Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
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: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.94172\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.94172 | −1.31558 | −0.657788 | − | 0.753203i | \(-0.728508\pi\) | ||||
−0.657788 | + | 0.753203i | \(0.728508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.78729 | −1.05350 | −0.526748 | − | 0.850021i | \(-0.676589\pi\) | ||||
−0.526748 | + | 0.850021i | \(0.676589\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.89000 | −1.17288 | −0.586440 | − | 0.809993i | \(-0.699471\pi\) | ||||
−0.586440 | + | 0.809993i | \(0.699471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.470621 | −0.130527 | −0.0652634 | − | 0.997868i | \(-0.520789\pi\) | ||||
−0.0652634 | + | 0.997868i | \(0.520789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.98914 | −1.21004 | −0.605022 | − | 0.796209i | \(-0.706836\pi\) | ||||
−0.605022 | + | 0.796209i | \(0.706836\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49771 | −0.343597 | −0.171799 | − | 0.985132i | \(-0.554958\pi\) | ||||
−0.171799 | + | 0.985132i | \(0.554958\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.667875 | −0.139262 | −0.0696308 | − | 0.997573i | \(-0.522182\pi\) | ||||
−0.0696308 | + | 0.997573i | \(0.522182\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.65370 | 0.730740 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0707310 | −0.0131344 | −0.00656721 | − | 0.999978i | \(-0.502090\pi\) | ||||
−0.00656721 | + | 0.999978i | \(0.502090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13165 | −0.562462 | −0.281231 | − | 0.959640i | \(-0.590743\pi\) | ||||
−0.281231 | + | 0.959640i | \(0.590743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.19942 | 1.38595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.64481 | −0.270406 | −0.135203 | − | 0.990818i | \(-0.543169\pi\) | ||||
−0.135203 | + | 0.990818i | \(0.543169\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.08147 | −1.26211 | −0.631057 | − | 0.775736i | \(-0.717379\pi\) | ||||
−0.631057 | + | 0.775736i | \(0.717379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.74446 | −0.418527 | −0.209263 | − | 0.977859i | \(-0.567107\pi\) | ||||
−0.209263 | + | 0.977859i | \(0.567107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.54043 | −0.662290 | −0.331145 | − | 0.943580i | \(-0.607435\pi\) | ||||
−0.331145 | + | 0.943580i | \(0.607435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.768985 | 0.109855 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1695 | −1.67161 | −0.835803 | − | 0.549029i | \(-0.814998\pi\) | ||||
−0.835803 | + | 0.549029i | \(0.814998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4433 | 1.54301 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.9713 | −1.55852 | −0.779262 | − | 0.626698i | \(-0.784406\pi\) | ||||
−0.779262 | + | 0.626698i | \(0.784406\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.07730 | 0.265971 | 0.132986 | − | 0.991118i | \(-0.457544\pi\) | ||||
0.132986 | + | 0.991118i | \(0.457544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.38443 | 0.171718 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.754501 | 0.0921770 | 0.0460885 | − | 0.998937i | \(-0.485324\pi\) | ||||
0.0460885 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.65397 | −0.196290 | −0.0981448 | − | 0.995172i | \(-0.531291\pi\) | ||||
−0.0981448 | + | 0.995172i | \(0.531291\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00915 | −0.352195 | −0.176097 | − | 0.984373i | \(-0.556347\pi\) | ||||
−0.176097 | + | 0.984373i | \(0.556347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8426 | 1.23563 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.37256 | −0.604461 | −0.302230 | − | 0.953235i | \(-0.597731\pi\) | ||||
−0.302230 | + | 0.953235i | \(0.597731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1661 | 1.22564 | 0.612820 | − | 0.790222i | \(-0.290035\pi\) | ||||
0.612820 | + | 0.790222i | \(0.290035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.6766 | 1.59191 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.06894 | 0.961306 | 0.480653 | − | 0.876911i | \(-0.340400\pi\) | ||||
0.480653 | + | 0.876911i | \(0.340400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.31176 | 0.137510 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.40582 | 0.452028 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.36503 | 0.240133 | 0.120066 | − | 0.992766i | \(-0.461689\pi\) | ||||
0.120066 | + | 0.992766i | \(0.461689\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3197 | −1.72337 | −0.861687 | − | 0.507440i | \(-0.830592\pi\) | ||||
−0.861687 | + | 0.507440i | \(0.830592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21898 | 0.120110 | 0.0600548 | − | 0.998195i | \(-0.480872\pi\) | ||||
0.0600548 | + | 0.998195i | \(0.480872\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.335485 | −0.0324325 | −0.0162163 | − | 0.999869i | \(-0.505162\pi\) | ||||
−0.0162163 | + | 0.999869i | \(0.505162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4356 | 1.67002 | 0.835012 | − | 0.550232i | \(-0.185461\pi\) | ||||
0.835012 | + | 0.550232i | \(0.185461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.41636 | 0.321384 | 0.160692 | − | 0.987005i | \(-0.448627\pi\) | ||||
0.160692 | + | 0.987005i | \(0.448627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.96470 | 0.183209 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.9062 | 1.27478 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.13213 | 0.375649 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.96043 | 0.354232 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9752 | 1.32883 | 0.664417 | − | 0.747362i | \(-0.268680\pi\) | ||||
0.664417 | + | 0.747362i | \(0.268680\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5029 | 0.917641 | 0.458820 | − | 0.888529i | \(-0.348272\pi\) | ||||
0.458820 | + | 0.888529i | \(0.348272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.17454 | 0.361978 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.5392 | −1.15673 | −0.578366 | − | 0.815778i | \(-0.696309\pi\) | ||||
−0.578366 | + | 0.815778i | \(0.696309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0800 | 0.939797 | 0.469899 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469899 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.83072 | 0.153092 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.208071 | 0.0172793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4865 | −1.26870 | −0.634351 | − | 0.773045i | \(-0.718733\pi\) | ||||
−0.634351 | + | 0.773045i | \(0.718733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5686 | 1.59247 | 0.796235 | − | 0.604987i | \(-0.206822\pi\) | ||||
0.796235 | + | 0.604987i | \(0.206822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.21244 | 0.739961 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.359659 | −0.0287039 | −0.0143520 | − | 0.999897i | \(-0.504569\pi\) | ||||
−0.0143520 | + | 0.999897i | \(0.504569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.86156 | 0.146712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.12275 | −0.0879403 | −0.0439701 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439701 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7785 | −0.982963 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0970 | −0.919719 | −0.459859 | − | 0.887992i | \(-0.652100\pi\) | ||||
−0.459859 | + | 0.887992i | \(0.652100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1839 | −0.769832 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.710737 | −0.0531230 | −0.0265615 | − | 0.999647i | \(-0.508456\pi\) | ||||
−0.0265615 | + | 0.999647i | \(0.508456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0045 | 1.18960 | 0.594801 | − | 0.803873i | \(-0.297231\pi\) | ||||
0.594801 | + | 0.803873i | \(0.297231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.83858 | 0.355739 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.4078 | 1.41924 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.85478 | −0.423637 | −0.211819 | − | 0.977309i | \(-0.567939\pi\) | ||||
−0.211819 | + | 0.977309i | \(0.567939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.19532 | −0.589912 | −0.294956 | − | 0.955511i | \(-0.595305\pi\) | ||||
−0.294956 | + | 0.955511i | \(0.595305\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.74323 | 0.409188 | 0.204594 | − | 0.978847i | \(-0.434413\pi\) | ||||
0.204594 | + | 0.978847i | \(0.434413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8466 | −0.910671 | −0.455335 | − | 0.890320i | \(-0.650481\pi\) | ||||
−0.455335 | + | 0.890320i | \(0.650481\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.197148 | 0.0138371 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.7734 | 1.66041 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.82608 | 0.402998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.76354 | −0.259093 | −0.129547 | − | 0.991573i | \(-0.541352\pi\) | ||||
−0.129547 | + | 0.991573i | \(0.541352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.07343 | 0.550604 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.72883 | 0.592551 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.34800 | 0.157943 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.189252 | 0.0126733 | 0.00633663 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633663 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8597 | 1.18539 | 0.592696 | − | 0.805427i | \(-0.298064\pi\) | ||||
0.592696 | + | 0.805427i | \(0.298064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7945 | 1.10981 | 0.554906 | − | 0.831913i | \(-0.312754\pi\) | ||||
0.554906 | + | 0.831913i | \(0.312754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0060 | 0.852052 | 0.426026 | − | 0.904711i | \(-0.359913\pi\) | ||||
0.426026 | + | 0.904711i | \(0.359913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.3567 | 0.871292 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.64337 | −0.300355 | −0.150177 | − | 0.988659i | \(-0.547985\pi\) | ||||
−0.150177 | + | 0.988659i | \(0.547985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.63503 | −0.298568 | −0.149284 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149284 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.26214 | −0.144523 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.704852 | 0.0448486 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.1447 | −1.71336 | −0.856680 | − | 0.515848i | \(-0.827477\pi\) | ||||
−0.856680 | + | 0.515848i | \(0.827477\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.59804 | 0.163337 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4905 | −0.779137 | −0.389569 | − | 0.920997i | \(-0.627376\pi\) | ||||
−0.389569 | + | 0.920997i | \(0.627376\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.58457 | 0.284872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.8246 | 1.28410 | 0.642051 | − | 0.766662i | \(-0.278084\pi\) | ||||
0.642051 | + | 0.766662i | \(0.278084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.7992 | 2.19913 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2227 | 0.684259 | 0.342130 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342130 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.75633 | −0.167435 | −0.0837177 | − | 0.996490i | \(-0.526679\pi\) | ||||
−0.0837177 | + | 0.996490i | \(0.526679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.2129 | −0.857071 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.6207 | −1.23898 | −0.619489 | − | 0.785005i | \(-0.712660\pi\) | ||||
−0.619489 | + | 0.785005i | \(0.712660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8580 | 1.00566 | 0.502832 | − | 0.864384i | \(-0.332291\pi\) | ||||
0.502832 | + | 0.864384i | \(0.332291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.1576 | −1.67379 | −0.836897 | − | 0.547361i | \(-0.815633\pi\) | ||||
−0.836897 | + | 0.547361i | \(0.815633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.5254 | 1.32963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.89154 | 0.464208 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.79839 | 0.514008 | 0.257004 | − | 0.966410i | \(-0.417265\pi\) | ||||
0.257004 | + | 0.966410i | \(0.417265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.2160 | 2.05036 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.314316 | 0.0181774 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.64961 | 0.440916 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.11083 | −0.349905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9804 | −0.854977 | −0.427489 | − | 0.904021i | \(-0.640602\pi\) | ||||
−0.427489 | + | 0.904021i | \(0.640602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.4300 | −1.15848 | −0.579240 | − | 0.815157i | \(-0.696650\pi\) | ||||
−0.579240 | + | 0.815157i | \(0.696650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.9100 | −1.35147 | −0.675737 | − | 0.737143i | \(-0.736174\pi\) | ||||
−0.675737 | + | 0.737143i | \(0.736174\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.2140 | 1.86548 | 0.932742 | − | 0.360545i | \(-0.117409\pi\) | ||||
0.932742 | + | 0.360545i | \(0.117409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.275144 | 0.0154051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.47226 | 0.415768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.71951 | −0.0953812 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.6555 | 0.697720 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.42341 | 0.408028 | 0.204014 | − | 0.978968i | \(-0.434601\pi\) | ||||
0.204014 | + | 0.978968i | \(0.434601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.21953 | −0.121266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.69696 | 0.528227 | 0.264113 | − | 0.964492i | \(-0.414921\pi\) | ||||
0.264113 | + | 0.964492i | \(0.414921\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.1821 | 0.659700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3676 | 0.937765 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.199217 | 0.0106945 | 0.00534727 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534727 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.73705 | −0.521213 | −0.260606 | − | 0.965445i | \(-0.583922\pi\) | ||||
−0.260606 | + | 0.965445i | \(0.583922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.40523 | 0.181242 | 0.0906211 | − | 0.995885i | \(-0.471115\pi\) | ||||
0.0906211 | + | 0.995885i | \(0.471115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.86550 | 0.258234 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.89035 | 0.416437 | 0.208218 | − | 0.978082i | \(-0.433234\pi\) | ||||
0.208218 | + | 0.978082i | \(0.433234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7569 | −0.881941 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.85208 | 0.463339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6686 | 1.02669 | 0.513347 | − | 0.858181i | \(-0.328405\pi\) | ||||
0.513347 | + | 0.858181i | \(0.328405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 33.9199 | 1.76103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4806 | −1.31934 | −0.659668 | − | 0.751557i | \(-0.729303\pi\) | ||||
−0.659668 | + | 0.751557i | \(0.729303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0332875 | 0.00171439 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.19297 | −0.318111 | −0.159056 | − | 0.987270i | \(-0.550845\pi\) | ||||
−0.159056 | + | 0.987270i | \(0.550845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.93978 | 0.303509 | 0.151754 | − | 0.988418i | \(-0.451508\pi\) | ||||
0.151754 | + | 0.988418i | \(0.451508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.8958 | −1.62556 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.9031 | 0.552810 | 0.276405 | − | 0.961041i | \(-0.410857\pi\) | ||||
0.276405 | + | 0.961041i | \(0.410857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.33212 | 0.168513 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.8046 | 0.795214 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.455424 | 0.0228571 | 0.0114285 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114285 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.94773 | 0.0972652 | 0.0486326 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486326 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.47382 | 0.0734163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.39833 | 0.317154 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.36458 | −0.215815 | −0.107907 | − | 0.994161i | \(-0.534415\pi\) | ||||
−0.107907 | + | 0.994161i | \(0.534415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.3674 | 1.64190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.8475 | −1.61242 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.0315 | −1.07631 | −0.538154 | − | 0.842847i | \(-0.680878\pi\) | ||||
−0.538154 | + | 0.842847i | \(0.680878\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.2357 | −1.57107 | −0.785535 | − | 0.618817i | \(-0.787612\pi\) | ||||
−0.785535 | + | 0.618817i | \(0.787612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.2288 | −0.884228 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.79004 | −0.280200 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.42440 | 0.261284 | 0.130642 | − | 0.991430i | \(-0.458296\pi\) | ||||
0.130642 | + | 0.991430i | \(0.458296\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.20893 | −0.442553 | −0.221276 | − | 0.975211i | \(-0.571022\pi\) | ||||
−0.221276 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00028 | 0.0478499 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.4748 | −1.54994 | −0.774969 | − | 0.632000i | \(-0.782234\pi\) | ||||
−0.774969 | + | 0.632000i | \(0.782234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.613271 | −0.0291374 | −0.0145687 | − | 0.999894i | \(-0.504638\pi\) | ||||
−0.0145687 | + | 0.999894i | \(0.504638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.6783 | −1.26467 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.30511 | 0.203171 | 0.101585 | − | 0.994827i | \(-0.467608\pi\) | ||||
0.101585 | + | 0.994827i | \(0.467608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.4370 | 1.48031 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.85882 | −0.180904 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.40530 | −0.252849 | −0.126425 | − | 0.991976i | \(-0.540350\pi\) | ||||
−0.126425 | + | 0.991976i | \(0.540350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5751 | 0.818552 | 0.409276 | − | 0.912411i | \(-0.365781\pi\) | ||||
0.409276 | + | 0.912411i | \(0.365781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.3864 | −1.04038 | −0.520192 | − | 0.854049i | \(-0.674140\pi\) | ||||
−0.520192 | + | 0.854049i | \(0.674140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8757 | 0.919736 | 0.459868 | − | 0.887987i | \(-0.347897\pi\) | ||||
0.459868 | + | 0.887987i | \(0.347897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.10301 | −0.0971081 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6760 | 0.490882 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.47217 | −0.251080 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2738 | −0.880643 | −0.440321 | − | 0.897840i | \(-0.645135\pi\) | ||||
−0.440321 | + | 0.897840i | \(0.645135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.774084 | 0.0352952 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.95725 | −0.315913 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.9329 | −0.948558 | −0.474279 | − | 0.880375i | \(-0.657291\pi\) | ||||
−0.474279 | + | 0.880375i | \(0.657291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.4989 | 0.925104 | 0.462552 | − | 0.886592i | \(-0.346934\pi\) | ||||
0.462552 | + | 0.886592i | \(0.346934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.352887 | 0.0158932 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.61008 | 0.206791 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.8985 | 1.56227 | 0.781136 | − | 0.624361i | \(-0.214640\pi\) | ||||
0.781136 | + | 0.624361i | \(0.214640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7974 | −0.615196 | −0.307598 | − | 0.951516i | \(-0.599525\pi\) | ||||
−0.307598 | + | 0.951516i | \(0.599525\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.9497 | 2.26723 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.0627 | −1.59845 | −0.799225 | − | 0.601031i | \(-0.794757\pi\) | ||||
−0.799225 | + | 0.601031i | \(0.794757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.38738 | 0.371036 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.58589 | −0.158013 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.6623 | 0.776787 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3865 | −0.761716 | −0.380858 | − | 0.924634i | \(-0.624371\pi\) | ||||
−0.380858 | + | 0.924634i | \(0.624371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.03478 | −0.176429 | −0.0882143 | − | 0.996102i | \(-0.528116\pi\) | ||||
−0.0882143 | + | 0.996102i | \(0.528116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6243 | 0.680604 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5539 | −0.980606 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.80331 | 0.164740 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.986901 | 0.0426674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.99135 | −0.128847 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0954 | 0.992951 | 0.496475 | − | 0.868051i | \(-0.334627\pi\) | ||||
0.496475 | + | 0.868051i | \(0.334627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.2905 | −2.19704 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.7888 | −0.632322 | −0.316161 | − | 0.948706i | \(-0.602394\pi\) | ||||
−0.316161 | + | 0.948706i | \(0.602394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.105934 | 0.00451295 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9749 | 0.636797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.2860 | 1.70697 | 0.853486 | − | 0.521116i | \(-0.174484\pi\) | ||||
0.853486 | + | 0.521116i | \(0.174484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.29160 | 0.0546290 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.767368 | 0.0323407 | 0.0161704 | − | 0.999869i | \(-0.494853\pi\) | ||||
0.0161704 | + | 0.999869i | \(0.494853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0500 | −0.422805 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.5129 | −0.985713 | −0.492857 | − | 0.870110i | \(-0.664047\pi\) | ||||
−0.492857 | + | 0.870110i | \(0.664047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.332900 | 0.0139314 | 0.00696571 | − | 0.999976i | \(-0.497783\pi\) | ||||
0.00696571 | + | 0.999976i | \(0.497783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.44022 | −0.101764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.29804 | 0.387082 | 0.193541 | − | 0.981092i | \(-0.438003\pi\) | ||||
0.193541 | + | 0.981092i | \(0.438003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.1232 | −1.29121 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.3393 | 1.96059 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.6733 | 0.770729 | 0.385364 | − | 0.922764i | \(-0.374076\pi\) | ||||
0.385364 | + | 0.922764i | \(0.374076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.69029 | 0.193260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.71101 | −0.275588 | −0.137794 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137794 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −40.9081 | −1.67707 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.80833 | −0.319040 | −0.159520 | − | 0.987195i | \(-0.550995\pi\) | ||||
−0.159520 | + | 0.987195i | \(0.550995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.6693 | −0.965493 | −0.482746 | − | 0.875760i | \(-0.660361\pi\) | ||||
−0.482746 | + | 0.875760i | \(0.660361\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.1556 | −0.494194 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9861 | 0.811210 | 0.405605 | − | 0.914048i | \(-0.367061\pi\) | ||||
0.405605 | + | 0.914048i | \(0.367061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.13682 | 0.0864466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.0681 | 1.01249 | 0.506246 | − | 0.862389i | \(-0.331033\pi\) | ||||
0.506246 | + | 0.862389i | \(0.331033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −48.1170 | −1.93712 | −0.968559 | − | 0.248784i | \(-0.919969\pi\) | ||||
−0.968559 | + | 0.248784i | \(0.919969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1162 | −0.969311 | −0.484655 | − | 0.874705i | \(-0.661055\pi\) | ||||
−0.484655 | + | 0.874705i | \(0.661055\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.2778 | −1.01273 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9190 | −1.19676 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.20621 | 0.327203 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8844 | 1.70720 | 0.853601 | − | 0.520927i | \(-0.174414\pi\) | ||||
0.853601 | + | 0.520927i | \(0.174414\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.0528 | −1.74818 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.361901 | −0.0143390 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.9879 | −1.46094 | −0.730468 | − | 0.682947i | \(-0.760698\pi\) | ||||
−0.730468 | + | 0.682947i | \(0.760698\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.90122 | −0.311594 | −0.155797 | − | 0.987789i | \(-0.549795\pi\) | ||||
−0.155797 | + | 0.987789i | \(0.549795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.01646 | 0.315160 | 0.157580 | − | 0.987506i | \(-0.449631\pi\) | ||||
0.157580 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.5682 | 1.82796 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.2813 | −0.676271 | −0.338136 | − | 0.941097i | \(-0.609796\pi\) | ||||
−0.338136 | + | 0.941097i | \(0.609796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.8965 | −1.20723 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.9189 | 1.00966 | 0.504829 | − | 0.863220i | \(-0.331556\pi\) | ||||
0.504829 | + | 0.863220i | \(0.331556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8718 | −0.850715 | −0.425357 | − | 0.905026i | \(-0.639852\pi\) | ||||
−0.425357 | + | 0.905026i | \(0.639852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.2803 | −0.476210 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0472395 | 0.00182912 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.08071 | −0.311952 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1707 | −0.700429 | −0.350214 | − | 0.936670i | \(-0.613891\pi\) | ||||
−0.350214 | + | 0.936670i | \(0.613891\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.6866 | 1.06408 | 0.532041 | − | 0.846719i | \(-0.321425\pi\) | ||||
0.532041 | + | 0.846719i | \(0.321425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.59203 | −0.252979 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.55246 | 0.288987 | 0.144493 | − | 0.989506i | \(-0.453845\pi\) | ||||
0.144493 | + | 0.989506i | \(0.453845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.8285 | 1.52177 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.72721 | 0.218189 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7496 | −0.713270 | −0.356635 | − | 0.934244i | \(-0.616076\pi\) | ||||
−0.356635 | + | 0.934244i | \(0.616076\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.5944 | −1.23637 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.3196 | 1.52721 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.15605 | 0.270280 | 0.135140 | − | 0.990826i | \(-0.456852\pi\) | ||||
0.135140 | + | 0.990826i | \(0.456852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.46345 | 0.0929107 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.2750 | 1.81557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.03676 | 0.264271 | 0.132136 | − | 0.991232i | \(-0.457817\pi\) | ||||
0.132136 | + | 0.991232i | \(0.457817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.09155 | 0.0783293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.38546 | −0.201405 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.0939 | 1.30878 | 0.654392 | − | 0.756156i | \(-0.272925\pi\) | ||||
0.654392 | + | 0.756156i | \(0.272925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.39765 | −0.126535 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.258430 | −0.00959784 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.9195 | 0.479160 | 0.239580 | − | 0.970877i | \(-0.422990\pi\) | ||||
0.239580 | + | 0.970877i | \(0.422990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.6925 | 0.506436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.6248 | −1.94374 | −0.971871 | − | 0.235516i | \(-0.924322\pi\) | ||||
−0.971871 | + | 0.235516i | \(0.924322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.93501 | −0.108113 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3792 | −0.492161 | −0.246081 | − | 0.969249i | \(-0.579143\pi\) | ||||
−0.246081 | + | 0.969249i | \(0.579143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.76762 | 0.248280 | 0.124140 | − | 0.992265i | \(-0.460383\pi\) | ||||
0.124140 | + | 0.992265i | \(0.460383\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.5569 | 1.66908 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.935093 | 0.0341676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8195 | 0.832694 | 0.416347 | − | 0.909206i | \(-0.363310\pi\) | ||||
0.416347 | + | 0.909206i | \(0.363310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −57.5653 | −2.09502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.27356 | −0.191671 | −0.0958353 | − | 0.995397i | \(-0.530552\pi\) | ||||
−0.0958353 | + | 0.995397i | \(0.530552\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.9457 | −0.578030 | −0.289015 | − | 0.957325i | \(-0.593328\pi\) | ||||
−0.289015 | + | 0.957325i | \(0.593328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.5980 | −1.75936 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.63392 | 0.203429 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.46687 | −0.0528968 | −0.0264484 | − | 0.999650i | \(-0.508420\pi\) | ||||
−0.0264484 | + | 0.999650i | \(0.508420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.0752 | 0.758022 | 0.379011 | − | 0.925392i | \(-0.376264\pi\) | ||||
0.379011 | + | 0.925392i | \(0.376264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.4421 | −0.411013 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1037 | 0.433659 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.43394 | 0.230224 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.05802 | 0.0377622 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1679 | 0.968431 | 0.484216 | − | 0.874949i | \(-0.339105\pi\) | ||||
0.484216 | + | 0.874949i | \(0.339105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.52239 | −0.338577 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.977622 | −0.0347164 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.1742 | −0.997982 | −0.498991 | − | 0.866607i | \(-0.666296\pi\) | ||||
−0.498991 | + | 0.866607i | \(0.666296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6528 | 0.801400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7056 | 0.413082 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.47619 | −0.193010 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.25972 | 0.255238 | 0.127619 | − | 0.991823i | \(-0.459267\pi\) | ||||
0.127619 | + | 0.991823i | \(0.459267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.87841 | 0.241534 | 0.120767 | − | 0.992681i | \(-0.461465\pi\) | ||||
0.120767 | + | 0.992681i | \(0.461465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.30280 | 0.115692 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.11040 | 0.143805 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.5748 | −1.38117 | −0.690585 | − | 0.723251i | \(-0.742647\pi\) | ||||
−0.690585 | + | 0.723251i | \(0.742647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.1407 | −1.29464 | −0.647322 | − | 0.762217i | \(-0.724111\pi\) | ||||
−0.647322 | + | 0.762217i | \(0.724111\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.4433 | 0.884750 | 0.442375 | − | 0.896830i | \(-0.354136\pi\) | ||||
0.442375 | + | 0.896830i | \(0.354136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.2955 | −0.878549 | −0.439275 | − | 0.898353i | \(-0.644764\pi\) | ||||
−0.439275 | + | 0.898353i | \(0.644764\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.83657 | −0.132929 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.94172 | −0.101802 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.1828 | −1.00750 | −0.503751 | − | 0.863849i | \(-0.668047\pi\) | ||||
−0.503751 | + | 0.863849i | \(0.668047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9950 | −0.999827 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.5908 | 1.29316 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.5175 | −0.395744 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09853 | 0.0376572 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2876 | −0.454957 | −0.227479 | − | 0.973783i | \(-0.573048\pi\) | ||||
−0.227479 | + | 0.973783i | \(0.573048\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4648 | −0.459949 | −0.229975 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229975 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.3283 | −0.727711 | −0.363856 | − | 0.931455i | \(-0.618540\pi\) | ||||
−0.363856 | + | 0.931455i | \(0.618540\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.5371 | 1.10758 | 0.553788 | − | 0.832658i | \(-0.313182\pi\) | ||||
0.553788 | + | 0.832658i | \(0.313182\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.5860 | 1.20996 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.8993 | 0.708960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.355084 | −0.0120316 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0389 | −0.373182 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0045 | 0.878109 | 0.439054 | − | 0.898460i | \(-0.355314\pi\) | ||||
0.439054 | + | 0.898460i | \(0.355314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.9012 | 1.44538 | 0.722689 | − | 0.691173i | \(-0.242906\pi\) | ||||
0.722689 | + | 0.691173i | \(0.242906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0829 | 1.34890 | 0.674449 | − | 0.738322i | \(-0.264381\pi\) | ||||
0.674449 | + | 0.738322i | \(0.264381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.80878 | −0.195040 | −0.0975198 | − | 0.995234i | \(-0.531091\pi\) | ||||
−0.0975198 | + | 0.995234i | \(0.531091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.7402 | −1.39992 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.80022 | 0.227561 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.09079 | 0.0698873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.221505 | 0.00738760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.7153 | 2.02272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.0806 | −1.56501 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.8347 | 0.924235 | 0.462117 | − | 0.886819i | \(-0.347090\pi\) | ||||
0.462117 | + | 0.886819i | \(0.347090\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.44183 | −0.246559 | −0.123279 | − | 0.992372i | \(-0.539341\pi\) | ||||
−0.123279 | + | 0.992372i | \(0.539341\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.4362 | −1.43753 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.2746 | −0.966731 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8849 | 0.952823 | 0.476412 | − | 0.879222i | \(-0.341937\pi\) | ||||
0.476412 | + | 0.879222i | \(0.341937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.778391 | 0.0256211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00966 | −0.197596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.25814 | −0.205323 | −0.102661 | − | 0.994716i | \(-0.532736\pi\) | ||||
−0.102661 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.15171 | −0.0377459 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −57.0922 | −1.86712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.4567 | −1.28899 | −0.644497 | − | 0.764607i | \(-0.722933\pi\) | ||||
−0.644497 | + | 0.764607i | \(0.722933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.6685 | 1.68434 | 0.842172 | − | 0.539209i | \(-0.181277\pi\) | ||||
0.842172 | + | 0.539209i | \(0.181277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.39742 | 0.175764 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.2141 | 1.01432 | 0.507161 | − | 0.861851i | \(-0.330695\pi\) | ||||
0.507161 | + | 0.861851i | \(0.330695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.41617 | 0.0459709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.5537 | −1.57281 | −0.786404 | − | 0.617712i | \(-0.788060\pi\) | ||||
−0.786404 | + | 0.617712i | \(0.788060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.2231 | 0.557327 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.7377 | 1.21861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.1927 | −0.683637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.1083 | 0.776074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.2557 | −0.619221 | −0.309610 | − | 0.950864i | \(-0.600199\pi\) | ||||
−0.309610 | + | 0.950864i | \(0.600199\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.8442 | −0.765195 | −0.382598 | − | 0.923915i | \(-0.624970\pi\) | ||||
−0.382598 | + | 0.923915i | \(0.624970\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.8833 | −0.990073 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.7167 | −0.822749 | −0.411374 | − | 0.911466i | \(-0.634951\pi\) | ||||
−0.411374 | + | 0.911466i | \(0.634951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.2782 | −1.12750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.0660 | −0.927061 | −0.463531 | − | 0.886081i | \(-0.653418\pi\) | ||||
−0.463531 | + | 0.886081i | \(0.653418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8950 | −0.538318 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.83296 | 0.0582847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0081 | −0.572047 | −0.286024 | − | 0.958223i | \(-0.592334\pi\) | ||||
−0.286024 | + | 0.958223i | \(0.592334\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.7910 | 1.19806 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7841 | −0.436547 | −0.218274 | − | 0.975888i | \(-0.570043\pi\) | ||||
−0.218274 | + | 0.975888i | \(0.570043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6012.2.a.i.1.3 | 9 | ||
3.2 | odd | 2 | 2004.2.a.c.1.7 | ✓ | 9 | ||
12.11 | even | 2 | 8016.2.a.bc.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.7 | ✓ | 9 | 3.2 | odd | 2 | ||
6012.2.a.i.1.3 | 9 | 1.1 | even | 1 | trivial | ||
8016.2.a.bc.1.7 | 9 | 12.11 | even | 2 |