Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | 2.18398 | 1.26092 | 0.630461 | − | 0.776221i | \(-0.282866\pi\) | ||||
0.630461 | + | 0.776221i | \(0.282866\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.76977 | 0.589922 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.59819 | 1.08490 | 0.542448 | − | 0.840089i | \(-0.317498\pi\) | ||||
0.542448 | + | 0.840089i | \(0.317498\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.85838 | 1.62482 | 0.812411 | − | 0.583085i | \(-0.198155\pi\) | ||||
0.812411 | + | 0.583085i | \(0.198155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.36121 | −1.54282 | −0.771410 | − | 0.636339i | \(-0.780448\pi\) | ||||
−0.771410 | + | 0.636339i | \(0.780448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.50283 | −1.03302 | −0.516510 | − | 0.856281i | \(-0.672769\pi\) | ||||
−0.516510 | + | 0.856281i | \(0.672769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.62814 | −0.548006 | −0.274003 | − | 0.961729i | \(-0.588348\pi\) | ||||
−0.274003 | + | 0.961729i | \(0.588348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.68681 | −0.517076 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05866 | 0.382284 | 0.191142 | − | 0.981562i | \(-0.438781\pi\) | ||||
0.191142 | + | 0.981562i | \(0.438781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.62814 | 1.19045 | 0.595225 | − | 0.803559i | \(-0.297063\pi\) | ||||
0.595225 | + | 0.803559i | \(0.297063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.85838 | 1.36797 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91704 | 0.972755 | 0.486378 | − | 0.873749i | \(-0.338318\pi\) | ||||
0.486378 | + | 0.873749i | \(0.338318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.7946 | 2.04877 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.22348 | −1.12812 | −0.564059 | − | 0.825734i | \(-0.690761\pi\) | ||||
−0.564059 | + | 0.825734i | \(0.690761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.34880 | 0.815684 | 0.407842 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407842 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.31885 | 0.338239 | 0.169119 | − | 0.985596i | \(-0.445908\pi\) | ||||
0.169119 | + | 0.985596i | \(0.445908\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.8927 | −1.94537 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.10777 | 0.564246 | 0.282123 | − | 0.959378i | \(-0.408961\pi\) | ||||
0.282123 | + | 0.959378i | \(0.408961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.83408 | −1.30256 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.07107 | 0.660197 | 0.330098 | − | 0.943947i | \(-0.392918\pi\) | ||||
0.330098 | + | 0.943947i | \(0.392918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.37361 | 0.944094 | 0.472047 | − | 0.881573i | \(-0.343515\pi\) | ||||
0.472047 | + | 0.881573i | \(0.343515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.39667 | −0.414969 | −0.207485 | − | 0.978238i | \(-0.566528\pi\) | ||||
−0.207485 | + | 0.978238i | \(0.566528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.73981 | −0.690992 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7224 | 1.98459 | 0.992293 | − | 0.123917i | \(-0.0395457\pi\) | ||||
0.992293 | + | 0.123917i | \(0.0395457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7184 | 1.72266 | 0.861328 | − | 0.508050i | \(-0.169633\pi\) | ||||
0.861328 | + | 0.508050i | \(0.169633\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.25505 | −0.366221 | −0.183111 | − | 0.983092i | \(-0.558617\pi\) | ||||
−0.183111 | + | 0.983092i | \(0.558617\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1772 | −1.24191 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6936 | 1.17377 | 0.586885 | − | 0.809670i | \(-0.300354\pi\) | ||||
0.586885 | + | 0.809670i | \(0.300354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.49607 | 0.482030 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1540 | −1.18232 | −0.591162 | − | 0.806553i | \(-0.701331\pi\) | ||||
−0.591162 | + | 0.806553i | \(0.701331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.4757 | 1.50106 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1896 | 1.74534 | 0.872671 | − | 0.488308i | \(-0.162386\pi\) | ||||
0.872671 | + | 0.488308i | \(0.162386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.36796 | 0.640004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.44131 | −0.342423 | −0.171212 | − | 0.985234i | \(-0.554768\pi\) | ||||
−0.171212 | + | 0.985234i | \(0.554768\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9757 | −1.18000 | −0.590000 | − | 0.807403i | \(-0.700872\pi\) | ||||
−0.590000 | + | 0.807403i | \(0.700872\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6760 | 1.03209 | 0.516045 | − | 0.856562i | \(-0.327404\pi\) | ||||
0.516045 | + | 0.856562i | \(0.327404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.33411 | −0.798263 | −0.399131 | − | 0.916894i | \(-0.630688\pi\) | ||||
−0.399131 | + | 0.916894i | \(0.630688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9227 | 1.22657 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1542 | 1.14337 | 0.571684 | − | 0.820474i | \(-0.306290\pi\) | ||||
0.571684 | + | 0.820474i | \(0.306290\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3680 | 0.958518 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.94699 | 0.176999 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.7759 | −1.42247 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.82453 | 0.871786 | 0.435893 | − | 0.899998i | \(-0.356433\pi\) | ||||
0.435893 | + | 0.899998i | \(0.356433\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.6817 | 1.02851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.95375 | −0.432811 | −0.216405 | − | 0.976304i | \(-0.569433\pi\) | ||||
−0.216405 | + | 0.976304i | \(0.569433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137 | 0.966595 | 0.483298 | − | 0.875456i | \(-0.339439\pi\) | ||||
0.483298 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.70311 | −0.738188 | −0.369094 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369094 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.06431 | 0.426492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.0796 | 1.76276 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.45268 | −0.528624 | −0.264312 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264312 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.02606 | −0.327636 | −0.163818 | − | 0.986491i | \(-0.552381\pi\) | ||||
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.2578 | −0.910143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5260 | 1.23911 | 0.619556 | − | 0.784953i | \(-0.287313\pi\) | ||||
0.619556 | + | 0.784953i | \(0.287313\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.97129 | 0.711470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.9610 | 1.95510 | 0.977549 | − | 0.210710i | \(-0.0675774\pi\) | ||||
0.977549 | + | 0.210710i | \(0.0675774\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0739 | −1.24384 | −0.621919 | − | 0.783082i | \(-0.713647\pi\) | ||||
−0.621919 | + | 0.783082i | \(0.713647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.3206 | 1.64005 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.96895 | −0.609401 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0356054 | −0.00270703 | −0.00135351 | − | 0.999999i | \(-0.500431\pi\) | ||||
−0.00135351 | + | 0.999999i | \(0.500431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0751 | 0.832456 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.45268 | −0.332809 | −0.166404 | − | 0.986058i | \(-0.553216\pi\) | ||||
−0.166404 | + | 0.986058i | \(0.553216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7377 | 1.69008 | 0.845039 | − | 0.534705i | \(-0.179577\pi\) | ||||
0.845039 | + | 0.534705i | \(0.179577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.1038 | 1.19043 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.8888 | −1.67380 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.5521 | −1.84888 | −0.924442 | − | 0.381323i | \(-0.875469\pi\) | ||||
−0.924442 | + | 0.381323i | \(0.875469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0904 | −1.51812 | −0.759059 | − | 0.651022i | \(-0.774341\pi\) | ||||
−0.759059 | + | 0.651022i | \(0.774341\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4622 | −1.17288 | −0.586442 | − | 0.809991i | \(-0.699472\pi\) | ||||
−0.586442 | + | 0.809991i | \(0.699472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9419 | 1.83897 | 0.919485 | − | 0.393126i | \(-0.128606\pi\) | ||||
0.919485 | + | 0.393126i | \(0.128606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41825 | −0.523243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.65120 | −0.323281 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.2020 | −1.12072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.84877 | 0.609174 | 0.304587 | − | 0.952484i | \(-0.401481\pi\) | ||||
0.304587 | + | 0.952484i | \(0.401481\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.5214 | 2.50241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 32.1446 | 2.17213 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.2664 | −2.50681 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.06042 | 0.271906 | 0.135953 | − | 0.990715i | \(-0.456590\pi\) | ||||
0.135953 | + | 0.990715i | \(0.456590\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9606 | −0.793856 | −0.396928 | − | 0.917850i | \(-0.629924\pi\) | ||||
−0.396928 | + | 0.917850i | \(0.629924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3042 | −0.747000 | −0.373500 | − | 0.927630i | \(-0.621842\pi\) | ||||
−0.373500 | + | 0.927630i | \(0.621842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.3059 | −1.39580 | −0.697898 | − | 0.716197i | \(-0.745881\pi\) | ||||
−0.697898 | + | 0.716197i | \(0.745881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.10896 | −0.461776 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5361 | −1.45774 | −0.728871 | − | 0.684651i | \(-0.759955\pi\) | ||||
−0.728871 | + | 0.684651i | \(0.759955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8477 | 0.827595 | 0.413798 | − | 0.910369i | \(-0.364202\pi\) | ||||
0.413798 | + | 0.910369i | \(0.364202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.3504 | −1.04888 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3793 | −1.67847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.3545 | 1.48003 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7361 | −1.49821 | −0.749103 | − | 0.662453i | \(-0.769515\pi\) | ||||
−0.749103 | + | 0.662453i | \(0.769515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.45657 | −0.594530 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2139 | 0.824262 | 0.412131 | − | 0.911125i | \(-0.364785\pi\) | ||||
0.412131 | + | 0.911125i | \(0.364785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.64335 | 0.225518 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.8532 | 1.77917 | 0.889584 | − | 0.456773i | \(-0.150995\pi\) | ||||
0.889584 | + | 0.456773i | \(0.150995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.3602 | −1.49082 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.57073 | −0.156740 | −0.0783700 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783700 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.74722 | −0.409865 | −0.204932 | − | 0.978776i | \(-0.565697\pi\) | ||||
−0.204932 | + | 0.978776i | \(0.565697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.25453 | 0.195546 | 0.0977730 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977730 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.7303 | 0.702273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.55422 | −0.152372 | −0.0761860 | − | 0.997094i | \(-0.524274\pi\) | ||||
−0.0761860 | + | 0.997094i | \(0.524274\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5136 | −0.743857 | −0.371929 | − | 0.928261i | \(-0.621303\pi\) | ||||
−0.371929 | + | 0.928261i | \(0.621303\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4649 | 1.38029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.5418 | 2.20074 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.6574 | −1.49892 | −0.749460 | − | 0.662050i | \(-0.769687\pi\) | ||||
−0.749460 | + | 0.662050i | \(0.769687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.66765 | −0.560974 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.3967 | −0.890412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.51575 | −0.431768 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9391 | −0.681398 | −0.340699 | − | 0.940172i | \(-0.610664\pi\) | ||||
−0.340699 | + | 0.940172i | \(0.610664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.1547 | −1.48789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.49879 | −0.481922 | −0.240961 | − | 0.970535i | \(-0.577463\pi\) | ||||
−0.240961 | + | 0.970535i | \(0.577463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.75612 | −0.0992616 | −0.0496308 | − | 0.998768i | \(-0.515804\pi\) | ||||
−0.0496308 | + | 0.998768i | \(0.515804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.96491 | −0.335023 | −0.167511 | − | 0.985870i | \(-0.553573\pi\) | ||||
−0.167511 | + | 0.985870i | \(0.553573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.40746 | 0.414738 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.3162 | 1.30138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.6434 | 1.59376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.2015 | −1.00655 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1038 | −0.775216 | −0.387608 | − | 0.921824i | \(-0.626699\pi\) | ||||
−0.387608 | + | 0.921824i | \(0.626699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.4718 | 0.573850 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.8876 | 1.24677 | 0.623384 | − | 0.781916i | \(-0.285758\pi\) | ||||
0.623384 | + | 0.781916i | \(0.285758\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.5445 | 1.44170 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.8493 | 1.29151 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.6586 | 1.27006 | 0.635030 | − | 0.772487i | \(-0.280988\pi\) | ||||
0.635030 | + | 0.772487i | \(0.280988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7912 | −1.48763 | −0.743814 | − | 0.668386i | \(-0.766985\pi\) | ||||
−0.743814 | + | 0.668386i | \(0.766985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7403 | −0.840157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1680 | 1.12666 | 0.563331 | − | 0.826231i | \(-0.309520\pi\) | ||||
0.563331 | + | 0.826231i | \(0.309520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.2843 | 1.91501 | 0.957505 | − | 0.288416i | \(-0.0931285\pi\) | ||||
0.957505 | + | 0.288416i | \(0.0931285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.27545 | 0.0671289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.25219 | 0.223182 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.1586 | −1.62646 | −0.813232 | − | 0.581939i | \(-0.802294\pi\) | ||||
−0.813232 | + | 0.581939i | \(0.802294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.7839 | −0.665502 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.67279 | 0.345504 | 0.172752 | − | 0.984965i | \(-0.444734\pi\) | ||||
0.172752 | + | 0.984965i | \(0.444734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0604 | 0.621143 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.3984 | 1.09916 | 0.549582 | − | 0.835440i | \(-0.314787\pi\) | ||||
0.549582 | + | 0.835440i | \(0.314787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.4566 | 1.09925 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.63453 | 0.185716 | 0.0928578 | − | 0.995679i | \(-0.470400\pi\) | ||||
0.0928578 | + | 0.995679i | \(0.470400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.46612 | 0.481190 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.8952 | 1.11013 | 0.555066 | − | 0.831806i | \(-0.312693\pi\) | ||||
0.555066 | + | 0.831806i | \(0.312693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7182 | 0.845474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8189 | −0.545740 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.9757 | −0.902175 | −0.451087 | − | 0.892480i | \(-0.648964\pi\) | ||||
−0.451087 | + | 0.892480i | \(0.648964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.6343 | 1.37999 | 0.689996 | − | 0.723813i | \(-0.257612\pi\) | ||||
0.689996 | + | 0.723813i | \(0.257612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.8302 | 1.93427 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2907 | 1.05534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.9261 | 1.97422 | 0.987108 | − | 0.160053i | \(-0.0511665\pi\) | ||||
0.987108 | + | 0.160053i | \(0.0511665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.7089 | 1.21880 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.0074 | −0.930797 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.89384 | −0.141373 | −0.0706867 | − | 0.997499i | \(-0.522519\pi\) | ||||
−0.0706867 | + | 0.997499i | \(0.522519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.5744 | −1.63632 | −0.818158 | − | 0.574993i | \(-0.805005\pi\) | ||||
−0.818158 | + | 0.574993i | \(0.805005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.10382 | 0.199534 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 46.0374 | 2.22270 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.330882 | 0.0159380 | 0.00796902 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00796902 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.573752 | −0.0275727 | −0.0137864 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137864 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.8341 | 0.566101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5165 | 1.31329 | 0.656645 | − | 0.754200i | \(-0.271975\pi\) | ||||
0.656645 | + | 0.754200i | \(0.271975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.7168 | 0.936771 | 0.468386 | − | 0.883524i | \(-0.344836\pi\) | ||||
0.468386 | + | 0.883524i | \(0.344836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0925 | −0.666553 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.6751 | 1.54203 | 0.771016 | − | 0.636816i | \(-0.219749\pi\) | ||||
0.771016 | + | 0.636816i | \(0.219749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.9915 | −1.22389 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.79282 | −0.413123 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.75112 | −0.175470 | −0.0877350 | − | 0.996144i | \(-0.527963\pi\) | ||||
−0.0877350 | + | 0.996144i | \(0.527963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.0913 | 0.797755 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.77983 | −0.408917 | −0.204459 | − | 0.978875i | \(-0.565543\pi\) | ||||
−0.204459 | + | 0.978875i | \(0.565543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.78203 | 0.222240 | 0.111120 | − | 0.993807i | \(-0.464556\pi\) | ||||
0.111120 | + | 0.993807i | \(0.464556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9198 | 1.01433 | 0.507165 | − | 0.861849i | \(-0.330694\pi\) | ||||
0.507165 | + | 0.861849i | \(0.330694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.9085 | 1.56242 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.2460 | 0.884933 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.26980 | 0.332861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.08861 | −0.232505 | −0.116252 | − | 0.993220i | \(-0.537088\pi\) | ||||
−0.116252 | + | 0.993220i | \(0.537088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6643 | 1.58055 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.05035 | −0.364796 | −0.182398 | − | 0.983225i | \(-0.558386\pi\) | ||||
−0.182398 | + | 0.983225i | \(0.558386\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 54.5143 | 2.46522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8081 | 0.578021 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.0956 | −0.589795 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5284 | −1.27710 | −0.638552 | − | 0.769578i | \(-0.720466\pi\) | ||||
−0.638552 | + | 0.769578i | \(0.720466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.1051 | −1.56838 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.56948 | −0.292919 | −0.146459 | − | 0.989217i | \(-0.546788\pi\) | ||||
−0.146459 | + | 0.989217i | \(0.546788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5638 | 2.06797 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.1574 | −1.07076 | −0.535379 | − | 0.844612i | \(-0.679831\pi\) | ||||
−0.535379 | + | 0.844612i | \(0.679831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.0982 | 0.534150 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.34366 | 0.366954 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0777615 | −0.00341335 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.8630 | −0.914024 | −0.457012 | − | 0.889460i | \(-0.651080\pi\) | ||||
−0.457012 | + | 0.889460i | \(0.651080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8708 | −0.562800 | −0.281400 | − | 0.959591i | \(-0.590799\pi\) | ||||
−0.281400 | + | 0.959591i | \(0.590799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.1630 | −1.83665 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0929 | −0.699689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.97460 | 0.389465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.3179 | −1.83299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.72455 | −0.419645 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.5361 | −1.05489 | −0.527446 | − | 0.849589i | \(-0.676850\pi\) | ||||
−0.527446 | + | 0.849589i | \(0.676850\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.6586 | 2.13105 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5781 | 1.17916 | 0.589578 | − | 0.807711i | \(-0.299294\pi\) | ||||
0.589578 | + | 0.807711i | \(0.299294\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.0496 | 0.556942 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.26980 | −0.394907 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.60260 | 0.279761 | 0.139881 | − | 0.990168i | \(-0.455328\pi\) | ||||
0.139881 | + | 0.990168i | \(0.455328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.3353 | 1.32534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −49.9888 | −2.11053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.97466 | −0.0832221 | −0.0416110 | − | 0.999134i | \(-0.513249\pi\) | ||||
−0.0416110 | + | 0.999134i | \(0.513249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7281 | −0.491666 | −0.245833 | − | 0.969312i | \(-0.579061\pi\) | ||||
−0.245833 | + | 0.969312i | \(0.579061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.69974 | 0.238527 | 0.119263 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119263 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.8052 | −2.33130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3343 | 0.971418 | 0.485709 | − | 0.874121i | \(-0.338562\pi\) | ||||
0.485709 | + | 0.874121i | \(0.338562\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46.0609 | −1.91423 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.7806 | 0.612148 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.8470 | −0.942997 | −0.471498 | − | 0.881867i | \(-0.656287\pi\) | ||||
−0.471498 | + | 0.881867i | \(0.656287\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8454 | −1.22976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.9532 | −1.47892 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.4810 | −0.594664 | −0.297332 | − | 0.954774i | \(-0.596097\pi\) | ||||
−0.297332 | + | 0.954774i | \(0.596097\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 56.6565 | 2.31880 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.13524 | −0.128102 | −0.0640512 | − | 0.997947i | \(-0.520402\pi\) | ||||
−0.0640512 | + | 0.997947i | \(0.520402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.2118 | −1.31395 | −0.656973 | − | 0.753914i | \(-0.728164\pi\) | ||||
−0.656973 | + | 0.753914i | \(0.728164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.01131 | −0.244799 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1586 | 0.452913 | 0.226456 | − | 0.974021i | \(-0.427286\pi\) | ||||
0.226456 | + | 0.974021i | \(0.427286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5847 | 0.549578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.53705 | −0.304418 | −0.152209 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152209 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7728 | 0.916797 | 0.458399 | − | 0.888747i | \(-0.348423\pi\) | ||||
0.458399 | + | 0.888747i | \(0.348423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.964766 | 0.0387772 | 0.0193886 | − | 0.999812i | \(-0.493828\pi\) | ||||
0.0193886 | + | 0.999812i | \(0.493828\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.06132 | 0.283361 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.3849 | −1.41314 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.6395 | −1.50079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.90059 | 0.274708 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3255 | 0.768121 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.5948 | 1.17075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.14433 | −0.0846961 | −0.0423481 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423481 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4980 | −1.08441 | −0.542207 | − | 0.840245i | \(-0.682411\pi\) | ||||
−0.542207 | + | 0.840245i | \(0.682411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.9482 | 1.21670 | 0.608350 | − | 0.793669i | \(-0.291832\pi\) | ||||
0.608350 | + | 0.793669i | \(0.291832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.2467 | 0.716245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.4448 | 1.54360 | 0.771798 | − | 0.635868i | \(-0.219358\pi\) | ||||
0.771798 | + | 0.635868i | \(0.219358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.0481 | 1.01623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.80237 | 0.342892 | 0.171446 | − | 0.985194i | \(-0.445156\pi\) | ||||
0.171446 | + | 0.985194i | \(0.445156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.1095 | −1.09333 | −0.546667 | − | 0.837350i | \(-0.684104\pi\) | ||||
−0.546667 | + | 0.837350i | \(0.684104\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −81.3889 | −3.16088 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.41046 | −0.209494 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.86787 | 0.342852 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.5317 | 1.02424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.7933 | 0.570241 | 0.285121 | − | 0.958492i | \(-0.407966\pi\) | ||||
0.285121 | + | 0.958492i | \(0.407966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.71162 | −0.104216 | −0.0521080 | − | 0.998641i | \(-0.516594\pi\) | ||||
−0.0521080 | + | 0.998641i | \(0.516594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.1218 | −1.00099 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.62633 | 0.0622297 | 0.0311149 | − | 0.999516i | \(-0.490094\pi\) | ||||
0.0311149 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.6880 | −0.941908 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0649 | 0.916799 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.8821 | −1.93565 | −0.967823 | − | 0.251632i | \(-0.919033\pi\) | ||||
−0.967823 | + | 0.251632i | \(0.919033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.9501 | 1.74048 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.5317 | −1.75999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.93106 | 0.299552 | 0.149776 | − | 0.988720i | \(-0.452145\pi\) | ||||
0.149776 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.6434 | −1.00488 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4922 | 0.656933 | 0.328466 | − | 0.944516i | \(-0.393468\pi\) | ||||
0.328466 | + | 0.944516i | \(0.393468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.76067 | −0.216042 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.4197 | −0.652374 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.2185 | −1.83810 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.1294 | −0.676111 | −0.338055 | − | 0.941126i | \(-0.609769\pi\) | ||||
−0.338055 | + | 0.941126i | \(0.609769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.0592 | 1.04353 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.42538 | 0.0899523 | 0.0449761 | − | 0.998988i | \(-0.485679\pi\) | ||||
0.0449761 | + | 0.998988i | \(0.485679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.17729 | −0.0806402 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.0248 | −1.25845 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.7659 | −0.730069 | −0.365035 | − | 0.930994i | \(-0.618943\pi\) | ||||
−0.365035 | + | 0.930994i | \(0.618943\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2219 | −0.450198 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.9065 | 1.46799 | 0.733993 | − | 0.679157i | \(-0.237655\pi\) | ||||
0.733993 | + | 0.679157i | \(0.237655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −57.6118 | −2.11642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.0921 | −1.21403 | −0.607016 | − | 0.794689i | \(-0.707634\pi\) | ||||
−0.607016 | + | 0.794689i | \(0.707634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.9251 | 0.692433 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.98531 | −0.254898 | −0.127449 | − | 0.991845i | \(-0.540679\pi\) | ||||
−0.127449 | + | 0.991845i | \(0.540679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −51.8391 | −1.88912 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.4796 | 0.889725 | 0.444863 | − | 0.895599i | \(-0.353253\pi\) | ||||
0.444863 | + | 0.895599i | \(0.353253\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.6530 | −0.749655 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.39511 | −0.340573 | −0.170286 | − | 0.985395i | \(-0.554469\pi\) | ||||
−0.170286 | + | 0.985395i | \(0.554469\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.7082 | 1.07270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.7183 | −1.07167 | −0.535835 | − | 0.844323i | \(-0.680003\pi\) | ||||
−0.535835 | + | 0.844323i | \(0.680003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.8590 | 1.03933 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.2108 | −1.37435 | −0.687173 | − | 0.726494i | \(-0.741148\pi\) | ||||
−0.687173 | + | 0.726494i | \(0.741148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.5261 | 1.16537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.1705 | 2.15307 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.53122 | −0.197670 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.8114 | 0.884431 | 0.442215 | − | 0.896909i | \(-0.354193\pi\) | ||||
0.442215 | + | 0.896909i | \(0.354193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.0149 | 2.24339 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.1974 | 1.53399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.9296 | −0.812210 | −0.406105 | − | 0.913826i | \(-0.633113\pi\) | ||||
−0.406105 | + | 0.913826i | \(0.633113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7507 | −0.521841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.7400 | −0.697479 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 52.9595 | 1.86890 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.61441 | −0.197637 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.2720 | −1.20494 | −0.602470 | − | 0.798142i | \(-0.705817\pi\) | ||||
−0.602470 | + | 0.798142i | \(0.705817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5925 | 1.32005 | 0.660025 | − | 0.751244i | \(-0.270546\pi\) | ||||
0.660025 | + | 0.751244i | \(0.270546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.7358 | −0.516807 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0847 | −0.842618 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.2643 | 1.09113 | 0.545565 | − | 0.838068i | \(-0.316315\pi\) | ||||
0.545565 | + | 0.838068i | \(0.316315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.4452 | 0.642959 | 0.321480 | − | 0.946916i | \(-0.395820\pi\) | ||||
0.321480 | + | 0.946916i | \(0.395820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5931 | −0.507450 | −0.253725 | − | 0.967276i | \(-0.581656\pi\) | ||||
−0.253725 | + | 0.967276i | \(0.581656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1057 | −0.420448 | −0.210224 | − | 0.977653i | \(-0.567419\pi\) | ||||
−0.210224 | + | 0.977653i | \(0.567419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.10783 | 0.246568 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.8085 | −0.615553 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.8245 | −0.477276 | −0.238638 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238638 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7619 | −0.853859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.57836 | −0.192129 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.3295 | −0.937946 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.5508 | −0.533076 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7912 | −0.540680 | −0.270340 | − | 0.962765i | \(-0.587136\pi\) | ||||
−0.270340 | + | 0.962765i | \(0.587136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4837 | −0.460593 | −0.230297 | − | 0.973120i | \(-0.573970\pi\) | ||||
−0.230297 | + | 0.973120i | \(0.573970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.8300 | −0.813071 | −0.406535 | − | 0.913635i | \(-0.633263\pi\) | ||||
−0.406535 | + | 0.913635i | \(0.633263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.35592 | −0.0801966 | −0.0400983 | − | 0.999196i | \(-0.512767\pi\) | ||||
−0.0400983 | + | 0.999196i | \(0.512767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 51.2469 | 1.74044 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7123 | −0.397312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.8990 | −0.674251 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.4216 | 1.02962 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.2892 | −0.887725 | −0.443862 | − | 0.896095i | \(-0.646392\pi\) | ||||
−0.443862 | + | 0.896095i | \(0.646392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −56.0352 | −1.89002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2476 | −1.55812 | −0.779061 | − | 0.626948i | \(-0.784304\pi\) | ||||
−0.779061 | + | 0.626948i | \(0.784304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.1184 | −1.35009 | −0.675045 | − | 0.737777i | \(-0.735876\pi\) | ||||
−0.675045 | + | 0.737777i | \(0.735876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.7685 | 1.10026 | 0.550130 | − | 0.835079i | \(-0.314578\pi\) | ||||
0.550130 | + | 0.835079i | \(0.314578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.2178 | −1.34735 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.4414 | −0.349407 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.6260 | −1.12274 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.6451 | 0.455090 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.1304 | −0.870529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.48710 | −0.182196 | −0.0910980 | − | 0.995842i | \(-0.529038\pi\) | ||||
−0.0910980 | + | 0.995842i | \(0.529038\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.09031 | −0.202003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3276 | −1.26985 | −0.634924 | − | 0.772574i | \(-0.718969\pi\) | ||||
−0.634924 | + | 0.772574i | \(0.718969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.4775 | 1.27342 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.6094 | −1.27361 | −0.636804 | − | 0.771026i | \(-0.719744\pi\) | ||||
−0.636804 | + | 0.771026i | \(0.719744\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.0747 | −0.859189 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 97.9662 | 3.22460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.1942 | −0.696108 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.3387 | −1.29066 | −0.645331 | − | 0.763903i | \(-0.723280\pi\) | ||||
−0.645331 | + | 0.763903i | \(0.723280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.5612 | −0.607666 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.4619 | −0.603124 | −0.301562 | − | 0.953447i | \(-0.597508\pi\) | ||||
−0.301562 | + | 0.953447i | \(0.597508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.83532 | −0.125161 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.6005 | 1.22574 | 0.612870 | − | 0.790184i | \(-0.290015\pi\) | ||||
0.612870 | + | 0.790184i | \(0.290015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.9844 | 0.618216 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4215 | 1.28103 | 0.640513 | − | 0.767947i | \(-0.278722\pi\) | ||||
0.640513 | + | 0.767947i | \(0.278722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 86.2258 | 2.79901 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.0272 | −0.422437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.4541 | −0.792148 | −0.396074 | − | 0.918219i | \(-0.629628\pi\) | ||||
−0.396074 | + | 0.918219i | \(0.629628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.1777 | 0.522952 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.9323 | 0.417171 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.8940 | 0.608852 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5757 | −0.725986 | −0.362993 | − | 0.931792i | \(-0.618245\pi\) | ||||
−0.362993 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 62.5566 | 2.00961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.1636 | −1.12845 | −0.564226 | − | 0.825620i | \(-0.690826\pi\) | ||||
−0.564226 | + | 0.825620i | \(0.690826\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.4910 | −0.847522 | −0.423761 | − | 0.905774i | \(-0.639290\pi\) | ||||
−0.423761 | + | 0.905774i | \(0.639290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.1343 | −1.28270 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7494 | −0.470913 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3380 | 0.871947 | 0.435974 | − | 0.899960i | \(-0.356404\pi\) | ||||
0.435974 | + | 0.899960i | \(0.356404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.0574 | −0.447000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.9900 | 1.90565 | 0.952823 | − | 0.303527i | \(-0.0981644\pi\) | ||||
0.952823 | + | 0.303527i | \(0.0981644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.8024 | −0.977486 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.4645 | −0.711458 | −0.355729 | − | 0.934589i | \(-0.615767\pi\) | ||||
−0.355729 | + | 0.934589i | \(0.615767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.8979 | −0.502989 |
(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 | 9800.2.a.cs.1.3 | 4 | ||
5.4 | even | 2 | 1960.2.a.x.1.2 | ✓ | 4 | ||
7.6 | odd | 2 | 9800.2.a.cl.1.2 | 4 | |||
20.19 | odd | 2 | 3920.2.a.ce.1.3 | 4 | |||
35.4 | even | 6 | 1960.2.q.y.961.3 | 8 | |||
35.9 | even | 6 | 1960.2.q.y.361.3 | 8 | |||
35.19 | odd | 6 | 1960.2.q.x.361.2 | 8 | |||
35.24 | odd | 6 | 1960.2.q.x.961.2 | 8 | |||
35.34 | odd | 2 | 1960.2.a.y.1.3 | yes | 4 | ||
140.139 | even | 2 | 3920.2.a.cd.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
1960.2.a.y.1.3 | yes | 4 | 35.34 | odd | 2 | ||
1960.2.q.x.361.2 | 8 | 35.19 | odd | 6 | |||
1960.2.q.x.961.2 | 8 | 35.24 | odd | 6 | |||
1960.2.q.y.361.3 | 8 | 35.9 | even | 6 | |||
1960.2.q.y.961.3 | 8 | 35.4 | even | 6 | |||
3920.2.a.cd.1.2 | 4 | 140.139 | even | 2 | |||
3920.2.a.ce.1.3 | 4 | 20.19 | odd | 2 | |||
9800.2.a.cl.1.2 | 4 | 7.6 | odd | 2 | |||
9800.2.a.cs.1.3 | 4 | 1.1 | even | 1 | trivial |