Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37986 | −1.68281 | −0.841406 | − | 0.540403i | \(-0.818272\pi\) | ||||
−0.841406 | + | 0.540403i | \(0.818272\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.66372 | 1.83186 | ||||||||
\(5\) | 3.68734 | 1.64903 | 0.824514 | − | 0.565841i | \(-0.191449\pi\) | ||||
0.824514 | + | 0.565841i | \(0.191449\pi\) | |||||||
\(6\) | −2.37986 | −0.971572 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.95941 | −1.39986 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.77534 | −2.77501 | ||||||||
\(11\) | −6.26313 | −1.88840 | −0.944202 | − | 0.329366i | \(-0.893165\pi\) | ||||
−0.944202 | + | 0.329366i | \(0.893165\pi\) | |||||||
\(12\) | 3.66372 | 1.05762 | ||||||||
\(13\) | −3.25624 | −0.903118 | −0.451559 | − | 0.892241i | \(-0.649132\pi\) | ||||
−0.451559 | + | 0.892241i | \(0.649132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.68734 | 0.952067 | ||||||||
\(16\) | 2.09539 | 0.523848 | ||||||||
\(17\) | 0.146265 | 0.0354744 | 0.0177372 | − | 0.999843i | \(-0.494354\pi\) | ||||
0.0177372 | + | 0.999843i | \(0.494354\pi\) | |||||||
\(18\) | −2.37986 | −0.560938 | ||||||||
\(19\) | −1.78602 | −0.409741 | −0.204870 | − | 0.978789i | \(-0.565677\pi\) | ||||
−0.204870 | + | 0.978789i | \(0.565677\pi\) | |||||||
\(20\) | 13.5094 | 3.02079 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.9053 | 3.17783 | ||||||||
\(23\) | −3.11368 | −0.649247 | −0.324623 | − | 0.945843i | \(-0.605238\pi\) | ||||
−0.324623 | + | 0.945843i | \(0.605238\pi\) | |||||||
\(24\) | −3.95941 | −0.808211 | ||||||||
\(25\) | 8.59647 | 1.71929 | ||||||||
\(26\) | 7.74938 | 1.51978 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.08462 | 0.758495 | 0.379247 | − | 0.925295i | \(-0.376183\pi\) | ||||
0.379247 | + | 0.925295i | \(0.376183\pi\) | |||||||
\(30\) | −8.77534 | −1.60215 | ||||||||
\(31\) | 1.31731 | 0.236596 | 0.118298 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118298 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(32\) | 2.93209 | 0.518325 | ||||||||
\(33\) | −6.26313 | −1.09027 | ||||||||
\(34\) | −0.348089 | −0.0596967 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.66372 | 0.610620 | ||||||||
\(37\) | 3.67591 | 0.604316 | 0.302158 | − | 0.953258i | \(-0.402293\pi\) | ||||
0.302158 | + | 0.953258i | \(0.402293\pi\) | |||||||
\(38\) | 4.25047 | 0.689517 | ||||||||
\(39\) | −3.25624 | −0.521415 | ||||||||
\(40\) | −14.5997 | −2.30841 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.08247 | −1.38506 | −0.692532 | − | 0.721388i | \(-0.743505\pi\) | ||||
−0.692532 | + | 0.721388i | \(0.743505\pi\) | |||||||
\(44\) | −22.9463 | −3.45929 | ||||||||
\(45\) | 3.68734 | 0.549676 | ||||||||
\(46\) | 7.41011 | 1.09256 | ||||||||
\(47\) | 11.5238 | 1.68093 | 0.840463 | − | 0.541869i | \(-0.182283\pi\) | ||||
0.840463 | + | 0.541869i | \(0.182283\pi\) | |||||||
\(48\) | 2.09539 | 0.302444 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −20.4584 | −2.89325 | ||||||||
\(51\) | 0.146265 | 0.0204811 | ||||||||
\(52\) | −11.9299 | −1.65438 | ||||||||
\(53\) | 4.41701 | 0.606723 | 0.303361 | − | 0.952876i | \(-0.401891\pi\) | ||||
0.303361 | + | 0.952876i | \(0.401891\pi\) | |||||||
\(54\) | −2.37986 | −0.323857 | ||||||||
\(55\) | −23.0943 | −3.11403 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.78602 | −0.236564 | ||||||||
\(58\) | −9.72081 | −1.27640 | ||||||||
\(59\) | 1.71894 | 0.223786 | 0.111893 | − | 0.993720i | \(-0.464309\pi\) | ||||
0.111893 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(60\) | 13.5094 | 1.74405 | ||||||||
\(61\) | 6.02287 | 0.771150 | 0.385575 | − | 0.922677i | \(-0.374003\pi\) | ||||
0.385575 | + | 0.922677i | \(0.374003\pi\) | |||||||
\(62\) | −3.13502 | −0.398147 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.1687 | −1.39609 | ||||||||
\(65\) | −12.0069 | −1.48927 | ||||||||
\(66\) | 14.9053 | 1.83472 | ||||||||
\(67\) | 1.38835 | 0.169615 | 0.0848073 | − | 0.996397i | \(-0.472973\pi\) | ||||
0.0848073 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(68\) | 0.535872 | 0.0649840 | ||||||||
\(69\) | −3.11368 | −0.374843 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.92495 | 1.05920 | 0.529598 | − | 0.848249i | \(-0.322343\pi\) | ||||
0.529598 | + | 0.848249i | \(0.322343\pi\) | |||||||
\(72\) | −3.95941 | −0.466621 | ||||||||
\(73\) | 8.93911 | 1.04624 | 0.523122 | − | 0.852258i | \(-0.324767\pi\) | ||||
0.523122 | + | 0.852258i | \(0.324767\pi\) | |||||||
\(74\) | −8.74814 | −1.01695 | ||||||||
\(75\) | 8.59647 | 0.992635 | ||||||||
\(76\) | −6.54346 | −0.750587 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.74938 | 0.877445 | ||||||||
\(79\) | −10.3689 | −1.16659 | −0.583294 | − | 0.812261i | \(-0.698237\pi\) | ||||
−0.583294 | + | 0.812261i | \(0.698237\pi\) | |||||||
\(80\) | 7.72642 | 0.863840 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.37986 | 0.262811 | ||||||||
\(83\) | −10.6436 | −1.16829 | −0.584146 | − | 0.811649i | \(-0.698570\pi\) | ||||
−0.584146 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.539327 | 0.0584982 | ||||||||
\(86\) | 21.6150 | 2.33080 | ||||||||
\(87\) | 4.08462 | 0.437917 | ||||||||
\(88\) | 24.7983 | 2.64351 | ||||||||
\(89\) | −1.75624 | −0.186161 | −0.0930805 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930805 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(90\) | −8.77534 | −0.925002 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −11.4076 | −1.18933 | ||||||||
\(93\) | 1.31731 | 0.136599 | ||||||||
\(94\) | −27.4251 | −2.82868 | ||||||||
\(95\) | −6.58565 | −0.675674 | ||||||||
\(96\) | 2.93209 | 0.299255 | ||||||||
\(97\) | 5.53442 | 0.561935 | 0.280968 | − | 0.959717i | \(-0.409345\pi\) | ||||
0.280968 | + | 0.959717i | \(0.409345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.26313 | −0.629468 | ||||||||
\(100\) | 31.4950 | 3.14950 | ||||||||
\(101\) | 15.9955 | 1.59161 | 0.795806 | − | 0.605552i | \(-0.207048\pi\) | ||||
0.795806 | + | 0.605552i | \(0.207048\pi\) | |||||||
\(102\) | −0.348089 | −0.0344659 | ||||||||
\(103\) | 18.2558 | 1.79880 | 0.899400 | − | 0.437127i | \(-0.144004\pi\) | ||||
0.899400 | + | 0.437127i | \(0.144004\pi\) | |||||||
\(104\) | 12.8928 | 1.26424 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.5118 | −1.02100 | ||||||||
\(107\) | −3.48468 | −0.336877 | −0.168439 | − | 0.985712i | \(-0.553872\pi\) | ||||
−0.168439 | + | 0.985712i | \(0.553872\pi\) | |||||||
\(108\) | 3.66372 | 0.352541 | ||||||||
\(109\) | 12.1345 | 1.16228 | 0.581138 | − | 0.813805i | \(-0.302608\pi\) | ||||
0.581138 | + | 0.813805i | \(0.302608\pi\) | |||||||
\(110\) | 54.9611 | 5.24033 | ||||||||
\(111\) | 3.67591 | 0.348902 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1948 | 1.05312 | 0.526558 | − | 0.850139i | \(-0.323482\pi\) | ||||
0.526558 | + | 0.850139i | \(0.323482\pi\) | |||||||
\(114\) | 4.25047 | 0.398093 | ||||||||
\(115\) | −11.4812 | −1.07063 | ||||||||
\(116\) | 14.9649 | 1.38946 | ||||||||
\(117\) | −3.25624 | −0.301039 | ||||||||
\(118\) | −4.09082 | −0.376591 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −14.5997 | −1.33276 | ||||||||
\(121\) | 28.2268 | 2.56607 | ||||||||
\(122\) | −14.3336 | −1.29770 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 4.82626 | 0.433411 | ||||||||
\(125\) | 13.2614 | 1.18614 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7467 | −1.75224 | −0.876119 | − | 0.482095i | \(-0.839876\pi\) | ||||
−0.876119 | + | 0.482095i | \(0.839876\pi\) | |||||||
\(128\) | 20.7158 | 1.83104 | ||||||||
\(129\) | −9.08247 | −0.799667 | ||||||||
\(130\) | 28.5746 | 2.50616 | ||||||||
\(131\) | 19.2431 | 1.68128 | 0.840640 | − | 0.541594i | \(-0.182179\pi\) | ||||
0.840640 | + | 0.541594i | \(0.182179\pi\) | |||||||
\(132\) | −22.9463 | −1.99722 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.30408 | −0.285429 | ||||||||
\(135\) | 3.68734 | 0.317356 | ||||||||
\(136\) | −0.579121 | −0.0496592 | ||||||||
\(137\) | −3.63718 | −0.310745 | −0.155373 | − | 0.987856i | \(-0.549658\pi\) | ||||
−0.155373 | + | 0.987856i | \(0.549658\pi\) | |||||||
\(138\) | 7.41011 | 0.630790 | ||||||||
\(139\) | 15.6912 | 1.33091 | 0.665457 | − | 0.746436i | \(-0.268237\pi\) | ||||
0.665457 | + | 0.746436i | \(0.268237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5238 | 0.970483 | ||||||||
\(142\) | −21.2401 | −1.78243 | ||||||||
\(143\) | 20.3942 | 1.70545 | ||||||||
\(144\) | 2.09539 | 0.174616 | ||||||||
\(145\) | 15.0614 | 1.25078 | ||||||||
\(146\) | −21.2738 | −1.76063 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.4675 | 1.10702 | ||||||||
\(149\) | 15.4694 | 1.26730 | 0.633651 | − | 0.773619i | \(-0.281555\pi\) | ||||
0.633651 | + | 0.773619i | \(0.281555\pi\) | |||||||
\(150\) | −20.4584 | −1.67042 | ||||||||
\(151\) | −6.09366 | −0.495895 | −0.247947 | − | 0.968774i | \(-0.579756\pi\) | ||||
−0.247947 | + | 0.968774i | \(0.579756\pi\) | |||||||
\(152\) | 7.07157 | 0.573580 | ||||||||
\(153\) | 0.146265 | 0.0118248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.85738 | 0.390154 | ||||||||
\(156\) | −11.9299 | −0.955160 | ||||||||
\(157\) | 2.07672 | 0.165740 | 0.0828701 | − | 0.996560i | \(-0.473591\pi\) | ||||
0.0828701 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(158\) | 24.6764 | 1.96315 | ||||||||
\(159\) | 4.41701 | 0.350292 | ||||||||
\(160\) | 10.8116 | 0.854732 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.37986 | −0.186979 | ||||||||
\(163\) | 11.3480 | 0.888841 | 0.444421 | − | 0.895818i | \(-0.353410\pi\) | ||||
0.444421 | + | 0.895818i | \(0.353410\pi\) | |||||||
\(164\) | −3.66372 | −0.286088 | ||||||||
\(165\) | −23.0943 | −1.79789 | ||||||||
\(166\) | 25.3303 | 1.96602 | ||||||||
\(167\) | 19.2640 | 1.49069 | 0.745347 | − | 0.666677i | \(-0.232284\pi\) | ||||
0.745347 | + | 0.666677i | \(0.232284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.39691 | −0.184378 | ||||||||
\(170\) | −1.28352 | −0.0984416 | ||||||||
\(171\) | −1.78602 | −0.136580 | ||||||||
\(172\) | −33.2756 | −2.53724 | ||||||||
\(173\) | −11.0874 | −0.842961 | −0.421481 | − | 0.906837i | \(-0.638489\pi\) | ||||
−0.421481 | + | 0.906837i | \(0.638489\pi\) | |||||||
\(174\) | −9.72081 | −0.736933 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.1237 | −0.989236 | ||||||||
\(177\) | 1.71894 | 0.129203 | ||||||||
\(178\) | 4.17960 | 0.313274 | ||||||||
\(179\) | 15.7592 | 1.17790 | 0.588951 | − | 0.808169i | \(-0.299541\pi\) | ||||
0.588951 | + | 0.808169i | \(0.299541\pi\) | |||||||
\(180\) | 13.5094 | 1.00693 | ||||||||
\(181\) | −3.24953 | −0.241536 | −0.120768 | − | 0.992681i | \(-0.538536\pi\) | ||||
−0.120768 | + | 0.992681i | \(0.538536\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.02287 | 0.445223 | ||||||||
\(184\) | 12.3283 | 0.908856 | ||||||||
\(185\) | 13.5543 | 0.996534 | ||||||||
\(186\) | −3.13502 | −0.229871 | ||||||||
\(187\) | −0.916074 | −0.0669900 | ||||||||
\(188\) | 42.2201 | 3.07922 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.6729 | 1.13703 | ||||||||
\(191\) | −0.889555 | −0.0643660 | −0.0321830 | − | 0.999482i | \(-0.510246\pi\) | ||||
−0.0321830 | + | 0.999482i | \(0.510246\pi\) | |||||||
\(192\) | −11.1687 | −0.806034 | ||||||||
\(193\) | −2.48347 | −0.178764 | −0.0893821 | − | 0.995997i | \(-0.528489\pi\) | ||||
−0.0893821 | + | 0.995997i | \(0.528489\pi\) | |||||||
\(194\) | −13.1711 | −0.945632 | ||||||||
\(195\) | −12.0069 | −0.859829 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0761 | −1.14537 | −0.572686 | − | 0.819775i | \(-0.694099\pi\) | ||||
−0.572686 | + | 0.819775i | \(0.694099\pi\) | |||||||
\(198\) | 14.9053 | 1.05928 | ||||||||
\(199\) | 6.08609 | 0.431432 | 0.215716 | − | 0.976456i | \(-0.430792\pi\) | ||||
0.215716 | + | 0.976456i | \(0.430792\pi\) | |||||||
\(200\) | −34.0370 | −2.40678 | ||||||||
\(201\) | 1.38835 | 0.0979270 | ||||||||
\(202\) | −38.0670 | −2.67838 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.535872 | 0.0375186 | ||||||||
\(205\) | −3.68734 | −0.257535 | ||||||||
\(206\) | −43.4462 | −3.02704 | ||||||||
\(207\) | −3.11368 | −0.216416 | ||||||||
\(208\) | −6.82309 | −0.473096 | ||||||||
\(209\) | 11.1861 | 0.773756 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.1991 | −1.80362 | −0.901809 | − | 0.432135i | \(-0.857761\pi\) | ||||
−0.901809 | + | 0.432135i | \(0.857761\pi\) | |||||||
\(212\) | 16.1827 | 1.11143 | ||||||||
\(213\) | 8.92495 | 0.611527 | ||||||||
\(214\) | 8.29305 | 0.566901 | ||||||||
\(215\) | −33.4901 | −2.28401 | ||||||||
\(216\) | −3.95941 | −0.269404 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −28.8784 | −1.95589 | ||||||||
\(219\) | 8.93911 | 0.604049 | ||||||||
\(220\) | −84.6109 | −5.70447 | ||||||||
\(221\) | −0.476272 | −0.0320375 | ||||||||
\(222\) | −8.74814 | −0.587137 | ||||||||
\(223\) | −18.3279 | −1.22733 | −0.613663 | − | 0.789568i | \(-0.710305\pi\) | ||||
−0.613663 | + | 0.789568i | \(0.710305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.59647 | 0.573098 | ||||||||
\(226\) | −26.6420 | −1.77220 | ||||||||
\(227\) | 18.3473 | 1.21776 | 0.608878 | − | 0.793264i | \(-0.291620\pi\) | ||||
0.608878 | + | 0.793264i | \(0.291620\pi\) | |||||||
\(228\) | −6.54346 | −0.433351 | ||||||||
\(229\) | 4.23971 | 0.280168 | 0.140084 | − | 0.990140i | \(-0.455263\pi\) | ||||
0.140084 | + | 0.990140i | \(0.455263\pi\) | |||||||
\(230\) | 27.3236 | 1.80166 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1727 | −1.06179 | ||||||||
\(233\) | 16.9183 | 1.10836 | 0.554179 | − | 0.832398i | \(-0.313032\pi\) | ||||
0.554179 | + | 0.832398i | \(0.313032\pi\) | |||||||
\(234\) | 7.74938 | 0.506593 | ||||||||
\(235\) | 42.4923 | 2.77189 | ||||||||
\(236\) | 6.29769 | 0.409945 | ||||||||
\(237\) | −10.3689 | −0.673530 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.6129 | −0.815859 | −0.407929 | − | 0.913014i | \(-0.633749\pi\) | ||||
−0.407929 | + | 0.913014i | \(0.633749\pi\) | |||||||
\(240\) | 7.72642 | 0.498738 | ||||||||
\(241\) | 28.8035 | 1.85539 | 0.927697 | − | 0.373334i | \(-0.121786\pi\) | ||||
0.927697 | + | 0.373334i | \(0.121786\pi\) | |||||||
\(242\) | −67.1757 | −4.31822 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 22.0661 | 1.41264 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.37986 | 0.151734 | ||||||||
\(247\) | 5.81570 | 0.370044 | ||||||||
\(248\) | −5.21578 | −0.331202 | ||||||||
\(249\) | −10.6436 | −0.674513 | ||||||||
\(250\) | −31.5603 | −1.99605 | ||||||||
\(251\) | 30.2514 | 1.90945 | 0.954726 | − | 0.297488i | \(-0.0961487\pi\) | ||||
0.954726 | + | 0.297488i | \(0.0961487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5014 | 1.22604 | ||||||||
\(254\) | 46.9943 | 2.94869 | ||||||||
\(255\) | 0.539327 | 0.0337740 | ||||||||
\(256\) | −26.9632 | −1.68520 | ||||||||
\(257\) | 18.8356 | 1.17493 | 0.587466 | − | 0.809249i | \(-0.300126\pi\) | ||||
0.587466 | + | 0.809249i | \(0.300126\pi\) | |||||||
\(258\) | 21.6150 | 1.34569 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −43.9897 | −2.72813 | ||||||||
\(261\) | 4.08462 | 0.252832 | ||||||||
\(262\) | −45.7959 | −2.82928 | ||||||||
\(263\) | 20.7414 | 1.27897 | 0.639486 | − | 0.768803i | \(-0.279147\pi\) | ||||
0.639486 | + | 0.768803i | \(0.279147\pi\) | |||||||
\(264\) | 24.7983 | 1.52623 | ||||||||
\(265\) | 16.2870 | 1.00050 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.75624 | −0.107480 | ||||||||
\(268\) | 5.08654 | 0.310710 | ||||||||
\(269\) | −2.26170 | −0.137898 | −0.0689492 | − | 0.997620i | \(-0.521965\pi\) | ||||
−0.0689492 | + | 0.997620i | \(0.521965\pi\) | |||||||
\(270\) | −8.77534 | −0.534050 | ||||||||
\(271\) | −25.1898 | −1.53017 | −0.765086 | − | 0.643928i | \(-0.777304\pi\) | ||||
−0.765086 | + | 0.643928i | \(0.777304\pi\) | |||||||
\(272\) | 0.306481 | 0.0185832 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.65597 | 0.522926 | ||||||||
\(275\) | −53.8408 | −3.24672 | ||||||||
\(276\) | −11.4076 | −0.686659 | ||||||||
\(277\) | −10.2447 | −0.615544 | −0.307772 | − | 0.951460i | \(-0.599583\pi\) | ||||
−0.307772 | + | 0.951460i | \(0.599583\pi\) | |||||||
\(278\) | −37.3429 | −2.23968 | ||||||||
\(279\) | 1.31731 | 0.0788655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.76403 | 0.403508 | 0.201754 | − | 0.979436i | \(-0.435336\pi\) | ||||
0.201754 | + | 0.979436i | \(0.435336\pi\) | |||||||
\(282\) | −27.4251 | −1.63314 | ||||||||
\(283\) | 2.07715 | 0.123474 | 0.0617369 | − | 0.998092i | \(-0.480336\pi\) | ||||
0.0617369 | + | 0.998092i | \(0.480336\pi\) | |||||||
\(284\) | 32.6985 | 1.94030 | ||||||||
\(285\) | −6.58565 | −0.390100 | ||||||||
\(286\) | −48.5354 | −2.86996 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.93209 | 0.172775 | ||||||||
\(289\) | −16.9786 | −0.998742 | ||||||||
\(290\) | −35.8439 | −2.10483 | ||||||||
\(291\) | 5.53442 | 0.324434 | ||||||||
\(292\) | 32.7504 | 1.91657 | ||||||||
\(293\) | −8.71064 | −0.508881 | −0.254440 | − | 0.967088i | \(-0.581891\pi\) | ||||
−0.254440 | + | 0.967088i | \(0.581891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.33830 | 0.369030 | ||||||||
\(296\) | −14.5544 | −0.845959 | ||||||||
\(297\) | −6.26313 | −0.363424 | ||||||||
\(298\) | −36.8150 | −2.13263 | ||||||||
\(299\) | 10.1389 | 0.586346 | ||||||||
\(300\) | 31.4950 | 1.81837 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.5020 | 0.834498 | ||||||||
\(303\) | 15.9955 | 0.918918 | ||||||||
\(304\) | −3.74240 | −0.214642 | ||||||||
\(305\) | 22.2084 | 1.27165 | ||||||||
\(306\) | −0.348089 | −0.0198989 | ||||||||
\(307\) | −27.2743 | −1.55662 | −0.778312 | − | 0.627877i | \(-0.783924\pi\) | ||||
−0.778312 | + | 0.627877i | \(0.783924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2558 | 1.03854 | ||||||||
\(310\) | −11.5599 | −0.656556 | ||||||||
\(311\) | 10.3281 | 0.585654 | 0.292827 | − | 0.956166i | \(-0.405404\pi\) | ||||
0.292827 | + | 0.956166i | \(0.405404\pi\) | |||||||
\(312\) | 12.8928 | 0.729910 | ||||||||
\(313\) | −30.1284 | −1.70296 | −0.851480 | − | 0.524387i | \(-0.824295\pi\) | ||||
−0.851480 | + | 0.524387i | \(0.824295\pi\) | |||||||
\(314\) | −4.94229 | −0.278910 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −37.9886 | −2.13703 | ||||||||
\(317\) | 19.6474 | 1.10351 | 0.551755 | − | 0.834006i | \(-0.313958\pi\) | ||||
0.551755 | + | 0.834006i | \(0.313958\pi\) | |||||||
\(318\) | −10.5118 | −0.589475 | ||||||||
\(319\) | −25.5825 | −1.43234 | ||||||||
\(320\) | −41.1829 | −2.30219 | ||||||||
\(321\) | −3.48468 | −0.194496 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.261231 | −0.0145353 | ||||||||
\(324\) | 3.66372 | 0.203540 | ||||||||
\(325\) | −27.9922 | −1.55273 | ||||||||
\(326\) | −27.0065 | −1.49575 | ||||||||
\(327\) | 12.1345 | 0.671040 | ||||||||
\(328\) | 3.95941 | 0.218622 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 54.9611 | 3.02551 | ||||||||
\(331\) | −33.1392 | −1.82150 | −0.910748 | − | 0.412962i | \(-0.864494\pi\) | ||||
−0.910748 | + | 0.412962i | \(0.864494\pi\) | |||||||
\(332\) | −38.9953 | −2.14015 | ||||||||
\(333\) | 3.67591 | 0.201439 | ||||||||
\(334\) | −45.8456 | −2.50856 | ||||||||
\(335\) | 5.11933 | 0.279699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6674 | 1.18030 | 0.590148 | − | 0.807295i | \(-0.299069\pi\) | ||||
0.590148 | + | 0.807295i | \(0.299069\pi\) | |||||||
\(338\) | 5.70430 | 0.310273 | ||||||||
\(339\) | 11.1948 | 0.608017 | ||||||||
\(340\) | 1.97594 | 0.107161 | ||||||||
\(341\) | −8.25050 | −0.446790 | ||||||||
\(342\) | 4.25047 | 0.229839 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 35.9612 | 1.93890 | ||||||||
\(345\) | −11.4812 | −0.618126 | ||||||||
\(346\) | 26.3865 | 1.41855 | ||||||||
\(347\) | 21.5837 | 1.15867 | 0.579337 | − | 0.815088i | \(-0.303311\pi\) | ||||
0.579337 | + | 0.815088i | \(0.303311\pi\) | |||||||
\(348\) | 14.9649 | 0.802202 | ||||||||
\(349\) | −22.1900 | −1.18781 | −0.593903 | − | 0.804537i | \(-0.702414\pi\) | ||||
−0.593903 | + | 0.804537i | \(0.702414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.25624 | −0.173805 | ||||||||
\(352\) | −18.3640 | −0.978807 | ||||||||
\(353\) | 17.7402 | 0.944215 | 0.472108 | − | 0.881541i | \(-0.343493\pi\) | ||||
0.472108 | + | 0.881541i | \(0.343493\pi\) | |||||||
\(354\) | −4.09082 | −0.217425 | ||||||||
\(355\) | 32.9093 | 1.74665 | ||||||||
\(356\) | −6.43436 | −0.341021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −37.5047 | −1.98219 | ||||||||
\(359\) | 8.89293 | 0.469351 | 0.234675 | − | 0.972074i | \(-0.424597\pi\) | ||||
0.234675 | + | 0.972074i | \(0.424597\pi\) | |||||||
\(360\) | −14.5997 | −0.769471 | ||||||||
\(361\) | −15.8101 | −0.832113 | ||||||||
\(362\) | 7.73343 | 0.406460 | ||||||||
\(363\) | 28.2268 | 1.48152 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9615 | 1.72529 | ||||||||
\(366\) | −14.3336 | −0.749228 | ||||||||
\(367\) | −0.601211 | −0.0313830 | −0.0156915 | − | 0.999877i | \(-0.504995\pi\) | ||||
−0.0156915 | + | 0.999877i | \(0.504995\pi\) | |||||||
\(368\) | −6.52437 | −0.340106 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −32.2574 | −1.67698 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.82626 | 0.250230 | ||||||||
\(373\) | 2.16528 | 0.112114 | 0.0560570 | − | 0.998428i | \(-0.482147\pi\) | ||||
0.0560570 | + | 0.998428i | \(0.482147\pi\) | |||||||
\(374\) | 2.18012 | 0.112732 | ||||||||
\(375\) | 13.2614 | 0.684817 | ||||||||
\(376\) | −45.6276 | −2.35307 | ||||||||
\(377\) | −13.3005 | −0.685010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.85097 | −0.300544 | −0.150272 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150272 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(380\) | −24.1280 | −1.23774 | ||||||||
\(381\) | −19.7467 | −1.01165 | ||||||||
\(382\) | 2.11701 | 0.108316 | ||||||||
\(383\) | 5.09873 | 0.260533 | 0.130267 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130267 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(384\) | 20.7158 | 1.05715 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.91030 | 0.300827 | ||||||||
\(387\) | −9.08247 | −0.461688 | ||||||||
\(388\) | 20.2766 | 1.02939 | ||||||||
\(389\) | −38.2594 | −1.93983 | −0.969914 | − | 0.243449i | \(-0.921721\pi\) | ||||
−0.969914 | + | 0.243449i | \(0.921721\pi\) | |||||||
\(390\) | 28.5746 | 1.44693 | ||||||||
\(391\) | −0.455421 | −0.0230316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.2431 | 0.970687 | ||||||||
\(394\) | 38.2587 | 1.92745 | ||||||||
\(395\) | −38.2335 | −1.92374 | ||||||||
\(396\) | −22.9463 | −1.15310 | ||||||||
\(397\) | 25.6318 | 1.28642 | 0.643210 | − | 0.765689i | \(-0.277602\pi\) | ||||
0.643210 | + | 0.765689i | \(0.277602\pi\) | |||||||
\(398\) | −14.4840 | −0.726018 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.0130 | 0.900649 | ||||||||
\(401\) | −6.94500 | −0.346817 | −0.173408 | − | 0.984850i | \(-0.555478\pi\) | ||||
−0.173408 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(402\) | −3.30408 | −0.164793 | ||||||||
\(403\) | −4.28949 | −0.213675 | ||||||||
\(404\) | 58.6030 | 2.91561 | ||||||||
\(405\) | 3.68734 | 0.183225 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.0227 | −1.14119 | ||||||||
\(408\) | −0.579121 | −0.0286708 | ||||||||
\(409\) | −35.3203 | −1.74648 | −0.873238 | − | 0.487294i | \(-0.837984\pi\) | ||||
−0.873238 | + | 0.487294i | \(0.837984\pi\) | |||||||
\(410\) | 8.77534 | 0.433383 | ||||||||
\(411\) | −3.63718 | −0.179409 | ||||||||
\(412\) | 66.8842 | 3.29515 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.41011 | 0.364187 | ||||||||
\(415\) | −39.2467 | −1.92655 | ||||||||
\(416\) | −9.54758 | −0.468109 | ||||||||
\(417\) | 15.6912 | 0.768403 | ||||||||
\(418\) | −26.6212 | −1.30209 | ||||||||
\(419\) | −9.50778 | −0.464485 | −0.232243 | − | 0.972658i | \(-0.574606\pi\) | ||||
−0.232243 | + | 0.972658i | \(0.574606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.1034 | −0.979781 | −0.489891 | − | 0.871784i | \(-0.662963\pi\) | ||||
−0.489891 | + | 0.871784i | \(0.662963\pi\) | |||||||
\(422\) | 62.3500 | 3.03515 | ||||||||
\(423\) | 11.5238 | 0.560309 | ||||||||
\(424\) | −17.4887 | −0.849329 | ||||||||
\(425\) | 1.25736 | 0.0609909 | ||||||||
\(426\) | −21.2401 | −1.02909 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.7669 | −0.617111 | ||||||||
\(429\) | 20.3942 | 0.984643 | ||||||||
\(430\) | 79.7017 | 3.84356 | ||||||||
\(431\) | −26.1665 | −1.26040 | −0.630199 | − | 0.776434i | \(-0.717027\pi\) | ||||
−0.630199 | + | 0.776434i | \(0.717027\pi\) | |||||||
\(432\) | 2.09539 | 0.100815 | ||||||||
\(433\) | 35.2333 | 1.69320 | 0.846601 | − | 0.532227i | \(-0.178645\pi\) | ||||
0.846601 | + | 0.532227i | \(0.178645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.0614 | 0.722138 | ||||||||
\(436\) | 44.4574 | 2.12912 | ||||||||
\(437\) | 5.56108 | 0.266023 | ||||||||
\(438\) | −21.2738 | −1.01650 | ||||||||
\(439\) | −10.1078 | −0.482419 | −0.241210 | − | 0.970473i | \(-0.577544\pi\) | ||||
−0.241210 | + | 0.970473i | \(0.577544\pi\) | |||||||
\(440\) | 91.4397 | 4.35922 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.13346 | 0.0539132 | ||||||||
\(443\) | 24.3692 | 1.15782 | 0.578908 | − | 0.815393i | \(-0.303479\pi\) | ||||
0.578908 | + | 0.815393i | \(0.303479\pi\) | |||||||
\(444\) | 13.4675 | 0.639139 | ||||||||
\(445\) | −6.47585 | −0.306985 | ||||||||
\(446\) | 43.6177 | 2.06536 | ||||||||
\(447\) | 15.4694 | 0.731678 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5381 | −0.922061 | −0.461031 | − | 0.887384i | \(-0.652520\pi\) | ||||
−0.461031 | + | 0.887384i | \(0.652520\pi\) | |||||||
\(450\) | −20.4584 | −0.964417 | ||||||||
\(451\) | 6.26313 | 0.294919 | ||||||||
\(452\) | 41.0145 | 1.92916 | ||||||||
\(453\) | −6.09366 | −0.286305 | ||||||||
\(454\) | −43.6640 | −2.04926 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.07157 | 0.331157 | ||||||||
\(457\) | 26.2573 | 1.22826 | 0.614132 | − | 0.789203i | \(-0.289506\pi\) | ||||
0.614132 | + | 0.789203i | \(0.289506\pi\) | |||||||
\(458\) | −10.0899 | −0.471471 | ||||||||
\(459\) | 0.146265 | 0.00682705 | ||||||||
\(460\) | −42.0638 | −1.96124 | ||||||||
\(461\) | 11.5537 | 0.538110 | 0.269055 | − | 0.963125i | \(-0.413289\pi\) | ||||
0.269055 | + | 0.963125i | \(0.413289\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.17471 | −0.0545936 | −0.0272968 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272968 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(464\) | 8.55887 | 0.397336 | ||||||||
\(465\) | 4.85738 | 0.225256 | ||||||||
\(466\) | −40.2632 | −1.86516 | ||||||||
\(467\) | 5.32580 | 0.246449 | 0.123224 | − | 0.992379i | \(-0.460677\pi\) | ||||
0.123224 | + | 0.992379i | \(0.460677\pi\) | |||||||
\(468\) | −11.9299 | −0.551462 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −101.126 | −4.66458 | ||||||||
\(471\) | 2.07672 | 0.0956901 | ||||||||
\(472\) | −6.80597 | −0.313270 | ||||||||
\(473\) | 56.8847 | 2.61556 | ||||||||
\(474\) | 24.6764 | 1.13343 | ||||||||
\(475\) | −15.3534 | −0.704465 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.41701 | 0.202241 | ||||||||
\(478\) | 30.0168 | 1.37294 | ||||||||
\(479\) | 25.6439 | 1.17170 | 0.585849 | − | 0.810420i | \(-0.300761\pi\) | ||||
0.585849 | + | 0.810420i | \(0.300761\pi\) | |||||||
\(480\) | 10.8116 | 0.493480 | ||||||||
\(481\) | −11.9696 | −0.545769 | ||||||||
\(482\) | −68.5481 | −3.12228 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 103.415 | 4.70068 | ||||||||
\(485\) | 20.4073 | 0.926647 | ||||||||
\(486\) | −2.37986 | −0.107952 | ||||||||
\(487\) | −3.25149 | −0.147339 | −0.0736696 | − | 0.997283i | \(-0.523471\pi\) | ||||
−0.0736696 | + | 0.997283i | \(0.523471\pi\) | |||||||
\(488\) | −23.8470 | −1.07950 | ||||||||
\(489\) | 11.3480 | 0.513173 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5010 | −0.880069 | −0.440034 | − | 0.897981i | \(-0.645034\pi\) | ||||
−0.440034 | + | 0.897981i | \(0.645034\pi\) | |||||||
\(492\) | −3.66372 | −0.165173 | ||||||||
\(493\) | 0.597435 | 0.0269071 | ||||||||
\(494\) | −13.8405 | −0.622715 | ||||||||
\(495\) | −23.0943 | −1.03801 | ||||||||
\(496\) | 2.76029 | 0.123941 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 25.3303 | 1.13508 | ||||||||
\(499\) | 32.6281 | 1.46064 | 0.730318 | − | 0.683107i | \(-0.239372\pi\) | ||||
0.730318 | + | 0.683107i | \(0.239372\pi\) | |||||||
\(500\) | 48.5861 | 2.17284 | ||||||||
\(501\) | 19.2640 | 0.860652 | ||||||||
\(502\) | −71.9940 | −3.21325 | ||||||||
\(503\) | −21.7937 | −0.971732 | −0.485866 | − | 0.874033i | \(-0.661496\pi\) | ||||
−0.485866 | + | 0.874033i | \(0.661496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 58.9808 | 2.62461 | ||||||||
\(506\) | −46.4105 | −2.06320 | ||||||||
\(507\) | −2.39691 | −0.106451 | ||||||||
\(508\) | −72.3464 | −3.20985 | ||||||||
\(509\) | −18.9583 | −0.840312 | −0.420156 | − | 0.907452i | \(-0.638025\pi\) | ||||
−0.420156 | + | 0.907452i | \(0.638025\pi\) | |||||||
\(510\) | −1.28352 | −0.0568353 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7369 | 1.00484 | ||||||||
\(513\) | −1.78602 | −0.0788546 | ||||||||
\(514\) | −44.8260 | −1.97719 | ||||||||
\(515\) | 67.3154 | 2.96627 | ||||||||
\(516\) | −33.2756 | −1.46488 | ||||||||
\(517\) | −72.1754 | −3.17427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.0874 | −0.486684 | ||||||||
\(520\) | 47.5401 | 2.08477 | ||||||||
\(521\) | −3.35523 | −0.146995 | −0.0734975 | − | 0.997295i | \(-0.523416\pi\) | ||||
−0.0734975 | + | 0.997295i | \(0.523416\pi\) | |||||||
\(522\) | −9.72081 | −0.425468 | ||||||||
\(523\) | −18.9321 | −0.827843 | −0.413922 | − | 0.910312i | \(-0.635841\pi\) | ||||
−0.413922 | + | 0.910312i | \(0.635841\pi\) | |||||||
\(524\) | 70.5014 | 3.07987 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −49.3617 | −2.15227 | ||||||||
\(527\) | 0.192676 | 0.00839311 | ||||||||
\(528\) | −13.1237 | −0.571136 | ||||||||
\(529\) | −13.3050 | −0.578479 | ||||||||
\(530\) | −38.7608 | −1.68366 | ||||||||
\(531\) | 1.71894 | 0.0745955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.25624 | 0.141043 | ||||||||
\(534\) | 4.17960 | 0.180869 | ||||||||
\(535\) | −12.8492 | −0.555520 | ||||||||
\(536\) | −5.49706 | −0.237437 | ||||||||
\(537\) | 15.7592 | 0.680062 | ||||||||
\(538\) | 5.38253 | 0.232057 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 13.5094 | 0.581351 | ||||||||
\(541\) | 28.6878 | 1.23339 | 0.616693 | − | 0.787204i | \(-0.288472\pi\) | ||||
0.616693 | + | 0.787204i | \(0.288472\pi\) | |||||||
\(542\) | 59.9482 | 2.57499 | ||||||||
\(543\) | −3.24953 | −0.139451 | ||||||||
\(544\) | 0.428861 | 0.0183872 | ||||||||
\(545\) | 44.7441 | 1.91662 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.8811 | 1.10659 | 0.553297 | − | 0.832984i | \(-0.313369\pi\) | ||||
0.553297 | + | 0.832984i | \(0.313369\pi\) | |||||||
\(548\) | −13.3256 | −0.569242 | ||||||||
\(549\) | 6.02287 | 0.257050 | ||||||||
\(550\) | 128.133 | 5.46363 | ||||||||
\(551\) | −7.29520 | −0.310786 | ||||||||
\(552\) | 12.3283 | 0.524728 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.3809 | 1.03585 | ||||||||
\(555\) | 13.5543 | 0.575349 | ||||||||
\(556\) | 57.4883 | 2.43805 | ||||||||
\(557\) | 23.2849 | 0.986614 | 0.493307 | − | 0.869855i | \(-0.335788\pi\) | ||||
0.493307 | + | 0.869855i | \(0.335788\pi\) | |||||||
\(558\) | −3.13502 | −0.132716 | ||||||||
\(559\) | 29.5747 | 1.25088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.916074 | −0.0386767 | ||||||||
\(562\) | −16.0974 | −0.679029 | ||||||||
\(563\) | −32.5005 | −1.36973 | −0.684867 | − | 0.728668i | \(-0.740140\pi\) | ||||
−0.684867 | + | 0.728668i | \(0.740140\pi\) | |||||||
\(564\) | 42.2201 | 1.77779 | ||||||||
\(565\) | 41.2790 | 1.73662 | ||||||||
\(566\) | −4.94332 | −0.207783 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.3375 | −1.48273 | ||||||||
\(569\) | −17.0193 | −0.713486 | −0.356743 | − | 0.934203i | \(-0.616113\pi\) | ||||
−0.356743 | + | 0.934203i | \(0.616113\pi\) | |||||||
\(570\) | 15.6729 | 0.656466 | ||||||||
\(571\) | 29.9442 | 1.25313 | 0.626564 | − | 0.779370i | \(-0.284461\pi\) | ||||
0.626564 | + | 0.779370i | \(0.284461\pi\) | |||||||
\(572\) | 74.7187 | 3.12415 | ||||||||
\(573\) | −0.889555 | −0.0371617 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.7666 | −1.11625 | ||||||||
\(576\) | −11.1687 | −0.465364 | ||||||||
\(577\) | −22.0478 | −0.917862 | −0.458931 | − | 0.888472i | \(-0.651767\pi\) | ||||
−0.458931 | + | 0.888472i | \(0.651767\pi\) | |||||||
\(578\) | 40.4066 | 1.68070 | ||||||||
\(579\) | −2.48347 | −0.103210 | ||||||||
\(580\) | 55.1806 | 2.29125 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.1711 | −0.545961 | ||||||||
\(583\) | −27.6643 | −1.14574 | ||||||||
\(584\) | −35.3936 | −1.46460 | ||||||||
\(585\) | −12.0069 | −0.496422 | ||||||||
\(586\) | 20.7301 | 0.856351 | ||||||||
\(587\) | −34.5456 | −1.42585 | −0.712924 | − | 0.701241i | \(-0.752630\pi\) | ||||
−0.712924 | + | 0.701241i | \(0.752630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.35274 | −0.0969431 | ||||||||
\(590\) | −15.0842 | −0.621009 | ||||||||
\(591\) | −16.0761 | −0.661281 | ||||||||
\(592\) | 7.70247 | 0.316569 | ||||||||
\(593\) | −20.0432 | −0.823076 | −0.411538 | − | 0.911393i | \(-0.635008\pi\) | ||||
−0.411538 | + | 0.911393i | \(0.635008\pi\) | |||||||
\(594\) | 14.9053 | 0.611574 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 56.6755 | 2.32152 | ||||||||
\(597\) | 6.08609 | 0.249087 | ||||||||
\(598\) | −24.1291 | −0.986711 | ||||||||
\(599\) | 28.6415 | 1.17026 | 0.585130 | − | 0.810940i | \(-0.301044\pi\) | ||||
0.585130 | + | 0.810940i | \(0.301044\pi\) | |||||||
\(600\) | −34.0370 | −1.38955 | ||||||||
\(601\) | 19.4285 | 0.792506 | 0.396253 | − | 0.918141i | \(-0.370310\pi\) | ||||
0.396253 | + | 0.918141i | \(0.370310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.38835 | 0.0565382 | ||||||||
\(604\) | −22.3254 | −0.908409 | ||||||||
\(605\) | 104.082 | 4.23153 | ||||||||
\(606\) | −38.0670 | −1.54637 | ||||||||
\(607\) | −9.75872 | −0.396094 | −0.198047 | − | 0.980193i | \(-0.563460\pi\) | ||||
−0.198047 | + | 0.980193i | \(0.563460\pi\) | |||||||
\(608\) | −5.23676 | −0.212379 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −52.8527 | −2.13994 | ||||||||
\(611\) | −37.5244 | −1.51807 | ||||||||
\(612\) | 0.535872 | 0.0216613 | ||||||||
\(613\) | 16.3639 | 0.660934 | 0.330467 | − | 0.943818i | \(-0.392794\pi\) | ||||
0.330467 | + | 0.943818i | \(0.392794\pi\) | |||||||
\(614\) | 64.9089 | 2.61951 | ||||||||
\(615\) | −3.68734 | −0.148688 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.22352 | −0.250549 | −0.125275 | − | 0.992122i | \(-0.539981\pi\) | ||||
−0.125275 | + | 0.992122i | \(0.539981\pi\) | |||||||
\(618\) | −43.4462 | −1.74766 | ||||||||
\(619\) | −36.5437 | −1.46882 | −0.734408 | − | 0.678709i | \(-0.762540\pi\) | ||||
−0.734408 | + | 0.678709i | \(0.762540\pi\) | |||||||
\(620\) | 17.7961 | 0.714707 | ||||||||
\(621\) | −3.11368 | −0.124948 | ||||||||
\(622\) | −24.5794 | −0.985545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.82309 | −0.273142 | ||||||||
\(625\) | 5.91698 | 0.236679 | ||||||||
\(626\) | 71.7014 | 2.86576 | ||||||||
\(627\) | 11.1861 | 0.446728 | ||||||||
\(628\) | 7.60851 | 0.303613 | ||||||||
\(629\) | 0.537655 | 0.0214377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.5755 | 1.37643 | 0.688215 | − | 0.725506i | \(-0.258394\pi\) | ||||
0.688215 | + | 0.725506i | \(0.258394\pi\) | |||||||
\(632\) | 41.0546 | 1.63306 | ||||||||
\(633\) | −26.1991 | −1.04132 | ||||||||
\(634\) | −46.7581 | −1.85700 | ||||||||
\(635\) | −72.8128 | −2.88949 | ||||||||
\(636\) | 16.1827 | 0.641685 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 60.8827 | 2.41037 | ||||||||
\(639\) | 8.92495 | 0.353066 | ||||||||
\(640\) | 76.3862 | 3.01943 | ||||||||
\(641\) | −45.6225 | −1.80198 | −0.900990 | − | 0.433839i | \(-0.857159\pi\) | ||||
−0.900990 | + | 0.433839i | \(0.857159\pi\) | |||||||
\(642\) | 8.29305 | 0.327300 | ||||||||
\(643\) | −6.12623 | −0.241595 | −0.120797 | − | 0.992677i | \(-0.538545\pi\) | ||||
−0.120797 | + | 0.992677i | \(0.538545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.4901 | −1.31867 | ||||||||
\(646\) | 0.621693 | 0.0244602 | ||||||||
\(647\) | −21.5628 | −0.847720 | −0.423860 | − | 0.905728i | \(-0.639325\pi\) | ||||
−0.423860 | + | 0.905728i | \(0.639325\pi\) | |||||||
\(648\) | −3.95941 | −0.155540 | ||||||||
\(649\) | −10.7659 | −0.422599 | ||||||||
\(650\) | 66.6173 | 2.61295 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 41.5757 | 1.62823 | ||||||||
\(653\) | −2.57822 | −0.100894 | −0.0504468 | − | 0.998727i | \(-0.516065\pi\) | ||||
−0.0504468 | + | 0.998727i | \(0.516065\pi\) | |||||||
\(654\) | −28.8784 | −1.12923 | ||||||||
\(655\) | 70.9559 | 2.77248 | ||||||||
\(656\) | −2.09539 | −0.0818113 | ||||||||
\(657\) | 8.93911 | 0.348748 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.93310 | 0.309030 | 0.154515 | − | 0.987990i | \(-0.450619\pi\) | ||||
0.154515 | + | 0.987990i | \(0.450619\pi\) | |||||||
\(660\) | −84.6109 | −3.29348 | ||||||||
\(661\) | −2.46160 | −0.0957452 | −0.0478726 | − | 0.998853i | \(-0.515244\pi\) | ||||
−0.0478726 | + | 0.998853i | \(0.515244\pi\) | |||||||
\(662\) | 78.8666 | 3.06524 | ||||||||
\(663\) | −0.476272 | −0.0184969 | ||||||||
\(664\) | 42.1425 | 1.63545 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.74814 | −0.338983 | ||||||||
\(667\) | −12.7182 | −0.492450 | ||||||||
\(668\) | 70.5779 | 2.73074 | ||||||||
\(669\) | −18.3279 | −0.708597 | ||||||||
\(670\) | −12.1833 | −0.470681 | ||||||||
\(671\) | −37.7220 | −1.45624 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.3505 | 1.78668 | 0.893339 | − | 0.449383i | \(-0.148356\pi\) | ||||
0.893339 | + | 0.449383i | \(0.148356\pi\) | |||||||
\(674\) | −51.5652 | −1.98622 | ||||||||
\(675\) | 8.59647 | 0.330878 | ||||||||
\(676\) | −8.78160 | −0.337754 | ||||||||
\(677\) | −22.5487 | −0.866617 | −0.433309 | − | 0.901246i | \(-0.642654\pi\) | ||||
−0.433309 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(678\) | −26.6420 | −1.02318 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.13542 | −0.0818895 | ||||||||
\(681\) | 18.3473 | 0.703072 | ||||||||
\(682\) | 19.6350 | 0.751864 | ||||||||
\(683\) | −5.94771 | −0.227583 | −0.113791 | − | 0.993505i | \(-0.536300\pi\) | ||||
−0.113791 | + | 0.993505i | \(0.536300\pi\) | |||||||
\(684\) | −6.54346 | −0.250196 | ||||||||
\(685\) | −13.4115 | −0.512428 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.23971 | 0.161755 | ||||||||
\(688\) | −19.0313 | −0.725562 | ||||||||
\(689\) | −14.3828 | −0.547942 | ||||||||
\(690\) | 27.3236 | 1.04019 | ||||||||
\(691\) | 46.6357 | 1.77411 | 0.887054 | − | 0.461666i | \(-0.152748\pi\) | ||||
0.887054 | + | 0.461666i | \(0.152748\pi\) | |||||||
\(692\) | −40.6212 | −1.54419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −51.3661 | −1.94983 | ||||||||
\(695\) | 57.8589 | 2.19471 | ||||||||
\(696\) | −16.1727 | −0.613024 | ||||||||
\(697\) | −0.146265 | −0.00554017 | ||||||||
\(698\) | 52.8091 | 1.99885 | ||||||||
\(699\) | 16.9183 | 0.639910 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9123 | −0.752078 | −0.376039 | − | 0.926604i | \(-0.622714\pi\) | ||||
−0.376039 | + | 0.926604i | \(0.622714\pi\) | |||||||
\(702\) | 7.74938 | 0.292482 | ||||||||
\(703\) | −6.56524 | −0.247613 | ||||||||
\(704\) | 69.9512 | 2.63639 | ||||||||
\(705\) | 42.4923 | 1.60035 | ||||||||
\(706\) | −42.2191 | −1.58894 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.29769 | 0.236682 | ||||||||
\(709\) | 23.9798 | 0.900580 | 0.450290 | − | 0.892882i | \(-0.351321\pi\) | ||||
0.450290 | + | 0.892882i | \(0.351321\pi\) | |||||||
\(710\) | −78.3195 | −2.93928 | ||||||||
\(711\) | −10.3689 | −0.388863 | ||||||||
\(712\) | 6.95367 | 0.260600 | ||||||||
\(713\) | −4.10169 | −0.153609 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 75.2005 | 2.81234 | ||||||||
\(716\) | 57.7374 | 2.15775 | ||||||||
\(717\) | −12.6129 | −0.471036 | ||||||||
\(718\) | −21.1639 | −0.789830 | ||||||||
\(719\) | −16.6841 | −0.622213 | −0.311107 | − | 0.950375i | \(-0.600700\pi\) | ||||
−0.311107 | + | 0.950375i | \(0.600700\pi\) | |||||||
\(720\) | 7.72642 | 0.287947 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.6259 | 1.40029 | ||||||||
\(723\) | 28.8035 | 1.07121 | ||||||||
\(724\) | −11.9054 | −0.442460 | ||||||||
\(725\) | 35.1133 | 1.30408 | ||||||||
\(726\) | −67.1757 | −2.49312 | ||||||||
\(727\) | −21.5134 | −0.797888 | −0.398944 | − | 0.916975i | \(-0.630623\pi\) | ||||
−0.398944 | + | 0.916975i | \(0.630623\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −78.4437 | −2.90333 | ||||||||
\(731\) | −1.32844 | −0.0491342 | ||||||||
\(732\) | 22.0661 | 0.815586 | ||||||||
\(733\) | 13.7896 | 0.509330 | 0.254665 | − | 0.967029i | \(-0.418035\pi\) | ||||
0.254665 | + | 0.967029i | \(0.418035\pi\) | |||||||
\(734\) | 1.43080 | 0.0528116 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.12958 | −0.336521 | ||||||||
\(737\) | −8.69544 | −0.320301 | ||||||||
\(738\) | 2.37986 | 0.0876037 | ||||||||
\(739\) | 52.1005 | 1.91655 | 0.958273 | − | 0.285854i | \(-0.0922773\pi\) | ||||
0.958273 | + | 0.285854i | \(0.0922773\pi\) | |||||||
\(740\) | 49.6592 | 1.82551 | ||||||||
\(741\) | 5.81570 | 0.213645 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.82960 | −0.287240 | −0.143620 | − | 0.989633i | \(-0.545874\pi\) | ||||
−0.143620 | + | 0.989633i | \(0.545874\pi\) | |||||||
\(744\) | −5.21578 | −0.191220 | ||||||||
\(745\) | 57.0409 | 2.08982 | ||||||||
\(746\) | −5.15306 | −0.188667 | ||||||||
\(747\) | −10.6436 | −0.389431 | ||||||||
\(748\) | −3.35624 | −0.122716 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −31.5603 | −1.15242 | ||||||||
\(751\) | 24.7094 | 0.901659 | 0.450829 | − | 0.892610i | \(-0.351128\pi\) | ||||
0.450829 | + | 0.892610i | \(0.351128\pi\) | |||||||
\(752\) | 24.1470 | 0.880549 | ||||||||
\(753\) | 30.2514 | 1.10242 | ||||||||
\(754\) | 31.6533 | 1.15274 | ||||||||
\(755\) | −22.4694 | −0.817744 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.24530 | 0.117952 | 0.0589762 | − | 0.998259i | \(-0.481216\pi\) | ||||
0.0589762 | + | 0.998259i | \(0.481216\pi\) | |||||||
\(758\) | 13.9245 | 0.505760 | ||||||||
\(759\) | 19.5014 | 0.707855 | ||||||||
\(760\) | 26.0753 | 0.945850 | ||||||||
\(761\) | −23.8904 | −0.866027 | −0.433013 | − | 0.901387i | \(-0.642550\pi\) | ||||
−0.433013 | + | 0.901387i | \(0.642550\pi\) | |||||||
\(762\) | 46.9943 | 1.70243 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.25908 | −0.117909 | ||||||||
\(765\) | 0.539327 | 0.0194994 | ||||||||
\(766\) | −12.1343 | −0.438429 | ||||||||
\(767\) | −5.59726 | −0.202106 | ||||||||
\(768\) | −26.9632 | −0.972950 | ||||||||
\(769\) | 7.71831 | 0.278329 | 0.139165 | − | 0.990269i | \(-0.455558\pi\) | ||||
0.139165 | + | 0.990269i | \(0.455558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.8356 | 0.678347 | ||||||||
\(772\) | −9.09873 | −0.327471 | ||||||||
\(773\) | 17.9179 | 0.644461 | 0.322231 | − | 0.946661i | \(-0.395567\pi\) | ||||
0.322231 | + | 0.946661i | \(0.395567\pi\) | |||||||
\(774\) | 21.6150 | 0.776934 | ||||||||
\(775\) | 11.3242 | 0.406779 | ||||||||
\(776\) | −21.9130 | −0.786632 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 91.0518 | 3.26437 | ||||||||
\(779\) | 1.78602 | 0.0639907 | ||||||||
\(780\) | −43.9897 | −1.57509 | ||||||||
\(781\) | −55.8981 | −2.00019 | ||||||||
\(782\) | 1.08384 | 0.0387579 | ||||||||
\(783\) | 4.08462 | 0.145972 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.65757 | 0.273310 | ||||||||
\(786\) | −45.7959 | −1.63349 | ||||||||
\(787\) | −27.3832 | −0.976104 | −0.488052 | − | 0.872814i | \(-0.662292\pi\) | ||||
−0.488052 | + | 0.872814i | \(0.662292\pi\) | |||||||
\(788\) | −58.8982 | −2.09816 | ||||||||
\(789\) | 20.7414 | 0.738415 | ||||||||
\(790\) | 90.9903 | 3.23729 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.7983 | 0.881169 | ||||||||
\(793\) | −19.6119 | −0.696439 | ||||||||
\(794\) | −60.9999 | −2.16481 | ||||||||
\(795\) | 16.2870 | 0.577641 | ||||||||
\(796\) | 22.2977 | 0.790322 | ||||||||
\(797\) | −11.0166 | −0.390229 | −0.195114 | − | 0.980781i | \(-0.562508\pi\) | ||||
−0.195114 | + | 0.980781i | \(0.562508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.68553 | 0.0596298 | ||||||||
\(800\) | 25.2056 | 0.891153 | ||||||||
\(801\) | −1.75624 | −0.0620537 | ||||||||
\(802\) | 16.5281 | 0.583627 | ||||||||
\(803\) | −55.9868 | −1.97573 | ||||||||
\(804\) | 5.08654 | 0.179388 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.2084 | 0.359574 | ||||||||
\(807\) | −2.26170 | −0.0796157 | ||||||||
\(808\) | −63.3327 | −2.22804 | ||||||||
\(809\) | −17.9023 | −0.629413 | −0.314706 | − | 0.949189i | \(-0.601906\pi\) | ||||
−0.314706 | + | 0.949189i | \(0.601906\pi\) | |||||||
\(810\) | −8.77534 | −0.308334 | ||||||||
\(811\) | 30.4616 | 1.06965 | 0.534826 | − | 0.844962i | \(-0.320377\pi\) | ||||
0.534826 | + | 0.844962i | \(0.320377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.1898 | −0.883446 | ||||||||
\(814\) | 54.7907 | 1.92041 | ||||||||
\(815\) | 41.8438 | 1.46572 | ||||||||
\(816\) | 0.306481 | 0.0107290 | ||||||||
\(817\) | 16.2214 | 0.567516 | ||||||||
\(818\) | 84.0572 | 2.93899 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.5094 | −0.471768 | ||||||||
\(821\) | 24.3154 | 0.848614 | 0.424307 | − | 0.905518i | \(-0.360518\pi\) | ||||
0.424307 | + | 0.905518i | \(0.360518\pi\) | |||||||
\(822\) | 8.65597 | 0.301912 | ||||||||
\(823\) | −47.9101 | −1.67004 | −0.835020 | − | 0.550220i | \(-0.814544\pi\) | ||||
−0.835020 | + | 0.550220i | \(0.814544\pi\) | |||||||
\(824\) | −72.2823 | −2.51807 | ||||||||
\(825\) | −53.8408 | −1.87450 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4163 | 0.605624 | 0.302812 | − | 0.953050i | \(-0.402075\pi\) | ||||
0.302812 | + | 0.953050i | \(0.402075\pi\) | |||||||
\(828\) | −11.4076 | −0.396443 | ||||||||
\(829\) | 5.83275 | 0.202580 | 0.101290 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101290 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(830\) | 93.4016 | 3.24202 | ||||||||
\(831\) | −10.2447 | −0.355385 | ||||||||
\(832\) | 36.3681 | 1.26084 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.3429 | −1.29308 | ||||||||
\(835\) | 71.0329 | 2.45820 | ||||||||
\(836\) | 40.9826 | 1.41741 | ||||||||
\(837\) | 1.31731 | 0.0455330 | ||||||||
\(838\) | 22.6271 | 0.781642 | ||||||||
\(839\) | 20.2271 | 0.698316 | 0.349158 | − | 0.937064i | \(-0.386468\pi\) | ||||
0.349158 | + | 0.937064i | \(0.386468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3159 | −0.424686 | ||||||||
\(842\) | 47.8433 | 1.64879 | ||||||||
\(843\) | 6.76403 | 0.232966 | ||||||||
\(844\) | −95.9860 | −3.30397 | ||||||||
\(845\) | −8.83822 | −0.304044 | ||||||||
\(846\) | −27.4251 | −0.942895 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.25536 | 0.317830 | ||||||||
\(849\) | 2.07715 | 0.0712876 | ||||||||
\(850\) | −2.99234 | −0.102636 | ||||||||
\(851\) | −11.4456 | −0.392350 | ||||||||
\(852\) | 32.6985 | 1.12023 | ||||||||
\(853\) | −12.0327 | −0.411992 | −0.205996 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205996 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.58565 | −0.225225 | ||||||||
\(856\) | 13.7973 | 0.471582 | ||||||||
\(857\) | 0.405363 | 0.0138469 | 0.00692347 | − | 0.999976i | \(-0.497796\pi\) | ||||
0.00692347 | + | 0.999976i | \(0.497796\pi\) | |||||||
\(858\) | −48.5354 | −1.65697 | ||||||||
\(859\) | −15.9365 | −0.543748 | −0.271874 | − | 0.962333i | \(-0.587643\pi\) | ||||
−0.271874 | + | 0.962333i | \(0.587643\pi\) | |||||||
\(860\) | −122.698 | −4.18398 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62.2726 | 2.12101 | ||||||||
\(863\) | −28.1342 | −0.957698 | −0.478849 | − | 0.877897i | \(-0.658946\pi\) | ||||
−0.478849 | + | 0.877897i | \(0.658946\pi\) | |||||||
\(864\) | 2.93209 | 0.0997517 | ||||||||
\(865\) | −40.8831 | −1.39007 | ||||||||
\(866\) | −83.8501 | −2.84934 | ||||||||
\(867\) | −16.9786 | −0.576624 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.9416 | 2.20299 | ||||||||
\(870\) | −35.8439 | −1.21522 | ||||||||
\(871\) | −4.52081 | −0.153182 | ||||||||
\(872\) | −48.0455 | −1.62703 | ||||||||
\(873\) | 5.53442 | 0.187312 | ||||||||
\(874\) | −13.2346 | −0.447666 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.7504 | 1.10653 | ||||||||
\(877\) | 4.69948 | 0.158690 | 0.0793451 | − | 0.996847i | \(-0.474717\pi\) | ||||
0.0793451 | + | 0.996847i | \(0.474717\pi\) | |||||||
\(878\) | 24.0551 | 0.811821 | ||||||||
\(879\) | −8.71064 | −0.293802 | ||||||||
\(880\) | −48.3916 | −1.63128 | ||||||||
\(881\) | −12.0182 | −0.404904 | −0.202452 | − | 0.979292i | \(-0.564891\pi\) | ||||
−0.202452 | + | 0.979292i | \(0.564891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 59.0988 | 1.98883 | 0.994417 | − | 0.105520i | \(-0.0336507\pi\) | ||||
0.994417 | + | 0.105520i | \(0.0336507\pi\) | |||||||
\(884\) | −1.74493 | −0.0586883 | ||||||||
\(885\) | 6.33830 | 0.213060 | ||||||||
\(886\) | −57.9952 | −1.94839 | ||||||||
\(887\) | 46.1453 | 1.54941 | 0.774704 | − | 0.632324i | \(-0.217899\pi\) | ||||
0.774704 | + | 0.632324i | \(0.217899\pi\) | |||||||
\(888\) | −14.5544 | −0.488415 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15.4116 | 0.516598 | ||||||||
\(891\) | −6.26313 | −0.209823 | ||||||||
\(892\) | −67.1482 | −2.24829 | ||||||||
\(893\) | −20.5818 | −0.688743 | ||||||||
\(894\) | −36.8150 | −1.23128 | ||||||||
\(895\) | 58.1097 | 1.94239 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1389 | 0.338527 | ||||||||
\(898\) | 46.4980 | 1.55166 | ||||||||
\(899\) | 5.38072 | 0.179457 | ||||||||
\(900\) | 31.4950 | 1.04983 | ||||||||
\(901\) | 0.646052 | 0.0215231 | ||||||||
\(902\) | −14.9053 | −0.496294 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −44.3247 | −1.47422 | ||||||||
\(905\) | −11.9821 | −0.398300 | ||||||||
\(906\) | 14.5020 | 0.481798 | ||||||||
\(907\) | 21.7744 | 0.723008 | 0.361504 | − | 0.932370i | \(-0.382263\pi\) | ||||
0.361504 | + | 0.932370i | \(0.382263\pi\) | |||||||
\(908\) | 67.2195 | 2.23076 | ||||||||
\(909\) | 15.9955 | 0.530537 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.8850 | 1.32145 | 0.660724 | − | 0.750629i | \(-0.270249\pi\) | ||||
0.660724 | + | 0.750629i | \(0.270249\pi\) | |||||||
\(912\) | −3.74240 | −0.123923 | ||||||||
\(913\) | 66.6625 | 2.20621 | ||||||||
\(914\) | −62.4886 | −2.06694 | ||||||||
\(915\) | 22.2084 | 0.734186 | ||||||||
\(916\) | 15.5331 | 0.513228 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.348089 | −0.0114886 | ||||||||
\(919\) | −50.3237 | −1.66002 | −0.830012 | − | 0.557745i | \(-0.811667\pi\) | ||||
−0.830012 | + | 0.557745i | \(0.811667\pi\) | |||||||
\(920\) | 45.4587 | 1.49873 | ||||||||
\(921\) | −27.2743 | −0.898718 | ||||||||
\(922\) | −27.4962 | −0.905538 | ||||||||
\(923\) | −29.0618 | −0.956580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.5999 | 1.03900 | ||||||||
\(926\) | 2.79565 | 0.0918707 | ||||||||
\(927\) | 18.2558 | 0.599600 | ||||||||
\(928\) | 11.9765 | 0.393147 | ||||||||
\(929\) | −23.1421 | −0.759267 | −0.379633 | − | 0.925137i | \(-0.623950\pi\) | ||||
−0.379633 | + | 0.925137i | \(0.623950\pi\) | |||||||
\(930\) | −11.5599 | −0.379063 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 61.9840 | 2.03035 | ||||||||
\(933\) | 10.3281 | 0.338127 | ||||||||
\(934\) | −12.6746 | −0.414727 | ||||||||
\(935\) | −3.37788 | −0.110468 | ||||||||
\(936\) | 12.8928 | 0.421414 | ||||||||
\(937\) | −28.0250 | −0.915535 | −0.457768 | − | 0.889072i | \(-0.651351\pi\) | ||||
−0.457768 | + | 0.889072i | \(0.651351\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.1284 | −0.983204 | ||||||||
\(940\) | 155.680 | 5.07772 | ||||||||
\(941\) | 1.30089 | 0.0424079 | 0.0212040 | − | 0.999775i | \(-0.493250\pi\) | ||||
0.0212040 | + | 0.999775i | \(0.493250\pi\) | |||||||
\(942\) | −4.94229 | −0.161029 | ||||||||
\(943\) | 3.11368 | 0.101395 | ||||||||
\(944\) | 3.60184 | 0.117230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −135.377 | −4.40150 | ||||||||
\(947\) | −28.0944 | −0.912944 | −0.456472 | − | 0.889738i | \(-0.650887\pi\) | ||||
−0.456472 | + | 0.889738i | \(0.650887\pi\) | |||||||
\(948\) | −37.9886 | −1.23381 | ||||||||
\(949\) | −29.1079 | −0.944882 | ||||||||
\(950\) | 36.5390 | 1.18548 | ||||||||
\(951\) | 19.6474 | 0.637112 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4370 | −1.05074 | −0.525368 | − | 0.850875i | \(-0.676073\pi\) | ||||
−0.525368 | + | 0.850875i | \(0.676073\pi\) | |||||||
\(954\) | −10.5118 | −0.340334 | ||||||||
\(955\) | −3.28009 | −0.106141 | ||||||||
\(956\) | −46.2100 | −1.49454 | ||||||||
\(957\) | −25.5825 | −0.826965 | ||||||||
\(958\) | −61.0287 | −1.97175 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −41.1829 | −1.32917 | ||||||||
\(961\) | −29.2647 | −0.944022 | ||||||||
\(962\) | 28.4860 | 0.918426 | ||||||||
\(963\) | −3.48468 | −0.112292 | ||||||||
\(964\) | 105.528 | 3.39882 | ||||||||
\(965\) | −9.15740 | −0.294787 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.6459 | −1.62866 | −0.814331 | − | 0.580401i | \(-0.802896\pi\) | ||||
−0.814331 | + | 0.580401i | \(0.802896\pi\) | |||||||
\(968\) | −111.761 | −3.59215 | ||||||||
\(969\) | −0.261231 | −0.00839195 | ||||||||
\(970\) | −48.5664 | −1.55937 | ||||||||
\(971\) | −11.8113 | −0.379042 | −0.189521 | − | 0.981877i | \(-0.560693\pi\) | ||||
−0.189521 | + | 0.981877i | \(0.560693\pi\) | |||||||
\(972\) | 3.66372 | 0.117514 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.73808 | 0.247944 | ||||||||
\(975\) | −27.9922 | −0.896467 | ||||||||
\(976\) | 12.6203 | 0.403965 | ||||||||
\(977\) | 54.8172 | 1.75376 | 0.876879 | − | 0.480710i | \(-0.159621\pi\) | ||||
0.876879 | + | 0.480710i | \(0.159621\pi\) | |||||||
\(978\) | −27.0065 | −0.863573 | ||||||||
\(979\) | 10.9996 | 0.351547 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1345 | 0.387425 | ||||||||
\(982\) | 46.4096 | 1.48099 | ||||||||
\(983\) | −5.79541 | −0.184845 | −0.0924224 | − | 0.995720i | \(-0.529461\pi\) | ||||
−0.0924224 | + | 0.995720i | \(0.529461\pi\) | |||||||
\(984\) | 3.95941 | 0.126221 | ||||||||
\(985\) | −59.2779 | −1.88875 | ||||||||
\(986\) | −1.42181 | −0.0452797 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.3071 | 0.677868 | ||||||||
\(989\) | 28.2799 | 0.899248 | ||||||||
\(990\) | 54.9611 | 1.74678 | ||||||||
\(991\) | −18.5305 | −0.588642 | −0.294321 | − | 0.955707i | \(-0.595093\pi\) | ||||
−0.294321 | + | 0.955707i | \(0.595093\pi\) | |||||||
\(992\) | 3.86248 | 0.122634 | ||||||||
\(993\) | −33.1392 | −1.05164 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.4415 | 0.711443 | ||||||||
\(996\) | −38.9953 | −1.23561 | ||||||||
\(997\) | 40.1082 | 1.27024 | 0.635119 | − | 0.772414i | \(-0.280951\pi\) | ||||
0.635119 | + | 0.772414i | \(0.280951\pi\) | |||||||
\(998\) | −77.6503 | −2.45798 | ||||||||
\(999\) | 3.67591 | 0.116301 |
(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 | 6027.2.a.bo.1.2 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.2 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.2 | yes | 24 | 1.1 | even | 1 | trivial |