Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, 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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1358429035\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-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 | ||||||||
\(3\) | −0.0692070 | −0.0399567 | −0.0199783 | − | 0.999800i | \(-0.506360\pi\) | ||||
−0.0199783 | + | 0.999800i | \(0.506360\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.775693 | 0.346900 | 0.173450 | − | 0.984843i | \(-0.444508\pi\) | ||||
0.173450 | + | 0.984843i | \(0.444508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.19948 | −1.58726 | −0.793628 | − | 0.608404i | \(-0.791810\pi\) | ||||
−0.793628 | + | 0.608404i | \(0.791810\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99521 | −0.998403 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.210429 | −0.0634466 | −0.0317233 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317233 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.86540 | −1.62677 | −0.813384 | − | 0.581727i | \(-0.802377\pi\) | ||||
−0.813384 | + | 0.581727i | \(0.802377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0536833 | −0.0138610 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.81669 | −1.65329 | −0.826646 | − | 0.562723i | \(-0.809754\pi\) | ||||
−0.826646 | + | 0.562723i | \(0.809754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.37312 | −1.69151 | −0.845755 | − | 0.533571i | \(-0.820850\pi\) | ||||
−0.845755 | + | 0.533571i | \(0.820850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.290633 | 0.0634214 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.64209 | 0.759428 | 0.379714 | − | 0.925104i | \(-0.376022\pi\) | ||||
0.379714 | + | 0.925104i | \(0.376022\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.39830 | −0.879660 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414910 | 0.0798495 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.37032 | −1.18294 | −0.591470 | − | 0.806327i | \(-0.701452\pi\) | ||||
−0.591470 | + | 0.806327i | \(0.701452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.26252 | −1.48399 | −0.741996 | − | 0.670404i | \(-0.766121\pi\) | ||||
−0.741996 | + | 0.670404i | \(0.766121\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0145631 | 0.00253512 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.25751 | −0.550620 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.38161 | 0.884731 | 0.442366 | − | 0.896835i | \(-0.354139\pi\) | ||||
0.442366 | + | 0.896835i | \(0.354139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.405926 | 0.0650002 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.37849 | 1.15233 | 0.576163 | − | 0.817335i | \(-0.304549\pi\) | ||||
0.576163 | + | 0.817335i | \(0.304549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.77900 | −0.728791 | −0.364395 | − | 0.931244i | \(-0.618724\pi\) | ||||
−0.364395 | + | 0.931244i | \(0.618724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.32336 | −0.346347 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.67625 | −1.11970 | −0.559848 | − | 0.828595i | \(-0.689141\pi\) | ||||
−0.559848 | + | 0.828595i | \(0.689141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6357 | 1.51938 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.471763 | 0.0660600 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.45001 | −0.611256 | −0.305628 | − | 0.952151i | \(-0.598866\pi\) | ||||
−0.305628 | + | 0.952151i | \(0.598866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.163228 | −0.0220097 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.510271 | 0.0675871 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.83062 | 0.498705 | 0.249352 | − | 0.968413i | \(-0.419782\pi\) | ||||
0.249352 | + | 0.968413i | \(0.419782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.08061 | 1.16265 | 0.581327 | − | 0.813670i | \(-0.302534\pi\) | ||||
0.581327 | + | 0.813670i | \(0.302534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.5783 | 1.58472 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.54975 | −0.564327 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5095 | 1.89478 | 0.947391 | − | 0.320079i | \(-0.103709\pi\) | ||||
0.947391 | + | 0.320079i | \(0.103709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.252058 | −0.0303442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.49435 | 1.00809 | 0.504047 | − | 0.863676i | \(-0.331844\pi\) | ||||
0.504047 | + | 0.863676i | \(0.331844\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1802 | −1.19151 | −0.595753 | − | 0.803168i | \(-0.703146\pi\) | ||||
−0.595753 | + | 0.803168i | \(0.703146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.304393 | 0.0351483 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.883692 | 0.100706 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.41891 | −0.384657 | −0.192329 | − | 0.981331i | \(-0.561604\pi\) | ||||
−0.192329 | + | 0.981331i | \(0.561604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.95692 | 0.995213 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8168 | 1.40683 | 0.703415 | − | 0.710780i | \(-0.251658\pi\) | ||||
0.703415 | + | 0.710780i | \(0.251658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.28766 | −0.573527 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.440871 | 0.0472663 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.76098 | −1.03466 | −0.517331 | − | 0.855785i | \(-0.673074\pi\) | ||||
−0.517331 | + | 0.855785i | \(0.673074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.6316 | 2.58210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.571824 | 0.0592954 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.71928 | −0.586786 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2642 | −1.44831 | −0.724153 | − | 0.689640i | \(-0.757769\pi\) | ||||
−0.724153 | + | 0.689640i | \(0.757769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.630278 | 0.0633454 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.22211 | −0.917634 | −0.458817 | − | 0.888531i | \(-0.651727\pi\) | ||||
−0.458817 | + | 0.888531i | \(0.651727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0736 | 1.28818 | 0.644090 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644090 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.225442 | 0.0220009 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.28095 | 0.510529 | 0.255264 | − | 0.966871i | \(-0.417838\pi\) | ||||
0.255264 | + | 0.966871i | \(0.417838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.92351 | 0.663152 | 0.331576 | − | 0.943428i | \(-0.392420\pi\) | ||||
0.331576 | + | 0.943428i | \(0.392420\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.372445 | −0.0353509 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0723 | −1.04159 | −0.520795 | − | 0.853682i | \(-0.674365\pi\) | ||||
−0.520795 | + | 0.853682i | \(0.674365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82514 | 0.263446 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.5681 | 1.62417 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.6266 | 2.62420 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9557 | −0.995975 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.510643 | −0.0460431 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.29020 | −0.652055 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.81998 | 0.605175 | 0.302588 | − | 0.953122i | \(-0.402149\pi\) | ||||
0.302588 | + | 0.953122i | \(0.402149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.330740 | 0.0291200 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.9420 | −1.39286 | −0.696430 | − | 0.717624i | \(-0.745229\pi\) | ||||
−0.696430 | + | 0.717624i | \(0.745229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.9633 | 2.68486 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.321843 | 0.0276998 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.19887 | 0.358734 | 0.179367 | − | 0.983782i | \(-0.442595\pi\) | ||||
0.179367 | + | 0.983782i | \(0.442595\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.46896 | −0.718328 | −0.359164 | − | 0.933274i | \(-0.616938\pi\) | ||||
−0.359164 | + | 0.933274i | \(0.616938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.531250 | 0.0447393 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.23425 | 0.103213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.94142 | −0.410362 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.736062 | −0.0607094 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4331 | −1.26433 | −0.632163 | − | 0.774835i | \(-0.717833\pi\) | ||||
−0.632163 | + | 0.774835i | \(0.717833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.07053 | −0.168497 | −0.0842485 | − | 0.996445i | \(-0.526849\pi\) | ||||
−0.0842485 | + | 0.996445i | \(0.526849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.4174 | 1.65065 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.40918 | −0.514798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.26357 | 0.260462 | 0.130231 | − | 0.991484i | \(-0.458428\pi\) | ||||
0.130231 | + | 0.991484i | \(0.458428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.307972 | 0.0244238 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.2949 | −1.20541 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.306747 | −0.0240263 | −0.0120132 | − | 0.999928i | \(-0.503824\pi\) | ||||
−0.0120132 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0112965 | 0.000879433 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.14321 | 0.243229 | 0.121614 | − | 0.992577i | \(-0.461193\pi\) | ||||
0.121614 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.4029 | 1.64637 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.0841 | 1.68881 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6604 | −0.886521 | −0.443260 | − | 0.896393i | \(-0.646178\pi\) | ||||
−0.443260 | + | 0.896393i | \(0.646178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.4706 | 1.39625 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.265106 | −0.0199266 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2220 | −0.838775 | −0.419388 | − | 0.907807i | \(-0.637755\pi\) | ||||
−0.419388 | + | 0.907807i | \(0.637755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3483 | 1.14083 | 0.570413 | − | 0.821358i | \(-0.306783\pi\) | ||||
0.570413 | + | 0.821358i | \(0.306783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.628442 | −0.0464557 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.17448 | 0.306914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.43443 | 0.104896 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.74241 | −0.126742 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3587 | 1.69018 | 0.845089 | − | 0.534625i | \(-0.179547\pi\) | ||||
0.845089 | + | 0.534625i | \(0.179547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.05700 | −0.435992 | −0.217996 | − | 0.975950i | \(-0.569952\pi\) | ||||
−0.217996 | + | 0.975950i | \(0.569952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.314874 | 0.0225486 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.86724 | 0.133036 | 0.0665178 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665178 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0349107 | 0.00247476 | 0.00123738 | − | 0.999999i | \(-0.499606\pi\) | ||||
0.00123738 | + | 0.999999i | \(0.499606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.07336 | −0.0757091 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.7521 | 1.87763 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.72344 | 0.399742 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.9088 | −0.758215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.55152 | 0.107321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.3298 | −1.95030 | −0.975150 | − | 0.221545i | \(-0.928890\pi\) | ||||
−0.975150 | + | 0.221545i | \(0.928890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.587868 | −0.0402800 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.70704 | −0.252818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.6983 | 2.35548 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.704543 | 0.0476086 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.9826 | 2.68952 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.13797 | −0.611924 | −0.305962 | − | 0.952044i | \(-0.598978\pi\) | ||||
−0.305962 | + | 0.952044i | \(0.598978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1738 | 0.878256 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.60876 | 0.438639 | 0.219319 | − | 0.975653i | \(-0.429616\pi\) | ||||
0.219319 | + | 0.975653i | \(0.429616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0974 | −0.733339 | −0.366670 | − | 0.930351i | \(-0.619502\pi\) | ||||
−0.366670 | + | 0.930351i | \(0.619502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0611576 | −0.00402388 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.2582 | −1.58921 | −0.794603 | − | 0.607130i | \(-0.792321\pi\) | ||||
−0.794603 | + | 0.607130i | \(0.792321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.95442 | −0.388423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.236612 | 0.0153696 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.9499 | −1.54919 | −0.774594 | − | 0.632458i | \(-0.782046\pi\) | ||||
−0.774594 | + | 0.632458i | \(0.782046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6884 | −1.33266 | −0.666330 | − | 0.745657i | \(-0.732136\pi\) | ||||
−0.666330 | + | 0.745657i | \(0.732136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.86461 | −0.119615 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.25001 | 0.527074 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.2463 | 2.75169 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.887013 | −0.0562122 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.766400 | −0.0481831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.365943 | 0.0229162 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.6036 | −1.90900 | −0.954499 | − | 0.298215i | \(-0.903609\pi\) | ||||
−0.954499 | + | 0.298215i | \(0.903609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.6000 | −1.40429 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.0805 | 1.18105 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5884 | 0.776235 | 0.388117 | − | 0.921610i | \(-0.373126\pi\) | ||||
0.388117 | + | 0.921610i | \(0.373126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.45184 | −0.212045 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.675528 | 0.0413416 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9303 | −0.788374 | −0.394187 | − | 0.919030i | \(-0.628974\pi\) | ||||
−0.394187 | + | 0.919030i | \(0.628974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4720 | 1.54731 | 0.773656 | − | 0.633606i | \(-0.218426\pi\) | ||||
0.773656 | + | 0.633606i | \(0.218426\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.70468 | −0.103172 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.925529 | 0.0558115 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.6018 | −1.59835 | −0.799173 | − | 0.601101i | \(-0.794729\pi\) | ||||
−0.799173 | + | 0.601101i | \(0.794729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.7480 | 1.48162 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.4661 | −1.16125 | −0.580626 | − | 0.814171i | \(-0.697192\pi\) | ||||
−0.580626 | + | 0.814171i | \(0.697192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.7787 | 1.77016 | 0.885079 | − | 0.465440i | \(-0.154104\pi\) | ||||
0.885079 | + | 0.465440i | \(0.154104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.395814 | 0.0234460 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.9858 | −1.82904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.4673 | 1.73337 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.987179 | 0.0578694 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.9066 | −1.45506 | −0.727529 | − | 0.686077i | \(-0.759331\pi\) | ||||
−0.727529 | + | 0.686077i | \(0.759331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.97139 | 0.173001 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0873090 | −0.00506618 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.3623 | −1.23541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0693 | 1.15678 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.638234 | 0.0366656 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.04377 | 0.403325 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9032 | −1.02179 | −0.510894 | − | 0.859644i | \(-0.670686\pi\) | ||||
−0.510894 | + | 0.859644i | \(0.670686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.904784 | −0.0514714 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.68659 | −0.322457 | −0.161228 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161228 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.58583 | −0.541823 | −0.270912 | − | 0.962604i | \(-0.587325\pi\) | ||||
−0.270912 | + | 0.962604i | \(0.587325\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.75693 | 0.549741 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.3110 | 0.747619 | 0.373809 | − | 0.927506i | \(-0.378051\pi\) | ||||
0.373809 | + | 0.927506i | \(0.378051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.34050 | 0.0750535 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.365478 | −0.0203990 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.2603 | 2.79656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.7978 | 1.43100 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.479155 | −0.0264974 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.2363 | 1.77724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2996 | −1.11577 | −0.557884 | − | 0.829919i | \(-0.688387\pi\) | ||||
−0.557884 | + | 0.829919i | \(0.688387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.1191 | −0.883319 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0306 | 0.657301 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4150 | 0.785236 | 0.392618 | − | 0.919702i | \(-0.371569\pi\) | ||||
0.392618 | + | 0.919702i | \(0.371569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.766278 | 0.0416185 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.73867 | 0.0941543 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.2679 | −0.824390 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.195519 | −0.0105264 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0670 | −0.916207 | −0.458103 | − | 0.888899i | \(-0.651471\pi\) | ||||
−0.458103 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2910 | −0.604392 | −0.302196 | − | 0.953246i | \(-0.597720\pi\) | ||||
−0.302196 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.43361 | −0.129897 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.54786 | 0.295283 | 0.147641 | − | 0.989041i | \(-0.452832\pi\) | ||||
0.147641 | + | 0.989041i | \(0.452832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.58900 | 0.349708 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.98116 | −0.104854 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.63433 | −0.455703 | −0.227851 | − | 0.973696i | \(-0.573170\pi\) | ||||
−0.227851 | + | 0.973696i | \(0.573170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.3629 | 1.86121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.758212 | 0.0397958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.89673 | −0.413334 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.4158 | 1.11790 | 0.558948 | − | 0.829203i | \(-0.311205\pi\) | ||||
0.558948 | + | 0.829203i | \(0.311205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.1001 | −1.15049 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.6878 | 0.970220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2168 | −0.787894 | −0.393947 | − | 0.919133i | \(-0.628891\pi\) | ||||
−0.393947 | + | 0.919133i | \(0.628891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.504532 | 0.0260539 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.3645 | 1.92437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.1173 | −1.75249 | −0.876244 | − | 0.481868i | \(-0.839959\pi\) | ||||
−0.876244 | + | 0.481868i | \(0.839959\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.471990 | −0.0241808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.9211 | −1.06902 | −0.534510 | − | 0.845162i | \(-0.679504\pi\) | ||||
−0.534510 | + | 0.845162i | \(0.679504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.685474 | 0.0349350 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.3141 | 0.727627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.01551 | −0.304998 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.8270 | −1.25556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.10330 | 0.0556540 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.65202 | −0.133438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7540 | −0.941237 | −0.470619 | − | 0.882337i | \(-0.655969\pi\) | ||||
−0.470619 | + | 0.882337i | \(0.655969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.14288 | −0.107278 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8115 | 0.739649 | 0.369825 | − | 0.929102i | \(-0.379418\pi\) | ||||
0.369825 | + | 0.929102i | \(0.379418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48.4629 | 2.41411 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.94782 | 0.345240 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.13245 | −0.0561332 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.4023 | −1.20662 | −0.603308 | − | 0.797509i | \(-0.706151\pi\) | ||||
−0.603308 | + | 0.797509i | \(0.706151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.290591 | −0.0143338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0866 | −0.791572 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.94192 | 0.488030 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.586111 | 0.0287020 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5520 | −1.68798 | −0.843988 | − | 0.536362i | \(-0.819798\pi\) | ||||
−0.843988 | + | 0.536362i | \(0.819798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.18666 | 0.252782 | 0.126391 | − | 0.991980i | \(-0.459661\pi\) | ||||
0.126391 | + | 0.991980i | \(0.459661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.9920 | 1.11791 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.9819 | 1.45433 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.1339 | −1.84543 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0854185 | −0.00412404 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.0787 | −1.11166 | −0.555830 | − | 0.831296i | \(-0.687600\pi\) | ||||
−0.555830 | + | 0.831296i | \(0.687600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.7554 | 1.62218 | 0.811091 | − | 0.584919i | \(-0.198874\pi\) | ||||
0.811091 | + | 0.584919i | \(0.198874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.341980 | 0.0163967 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.8536 | −1.28458 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.4275 | 1.11814 | 0.559068 | − | 0.829122i | \(-0.311159\pi\) | ||||
0.559068 | + | 0.829122i | \(0.311159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.8560 | −1.51695 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3445 | −0.681526 | −0.340763 | − | 0.940149i | \(-0.610685\pi\) | ||||
−0.340763 | + | 0.940149i | \(0.610685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.57152 | −0.358925 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.06808 | 0.0505182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0335 | 1.13421 | 0.567104 | − | 0.823646i | \(-0.308064\pi\) | ||||
0.567104 | + | 0.823646i | \(0.308064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55265 | −0.0731112 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.143295 | 0.00673257 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.1066 | 0.895730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8243 | 1.20801 | 0.604005 | − | 0.796981i | \(-0.293571\pi\) | ||||
0.604005 | + | 0.796981i | \(0.293571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82832 | −0.132015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.12699 | 0.331937 | 0.165968 | − | 0.986131i | \(-0.446925\pi\) | ||||
0.165968 | + | 0.986131i | \(0.446925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7942 | 0.548124 | 0.274062 | − | 0.961712i | \(-0.411633\pi\) | ||||
0.274062 | + | 0.961712i | \(0.411633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.443560 | 0.0205696 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.6347 | 0.816038 | 0.408019 | − | 0.912974i | \(-0.366220\pi\) | ||||
0.408019 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −65.1317 | −3.00750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.225862 | −0.0104072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00564 | 0.0462393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.4292 | 1.48795 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3287 | 0.610280 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1081 | −0.553233 | −0.276616 | − | 0.960980i | \(-0.589213\pi\) | ||||
−0.276616 | + | 0.960980i | \(0.589213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.5653 | −1.43925 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.05851 | 0.0481640 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.0646 | −0.502418 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.5399 | 1.47452 | 0.737262 | − | 0.675607i | \(-0.236118\pi\) | ||||
0.737262 | + | 0.675607i | \(0.236118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0212291 | 0.000960011 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.1411 | −1.17973 | −0.589865 | − | 0.807502i | \(-0.700819\pi\) | ||||
−0.589865 | + | 0.807502i | \(0.700819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.4246 | 1.95574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.488902 | 0.0219745 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.6719 | −1.60010 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8538 | −0.485881 | −0.242941 | − | 0.970041i | \(-0.578112\pi\) | ||||
−0.242941 | + | 0.970041i | \(0.578112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.217532 | −0.00971861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.38641 | −0.0618171 | −0.0309086 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309086 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.15352 | −0.318328 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.48123 | −0.0657836 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.1097 | 0.714049 | 0.357024 | − | 0.934095i | \(-0.383791\pi\) | ||||
0.357024 | + | 0.934095i | \(0.383791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.7517 | 1.89122 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.05918 | −0.135066 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.1411 | 0.446870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61530 | 0.0710410 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.806978 | 0.0354224 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.88288 | 0.257734 | 0.128867 | − | 0.991662i | \(-0.458866\pi\) | ||||
0.128867 | + | 0.991662i | \(0.458866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.6311 | −0.770953 | −0.385477 | − | 0.922718i | \(-0.625963\pi\) | ||||
−0.385477 | + | 0.922718i | \(0.625963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.27829 | −0.0557893 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.3231 | 2.45347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.73520 | −0.423269 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.4735 | −0.497908 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.2777 | −1.87457 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.09640 | 0.177103 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.776644 | 0.0335146 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.23805 | −0.0963996 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.94447 | 0.255573 | 0.127786 | − | 0.991802i | \(-0.459213\pi\) | ||||
0.127786 | + | 0.991802i | \(0.459213\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.06221 | −0.0455836 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.37052 | 0.230048 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6895 | −1.14116 | −0.570581 | − | 0.821241i | \(-0.693282\pi\) | ||||
−0.570581 | + | 0.821241i | \(0.693282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.1984 | −1.16080 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.9692 | 2.00095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3577 | 0.610550 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.288903 | −0.0122632 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.9253 | 1.94592 | 0.972959 | − | 0.230976i | \(-0.0741920\pi\) | ||||
0.972959 | + | 0.230976i | \(0.0741920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.0307 | 1.18557 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0992724 | −0.00419128 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0439 | −0.886896 | −0.443448 | − | 0.896300i | \(-0.646245\pi\) | ||||
−0.443448 | + | 0.896300i | \(0.646245\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.58868 | −0.361328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.6144 | −1.57966 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.7311 | 0.659481 | 0.329741 | − | 0.944072i | \(-0.393039\pi\) | ||||
0.329741 | + | 0.944072i | \(0.393039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3361 | 1.47877 | 0.739385 | − | 0.673283i | \(-0.235117\pi\) | ||||
0.739385 | + | 0.673283i | \(0.235117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.61659 | −0.0675339 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0190 | −0.668038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −46.9962 | −1.95648 | −0.978240 | − | 0.207478i | \(-0.933474\pi\) | ||||
−0.978240 | + | 0.207478i | \(0.933474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.419187 | 0.0174208 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.8240 | −2.23300 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.936411 | 0.0387822 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.6274 | 0.563426 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.6596 | −1.05909 | −0.529544 | − | 0.848283i | \(-0.677637\pi\) | ||||
−0.529544 | + | 0.848283i | \(0.677637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.9206 | 2.51019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.129226 | −0.00531566 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.8400 | −1.71816 | −0.859082 | − | 0.511838i | \(-0.828965\pi\) | ||||
−0.859082 | + | 0.511838i | \(0.828965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.2055 | 0.910335 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.00241606 | −9.88830e−5 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.1392 | 1.02716 | 0.513581 | − | 0.858041i | \(-0.328319\pi\) | ||||
0.513581 | + | 0.858041i | \(0.328319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43174 | 0.0584019 | 0.0292009 | − | 0.999574i | \(-0.490704\pi\) | ||||
0.0292009 | + | 0.999574i | \(0.490704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.4541 | −1.89176 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.49827 | −0.345504 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1312 | 0.776513 | 0.388257 | − | 0.921551i | \(-0.373077\pi\) | ||||
0.388257 | + | 0.921551i | \(0.373077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.85143 | −0.0750237 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.0243 | 1.82149 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.9549 | 0.805972 | 0.402986 | − | 0.915206i | \(-0.367972\pi\) | ||||
0.402986 | + | 0.915206i | \(0.367972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.396102 | −0.0159724 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6157 | −0.507890 | −0.253945 | − | 0.967219i | \(-0.581728\pi\) | ||||
−0.253945 | + | 0.967219i | \(0.581728\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.6717 | 1.15241 | 0.576207 | − | 0.817304i | \(-0.304532\pi\) | ||||
0.576207 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.51114 | 0.0606399 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 40.9911 | 1.64227 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3365 | 0.653462 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.107376 | −0.00428817 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.6848 | −1.46272 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6711 | −0.464619 | −0.232309 | − | 0.972642i | \(-0.574628\pi\) | ||||
−0.232309 | + | 0.972642i | \(0.574628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.96062 | 0.0779275 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.29021 | 0.209936 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.3824 | −2.47168 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.4424 | −1.00648 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.4576 | 1.51898 | 0.759491 | − | 0.650517i | \(-0.225448\pi\) | ||||
0.759491 | + | 0.650517i | \(0.225448\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.3532 | −1.11814 | −0.559070 | − | 0.829121i | \(-0.688842\pi\) | ||||
−0.559070 | + | 0.829121i | \(0.688842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.256553 | 0.0101018 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9339 | 1.60928 | 0.804638 | − | 0.593766i | \(-0.202359\pi\) | ||||
0.804638 | + | 0.593766i | \(0.202359\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.806073 | −0.0316411 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40136 | −0.0941169 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.2157 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.3661 | −0.483184 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.4919 | 1.18960 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.6483 | 1.54448 | 0.772238 | − | 0.635333i | \(-0.219137\pi\) | ||||
0.772238 | + | 0.635333i | \(0.219137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2438 | −0.437332 | −0.218666 | − | 0.975800i | \(-0.570170\pi\) | ||||
−0.218666 | + | 0.975800i | \(0.570170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.76707 | −0.107464 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0180 | 0.931379 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.2013 | −0.898357 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.632411 | 0.0244504 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.91082 | −0.0737665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1182 | 0.736953 | 0.368476 | − | 0.929637i | \(-0.379880\pi\) | ||||
0.368476 | + | 0.929637i | \(0.379880\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.82490 | −0.0702404 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.5297 | 1.05805 | 0.529025 | − | 0.848606i | \(-0.322558\pi\) | ||||
0.529025 | + | 0.848606i | \(0.322558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.9021 | 2.29883 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.457372 | −0.0175265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.1368 | 0.655721 | 0.327860 | − | 0.944726i | \(-0.393672\pi\) | ||||
0.327860 | + | 0.944726i | \(0.393672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.25703 | 0.124445 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.768020 | 0.0293018 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.1011 | 0.994372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.04409 | −0.115803 | −0.0579013 | − | 0.998322i | \(-0.518441\pi\) | ||||
−0.0579013 | + | 0.998322i | \(0.518441\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.64684 | −0.100545 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.56931 | −0.249188 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.2969 | −1.90513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.67883 | 0.0634993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.31631 | 0.238564 | 0.119282 | − | 0.992860i | \(-0.461941\pi\) | ||||
0.119282 | + | 0.992860i | \(0.461941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6793 | −1.49653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.412087 | 0.0155201 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.7281 | 1.45652 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5850 | −0.923307 | −0.461654 | − | 0.887060i | \(-0.652744\pi\) | ||||
−0.461654 | + | 0.887060i | \(0.652744\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2404 | 0.384043 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.0928 | −1.12699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.957397 | 0.0358046 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.65750 | 0.0619004 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.1473 | −0.714074 | −0.357037 | − | 0.934090i | \(-0.616213\pi\) | ||||
−0.357037 | + | 0.934090i | \(0.616213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.9024 | −2.04467 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.43178 | 0.0532486 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.0186 | 1.04058 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.0078 | −1.63216 | −0.816079 | − | 0.577941i | \(-0.803856\pi\) | ||||
−0.816079 | + | 0.577941i | \(0.803856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.7417 | −0.990434 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.5770 | 1.20490 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.23897 | −0.304313 | −0.152157 | − | 0.988356i | \(-0.548622\pi\) | ||||
−0.152157 | + | 0.988356i | \(0.548622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.570958 | −0.0210601 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.26364 | −0.120218 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.0954 | −1.29101 | −0.645503 | − | 0.763758i | \(-0.723352\pi\) | ||||
−0.645503 | + | 0.763758i | \(0.723352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.99294 | −0.109949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.8727 | 1.05924 | 0.529618 | − | 0.848236i | \(-0.322335\pi\) | ||||
0.529618 | + | 0.848236i | \(0.322335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9713 | −0.438595 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38.3891 | −1.40458 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.1773 | −0.810340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.39807 | −0.0875069 | −0.0437535 | − | 0.999042i | \(-0.513932\pi\) | ||||
−0.0437535 | + | 0.999042i | \(0.513932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0692070 | −0.00252204 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.60609 | −0.0584517 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0017 | 1.30851 | 0.654253 | − | 0.756276i | \(-0.272983\pi\) | ||||
0.654253 | + | 0.756276i | \(0.272983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0530402 | 0.00192524 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.2342 | −1.49474 | −0.747369 | − | 0.664409i | \(-0.768683\pi\) | ||||
−0.747369 | + | 0.664409i | \(0.768683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.0752 | −1.05259 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.8377 | 0.572612 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.4681 | −0.811277 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6825 | −0.529465 | −0.264733 | − | 0.964322i | \(-0.585284\pi\) | ||||
−0.264733 | + | 0.964322i | \(0.585284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.11798 | 0.0762771 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.1545 | 0.509103 | 0.254551 | − | 0.967059i | \(-0.418072\pi\) | ||||
0.254551 | + | 0.967059i | \(0.418072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3410 | 1.30541 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.56408 | 0.0561109 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −54.4025 | −1.94917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.78745 | −0.0639601 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.64311 | −0.0944571 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.53153 | 0.0903542 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.1095 | −1.00200 | −0.500998 | − | 0.865449i | \(-0.667034\pi\) | ||||
−0.500998 | + | 0.865449i | \(0.667034\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.871206 | −0.0310157 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.4978 | 1.65327 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.2614 | −1.89137 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.238892 | 0.00847261 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.152801 | −0.00541250 | −0.00270625 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270625 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.3267 | 1.85118 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.2362 | 1.03301 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.14221 | 0.0755971 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8641 | −0.418156 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.894867 | 0.0315008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.7952 | 0.449855 | 0.224928 | − | 0.974375i | \(-0.427785\pi\) | ||||
0.224928 | + | 0.974375i | \(0.427785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.2650 | 0.816943 | 0.408472 | − | 0.912771i | \(-0.366062\pi\) | ||||
0.408472 | + | 0.912771i | \(0.366062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.76284 | −0.0618254 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.237942 | −0.00833474 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.2362 | 1.23276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −73.7769 | −2.57797 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4830 | 0.714862 | 0.357431 | − | 0.933940i | \(-0.383653\pi\) | ||||
0.357431 | + | 0.933940i | \(0.383653\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.92637 | 0.311154 | 0.155577 | − | 0.987824i | \(-0.450276\pi\) | ||||
0.155577 | + | 0.987824i | \(0.450276\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0640530 | −0.00223004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.5117 | 0.713261 | 0.356631 | − | 0.934245i | \(-0.383925\pi\) | ||||
0.356631 | + | 0.934245i | \(0.383925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.2764 | −1.36413 | −0.682063 | − | 0.731294i | \(-0.738917\pi\) | ||||
−0.682063 | + | 0.731294i | \(0.738917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.84103 | 0.0638646 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −72.5001 | −2.51198 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.43817 | 0.0843762 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.42820 | −0.118496 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.7251 | −0.784558 | −0.392279 | − | 0.919846i | \(-0.628313\pi\) | ||||
−0.392279 | + | 0.919846i | \(0.628313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5810 | 0.399346 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.34719 | 0.0463997 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.6020 | 0.571128 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.0084 | 1.58087 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.06089 | −0.0707296 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6003 | 0.671889 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.45379 | 0.118256 | 0.0591278 | − | 0.998250i | \(-0.481168\pi\) | ||||
0.0591278 | + | 0.998250i | \(0.481168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.1304 | 0.585849 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.792349 | −0.0270661 | −0.0135331 | − | 0.999908i | \(-0.504308\pi\) | ||||
−0.0135331 | + | 0.999908i | \(0.504308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5855 | −0.702367 | −0.351184 | − | 0.936307i | \(-0.614221\pi\) | ||||
−0.351184 | + | 0.936307i | \(0.614221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.14443 | 0.0730821 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.8872 | −1.59606 | −0.798030 | − | 0.602618i | \(-0.794124\pi\) | ||||
−0.798030 | + | 0.602618i | \(0.794124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.04486 | −0.307534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.03934 | −0.0692597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.719437 | 0.0244052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −90.9691 | −3.08237 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.7241 | 1.44599 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.6151 | 1.03498 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4198 | 1.26358 | 0.631788 | − | 0.775141i | \(-0.282321\pi\) | ||||
0.631788 | + | 0.775141i | \(0.282321\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.72371 | 0.0581392 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4578 | 0.756622 | 0.378311 | − | 0.925679i | \(-0.376505\pi\) | ||||
0.378311 | + | 0.925679i | \(0.376505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.6243 | −0.761370 | −0.380685 | − | 0.924705i | \(-0.624312\pi\) | ||||
−0.380685 | + | 0.924705i | \(0.624312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.205641 | −0.00691254 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.3680 | −1.22112 | −0.610559 | − | 0.791971i | \(-0.709055\pi\) | ||||
−0.610559 | + | 0.791971i | \(0.709055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.6404 | −0.960568 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.88479 | −0.0631429 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 56.5980 | 1.89398 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.70486 | −0.290971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.47842 | 0.0493630 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 52.6349 | 1.75547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.3344 | 1.01058 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.38894 | −0.0462209 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.9055 | 0.395753 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.8371 | −1.12354 | −0.561771 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561771 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.6222 | 0.916169 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.76626 | −0.191045 | −0.0955223 | − | 0.995427i | \(-0.530452\pi\) | ||||
−0.0955223 | + | 0.995427i | \(0.530452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.69703 | −0.0892586 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.487478 | −0.0161155 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 66.9482 | 2.21083 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.7214 | 1.54120 | 0.770599 | − | 0.637321i | \(-0.219957\pi\) | ||||
0.770599 | + | 0.637321i | \(0.219957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.23902 | 0.0408273 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.8227 | −1.63993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6699 | −0.778263 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.1582 | −1.28612 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3107 | 0.764800 | 0.382400 | − | 0.923997i | \(-0.375098\pi\) | ||||
0.382400 | + | 0.923997i | \(0.375098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78.4181 | −2.57005 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.393551 | 0.0128843 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.11268 | 0.0363884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.2306 | 0.432225 | 0.216113 | − | 0.976368i | \(-0.430662\pi\) | ||||
0.216113 | + | 0.976368i | \(0.430662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.663406 | 0.0216494 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.79636 | −0.0911588 | −0.0455794 | − | 0.998961i | \(-0.514513\pi\) | ||||
−0.0455794 | + | 0.998961i | \(0.514513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.8731 | 0.875108 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.35157 | −0.0439667 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.4701 | 1.77004 | 0.885020 | − | 0.465553i | \(-0.154144\pi\) | ||||
0.885020 | + | 0.465553i | \(0.154144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.7111 | 1.93830 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.921212 | −0.0298723 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4756 | 0.598485 | 0.299243 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299243 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1192 | 0.586324 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0927719 | −0.00299889 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.6331 | −0.569402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.2692 | 1.20223 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.8176 | −0.509714 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.69837 | −0.151246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.8946 | 1.86176 | 0.930882 | − | 0.365321i | \(-0.119041\pi\) | ||||
0.930882 | + | 0.365321i | \(0.119041\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.47836 | −0.111741 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.52061 | −0.273439 | −0.136720 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136720 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.5653 | 1.14017 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.78538 | −0.0571781 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7051 | 0.758394 | 0.379197 | − | 0.925316i | \(-0.376200\pi\) | ||||
0.379197 | + | 0.925316i | \(0.376200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.05399 | 0.0656458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.7374 | −0.662094 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.9747 | 1.46637 | 0.733183 | − | 0.680031i | \(-0.238034\pi\) | ||||
0.733183 | + | 0.680031i | \(0.238034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.44841 | 0.0461501 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.23098 | −0.0710128 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.4055 | −0.553464 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.1192 | 1.43326 | 0.716629 | − | 0.697454i | \(-0.245684\pi\) | ||||
0.716629 | + | 0.697454i | \(0.245684\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.40487 | 0.0445823 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0270800 | 0.000858494 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.6920 | 1.38374 | 0.691869 | − | 0.722023i | \(-0.256787\pi\) | ||||
0.691869 | + | 0.722023i | \(0.256787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.23288 | 0.0706454 |
(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 | 8032.2.a.i.1.15 | yes | 30 | |
4.3 | odd | 2 | 8032.2.a.h.1.16 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.h.1.16 | ✓ | 30 | 4.3 | odd | 2 | ||
8032.2.a.i.1.15 | yes | 30 | 1.1 | even | 1 | trivial |