Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 26x^{16} + 281x^{14} - 1632x^{12} + 5482x^{10} - 10620x^{8} + 11052x^{6} - 5165x^{4} + 760x^{2} - 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.14790\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.14790 | 1.51879 | 0.759397 | − | 0.650628i | \(-0.225494\pi\) | ||||
0.759397 | + | 0.650628i | \(0.225494\pi\) | |||||||
\(3\) | −2.37435 | −1.37083 | −0.685416 | − | 0.728152i | \(-0.740379\pi\) | ||||
−0.685416 | + | 0.728152i | \(0.740379\pi\) | |||||||
\(4\) | 2.61347 | 1.30673 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.09986 | −2.08201 | ||||||||
\(7\) | 3.54879 | 1.34132 | 0.670658 | − | 0.741767i | \(-0.266012\pi\) | ||||
0.670658 | + | 0.741767i | \(0.266012\pi\) | |||||||
\(8\) | 1.31766 | 0.465865 | ||||||||
\(9\) | 2.63754 | 0.879179 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.08852 | −0.629713 | −0.314857 | − | 0.949139i | \(-0.601956\pi\) | ||||
−0.314857 | + | 0.949139i | \(0.601956\pi\) | |||||||
\(12\) | −6.20528 | −1.79131 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 7.62244 | 2.03718 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.39672 | −0.599181 | ||||||||
\(17\) | −6.00072 | −1.45539 | −0.727695 | − | 0.685901i | \(-0.759408\pi\) | ||||
−0.727695 | + | 0.685901i | \(0.759408\pi\) | |||||||
\(18\) | 5.66516 | 1.33529 | ||||||||
\(19\) | 5.04725 | 1.15792 | 0.578959 | − | 0.815357i | \(-0.303459\pi\) | ||||
0.578959 | + | 0.815357i | \(0.303459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.42607 | −1.83872 | ||||||||
\(22\) | −4.48593 | −0.956405 | ||||||||
\(23\) | −2.12673 | −0.443454 | −0.221727 | − | 0.975109i | \(-0.571169\pi\) | ||||
−0.221727 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(24\) | −3.12860 | −0.638622 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.860615 | 0.165625 | ||||||||
\(28\) | 9.27464 | 1.75274 | ||||||||
\(29\) | −10.1431 | −1.88352 | −0.941762 | − | 0.336281i | \(-0.890831\pi\) | ||||
−0.941762 | + | 0.336281i | \(0.890831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.10862 | −0.558324 | −0.279162 | − | 0.960244i | \(-0.590057\pi\) | ||||
−0.279162 | + | 0.960244i | \(0.590057\pi\) | |||||||
\(32\) | −7.78325 | −1.37590 | ||||||||
\(33\) | 4.95888 | 0.863231 | ||||||||
\(34\) | −12.8889 | −2.21044 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.89311 | 1.14885 | ||||||||
\(37\) | −0.0998988 | −0.0164233 | −0.00821163 | − | 0.999966i | \(-0.502614\pi\) | ||||
−0.00821163 | + | 0.999966i | \(0.502614\pi\) | |||||||
\(38\) | 10.8410 | 1.75864 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.79617 | −0.592862 | −0.296431 | − | 0.955054i | \(-0.595797\pi\) | ||||
−0.296431 | + | 0.955054i | \(0.595797\pi\) | |||||||
\(42\) | −18.0983 | −2.79263 | ||||||||
\(43\) | 2.11661 | 0.322779 | 0.161390 | − | 0.986891i | \(-0.448402\pi\) | ||||
0.161390 | + | 0.986891i | \(0.448402\pi\) | |||||||
\(44\) | −5.45829 | −0.822868 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.56800 | −0.673515 | ||||||||
\(47\) | 5.00374 | 0.729870 | 0.364935 | − | 0.931033i | \(-0.381091\pi\) | ||||
0.364935 | + | 0.931033i | \(0.381091\pi\) | |||||||
\(48\) | 5.69066 | 0.821376 | ||||||||
\(49\) | 5.59390 | 0.799129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.2478 | 1.99509 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.29557 | −0.727402 | −0.363701 | − | 0.931516i | \(-0.618487\pi\) | ||||
−0.363701 | + | 0.931516i | \(0.618487\pi\) | |||||||
\(54\) | 1.84851 | 0.251551 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.67611 | 0.624872 | ||||||||
\(57\) | −11.9839 | −1.58731 | ||||||||
\(58\) | −21.7863 | −2.86068 | ||||||||
\(59\) | 3.00358 | 0.391033 | 0.195517 | − | 0.980700i | \(-0.437362\pi\) | ||||
0.195517 | + | 0.980700i | \(0.437362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.76673 | −0.610317 | −0.305158 | − | 0.952302i | \(-0.598709\pi\) | ||||
−0.305158 | + | 0.952302i | \(0.598709\pi\) | |||||||
\(62\) | −6.67699 | −0.847979 | ||||||||
\(63\) | 9.36006 | 1.17926 | ||||||||
\(64\) | −11.9242 | −1.49052 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.6512 | 1.31107 | ||||||||
\(67\) | 6.77655 | 0.827887 | 0.413944 | − | 0.910303i | \(-0.364151\pi\) | ||||
0.413944 | + | 0.910303i | \(0.364151\pi\) | |||||||
\(68\) | −15.6827 | −1.90181 | ||||||||
\(69\) | 5.04961 | 0.607901 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.89593 | 0.581040 | 0.290520 | − | 0.956869i | \(-0.406172\pi\) | ||||
0.290520 | + | 0.956869i | \(0.406172\pi\) | |||||||
\(72\) | 3.47539 | 0.409578 | ||||||||
\(73\) | 4.02118 | 0.470643 | 0.235321 | − | 0.971918i | \(-0.424386\pi\) | ||||
0.235321 | + | 0.971918i | \(0.424386\pi\) | |||||||
\(74\) | −0.214573 | −0.0249436 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.1908 | 1.51309 | ||||||||
\(77\) | −7.41173 | −0.844645 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.71456 | −0.530429 | −0.265215 | − | 0.964189i | \(-0.585443\pi\) | ||||
−0.265215 | + | 0.964189i | \(0.585443\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.95601 | −1.10622 | ||||||||
\(82\) | −8.15379 | −0.900436 | ||||||||
\(83\) | −11.2703 | −1.23707 | −0.618536 | − | 0.785757i | \(-0.712274\pi\) | ||||
−0.618536 | + | 0.785757i | \(0.712274\pi\) | |||||||
\(84\) | −22.0212 | −2.40271 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.54625 | 0.490235 | ||||||||
\(87\) | 24.0832 | 2.58199 | ||||||||
\(88\) | −2.75197 | −0.293361 | ||||||||
\(89\) | −1.90467 | −0.201895 | −0.100948 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100948 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.55814 | −0.579477 | ||||||||
\(93\) | 7.38094 | 0.765368 | ||||||||
\(94\) | 10.7475 | 1.10852 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 18.4802 | 1.88612 | ||||||||
\(97\) | −5.36940 | −0.545180 | −0.272590 | − | 0.962130i | \(-0.587880\pi\) | ||||
−0.272590 | + | 0.962130i | \(0.587880\pi\) | |||||||
\(98\) | 12.0151 | 1.21371 | ||||||||
\(99\) | −5.50856 | −0.553631 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2109 | −1.11553 | −0.557765 | − | 0.829999i | \(-0.688341\pi\) | ||||
−0.557765 | + | 0.829999i | \(0.688341\pi\) | |||||||
\(102\) | 30.6029 | 3.03013 | ||||||||
\(103\) | −11.8123 | −1.16390 | −0.581951 | − | 0.813224i | \(-0.697710\pi\) | ||||
−0.581951 | + | 0.813224i | \(0.697710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.3743 | −1.10477 | ||||||||
\(107\) | 5.51439 | 0.533097 | 0.266548 | − | 0.963822i | \(-0.414117\pi\) | ||||
0.266548 | + | 0.963822i | \(0.414117\pi\) | |||||||
\(108\) | 2.24919 | 0.216428 | ||||||||
\(109\) | 12.0982 | 1.15880 | 0.579401 | − | 0.815043i | \(-0.303287\pi\) | ||||
0.579401 | + | 0.815043i | \(0.303287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.237195 | 0.0225135 | ||||||||
\(112\) | −8.50547 | −0.803691 | ||||||||
\(113\) | −5.96413 | −0.561058 | −0.280529 | − | 0.959846i | \(-0.590510\pi\) | ||||
−0.280529 | + | 0.959846i | \(0.590510\pi\) | |||||||
\(114\) | −25.7403 | −2.41080 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −26.5086 | −2.46126 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.45139 | 0.593898 | ||||||||
\(119\) | −21.2953 | −1.95214 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.63807 | −0.603461 | ||||||||
\(122\) | −10.2384 | −0.926945 | ||||||||
\(123\) | 9.01344 | 0.812714 | ||||||||
\(124\) | −8.12427 | −0.729581 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20.1045 | 1.79105 | ||||||||
\(127\) | −11.9901 | −1.06395 | −0.531973 | − | 0.846761i | \(-0.678549\pi\) | ||||
−0.531973 | + | 0.846761i | \(0.678549\pi\) | |||||||
\(128\) | −10.0454 | −0.887899 | ||||||||
\(129\) | −5.02556 | −0.442476 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.5464 | −1.70777 | −0.853886 | − | 0.520459i | \(-0.825761\pi\) | ||||
−0.853886 | + | 0.520459i | \(0.825761\pi\) | |||||||
\(132\) | 12.9599 | 1.12801 | ||||||||
\(133\) | 17.9116 | 1.55313 | ||||||||
\(134\) | 14.5553 | 1.25739 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.90694 | −0.678015 | ||||||||
\(137\) | 12.8391 | 1.09692 | 0.548461 | − | 0.836176i | \(-0.315214\pi\) | ||||
0.548461 | + | 0.836176i | \(0.315214\pi\) | |||||||
\(138\) | 10.8460 | 0.923276 | ||||||||
\(139\) | 5.38253 | 0.456540 | 0.228270 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228270 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8806 | −1.00053 | ||||||||
\(142\) | 10.5160 | 0.882479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.32145 | −0.526787 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.63708 | 0.714809 | ||||||||
\(147\) | −13.2819 | −1.09547 | ||||||||
\(148\) | −0.261082 | −0.0214608 | ||||||||
\(149\) | −15.5515 | −1.27403 | −0.637013 | − | 0.770853i | \(-0.719830\pi\) | ||||
−0.637013 | + | 0.770853i | \(0.719830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6494 | −0.948012 | −0.474006 | − | 0.880522i | \(-0.657192\pi\) | ||||
−0.474006 | + | 0.880522i | \(0.657192\pi\) | |||||||
\(152\) | 6.65058 | 0.539433 | ||||||||
\(153\) | −15.8271 | −1.27955 | ||||||||
\(154\) | −15.9196 | −1.28284 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.02732 | −0.161798 | −0.0808989 | − | 0.996722i | \(-0.525779\pi\) | ||||
−0.0808989 | + | 0.996722i | \(0.525779\pi\) | |||||||
\(158\) | −10.1264 | −0.805613 | ||||||||
\(159\) | 12.5735 | 0.997146 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.54732 | −0.594812 | ||||||||
\(162\) | −21.3845 | −1.68012 | ||||||||
\(163\) | 8.48371 | 0.664495 | 0.332248 | − | 0.943192i | \(-0.392193\pi\) | ||||
0.332248 | + | 0.943192i | \(0.392193\pi\) | |||||||
\(164\) | −9.92117 | −0.774713 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.2074 | −1.87886 | ||||||||
\(167\) | −4.52950 | −0.350503 | −0.175252 | − | 0.984524i | \(-0.556074\pi\) | ||||
−0.175252 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(168\) | −11.1027 | −0.856594 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.3123 | 1.01802 | ||||||||
\(172\) | 5.53168 | 0.421787 | ||||||||
\(173\) | −1.03121 | −0.0784013 | −0.0392006 | − | 0.999231i | \(-0.512481\pi\) | ||||
−0.0392006 | + | 0.999231i | \(0.512481\pi\) | |||||||
\(174\) | 51.7283 | 3.92151 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00561 | 0.377312 | ||||||||
\(177\) | −7.13155 | −0.536040 | ||||||||
\(178\) | −4.09105 | −0.306637 | ||||||||
\(179\) | −17.4031 | −1.30077 | −0.650386 | − | 0.759604i | \(-0.725393\pi\) | ||||
−0.650386 | + | 0.759604i | \(0.725393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.2540 | −1.65412 | −0.827062 | − | 0.562111i | \(-0.809989\pi\) | ||||
−0.827062 | + | 0.562111i | \(0.809989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3179 | 0.836642 | ||||||||
\(184\) | −2.80232 | −0.206590 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.8535 | 1.16244 | ||||||||
\(187\) | 12.5326 | 0.916478 | ||||||||
\(188\) | 13.0771 | 0.953746 | ||||||||
\(189\) | 3.05414 | 0.222156 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.05937 | −0.510798 | −0.255399 | − | 0.966836i | \(-0.582207\pi\) | ||||
−0.255399 | + | 0.966836i | \(0.582207\pi\) | |||||||
\(192\) | 28.3122 | 2.04325 | ||||||||
\(193\) | 21.7870 | 1.56826 | 0.784130 | − | 0.620596i | \(-0.213109\pi\) | ||||
0.784130 | + | 0.620596i | \(0.213109\pi\) | |||||||
\(194\) | −11.5329 | −0.828016 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.6195 | 1.04425 | ||||||||
\(197\) | 22.4438 | 1.59905 | 0.799526 | − | 0.600631i | \(-0.205084\pi\) | ||||
0.799526 | + | 0.600631i | \(0.205084\pi\) | |||||||
\(198\) | −11.8318 | −0.840851 | ||||||||
\(199\) | −12.2097 | −0.865520 | −0.432760 | − | 0.901509i | \(-0.642460\pi\) | ||||
−0.432760 | + | 0.901509i | \(0.642460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0899 | −1.13489 | ||||||||
\(202\) | −24.0800 | −1.69426 | ||||||||
\(203\) | −35.9957 | −2.52640 | ||||||||
\(204\) | 37.2362 | 2.60705 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −25.3716 | −1.76773 | ||||||||
\(207\) | −5.60933 | −0.389876 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5413 | −0.729156 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3180 | 1.19222 | 0.596111 | − | 0.802902i | \(-0.296712\pi\) | ||||
0.596111 | + | 0.802902i | \(0.296712\pi\) | |||||||
\(212\) | −13.8398 | −0.950521 | ||||||||
\(213\) | −11.6246 | −0.796507 | ||||||||
\(214\) | 11.8444 | 0.809664 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.13400 | 0.0771591 | ||||||||
\(217\) | −11.0318 | −0.748889 | ||||||||
\(218\) | 25.9858 | 1.75998 | ||||||||
\(219\) | −9.54768 | −0.645172 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.509470 | 0.0341934 | ||||||||
\(223\) | −5.28335 | −0.353800 | −0.176900 | − | 0.984229i | \(-0.556607\pi\) | ||||
−0.176900 | + | 0.984229i | \(0.556607\pi\) | |||||||
\(224\) | −27.6211 | −1.84551 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.8103 | −0.852131 | ||||||||
\(227\) | 2.94943 | 0.195760 | 0.0978802 | − | 0.995198i | \(-0.468794\pi\) | ||||
0.0978802 | + | 0.995198i | \(0.468794\pi\) | |||||||
\(228\) | −31.3196 | −2.07419 | ||||||||
\(229\) | 3.09371 | 0.204438 | 0.102219 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102219 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.5980 | 1.15787 | ||||||||
\(232\) | −13.3652 | −0.877467 | ||||||||
\(233\) | 6.38449 | 0.418262 | 0.209131 | − | 0.977888i | \(-0.432937\pi\) | ||||
0.209131 | + | 0.977888i | \(0.432937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.84976 | 0.510976 | ||||||||
\(237\) | 11.1940 | 0.727129 | ||||||||
\(238\) | −45.7401 | −2.96489 | ||||||||
\(239\) | −23.8468 | −1.54252 | −0.771260 | − | 0.636521i | \(-0.780373\pi\) | ||||
−0.771260 | + | 0.636521i | \(0.780373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5319 | 1.77349 | 0.886744 | − | 0.462261i | \(-0.152962\pi\) | ||||
0.886744 | + | 0.462261i | \(0.152962\pi\) | |||||||
\(242\) | −14.2579 | −0.916533 | ||||||||
\(243\) | 21.0572 | 1.35082 | ||||||||
\(244\) | −12.4577 | −0.797522 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.3600 | 1.23435 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.09611 | −0.260104 | ||||||||
\(249\) | 26.7595 | 1.69582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.230820 | 0.0145692 | 0.00728462 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728462 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(252\) | 24.4622 | 1.54097 | ||||||||
\(253\) | 4.44173 | 0.279249 | ||||||||
\(254\) | −25.7534 | −1.61591 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.27181 | 0.141988 | ||||||||
\(257\) | 12.9414 | 0.807260 | 0.403630 | − | 0.914922i | \(-0.367748\pi\) | ||||
0.403630 | + | 0.914922i | \(0.367748\pi\) | |||||||
\(258\) | −10.7944 | −0.672030 | ||||||||
\(259\) | −0.354520 | −0.0220288 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.7528 | −1.65595 | ||||||||
\(262\) | −41.9836 | −2.59375 | ||||||||
\(263\) | 9.89693 | 0.610271 | 0.305135 | − | 0.952309i | \(-0.401298\pi\) | ||||
0.305135 | + | 0.952309i | \(0.401298\pi\) | |||||||
\(264\) | 6.53415 | 0.402149 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 38.4723 | 2.35889 | ||||||||
\(267\) | 4.52236 | 0.276764 | ||||||||
\(268\) | 17.7103 | 1.08183 | ||||||||
\(269\) | 12.6400 | 0.770674 | 0.385337 | − | 0.922776i | \(-0.374085\pi\) | ||||
0.385337 | + | 0.922776i | \(0.374085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4775 | −1.18318 | −0.591588 | − | 0.806240i | \(-0.701499\pi\) | ||||
−0.591588 | + | 0.806240i | \(0.701499\pi\) | |||||||
\(272\) | 14.3821 | 0.872042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.5772 | 1.66600 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.1970 | 0.794365 | ||||||||
\(277\) | 27.8610 | 1.67401 | 0.837004 | − | 0.547197i | \(-0.184305\pi\) | ||||
0.837004 | + | 0.547197i | \(0.184305\pi\) | |||||||
\(278\) | 11.5611 | 0.693390 | ||||||||
\(279\) | −8.19909 | −0.490867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0533 | 1.31559 | 0.657796 | − | 0.753197i | \(-0.271489\pi\) | ||||
0.657796 | + | 0.753197i | \(0.271489\pi\) | |||||||
\(282\) | −25.5184 | −1.51960 | ||||||||
\(283\) | −25.1358 | −1.49417 | −0.747083 | − | 0.664730i | \(-0.768546\pi\) | ||||
−0.747083 | + | 0.664730i | \(0.768546\pi\) | |||||||
\(284\) | 12.7953 | 0.759264 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4718 | −0.795216 | ||||||||
\(288\) | −20.5286 | −1.20966 | ||||||||
\(289\) | 19.0087 | 1.11816 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7488 | 0.747350 | ||||||||
\(292\) | 10.5092 | 0.615005 | ||||||||
\(293\) | −7.24385 | −0.423190 | −0.211595 | − | 0.977357i | \(-0.567866\pi\) | ||||
−0.211595 | + | 0.977357i | \(0.567866\pi\) | |||||||
\(294\) | −28.5281 | −1.66379 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.131633 | −0.00765102 | ||||||||
\(297\) | −1.79741 | −0.104297 | ||||||||
\(298\) | −33.4030 | −1.93498 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.51139 | 0.432949 | ||||||||
\(302\) | −25.0216 | −1.43983 | ||||||||
\(303\) | 26.6187 | 1.52920 | ||||||||
\(304\) | −12.0969 | −0.693802 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −33.9951 | −1.94337 | ||||||||
\(307\) | 29.4770 | 1.68234 | 0.841170 | − | 0.540770i | \(-0.181867\pi\) | ||||
0.841170 | + | 0.540770i | \(0.181867\pi\) | |||||||
\(308\) | −19.3703 | −1.10373 | ||||||||
\(309\) | 28.0466 | 1.59551 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3474 | −0.926978 | −0.463489 | − | 0.886103i | \(-0.653403\pi\) | ||||
−0.463489 | + | 0.886103i | \(0.653403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.4517 | −1.66471 | −0.832355 | − | 0.554244i | \(-0.813008\pi\) | ||||
−0.832355 | + | 0.554244i | \(0.813008\pi\) | |||||||
\(314\) | −4.35448 | −0.245737 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3213 | −0.693130 | ||||||||
\(317\) | −16.8218 | −0.944804 | −0.472402 | − | 0.881383i | \(-0.656613\pi\) | ||||
−0.472402 | + | 0.881383i | \(0.656613\pi\) | |||||||
\(318\) | 27.0067 | 1.51446 | ||||||||
\(319\) | 21.1841 | 1.18608 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.0931 | −0.730786 | ||||||||
\(322\) | −16.2109 | −0.903397 | ||||||||
\(323\) | −30.2871 | −1.68522 | ||||||||
\(324\) | −26.0197 | −1.44554 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.2221 | 1.00923 | ||||||||
\(327\) | −28.7255 | −1.58852 | ||||||||
\(328\) | −5.00208 | −0.276194 | ||||||||
\(329\) | 17.7572 | 0.978987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.15049 | −0.118202 | −0.0591009 | − | 0.998252i | \(-0.518823\pi\) | ||||
−0.0591009 | + | 0.998252i | \(0.518823\pi\) | |||||||
\(332\) | −29.4544 | −1.61652 | ||||||||
\(333\) | −0.263487 | −0.0144390 | ||||||||
\(334\) | −9.72890 | −0.532342 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 20.1950 | 1.10173 | ||||||||
\(337\) | −2.37962 | −0.129626 | −0.0648131 | − | 0.997897i | \(-0.520645\pi\) | ||||
−0.0648131 | + | 0.997897i | \(0.520645\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1609 | 0.769116 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.49242 | 0.351584 | ||||||||
\(342\) | 28.5935 | 1.54616 | ||||||||
\(343\) | −4.98994 | −0.269431 | ||||||||
\(344\) | 2.78898 | 0.150372 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.21493 | −0.119075 | ||||||||
\(347\) | 26.0916 | 1.40067 | 0.700336 | − | 0.713813i | \(-0.253033\pi\) | ||||
0.700336 | + | 0.713813i | \(0.253033\pi\) | |||||||
\(348\) | 62.9407 | 3.37398 | ||||||||
\(349\) | −16.3589 | −0.875674 | −0.437837 | − | 0.899054i | \(-0.644255\pi\) | ||||
−0.437837 | + | 0.899054i | \(0.644255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2555 | 0.866421 | ||||||||
\(353\) | 2.76979 | 0.147421 | 0.0737105 | − | 0.997280i | \(-0.476516\pi\) | ||||
0.0737105 | + | 0.997280i | \(0.476516\pi\) | |||||||
\(354\) | −15.3179 | −0.814135 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.97780 | −0.263823 | ||||||||
\(357\) | 50.5625 | 2.67605 | ||||||||
\(358\) | −37.3802 | −1.97560 | ||||||||
\(359\) | −17.9581 | −0.947791 | −0.473896 | − | 0.880581i | \(-0.657153\pi\) | ||||
−0.473896 | + | 0.880581i | \(0.657153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.47470 | 0.340774 | ||||||||
\(362\) | −47.7992 | −2.51227 | ||||||||
\(363\) | 15.7611 | 0.827243 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.3097 | 1.27069 | ||||||||
\(367\) | 27.0501 | 1.41200 | 0.706001 | − | 0.708211i | \(-0.250497\pi\) | ||||
0.706001 | + | 0.708211i | \(0.250497\pi\) | |||||||
\(368\) | 5.09719 | 0.265709 | ||||||||
\(369\) | −10.0125 | −0.521232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.7928 | −0.975676 | ||||||||
\(372\) | 19.2899 | 1.00013 | ||||||||
\(373\) | 0.658276 | 0.0340842 | 0.0170421 | − | 0.999855i | \(-0.494575\pi\) | ||||
0.0170421 | + | 0.999855i | \(0.494575\pi\) | |||||||
\(374\) | 26.9189 | 1.39194 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.59325 | 0.340021 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.55999 | 0.337409 | ||||||||
\(379\) | 17.9715 | 0.923135 | 0.461568 | − | 0.887105i | \(-0.347287\pi\) | ||||
0.461568 | + | 0.887105i | \(0.347287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.4686 | 1.45849 | ||||||||
\(382\) | −15.1628 | −0.775797 | ||||||||
\(383\) | 1.37967 | 0.0704978 | 0.0352489 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352489 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(384\) | 23.8514 | 1.21716 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 46.7962 | 2.38186 | ||||||||
\(387\) | 5.58262 | 0.283781 | ||||||||
\(388\) | −14.0327 | −0.712405 | ||||||||
\(389\) | 6.64124 | 0.336724 | 0.168362 | − | 0.985725i | \(-0.446152\pi\) | ||||
0.168362 | + | 0.985725i | \(0.446152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7619 | 0.645399 | ||||||||
\(392\) | 7.37089 | 0.372286 | ||||||||
\(393\) | 46.4099 | 2.34107 | ||||||||
\(394\) | 48.2070 | 2.42863 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.3964 | −0.723448 | ||||||||
\(397\) | −17.4163 | −0.874097 | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(398\) | −26.2251 | −1.31455 | ||||||||
\(399\) | −42.5284 | −2.12908 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.1562 | 1.35612 | 0.678058 | − | 0.735009i | \(-0.262822\pi\) | ||||
0.678058 | + | 0.735009i | \(0.262822\pi\) | |||||||
\(402\) | −34.5595 | −1.72367 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −29.2994 | −1.45770 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −77.3150 | −3.83708 | ||||||||
\(407\) | 0.208641 | 0.0103420 | ||||||||
\(408\) | 18.7738 | 0.929444 | ||||||||
\(409\) | 3.12154 | 0.154350 | 0.0771751 | − | 0.997018i | \(-0.475410\pi\) | ||||
0.0771751 | + | 0.997018i | \(0.475410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.4846 | −1.50370 | ||||||||
\(412\) | −30.8711 | −1.52091 | ||||||||
\(413\) | 10.6591 | 0.524499 | ||||||||
\(414\) | −12.0483 | −0.592141 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.7800 | −0.625840 | ||||||||
\(418\) | −22.6416 | −1.10744 | ||||||||
\(419\) | −3.35864 | −0.164080 | −0.0820402 | − | 0.996629i | \(-0.526144\pi\) | ||||
−0.0820402 | + | 0.996629i | \(0.526144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50793 | 0.463388 | 0.231694 | − | 0.972789i | \(-0.425573\pi\) | ||||
0.231694 | + | 0.972789i | \(0.425573\pi\) | |||||||
\(422\) | 37.1974 | 1.81074 | ||||||||
\(423\) | 13.1975 | 0.641686 | ||||||||
\(424\) | −6.97778 | −0.338871 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.9685 | −1.20973 | ||||||||
\(427\) | −16.9161 | −0.818628 | ||||||||
\(428\) | 14.4117 | 0.696615 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.7029 | −1.81609 | −0.908043 | − | 0.418878i | \(-0.862424\pi\) | ||||
−0.908043 | + | 0.418878i | \(0.862424\pi\) | |||||||
\(432\) | −2.06266 | −0.0992397 | ||||||||
\(433\) | −20.9632 | −1.00742 | −0.503712 | − | 0.863871i | \(-0.668033\pi\) | ||||
−0.503712 | + | 0.863871i | \(0.668033\pi\) | |||||||
\(434\) | −23.6952 | −1.13741 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.6184 | 1.51425 | ||||||||
\(437\) | −10.7341 | −0.513484 | ||||||||
\(438\) | −20.5074 | −0.979883 | ||||||||
\(439\) | −10.4601 | −0.499231 | −0.249616 | − | 0.968345i | \(-0.580304\pi\) | ||||
−0.249616 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.7541 | 0.702577 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6909 | 0.935543 | 0.467772 | − | 0.883849i | \(-0.345057\pi\) | ||||
0.467772 | + | 0.883849i | \(0.345057\pi\) | |||||||
\(444\) | 0.619901 | 0.0294192 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.3481 | −0.537349 | ||||||||
\(447\) | 36.9246 | 1.74648 | ||||||||
\(448\) | −42.3164 | −1.99926 | ||||||||
\(449\) | −7.93865 | −0.374648 | −0.187324 | − | 0.982298i | \(-0.559981\pi\) | ||||
−0.187324 | + | 0.982298i | \(0.559981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.92839 | 0.373333 | ||||||||
\(452\) | −15.5871 | −0.733154 | ||||||||
\(453\) | 27.6597 | 1.29956 | ||||||||
\(454\) | 6.33507 | 0.297319 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.7908 | −0.739472 | ||||||||
\(457\) | 7.10597 | 0.332403 | 0.166202 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166202 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(458\) | 6.64498 | 0.310500 | ||||||||
\(459\) | −5.16431 | −0.241050 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3424 | −0.714566 | −0.357283 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357283 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(462\) | 37.7988 | 1.75856 | ||||||||
\(463\) | 10.1047 | 0.469606 | 0.234803 | − | 0.972043i | \(-0.424555\pi\) | ||||
0.234803 | + | 0.972043i | \(0.424555\pi\) | |||||||
\(464\) | 24.3102 | 1.12857 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.7132 | 0.635253 | ||||||||
\(467\) | 14.2884 | 0.661190 | 0.330595 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330595 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0485 | 1.11046 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.81357 | 0.221797 | ||||||||
\(472\) | 3.95771 | 0.182169 | ||||||||
\(473\) | −4.42058 | −0.203258 | ||||||||
\(474\) | 24.0436 | 1.10436 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −55.6546 | −2.55092 | ||||||||
\(477\) | −13.9673 | −0.639516 | ||||||||
\(478\) | −51.2204 | −2.34277 | ||||||||
\(479\) | −33.8677 | −1.54745 | −0.773727 | − | 0.633519i | \(-0.781610\pi\) | ||||
−0.773727 | + | 0.633519i | \(0.781610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 59.1358 | 2.69356 | ||||||||
\(483\) | 17.9200 | 0.815388 | ||||||||
\(484\) | −17.3484 | −0.788563 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 45.2287 | 2.05162 | ||||||||
\(487\) | −13.0574 | −0.591689 | −0.295844 | − | 0.955236i | \(-0.595601\pi\) | ||||
−0.295844 | + | 0.955236i | \(0.595601\pi\) | |||||||
\(488\) | −6.28095 | −0.284325 | ||||||||
\(489\) | −20.1433 | −0.910911 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.8205 | 1.84220 | 0.921101 | − | 0.389325i | \(-0.127292\pi\) | ||||
0.921101 | + | 0.389325i | \(0.127292\pi\) | |||||||
\(492\) | 23.5563 | 1.06200 | ||||||||
\(493\) | 60.8658 | 2.74126 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.45050 | 0.334537 | ||||||||
\(497\) | 17.3746 | 0.779358 | ||||||||
\(498\) | 57.4767 | 2.57559 | ||||||||
\(499\) | 34.5723 | 1.54767 | 0.773833 | − | 0.633389i | \(-0.218337\pi\) | ||||
0.773833 | + | 0.633389i | \(0.218337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7546 | 0.480481 | ||||||||
\(502\) | 0.495779 | 0.0221277 | ||||||||
\(503\) | 44.0662 | 1.96481 | 0.982407 | − | 0.186754i | \(-0.0597967\pi\) | ||||
0.982407 | + | 0.186754i | \(0.0597967\pi\) | |||||||
\(504\) | 12.3334 | 0.549374 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.54038 | 0.424122 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −31.3356 | −1.39029 | ||||||||
\(509\) | −42.1772 | −1.86947 | −0.934735 | − | 0.355345i | \(-0.884363\pi\) | ||||
−0.934735 | + | 0.355345i | \(0.884363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2703 | 0.631281 | ||||||||
\(512\) | 24.9705 | 1.10355 | ||||||||
\(513\) | 4.34374 | 0.191781 | ||||||||
\(514\) | 27.7967 | 1.22606 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.1341 | −0.578198 | ||||||||
\(517\) | −10.4504 | −0.459609 | ||||||||
\(518\) | −0.761473 | −0.0334572 | ||||||||
\(519\) | 2.44845 | 0.107475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.6488 | 1.25513 | 0.627564 | − | 0.778565i | \(-0.284052\pi\) | ||||
0.627564 | + | 0.778565i | \(0.284052\pi\) | |||||||
\(522\) | −57.4622 | −2.51505 | ||||||||
\(523\) | 20.6845 | 0.904471 | 0.452235 | − | 0.891899i | \(-0.350627\pi\) | ||||
0.452235 | + | 0.891899i | \(0.350627\pi\) | |||||||
\(524\) | −51.0838 | −2.23160 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2576 | 0.926875 | ||||||||
\(527\) | 18.6540 | 0.812579 | ||||||||
\(528\) | −11.8851 | −0.517232 | ||||||||
\(529\) | −18.4770 | −0.803348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.92206 | 0.343788 | ||||||||
\(532\) | 46.8114 | 2.02953 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.71357 | 0.420347 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.92922 | 0.385684 | ||||||||
\(537\) | 41.3211 | 1.78314 | ||||||||
\(538\) | 27.1494 | 1.17049 | ||||||||
\(539\) | −11.6830 | −0.503222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8647 | 1.11201 | 0.556005 | − | 0.831179i | \(-0.312334\pi\) | ||||
0.556005 | + | 0.831179i | \(0.312334\pi\) | |||||||
\(542\) | −41.8358 | −1.79700 | ||||||||
\(543\) | 52.8387 | 2.26752 | ||||||||
\(544\) | 46.7051 | 2.00247 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.5937 | 1.26533 | 0.632667 | − | 0.774424i | \(-0.281960\pi\) | ||||
0.632667 | + | 0.774424i | \(0.281960\pi\) | |||||||
\(548\) | 33.5547 | 1.43338 | ||||||||
\(549\) | −12.5724 | −0.536578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.1947 | −2.18097 | ||||||||
\(552\) | 6.65369 | 0.283200 | ||||||||
\(553\) | −16.7310 | −0.711473 | ||||||||
\(554\) | 59.8427 | 2.54247 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.0671 | 0.596576 | ||||||||
\(557\) | 28.3520 | 1.20131 | 0.600657 | − | 0.799507i | \(-0.294906\pi\) | ||||
0.600657 | + | 0.799507i | \(0.294906\pi\) | |||||||
\(558\) | −17.6108 | −0.745525 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.7569 | −1.25634 | ||||||||
\(562\) | 47.3683 | 1.99811 | ||||||||
\(563\) | 13.2071 | 0.556615 | 0.278307 | − | 0.960492i | \(-0.410227\pi\) | ||||
0.278307 | + | 0.960492i | \(0.410227\pi\) | |||||||
\(564\) | −31.0496 | −1.30742 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −53.9891 | −2.26933 | ||||||||
\(567\) | −35.3318 | −1.48380 | ||||||||
\(568\) | 6.45119 | 0.270686 | ||||||||
\(569\) | −10.8594 | −0.455248 | −0.227624 | − | 0.973749i | \(-0.573096\pi\) | ||||
−0.227624 | + | 0.973749i | \(0.573096\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.37601 | 0.141282 | 0.0706409 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706409 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.7614 | 0.700218 | ||||||||
\(574\) | −28.9361 | −1.20777 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −31.4505 | −1.31044 | ||||||||
\(577\) | 0.958534 | 0.0399043 | 0.0199521 | − | 0.999801i | \(-0.493649\pi\) | ||||
0.0199521 | + | 0.999801i | \(0.493649\pi\) | |||||||
\(578\) | 40.8287 | 1.69825 | ||||||||
\(579\) | −51.7299 | −2.14982 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.9958 | −1.65930 | ||||||||
\(582\) | 27.3832 | 1.13507 | ||||||||
\(583\) | 11.0599 | 0.458055 | ||||||||
\(584\) | 5.29856 | 0.219256 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.5590 | −0.642738 | ||||||||
\(587\) | −21.6825 | −0.894934 | −0.447467 | − | 0.894300i | \(-0.647674\pi\) | ||||
−0.447467 | + | 0.894300i | \(0.647674\pi\) | |||||||
\(588\) | −34.7118 | −1.43149 | ||||||||
\(589\) | −15.6900 | −0.646493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −53.2894 | −2.19203 | ||||||||
\(592\) | 0.239430 | 0.00984051 | ||||||||
\(593\) | 37.9527 | 1.55853 | 0.779264 | − | 0.626695i | \(-0.215593\pi\) | ||||
0.779264 | + | 0.626695i | \(0.215593\pi\) | |||||||
\(594\) | −3.86066 | −0.158405 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −40.6433 | −1.66481 | ||||||||
\(597\) | 28.9900 | 1.18648 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.17043 | −0.170399 | −0.0851995 | − | 0.996364i | \(-0.527153\pi\) | ||||
−0.0851995 | + | 0.996364i | \(0.527153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.2234 | 1.72233 | 0.861165 | − | 0.508326i | \(-0.169736\pi\) | ||||
0.861165 | + | 0.508326i | \(0.169736\pi\) | |||||||
\(602\) | 16.1337 | 0.657560 | ||||||||
\(603\) | 17.8734 | 0.727861 | ||||||||
\(604\) | −30.4452 | −1.23880 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 57.1742 | 2.32254 | ||||||||
\(607\) | −8.63499 | −0.350483 | −0.175242 | − | 0.984525i | \(-0.556071\pi\) | ||||
−0.175242 | + | 0.984525i | \(0.556071\pi\) | |||||||
\(608\) | −39.2840 | −1.59318 | ||||||||
\(609\) | 85.4663 | 3.46327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −41.3637 | −1.67203 | ||||||||
\(613\) | −35.7619 | −1.44441 | −0.722205 | − | 0.691679i | \(-0.756871\pi\) | ||||
−0.722205 | + | 0.691679i | \(0.756871\pi\) | |||||||
\(614\) | 63.3136 | 2.55513 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.76617 | −0.393490 | ||||||||
\(617\) | 1.13565 | 0.0457197 | 0.0228599 | − | 0.999739i | \(-0.492723\pi\) | ||||
0.0228599 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(618\) | 60.2412 | 2.42326 | ||||||||
\(619\) | 47.6316 | 1.91447 | 0.957237 | − | 0.289305i | \(-0.0934241\pi\) | ||||
0.957237 | + | 0.289305i | \(0.0934241\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.83030 | −0.0734473 | ||||||||
\(622\) | −35.1126 | −1.40789 | ||||||||
\(623\) | −6.75929 | −0.270805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −63.2593 | −2.52835 | ||||||||
\(627\) | 25.0287 | 0.999550 | ||||||||
\(628\) | −5.29833 | −0.211427 | ||||||||
\(629\) | 0.599465 | 0.0239022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.67241 | 0.305434 | 0.152717 | − | 0.988270i | \(-0.451198\pi\) | ||||
0.152717 | + | 0.988270i | \(0.451198\pi\) | |||||||
\(632\) | −6.21221 | −0.247108 | ||||||||
\(633\) | −41.1191 | −1.63434 | ||||||||
\(634\) | −36.1314 | −1.43496 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 32.8605 | 1.30300 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 45.5012 | 1.80141 | ||||||||
\(639\) | 12.9132 | 0.510838 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.8544 | −0.626213 | −0.313106 | − | 0.949718i | \(-0.601370\pi\) | ||||
−0.313106 | + | 0.949718i | \(0.601370\pi\) | |||||||
\(642\) | −28.1226 | −1.10991 | ||||||||
\(643\) | −20.4282 | −0.805611 | −0.402806 | − | 0.915285i | \(-0.631965\pi\) | ||||
−0.402806 | + | 0.915285i | \(0.631965\pi\) | |||||||
\(644\) | −19.7247 | −0.777261 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −65.0537 | −2.55950 | ||||||||
\(647\) | −23.8101 | −0.936073 | −0.468036 | − | 0.883709i | \(-0.655038\pi\) | ||||
−0.468036 | + | 0.883709i | \(0.655038\pi\) | |||||||
\(648\) | −13.1187 | −0.515351 | ||||||||
\(649\) | −6.27305 | −0.246239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.1934 | 1.02660 | ||||||||
\(652\) | 22.1719 | 0.868318 | ||||||||
\(653\) | −31.1678 | −1.21969 | −0.609844 | − | 0.792521i | \(-0.708768\pi\) | ||||
−0.609844 | + | 0.792521i | \(0.708768\pi\) | |||||||
\(654\) | −61.6994 | −2.41264 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.09838 | 0.355232 | ||||||||
\(657\) | 10.6060 | 0.413779 | ||||||||
\(658\) | 38.1407 | 1.48688 | ||||||||
\(659\) | 35.0918 | 1.36698 | 0.683492 | − | 0.729958i | \(-0.260460\pi\) | ||||
0.683492 | + | 0.729958i | \(0.260460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.3641 | 0.636489 | 0.318244 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318244 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(662\) | −4.61904 | −0.179524 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.8504 | −0.576308 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.565943 | −0.0219298 | ||||||||
\(667\) | 21.5716 | 0.835257 | ||||||||
\(668\) | −11.8377 | −0.458014 | ||||||||
\(669\) | 12.5445 | 0.485000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.95542 | 0.384325 | ||||||||
\(672\) | 65.5822 | 2.52989 | ||||||||
\(673\) | −47.1689 | −1.81823 | −0.909114 | − | 0.416548i | \(-0.863240\pi\) | ||||
−0.909114 | + | 0.416548i | \(0.863240\pi\) | |||||||
\(674\) | −5.11118 | −0.196875 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.68421 | −0.256895 | −0.128448 | − | 0.991716i | \(-0.540999\pi\) | ||||
−0.128448 | + | 0.991716i | \(0.540999\pi\) | |||||||
\(678\) | 30.4162 | 1.16813 | ||||||||
\(679\) | −19.0549 | −0.731259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00297 | −0.268354 | ||||||||
\(682\) | 13.9451 | 0.533984 | ||||||||
\(683\) | 21.4574 | 0.821043 | 0.410522 | − | 0.911851i | \(-0.365347\pi\) | ||||
0.410522 | + | 0.911851i | \(0.365347\pi\) | |||||||
\(684\) | 34.7912 | 1.33028 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.7179 | −0.409211 | ||||||||
\(687\) | −7.34556 | −0.280251 | ||||||||
\(688\) | −5.07292 | −0.193403 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7873 | 1.39946 | 0.699728 | − | 0.714409i | \(-0.253304\pi\) | ||||
0.699728 | + | 0.714409i | \(0.253304\pi\) | |||||||
\(692\) | −2.69503 | −0.102450 | ||||||||
\(693\) | −19.5487 | −0.742594 | ||||||||
\(694\) | 56.0422 | 2.12733 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 31.7336 | 1.20286 | ||||||||
\(697\) | 22.7798 | 0.862846 | ||||||||
\(698\) | −35.1373 | −1.32997 | ||||||||
\(699\) | −15.1590 | −0.573367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7626 | 1.01081 | 0.505404 | − | 0.862883i | \(-0.331344\pi\) | ||||
0.505404 | + | 0.862883i | \(0.331344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.504214 | −0.0190168 | ||||||||
\(704\) | 24.9039 | 0.938602 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.94923 | 0.223902 | ||||||||
\(707\) | −39.7853 | −1.49628 | ||||||||
\(708\) | −18.6381 | −0.700462 | ||||||||
\(709\) | 23.4847 | 0.881988 | 0.440994 | − | 0.897510i | \(-0.354626\pi\) | ||||
0.440994 | + | 0.897510i | \(0.354626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.4348 | −0.466342 | ||||||||
\(712\) | −2.50972 | −0.0940558 | ||||||||
\(713\) | 6.61120 | 0.247591 | ||||||||
\(714\) | 108.603 | 4.06437 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −45.4825 | −1.69976 | ||||||||
\(717\) | 56.6206 | 2.11453 | ||||||||
\(718\) | −38.5721 | −1.43950 | ||||||||
\(719\) | −17.3284 | −0.646241 | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323121 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.9194 | −1.56116 | ||||||||
\(722\) | 13.9070 | 0.517565 | ||||||||
\(723\) | −65.3704 | −2.43115 | ||||||||
\(724\) | −58.1600 | −2.16150 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 33.8532 | 1.25641 | ||||||||
\(727\) | 2.13255 | 0.0790919 | 0.0395460 | − | 0.999218i | \(-0.487409\pi\) | ||||
0.0395460 | + | 0.999218i | \(0.487409\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.1291 | −0.745524 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.7012 | −0.469769 | ||||||||
\(732\) | 29.5789 | 1.09327 | ||||||||
\(733\) | −4.01857 | −0.148429 | −0.0742147 | − | 0.997242i | \(-0.523645\pi\) | ||||
−0.0742147 | + | 0.997242i | \(0.523645\pi\) | |||||||
\(734\) | 58.1008 | 2.14454 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.5529 | 0.610147 | ||||||||
\(737\) | −14.1530 | −0.521332 | ||||||||
\(738\) | −21.5059 | −0.791644 | ||||||||
\(739\) | −2.00491 | −0.0737519 | −0.0368759 | − | 0.999320i | \(-0.511741\pi\) | ||||
−0.0368759 | + | 0.999320i | \(0.511741\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −40.3651 | −1.48185 | ||||||||
\(743\) | 6.48999 | 0.238094 | 0.119047 | − | 0.992889i | \(-0.462016\pi\) | ||||
0.119047 | + | 0.992889i | \(0.462016\pi\) | |||||||
\(744\) | 9.72561 | 0.356558 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.41391 | 0.0517669 | ||||||||
\(747\) | −29.7257 | −1.08761 | ||||||||
\(748\) | 32.7537 | 1.19759 | ||||||||
\(749\) | 19.5694 | 0.715051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.7393 | −1.04871 | −0.524355 | − | 0.851500i | \(-0.675694\pi\) | ||||
−0.524355 | + | 0.851500i | \(0.675694\pi\) | |||||||
\(752\) | −11.9926 | −0.437324 | ||||||||
\(753\) | −0.548048 | −0.0199720 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.98190 | 0.290299 | ||||||||
\(757\) | −43.1705 | −1.56906 | −0.784530 | − | 0.620091i | \(-0.787095\pi\) | ||||
−0.784530 | + | 0.620091i | \(0.787095\pi\) | |||||||
\(758\) | 38.6010 | 1.40205 | ||||||||
\(759\) | −10.5462 | −0.382803 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.01133 | −0.181661 | −0.0908303 | − | 0.995866i | \(-0.528952\pi\) | ||||
−0.0908303 | + | 0.995866i | \(0.528952\pi\) | |||||||
\(762\) | 61.1477 | 2.21515 | ||||||||
\(763\) | 42.9341 | 1.55432 | ||||||||
\(764\) | −18.4494 | −0.667477 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.96339 | 0.107072 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −5.39406 | −0.194642 | ||||||||
\(769\) | 0.117089 | 0.00422232 | 0.00211116 | − | 0.999998i | \(-0.499328\pi\) | ||||
0.00211116 | + | 0.999998i | \(0.499328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7273 | −1.10662 | ||||||||
\(772\) | 56.9395 | 2.04930 | ||||||||
\(773\) | 21.8395 | 0.785512 | 0.392756 | − | 0.919643i | \(-0.371522\pi\) | ||||
0.392756 | + | 0.919643i | \(0.371522\pi\) | |||||||
\(774\) | 11.9909 | 0.431004 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.07507 | −0.253980 | ||||||||
\(777\) | 0.841754 | 0.0301978 | ||||||||
\(778\) | 14.2647 | 0.511415 | ||||||||
\(779\) | −19.1602 | −0.686486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2253 | −0.365888 | ||||||||
\(782\) | 27.4113 | 0.980227 | ||||||||
\(783\) | −8.72929 | −0.311960 | ||||||||
\(784\) | −13.4070 | −0.478823 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 99.6837 | 3.55560 | ||||||||
\(787\) | −27.7621 | −0.989613 | −0.494807 | − | 0.869003i | \(-0.664761\pi\) | ||||
−0.494807 | + | 0.869003i | \(0.664761\pi\) | |||||||
\(788\) | 58.6561 | 2.08954 | ||||||||
\(789\) | −23.4988 | −0.836579 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1654 | −0.752556 | ||||||||
\(792\) | −7.25843 | −0.257917 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −37.4084 | −1.32757 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.9096 | −1.13100 | ||||||||
\(797\) | −41.9565 | −1.48618 | −0.743088 | − | 0.669194i | \(-0.766640\pi\) | ||||
−0.743088 | + | 0.669194i | \(0.766640\pi\) | |||||||
\(798\) | −91.3468 | −3.23364 | ||||||||
\(799\) | −30.0260 | −1.06224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.02365 | −0.177502 | ||||||||
\(802\) | 58.3287 | 2.05966 | ||||||||
\(803\) | −8.39832 | −0.296370 | ||||||||
\(804\) | −42.0504 | −1.48300 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0117 | −1.05646 | ||||||||
\(808\) | −14.7723 | −0.519686 | ||||||||
\(809\) | 8.06707 | 0.283623 | 0.141812 | − | 0.989894i | \(-0.454707\pi\) | ||||
0.141812 | + | 0.989894i | \(0.454707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0953 | −0.565181 | −0.282591 | − | 0.959241i | \(-0.591194\pi\) | ||||
−0.282591 | + | 0.959241i | \(0.591194\pi\) | |||||||
\(812\) | −94.0735 | −3.30133 | ||||||||
\(813\) | 46.2465 | 1.62194 | ||||||||
\(814\) | 0.448140 | 0.0157073 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −34.1481 | −1.19542 | ||||||||
\(817\) | 10.6830 | 0.373752 | ||||||||
\(818\) | 6.70475 | 0.234426 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5777 | 0.578564 | 0.289282 | − | 0.957244i | \(-0.406583\pi\) | ||||
0.289282 | + | 0.957244i | \(0.406583\pi\) | |||||||
\(822\) | −65.4779 | −2.28380 | ||||||||
\(823\) | 24.9895 | 0.871079 | 0.435540 | − | 0.900170i | \(-0.356558\pi\) | ||||
0.435540 | + | 0.900170i | \(0.356558\pi\) | |||||||
\(824\) | −15.5647 | −0.542221 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.8946 | 0.796606 | ||||||||
\(827\) | −9.28575 | −0.322897 | −0.161449 | − | 0.986881i | \(-0.551617\pi\) | ||||
−0.161449 | + | 0.986881i | \(0.551617\pi\) | |||||||
\(828\) | −14.6598 | −0.509464 | ||||||||
\(829\) | 48.3689 | 1.67992 | 0.839961 | − | 0.542646i | \(-0.182578\pi\) | ||||
0.839961 | + | 0.542646i | \(0.182578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −66.1519 | −2.29478 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.5675 | −1.16304 | ||||||||
\(834\) | −27.4502 | −0.950521 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −27.5493 | −0.952813 | ||||||||
\(837\) | −2.67532 | −0.0924727 | ||||||||
\(838\) | −7.21402 | −0.249204 | ||||||||
\(839\) | −27.5771 | −0.952068 | −0.476034 | − | 0.879427i | \(-0.657926\pi\) | ||||
−0.476034 | + | 0.879427i | \(0.657926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.8822 | 2.54766 | ||||||||
\(842\) | 20.4221 | 0.703791 | ||||||||
\(843\) | −52.3623 | −1.80345 | ||||||||
\(844\) | 45.2601 | 1.55792 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.3470 | 0.974589 | ||||||||
\(847\) | −23.5571 | −0.809432 | ||||||||
\(848\) | 12.6920 | 0.435846 | ||||||||
\(849\) | 59.6811 | 2.04825 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.212458 | 0.00728297 | ||||||||
\(852\) | −30.3806 | −1.04082 | ||||||||
\(853\) | 36.3384 | 1.24420 | 0.622101 | − | 0.782937i | \(-0.286279\pi\) | ||||
0.622101 | + | 0.782937i | \(0.286279\pi\) | |||||||
\(854\) | −36.3341 | −1.24333 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.26612 | 0.248351 | ||||||||
\(857\) | 18.4246 | 0.629373 | 0.314687 | − | 0.949196i | \(-0.398101\pi\) | ||||
0.314687 | + | 0.949196i | \(0.398101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.8252 | −1.25646 | −0.628229 | − | 0.778028i | \(-0.716220\pi\) | ||||
−0.628229 | + | 0.778028i | \(0.716220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.9868 | 1.09011 | ||||||||
\(862\) | −80.9820 | −2.75826 | ||||||||
\(863\) | 12.0557 | 0.410380 | 0.205190 | − | 0.978722i | \(-0.434219\pi\) | ||||
0.205190 | + | 0.978722i | \(0.434219\pi\) | |||||||
\(864\) | −6.69838 | −0.227884 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −45.0267 | −1.53007 | ||||||||
\(867\) | −45.1332 | −1.53281 | ||||||||
\(868\) | −28.8313 | −0.978599 | ||||||||
\(869\) | 9.84646 | 0.334018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 15.9414 | 0.539845 | ||||||||
\(873\) | −14.1620 | −0.479311 | ||||||||
\(874\) | −23.0558 | −0.779876 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.9525 | −0.843068 | ||||||||
\(877\) | 18.4435 | 0.622793 | 0.311396 | − | 0.950280i | \(-0.399203\pi\) | ||||
0.311396 | + | 0.950280i | \(0.399203\pi\) | |||||||
\(878\) | −22.4671 | −0.758230 | ||||||||
\(879\) | 17.1994 | 0.580122 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4371 | 1.46343 | 0.731716 | − | 0.681610i | \(-0.238720\pi\) | ||||
0.731716 | + | 0.681610i | \(0.238720\pi\) | |||||||
\(882\) | 31.6904 | 1.06707 | ||||||||
\(883\) | −26.7242 | −0.899341 | −0.449670 | − | 0.893195i | \(-0.648459\pi\) | ||||
−0.449670 | + | 0.893195i | \(0.648459\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.2941 | 1.42090 | ||||||||
\(887\) | −42.3744 | −1.42279 | −0.711396 | − | 0.702791i | \(-0.751937\pi\) | ||||
−0.711396 | + | 0.702791i | \(0.751937\pi\) | |||||||
\(888\) | 0.312543 | 0.0104883 | ||||||||
\(889\) | −42.5502 | −1.42709 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.7934 | 0.696604 | ||||||||
\(892\) | −13.8079 | −0.462322 | ||||||||
\(893\) | 25.2551 | 0.845130 | ||||||||
\(894\) | 79.3104 | 2.65254 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −35.6491 | −1.19095 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.0514 | −0.569013 | ||||||||
\(899\) | 31.5310 | 1.05162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.7772 | 1.05865 | ||||||||
\(902\) | 17.0294 | 0.567016 | ||||||||
\(903\) | −17.8347 | −0.593500 | ||||||||
\(904\) | −7.85872 | −0.261377 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 59.4101 | 1.97377 | ||||||||
\(907\) | −20.4291 | −0.678337 | −0.339168 | − | 0.940726i | \(-0.610146\pi\) | ||||
−0.339168 | + | 0.940726i | \(0.610146\pi\) | |||||||
\(908\) | 7.70823 | 0.255807 | ||||||||
\(909\) | −29.5693 | −0.980751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.7626 | 0.787290 | 0.393645 | − | 0.919263i | \(-0.371214\pi\) | ||||
0.393645 | + | 0.919263i | \(0.371214\pi\) | |||||||
\(912\) | 28.7222 | 0.951086 | ||||||||
\(913\) | 23.5382 | 0.779000 | ||||||||
\(914\) | 15.2629 | 0.504852 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.08532 | 0.267146 | ||||||||
\(917\) | −69.3659 | −2.29066 | ||||||||
\(918\) | −11.0924 | −0.366104 | ||||||||
\(919\) | −6.47619 | −0.213630 | −0.106815 | − | 0.994279i | \(-0.534065\pi\) | ||||
−0.106815 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −69.9887 | −2.30621 | ||||||||
\(922\) | −32.9539 | −1.08528 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 45.9919 | 1.51302 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.7039 | 0.713235 | ||||||||
\(927\) | −31.1554 | −1.02328 | ||||||||
\(928\) | 78.9462 | 2.59153 | ||||||||
\(929\) | 20.8206 | 0.683101 | 0.341551 | − | 0.939863i | \(-0.389048\pi\) | ||||
0.341551 | + | 0.939863i | \(0.389048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.2338 | 0.925326 | ||||||||
\(932\) | 16.6857 | 0.546557 | ||||||||
\(933\) | 38.8145 | 1.27073 | ||||||||
\(934\) | 30.6901 | 1.00421 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1838 | 0.594039 | 0.297019 | − | 0.954871i | \(-0.404007\pi\) | ||||
0.297019 | + | 0.954871i | \(0.404007\pi\) | |||||||
\(938\) | 51.6538 | 1.68656 | ||||||||
\(939\) | 69.9287 | 2.28204 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.73191 | 0.154256 | 0.0771279 | − | 0.997021i | \(-0.475425\pi\) | ||||
0.0771279 | + | 0.997021i | \(0.475425\pi\) | |||||||
\(942\) | 10.3391 | 0.336864 | ||||||||
\(943\) | 8.07344 | 0.262907 | ||||||||
\(944\) | −7.19876 | −0.234300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.49495 | −0.308708 | ||||||||
\(947\) | 29.5954 | 0.961721 | 0.480861 | − | 0.876797i | \(-0.340324\pi\) | ||||
0.480861 | + | 0.876797i | \(0.340324\pi\) | |||||||
\(948\) | 29.2552 | 0.950164 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.9408 | 1.29517 | ||||||||
\(952\) | −28.0601 | −0.909432 | ||||||||
\(953\) | −1.49339 | −0.0483755 | −0.0241877 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241877 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(954\) | −30.0002 | −0.971293 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −62.3228 | −2.01566 | ||||||||
\(957\) | −50.2984 | −1.62592 | ||||||||
\(958\) | −72.7443 | −2.35026 | ||||||||
\(959\) | 45.5634 | 1.47132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3365 | −0.688274 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.5444 | 0.468687 | ||||||||
\(964\) | 71.9538 | 2.31748 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 38.4903 | 1.23841 | ||||||||
\(967\) | 10.0656 | 0.323687 | 0.161844 | − | 0.986816i | \(-0.448256\pi\) | ||||
0.161844 | + | 0.986816i | \(0.448256\pi\) | |||||||
\(968\) | −8.74675 | −0.281131 | ||||||||
\(969\) | 71.9122 | 2.31015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.3186 | −0.395322 | −0.197661 | − | 0.980270i | \(-0.563334\pi\) | ||||
−0.197661 | + | 0.980270i | \(0.563334\pi\) | |||||||
\(972\) | 55.0323 | 1.76516 | ||||||||
\(973\) | 19.1015 | 0.612365 | ||||||||
\(974\) | −28.0460 | −0.898653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.4245 | 0.365690 | ||||||||
\(977\) | 14.8608 | 0.475438 | 0.237719 | − | 0.971334i | \(-0.423600\pi\) | ||||
0.237719 | + | 0.971334i | \(0.423600\pi\) | |||||||
\(978\) | −43.2657 | −1.38349 | ||||||||
\(979\) | 3.97796 | 0.127136 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.9096 | 1.01879 | ||||||||
\(982\) | 87.6782 | 2.79792 | ||||||||
\(983\) | −51.5408 | −1.64390 | −0.821948 | − | 0.569562i | \(-0.807113\pi\) | ||||
−0.821948 | + | 0.569562i | \(0.807113\pi\) | |||||||
\(984\) | 11.8767 | 0.378615 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 130.734 | 4.16341 | ||||||||
\(987\) | −42.1618 | −1.34203 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50145 | −0.143138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.57520 | −0.177102 | −0.0885511 | − | 0.996072i | \(-0.528224\pi\) | ||||
−0.0885511 | + | 0.996072i | \(0.528224\pi\) | |||||||
\(992\) | 24.1951 | 0.768197 | ||||||||
\(993\) | 5.10602 | 0.162035 | ||||||||
\(994\) | 37.3189 | 1.18368 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 69.9351 | 2.21598 | ||||||||
\(997\) | 25.7010 | 0.813959 | 0.406979 | − | 0.913437i | \(-0.366582\pi\) | ||||
0.406979 | + | 0.913437i | \(0.366582\pi\) | |||||||
\(998\) | 74.2577 | 2.35059 | ||||||||
\(999\) | −0.0859745 | −0.00272011 |
(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 | 4225.2.a.ca.1.16 | 18 | ||
5.2 | odd | 4 | 845.2.b.g.339.16 | yes | 18 | ||
5.3 | odd | 4 | 845.2.b.g.339.3 | ✓ | 18 | ||
5.4 | even | 2 | inner | 4225.2.a.ca.1.3 | 18 | ||
13.12 | even | 2 | 4225.2.a.cb.1.3 | 18 | |||
65.2 | even | 12 | 845.2.l.g.654.5 | 72 | |||
65.3 | odd | 12 | 845.2.n.i.529.16 | 36 | |||
65.7 | even | 12 | 845.2.l.g.699.32 | 72 | |||
65.8 | even | 4 | 845.2.d.e.844.31 | 36 | |||
65.12 | odd | 4 | 845.2.b.h.339.3 | yes | 18 | ||
65.17 | odd | 12 | 845.2.n.h.484.3 | 36 | |||
65.18 | even | 4 | 845.2.d.e.844.5 | 36 | |||
65.22 | odd | 12 | 845.2.n.i.484.16 | 36 | |||
65.23 | odd | 12 | 845.2.n.h.529.3 | 36 | |||
65.28 | even | 12 | 845.2.l.g.654.32 | 72 | |||
65.32 | even | 12 | 845.2.l.g.699.6 | 72 | |||
65.33 | even | 12 | 845.2.l.g.699.5 | 72 | |||
65.37 | even | 12 | 845.2.l.g.654.31 | 72 | |||
65.38 | odd | 4 | 845.2.b.h.339.16 | yes | 18 | ||
65.42 | odd | 12 | 845.2.n.i.529.3 | 36 | |||
65.43 | odd | 12 | 845.2.n.h.484.16 | 36 | |||
65.47 | even | 4 | 845.2.d.e.844.6 | 36 | |||
65.48 | odd | 12 | 845.2.n.i.484.3 | 36 | |||
65.57 | even | 4 | 845.2.d.e.844.32 | 36 | |||
65.58 | even | 12 | 845.2.l.g.699.31 | 72 | |||
65.62 | odd | 12 | 845.2.n.h.529.16 | 36 | |||
65.63 | even | 12 | 845.2.l.g.654.6 | 72 | |||
65.64 | even | 2 | 4225.2.a.cb.1.16 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.b.g.339.3 | ✓ | 18 | 5.3 | odd | 4 | ||
845.2.b.g.339.16 | yes | 18 | 5.2 | odd | 4 | ||
845.2.b.h.339.3 | yes | 18 | 65.12 | odd | 4 | ||
845.2.b.h.339.16 | yes | 18 | 65.38 | odd | 4 | ||
845.2.d.e.844.5 | 36 | 65.18 | even | 4 | |||
845.2.d.e.844.6 | 36 | 65.47 | even | 4 | |||
845.2.d.e.844.31 | 36 | 65.8 | even | 4 | |||
845.2.d.e.844.32 | 36 | 65.57 | even | 4 | |||
845.2.l.g.654.5 | 72 | 65.2 | even | 12 | |||
845.2.l.g.654.6 | 72 | 65.63 | even | 12 | |||
845.2.l.g.654.31 | 72 | 65.37 | even | 12 | |||
845.2.l.g.654.32 | 72 | 65.28 | even | 12 | |||
845.2.l.g.699.5 | 72 | 65.33 | even | 12 | |||
845.2.l.g.699.6 | 72 | 65.32 | even | 12 | |||
845.2.l.g.699.31 | 72 | 65.58 | even | 12 | |||
845.2.l.g.699.32 | 72 | 65.7 | even | 12 | |||
845.2.n.h.484.3 | 36 | 65.17 | odd | 12 | |||
845.2.n.h.484.16 | 36 | 65.43 | odd | 12 | |||
845.2.n.h.529.3 | 36 | 65.23 | odd | 12 | |||
845.2.n.h.529.16 | 36 | 65.62 | odd | 12 | |||
845.2.n.i.484.3 | 36 | 65.48 | odd | 12 | |||
845.2.n.i.484.16 | 36 | 65.22 | odd | 12 | |||
845.2.n.i.529.3 | 36 | 65.42 | odd | 12 | |||
845.2.n.i.529.16 | 36 | 65.3 | odd | 12 | |||
4225.2.a.ca.1.3 | 18 | 5.4 | even | 2 | inner | ||
4225.2.a.ca.1.16 | 18 | 1.1 | even | 1 | trivial | ||
4225.2.a.cb.1.3 | 18 | 13.12 | even | 2 | |||
4225.2.a.cb.1.16 | 18 | 65.64 | even | 2 |