525493 | + | 0.850798i | \(0.676119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.675297 | −0.0238903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.8467 | −0.383250 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.6306 | −0.798616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.106120 | −0.00374023 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.3190 | −0.961674 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.8870 | −1.92972 | −0.964861 | − | 0.262760i | \(-0.915367\pi\) | ||||
−0.964861 | + | 0.262760i | \(0.915367\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8967 | 0.839125 | 0.419563 | − | 0.907726i | \(-0.362183\pi\) | ||||
0.419563 | + | 0.907726i | \(0.362183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0681 | −0.563532 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.1654 | 0.356079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50456 | −0.122609 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.249004 | −0.00870092 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5078 | 0.680826 | 0.340413 | − | 0.940276i | \(-0.389433\pi\) | ||||
0.340413 | + | 0.940276i | \(0.389433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.42346 | −0.119334 | −0.0596672 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596672 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.93699 | −0.0674375 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.17349 | 0.110353 | 0.0551766 | − | 0.998477i | \(-0.482428\pi\) | ||||
0.0551766 | + | 0.998477i | \(0.482428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.92777 | −0.240612 | −0.120306 | − | 0.992737i | \(-0.538388\pi\) | ||||
−0.120306 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.15554 | −0.282913 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.6836 | 0.751292 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.54352 | 0.226448 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.3459 | −1.87847 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.4946 | −0.742077 | −0.371039 | − | 0.928617i | \(-0.620998\pi\) | ||||
−0.371039 | + | 0.928617i | \(0.620998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.35524 | −0.115698 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9040 | −0.995507 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.27129 | −0.0781348 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.416106 | −0.0142976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.9988 | 1.20116 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.6228 | 0.741222 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.72028 | 0.332816 | 0.166408 | − | 0.986057i | \(-0.446783\pi\) | ||||
0.166408 | + | 0.986057i | \(0.446783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.1483 | 0.381263 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.1493 | 0.449172 | 0.224586 | − | 0.974454i | \(-0.427897\pi\) | ||||
0.224586 | + | 0.974454i | \(0.427897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.6717 | 1.11474 | 0.557372 | − | 0.830263i | \(-0.311810\pi\) | ||||
0.557372 | + | 0.830263i | \(0.311810\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.657503 | −0.0224076 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.0210 | −1.39637 | −0.698186 | − | 0.715917i | \(-0.746009\pi\) | ||||
−0.698186 | + | 0.715917i | \(0.746009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.8658 | −0.403449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.53601 | 0.323860 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.17571 | 0.141651 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0607229 | 0.00205752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.8534 | 0.604246 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.0476003 | −0.00160918 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.21474 | 0.0747864 | 0.0373932 | − | 0.999301i | \(-0.488095\pi\) | ||||
0.0373932 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.5917 | −0.627084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.5186 | 0.893435 | 0.446717 | − | 0.894675i | \(-0.352593\pi\) | ||||
0.446717 | + | 0.894675i | \(0.352593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5822 | −0.558035 | −0.279017 | − | 0.960286i | \(-0.590009\pi\) | ||||
−0.279017 | + | 0.960286i | \(0.590009\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.73226 | −0.0918438 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.6449 | −1.73407 | −0.867033 | − | 0.498250i | \(-0.833976\pi\) | ||||
−0.867033 | + | 0.498250i | \(0.833976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0466055 | 0.00156310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.79717 | −0.160711 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.81497 | 0.0607356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.47248 | 0.0492197 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.2294 | −0.374940 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.2131 | 1.64135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.72353 | 0.0907339 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0258184 | 0.000859182 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0925 | 0.335485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3896 | 1.60675 | 0.803376 | − | 0.595472i | \(-0.203035\pi\) | ||||
0.803376 | + | 0.595472i | \(0.203035\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.14534 | −0.104324 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.9760 | −1.05941 | −0.529705 | − | 0.848182i | \(-0.677698\pi\) | ||||
−0.529705 | + | 0.848182i | \(0.677698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.80829 | −0.0598456 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0953530 | −0.00315227 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.338730 | 0.0111858 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.9970 | 1.35237 | 0.676183 | − | 0.736734i | \(-0.263633\pi\) | ||||
0.676183 | + | 0.736734i | \(0.263633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4096 | 0.804322 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.64281 | −0.284482 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.69898 | 0.318900 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.43139 | 0.145546 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.0422 | 1.14970 | 0.574849 | − | 0.818260i | \(-0.305061\pi\) | ||||
0.574849 | + | 0.818260i | \(0.305061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.2781 | −1.90999 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.8686 | −0.715944 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.65659 | 0.152287 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.40509 | 0.0459024 | 0.0229512 | − | 0.999737i | \(-0.492694\pi\) | ||||
0.0229512 | + | 0.999737i | \(0.492694\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8179 | 0.418297 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5816 | 1.22512 | 0.612562 | − | 0.790422i | \(-0.290139\pi\) | ||||
0.612562 | + | 0.790422i | \(0.290139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.8914 | 0.778010 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.266192 | −0.00865924 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.3815 | −1.21473 | −0.607367 | − | 0.794421i | \(-0.707774\pi\) | ||||
−0.607367 | + | 0.794421i | \(0.707774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −58.8490 | −1.91032 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.5169 | −1.47599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.2683 | 1.17485 | 0.587423 | − | 0.809280i | \(-0.300142\pi\) | ||||
0.587423 | + | 0.809280i | \(0.300142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.6202 | −0.440741 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.80906 | 0.317082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.970711 | −0.0313459 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.4414 | 2.04650 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.5418 | −0.823074 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.10873 | 0.293220 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.93926 | −0.287467 | −0.143734 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143734 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.2625 | 1.06855 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.01371 | 0.0967147 | 0.0483574 | − | 0.998830i | \(-0.484601\pi\) | ||||
0.0483574 | + | 0.998830i | \(0.484601\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.240247 | 0.00770195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.03700 | −0.161313 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.0313 | 0.320930 | 0.160465 | − | 0.987042i | \(-0.448701\pi\) | ||||
0.160465 | + | 0.987042i | \(0.448701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1768 | 0.389172 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.27610 | 0.0726703 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.0557 | 1.40516 | 0.702579 | − | 0.711606i | \(-0.252032\pi\) | ||||
0.702579 | + | 0.711606i | \(0.252032\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.0669 | 0.543797 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0133710 | −0.000425604 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.938149 | −0.0298314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.7710 | 1.32690 | 0.663450 | − | 0.748220i | \(-0.269091\pi\) | ||||
0.663450 | + | 0.748220i | \(0.269091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.8084 | 1.45368 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.1476 | 0.765532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.6004 | 1.47585 | 0.737925 | − | 0.674882i | \(-0.235806\pi\) | ||||
0.737925 | + | 0.674882i | \(0.235806\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.2390 | 1.71605 |
(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 | 8020.2.a.e.1.13 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.e.1.13 | ✓ | 35 | 1.1 | even | 1 | trivial |