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: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
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 | ||||||||
\(3\) | 0.356039 | 0.205559 | 0.102780 | − | 0.994704i | \(-0.467226\pi\) | ||||
0.102780 | + | 0.994704i | \(0.467226\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.400497 | −0.151374 | −0.0756869 | − | 0.997132i | \(-0.524115\pi\) | ||||
−0.0756869 | + | 0.997132i | \(0.524115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87324 | −0.957745 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.436499 | −0.131610 | −0.0658048 | − | 0.997833i | \(-0.520961\pi\) | ||||
−0.0658048 | + | 0.997833i | \(0.520961\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.615654 | −0.170752 | −0.0853758 | − | 0.996349i | \(-0.527209\pi\) | ||||
−0.0853758 | + | 0.996349i | \(0.527209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.356039 | −0.0919288 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.540511 | −0.131093 | −0.0655466 | − | 0.997850i | \(-0.520879\pi\) | ||||
−0.0655466 | + | 0.997850i | \(0.520879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.98251 | 0.454819 | 0.227409 | − | 0.973799i | \(-0.426974\pi\) | ||||
0.227409 | + | 0.973799i | \(0.426974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.142593 | −0.0311163 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0321294 | 0.00669945 | 0.00334972 | − | 0.999994i | \(-0.498934\pi\) | ||||
0.00334972 | + | 0.999994i | \(0.498934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.09110 | −0.402433 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.32938 | 1.36103 | 0.680516 | − | 0.732733i | \(-0.261756\pi\) | ||||
0.680516 | + | 0.732733i | \(0.261756\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.85305 | −0.332818 | −0.166409 | − | 0.986057i | \(-0.553217\pi\) | ||||
−0.166409 | + | 0.986057i | \(0.553217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.155411 | −0.0270535 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.400497 | 0.0676964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.34276 | 0.220748 | 0.110374 | − | 0.993890i | \(-0.464795\pi\) | ||||
0.110374 | + | 0.993890i | \(0.464795\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.219197 | −0.0350996 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.68506 | 1.20020 | 0.600102 | − | 0.799923i | \(-0.295126\pi\) | ||||
0.600102 | + | 0.799923i | \(0.295126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.12708 | 0.629374 | 0.314687 | − | 0.949195i | \(-0.398100\pi\) | ||||
0.314687 | + | 0.949195i | \(0.398100\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.87324 | 0.428317 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3077 | 1.64939 | 0.824695 | − | 0.565577i | \(-0.191347\pi\) | ||||
0.824695 | + | 0.565577i | \(0.191347\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.83960 | −0.977086 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.192443 | −0.0269474 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.77405 | −0.518405 | −0.259203 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259203 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.436499 | 0.0588576 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.705850 | 0.0934921 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.82501 | 0.497973 | 0.248987 | − | 0.968507i | \(-0.419902\pi\) | ||||
0.248987 | + | 0.968507i | \(0.419902\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.59871 | −0.204693 | −0.102347 | − | 0.994749i | \(-0.532635\pi\) | ||||
−0.102347 | + | 0.994749i | \(0.532635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.15072 | 0.144978 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.615654 | 0.0763625 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1573 | −1.24092 | −0.620458 | − | 0.784239i | \(-0.713053\pi\) | ||||
−0.620458 | + | 0.784239i | \(0.713053\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0114393 | 0.00137713 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.53890 | −1.01338 | −0.506690 | − | 0.862128i | \(-0.669131\pi\) | ||||
−0.506690 | + | 0.862128i | \(0.669131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.94694 | 0.227872 | 0.113936 | − | 0.993488i | \(-0.463654\pi\) | ||||
0.113936 | + | 0.993488i | \(0.463654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.356039 | 0.0411118 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.174817 | 0.0199222 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.05854 | −0.231604 | −0.115802 | − | 0.993272i | \(-0.536944\pi\) | ||||
−0.115802 | + | 0.993272i | \(0.536944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.87520 | 0.875022 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.42087 | 0.375490 | 0.187745 | − | 0.982218i | \(-0.439882\pi\) | ||||
0.187745 | + | 0.982218i | \(0.439882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.540511 | 0.0586267 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60954 | 0.279772 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.88151 | −1.04744 | −0.523719 | − | 0.851891i | \(-0.675456\pi\) | ||||
−0.523719 | + | 0.851891i | \(0.675456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.246568 | 0.0258473 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.659760 | −0.0684139 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.98251 | −0.203401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.60530 | −0.467597 | −0.233799 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233799 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25417 | 0.126048 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7271 | −1.46540 | −0.732701 | − | 0.680550i | \(-0.761741\pi\) | ||||
−0.732701 | + | 0.680550i | \(0.761741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.01280 | −0.690992 | −0.345496 | − | 0.938420i | \(-0.612289\pi\) | ||||
−0.345496 | + | 0.938420i | \(0.612289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.142593 | 0.0139156 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0600 | −1.35923 | −0.679616 | − | 0.733568i | \(-0.737853\pi\) | ||||
−0.679616 | + | 0.733568i | \(0.737853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.24267 | −0.502157 | −0.251079 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251079 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.478074 | 0.0453768 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.01042 | 0.565413 | 0.282706 | − | 0.959207i | \(-0.408768\pi\) | ||||
0.282706 | + | 0.959207i | \(0.408768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0321294 | −0.00299608 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.76892 | 0.163537 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.216473 | 0.0198441 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8095 | −0.982679 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.73618 | 0.246713 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.232932 | 0.0206694 | 0.0103347 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103347 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.46940 | 0.129374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.38264 | −0.645025 | −0.322512 | − | 0.946565i | \(-0.604527\pi\) | ||||
−0.322512 | + | 0.946565i | \(0.604527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.793990 | −0.0688476 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.09110 | 0.179973 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8082 | 0.923408 | 0.461704 | − | 0.887034i | \(-0.347238\pi\) | ||||
0.461704 | + | 0.887034i | \(0.347238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.01742 | 0.510391 | 0.255196 | − | 0.966889i | \(-0.417860\pi\) | ||||
0.255196 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.02596 | 0.339047 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.268733 | 0.0224726 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.32938 | −0.608672 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.43516 | −0.200849 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.190471 | −0.0156040 | −0.00780202 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00780202 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8656 | −1.04699 | −0.523495 | − | 0.852029i | \(-0.675372\pi\) | ||||
−0.523495 | + | 0.852029i | \(0.675372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.55302 | 0.125554 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.85305 | 0.148841 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.08796 | 0.246446 | 0.123223 | − | 0.992379i | \(-0.460677\pi\) | ||||
0.123223 | + | 0.992379i | \(0.460677\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.34371 | −0.106563 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0128678 | −0.00101412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.25329 | −0.411470 | −0.205735 | − | 0.978608i | \(-0.565958\pi\) | ||||
−0.205735 | + | 0.978608i | \(0.565958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.155411 | 0.0120987 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.8138 | −1.45585 | −0.727926 | − | 0.685656i | \(-0.759516\pi\) | ||||
−0.727926 | + | 0.685656i | \(0.759516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6210 | −0.970844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.69622 | −0.435600 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7085 | −1.34635 | −0.673177 | − | 0.739481i | \(-0.735071\pi\) | ||||
−0.673177 | + | 0.739481i | \(0.735071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.400497 | −0.0302748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.36185 | 0.102363 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1574 | −1.13292 | −0.566460 | − | 0.824089i | \(-0.691687\pi\) | ||||
−0.566460 | + | 0.824089i | \(0.691687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7964 | 1.09981 | 0.549905 | − | 0.835227i | \(-0.314664\pi\) | ||||
0.549905 | + | 0.835227i | \(0.314664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.569201 | −0.0420766 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.34276 | −0.0987215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.235933 | 0.0172531 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.837480 | 0.0609177 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.1176 | 1.88981 | 0.944903 | − | 0.327352i | \(-0.106156\pi\) | ||||
0.944903 | + | 0.327352i | \(0.106156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.54721 | −0.399297 | −0.199649 | − | 0.979868i | \(-0.563980\pi\) | ||||
−0.199649 | + | 0.979868i | \(0.563980\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.219197 | 0.0156970 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.16628 | −0.225588 | −0.112794 | − | 0.993618i | \(-0.535980\pi\) | ||||
−0.112794 | + | 0.993618i | \(0.535980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.965855 | −0.0684677 | −0.0342338 | − | 0.999414i | \(-0.510899\pi\) | ||||
−0.0342338 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.61641 | −0.255082 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.93540 | −0.206024 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.68506 | −0.536748 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0923154 | −0.00641637 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.865364 | −0.0598585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8110 | 0.744263 | 0.372132 | − | 0.928180i | \(-0.378627\pi\) | ||||
0.372132 | + | 0.928180i | \(0.378627\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.04018 | −0.208310 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.12708 | −0.281465 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.742144 | 0.0503800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.693186 | 0.0468411 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.332768 | 0.0223844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.10871 | −0.543000 | −0.271500 | − | 0.962438i | \(-0.587520\pi\) | ||||
−0.271500 | + | 0.962438i | \(0.587520\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.87324 | −0.191549 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.2653 | −1.74329 | −0.871644 | − | 0.490139i | \(-0.836946\pi\) | ||||
−0.871644 | + | 0.490139i | \(0.836946\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4473 | 1.28511 | 0.642557 | − | 0.766238i | \(-0.277874\pi\) | ||||
0.642557 | + | 0.766238i | \(0.277874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0622416 | 0.00409520 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.7846 | 1.36165 | 0.680823 | − | 0.732448i | \(-0.261622\pi\) | ||||
0.680823 | + | 0.732448i | \(0.261622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3077 | −0.737630 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.732921 | −0.0476083 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6909 | −0.885590 | −0.442795 | − | 0.896623i | \(-0.646013\pi\) | ||||
−0.442795 | + | 0.896623i | \(0.646013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.64027 | 0.170075 | 0.0850375 | − | 0.996378i | \(-0.472899\pi\) | ||||
0.0850375 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.07718 | 0.582301 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.83960 | 0.436966 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.22054 | −0.0776610 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.21796 | 0.0771854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.53695 | −0.349489 | −0.174745 | − | 0.984614i | \(-0.555910\pi\) | ||||
−0.174745 | + | 0.984614i | \(0.555910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0140245 | −0.000881711 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.192443 | 0.0120512 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.5774 | −1.72023 | −0.860115 | − | 0.510101i | \(-0.829608\pi\) | ||||
−0.860115 | + | 0.510101i | \(0.829608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.537771 | −0.0334155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.0590 | −1.30352 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2506 | 1.00206 | 0.501028 | − | 0.865431i | \(-0.332955\pi\) | ||||
0.501028 | + | 0.865431i | \(0.332955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.77405 | 0.231838 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.51820 | −0.215310 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.9729 | −1.09583 | −0.547913 | − | 0.836535i | \(-0.684577\pi\) | ||||
−0.547913 | + | 0.836535i | \(0.684577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5126 | −1.06381 | −0.531907 | − | 0.846803i | \(-0.678524\pi\) | ||||
−0.531907 | + | 0.846803i | \(0.678524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0877877 | 0.00531316 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.436499 | −0.0263219 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.23224 | −0.194206 | −0.0971031 | − | 0.995274i | \(-0.530958\pi\) | ||||
−0.0971031 | + | 0.995274i | \(0.530958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.32426 | 0.318755 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92462 | −0.114813 | −0.0574065 | − | 0.998351i | \(-0.518283\pi\) | ||||
−0.0574065 | + | 0.998351i | \(0.518283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.99800 | 0.297100 | 0.148550 | − | 0.988905i | \(-0.452539\pi\) | ||||
0.148550 | + | 0.988905i | \(0.452539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.705850 | −0.0418110 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.07785 | −0.181680 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7078 | −0.982815 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.63967 | −0.0961189 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.66831 | −0.272726 | −0.136363 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136363 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.82501 | −0.222700 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.912764 | 0.0529640 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0197806 | −0.00114394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65289 | −0.0952708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.24343 | −0.301227 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.59871 | 0.0915416 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1043 | −1.03327 | −0.516634 | − | 0.856206i | \(-0.672815\pi\) | ||||
−0.516634 | + | 0.856206i | \(0.672815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.49683 | −0.142040 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.4713 | −1.89798 | −0.948992 | − | 0.315300i | \(-0.897895\pi\) | ||||
−0.948992 | + | 0.315300i | \(0.897895\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.67831 | 0.207910 | 0.103955 | − | 0.994582i | \(-0.466850\pi\) | ||||
0.103955 | + | 0.994582i | \(0.466850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.15072 | −0.0648359 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0864 | −0.678841 | −0.339420 | − | 0.940635i | \(-0.610231\pi\) | ||||
−0.339420 | + | 0.940635i | \(0.610231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.19927 | −0.179125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.00591 | −0.279402 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.07157 | −0.0596236 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.615654 | −0.0341503 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.86660 | −0.103223 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.52869 | −0.249674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19704 | 0.230690 | 0.115345 | − | 0.993325i | \(-0.463203\pi\) | ||||
0.115345 | + | 0.993325i | \(0.463203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.85806 | −0.211420 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.1573 | 0.554955 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.4211 | 1.65714 | 0.828571 | − | 0.559884i | \(-0.189154\pi\) | ||||
0.828571 | + | 0.559884i | \(0.189154\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.13994 | 0.116226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.808858 | 0.0438021 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.54272 | 0.299279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0114393 | −0.000615873 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.3677 | −1.95232 | −0.976161 | − | 0.217047i | \(-0.930357\pi\) | ||||
−0.976161 | + | 0.217047i | \(0.930357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0876 | 1.50349 | 0.751747 | − | 0.659452i | \(-0.229212\pi\) | ||||
0.751747 | + | 0.659452i | \(0.229212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.28739 | 0.0687160 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.9754 | 1.06318 | 0.531591 | − | 0.847001i | \(-0.321594\pi\) | ||||
0.531591 | + | 0.847001i | \(0.321594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.53890 | 0.453198 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0770729 | 0.00407913 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.5820 | 1.87795 | 0.938973 | − | 0.343990i | \(-0.111779\pi\) | ||||
0.938973 | + | 0.343990i | \(0.111779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0697 | −0.793140 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.84859 | −0.201999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.94694 | −0.101907 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.1552 | 1.83508 | 0.917542 | − | 0.397638i | \(-0.130170\pi\) | ||||
0.917542 | + | 0.397638i | \(0.130170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.0810 | −1.14949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.51150 | 0.0784730 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.4843 | 1.26775 | 0.633874 | − | 0.773437i | \(-0.281464\pi\) | ||||
0.633874 | + | 0.773437i | \(0.281464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.356039 | −0.0183858 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.51236 | −0.232398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.2262 | 1.60398 | 0.801991 | − | 0.597336i | \(-0.203774\pi\) | ||||
0.801991 | + | 0.597336i | \(0.203774\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0829328 | 0.00424878 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9086 | −0.659598 | −0.329799 | − | 0.944051i | \(-0.606981\pi\) | ||||
−0.329799 | + | 0.944051i | \(0.606981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.174817 | −0.00890950 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.8581 | −0.602780 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.62994 | 0.0826410 | 0.0413205 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413205 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0173663 | −0.000878252 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.62851 | −0.132591 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.05854 | 0.103577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7581 | −1.64408 | −0.822040 | − | 0.569430i | \(-0.807164\pi\) | ||||
−0.822040 | + | 0.569430i | \(0.807164\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.282691 | −0.0141523 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.14084 | 0.0568293 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.87520 | −0.391322 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.586113 | −0.0290525 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.7689 | 1.66977 | 0.834883 | − | 0.550427i | \(-0.185535\pi\) | ||||
0.834883 | + | 0.550427i | \(0.185535\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.84815 | 0.189815 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.53191 | −0.0753801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.42087 | −0.167924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.14244 | 0.104916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2504 | −1.03815 | −0.519075 | − | 0.854729i | \(-0.673724\pi\) | ||||
−0.519075 | + | 0.854729i | \(0.673724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.61538 | −0.273677 | −0.136839 | − | 0.990593i | \(-0.543694\pi\) | ||||
−0.136839 | + | 0.990593i | \(0.543694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.4896 | −1.57970 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.540511 | −0.0262186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.640278 | 0.0309852 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0956793 | 0.00461944 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.9645 | 1.53968 | 0.769838 | − | 0.638239i | \(-0.220337\pi\) | ||||
0.769838 | + | 0.638239i | \(0.220337\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6145 | −0.558158 | −0.279079 | − | 0.960268i | \(-0.590029\pi\) | ||||
−0.279079 | + | 0.960268i | \(0.590029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.60954 | −0.125118 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0636969 | 0.00304703 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.73907 | −0.178456 | −0.0892281 | − | 0.996011i | \(-0.528440\pi\) | ||||
−0.0892281 | + | 0.996011i | \(0.528440\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.6518 | 0.935800 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.3407 | 0.728858 | 0.364429 | − | 0.931231i | \(-0.381264\pi\) | ||||
0.364429 | + | 0.931231i | \(0.381264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.88151 | 0.468428 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0678153 | −0.00320755 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2372 | −0.813472 | −0.406736 | − | 0.913546i | \(-0.633333\pi\) | ||||
−0.406736 | + | 0.913546i | \(0.633333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.35453 | −0.157958 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.58066 | −0.215218 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.246568 | −0.0115593 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.5103 | −1.61433 | −0.807163 | − | 0.590329i | \(-0.798998\pi\) | ||||
−0.807163 | + | 0.590329i | \(0.798998\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.13026 | 0.0527562 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0567 | −0.840984 | −0.420492 | − | 0.907296i | \(-0.638142\pi\) | ||||
−0.420492 | + | 0.907296i | \(0.638142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.67140 | −0.310046 | −0.155023 | − | 0.987911i | \(-0.549545\pi\) | ||||
−0.155023 | + | 0.987911i | \(0.549545\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.659760 | 0.0305956 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5080 | 0.532527 | 0.266263 | − | 0.963900i | \(-0.414211\pi\) | ||||
0.266263 | + | 0.963900i | \(0.414211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.06799 | 0.187842 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.09943 | 0.0506592 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.80147 | −0.0828317 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.98251 | 0.0909637 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8437 | 0.496500 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5921 | −0.621040 | −0.310520 | − | 0.950567i | \(-0.600503\pi\) | ||||
−0.310520 | + | 0.950567i | \(0.600503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.826674 | −0.0376931 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.00458142 | −0.000208462 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.60530 | 0.209116 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.70563 | −0.258547 | −0.129273 | − | 0.991609i | \(-0.541264\pi\) | ||||
−0.129273 | + | 0.991609i | \(0.541264\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.87038 | −0.0845814 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.8351 | −1.61721 | −0.808607 | − | 0.588350i | \(-0.799778\pi\) | ||||
−0.808607 | + | 0.588350i | \(0.799778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.96161 | −0.178422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.25417 | −0.0563706 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.41981 | 0.153399 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7161 | 1.06168 | 0.530838 | − | 0.847473i | \(-0.321877\pi\) | ||||
0.530838 | + | 0.847473i | \(0.321877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.69843 | −0.299264 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.85775 | 0.439535 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7271 | 0.655348 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.49356 | −0.199566 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.7129 | −1.09538 | −0.547691 | − | 0.836681i | \(-0.684493\pi\) | ||||
−0.547691 | + | 0.836681i | \(0.684493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.779744 | −0.0344938 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.14562 | −0.183034 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.01280 | 0.309021 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.93578 | −0.217076 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.30493 | −0.276756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.0849929 | 0.00372361 | 0.00186180 | − | 0.999998i | \(-0.499407\pi\) | ||||
0.00186180 | + | 0.999998i | \(0.499407\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.5506 | 1.51079 | 0.755397 | − | 0.655267i | \(-0.227444\pi\) | ||||
0.755397 | + | 0.655267i | \(0.227444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.142593 | −0.00622325 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.00160 | 0.0436302 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9990 | −0.999955 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9901 | −0.476932 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.73134 | −0.204937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0600 | 0.607867 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.39664 | −0.232882 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.98548 | 0.128594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2339 | −0.826932 | −0.413466 | − | 0.910520i | \(-0.635682\pi\) | ||||
−0.413466 | + | 0.910520i | \(0.635682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.26810 | 0.226076 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.24267 | 0.224571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5792 | 0.794391 | 0.397195 | − | 0.917734i | \(-0.369984\pi\) | ||||
0.397195 | + | 0.917734i | \(0.369984\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.59346 | 0.196044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.5306 | 0.619022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.824441 | 0.0350588 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.478074 | −0.0202931 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.8733 | −0.926802 | −0.463401 | − | 0.886149i | \(-0.653371\pi\) | ||||
−0.463401 | + | 0.886149i | \(0.653371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.54086 | −0.107467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0840013 | 0.00354654 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.25953 | −0.348098 | −0.174049 | − | 0.984737i | \(-0.555685\pi\) | ||||
−0.174049 | + | 0.984737i | \(0.555685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.01042 | −0.252860 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.15400 | −0.132455 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.00280 | 0.293573 | 0.146786 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146786 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.81284 | 0.159562 | 0.0797812 | − | 0.996812i | \(-0.474578\pi\) | ||||
0.0797812 | + | 0.996812i | \(0.474578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.29889 | 0.388467 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0321294 | 0.00133989 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5748 | 0.523497 | 0.261749 | − | 0.965136i | \(-0.415701\pi\) | ||||
0.261749 | + | 0.965136i | \(0.415701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.97502 | −0.0820792 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.37005 | −0.0568393 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.64737 | 0.0682271 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.76892 | −0.0731358 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.55733 | 0.353199 | 0.176599 | − | 0.984283i | \(-0.443490\pi\) | ||||
0.176599 | + | 0.984283i | \(0.443490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.67370 | −0.151372 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.12732 | −0.0463717 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5437 | −1.00789 | −0.503944 | − | 0.863736i | \(-0.668118\pi\) | ||||
−0.503944 | + | 0.863736i | \(0.668118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.216473 | −0.00887454 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.343882 | −0.0140742 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.13865 | −0.0465239 | −0.0232619 | − | 0.999729i | \(-0.507405\pi\) | ||||
−0.0232619 | + | 0.999729i | \(0.507405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5084 | 0.795765 | 0.397883 | − | 0.917436i | \(-0.369745\pi\) | ||||
0.397883 | + | 0.917436i | \(0.369745\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.1844 | 1.18848 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8095 | 0.439467 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.22651 | −0.333904 | −0.166952 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166952 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.04512 | −0.0423502 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.96160 | −0.281636 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.8604 | −0.882933 | −0.441466 | − | 0.897278i | \(-0.645542\pi\) | ||||
−0.441466 | + | 0.897278i | \(0.645542\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.73618 | −0.110333 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.7716 | −1.39985 | −0.699927 | − | 0.714215i | \(-0.746784\pi\) | ||||
−0.699927 | + | 0.714215i | \(0.746784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.8902 | −1.24158 | −0.620791 | − | 0.783976i | \(-0.713189\pi\) | ||||
−0.620791 | + | 0.783976i | \(0.713189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0671859 | −0.00269608 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.95752 | 0.158555 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.308103 | −0.0123045 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.725775 | −0.0289386 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1831 | −0.644238 | −0.322119 | − | 0.946699i | \(-0.604395\pi\) | ||||
−0.322119 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.84915 | 0.152990 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.232932 | −0.00924362 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.21083 | 0.166839 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.5343 | 0.970561 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.4255 | −1.83370 | −0.916849 | − | 0.399234i | \(-0.869276\pi\) | ||||
−0.916849 | + | 0.399234i | \(0.869276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9269 | 1.37738 | 0.688691 | − | 0.725055i | \(-0.258186\pi\) | ||||
0.688691 | + | 0.725055i | \(0.258186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.46940 | −0.0578577 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.2857 | 0.876139 | 0.438070 | − | 0.898941i | \(-0.355662\pi\) | ||||
0.438070 | + | 0.898941i | \(0.355662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.66961 | −0.0655381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.264232 | 0.0103561 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.67149 | 0.221943 | 0.110971 | − | 0.993824i | \(-0.464604\pi\) | ||||
0.110971 | + | 0.993824i | \(0.464604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.38264 | 0.288464 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.59401 | −0.218243 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.7446 | 1.11973 | 0.559865 | − | 0.828584i | \(-0.310853\pi\) | ||||
0.559865 | + | 0.828584i | \(0.310853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7992 | 0.458934 | 0.229467 | − | 0.973316i | \(-0.426302\pi\) | ||||
0.229467 | + | 0.973316i | \(0.426302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.118478 | 0.00460132 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.793990 | 0.0307896 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.235489 | 0.00911816 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.88702 | −0.111619 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.697834 | 0.0269396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2674 | 0.858345 | 0.429173 | − | 0.903222i | \(-0.358805\pi\) | ||||
0.429173 | + | 0.903222i | \(0.358805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.09110 | −0.0804865 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.463396 | 0.0178097 | 0.00890487 | − | 0.999960i | \(-0.497165\pi\) | ||||
0.00890487 | + | 0.999960i | \(0.497165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.84441 | 0.0707820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.35147 | −0.358349 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 51.7674 | 1.98083 | 0.990413 | − | 0.138139i | \(-0.0441120\pi\) | ||||
0.990413 | + | 0.138139i | \(0.0441120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8082 | −0.412961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.92400 | 0.264167 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.32351 | 0.0885186 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.94058 | 0.0738231 | 0.0369116 | − | 0.999319i | \(-0.488248\pi\) | ||||
0.0369116 | + | 0.999319i | \(0.488248\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.502290 | −0.0190804 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.01742 | −0.228254 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.15386 | −0.157339 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.40014 | 0.279899 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.2092 | −1.85861 | −0.929303 | − | 0.369319i | \(-0.879591\pi\) | ||||
−0.929303 | + | 0.369319i | \(0.879591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.66203 | 0.100400 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.02596 | −0.151627 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.89817 | 0.221824 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2333 | −0.684766 | −0.342383 | − | 0.939560i | \(-0.611234\pi\) | ||||
−0.342383 | + | 0.939560i | \(0.611234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.91468 | 0.221818 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0595376 | −0.00222970 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.268733 | −0.0100500 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.87449 | −0.182041 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.5673 | −1.40102 | −0.700512 | − | 0.713640i | \(-0.747045\pi\) | ||||
−0.700512 | + | 0.713640i | \(0.747045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.80861 | 0.104598 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.940040 | 0.0349605 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.32938 | 0.272206 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3326 | 0.605742 | 0.302871 | − | 0.953032i | \(-0.402055\pi\) | ||||
0.302871 | + | 0.953032i | \(0.402055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3938 | −0.755324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.23073 | −0.0825067 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6423 | −1.50116 | −0.750578 | − | 0.660781i | \(-0.770225\pi\) | ||||
−0.750578 | + | 0.660781i | \(0.770225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.43516 | 0.0898224 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.43367 | 0.163316 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.7567 | −0.837119 | −0.418559 | − | 0.908189i | \(-0.637465\pi\) | ||||
−0.418559 | + | 0.908189i | \(0.637465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.434559 | −0.0159639 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4053 | 1.40895 | 0.704477 | − | 0.709727i | \(-0.251182\pi\) | ||||
0.704477 | + | 0.709727i | \(0.251182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.190471 | 0.00697834 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.82898 | −0.359624 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.63099 | 0.205752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4702 | −0.382063 | −0.191032 | − | 0.981584i | \(-0.561183\pi\) | ||||
−0.191032 | + | 0.981584i | \(0.561183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.97137 | −0.0718408 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.8656 | 0.468228 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5176 | −1.10918 | −0.554591 | − | 0.832123i | \(-0.687125\pi\) | ||||
−0.554591 | + | 0.832123i | \(0.687125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.00499326 | −0.000181244 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.9403 | 1.81034 | 0.905168 | − | 0.425055i | \(-0.139745\pi\) | ||||
0.905168 | + | 0.425055i | \(0.139745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.09968 | 0.0760134 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.55302 | −0.0561494 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.35488 | −0.0850298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.5588 | −0.813492 | −0.406746 | − | 0.913541i | \(-0.633337\pi\) | ||||
−0.406746 | + | 0.913541i | \(0.633337\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.81862 | −0.353609 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.3025 | −0.586360 | −0.293180 | − | 0.956057i | \(-0.594714\pi\) | ||||
−0.293180 | + | 0.956057i | \(0.594714\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85305 | −0.0665637 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.191467 | −0.00686885 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.2357 | 0.545876 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.72722 | 0.133371 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.3265 | −0.547723 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.08796 | −0.110214 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6865 | 0.380933 | 0.190467 | − | 0.981694i | \(-0.439000\pi\) | ||||
0.190467 | + | 0.981694i | \(0.439000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.78585 | 0.205982 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.40716 | −0.0855887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.984249 | 0.0349517 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.34371 | 0.0476564 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.3307 | 1.10979 | 0.554895 | − | 0.831921i | \(-0.312759\pi\) | ||||
0.554895 | + | 0.831921i | \(0.312759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.11191 | −0.216224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.3919 | 1.00318 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.849837 | −0.0299901 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0128678 | 0.000453529 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.39904 | −0.225257 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6531 | −1.07770 | −0.538852 | − | 0.842400i | \(-0.681142\pi\) | ||||
−0.538852 | + | 0.842400i | \(0.681142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.55427 | −0.0545779 | −0.0272890 | − | 0.999628i | \(-0.508687\pi\) | ||||
−0.0272890 | + | 0.999628i | \(0.508687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.23516 | −0.218677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.25329 | 0.184015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.18198 | 0.286251 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.708448 | −0.0247552 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.3493 | 1.75720 | 0.878602 | − | 0.477555i | \(-0.158477\pi\) | ||||
0.878602 | + | 0.477555i | \(0.158477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.33143 | −0.0464108 | −0.0232054 | − | 0.999731i | \(-0.507387\pi\) | ||||
−0.0232054 | + | 0.999731i | \(0.507387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.155411 | −0.00541071 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6659 | 1.20545 | 0.602726 | − | 0.797948i | \(-0.294081\pi\) | ||||
0.602726 | + | 0.797948i | \(0.294081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0049 | −0.382214 | −0.191107 | − | 0.981569i | \(-0.561208\pi\) | ||||
−0.191107 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.15080 | −0.0399209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.69688 | 0.128089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.8138 | 0.651077 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.87492 | 0.133937 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.4008 | −1.67098 | −0.835490 | − | 0.549505i | \(-0.814816\pi\) | ||||
−0.835490 | + | 0.549505i | \(0.814816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7198 | 0.852406 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.685239 | −0.0236009 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6210 | 0.434175 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.32916 | 0.148752 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.77948 | 0.0610717 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0431420 | 0.00147889 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.13891 | −0.312910 | −0.156455 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156455 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.69622 | 0.194806 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.3654 | 1.92541 | 0.962704 | − | 0.270559i | \(-0.0872084\pi\) | ||||
0.962704 | + | 0.270559i | \(0.0872084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.13001 | −0.0726749 | −0.0363375 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363375 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.09583 | −0.0373459 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.8224 | −1.42365 | −0.711826 | − | 0.702355i | \(-0.752132\pi\) | ||||
−0.711826 | + | 0.702355i | \(0.752132\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.7085 | 0.602108 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.94864 | −0.202027 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.898553 | 0.0304813 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.25341 | 0.211889 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2321 | 0.447839 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.400497 | 0.0135393 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6853 | 0.529656 | 0.264828 | − | 0.964296i | \(-0.414685\pi\) | ||||
0.264828 | + | 0.964296i | \(0.414685\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.66210 | −0.0560613 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9249 | −0.907122 | −0.453561 | − | 0.891225i | \(-0.649847\pi\) | ||||
−0.453561 | + | 0.891225i | \(0.649847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.96791 | −0.167184 | −0.0835918 | − | 0.996500i | \(-0.526639\pi\) | ||||
−0.0835918 | + | 0.996500i | \(0.526639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36185 | −0.0457781 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.2180 | −0.544546 | −0.272273 | − | 0.962220i | \(-0.587775\pi\) | ||||
−0.272273 | + | 0.962220i | \(0.587775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0932886 | −0.00312880 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.43752 | −0.115161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.4175 | 0.750173 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.1574 | 0.506657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.00704267 | −0.000235148 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.5817 | −0.452976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.03991 | 0.0679594 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.588492 | −0.0195838 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.7964 | −0.491850 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.9005 | −0.727194 | −0.363597 | − | 0.931556i | \(-0.618451\pi\) | ||||
−0.363597 | + | 0.931556i | \(0.618451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.3145 | 1.40348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4363 | −0.975268 | −0.487634 | − | 0.873048i | \(-0.662140\pi\) | ||||
−0.487634 | + | 0.873048i | \(0.662140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.49321 | −0.0494180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.569201 | 0.0188172 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.95673 | 0.0976398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.2212 | −0.996906 | −0.498453 | − | 0.866917i | \(-0.666098\pi\) | ||||
−0.498453 | + | 0.866917i | \(0.666098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.44584 | −0.212398 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.25701 | 0.173036 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34276 | 0.0441496 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1494 | 0.661795 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.2151 | −1.54908 | −0.774538 | − | 0.632528i | \(-0.782017\pi\) | ||||
−0.774538 | + | 0.632528i | \(0.782017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.5596 | −0.444397 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.9171 | −0.390148 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.235933 | −0.00771583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5255 | −0.539864 | −0.269932 | − | 0.962879i | \(-0.587001\pi\) | ||||
−0.269932 | + | 0.962879i | \(0.587001\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30962 | 0.0427378 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.9812 | −1.30335 | −0.651675 | − | 0.758498i | \(-0.725934\pi\) | ||||
−0.651675 | + | 0.758498i | \(0.725934\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.246917 | 0.00804071 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.837480 | −0.0272432 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8596 | −0.775334 | −0.387667 | − | 0.921800i | \(-0.626719\pi\) | ||||
−0.387667 | + | 0.921800i | \(0.626719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.19864 | −0.0389095 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.30323 | −0.139542 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1617 | 0.393955 | 0.196977 | − | 0.980408i | \(-0.436887\pi\) | ||||
0.196977 | + | 0.980408i | \(0.436887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.1176 | −0.845147 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.13906 | −0.0368207 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.32866 | −0.139780 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5662 | −0.889232 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.3977 | 1.30180 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.54721 | 0.178571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.2333 | 0.972238 | 0.486119 | − | 0.873893i | \(-0.338412\pi\) | ||||
0.486119 | + | 0.873893i | \(0.338412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.381520 | −0.0122562 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.5007 | −1.01091 | −0.505453 | − | 0.862854i | \(-0.668675\pi\) | ||||
−0.505453 | + | 0.862854i | \(0.668675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.40996 | −0.0772598 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.219197 | −0.00701991 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9078 | 0.764878 | 0.382439 | − | 0.923981i | \(-0.375084\pi\) | ||||
0.382439 | + | 0.923981i | \(0.375084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.31327 | 0.137853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0634 | 0.480939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.2823 | 0.455534 | 0.227767 | − | 0.973716i | \(-0.426858\pi\) | ||||
0.227767 | + | 0.973716i | \(0.426858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.16628 | 0.100886 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.61239 | −0.0513229 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.132601 | 0.00421646 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6236 | 0.941025 | 0.470513 | − | 0.882393i | \(-0.344069\pi\) | ||||
0.470513 | + | 0.882393i | \(0.344069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.49431 | 0.0474205 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.965855 | 0.0306197 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.51954 | 0.174806 | 0.0874028 | − | 0.996173i | \(-0.472143\pi\) | ||||
0.0874028 | + | 0.996173i | \(0.472143\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.80784 | −0.0888361 |
(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.c.1.16 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.16 | ✓ | 28 | 1.1 | even | 1 | trivial |