Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, 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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.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: | \(64.1358429035\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-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 | ||||||||
\(3\) | 0.797542 | 0.460461 | 0.230231 | − | 0.973136i | \(-0.426052\pi\) | ||||
0.230231 | + | 0.973136i | \(0.426052\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59101 | −0.711520 | −0.355760 | − | 0.934577i | \(-0.615778\pi\) | ||||
−0.355760 | + | 0.934577i | \(0.615778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45275 | −0.549090 | −0.274545 | − | 0.961574i | \(-0.588527\pi\) | ||||
−0.274545 | + | 0.961574i | \(0.588527\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.36393 | −0.787976 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.08436 | 1.53299 | 0.766496 | − | 0.642249i | \(-0.221999\pi\) | ||||
0.766496 | + | 0.642249i | \(0.221999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23817 | −0.898107 | −0.449053 | − | 0.893505i | \(-0.648239\pi\) | ||||
−0.449053 | + | 0.893505i | \(0.648239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26890 | −0.327627 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.47535 | −0.357824 | −0.178912 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34209 | 0.996144 | 0.498072 | − | 0.867136i | \(-0.334042\pi\) | ||||
0.498072 | + | 0.867136i | \(0.334042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.15863 | −0.252834 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.66973 | 1.80776 | 0.903882 | − | 0.427782i | \(-0.140705\pi\) | ||||
0.903882 | + | 0.427782i | \(0.140705\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46870 | −0.493739 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.27796 | −0.823293 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.07637 | 0.385572 | 0.192786 | − | 0.981241i | \(-0.438248\pi\) | ||||
0.192786 | + | 0.981241i | \(0.438248\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.368627 | −0.0662073 | −0.0331037 | − | 0.999452i | \(-0.510539\pi\) | ||||
−0.0331037 | + | 0.999452i | \(0.510539\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.05499 | 0.705883 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.31134 | 0.390688 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1998 | −1.67683 | −0.838416 | − | 0.545031i | \(-0.816518\pi\) | ||||
−0.838416 | + | 0.545031i | \(0.816518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.58258 | −0.413543 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.84460 | 0.444252 | 0.222126 | − | 0.975018i | \(-0.428700\pi\) | ||||
0.222126 | + | 0.975018i | \(0.428700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.220232 | 0.0335850 | 0.0167925 | − | 0.999859i | \(-0.494655\pi\) | ||||
0.0167925 | + | 0.999859i | \(0.494655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.76102 | 0.560660 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.444696 | 0.0648656 | 0.0324328 | − | 0.999474i | \(-0.489675\pi\) | ||||
0.0324328 | + | 0.999474i | \(0.489675\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.88950 | −0.698500 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.17665 | −0.164764 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.52007 | −0.483519 | −0.241760 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241760 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.08925 | −1.09075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46300 | 0.458685 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.14881 | 0.149563 | 0.0747813 | − | 0.997200i | \(-0.476174\pi\) | ||||
0.0747813 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.23654 | −1.05458 | −0.527291 | − | 0.849685i | \(-0.676792\pi\) | ||||
−0.527291 | + | 0.849685i | \(0.676792\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.43421 | 0.432669 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.15195 | 0.639021 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.03182 | 0.492565 | 0.246283 | − | 0.969198i | \(-0.420791\pi\) | ||||
0.246283 | + | 0.969198i | \(0.420791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.91447 | 0.832405 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.27655 | 0.270176 | 0.135088 | − | 0.990834i | \(-0.456868\pi\) | ||||
0.135088 | + | 0.990834i | \(0.456868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.98502 | 0.700493 | 0.350247 | − | 0.936658i | \(-0.386098\pi\) | ||||
0.350247 | + | 0.936658i | \(0.386098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.96889 | −0.227348 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.38633 | −0.841750 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.87656 | 0.886182 | 0.443091 | − | 0.896477i | \(-0.353882\pi\) | ||||
0.443091 | + | 0.896477i | \(0.353882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.67993 | 0.408881 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.55280 | −0.609499 | −0.304750 | − | 0.952432i | \(-0.598573\pi\) | ||||
−0.304750 | + | 0.952432i | \(0.598573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.34729 | 0.254599 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.65599 | 0.177541 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.51285 | 0.796361 | 0.398180 | − | 0.917307i | \(-0.369642\pi\) | ||||
0.398180 | + | 0.917307i | \(0.369642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.70427 | 0.493141 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.293995 | −0.0304859 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.90830 | −0.708776 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.608887 | 0.0618231 | 0.0309116 | − | 0.999522i | \(-0.490159\pi\) | ||||
0.0309116 | + | 0.999522i | \(0.490159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0191 | −1.20796 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.69354 | 0.467024 | 0.233512 | − | 0.972354i | \(-0.424978\pi\) | ||||
0.233512 | + | 0.972354i | \(0.424978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4987 | −1.52714 | −0.763568 | − | 0.645728i | \(-0.776554\pi\) | ||||
−0.763568 | + | 0.645728i | \(0.776554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.84339 | 0.179897 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4010 | 1.10218 | 0.551089 | − | 0.834447i | \(-0.314213\pi\) | ||||
0.551089 | + | 0.834447i | \(0.314213\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0275 | −1.15203 | −0.576013 | − | 0.817440i | \(-0.695392\pi\) | ||||
−0.576013 | + | 0.817440i | \(0.695392\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.13474 | −0.772116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.501043 | −0.0471342 | −0.0235671 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235671 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7936 | −1.28626 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.65480 | 0.707686 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14332 | 0.196478 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8507 | 1.35006 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.26869 | 0.204561 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8827 | 1.06283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9915 | −1.24155 | −0.620774 | − | 0.783990i | \(-0.713181\pi\) | ||||
−0.620774 | + | 0.783990i | \(0.713181\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.175644 | 0.0154646 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.16074 | 0.101414 | 0.0507071 | − | 0.998714i | \(-0.483852\pi\) | ||||
0.0507071 | + | 0.998714i | \(0.483852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.30799 | −0.546972 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.80626 | 0.585790 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.04220 | −0.345348 | −0.172674 | − | 0.984979i | \(-0.555241\pi\) | ||||
−0.172674 | + | 0.984979i | \(0.555241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0269 | 1.61384 | 0.806920 | − | 0.590661i | \(-0.201133\pi\) | ||||
0.806920 | + | 0.590661i | \(0.201133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.354664 | 0.0298681 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.4640 | −1.37679 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.30352 | −0.274342 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.89958 | −0.321632 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.48371 | −0.121551 | −0.0607753 | − | 0.998151i | \(-0.519357\pi\) | ||||
−0.0607753 | + | 0.998151i | \(0.519357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.20708 | −0.667883 | −0.333941 | − | 0.942594i | \(-0.608379\pi\) | ||||
−0.333941 | + | 0.942594i | \(0.608379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.48761 | 0.281957 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.586488 | 0.0471078 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.30831 | −0.423649 | −0.211824 | − | 0.977308i | \(-0.567941\pi\) | ||||
−0.211824 | + | 0.977308i | \(0.567941\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.80741 | −0.222642 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5950 | −0.992624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1590 | −0.795714 | −0.397857 | − | 0.917447i | \(-0.630246\pi\) | ||||
−0.397857 | + | 0.917447i | \(0.630246\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.45152 | −0.502250 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4519 | −0.886171 | −0.443086 | − | 0.896479i | \(-0.646116\pi\) | ||||
−0.443086 | + | 0.896479i | \(0.646116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.51425 | −0.193404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.2644 | −0.784937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.9663 | −1.74610 | −0.873050 | − | 0.487631i | \(-0.837861\pi\) | ||||
−0.873050 | + | 0.487631i | \(0.837861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.58641 | 0.271107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.916226 | 0.0688677 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0902 | −0.754174 | −0.377087 | − | 0.926178i | \(-0.623074\pi\) | ||||
−0.377087 | + | 0.926178i | \(0.623074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2139 | −1.79981 | −0.899904 | − | 0.436088i | \(-0.856364\pi\) | ||||
−0.899904 | + | 0.436088i | \(0.856364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.56899 | −0.485594 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.2279 | 1.19310 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.50120 | −0.548542 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.21482 | 0.452062 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.57567 | 0.548156 | 0.274078 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274078 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3191 | −0.886749 | −0.443375 | − | 0.896336i | \(-0.646219\pi\) | ||||
−0.443375 | + | 0.896336i | \(0.646219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.10890 | 0.294244 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4706 | 0.745997 | 0.372998 | − | 0.927832i | \(-0.378330\pi\) | ||||
0.372998 | + | 0.927832i | \(0.378330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.38657 | −0.523620 | −0.261810 | − | 0.965119i | \(-0.584319\pi\) | ||||
−0.261810 | + | 0.965119i | \(0.584319\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.21555 | 0.226807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.01646 | −0.211714 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.52578 | −0.316094 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.4946 | −1.42447 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.0767 | 1.52708 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.20288 | −0.564709 | −0.282355 | − | 0.959310i | \(-0.591116\pi\) | ||||
−0.282355 | + | 0.959310i | \(0.591116\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.81564 | 0.124406 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.350390 | −0.0238964 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.535524 | 0.0363538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.77330 | 0.322550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.77743 | 0.321364 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1402 | 0.812966 | 0.406483 | − | 0.913658i | \(-0.366755\pi\) | ||||
0.406483 | + | 0.913658i | \(0.366755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.83582 | 0.389055 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.62461 | 0.638808 | 0.319404 | − | 0.947619i | \(-0.396517\pi\) | ||||
0.319404 | + | 0.947619i | \(0.396517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2400 | −0.941005 | −0.470503 | − | 0.882399i | \(-0.655927\pi\) | ||||
−0.470503 | + | 0.882399i | \(0.655927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.89091 | −0.387593 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.9411 | −1.69946 | −0.849728 | − | 0.527221i | \(-0.823234\pi\) | ||||
−0.849728 | + | 0.527221i | \(0.823234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.707515 | −0.0461532 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.28189 | 0.408053 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.87455 | −0.315308 | −0.157654 | − | 0.987494i | \(-0.550393\pi\) | ||||
−0.157654 | + | 0.987494i | \(0.550393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.2622 | −1.04754 | −0.523770 | − | 0.851860i | \(-0.675475\pi\) | ||||
−0.523770 | + | 0.851860i | \(0.675475\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7688 | 1.01157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.77923 | 0.496997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0604 | −0.894643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.42859 | −0.280651 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.0800 | 2.77129 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.87206 | 0.117233 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5663 | −0.721485 | −0.360743 | − | 0.932665i | \(-0.617477\pi\) | ||||
−0.360743 | + | 0.932665i | \(0.617477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8178 | 0.920731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.90838 | −0.303821 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.6584 | −1.21219 | −0.606095 | − | 0.795392i | \(-0.707265\pi\) | ||||
−0.606095 | + | 0.795392i | \(0.707265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.60046 | 0.344034 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.99182 | 0.366693 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.5590 | 1.68030 | 0.840152 | − | 0.542351i | \(-0.182466\pi\) | ||||
0.840152 | + | 0.542351i | \(0.182466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4953 | −0.880525 | −0.440263 | − | 0.897869i | \(-0.645115\pi\) | ||||
−0.440263 | + | 0.897869i | \(0.645115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.75185 | 0.227072 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.5517 | −0.756898 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.1876 | −1.87388 | −0.936942 | − | 0.349486i | \(-0.886356\pi\) | ||||
−0.936942 | + | 0.349486i | \(0.886356\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.871406 | 0.0521697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.6416 | −1.35068 | −0.675341 | − | 0.737506i | \(-0.736004\pi\) | ||||
−0.675341 | + | 0.737506i | \(0.736004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3541 | 0.912707 | 0.456354 | − | 0.889799i | \(-0.349155\pi\) | ||||
0.456354 | + | 0.889799i | \(0.349155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.50966 | −0.326364 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.13251 | −0.243934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8233 | −0.871962 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.485613 | 0.0284672 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6294 | 0.913082 | 0.456541 | − | 0.889702i | \(-0.349088\pi\) | ||||
0.456541 | + | 0.889702i | \(0.349088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.82777 | −0.106417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.7507 | −1.26210 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.0741 | −1.62356 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.319943 | −0.0184412 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.74329 | 0.215047 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1044 | 0.750356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.79473 | −0.501942 | −0.250971 | − | 0.967995i | \(-0.580750\pi\) | ||||
−0.250971 | + | 0.967995i | \(0.580750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.3609 | −0.703186 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6368 | −1.68055 | −0.840275 | − | 0.542160i | \(-0.817607\pi\) | ||||
−0.840275 | + | 0.542160i | \(0.817607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.99611 | 0.112827 | 0.0564134 | − | 0.998407i | \(-0.482034\pi\) | ||||
0.0564134 | + | 0.998407i | \(0.482034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.46385 | −0.307853 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.2246 | −1.13593 | −0.567963 | − | 0.823054i | \(-0.692268\pi\) | ||||
−0.567963 | + | 0.823054i | \(0.692268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.5570 | 0.591079 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.09279 | 0.507510 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.40609 | −0.356444 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.99406 | 0.443431 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.59244 | −0.530463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.646034 | −0.0356170 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6830 | −0.916982 | −0.458491 | − | 0.888699i | \(-0.651610\pi\) | ||||
−0.458491 | + | 0.888699i | \(0.651610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.1115 | 1.32130 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.41466 | −0.350470 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5413 | −1.55474 | −0.777371 | − | 0.629043i | \(-0.783447\pi\) | ||||
−0.777371 | + | 0.629043i | \(0.783447\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.399603 | −0.0217035 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.87423 | −0.101495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2725 | 0.932629 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0010 | −0.592273 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.79212 | 0.364620 | 0.182310 | − | 0.983241i | \(-0.441642\pi\) | ||||
0.182310 | + | 0.983241i | \(0.441642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.5327 | 0.992035 | 0.496017 | − | 0.868313i | \(-0.334795\pi\) | ||||
0.496017 | + | 0.868313i | \(0.334795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8528 | 0.739405 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.9360 | 1.54011 | 0.770055 | − | 0.637977i | \(-0.220229\pi\) | ||||
0.770055 | + | 0.637977i | \(0.220229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.62200 | −0.192236 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.70939 | 0.0904703 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.2287 | −0.592628 | −0.296314 | − | 0.955091i | \(-0.595757\pi\) | ||||
−0.296314 | + | 0.955091i | \(0.595757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.146258 | −0.00769777 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8441 | 0.621652 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.52220 | −0.498415 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.6694 | −1.75753 | −0.878763 | − | 0.477258i | \(-0.841631\pi\) | ||||
−0.878763 | + | 0.477258i | \(0.841631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.72443 | −0.350060 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.11380 | 0.265495 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6550 | 1.22481 | 0.612405 | − | 0.790544i | \(-0.290202\pi\) | ||||
0.612405 | + | 0.790544i | \(0.290202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.47699 | 0.489390 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.72364 | −0.346285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6340 | 1.52219 | 0.761097 | − | 0.648638i | \(-0.224661\pi\) | ||||
0.761097 | + | 0.648638i | \(0.224661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.1588 | −0.571684 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.3473 | 0.886406 | 0.443203 | − | 0.896421i | \(-0.353842\pi\) | ||||
0.443203 | + | 0.896421i | \(0.353842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.7517 | 0.598922 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.520612 | −0.0264642 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.3614 | 1.38728 | 0.693639 | − | 0.720322i | \(-0.256006\pi\) | ||||
0.693639 | + | 0.720322i | \(0.256006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7909 | −0.646862 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.925738 | 0.0466973 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.5317 | −0.630536 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.56136 | 0.178739 | 0.0893697 | − | 0.995999i | \(-0.471515\pi\) | ||||
0.0893697 | + | 0.995999i | \(0.471515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.03089 | −0.251859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2223 | −1.35942 | −0.679709 | − | 0.733482i | \(-0.737894\pi\) | ||||
−0.679709 | + | 0.733482i | \(0.737894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19368 | 0.0594612 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.85479 | −0.290927 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.8593 | −2.57057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.31647 | 0.0650955 | 0.0325477 | − | 0.999470i | \(-0.489638\pi\) | ||||
0.0325477 | + | 0.999470i | \(0.489638\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.22382 | −0.159019 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.66894 | −0.0821232 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.83455 | 0.433671 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.1747 | 0.743111 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.8987 | −1.50950 | −0.754750 | − | 0.656012i | \(-0.772242\pi\) | ||||
−0.754750 | + | 0.656012i | \(0.772242\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.3745 | −0.505620 | −0.252810 | − | 0.967516i | \(-0.581355\pi\) | ||||
−0.252810 | + | 0.967516i | \(0.581355\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.05123 | −0.0511125 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.64219 | 0.176672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9657 | 0.579060 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.1307 | −0.633958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2148 | 0.492030 | 0.246015 | − | 0.969266i | \(-0.420879\pi\) | ||||
0.246015 | + | 0.969266i | \(0.420879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2704 | 0.637733 | 0.318867 | − | 0.947800i | \(-0.396698\pi\) | ||||
0.318867 | + | 0.947800i | \(0.396698\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.63469 | −0.126324 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.6447 | 1.80079 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.324821 | 0.0155029 | 0.00775144 | − | 0.999970i | \(-0.497533\pi\) | ||||
0.00775144 | + | 0.999970i | \(0.497533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.5584 | 0.550401 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5792 | −0.930237 | −0.465118 | − | 0.885249i | \(-0.653988\pi\) | ||||
−0.465118 | + | 0.885249i | \(0.653988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.9530 | −0.566627 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.18332 | −0.0559693 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7665 | 0.602487 | 0.301244 | − | 0.953547i | \(-0.402598\pi\) | ||||
0.301244 | + | 0.953547i | \(0.402598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4630 | 0.681035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.54549 | −0.307534 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.48452 | −0.350880 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.7867 | −1.58048 | −0.790238 | − | 0.612799i | \(-0.790043\pi\) | ||||
−0.790238 | + | 0.612799i | \(0.790043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.31147 | 0.294594 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.6532 | −1.00849 | −0.504245 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504245 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8083 | −1.15294 | −0.576471 | − | 0.817118i | \(-0.695570\pi\) | ||||
−0.576471 | + | 0.817118i | \(0.695570\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.467749 | 0.0216913 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1799 | 0.563618 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.85725 | −0.270463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.23360 | −0.195074 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.11974 | 0.0514856 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7193 | −0.491835 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.32119 | 0.381001 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5662 | 0.711240 | 0.355620 | − | 0.934631i | \(-0.384270\pi\) | ||||
0.355620 | + | 0.934631i | \(0.384270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.0286 | 1.50597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.0450 | −0.457065 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.968744 | −0.0439884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.2701 | 0.827899 | 0.413950 | − | 0.910300i | \(-0.364149\pi\) | ||||
0.413950 | + | 0.910300i | \(0.364149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.10223 | −0.366395 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8632 | −0.625640 | −0.312820 | − | 0.949812i | \(-0.601274\pi\) | ||||
−0.312820 | + | 0.949812i | \(0.601274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.06337 | −0.137967 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.1224 | 0.859488 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.30727 | −0.148351 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3645 | 0.777342 | 0.388671 | − | 0.921377i | \(-0.372934\pi\) | ||||
0.388671 | + | 0.921377i | \(0.372934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.13334 | −0.408047 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8255 | −0.616448 | −0.308224 | − | 0.951314i | \(-0.599735\pi\) | ||||
−0.308224 | + | 0.951314i | \(0.599735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.46745 | −0.332297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.00522 | −0.0890551 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.25942 | −0.100147 | −0.0500734 | − | 0.998746i | \(-0.515946\pi\) | ||||
−0.0500734 | + | 0.998746i | \(0.515946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.69476 | −0.384634 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.5753 | −0.820118 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6586 | 1.08659 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.26099 | 0.0994384 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.3166 | −0.804011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.22270 | 0.141189 | 0.0705945 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705945 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5339 | −1.16025 | −0.580123 | − | 0.814529i | \(-0.696995\pi\) | ||||
−0.580123 | + | 0.814529i | \(0.696995\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.86031 | 0.124834 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.543852 | 0.0236906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.1642 | 2.26801 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.71571 | −0.117852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.21130 | −0.398986 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1391 | −0.784221 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.04732 | −0.347268 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.8600 | −1.07080 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.55225 | −0.367690 | −0.183845 | − | 0.982955i | \(-0.558854\pi\) | ||||
−0.183845 | + | 0.982955i | \(0.558854\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.3116 | −0.828742 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.1359 | 0.819690 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6962 | 1.05593 | 0.527967 | − | 0.849265i | \(-0.322955\pi\) | ||||
0.527967 | + | 0.849265i | \(0.322955\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.4706 | 0.830984 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.01578 | 0.384085 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4427 | −0.486594 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9424 | 0.549376 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.1650 | −1.02390 | −0.511951 | − | 0.859015i | \(-0.671077\pi\) | ||||
−0.511951 | + | 0.859015i | \(0.671077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.713148 | −0.0301630 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.98252 | −0.252582 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.2975 | −1.44547 | −0.722734 | − | 0.691126i | \(-0.757115\pi\) | ||||
−0.722734 | + | 0.691126i | \(0.757115\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.797163 | 0.0335369 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.34603 | −0.224512 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.9009 | 0.876212 | 0.438106 | − | 0.898923i | \(-0.355649\pi\) | ||||
0.438106 | + | 0.898923i | \(0.355649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2036 | 1.38953 | 0.694764 | − | 0.719238i | \(-0.255509\pi\) | ||||
0.694764 | + | 0.719238i | \(0.255509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.04192 | 0.252405 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.4029 | −0.892564 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.3457 | −0.680479 | −0.340240 | − | 0.940339i | \(-0.610508\pi\) | ||||
−0.340240 | + | 0.940339i | \(0.610508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.82501 | −0.408314 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.06686 | 0.334670 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.8973 | −0.741231 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.1788 | −0.503533 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.8472 | 1.47957 | 0.739786 | − | 0.672842i | \(-0.234927\pi\) | ||||
0.739786 | + | 0.672842i | \(0.234927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.60061 | −0.0659520 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.35071 | 0.343502 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.97842 | −0.286569 | −0.143285 | − | 0.989682i | \(-0.545766\pi\) | ||||
−0.143285 | + | 0.989682i | \(0.545766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.41003 | −0.139798 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.89110 | −0.241107 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.642098 | 0.0262354 | 0.0131177 | − | 0.999914i | \(-0.495824\pi\) | ||||
0.0131177 | + | 0.999914i | \(0.495824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1282 | 1.35133 | 0.675664 | − | 0.737209i | \(-0.263857\pi\) | ||||
0.675664 | + | 0.737209i | \(0.263857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.53093 | −0.388129 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.6276 | −0.960597 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.462154 | 0.0187583 | 0.00937913 | − | 0.999956i | \(-0.497014\pi\) | ||||
0.00937913 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.40575 | −0.0974859 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.44000 | −0.0582562 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.24069 | 0.130890 | 0.0654450 | − | 0.997856i | \(-0.479153\pi\) | ||||
0.0654450 | + | 0.997856i | \(0.479153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.60950 | −0.145549 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.75861 | −0.0707990 | −0.0353995 | − | 0.999373i | \(-0.511270\pi\) | ||||
−0.0353995 | + | 0.999373i | \(0.511270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9414 | 0.640738 | 0.320369 | − | 0.947293i | \(-0.396193\pi\) | ||||
0.320369 | + | 0.947293i | \(0.396193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −37.0887 | −1.48832 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9143 | −0.437274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.56205 | −0.262482 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.6071 | 0.703161 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0482 | 0.600011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.4070 | 1.64839 | 0.824194 | − | 0.566308i | \(-0.191629\pi\) | ||||
0.824194 | + | 0.566308i | \(0.191629\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.54214 | −0.260027 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.2606 | 0.883386 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8330 | 0.627328 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.38159 | −0.212892 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.0260 | 1.54143 | 0.770717 | − | 0.637178i | \(-0.219898\pi\) | ||||
0.770717 | + | 0.637178i | \(0.219898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.75645 | −0.305884 | −0.152942 | − | 0.988235i | \(-0.548875\pi\) | ||||
−0.152942 | + | 0.988235i | \(0.548875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.279451 | −0.0110034 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.04119 | −0.0802474 | −0.0401237 | − | 0.999195i | \(-0.512775\pi\) | ||||
−0.0401237 | + | 0.999195i | \(0.512775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.84097 | 0.229278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.427103 | 0.0167395 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.83838 | −0.385006 | −0.192503 | − | 0.981296i | \(-0.561660\pi\) | ||||
−0.192503 | + | 0.981296i | \(0.561660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.84674 | −0.0721583 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.1481 | −0.551971 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0432 | −1.48195 | −0.740976 | − | 0.671532i | \(-0.765637\pi\) | ||||
−0.740976 | + | 0.671532i | \(0.765637\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6749 | 0.687474 | 0.343737 | − | 0.939066i | \(-0.388307\pi\) | ||||
0.343737 | + | 0.939066i | \(0.388307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.81020 | 0.147976 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0361 | 0.389182 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0016 | 0.697023 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.68229 | 0.374339 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.8775 | −1.61666 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3861 | 0.400357 | 0.200178 | − | 0.979759i | \(-0.435848\pi\) | ||||
0.200178 | + | 0.979759i | \(0.435848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.5610 | 0.406492 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.80298 | −0.0692940 | −0.0346470 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346470 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.884564 | −0.0339464 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.67603 | 0.294146 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.3787 | 1.62158 | 0.810789 | − | 0.585339i | \(-0.199038\pi\) | ||||
0.810789 | + | 0.585339i | \(0.199038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.43116 | 0.245722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.3570 | −0.433296 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3986 | 0.434252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.61896 | −0.327881 | −0.163940 | − | 0.986470i | \(-0.552420\pi\) | ||||
−0.163940 | + | 0.986470i | \(0.552420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.4607 | 0.663278 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.2719 | −1.14828 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.19678 | −0.158964 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.6891 | −0.782534 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.2804 | 1.21922 | 0.609608 | − | 0.792703i | \(-0.291327\pi\) | ||||
0.609608 | + | 0.792703i | \(0.291327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.2883 | −1.67036 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.564273 | −0.0212517 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.81856 | −0.256438 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.2241 | 0.984867 | 0.492433 | − | 0.870350i | \(-0.336107\pi\) | ||||
0.492433 | + | 0.870350i | \(0.336107\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.6196 | −0.698290 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.19589 | −0.119687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.1944 | 0.979614 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.88766 | −0.145187 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.9547 | 0.893360 | 0.446680 | − | 0.894694i | \(-0.352606\pi\) | ||||
0.446680 | + | 0.894694i | \(0.352606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.5159 | 0.838534 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.9698 | −0.482352 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.12592 | −0.190372 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7671 | 0.881474 | 0.440737 | − | 0.897636i | \(-0.354717\pi\) | ||||
0.440737 | + | 0.897636i | \(0.354717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.53647 | 0.0569064 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.324919 | −0.0120175 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9899 | 1.07077 | 0.535383 | − | 0.844610i | \(-0.320167\pi\) | ||||
0.535383 | + | 0.844610i | \(0.320167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.20427 | 0.228848 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.4992 | 0.755099 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.86810 | 0.142290 | 0.0711451 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711451 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.2138 | −0.411949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.26145 | −0.193024 | −0.0965120 | − | 0.995332i | \(-0.530769\pi\) | ||||
−0.0965120 | + | 0.995332i | \(0.530769\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.36060 | 0.0864857 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1264 | 0.480271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.5629 | −0.605194 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.15809 | −0.0787498 | −0.0393749 | − | 0.999225i | \(-0.512537\pi\) | ||||
−0.0393749 | + | 0.999225i | \(0.512537\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.797542 | −0.0290640 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.0575 | 0.475212 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.9482 | −1.56098 | −0.780490 | − | 0.625168i | \(-0.785030\pi\) | ||||
−0.780490 | + | 0.625168i | \(0.785030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 35.1557 | 1.27607 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.8703 | 0.466549 | 0.233274 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233274 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.4730 | 0.632566 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.54882 | −0.200618 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.72005 | −0.134323 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.4367 | 1.02545 | 0.512727 | − | 0.858552i | \(-0.328635\pi\) | ||||
0.512727 | + | 0.858552i | \(0.328635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.22460 | −0.332216 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.3288 | 0.407467 | 0.203734 | − | 0.979026i | \(-0.434692\pi\) | ||||
0.203734 | + | 0.979026i | \(0.434692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.910027 | 0.0326892 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.8178 | 0.423961 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.3515 | 0.442539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5748 | 0.414178 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.88262 | −0.317439 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.44555 | 0.301435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.89964 | −0.352884 | −0.176442 | − | 0.984311i | \(-0.556459\pi\) | ||||
−0.176442 | + | 0.984311i | \(0.556459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6784 | −0.558167 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.727893 | 0.0258809 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.6713 | 0.947127 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.46660 | 0.158414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.4484 | 0.936850 | 0.468425 | − | 0.883503i | \(-0.344822\pi\) | ||||
0.468425 | + | 0.883503i | \(0.344822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.656081 | −0.0232105 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7598 | −0.627513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.4300 | 1.07385 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.0387 | 0.706272 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.9795 | 0.773715 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.6352 | 0.866129 | 0.433064 | − | 0.901363i | \(-0.357432\pi\) | ||||
0.433064 | + | 0.901363i | \(0.357432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.9804 | 1.01764 | 0.508820 | − | 0.860873i | \(-0.330082\pi\) | ||||
0.508820 | + | 0.860873i | \(0.330082\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.5606 | −0.405448 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.1630 | 0.566166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.956267 | 0.0334555 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.1205 | −0.388583 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.7663 | −0.410646 | −0.205323 | − | 0.978694i | \(-0.565824\pi\) | ||||
−0.205323 | + | 0.978694i | \(0.565824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.87270 | −0.274425 | −0.137213 | − | 0.990542i | \(-0.543814\pi\) | ||||
−0.137213 | + | 0.990542i | \(0.543814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.0105 | −0.348522 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1513 | −0.492087 | −0.246044 | − | 0.969259i | \(-0.579131\pi\) | ||||
−0.246044 | + | 0.969259i | \(0.579131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3282 | −0.462907 | −0.231453 | − | 0.972846i | \(-0.574348\pi\) | ||||
−0.231453 | + | 0.972846i | \(0.574348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8735 | −0.862850 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.21372 | 0.249940 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.2200 | 0.630529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.57697 | 0.0545080 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.59858 | −0.262332 | −0.131166 | − | 0.991360i | \(-0.541872\pi\) | ||||
−0.131166 | + | 0.991360i | \(0.541872\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6887 | −0.851334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.0576 | −0.621937 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00019 | 0.137611 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.5744 | −0.741306 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.2455 | 0.420266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −88.4292 | −3.03131 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6594 | 0.399210 | 0.199605 | − | 0.979876i | \(-0.436034\pi\) | ||||
0.199605 | + | 0.979876i | \(0.436034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.3307 | 0.558498 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.2226 | −0.519994 | −0.259997 | − | 0.965609i | \(-0.583722\pi\) | ||||
−0.259997 | + | 0.965609i | \(0.583722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.85587 | 0.199800 | 0.0998998 | − | 0.994998i | \(-0.468148\pi\) | ||||
0.0998998 | + | 0.994998i | \(0.468148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.29585 | −0.112322 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.1781 | 0.380509 | 0.190254 | − | 0.981735i | \(-0.439069\pi\) | ||||
0.190254 | + | 0.981735i | \(0.439069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.5396 | 1.24238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8222 | −0.401505 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.0473 | 1.35851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0557 | −0.442376 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.43936 | −0.0487151 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.2627 | −0.583586 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.91919 | 0.132342 | 0.0661709 | − | 0.997808i | \(-0.478922\pi\) | ||||
0.0661709 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.4651 | 0.420439 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.5304 | −0.792761 | −0.396380 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396380 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.8715 | −1.03891 | −0.519454 | − | 0.854499i | \(-0.673865\pi\) | ||||
−0.519454 | + | 0.854499i | \(0.673865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45772 | −0.0490008 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.4426 | 0.518512 | 0.259256 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259256 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3263 | 0.681721 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.7101 | 0.626811 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.93091 | 0.0646155 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0535 | 0.536610 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.3902 | −0.747589 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.765405 | −0.0255277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19333 | 0.173015 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.255168 | −0.00849146 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.5245 | 1.28060 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.8410 | 0.625604 | 0.312802 | − | 0.949818i | \(-0.398732\pi\) | ||||
0.312802 | + | 0.949818i | \(0.398732\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.0952 | −0.368004 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0658 | −1.32744 | −0.663720 | − | 0.747981i | \(-0.731023\pi\) | ||||
−0.663720 | + | 0.747981i | \(0.731023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2324 | −0.934357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.4513 | 0.345510 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.68627 | −0.0556855 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1658 | 0.731184 | 0.365592 | − | 0.930775i | \(-0.380867\pi\) | ||||
0.365592 | + | 0.930775i | \(0.380867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.01417 | −0.231125 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.37185 | −0.242647 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.1801 | 0.827918 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.6379 | 1.20335 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.2554 | −0.533322 | −0.266661 | − | 0.963790i | \(-0.585920\pi\) | ||||
−0.266661 | + | 0.963790i | \(0.585920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2307 | −0.695807 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.6366 | −0.773828 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.9345 | 0.390298 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.2139 | −1.67308 | −0.836542 | − | 0.547903i | \(-0.815426\pi\) | ||||
−0.836542 | + | 0.547903i | \(0.815426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.59198 | 0.0519523 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.48359 | −0.178760 | −0.0893799 | − | 0.995998i | \(-0.528489\pi\) | ||||
−0.0893799 | + | 0.995998i | \(0.528489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.6619 | 0.803103 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.88783 | −0.321651 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7120 | 0.348094 | 0.174047 | − | 0.984737i | \(-0.444315\pi\) | ||||
0.174047 | + | 0.984737i | \(0.444315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3805 | −0.629118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.1299 | −0.523049 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.9499 | −0.905384 | −0.452692 | − | 0.891667i | \(-0.649536\pi\) | ||||
−0.452692 | + | 0.891667i | \(0.649536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0529 | −0.390024 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.41966 | 0.272169 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.87232 | 0.189627 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8641 | −0.995617 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.9512 | −0.868489 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5998 | 0.630940 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.9393 | −1.50947 | −0.754733 | − | 0.656032i | \(-0.772234\pi\) | ||||
−0.754733 | + | 0.656032i | \(0.772234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.10913 | −0.164129 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.0455 | 1.50976 | 0.754881 | − | 0.655862i | \(-0.227695\pi\) | ||||
0.754881 | + | 0.655862i | \(0.227695\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.6414 | −0.886143 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.37560 | 0.204183 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.5783 | −1.07427 | −0.537133 | − | 0.843497i | \(-0.680493\pi\) | ||||
−0.537133 | + | 0.843497i | \(0.680493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.1980 | 1.22081 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.4321 | 0.907769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.84733 | −0.282186 | −0.141093 | − | 0.989996i | \(-0.545062\pi\) | ||||
−0.141093 | + | 0.989996i | \(0.545062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.6587 | −0.530792 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.515240 | −0.0164003 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.90935 | 0.0607138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5140 | 1.19167 | 0.595836 | − | 0.803106i | \(-0.296821\pi\) | ||||
0.595836 | + | 0.803106i | \(0.296821\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.3054 | −0.422235 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7521 | 0.372566 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.5315 | 0.966944 | 0.483472 | − | 0.875360i | \(-0.339376\pi\) | ||||
0.483472 | + | 0.875360i | \(0.339376\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.6342 | 1.38052 |
(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 | 8032.2.a.h.1.19 | ✓ | 30 | |
4.3 | odd | 2 | 8032.2.a.i.1.12 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.h.1.19 | ✓ | 30 | 1.1 | even | 1 | trivial | |
8032.2.a.i.1.12 | yes | 30 | 4.3 | odd | 2 |