Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26445 | −0.894101 | −0.447051 | − | 0.894509i | \(-0.647526\pi\) | ||||
−0.447051 | + | 0.894509i | \(0.647526\pi\) | |||||||
\(3\) | 0.637501 | 0.368061 | 0.184031 | − | 0.982921i | \(-0.441085\pi\) | ||||
0.184031 | + | 0.982921i | \(0.441085\pi\) | |||||||
\(4\) | −0.401165 | −0.200583 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.806088 | −0.329084 | ||||||||
\(7\) | 3.31632 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(8\) | 3.03615 | 1.07344 | ||||||||
\(9\) | −2.59359 | −0.864531 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24228 | −1.27910 | −0.639548 | − | 0.768752i | \(-0.720878\pi\) | ||||
−0.639548 | + | 0.768752i | \(0.720878\pi\) | |||||||
\(12\) | −0.255743 | −0.0738267 | ||||||||
\(13\) | 4.96033 | 1.37575 | 0.687874 | − | 0.725831i | \(-0.258544\pi\) | ||||
0.687874 | + | 0.725831i | \(0.258544\pi\) | |||||||
\(14\) | −4.19333 | −1.12071 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.03674 | −0.759184 | ||||||||
\(17\) | −0.765219 | −0.185593 | −0.0927965 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927965 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(18\) | 3.27947 | 0.772978 | ||||||||
\(19\) | −0.395721 | −0.0907847 | −0.0453923 | − | 0.998969i | \(-0.514454\pi\) | ||||
−0.0453923 | + | 0.998969i | \(0.514454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.11416 | 0.461347 | ||||||||
\(22\) | 5.36415 | 1.14364 | ||||||||
\(23\) | 0.736028 | 0.153472 | 0.0767362 | − | 0.997051i | \(-0.475550\pi\) | ||||
0.0767362 | + | 0.997051i | \(0.475550\pi\) | |||||||
\(24\) | 1.93555 | 0.395093 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.27209 | −1.23006 | ||||||||
\(27\) | −3.56592 | −0.686262 | ||||||||
\(28\) | −1.33039 | −0.251421 | ||||||||
\(29\) | 0.111486 | 0.0207024 | 0.0103512 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103512 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.87704 | −0.875942 | −0.437971 | − | 0.898989i | \(-0.644303\pi\) | ||||
−0.437971 | + | 0.898989i | \(0.644303\pi\) | |||||||
\(32\) | −2.23251 | −0.394655 | ||||||||
\(33\) | −2.70446 | −0.470785 | ||||||||
\(34\) | 0.967582 | 0.165939 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.04046 | 0.173410 | ||||||||
\(37\) | 5.92852 | 0.974642 | 0.487321 | − | 0.873223i | \(-0.337974\pi\) | ||||
0.487321 | + | 0.873223i | \(0.337974\pi\) | |||||||
\(38\) | 0.500370 | 0.0811707 | ||||||||
\(39\) | 3.16221 | 0.506359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0798 | −1.57420 | −0.787101 | − | 0.616824i | \(-0.788419\pi\) | ||||
−0.787101 | + | 0.616824i | \(0.788419\pi\) | |||||||
\(42\) | −2.67325 | −0.412491 | ||||||||
\(43\) | 11.7509 | 1.79199 | 0.895997 | − | 0.444061i | \(-0.146463\pi\) | ||||
0.895997 | + | 0.444061i | \(0.146463\pi\) | |||||||
\(44\) | 1.70186 | 0.256564 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.930671 | −0.137220 | ||||||||
\(47\) | 0.146161 | 0.0213198 | 0.0106599 | − | 0.999943i | \(-0.496607\pi\) | ||||
0.0106599 | + | 0.999943i | \(0.496607\pi\) | |||||||
\(48\) | −1.93592 | −0.279426 | ||||||||
\(49\) | 3.99800 | 0.571142 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.487828 | −0.0683096 | ||||||||
\(52\) | −1.98991 | −0.275951 | ||||||||
\(53\) | −12.9699 | −1.78155 | −0.890776 | − | 0.454442i | \(-0.849839\pi\) | ||||
−0.890776 | + | 0.454442i | \(0.849839\pi\) | |||||||
\(54\) | 4.50893 | 0.613588 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.0689 | 1.34551 | ||||||||
\(57\) | −0.252273 | −0.0334143 | ||||||||
\(58\) | −0.140969 | −0.0185101 | ||||||||
\(59\) | −7.84684 | −1.02157 | −0.510786 | − | 0.859708i | \(-0.670646\pi\) | ||||
−0.510786 | + | 0.859708i | \(0.670646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.56240 | −0.584156 | −0.292078 | − | 0.956395i | \(-0.594347\pi\) | ||||
−0.292078 | + | 0.956395i | \(0.594347\pi\) | |||||||
\(62\) | 6.16678 | 0.783181 | ||||||||
\(63\) | −8.60119 | −1.08365 | ||||||||
\(64\) | 8.89637 | 1.11205 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.41965 | 0.420930 | ||||||||
\(67\) | −9.50170 | −1.16082 | −0.580409 | − | 0.814325i | \(-0.697107\pi\) | ||||
−0.580409 | + | 0.814325i | \(0.697107\pi\) | |||||||
\(68\) | 0.306979 | 0.0372267 | ||||||||
\(69\) | 0.469218 | 0.0564873 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.93643 | 0.229812 | 0.114906 | − | 0.993376i | \(-0.463343\pi\) | ||||
0.114906 | + | 0.993376i | \(0.463343\pi\) | |||||||
\(72\) | −7.87455 | −0.928024 | ||||||||
\(73\) | 6.60869 | 0.773488 | 0.386744 | − | 0.922187i | \(-0.373600\pi\) | ||||
0.386744 | + | 0.922187i | \(0.373600\pi\) | |||||||
\(74\) | −7.49631 | −0.871429 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.158750 | 0.0182098 | ||||||||
\(77\) | −14.0688 | −1.60328 | ||||||||
\(78\) | −3.99846 | −0.452737 | ||||||||
\(79\) | 3.83638 | 0.431627 | 0.215813 | − | 0.976435i | \(-0.430760\pi\) | ||||
0.215813 | + | 0.976435i | \(0.430760\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50750 | 0.611945 | ||||||||
\(82\) | 12.7454 | 1.40750 | ||||||||
\(83\) | 12.1432 | 1.33289 | 0.666446 | − | 0.745553i | \(-0.267815\pi\) | ||||
0.666446 | + | 0.745553i | \(0.267815\pi\) | |||||||
\(84\) | −0.848127 | −0.0925383 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.8584 | −1.60222 | ||||||||
\(87\) | 0.0710725 | 0.00761977 | ||||||||
\(88\) | −12.8802 | −1.37304 | ||||||||
\(89\) | 3.43003 | 0.363582 | 0.181791 | − | 0.983337i | \(-0.441810\pi\) | ||||
0.181791 | + | 0.983337i | \(0.441810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.4500 | 1.72443 | ||||||||
\(92\) | −0.295269 | −0.0307839 | ||||||||
\(93\) | −3.10912 | −0.322400 | ||||||||
\(94\) | −0.184813 | −0.0190620 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.42323 | −0.145257 | ||||||||
\(97\) | −3.58285 | −0.363783 | −0.181891 | − | 0.983319i | \(-0.558222\pi\) | ||||
−0.181891 | + | 0.983319i | \(0.558222\pi\) | |||||||
\(98\) | −5.05527 | −0.510659 | ||||||||
\(99\) | 11.0027 | 1.10582 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.2822 | −1.42113 | −0.710565 | − | 0.703631i | \(-0.751561\pi\) | ||||
−0.710565 | + | 0.703631i | \(0.751561\pi\) | |||||||
\(102\) | 0.616834 | 0.0610757 | ||||||||
\(103\) | −17.4214 | −1.71658 | −0.858289 | − | 0.513166i | \(-0.828473\pi\) | ||||
−0.858289 | + | 0.513166i | \(0.828473\pi\) | |||||||
\(104\) | 15.0603 | 1.47679 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.3998 | 1.59289 | ||||||||
\(107\) | 2.69267 | 0.260310 | 0.130155 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130155 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(108\) | 1.43052 | 0.137652 | ||||||||
\(109\) | −11.9114 | −1.14091 | −0.570454 | − | 0.821330i | \(-0.693233\pi\) | ||||
−0.570454 | + | 0.821330i | \(0.693233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.77943 | 0.358728 | ||||||||
\(112\) | −10.0708 | −0.951601 | ||||||||
\(113\) | 9.95943 | 0.936905 | 0.468452 | − | 0.883489i | \(-0.344812\pi\) | ||||
0.468452 | + | 0.883489i | \(0.344812\pi\) | |||||||
\(114\) | 0.318986 | 0.0298758 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0447243 | −0.00415255 | ||||||||
\(117\) | −12.8651 | −1.18938 | ||||||||
\(118\) | 9.92194 | 0.913389 | ||||||||
\(119\) | −2.53771 | −0.232632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.99693 | 0.636085 | ||||||||
\(122\) | 5.76893 | 0.522295 | ||||||||
\(123\) | −6.42589 | −0.579403 | ||||||||
\(124\) | 1.95650 | 0.175699 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.8758 | 0.968891 | ||||||||
\(127\) | −4.52799 | −0.401794 | −0.200897 | − | 0.979612i | \(-0.564386\pi\) | ||||
−0.200897 | + | 0.979612i | \(0.564386\pi\) | |||||||
\(128\) | −6.78400 | −0.599626 | ||||||||
\(129\) | 7.49120 | 0.659563 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0767 | −0.967774 | −0.483887 | − | 0.875131i | \(-0.660775\pi\) | ||||
−0.483887 | + | 0.875131i | \(0.660775\pi\) | |||||||
\(132\) | 1.08493 | 0.0944314 | ||||||||
\(133\) | −1.31234 | −0.113794 | ||||||||
\(134\) | 12.0144 | 1.03789 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.32332 | −0.199223 | ||||||||
\(137\) | −17.3794 | −1.48482 | −0.742411 | − | 0.669944i | \(-0.766318\pi\) | ||||
−0.742411 | + | 0.669944i | \(0.766318\pi\) | |||||||
\(138\) | −0.593303 | −0.0505053 | ||||||||
\(139\) | 18.1370 | 1.53836 | 0.769182 | − | 0.639030i | \(-0.220664\pi\) | ||||
0.769182 | + | 0.639030i | \(0.220664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0931778 | 0.00784698 | ||||||||
\(142\) | −2.44852 | −0.205475 | ||||||||
\(143\) | −21.0431 | −1.75971 | ||||||||
\(144\) | 7.87606 | 0.656338 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.35636 | −0.691577 | ||||||||
\(147\) | 2.54873 | 0.210215 | ||||||||
\(148\) | −2.37832 | −0.195496 | ||||||||
\(149\) | 3.84207 | 0.314755 | 0.157377 | − | 0.987539i | \(-0.449696\pi\) | ||||
0.157377 | + | 0.987539i | \(0.449696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56714 | 0.208911 | 0.104455 | − | 0.994530i | \(-0.466690\pi\) | ||||
0.104455 | + | 0.994530i | \(0.466690\pi\) | |||||||
\(152\) | −1.20147 | −0.0974521 | ||||||||
\(153\) | 1.98467 | 0.160451 | ||||||||
\(154\) | 17.7893 | 1.43350 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.26857 | −0.101567 | ||||||||
\(157\) | 17.2668 | 1.37804 | 0.689019 | − | 0.724744i | \(-0.258042\pi\) | ||||
0.689019 | + | 0.724744i | \(0.258042\pi\) | |||||||
\(158\) | −4.85092 | −0.385918 | ||||||||
\(159\) | −8.26832 | −0.655720 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.44091 | 0.192370 | ||||||||
\(162\) | −6.96396 | −0.547140 | ||||||||
\(163\) | −23.3540 | −1.82922 | −0.914612 | − | 0.404334i | \(-0.867503\pi\) | ||||
−0.914612 | + | 0.404334i | \(0.867503\pi\) | |||||||
\(164\) | 4.04367 | 0.315758 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3545 | −1.19174 | ||||||||
\(167\) | −8.41952 | −0.651522 | −0.325761 | − | 0.945452i | \(-0.605621\pi\) | ||||
−0.325761 | + | 0.945452i | \(0.605621\pi\) | |||||||
\(168\) | 6.41891 | 0.495230 | ||||||||
\(169\) | 11.6048 | 0.892680 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.02634 | 0.0784862 | ||||||||
\(172\) | −4.71405 | −0.359443 | ||||||||
\(173\) | 17.0232 | 1.29425 | 0.647125 | − | 0.762384i | \(-0.275971\pi\) | ||||
0.647125 | + | 0.762384i | \(0.275971\pi\) | |||||||
\(174\) | −0.0898676 | −0.00681284 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.8827 | 0.971068 | ||||||||
\(177\) | −5.00237 | −0.376001 | ||||||||
\(178\) | −4.33710 | −0.325080 | ||||||||
\(179\) | −6.03220 | −0.450868 | −0.225434 | − | 0.974258i | \(-0.572380\pi\) | ||||
−0.225434 | + | 0.974258i | \(0.572380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.22485 | 0.0910422 | 0.0455211 | − | 0.998963i | \(-0.485505\pi\) | ||||
0.0455211 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(182\) | −20.8003 | −1.54182 | ||||||||
\(183\) | −2.90854 | −0.215005 | ||||||||
\(184\) | 2.23469 | 0.164744 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.93132 | 0.288259 | ||||||||
\(187\) | 3.24627 | 0.237391 | ||||||||
\(188\) | −0.0586347 | −0.00427638 | ||||||||
\(189\) | −11.8257 | −0.860196 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8963 | −1.07786 | −0.538930 | − | 0.842350i | \(-0.681171\pi\) | ||||
−0.538930 | + | 0.842350i | \(0.681171\pi\) | |||||||
\(192\) | 5.67144 | 0.409301 | ||||||||
\(193\) | 10.1687 | 0.731959 | 0.365979 | − | 0.930623i | \(-0.380734\pi\) | ||||
0.365979 | + | 0.930623i | \(0.380734\pi\) | |||||||
\(194\) | 4.53033 | 0.325259 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.60386 | −0.114561 | ||||||||
\(197\) | −7.97563 | −0.568240 | −0.284120 | − | 0.958789i | \(-0.591701\pi\) | ||||
−0.284120 | + | 0.958789i | \(0.591701\pi\) | |||||||
\(198\) | −13.9124 | −0.988713 | ||||||||
\(199\) | 11.9098 | 0.844266 | 0.422133 | − | 0.906534i | \(-0.361282\pi\) | ||||
0.422133 | + | 0.906534i | \(0.361282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05734 | −0.427252 | ||||||||
\(202\) | 18.0591 | 1.27063 | ||||||||
\(203\) | 0.369724 | 0.0259495 | ||||||||
\(204\) | 0.195700 | 0.0137017 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 22.0285 | 1.53480 | ||||||||
\(207\) | −1.90896 | −0.132682 | ||||||||
\(208\) | −15.0632 | −1.04445 | ||||||||
\(209\) | 1.67876 | 0.116122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.78994 | −0.605125 | −0.302562 | − | 0.953130i | \(-0.597842\pi\) | ||||
−0.302562 | + | 0.953130i | \(0.597842\pi\) | |||||||
\(212\) | 5.20307 | 0.357349 | ||||||||
\(213\) | 1.23448 | 0.0845850 | ||||||||
\(214\) | −3.40474 | −0.232743 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.8267 | −0.736663 | ||||||||
\(217\) | −16.1738 | −1.09795 | ||||||||
\(218\) | 15.0614 | 1.02009 | ||||||||
\(219\) | 4.21304 | 0.284691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.79574 | −0.255329 | ||||||||
\(222\) | −4.77891 | −0.320739 | ||||||||
\(223\) | 21.1387 | 1.41555 | 0.707777 | − | 0.706436i | \(-0.249698\pi\) | ||||
0.707777 | + | 0.706436i | \(0.249698\pi\) | |||||||
\(224\) | −7.40371 | −0.494681 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.5932 | −0.837688 | ||||||||
\(227\) | −14.0271 | −0.931014 | −0.465507 | − | 0.885044i | \(-0.654128\pi\) | ||||
−0.465507 | + | 0.885044i | \(0.654128\pi\) | |||||||
\(228\) | 0.101203 | 0.00670233 | ||||||||
\(229\) | −11.7594 | −0.777086 | −0.388543 | − | 0.921431i | \(-0.627021\pi\) | ||||
−0.388543 | + | 0.921431i | \(0.627021\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.96885 | −0.590107 | ||||||||
\(232\) | 0.338489 | 0.0222229 | ||||||||
\(233\) | 23.7103 | 1.55331 | 0.776657 | − | 0.629924i | \(-0.216914\pi\) | ||||
0.776657 | + | 0.629924i | \(0.216914\pi\) | |||||||
\(234\) | 16.2672 | 1.06342 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.14788 | 0.204910 | ||||||||
\(237\) | 2.44570 | 0.158865 | ||||||||
\(238\) | 3.20881 | 0.207996 | ||||||||
\(239\) | 11.9660 | 0.774018 | 0.387009 | − | 0.922076i | \(-0.373508\pi\) | ||||
0.387009 | + | 0.922076i | \(0.373508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −8.84727 | −0.568724 | ||||||||
\(243\) | 14.2088 | 0.911495 | ||||||||
\(244\) | 1.83028 | 0.117172 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.12522 | 0.518045 | ||||||||
\(247\) | −1.96291 | −0.124897 | ||||||||
\(248\) | −14.8074 | −0.940274 | ||||||||
\(249\) | 7.74132 | 0.490586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0885 | −0.889255 | −0.444628 | − | 0.895715i | \(-0.646664\pi\) | ||||
−0.444628 | + | 0.895715i | \(0.646664\pi\) | |||||||
\(252\) | 3.45050 | 0.217361 | ||||||||
\(253\) | −3.12244 | −0.196306 | ||||||||
\(254\) | 5.72542 | 0.359245 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.21470 | −0.575919 | ||||||||
\(257\) | −17.9138 | −1.11743 | −0.558716 | − | 0.829359i | \(-0.688706\pi\) | ||||
−0.558716 | + | 0.829359i | \(0.688706\pi\) | |||||||
\(258\) | −9.47225 | −0.589716 | ||||||||
\(259\) | 19.6609 | 1.22167 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.289149 | −0.0178979 | ||||||||
\(262\) | 14.0059 | 0.865288 | ||||||||
\(263\) | 29.1480 | 1.79734 | 0.898671 | − | 0.438624i | \(-0.144534\pi\) | ||||
0.898671 | + | 0.438624i | \(0.144534\pi\) | |||||||
\(264\) | −8.21115 | −0.505361 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.65939 | 0.101744 | ||||||||
\(267\) | 2.18665 | 0.133821 | ||||||||
\(268\) | 3.81175 | 0.232840 | ||||||||
\(269\) | 2.13547 | 0.130202 | 0.0651010 | − | 0.997879i | \(-0.479263\pi\) | ||||
0.0651010 | + | 0.997879i | \(0.479263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.0330 | −1.58139 | −0.790696 | − | 0.612209i | \(-0.790281\pi\) | ||||
−0.790696 | + | 0.612209i | \(0.790281\pi\) | |||||||
\(272\) | 2.32377 | 0.140899 | ||||||||
\(273\) | 10.4869 | 0.634697 | ||||||||
\(274\) | 21.9754 | 1.32758 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.188234 | −0.0113304 | ||||||||
\(277\) | 28.6489 | 1.72134 | 0.860672 | − | 0.509160i | \(-0.170044\pi\) | ||||
0.860672 | + | 0.509160i | \(0.170044\pi\) | |||||||
\(278\) | −22.9334 | −1.37545 | ||||||||
\(279\) | 12.6491 | 0.757279 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4049 | −0.740017 | −0.370008 | − | 0.929028i | \(-0.620645\pi\) | ||||
−0.370008 | + | 0.929028i | \(0.620645\pi\) | |||||||
\(282\) | −0.117819 | −0.00701600 | ||||||||
\(283\) | −11.8834 | −0.706397 | −0.353199 | − | 0.935548i | \(-0.614906\pi\) | ||||
−0.353199 | + | 0.935548i | \(0.614906\pi\) | |||||||
\(284\) | −0.776830 | −0.0460964 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.6079 | 1.57336 | ||||||||
\(287\) | −33.4279 | −1.97319 | ||||||||
\(288\) | 5.79021 | 0.341192 | ||||||||
\(289\) | −16.4144 | −0.965555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.28407 | −0.133894 | ||||||||
\(292\) | −2.65118 | −0.155148 | ||||||||
\(293\) | −22.2128 | −1.29769 | −0.648844 | − | 0.760921i | \(-0.724747\pi\) | ||||
−0.648844 | + | 0.760921i | \(0.724747\pi\) | |||||||
\(294\) | −3.22274 | −0.187954 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.9999 | 1.04622 | ||||||||
\(297\) | 15.1276 | 0.877794 | ||||||||
\(298\) | −4.85811 | −0.281423 | ||||||||
\(299\) | 3.65094 | 0.211139 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.9697 | 2.24618 | ||||||||
\(302\) | −3.24602 | −0.186787 | ||||||||
\(303\) | −9.10491 | −0.523063 | ||||||||
\(304\) | 1.20170 | 0.0689223 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.50951 | −0.143459 | ||||||||
\(307\) | 17.1344 | 0.977913 | 0.488956 | − | 0.872308i | \(-0.337378\pi\) | ||||
0.488956 | + | 0.872308i | \(0.337378\pi\) | |||||||
\(308\) | 5.64390 | 0.321591 | ||||||||
\(309\) | −11.1061 | −0.631806 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1453 | 0.688699 | 0.344349 | − | 0.938842i | \(-0.388100\pi\) | ||||
0.344349 | + | 0.938842i | \(0.388100\pi\) | |||||||
\(312\) | 9.60097 | 0.543548 | ||||||||
\(313\) | −13.8694 | −0.783945 | −0.391972 | − | 0.919977i | \(-0.628207\pi\) | ||||
−0.391972 | + | 0.919977i | \(0.628207\pi\) | |||||||
\(314\) | −21.8330 | −1.23210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.53902 | −0.0865769 | ||||||||
\(317\) | 31.9236 | 1.79301 | 0.896504 | − | 0.443035i | \(-0.146098\pi\) | ||||
0.896504 | + | 0.443035i | \(0.146098\pi\) | |||||||
\(318\) | 10.4549 | 0.586281 | ||||||||
\(319\) | −0.472955 | −0.0264804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.71658 | 0.0958100 | ||||||||
\(322\) | −3.08640 | −0.171999 | ||||||||
\(323\) | 0.302813 | 0.0168490 | ||||||||
\(324\) | −2.20942 | −0.122745 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.5299 | 1.63551 | ||||||||
\(327\) | −7.59354 | −0.419924 | ||||||||
\(328\) | −30.6039 | −1.68982 | ||||||||
\(329\) | 0.484717 | 0.0267233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6477 | −0.915041 | −0.457521 | − | 0.889199i | \(-0.651262\pi\) | ||||
−0.457521 | + | 0.889199i | \(0.651262\pi\) | |||||||
\(332\) | −4.87144 | −0.267355 | ||||||||
\(333\) | −15.3762 | −0.842608 | ||||||||
\(334\) | 10.6461 | 0.582527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.42014 | −0.350247 | ||||||||
\(337\) | −7.65951 | −0.417240 | −0.208620 | − | 0.977997i | \(-0.566897\pi\) | ||||
−0.208620 | + | 0.977997i | \(0.566897\pi\) | |||||||
\(338\) | −14.6737 | −0.798147 | ||||||||
\(339\) | 6.34915 | 0.344838 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6898 | 1.12041 | ||||||||
\(342\) | −1.29776 | −0.0701746 | ||||||||
\(343\) | −9.95562 | −0.537553 | ||||||||
\(344\) | 35.6775 | 1.92360 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.5250 | −1.15719 | ||||||||
\(347\) | −19.9181 | −1.06926 | −0.534629 | − | 0.845087i | \(-0.679549\pi\) | ||||
−0.534629 | + | 0.845087i | \(0.679549\pi\) | |||||||
\(348\) | −0.0285118 | −0.00152839 | ||||||||
\(349\) | −22.4664 | −1.20260 | −0.601300 | − | 0.799023i | \(-0.705351\pi\) | ||||
−0.601300 | + | 0.799023i | \(0.705351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.6881 | −0.944122 | ||||||||
\(352\) | 9.47092 | 0.504802 | ||||||||
\(353\) | 7.94392 | 0.422812 | 0.211406 | − | 0.977398i | \(-0.432196\pi\) | ||||
0.211406 | + | 0.977398i | \(0.432196\pi\) | |||||||
\(354\) | 6.32525 | 0.336183 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.37601 | −0.0729283 | ||||||||
\(357\) | −1.61779 | −0.0856228 | ||||||||
\(358\) | 7.62741 | 0.403121 | ||||||||
\(359\) | −33.5124 | −1.76872 | −0.884359 | − | 0.466808i | \(-0.845404\pi\) | ||||
−0.884359 | + | 0.466808i | \(0.845404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8434 | −0.991758 | ||||||||
\(362\) | −1.54876 | −0.0814009 | ||||||||
\(363\) | 4.46055 | 0.234118 | ||||||||
\(364\) | −6.59919 | −0.345891 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.67770 | 0.192236 | ||||||||
\(367\) | 7.64133 | 0.398874 | 0.199437 | − | 0.979911i | \(-0.436089\pi\) | ||||
0.199437 | + | 0.979911i | \(0.436089\pi\) | |||||||
\(368\) | −2.23512 | −0.116514 | ||||||||
\(369\) | 26.1429 | 1.36095 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.0124 | −2.23309 | ||||||||
\(372\) | 1.24727 | 0.0646679 | ||||||||
\(373\) | 14.5227 | 0.751954 | 0.375977 | − | 0.926629i | \(-0.377307\pi\) | ||||
0.375977 | + | 0.926629i | \(0.377307\pi\) | |||||||
\(374\) | −4.10475 | −0.212252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.443767 | 0.0228856 | ||||||||
\(377\) | 0.553007 | 0.0284813 | ||||||||
\(378\) | 14.9531 | 0.769103 | ||||||||
\(379\) | −1.63841 | −0.0841594 | −0.0420797 | − | 0.999114i | \(-0.513398\pi\) | ||||
−0.0420797 | + | 0.999114i | \(0.513398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.88660 | −0.147885 | ||||||||
\(382\) | 18.8357 | 0.963716 | ||||||||
\(383\) | 7.38637 | 0.377426 | 0.188713 | − | 0.982032i | \(-0.439568\pi\) | ||||
0.188713 | + | 0.982032i | \(0.439568\pi\) | |||||||
\(384\) | −4.32480 | −0.220699 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.8578 | −0.654445 | ||||||||
\(387\) | −30.4770 | −1.54923 | ||||||||
\(388\) | 1.43731 | 0.0729685 | ||||||||
\(389\) | −17.6275 | −0.893752 | −0.446876 | − | 0.894596i | \(-0.647463\pi\) | ||||
−0.446876 | + | 0.894596i | \(0.647463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.563223 | −0.0284834 | ||||||||
\(392\) | 12.1385 | 0.613088 | ||||||||
\(393\) | −7.06139 | −0.356200 | ||||||||
\(394\) | 10.0848 | 0.508064 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.41392 | −0.221808 | ||||||||
\(397\) | −16.2623 | −0.816180 | −0.408090 | − | 0.912942i | \(-0.633805\pi\) | ||||
−0.408090 | + | 0.912942i | \(0.633805\pi\) | |||||||
\(398\) | −15.0594 | −0.754859 | ||||||||
\(399\) | −0.836617 | −0.0418833 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.8733 | 0.842613 | 0.421306 | − | 0.906918i | \(-0.361572\pi\) | ||||
0.421306 | + | 0.906918i | \(0.361572\pi\) | |||||||
\(402\) | 7.65921 | 0.382007 | ||||||||
\(403\) | −24.1917 | −1.20508 | ||||||||
\(404\) | 5.72952 | 0.285054 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.467497 | −0.0232015 | ||||||||
\(407\) | −25.1504 | −1.24666 | ||||||||
\(408\) | −1.48112 | −0.0733264 | ||||||||
\(409\) | −24.7239 | −1.22252 | −0.611258 | − | 0.791431i | \(-0.709336\pi\) | ||||
−0.611258 | + | 0.791431i | \(0.709336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0794 | −0.546506 | ||||||||
\(412\) | 6.98885 | 0.344316 | ||||||||
\(413\) | −26.0227 | −1.28049 | ||||||||
\(414\) | 2.41378 | 0.118631 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.0740 | −0.542946 | ||||||||
\(417\) | 11.5624 | 0.566212 | ||||||||
\(418\) | −2.12271 | −0.103825 | ||||||||
\(419\) | −7.14295 | −0.348956 | −0.174478 | − | 0.984661i | \(-0.555824\pi\) | ||||
−0.174478 | + | 0.984661i | \(0.555824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7862 | 1.50043 | 0.750213 | − | 0.661196i | \(-0.229951\pi\) | ||||
0.750213 | + | 0.661196i | \(0.229951\pi\) | |||||||
\(422\) | 11.1144 | 0.541043 | ||||||||
\(423\) | −0.379082 | −0.0184316 | ||||||||
\(424\) | −39.3786 | −1.91239 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.56094 | −0.0756276 | ||||||||
\(427\) | −15.1304 | −0.732211 | ||||||||
\(428\) | −1.08020 | −0.0522137 | ||||||||
\(429\) | −13.4150 | −0.647682 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.8620 | −1.67924 | −0.839622 | − | 0.543172i | \(-0.817223\pi\) | ||||
−0.839622 | + | 0.543172i | \(0.817223\pi\) | |||||||
\(432\) | 10.8288 | 0.520999 | ||||||||
\(433\) | −23.9224 | −1.14964 | −0.574819 | − | 0.818281i | \(-0.694928\pi\) | ||||
−0.574819 | + | 0.818281i | \(0.694928\pi\) | |||||||
\(434\) | 20.4510 | 0.981680 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.77845 | 0.228846 | ||||||||
\(437\) | −0.291262 | −0.0139329 | ||||||||
\(438\) | −5.32718 | −0.254543 | ||||||||
\(439\) | −12.4505 | −0.594228 | −0.297114 | − | 0.954842i | \(-0.596024\pi\) | ||||
−0.297114 | + | 0.954842i | \(0.596024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.3692 | −0.493770 | ||||||||
\(442\) | 4.79952 | 0.228290 | ||||||||
\(443\) | −3.23466 | −0.153683 | −0.0768416 | − | 0.997043i | \(-0.524484\pi\) | ||||
−0.0768416 | + | 0.997043i | \(0.524484\pi\) | |||||||
\(444\) | −1.51618 | −0.0719546 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −26.7289 | −1.26565 | ||||||||
\(447\) | 2.44932 | 0.115849 | ||||||||
\(448\) | 29.5032 | 1.39390 | ||||||||
\(449\) | −9.28417 | −0.438147 | −0.219073 | − | 0.975708i | \(-0.570303\pi\) | ||||
−0.219073 | + | 0.975708i | \(0.570303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.7614 | 2.01355 | ||||||||
\(452\) | −3.99538 | −0.187927 | ||||||||
\(453\) | 1.63655 | 0.0768920 | ||||||||
\(454\) | 17.7366 | 0.832421 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.765939 | −0.0358684 | ||||||||
\(457\) | −33.9918 | −1.59007 | −0.795034 | − | 0.606565i | \(-0.792547\pi\) | ||||
−0.795034 | + | 0.606565i | \(0.792547\pi\) | |||||||
\(458\) | 14.8692 | 0.694793 | ||||||||
\(459\) | 2.72871 | 0.127365 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.28714 | 0.246247 | 0.123123 | − | 0.992391i | \(-0.460709\pi\) | ||||
0.123123 | + | 0.992391i | \(0.460709\pi\) | |||||||
\(462\) | 11.3407 | 0.527615 | ||||||||
\(463\) | −37.1728 | −1.72757 | −0.863783 | − | 0.503865i | \(-0.831911\pi\) | ||||
−0.863783 | + | 0.503865i | \(0.831911\pi\) | |||||||
\(464\) | −0.338554 | −0.0157170 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.9805 | −1.38882 | ||||||||
\(467\) | 1.01602 | 0.0470159 | 0.0235080 | − | 0.999724i | \(-0.492516\pi\) | ||||
0.0235080 | + | 0.999724i | \(0.492516\pi\) | |||||||
\(468\) | 5.16102 | 0.238568 | ||||||||
\(469\) | −31.5107 | −1.45503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0076 | 0.507202 | ||||||||
\(472\) | −23.8242 | −1.09660 | ||||||||
\(473\) | −49.8505 | −2.29213 | ||||||||
\(474\) | −3.09246 | −0.142042 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.01804 | 0.0466619 | ||||||||
\(477\) | 33.6386 | 1.54021 | ||||||||
\(478\) | −15.1305 | −0.692051 | ||||||||
\(479\) | 22.0556 | 1.00775 | 0.503874 | − | 0.863777i | \(-0.331908\pi\) | ||||
0.503874 | + | 0.863777i | \(0.331908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4074 | 1.34086 | ||||||||
\(482\) | 1.26445 | 0.0575941 | ||||||||
\(483\) | 1.55608 | 0.0708041 | ||||||||
\(484\) | −2.80693 | −0.127588 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17.9663 | −0.814969 | ||||||||
\(487\) | 2.46699 | 0.111790 | 0.0558949 | − | 0.998437i | \(-0.482199\pi\) | ||||
0.0558949 | + | 0.998437i | \(0.482199\pi\) | |||||||
\(488\) | −13.8522 | −0.627058 | ||||||||
\(489\) | −14.8882 | −0.673266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5530 | −1.24345 | −0.621725 | − | 0.783236i | \(-0.713568\pi\) | ||||
−0.621725 | + | 0.783236i | \(0.713568\pi\) | |||||||
\(492\) | 2.57784 | 0.116218 | ||||||||
\(493\) | −0.0853113 | −0.00384223 | ||||||||
\(494\) | 2.48200 | 0.111670 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.8103 | 0.665001 | ||||||||
\(497\) | 6.42183 | 0.288059 | ||||||||
\(498\) | −9.78851 | −0.438634 | ||||||||
\(499\) | −1.27747 | −0.0571873 | −0.0285937 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285937 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.36745 | −0.239800 | ||||||||
\(502\) | 17.8141 | 0.795084 | ||||||||
\(503\) | 16.4394 | 0.732996 | 0.366498 | − | 0.930419i | \(-0.380557\pi\) | ||||
0.366498 | + | 0.930419i | \(0.380557\pi\) | |||||||
\(504\) | −26.1145 | −1.16323 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.94816 | 0.175517 | ||||||||
\(507\) | 7.39810 | 0.328561 | ||||||||
\(508\) | 1.81647 | 0.0805929 | ||||||||
\(509\) | −14.2702 | −0.632514 | −0.316257 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316257 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.9165 | 0.969530 | ||||||||
\(512\) | 25.2195 | 1.11456 | ||||||||
\(513\) | 1.41111 | 0.0623020 | ||||||||
\(514\) | 22.6511 | 0.999097 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00521 | −0.132297 | ||||||||
\(517\) | −0.620056 | −0.0272700 | ||||||||
\(518\) | −24.8602 | −1.09229 | ||||||||
\(519\) | 10.8523 | 0.476363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.63068 | −0.246685 | −0.123342 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123342 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(522\) | 0.365615 | 0.0160025 | ||||||||
\(523\) | −19.1152 | −0.835848 | −0.417924 | − | 0.908482i | \(-0.637242\pi\) | ||||
−0.417924 | + | 0.908482i | \(0.637242\pi\) | |||||||
\(524\) | 4.44358 | 0.194119 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.8562 | −1.60701 | ||||||||
\(527\) | 3.73201 | 0.162569 | ||||||||
\(528\) | 8.21272 | 0.357413 | ||||||||
\(529\) | −22.4583 | −0.976446 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.3515 | 0.883180 | ||||||||
\(532\) | 0.526465 | 0.0228252 | ||||||||
\(533\) | −49.9992 | −2.16570 | ||||||||
\(534\) | −2.76491 | −0.119649 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.8486 | −1.24607 | ||||||||
\(537\) | −3.84553 | −0.165947 | ||||||||
\(538\) | −2.70020 | −0.116414 | ||||||||
\(539\) | −16.9606 | −0.730545 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9837 | −1.03114 | −0.515569 | − | 0.856848i | \(-0.672420\pi\) | ||||
−0.515569 | + | 0.856848i | \(0.672420\pi\) | |||||||
\(542\) | 32.9174 | 1.41392 | ||||||||
\(543\) | 0.780841 | 0.0335091 | ||||||||
\(544\) | 1.70836 | 0.0732452 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.2602 | −0.567484 | ||||||||
\(547\) | −2.05189 | −0.0877326 | −0.0438663 | − | 0.999037i | \(-0.513968\pi\) | ||||
−0.0438663 | + | 0.999037i | \(0.513968\pi\) | |||||||
\(548\) | 6.97201 | 0.297830 | ||||||||
\(549\) | 11.8330 | 0.505021 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0441174 | −0.00187946 | ||||||||
\(552\) | 1.42462 | 0.0606358 | ||||||||
\(553\) | 12.7227 | 0.541024 | ||||||||
\(554\) | −36.2251 | −1.53906 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.27595 | −0.308569 | ||||||||
\(557\) | −15.2105 | −0.644488 | −0.322244 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322244 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(558\) | −15.9941 | −0.677084 | ||||||||
\(559\) | 58.2882 | 2.46533 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.06950 | 0.0873744 | ||||||||
\(562\) | 15.6854 | 0.661650 | ||||||||
\(563\) | −39.9537 | −1.68385 | −0.841924 | − | 0.539597i | \(-0.818577\pi\) | ||||
−0.841924 | + | 0.539597i | \(0.818577\pi\) | |||||||
\(564\) | −0.0373797 | −0.00157397 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.0260 | 0.631591 | ||||||||
\(567\) | 18.2646 | 0.767043 | ||||||||
\(568\) | 5.87931 | 0.246690 | ||||||||
\(569\) | −14.4798 | −0.607025 | −0.303513 | − | 0.952827i | \(-0.598159\pi\) | ||||
−0.303513 | + | 0.952827i | \(0.598159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0730 | 1.67700 | 0.838501 | − | 0.544901i | \(-0.183433\pi\) | ||||
0.838501 | + | 0.544901i | \(0.183433\pi\) | |||||||
\(572\) | 8.44176 | 0.352968 | ||||||||
\(573\) | −9.49642 | −0.396719 | ||||||||
\(574\) | 42.2679 | 1.76423 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.0735 | −0.961398 | ||||||||
\(577\) | −8.10574 | −0.337446 | −0.168723 | − | 0.985663i | \(-0.553964\pi\) | ||||
−0.168723 | + | 0.985663i | \(0.553964\pi\) | |||||||
\(578\) | 20.7552 | 0.863304 | ||||||||
\(579\) | 6.48255 | 0.269406 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.2709 | 1.67072 | ||||||||
\(582\) | 2.88809 | 0.119715 | ||||||||
\(583\) | 55.0219 | 2.27878 | ||||||||
\(584\) | 20.0650 | 0.830295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.0870 | 1.16026 | ||||||||
\(587\) | −18.2675 | −0.753981 | −0.376991 | − | 0.926217i | \(-0.623041\pi\) | ||||
−0.376991 | + | 0.926217i | \(0.623041\pi\) | |||||||
\(588\) | −1.02246 | −0.0421656 | ||||||||
\(589\) | 1.92995 | 0.0795221 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.08447 | −0.209147 | ||||||||
\(592\) | −18.0033 | −0.739933 | ||||||||
\(593\) | 36.5874 | 1.50246 | 0.751232 | − | 0.660038i | \(-0.229460\pi\) | ||||
0.751232 | + | 0.660038i | \(0.229460\pi\) | |||||||
\(594\) | −19.1281 | −0.784837 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.54131 | −0.0631344 | ||||||||
\(597\) | 7.59253 | 0.310742 | ||||||||
\(598\) | −4.61643 | −0.188780 | ||||||||
\(599\) | 38.6587 | 1.57955 | 0.789775 | − | 0.613396i | \(-0.210197\pi\) | ||||
0.789775 | + | 0.613396i | \(0.210197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7738 | 0.684219 | 0.342110 | − | 0.939660i | \(-0.388859\pi\) | ||||
0.342110 | + | 0.939660i | \(0.388859\pi\) | |||||||
\(602\) | −49.2753 | −2.00831 | ||||||||
\(603\) | 24.6435 | 1.00356 | ||||||||
\(604\) | −1.02985 | −0.0419039 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.5127 | 0.467672 | ||||||||
\(607\) | 21.6480 | 0.878664 | 0.439332 | − | 0.898325i | \(-0.355215\pi\) | ||||
0.439332 | + | 0.898325i | \(0.355215\pi\) | |||||||
\(608\) | 0.883450 | 0.0358286 | ||||||||
\(609\) | 0.235699 | 0.00955101 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.725006 | 0.0293306 | ||||||||
\(612\) | −0.796180 | −0.0321837 | ||||||||
\(613\) | −30.5788 | −1.23507 | −0.617533 | − | 0.786545i | \(-0.711868\pi\) | ||||
−0.617533 | + | 0.786545i | \(0.711868\pi\) | |||||||
\(614\) | −21.6656 | −0.874353 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42.7149 | −1.72103 | ||||||||
\(617\) | −31.9095 | −1.28463 | −0.642314 | − | 0.766442i | \(-0.722026\pi\) | ||||
−0.642314 | + | 0.766442i | \(0.722026\pi\) | |||||||
\(618\) | 14.0432 | 0.564899 | ||||||||
\(619\) | −2.60539 | −0.104720 | −0.0523598 | − | 0.998628i | \(-0.516674\pi\) | ||||
−0.0523598 | + | 0.998628i | \(0.516674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.62462 | −0.105322 | ||||||||
\(622\) | −15.3572 | −0.615766 | ||||||||
\(623\) | 11.3751 | 0.455733 | ||||||||
\(624\) | −9.60280 | −0.384420 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.5372 | 0.700926 | ||||||||
\(627\) | 1.07021 | 0.0427401 | ||||||||
\(628\) | −6.92682 | −0.276410 | ||||||||
\(629\) | −4.53661 | −0.180887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.43947 | −0.176732 | −0.0883662 | − | 0.996088i | \(-0.528165\pi\) | ||||
−0.0883662 | + | 0.996088i | \(0.528165\pi\) | |||||||
\(632\) | 11.6479 | 0.463327 | ||||||||
\(633\) | −5.60360 | −0.222723 | ||||||||
\(634\) | −40.3658 | −1.60313 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.31696 | 0.131526 | ||||||||
\(637\) | 19.8314 | 0.785747 | ||||||||
\(638\) | 0.598028 | 0.0236762 | ||||||||
\(639\) | −5.02232 | −0.198680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0249 | 0.672441 | 0.336221 | − | 0.941783i | \(-0.390851\pi\) | ||||
0.336221 | + | 0.941783i | \(0.390851\pi\) | |||||||
\(642\) | −2.17053 | −0.0856639 | ||||||||
\(643\) | 27.2144 | 1.07323 | 0.536616 | − | 0.843827i | \(-0.319702\pi\) | ||||
0.536616 | + | 0.843827i | \(0.319702\pi\) | |||||||
\(644\) | −0.979207 | −0.0385862 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.382893 | −0.0150647 | ||||||||
\(647\) | 34.5285 | 1.35745 | 0.678727 | − | 0.734391i | \(-0.262532\pi\) | ||||
0.678727 | + | 0.734391i | \(0.262532\pi\) | |||||||
\(648\) | 16.7216 | 0.656887 | ||||||||
\(649\) | 33.2885 | 1.30669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3108 | −0.404114 | ||||||||
\(652\) | 9.36880 | 0.366910 | ||||||||
\(653\) | 28.1181 | 1.10035 | 0.550173 | − | 0.835051i | \(-0.314562\pi\) | ||||
0.550173 | + | 0.835051i | \(0.314562\pi\) | |||||||
\(654\) | 9.60166 | 0.375455 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.6097 | 1.19511 | ||||||||
\(657\) | −17.1402 | −0.668704 | ||||||||
\(658\) | −0.612901 | −0.0238934 | ||||||||
\(659\) | −30.6584 | −1.19428 | −0.597142 | − | 0.802136i | \(-0.703697\pi\) | ||||
−0.597142 | + | 0.802136i | \(0.703697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2109 | 0.747219 | 0.373610 | − | 0.927586i | \(-0.378120\pi\) | ||||
0.373610 | + | 0.927586i | \(0.378120\pi\) | |||||||
\(662\) | 21.0502 | 0.818139 | ||||||||
\(663\) | −2.41979 | −0.0939767 | ||||||||
\(664\) | 36.8687 | 1.43078 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.4424 | 0.753377 | ||||||||
\(667\) | 0.0820568 | 0.00317725 | ||||||||
\(668\) | 3.37762 | 0.130684 | ||||||||
\(669\) | 13.4760 | 0.521011 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3550 | 0.747191 | ||||||||
\(672\) | −4.71987 | −0.182073 | ||||||||
\(673\) | −24.0589 | −0.927401 | −0.463700 | − | 0.885992i | \(-0.653479\pi\) | ||||
−0.463700 | + | 0.885992i | \(0.653479\pi\) | |||||||
\(674\) | 9.68507 | 0.373055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.65546 | −0.179056 | ||||||||
\(677\) | 11.7427 | 0.451308 | 0.225654 | − | 0.974208i | \(-0.427548\pi\) | ||||
0.225654 | + | 0.974208i | \(0.427548\pi\) | |||||||
\(678\) | −8.02818 | −0.308320 | ||||||||
\(679\) | −11.8819 | −0.455984 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.94231 | −0.342670 | ||||||||
\(682\) | −26.1612 | −1.00176 | ||||||||
\(683\) | −19.2688 | −0.737301 | −0.368650 | − | 0.929568i | \(-0.620180\pi\) | ||||
−0.368650 | + | 0.929568i | \(0.620180\pi\) | |||||||
\(684\) | −0.411732 | −0.0157430 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.5884 | 0.480627 | ||||||||
\(687\) | −7.49665 | −0.286015 | ||||||||
\(688\) | −35.6843 | −1.36045 | ||||||||
\(689\) | −64.3349 | −2.45097 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.497698 | 0.0189333 | 0.00946666 | − | 0.999955i | \(-0.496987\pi\) | ||||
0.00946666 | + | 0.999955i | \(0.496987\pi\) | |||||||
\(692\) | −6.82912 | −0.259604 | ||||||||
\(693\) | 36.4886 | 1.38609 | ||||||||
\(694\) | 25.1854 | 0.956025 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.215787 | 0.00817938 | ||||||||
\(697\) | 7.71327 | 0.292161 | ||||||||
\(698\) | 28.4077 | 1.07525 | ||||||||
\(699\) | 15.1153 | 0.571715 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5246 | −1.00182 | −0.500910 | − | 0.865499i | \(-0.667001\pi\) | ||||
−0.500910 | + | 0.865499i | \(0.667001\pi\) | |||||||
\(702\) | 22.3658 | 0.844141 | ||||||||
\(703\) | −2.34604 | −0.0884826 | ||||||||
\(704\) | −37.7409 | −1.42241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.0447 | −0.378037 | ||||||||
\(707\) | −47.3643 | −1.78132 | ||||||||
\(708\) | 2.00678 | 0.0754193 | ||||||||
\(709\) | −23.0989 | −0.867497 | −0.433748 | − | 0.901034i | \(-0.642809\pi\) | ||||
−0.433748 | + | 0.901034i | \(0.642809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.95002 | −0.373155 | ||||||||
\(712\) | 10.4141 | 0.390285 | ||||||||
\(713\) | −3.58964 | −0.134433 | ||||||||
\(714\) | 2.04562 | 0.0765554 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.41991 | 0.0904362 | ||||||||
\(717\) | 7.62836 | 0.284886 | ||||||||
\(718\) | 42.3748 | 1.58141 | ||||||||
\(719\) | −29.3624 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684427\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684427\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −57.7749 | −2.15165 | ||||||||
\(722\) | 23.8265 | 0.886732 | ||||||||
\(723\) | −0.637501 | −0.0237089 | ||||||||
\(724\) | −0.491366 | −0.0182615 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.64014 | −0.209325 | ||||||||
\(727\) | −17.0424 | −0.632069 | −0.316035 | − | 0.948748i | \(-0.602352\pi\) | ||||
−0.316035 | + | 0.948748i | \(0.602352\pi\) | |||||||
\(728\) | 49.9449 | 1.85108 | ||||||||
\(729\) | −7.46438 | −0.276459 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.99200 | −0.332581 | ||||||||
\(732\) | 1.16680 | 0.0431263 | ||||||||
\(733\) | 43.2745 | 1.59838 | 0.799190 | − | 0.601079i | \(-0.205262\pi\) | ||||
0.799190 | + | 0.601079i | \(0.205262\pi\) | |||||||
\(734\) | −9.66209 | −0.356634 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.64319 | −0.0605687 | ||||||||
\(737\) | 40.3089 | 1.48480 | ||||||||
\(738\) | −33.0564 | −1.21682 | ||||||||
\(739\) | −12.5494 | −0.461639 | −0.230819 | − | 0.972997i | \(-0.574141\pi\) | ||||
−0.230819 | + | 0.972997i | \(0.574141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.25135 | −0.0459697 | ||||||||
\(742\) | 54.3870 | 1.99661 | ||||||||
\(743\) | 11.7612 | 0.431475 | 0.215737 | − | 0.976451i | \(-0.430784\pi\) | ||||
0.215737 | + | 0.976451i | \(0.430784\pi\) | |||||||
\(744\) | −9.43976 | −0.346078 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.3632 | −0.672323 | ||||||||
\(747\) | −31.4946 | −1.15233 | ||||||||
\(748\) | −1.30229 | −0.0476165 | ||||||||
\(749\) | 8.92975 | 0.326286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.9386 | 0.800552 | 0.400276 | − | 0.916395i | \(-0.368914\pi\) | ||||
0.400276 | + | 0.916395i | \(0.368914\pi\) | |||||||
\(752\) | −0.443852 | −0.0161856 | ||||||||
\(753\) | −8.98140 | −0.327300 | ||||||||
\(754\) | −0.699250 | −0.0254652 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.74408 | 0.172540 | ||||||||
\(757\) | 31.1830 | 1.13337 | 0.566683 | − | 0.823936i | \(-0.308226\pi\) | ||||
0.566683 | + | 0.823936i | \(0.308226\pi\) | |||||||
\(758\) | 2.07169 | 0.0752470 | ||||||||
\(759\) | −1.99056 | −0.0722526 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5289 | 0.852922 | 0.426461 | − | 0.904506i | \(-0.359760\pi\) | ||||
0.426461 | + | 0.904506i | \(0.359760\pi\) | |||||||
\(762\) | 3.64996 | 0.132224 | ||||||||
\(763\) | −39.5021 | −1.43007 | ||||||||
\(764\) | 5.97589 | 0.216200 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.33970 | −0.337457 | ||||||||
\(767\) | −38.9229 | −1.40542 | ||||||||
\(768\) | −5.87438 | −0.211973 | ||||||||
\(769\) | −32.4863 | −1.17148 | −0.585742 | − | 0.810497i | \(-0.699197\pi\) | ||||
−0.585742 | + | 0.810497i | \(0.699197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4201 | −0.411283 | ||||||||
\(772\) | −4.07933 | −0.146818 | ||||||||
\(773\) | 1.41782 | 0.0509955 | 0.0254977 | − | 0.999675i | \(-0.491883\pi\) | ||||
0.0254977 | + | 0.999675i | \(0.491883\pi\) | |||||||
\(774\) | 38.5367 | 1.38517 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.8781 | −0.390500 | ||||||||
\(777\) | 12.5338 | 0.449648 | ||||||||
\(778\) | 22.2892 | 0.799105 | ||||||||
\(779\) | 3.98880 | 0.142913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.21489 | −0.293952 | ||||||||
\(782\) | 0.712167 | 0.0254670 | ||||||||
\(783\) | −0.397550 | −0.0142073 | ||||||||
\(784\) | −12.1409 | −0.433602 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.92878 | 0.318479 | ||||||||
\(787\) | −24.1473 | −0.860759 | −0.430380 | − | 0.902648i | \(-0.641620\pi\) | ||||
−0.430380 | + | 0.902648i | \(0.641620\pi\) | |||||||
\(788\) | 3.19955 | 0.113979 | ||||||||
\(789\) | 18.5819 | 0.661532 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.0287 | 1.17437 | ||||||||
\(792\) | 33.4060 | 1.18703 | ||||||||
\(793\) | −22.6310 | −0.803651 | ||||||||
\(794\) | 20.5628 | 0.729748 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.77781 | −0.169345 | ||||||||
\(797\) | −47.3782 | −1.67822 | −0.839111 | − | 0.543960i | \(-0.816924\pi\) | ||||
−0.839111 | + | 0.543960i | \(0.816924\pi\) | |||||||
\(798\) | 1.05786 | 0.0374479 | ||||||||
\(799\) | −0.111845 | −0.00395680 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.89610 | −0.314328 | ||||||||
\(802\) | −21.3355 | −0.753381 | ||||||||
\(803\) | −28.0359 | −0.989365 | ||||||||
\(804\) | 2.43000 | 0.0856994 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.5892 | 1.07746 | ||||||||
\(807\) | 1.36136 | 0.0479223 | ||||||||
\(808\) | −43.3629 | −1.52550 | ||||||||
\(809\) | −4.46224 | −0.156884 | −0.0784420 | − | 0.996919i | \(-0.524995\pi\) | ||||
−0.0784420 | + | 0.996919i | \(0.524995\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09836 | −0.0385685 | −0.0192843 | − | 0.999814i | \(-0.506139\pi\) | ||||
−0.0192843 | + | 0.999814i | \(0.506139\pi\) | |||||||
\(812\) | −0.148320 | −0.00520502 | ||||||||
\(813\) | −16.5961 | −0.582049 | ||||||||
\(814\) | 31.8015 | 1.11464 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.48140 | 0.0518595 | ||||||||
\(817\) | −4.65007 | −0.162686 | ||||||||
\(818\) | 31.2621 | 1.09305 | ||||||||
\(819\) | −42.6647 | −1.49083 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8213 | 1.28507 | 0.642536 | − | 0.766255i | \(-0.277882\pi\) | ||||
0.642536 | + | 0.766255i | \(0.277882\pi\) | |||||||
\(822\) | 14.0093 | 0.488631 | ||||||||
\(823\) | −37.0100 | −1.29009 | −0.645043 | − | 0.764146i | \(-0.723161\pi\) | ||||
−0.645043 | + | 0.764146i | \(0.723161\pi\) | |||||||
\(824\) | −52.8940 | −1.84265 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32.9044 | 1.14489 | ||||||||
\(827\) | 25.5191 | 0.887388 | 0.443694 | − | 0.896178i | \(-0.353668\pi\) | ||||
0.443694 | + | 0.896178i | \(0.353668\pi\) | |||||||
\(828\) | 0.765807 | 0.0266136 | ||||||||
\(829\) | −16.4498 | −0.571324 | −0.285662 | − | 0.958330i | \(-0.592214\pi\) | ||||
−0.285662 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2637 | 0.633560 | ||||||||
\(832\) | 44.1289 | 1.52989 | ||||||||
\(833\) | −3.05934 | −0.106000 | ||||||||
\(834\) | −14.6200 | −0.506251 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.673460 | −0.0232921 | ||||||||
\(837\) | 17.3911 | 0.601126 | ||||||||
\(838\) | 9.03191 | 0.312002 | ||||||||
\(839\) | 51.1330 | 1.76531 | 0.882653 | − | 0.470025i | \(-0.155755\pi\) | ||||
0.882653 | + | 0.470025i | \(0.155755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9876 | −0.999571 | ||||||||
\(842\) | −38.9276 | −1.34153 | ||||||||
\(843\) | −7.90816 | −0.272371 | ||||||||
\(844\) | 3.52622 | 0.121377 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.479330 | 0.0164797 | ||||||||
\(847\) | 23.2041 | 0.797301 | ||||||||
\(848\) | 39.3862 | 1.35253 | ||||||||
\(849\) | −7.57570 | −0.259997 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.36355 | 0.149581 | ||||||||
\(852\) | −0.495230 | −0.0169663 | ||||||||
\(853\) | −45.0455 | −1.54233 | −0.771164 | − | 0.636636i | \(-0.780325\pi\) | ||||
−0.771164 | + | 0.636636i | \(0.780325\pi\) | |||||||
\(854\) | 19.1316 | 0.654671 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.17535 | 0.279428 | ||||||||
\(857\) | 0.941226 | 0.0321517 | 0.0160758 | − | 0.999871i | \(-0.494883\pi\) | ||||
0.0160758 | + | 0.999871i | \(0.494883\pi\) | |||||||
\(858\) | 16.9626 | 0.579093 | ||||||||
\(859\) | 4.59938 | 0.156929 | 0.0784644 | − | 0.996917i | \(-0.474998\pi\) | ||||
0.0784644 | + | 0.996917i | \(0.474998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.3103 | −0.726254 | ||||||||
\(862\) | 44.0813 | 1.50141 | ||||||||
\(863\) | −12.8946 | −0.438937 | −0.219469 | − | 0.975620i | \(-0.570432\pi\) | ||||
−0.219469 | + | 0.975620i | \(0.570432\pi\) | |||||||
\(864\) | 7.96094 | 0.270837 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.2487 | 1.02789 | ||||||||
\(867\) | −10.4642 | −0.355384 | ||||||||
\(868\) | 6.48838 | 0.220230 | ||||||||
\(869\) | −16.2750 | −0.552092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.1316 | −1.59699 | ||||||||
\(872\) | −36.1649 | −1.22470 | ||||||||
\(873\) | 9.29244 | 0.314501 | ||||||||
\(874\) | 0.368286 | 0.0124575 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.69013 | −0.0571041 | ||||||||
\(877\) | −1.28343 | −0.0433383 | −0.0216691 | − | 0.999765i | \(-0.506898\pi\) | ||||
−0.0216691 | + | 0.999765i | \(0.506898\pi\) | |||||||
\(878\) | 15.7430 | 0.531300 | ||||||||
\(879\) | −14.1607 | −0.477629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.72028 | −0.192721 | −0.0963606 | − | 0.995346i | \(-0.530720\pi\) | ||||
−0.0963606 | + | 0.995346i | \(0.530720\pi\) | |||||||
\(882\) | 13.1113 | 0.441481 | ||||||||
\(883\) | −20.1652 | −0.678614 | −0.339307 | − | 0.940676i | \(-0.610192\pi\) | ||||
−0.339307 | + | 0.940676i | \(0.610192\pi\) | |||||||
\(884\) | 1.52272 | 0.0512146 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.09006 | 0.137408 | ||||||||
\(887\) | 13.7132 | 0.460443 | 0.230221 | − | 0.973138i | \(-0.426055\pi\) | ||||
0.230221 | + | 0.973138i | \(0.426055\pi\) | |||||||
\(888\) | 11.4749 | 0.385074 | ||||||||
\(889\) | −15.0163 | −0.503630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.3644 | −0.782735 | ||||||||
\(892\) | −8.48013 | −0.283936 | ||||||||
\(893\) | −0.0578390 | −0.00193551 | ||||||||
\(894\) | −3.09705 | −0.103581 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.4979 | −0.751603 | ||||||||
\(897\) | 2.32748 | 0.0777122 | ||||||||
\(898\) | 11.7394 | 0.391748 | ||||||||
\(899\) | −0.543722 | −0.0181341 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.92481 | 0.330644 | ||||||||
\(902\) | −54.0696 | −1.80032 | ||||||||
\(903\) | 24.8432 | 0.826731 | ||||||||
\(904\) | 30.2384 | 1.00571 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.06934 | −0.0687492 | ||||||||
\(907\) | 11.7711 | 0.390853 | 0.195427 | − | 0.980718i | \(-0.437391\pi\) | ||||
0.195427 | + | 0.980718i | \(0.437391\pi\) | |||||||
\(908\) | 5.62720 | 0.186745 | ||||||||
\(909\) | 37.0422 | 1.22861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3287 | 0.408469 | 0.204234 | − | 0.978922i | \(-0.434530\pi\) | ||||
0.204234 | + | 0.978922i | \(0.434530\pi\) | |||||||
\(912\) | 0.766085 | 0.0253676 | ||||||||
\(913\) | −51.5150 | −1.70490 | ||||||||
\(914\) | 42.9809 | 1.42168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.71748 | 0.155870 | ||||||||
\(917\) | −36.7338 | −1.21306 | ||||||||
\(918\) | −3.45032 | −0.113878 | ||||||||
\(919\) | 27.1688 | 0.896216 | 0.448108 | − | 0.893980i | \(-0.352098\pi\) | ||||
0.448108 | + | 0.893980i | \(0.352098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9232 | 0.359932 | ||||||||
\(922\) | −6.68533 | −0.220170 | ||||||||
\(923\) | 9.60534 | 0.316164 | ||||||||
\(924\) | 3.59799 | 0.118365 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 47.0031 | 1.54462 | ||||||||
\(927\) | 45.1839 | 1.48404 | ||||||||
\(928\) | −0.248893 | −0.00817033 | ||||||||
\(929\) | 6.23154 | 0.204450 | 0.102225 | − | 0.994761i | \(-0.467404\pi\) | ||||
0.102225 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.58209 | −0.0518510 | ||||||||
\(932\) | −9.51176 | −0.311568 | ||||||||
\(933\) | 7.74266 | 0.253483 | ||||||||
\(934\) | −1.28471 | −0.0420370 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.0603 | −1.27673 | ||||||||
\(937\) | 33.4598 | 1.09308 | 0.546542 | − | 0.837432i | \(-0.315944\pi\) | ||||
0.546542 | + | 0.837432i | \(0.315944\pi\) | |||||||
\(938\) | 39.8437 | 1.30094 | ||||||||
\(939\) | −8.84175 | −0.288540 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9090 | −0.942406 | −0.471203 | − | 0.882025i | \(-0.656180\pi\) | ||||
−0.471203 | + | 0.882025i | \(0.656180\pi\) | |||||||
\(942\) | −13.9185 | −0.453490 | ||||||||
\(943\) | −7.41902 | −0.241597 | ||||||||
\(944\) | 23.8288 | 0.775561 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.0335 | 2.04940 | ||||||||
\(947\) | −12.2378 | −0.397675 | −0.198837 | − | 0.980033i | \(-0.563717\pi\) | ||||
−0.198837 | + | 0.980033i | \(0.563717\pi\) | |||||||
\(948\) | −0.981129 | −0.0318656 | ||||||||
\(949\) | 32.7812 | 1.06412 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.3513 | 0.659937 | ||||||||
\(952\) | −7.70489 | −0.249717 | ||||||||
\(953\) | 29.2078 | 0.946133 | 0.473066 | − | 0.881027i | \(-0.343147\pi\) | ||||
0.473066 | + | 0.881027i | \(0.343147\pi\) | |||||||
\(954\) | −42.5344 | −1.37710 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.80036 | −0.155255 | ||||||||
\(957\) | −0.301509 | −0.00974641 | ||||||||
\(958\) | −27.8883 | −0.901029 | ||||||||
\(959\) | −57.6357 | −1.86115 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.21448 | −0.232725 | ||||||||
\(962\) | −37.1842 | −1.19887 | ||||||||
\(963\) | −6.98368 | −0.225046 | ||||||||
\(964\) | 0.401165 | 0.0129207 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.96759 | −0.0633060 | ||||||||
\(967\) | −2.99676 | −0.0963693 | −0.0481847 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481847 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(968\) | 21.2438 | 0.682800 | ||||||||
\(969\) | 0.193044 | 0.00620146 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.6237 | −1.14322 | −0.571609 | − | 0.820526i | \(-0.693681\pi\) | ||||
−0.571609 | + | 0.820526i | \(0.693681\pi\) | |||||||
\(972\) | −5.70008 | −0.182830 | ||||||||
\(973\) | 60.1483 | 1.92826 | ||||||||
\(974\) | −3.11938 | −0.0999515 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8548 | 0.443482 | ||||||||
\(977\) | −32.0035 | −1.02388 | −0.511942 | − | 0.859020i | \(-0.671074\pi\) | ||||
−0.511942 | + | 0.859020i | \(0.671074\pi\) | |||||||
\(978\) | 18.8253 | 0.601968 | ||||||||
\(979\) | −14.5511 | −0.465057 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.8934 | 0.986350 | ||||||||
\(982\) | 34.8394 | 1.11177 | ||||||||
\(983\) | −36.9419 | −1.17826 | −0.589132 | − | 0.808037i | \(-0.700530\pi\) | ||||
−0.589132 | + | 0.808037i | \(0.700530\pi\) | |||||||
\(984\) | −19.5100 | −0.621956 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.107872 | 0.00343534 | ||||||||
\(987\) | 0.309008 | 0.00983582 | ||||||||
\(988\) | 0.787450 | 0.0250521 | ||||||||
\(989\) | 8.64898 | 0.275022 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2274 | 1.18257 | 0.591283 | − | 0.806464i | \(-0.298622\pi\) | ||||
0.591283 | + | 0.806464i | \(0.298622\pi\) | |||||||
\(992\) | 10.8880 | 0.345695 | ||||||||
\(993\) | −10.6129 | −0.336791 | ||||||||
\(994\) | −8.12009 | −0.257554 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.10555 | −0.0984031 | ||||||||
\(997\) | 56.6610 | 1.79447 | 0.897237 | − | 0.441550i | \(-0.145571\pi\) | ||||
0.897237 | + | 0.441550i | \(0.145571\pi\) | |||||||
\(998\) | 1.61529 | 0.0511313 | ||||||||
\(999\) | −21.1406 | −0.668859 |
(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 | 6025.2.a.l.1.14 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.27 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.14 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.27 | yes | 40 | 5.4 | even | 2 |