Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.985991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.98599 | −0.888162 | −0.444081 | − | 0.895987i | \(-0.646470\pi\) | ||||
−0.444081 | + | 0.895987i | \(0.646470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0909950 | −0.0343929 | −0.0171964 | − | 0.999852i | \(-0.505474\pi\) | ||||
−0.0171964 | + | 0.999852i | \(0.505474\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.35607 | −0.710380 | −0.355190 | − | 0.934794i | \(-0.615584\pi\) | ||||
−0.355190 | + | 0.934794i | \(0.615584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.834094 | 0.231336 | 0.115668 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115668 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.98599 | −0.512781 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.08503 | 1.71837 | 0.859186 | − | 0.511663i | \(-0.170970\pi\) | ||||
0.859186 | + | 0.511663i | \(0.170970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.66738 | −0.382522 | −0.191261 | − | 0.981539i | \(-0.561258\pi\) | ||||
−0.191261 | + | 0.981539i | \(0.561258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0909950 | −0.0198567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.49969 | −0.521221 | −0.260611 | − | 0.965444i | \(-0.583924\pi\) | ||||
−0.260611 | + | 0.965444i | \(0.583924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.05584 | −0.211168 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96700 | −0.736652 | −0.368326 | − | 0.929697i | \(-0.620069\pi\) | ||||
−0.368326 | + | 0.929697i | \(0.620069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.52738 | −0.633535 | −0.316768 | − | 0.948503i | \(-0.602598\pi\) | ||||
−0.316768 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.35607 | −0.410138 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.180715 | 0.0305465 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.64278 | −0.270071 | −0.135036 | − | 0.990841i | \(-0.543115\pi\) | ||||
−0.135036 | + | 0.990841i | \(0.543115\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.834094 | 0.133562 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.142888 | 0.0223154 | 0.0111577 | − | 0.999938i | \(-0.496448\pi\) | ||||
0.0111577 | + | 0.999938i | \(0.496448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.36216 | −0.817721 | −0.408861 | − | 0.912597i | \(-0.634074\pi\) | ||||
−0.408861 | + | 0.912597i | \(0.634074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.98599 | −0.296054 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.35086 | −0.926369 | −0.463184 | − | 0.886262i | \(-0.653293\pi\) | ||||
−0.463184 | + | 0.886262i | \(0.653293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99172 | −0.998817 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.08503 | 0.992103 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4619 | 1.84914 | 0.924569 | − | 0.381015i | \(-0.124425\pi\) | ||||
0.924569 | + | 0.381015i | \(0.124425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.67913 | 0.630933 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.66738 | −0.220849 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.39116 | 0.571680 | 0.285840 | − | 0.958277i | \(-0.407727\pi\) | ||||
0.285840 | + | 0.958277i | \(0.407727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0766485 | 0.00981383 | 0.00490692 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490692 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0909950 | −0.0114643 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.65650 | −0.205464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.51021 | 0.551010 | 0.275505 | − | 0.961300i | \(-0.411155\pi\) | ||||
0.275505 | + | 0.961300i | \(0.411155\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.49969 | −0.300927 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.17932 | 0.377316 | 0.188658 | − | 0.982043i | \(-0.439586\pi\) | ||||
0.188658 | + | 0.982043i | \(0.439586\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.30247 | 1.08877 | 0.544386 | − | 0.838835i | \(-0.316763\pi\) | ||||
0.544386 | + | 0.838835i | \(0.316763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.05584 | −0.121918 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.214390 | 0.0244320 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.3241 | −1.94912 | −0.974558 | − | 0.224137i | \(-0.928044\pi\) | ||||
−0.974558 | + | 0.224137i | \(0.928044\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0141153 | 0.00154936 | 0.000774679 | − | 1.00000i | \(-0.499753\pi\) | ||||
0.000774679 | 1.00000i | \(0.499753\pi\) | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.0708 | −1.52619 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.96700 | −0.425307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.96099 | −0.843863 | −0.421932 | − | 0.906628i | \(-0.638648\pi\) | ||||
−0.421932 | + | 0.906628i | \(0.638648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0758984 | −0.00795631 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.52738 | −0.365772 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.31139 | 0.339742 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8801 | −1.30778 | −0.653888 | − | 0.756591i | \(-0.726863\pi\) | ||||
−0.653888 | + | 0.756591i | \(0.726863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.35607 | −0.236793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6926 | −1.46197 | −0.730983 | − | 0.682396i | \(-0.760938\pi\) | ||||
−0.730983 | + | 0.682396i | \(0.760938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.05118 | −0.399174 | −0.199587 | − | 0.979880i | \(-0.563960\pi\) | ||||
−0.199587 | + | 0.979880i | \(0.563960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.180715 | 0.0176360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1492 | 0.981161 | 0.490581 | − | 0.871396i | \(-0.336785\pi\) | ||||
0.490581 | + | 0.871396i | \(0.336785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.51988 | −0.432926 | −0.216463 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216463 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.64278 | −0.155926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4542 | −1.35974 | −0.679869 | − | 0.733333i | \(-0.737963\pi\) | ||||
−0.679869 | + | 0.733333i | \(0.737963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.96436 | 0.462929 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.834094 | 0.0771120 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.644702 | −0.0590998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.44896 | −0.495360 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.142888 | 0.0128838 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0268 | 1.07571 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7384 | −1.66277 | −0.831383 | − | 0.555700i | \(-0.812450\pi\) | ||||
−0.831383 | + | 0.555700i | \(0.812450\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.36216 | −0.472112 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.50104 | 0.567998 | 0.283999 | − | 0.958825i | \(-0.408339\pi\) | ||||
0.283999 | + | 0.958825i | \(0.408339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.151723 | 0.0131560 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.98599 | −0.170927 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.41640 | −0.377319 | −0.188659 | − | 0.982043i | \(-0.560414\pi\) | ||||
−0.188659 | + | 0.982043i | \(0.560414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.57252 | 0.303017 | 0.151508 | − | 0.988456i | \(-0.451587\pi\) | ||||
0.151508 | + | 0.988456i | \(0.451587\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.35086 | −0.534839 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.96518 | −0.164337 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.87842 | 0.654267 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.99172 | −0.576667 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.73856 | −0.306275 | −0.153137 | − | 0.988205i | \(-0.548938\pi\) | ||||
−0.153137 | + | 0.988205i | \(0.548938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.88374 | −0.804327 | −0.402164 | − | 0.915568i | \(-0.631742\pi\) | ||||
−0.402164 | + | 0.915568i | \(0.631742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.08503 | 0.572791 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.00534 | 0.562682 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.704086 | −0.0561922 | −0.0280961 | − | 0.999605i | \(-0.508944\pi\) | ||||
−0.0280961 | + | 0.999605i | \(0.508944\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4619 | 1.06760 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.227459 | 0.0179263 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.79586 | −0.297315 | −0.148658 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148658 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.67913 | 0.364269 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3043 | −0.946484 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.66738 | −0.127507 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.35209 | −0.406912 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0960759 | 0.00726266 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.39116 | 0.330060 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.68131 | −0.200410 | −0.100205 | − | 0.994967i | \(-0.531950\pi\) | ||||
−0.100205 | + | 0.994967i | \(0.531950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8000 | −1.62038 | −0.810189 | − | 0.586169i | \(-0.800635\pi\) | ||||
−0.810189 | + | 0.586169i | \(0.800635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0766485 | 0.00566602 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.26255 | 0.239867 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.6928 | −1.22070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0909950 | −0.00661891 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.2790 | −1.90148 | −0.950740 | − | 0.309989i | \(-0.899675\pi\) | ||||
−0.950740 | + | 0.309989i | \(0.899675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3316 | 1.31953 | 0.659767 | − | 0.751470i | \(-0.270655\pi\) | ||||
0.659767 | + | 0.751470i | \(0.270655\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.65650 | −0.118625 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1522 | 1.00830 | 0.504150 | − | 0.863616i | \(-0.331806\pi\) | ||||
0.504150 | + | 0.863616i | \(0.331806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7862 | −1.26083 | −0.630414 | − | 0.776259i | \(-0.717115\pi\) | ||||
−0.630414 | + | 0.776259i | \(0.717115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.51021 | 0.318126 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.360977 | 0.0253356 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.283775 | −0.0198197 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.49969 | −0.173740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.92845 | 0.271736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.74876 | 0.189232 | 0.0946161 | − | 0.995514i | \(-0.469838\pi\) | ||||
0.0946161 | + | 0.995514i | \(0.469838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.17932 | 0.217843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.6492 | 0.726269 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.320973 | 0.0217891 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.30247 | 0.628602 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.90958 | 0.397522 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.97542 | −0.400143 | −0.200072 | − | 0.979781i | \(-0.564118\pi\) | ||||
−0.200072 | + | 0.979781i | \(0.564118\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.05584 | −0.0703892 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.438914 | 0.0291318 | 0.0145659 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145659 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.49354 | 0.0986960 | 0.0493480 | − | 0.998782i | \(-0.484286\pi\) | ||||
0.0493480 | + | 0.998782i | \(0.484286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.214390 | 0.0141058 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.5018 | −1.14658 | −0.573291 | − | 0.819352i | \(-0.694333\pi\) | ||||
−0.573291 | + | 0.819352i | \(0.694333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6128 | 0.822766 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.3241 | −1.12532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.14251 | −0.203272 | −0.101636 | − | 0.994822i | \(-0.532408\pi\) | ||||
−0.101636 | + | 0.994822i | \(0.532408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6616 | 1.20210 | 0.601050 | − | 0.799211i | \(-0.294749\pi\) | ||||
0.601050 | + | 0.799211i | \(0.294749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.8855 | 0.887112 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.39075 | −0.0884912 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0141153 | 0.000894522 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.34821 | 0.211337 | 0.105668 | − | 0.994401i | \(-0.466302\pi\) | ||||
0.105668 | + | 0.994401i | \(0.466302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.88943 | 0.370265 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.0708 | −0.881148 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.22045 | 0.450399 | 0.225200 | − | 0.974313i | \(-0.427697\pi\) | ||||
0.225200 | + | 0.974313i | \(0.427697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.149485 | 0.00928853 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.96700 | −0.245551 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.01628 | 0.432642 | 0.216321 | − | 0.976322i | \(-0.430594\pi\) | ||||
0.216321 | + | 0.976322i | \(0.430594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.7353 | −1.64233 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.96099 | −0.487205 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.2316 | 1.05063 | 0.525316 | − | 0.850907i | \(-0.323947\pi\) | ||||
0.525316 | + | 0.850907i | \(0.323947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.6572 | −1.68005 | −0.840027 | − | 0.542545i | \(-0.817461\pi\) | ||||
−0.840027 | + | 0.542545i | \(0.817461\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0758984 | −0.00459358 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.48762 | 0.150009 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.7248 | 1.48557 | 0.742785 | − | 0.669529i | \(-0.233504\pi\) | ||||
0.742785 | + | 0.669529i | \(0.233504\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.52738 | −0.211178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.24892 | −0.0745041 | −0.0372520 | − | 0.999306i | \(-0.511860\pi\) | ||||
−0.0372520 | + | 0.999306i | \(0.511860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.7744 | −1.59158 | −0.795788 | − | 0.605576i | \(-0.792943\pi\) | ||||
−0.795788 | + | 0.605576i | \(0.792943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.31139 | 0.196150 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0130021 | −0.000767491 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.1977 | 1.95280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8801 | −0.755045 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.2333 | 1.47414 | 0.737072 | − | 0.675814i | \(-0.236208\pi\) | ||||
0.737072 | + | 0.675814i | \(0.236208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.72080 | −0.507745 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.35607 | −0.136713 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.08498 | −0.120577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.487929 | 0.0281238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.6926 | −0.844066 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.152223 | −0.00871628 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.20268 | 0.182786 | 0.0913932 | − | 0.995815i | \(-0.470868\pi\) | ||||
0.0913932 | + | 0.995815i | \(0.470868\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.05118 | −0.230463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.45554 | −0.195946 | −0.0979729 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979729 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.7617 | 1.79528 | 0.897638 | − | 0.440734i | \(-0.145282\pi\) | ||||
0.897638 | + | 0.440734i | \(0.145282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.180715 | 0.0101822 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.1696 | −1.41367 | −0.706834 | − | 0.707380i | \(-0.749877\pi\) | ||||
−0.706834 | + | 0.707380i | \(0.749877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.34650 | 0.523304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.1492 | 0.566474 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.8134 | −0.657316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.880668 | −0.0488507 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.51988 | −0.249950 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.577897 | 0.0318605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.94004 | −0.491389 | −0.245694 | − | 0.969347i | \(-0.579016\pi\) | ||||
−0.245694 | + | 0.969347i | \(0.579016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.64278 | −0.0900238 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.95724 | −0.489387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.25049 | −0.122592 | −0.0612959 | − | 0.998120i | \(-0.519523\pi\) | ||||
−0.0612959 | + | 0.998120i | \(0.519523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.4542 | −0.785045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.31073 | 0.450051 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.27318 | 0.0687451 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.96436 | 0.267272 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.88275 | 0.262119 | 0.131060 | − | 0.991374i | \(-0.458162\pi\) | ||||
0.131060 | + | 0.991374i | \(0.458162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.94280 | 0.371639 | 0.185820 | − | 0.982584i | \(-0.440506\pi\) | ||||
0.185820 | + | 0.982584i | \(0.440506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.834094 | 0.0445207 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9864 | −0.691199 | −0.345599 | − | 0.938382i | \(-0.612324\pi\) | ||||
−0.345599 | + | 0.938382i | \(0.612324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.31410 | −0.335118 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.644702 | −0.0341213 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.00276 | −0.105702 | −0.0528509 | − | 0.998602i | \(-0.516831\pi\) | ||||
−0.0528509 | + | 0.998602i | \(0.516831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2199 | −0.853677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.44896 | −0.285996 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4746 | −0.967006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1645 | 1.47017 | 0.735087 | − | 0.677973i | \(-0.237141\pi\) | ||||
0.735087 | + | 0.677973i | \(0.237141\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.142888 | 0.00743848 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.22497 | −0.0635971 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.470865 | −0.0243804 | −0.0121902 | − | 0.999926i | \(-0.503880\pi\) | ||||
−0.0121902 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0268 | 0.621063 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.30885 | −0.170414 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1101 | −0.827519 | −0.413760 | − | 0.910386i | \(-0.635785\pi\) | ||||
−0.413760 | + | 0.910386i | \(0.635785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.7384 | −0.959999 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.3788 | 1.90997 | 0.954984 | − | 0.296656i | \(-0.0958716\pi\) | ||||
0.954984 | + | 0.296656i | \(0.0958716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.425777 | −0.0216996 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.36216 | −0.272574 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.93497 | 0.453021 | 0.226511 | − | 0.974009i | \(-0.427268\pi\) | ||||
0.226511 | + | 0.974009i | \(0.427268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.7104 | −0.895652 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.50104 | 0.327934 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.4055 | 1.73113 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.164468 | 0.00825442 | 0.00412721 | − | 0.999991i | \(-0.498686\pi\) | ||||
0.00412721 | + | 0.999991i | \(0.498686\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.151723 | 0.00759564 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.07799 | 0.253583 | 0.126791 | − | 0.991929i | \(-0.459532\pi\) | ||||
0.126791 | + | 0.991929i | \(0.459532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.94216 | −0.146560 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.98599 | −0.0986847 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.87050 | 0.191853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1261 | 1.53909 | 0.769544 | − | 0.638594i | \(-0.220484\pi\) | ||||
0.769544 | + | 0.638594i | \(0.220484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.41640 | −0.217845 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.399573 | −0.0196617 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0280329 | −0.00137608 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.57252 | 0.174947 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.9570 | −1.17037 | −0.585187 | − | 0.810898i | \(-0.698979\pi\) | ||||
−0.585187 | + | 0.810898i | \(0.698979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3408 | 0.942612 | 0.471306 | − | 0.881970i | \(-0.343783\pi\) | ||||
0.471306 | + | 0.881970i | \(0.343783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.35086 | −0.308790 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.48064 | −0.362865 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.00697463 | −0.000337526 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.96518 | −0.0948798 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.52144 | −0.362295 | −0.181147 | − | 0.983456i | \(-0.557981\pi\) | ||||
−0.181147 | + | 0.983456i | \(0.557981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.3240 | 1.69756 | 0.848781 | − | 0.528745i | \(-0.177337\pi\) | ||||
0.848781 | + | 0.528745i | \(0.177337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.87842 | 0.377741 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.16792 | 0.199379 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.59035 | −0.171358 | −0.0856790 | − | 0.996323i | \(-0.527306\pi\) | ||||
−0.0856790 | + | 0.996323i | \(0.527306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99172 | −0.332939 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2209 | 0.533121 | 0.266560 | − | 0.963818i | \(-0.414113\pi\) | ||||
0.266560 | + | 0.963818i | \(0.414113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8105 | 0.749488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.73856 | −0.176828 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.4857 | −0.683622 | −0.341811 | − | 0.939769i | \(-0.611040\pi\) | ||||
−0.341811 | + | 0.939769i | \(0.611040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.336655 | −0.0158524 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.88374 | −0.464379 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.150734 | 0.00706650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0839 | 0.845929 | 0.422965 | − | 0.906146i | \(-0.360989\pi\) | ||||
0.422965 | + | 0.906146i | \(0.360989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.08503 | 0.330701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4205 | −0.531904 | −0.265952 | − | 0.963986i | \(-0.585686\pi\) | ||||
−0.265952 | + | 0.963986i | \(0.585686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4961 | 0.534268 | 0.267134 | − | 0.963659i | \(-0.413923\pi\) | ||||
0.267134 | + | 0.963659i | \(0.413923\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.00534 | 0.324865 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.3176 | 1.31038 | 0.655191 | − | 0.755463i | \(-0.272588\pi\) | ||||
0.655191 | + | 0.755463i | \(0.272588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.410407 | −0.0189508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.704086 | −0.0324426 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.6336 | 0.580893 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.76048 | 0.0807763 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.4619 | 0.616379 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.851972 | 0.0389276 | 0.0194638 | − | 0.999811i | \(-0.493804\pi\) | ||||
0.0194638 | + | 0.999811i | \(0.493804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.37023 | −0.0624772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.227459 | 0.0103498 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.5798 | 1.16152 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8841 | −0.765091 | −0.382546 | − | 0.923937i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923937i | \(0.624953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.79586 | −0.171655 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.5909 | 1.83184 | 0.915921 | − | 0.401359i | \(-0.131462\pi\) | ||||
0.915921 | + | 0.401359i | \(0.131462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.1063 | −1.26584 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.67913 | 0.210311 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.289302 | −0.0129770 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.31828 | 0.0590143 | 0.0295071 | − | 0.999565i | \(-0.490606\pi\) | ||||
0.0295071 | + | 0.999565i | \(0.490606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.3191 | −0.905983 | −0.452991 | − | 0.891515i | \(-0.649643\pi\) | ||||
−0.452991 | + | 0.891515i | \(0.649643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.1793 | 1.29846 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3043 | −0.546453 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.7984 | 1.76403 | 0.882016 | − | 0.471219i | \(-0.156186\pi\) | ||||
0.882016 | + | 0.471219i | \(0.156186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.846478 | −0.0374460 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.66738 | −0.0736164 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.04560 | 0.354532 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9631 | 0.658074 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.35209 | −0.234931 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.30626 | 0.363904 | 0.181952 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181952 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.3330 | −1.15146 | −0.575731 | − | 0.817639i | \(-0.695283\pi\) | ||||
−0.575731 | + | 0.817639i | \(0.695283\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0960759 | 0.00419310 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.9916 | −1.08865 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7516 | −0.728328 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.39116 | 0.190560 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.119182 | 0.00516236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.1562 | −0.871431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.68131 | −0.115707 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.4729 | 0.709540 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1502 | −0.608365 | −0.304182 | − | 0.952614i | \(-0.598383\pi\) | ||||
−0.304182 | + | 0.952614i | \(0.598383\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.8000 | −0.935525 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.97645 | 0.384509 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.6028 | −1.05194 | −0.525971 | − | 0.850503i | \(-0.676298\pi\) | ||||
−0.525971 | + | 0.850503i | \(0.676298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0766485 | 0.00327128 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.61447 | 0.281786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.57641 | 0.0670357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.26255 | 0.138487 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.1405 | −0.980493 | −0.490246 | − | 0.871584i | \(-0.663093\pi\) | ||||
−0.490246 | + | 0.871584i | \(0.663093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.47254 | −0.189168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.6928 | −0.704770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.8347 | 0.793787 | 0.396894 | − | 0.917865i | \(-0.370088\pi\) | ||||
0.396894 | + | 0.917865i | \(0.370088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.7060 | 1.20767 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0909950 | −0.00382143 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.2495 | 1.60350 | 0.801752 | − | 0.597657i | \(-0.203901\pi\) | ||||
0.801752 | + | 0.597657i | \(0.203901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5374 | 1.19425 | 0.597126 | − | 0.802148i | \(-0.296309\pi\) | ||||
0.597126 | + | 0.802148i | \(0.296309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.2790 | −1.09782 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.63927 | 0.110065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7985 | −0.491178 | −0.245589 | − | 0.969374i | \(-0.578981\pi\) | ||||
−0.245589 | + | 0.969374i | \(0.578981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3316 | 0.761833 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.00128442 | −5.32868e−5 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.7172 | −1.31359 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.65650 | −0.0684880 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.16607 | −0.0481287 | −0.0240644 | − | 0.999710i | \(-0.507661\pi\) | ||||
−0.0240644 | + | 0.999710i | \(0.507661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.88146 | 0.242341 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1522 | 0.582142 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.2574 | 0.831870 | 0.415935 | − | 0.909394i | \(-0.363454\pi\) | ||||
0.415935 | + | 0.909394i | \(0.363454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.28037 | 0.0524902 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.7862 | −0.727940 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.8580 | −1.46512 | −0.732559 | − | 0.680703i | \(-0.761674\pi\) | ||||
−0.732559 | + | 0.680703i | \(0.761674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.0525 | −1.18507 | −0.592537 | − | 0.805543i | \(-0.701874\pi\) | ||||
−0.592537 | + | 0.805543i | \(0.701874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.51021 | 0.183670 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8216 | 0.439960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0950 | −0.734455 | −0.367227 | − | 0.930131i | \(-0.619693\pi\) | ||||
−0.367227 | + | 0.930131i | \(0.619693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.360977 | 0.0146275 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.29722 | −0.214303 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.0458 | 1.45588 | 0.727939 | − | 0.685642i | \(-0.240478\pi\) | ||||
0.727939 | + | 0.685642i | \(0.240478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.283775 | −0.0114429 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.3584 | 0.980632 | 0.490316 | − | 0.871545i | \(-0.336881\pi\) | ||||
0.490316 | + | 0.871545i | \(0.336881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.2196 | −1.05386 | −0.526928 | − | 0.849910i | \(-0.676656\pi\) | ||||
−0.526928 | + | 0.849910i | \(0.676656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.49969 | −0.100309 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.724410 | 0.0290229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.6060 | −0.744241 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.92845 | 0.156887 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.6391 | −0.464083 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.0723 | 1.55544 | 0.777722 | − | 0.628609i | \(-0.216375\pi\) | ||||
0.777722 | + | 0.628609i | \(0.216375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.74876 | 0.109253 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.2144 | 1.47681 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.83175 | −0.231062 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.17932 | 0.125772 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.3708 | 0.528116 | 0.264058 | − | 0.964507i | \(-0.414939\pi\) | ||||
0.264058 | + | 0.964507i | \(0.414939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3204 | 1.11685 | 0.558424 | − | 0.829555i | \(-0.311406\pi\) | ||||
0.558424 | + | 0.829555i | \(0.311406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6492 | 0.419312 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.7492 | 0.540539 | 0.270269 | − | 0.962785i | \(-0.412887\pi\) | ||||
0.270269 | + | 0.962785i | \(0.412887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3459 | −0.406110 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.320973 | 0.0125799 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.5266 | −0.920667 | −0.460334 | − | 0.887746i | \(-0.652270\pi\) | ||||
−0.460334 | + | 0.887746i | \(0.652270\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9110 | −0.504475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.30247 | 0.362924 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.7144 | −1.46914 | −0.734571 | − | 0.678531i | \(-0.762617\pi\) | ||||
−0.734571 | + | 0.678531i | \(0.762617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3286 | −0.868483 | −0.434241 | − | 0.900797i | \(-0.642984\pi\) | ||||
−0.434241 | + | 0.900797i | \(0.642984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.90958 | 0.229509 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.301320 | −0.0116847 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.91626 | 0.383959 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.97542 | −0.231023 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.180589 | −0.00697155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.89185 | −0.0729256 | −0.0364628 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364628 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.05584 | −0.0406392 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.6117 | 1.21494 | 0.607468 | − | 0.794344i | \(-0.292185\pi\) | ||||
0.607468 | + | 0.794344i | \(0.292185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17202 | 0.0449782 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.438914 | 0.0168192 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.1816 | 0.733962 | 0.366981 | − | 0.930228i | \(-0.380391\pi\) | ||||
0.366981 | + | 0.930228i | \(0.380391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.77094 | 0.335120 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.49354 | 0.0569822 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.2285 | 0.427772 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.4533 | 0.740037 | 0.370019 | − | 0.929024i | \(-0.379351\pi\) | ||||
0.370019 | + | 0.929024i | \(0.379351\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.214390 | 0.00814401 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.09499 | −0.269128 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.01237 | 0.0383462 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.5018 | −0.661979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.81290 | −0.106242 | −0.0531208 | − | 0.998588i | \(-0.516917\pi\) | ||||
−0.0531208 | + | 0.998588i | \(0.516917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.73913 | 0.103308 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.6128 | 0.475024 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.33695 | 0.0502812 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0623 | −1.24168 | −0.620841 | − | 0.783936i | \(-0.713209\pi\) | ||||
−0.620841 | + | 0.783936i | \(0.713209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.3241 | −0.649705 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.81734 | 0.330212 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.90283 | 0.145958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.14251 | −0.117359 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.3189 | −1.72740 | −0.863701 | − | 0.504004i | \(-0.831860\pi\) | ||||
−0.863701 | + | 0.504004i | \(0.831860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.368637 | 0.0137287 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.6616 | 0.694033 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.18850 | 0.155557 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5142 | 0.835004 | 0.417502 | − | 0.908676i | \(-0.362906\pi\) | ||||
0.417502 | + | 0.908676i | \(0.362906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.9910 | −1.40515 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.7476 | −0.840202 | −0.420101 | − | 0.907477i | \(-0.638005\pi\) | ||||
−0.420101 | + | 0.907477i | \(0.638005\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.8855 | 0.512174 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6264 | −0.391427 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.1147 | −1.84350 | −0.921750 | − | 0.387785i | \(-0.873240\pi\) | ||||
−0.921750 | + | 0.387785i | \(0.873240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.39075 | −0.0510904 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3798 | −1.07784 | −0.538920 | − | 0.842357i | \(-0.681167\pi\) | ||||
−0.538920 | + | 0.842357i | \(0.681167\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.42474 | 0.272022 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0141153 | 0.000516452 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.923527 | −0.0337449 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.8288 | −1.67232 | −0.836159 | − | 0.548487i | \(-0.815204\pi\) | ||||
−0.836159 | + | 0.548487i | \(0.815204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.34821 | 0.122015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.6290 | 0.714373 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.36638 | −0.0496621 | −0.0248310 | − | 0.999692i | \(-0.507905\pi\) | ||||
−0.0248310 | + | 0.999692i | \(0.507905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.88943 | 0.213773 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.1549 | 1.49187 | 0.745933 | − | 0.666021i | \(-0.232004\pi\) | ||||
0.745933 | + | 0.666021i | \(0.232004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.411287 | 0.0148896 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.0708 | −0.508731 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.66264 | 0.132250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.65538 | −0.239999 | −0.120000 | − | 0.992774i | \(-0.538289\pi\) | ||||
−0.120000 | + | 0.992774i | \(0.538289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.22045 | 0.260038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.8303 | −1.10889 | −0.554444 | − | 0.832221i | \(-0.687069\pi\) | ||||
−0.554444 | + | 0.832221i | \(0.687069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.72434 | 0.133782 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.149485 | 0.00536273 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.238249 | −0.00853615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.49068 | −0.268038 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.96700 | −0.141769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.39831 | 0.0499078 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.92617 | 0.353830 | 0.176915 | − | 0.984226i | \(-0.443388\pi\) | ||||
0.176915 | + | 0.984226i | \(0.443388\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.01628 | 0.249786 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.31526 | 0.0467653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0639321 | 0.00227029 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.7353 | −0.948202 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.4507 | −0.724402 | −0.362201 | − | 0.932100i | \(-0.617975\pi\) | ||||
−0.362201 | + | 0.932100i | \(0.617975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.9961 | −1.59185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.96099 | −0.281288 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.9172 | −0.773442 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.451732 | −0.0159215 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.2316 | 0.606582 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0254 | −0.387631 | −0.193815 | − | 0.981038i | \(-0.562086\pi\) | ||||
−0.193815 | + | 0.981038i | \(0.562086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.7185 | 1.39471 | 0.697353 | − | 0.716728i | \(-0.254361\pi\) | ||||
0.697353 | + | 0.716728i | \(0.254361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.6572 | −0.969979 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.53855 | 0.264064 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.94073 | 0.312797 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0758984 | −0.00265210 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.78084 | 0.166853 | 0.0834263 | − | 0.996514i | \(-0.473414\pi\) | ||||
0.0834263 | + | 0.996514i | \(0.473414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8312 | 0.412408 | 0.206204 | − | 0.978509i | \(-0.433889\pi\) | ||||
0.206204 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.48762 | 0.0866079 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7394 | 0.895045 | 0.447523 | − | 0.894273i | \(-0.352306\pi\) | ||||
0.447523 | + | 0.894273i | \(0.352306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.37091 | 0.221271 | 0.110636 | − | 0.993861i | \(-0.464711\pi\) | ||||
0.110636 | + | 0.993861i | \(0.464711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.7248 | 0.857695 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.5366 | −1.71634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.98599 | 0.0687281 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.52738 | −0.121924 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.3021 | 1.21876 | 0.609381 | − | 0.792877i | \(-0.291418\pi\) | ||||
0.609381 | + | 0.792877i | \(0.291418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2630 | −0.457343 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.24892 | −0.0430150 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.4362 | 0.840631 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.495828 | 0.0170368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.7744 | −0.918897 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10644 | 0.140767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.70883 | 0.229706 | 0.114853 | − | 0.993383i | \(-0.463360\pi\) | ||||
0.114853 | + | 0.993383i | \(0.463360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.31139 | 0.113247 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0043 | 0.854130 | 0.427065 | − | 0.904221i | \(-0.359548\pi\) | ||||
0.427065 | + | 0.904221i | \(0.359548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.4079 | −0.730429 | −0.365214 | − | 0.930923i | \(-0.619004\pi\) | ||||
−0.365214 | + | 0.930923i | \(0.619004\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0130021 | −0.000443111 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1799 | 0.789053 | 0.394527 | − | 0.918885i | \(-0.370909\pi\) | ||||
0.394527 | + | 0.918885i | \(0.370909\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.6292 | 0.361404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.1977 | 1.12745 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.8167 | 1.38461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.76194 | 0.127469 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.8801 | −0.435926 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.09438 | −0.0369969 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.9817 | −0.674734 | −0.337367 | − | 0.941373i | \(-0.609536\pi\) | ||||
−0.337367 | + | 0.941373i | \(0.609536\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.2333 | 0.851098 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0252 | 1.04527 | 0.522633 | − | 0.852557i | \(-0.324950\pi\) | ||||
0.522633 | + | 0.852557i | \(0.324950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.97713 | −0.234799 | −0.117400 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117400 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.72080 | −0.293147 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.9000 | 1.07110 | 0.535549 | − | 0.844504i | \(-0.320105\pi\) | ||||
0.535549 | + | 0.844504i | \(0.320105\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.70510 | 0.0571873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.35607 | −0.0789312 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5893 | 0.354357 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.32506 | 0.177997 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.08498 | −0.0696153 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9931 | 0.466695 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 95.3782 | 3.17751 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.487929 | 0.0162373 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.2945 | 1.43916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.59465 | −0.318585 | −0.159293 | − | 0.987231i | \(-0.550921\pi\) | ||||
−0.159293 | + | 0.987231i | \(0.550921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.6926 | −0.487322 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.1540 | 0.866520 | 0.433260 | − | 0.901269i | \(-0.357363\pi\) | ||||
0.433260 | + | 0.901269i | \(0.357363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0332566 | −0.00110063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.152223 | −0.00503234 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.591562 | −0.0195351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.18144 | 0.0389722 | 0.0194861 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194861 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.20268 | 0.105532 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.65185 | 0.0872867 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.73451 | 0.0570303 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.05118 | −0.133058 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.5999 | 1.43046 | 0.715232 | − | 0.698887i | \(-0.246321\pi\) | ||||
0.715232 | + | 0.698887i | \(0.246321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6578 | 0.382070 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.45554 | −0.113129 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.1518 | 1.08418 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.5235 | 0.507130 | 0.253565 | − | 0.967318i | \(-0.418397\pi\) | ||||
0.253565 | + | 0.967318i | \(0.418397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.7617 | 1.03650 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.1806 | −0.494874 | −0.247437 | − | 0.968904i | \(-0.579588\pi\) | ||||
−0.247437 | + | 0.968904i | \(0.579588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.357177 | −0.0116313 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.180715 | 0.00587867 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.6669 | −0.736574 | −0.368287 | − | 0.929712i | \(-0.620056\pi\) | ||||
−0.368287 | + | 0.929712i | \(0.620056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.75913 | 0.251872 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.1696 | −0.816181 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.4316 | −1.82800 | −0.914000 | − | 0.405715i | \(-0.867022\pi\) | ||||
−0.914000 | + | 0.405715i | \(0.867022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.1898 | 1.68882 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.34650 | 0.302129 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.401871 | 0.0129771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.5576 | −0.598633 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1492 | 0.327054 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.4063 | −1.17196 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1287 | 0.454349 | 0.227174 | − | 0.973854i | \(-0.427051\pi\) | ||||
0.227174 | + | 0.973854i | \(0.427051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8134 | −0.379501 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.4175 | −0.526863 | −0.263431 | − | 0.964678i | \(-0.584854\pi\) | ||||
−0.263431 | + | 0.964678i | \(0.584854\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.325081 | −0.0104216 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.880668 | −0.0282040 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.1986 | −0.486248 | −0.243124 | − | 0.969995i | \(-0.578172\pi\) | ||||
−0.243124 | + | 0.969995i | \(0.578172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.7566 | 0.599464 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.51988 | −0.144309 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.0518 | −0.352499 | −0.176249 | − | 0.984346i | \(-0.556397\pi\) | ||||
−0.176249 | + | 0.984346i | \(0.556397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1061 | −0.895534 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.577897 | 0.0183947 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.4037 | 0.426214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.0573 | 0.414780 | 0.207390 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207390 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.94004 | −0.283703 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.3232 | 1.11982 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.9089 | 1.29560 | 0.647799 | − | 0.761811i | \(-0.275690\pi\) | ||||
0.647799 | + | 0.761811i | \(0.275690\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.64278 | −0.0519752 |
(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 | 4008.2.a.i.1.3 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.3 | 9 | 4.3 | odd | 2 |