Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53628 | 1.08631 | 0.543156 | − | 0.839632i | \(-0.317229\pi\) | ||||
0.543156 | + | 0.839632i | \(0.317229\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.360147 | 0.180074 | ||||||||
\(5\) | −2.16725 | −0.969225 | −0.484612 | − | 0.874729i | \(-0.661039\pi\) | ||||
−0.484612 | + | 0.874729i | \(0.661039\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.96367 | 1.12016 | 0.560081 | − | 0.828438i | \(-0.310770\pi\) | ||||
0.560081 | + | 0.828438i | \(0.310770\pi\) | |||||||
\(8\) | −2.51927 | −0.890696 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.32950 | −1.05288 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.11824 | 0.310145 | 0.155073 | − | 0.987903i | \(-0.450439\pi\) | ||||
0.155073 | + | 0.987903i | \(0.450439\pi\) | |||||||
\(14\) | 4.55302 | 1.21684 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.59059 | −1.14765 | ||||||||
\(17\) | −6.92345 | −1.67918 | −0.839592 | − | 0.543218i | \(-0.817206\pi\) | ||||
−0.839592 | + | 0.543218i | \(0.817206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.93391 | 1.59075 | 0.795374 | − | 0.606118i | \(-0.207274\pi\) | ||||
0.795374 | + | 0.606118i | \(0.207274\pi\) | |||||||
\(20\) | −0.780531 | −0.174532 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.53628 | 0.327535 | ||||||||
\(23\) | 0.602257 | 0.125579 | 0.0627896 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627896 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.303015 | −0.0606030 | ||||||||
\(26\) | 1.71793 | 0.336914 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.06736 | 0.201712 | ||||||||
\(29\) | −4.99192 | −0.926976 | −0.463488 | − | 0.886103i | \(-0.653402\pi\) | ||||
−0.463488 | + | 0.886103i | \(0.653402\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.25237 | −0.224932 | −0.112466 | − | 0.993656i | \(-0.535875\pi\) | ||||
−0.112466 | + | 0.993656i | \(0.535875\pi\) | |||||||
\(32\) | −2.01388 | −0.356007 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.6363 | −1.82412 | ||||||||
\(35\) | −6.42302 | −1.08569 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.94654 | −0.648807 | −0.324404 | − | 0.945919i | \(-0.605164\pi\) | ||||
−0.324404 | + | 0.945919i | \(0.605164\pi\) | |||||||
\(38\) | 10.6524 | 1.72805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.45989 | 0.863285 | ||||||||
\(41\) | 1.36557 | 0.213266 | 0.106633 | − | 0.994298i | \(-0.465993\pi\) | ||||
0.106633 | + | 0.994298i | \(0.465993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4226 | 1.74193 | 0.870964 | − | 0.491348i | \(-0.163495\pi\) | ||||
0.870964 | + | 0.491348i | \(0.163495\pi\) | |||||||
\(44\) | 0.360147 | 0.0542943 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.925234 | 0.136418 | ||||||||
\(47\) | 3.48067 | 0.507708 | 0.253854 | − | 0.967242i | \(-0.418302\pi\) | ||||
0.253854 | + | 0.967242i | \(0.418302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.78333 | 0.254761 | ||||||||
\(50\) | −0.465515 | −0.0658338 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.402733 | 0.0558490 | ||||||||
\(53\) | −9.97119 | −1.36965 | −0.684824 | − | 0.728708i | \(-0.740121\pi\) | ||||
−0.684824 | + | 0.728708i | \(0.740121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.16725 | −0.292232 | ||||||||
\(56\) | −7.46627 | −0.997723 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.66897 | −1.00698 | ||||||||
\(59\) | −4.08773 | −0.532177 | −0.266088 | − | 0.963949i | \(-0.585731\pi\) | ||||
−0.266088 | + | 0.963949i | \(0.585731\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −1.92398 | −0.244346 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08730 | 0.760912 | ||||||||
\(65\) | −2.42352 | −0.300600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.56579 | −0.679970 | −0.339985 | − | 0.940431i | \(-0.610422\pi\) | ||||
−0.339985 | + | 0.940431i | \(0.610422\pi\) | |||||||
\(68\) | −2.49346 | −0.302377 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.86753 | −1.17940 | ||||||||
\(71\) | −6.01977 | −0.714415 | −0.357208 | − | 0.934025i | \(-0.616271\pi\) | ||||
−0.357208 | + | 0.934025i | \(0.616271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24844 | 0.497242 | 0.248621 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248621 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(74\) | −6.06298 | −0.704807 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.49723 | 0.286452 | ||||||||
\(77\) | 2.96367 | 0.337741 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1185 | −1.70096 | −0.850482 | − | 0.526005i | \(-0.823689\pi\) | ||||
−0.850482 | + | 0.526005i | \(0.823689\pi\) | |||||||
\(80\) | 9.94897 | 1.11233 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.09790 | 0.231674 | ||||||||
\(83\) | −10.9464 | −1.20152 | −0.600761 | − | 0.799429i | \(-0.705136\pi\) | ||||
−0.600761 | + | 0.799429i | \(0.705136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.0049 | 1.62751 | ||||||||
\(86\) | 17.5482 | 1.89228 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.51927 | −0.268555 | ||||||||
\(89\) | 3.58975 | 0.380513 | 0.190256 | − | 0.981734i | \(-0.439068\pi\) | ||||
0.190256 | + | 0.981734i | \(0.439068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.31410 | 0.347412 | ||||||||
\(92\) | 0.216901 | 0.0226135 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.34728 | 0.551530 | ||||||||
\(95\) | −15.0275 | −1.54179 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.8550 | −1.60983 | −0.804914 | − | 0.593391i | \(-0.797789\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(98\) | 2.73968 | 0.276750 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.109130 | −0.0109130 | ||||||||
\(101\) | −1.66067 | −0.165243 | −0.0826216 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826216 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6642 | −1.14930 | −0.574652 | − | 0.818398i | \(-0.694862\pi\) | ||||
−0.574652 | + | 0.818398i | \(0.694862\pi\) | |||||||
\(104\) | −2.81716 | −0.276245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.3185 | −1.48787 | ||||||||
\(107\) | −5.00509 | −0.483860 | −0.241930 | − | 0.970294i | \(-0.577780\pi\) | ||||
−0.241930 | + | 0.970294i | \(0.577780\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0556 | 1.05894 | 0.529469 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529469 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(110\) | −3.32950 | −0.317455 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.6050 | −1.28555 | ||||||||
\(113\) | 0.0342434 | 0.00322135 | 0.00161067 | − | 0.999999i | \(-0.499487\pi\) | ||||
0.00161067 | + | 0.999999i | \(0.499487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.30524 | −0.121715 | ||||||||
\(116\) | −1.79783 | −0.166924 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.27988 | −0.578110 | ||||||||
\(119\) | −20.5188 | −1.88096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.53628 | 0.139088 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.451037 | −0.0405043 | ||||||||
\(125\) | 11.4930 | 1.02796 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8091 | 1.13662 | 0.568312 | − | 0.822813i | \(-0.307597\pi\) | ||||
0.568312 | + | 0.822813i | \(0.307597\pi\) | |||||||
\(128\) | 13.3795 | 1.18260 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.72319 | −0.326546 | ||||||||
\(131\) | −2.28901 | −0.199992 | −0.0999960 | − | 0.994988i | \(-0.531883\pi\) | ||||
−0.0999960 | + | 0.994988i | \(0.531883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.5498 | 1.78190 | ||||||||
\(134\) | −8.55060 | −0.738659 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.4420 | 1.49564 | ||||||||
\(137\) | −12.8333 | −1.09643 | −0.548213 | − | 0.836339i | \(-0.684692\pi\) | ||||
−0.548213 | + | 0.836339i | \(0.684692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3877 | −1.22035 | −0.610174 | − | 0.792268i | \(-0.708900\pi\) | ||||
−0.610174 | + | 0.792268i | \(0.708900\pi\) | |||||||
\(140\) | −2.31323 | −0.195504 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.24803 | −0.776078 | ||||||||
\(143\) | 1.11824 | 0.0935123 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8187 | 0.898448 | ||||||||
\(146\) | 6.52678 | 0.540160 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.42134 | −0.116833 | ||||||||
\(149\) | 1.61267 | 0.132115 | 0.0660577 | − | 0.997816i | \(-0.478958\pi\) | ||||
0.0660577 | + | 0.997816i | \(0.478958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.44516 | −0.117605 | −0.0588025 | − | 0.998270i | \(-0.518728\pi\) | ||||
−0.0588025 | + | 0.998270i | \(0.518728\pi\) | |||||||
\(152\) | −17.4684 | −1.41687 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.55302 | 0.366892 | ||||||||
\(155\) | 2.71420 | 0.218010 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.08168 | 0.166136 | 0.0830681 | − | 0.996544i | \(-0.473528\pi\) | ||||
0.0830681 | + | 0.996544i | \(0.473528\pi\) | |||||||
\(158\) | −23.2262 | −1.84778 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.36459 | 0.345051 | ||||||||
\(161\) | 1.78489 | 0.140669 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8859 | −1.08763 | −0.543816 | − | 0.839205i | \(-0.683021\pi\) | ||||
−0.543816 | + | 0.839205i | \(0.683021\pi\) | |||||||
\(164\) | 0.491807 | 0.0384037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.8167 | −1.30523 | ||||||||
\(167\) | 4.64625 | 0.359538 | 0.179769 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179769 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7495 | −0.903810 | ||||||||
\(170\) | 23.0516 | 1.76798 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.11381 | 0.313675 | ||||||||
\(173\) | −18.2979 | −1.39116 | −0.695580 | − | 0.718448i | \(-0.744853\pi\) | ||||
−0.695580 | + | 0.718448i | \(0.744853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.898036 | −0.0678852 | ||||||||
\(176\) | −4.59059 | −0.346029 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.51485 | 0.413355 | ||||||||
\(179\) | −1.14913 | −0.0858900 | −0.0429450 | − | 0.999077i | \(-0.513674\pi\) | ||||
−0.0429450 | + | 0.999077i | \(0.513674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3074 | −1.06346 | −0.531731 | − | 0.846913i | \(-0.678458\pi\) | ||||
−0.531731 | + | 0.846913i | \(0.678458\pi\) | |||||||
\(182\) | 5.09138 | 0.377398 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.51725 | −0.111853 | ||||||||
\(185\) | 8.55315 | 0.628840 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92345 | −0.506293 | ||||||||
\(188\) | 1.25356 | 0.0914250 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.0865 | −1.67487 | ||||||||
\(191\) | 1.63500 | 0.118305 | 0.0591524 | − | 0.998249i | \(-0.481160\pi\) | ||||
0.0591524 | + | 0.998249i | \(0.481160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.1138 | 1.66377 | 0.831883 | − | 0.554951i | \(-0.187263\pi\) | ||||
0.831883 | + | 0.554951i | \(0.187263\pi\) | |||||||
\(194\) | −24.3576 | −1.74878 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.642261 | 0.0458758 | ||||||||
\(197\) | 11.9309 | 0.850039 | 0.425020 | − | 0.905184i | \(-0.360267\pi\) | ||||
0.425020 | + | 0.905184i | \(0.360267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.55582 | −0.252065 | −0.126033 | − | 0.992026i | \(-0.540224\pi\) | ||||
−0.126033 | + | 0.992026i | \(0.540224\pi\) | |||||||
\(200\) | 0.763376 | 0.0539789 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.55125 | −0.179506 | ||||||||
\(203\) | −14.7944 | −1.03836 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.95954 | −0.206703 | ||||||||
\(206\) | −17.9194 | −1.24850 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.13340 | −0.355937 | ||||||||
\(209\) | 6.93391 | 0.479629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1085 | −0.902425 | −0.451212 | − | 0.892417i | \(-0.649008\pi\) | ||||
−0.451212 | + | 0.892417i | \(0.649008\pi\) | |||||||
\(212\) | −3.59110 | −0.246638 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.68920 | −0.525623 | ||||||||
\(215\) | −24.7556 | −1.68832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.71160 | −0.251960 | ||||||||
\(218\) | 16.9845 | 1.15034 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.780531 | −0.0526234 | ||||||||
\(221\) | −7.74211 | −0.520791 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4695 | −1.57163 | −0.785816 | − | 0.618461i | \(-0.787757\pi\) | ||||
−0.785816 | + | 0.618461i | \(0.787757\pi\) | |||||||
\(224\) | −5.96847 | −0.398785 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0526073 | 0.00349939 | ||||||||
\(227\) | −29.3689 | −1.94928 | −0.974640 | − | 0.223777i | \(-0.928161\pi\) | ||||
−0.974640 | + | 0.223777i | \(0.928161\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.9810 | −1.91512 | −0.957559 | − | 0.288239i | \(-0.906930\pi\) | ||||
−0.957559 | + | 0.288239i | \(0.906930\pi\) | |||||||
\(230\) | −2.00522 | −0.132220 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.5760 | 0.825653 | ||||||||
\(233\) | 17.1527 | 1.12371 | 0.561855 | − | 0.827236i | \(-0.310088\pi\) | ||||
0.561855 | + | 0.827236i | \(0.310088\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.54350 | −0.492084 | ||||||||
\(236\) | −1.47218 | −0.0958310 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −31.5226 | −2.04331 | ||||||||
\(239\) | 24.6961 | 1.59746 | 0.798729 | − | 0.601690i | \(-0.205506\pi\) | ||||
0.798729 | + | 0.601690i | \(0.205506\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6705 | −1.07384 | −0.536919 | − | 0.843634i | \(-0.680412\pi\) | ||||
−0.536919 | + | 0.843634i | \(0.680412\pi\) | |||||||
\(242\) | 1.53628 | 0.0987556 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.360147 | 0.0230561 | ||||||||
\(245\) | −3.86492 | −0.246921 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.75381 | 0.493363 | ||||||||
\(248\) | 3.15505 | 0.200346 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.6564 | 1.11669 | ||||||||
\(251\) | −22.5316 | −1.42218 | −0.711091 | − | 0.703100i | \(-0.751799\pi\) | ||||
−0.711091 | + | 0.703100i | \(0.751799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.602257 | 0.0378636 | ||||||||
\(254\) | 19.6783 | 1.23473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.38008 | 0.523755 | ||||||||
\(257\) | 14.2743 | 0.890409 | 0.445205 | − | 0.895429i | \(-0.353131\pi\) | ||||
0.445205 | + | 0.895429i | \(0.353131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6962 | −0.726769 | ||||||||
\(260\) | −0.872824 | −0.0541302 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.51656 | −0.217254 | ||||||||
\(263\) | 11.6036 | 0.715510 | 0.357755 | − | 0.933816i | \(-0.383542\pi\) | ||||
0.357755 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.6101 | 1.32750 | ||||||||
\(266\) | 31.5702 | 1.93569 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00451 | −0.122445 | ||||||||
\(269\) | 26.6831 | 1.62690 | 0.813449 | − | 0.581636i | \(-0.197587\pi\) | ||||
0.813449 | + | 0.581636i | \(0.197587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5820 | −1.18952 | −0.594761 | − | 0.803903i | \(-0.702753\pi\) | ||||
−0.594761 | + | 0.803903i | \(0.702753\pi\) | |||||||
\(272\) | 31.7827 | 1.92711 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.7156 | −1.19106 | ||||||||
\(275\) | −0.303015 | −0.0182725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.54773 | 0.333331 | 0.166665 | − | 0.986013i | \(-0.446700\pi\) | ||||
0.166665 | + | 0.986013i | \(0.446700\pi\) | |||||||
\(278\) | −22.1035 | −1.32568 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 16.1813 | 0.967018 | ||||||||
\(281\) | 4.91656 | 0.293297 | 0.146649 | − | 0.989189i | \(-0.453151\pi\) | ||||
0.146649 | + | 0.989189i | \(0.453151\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.1732 | 1.02084 | 0.510420 | − | 0.859925i | \(-0.329490\pi\) | ||||
0.510420 | + | 0.859925i | \(0.329490\pi\) | |||||||
\(284\) | −2.16800 | −0.128647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.71793 | 0.101583 | ||||||||
\(287\) | 4.04710 | 0.238893 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.9342 | 1.81966 | ||||||||
\(290\) | 16.6206 | 0.975995 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.53007 | 0.0895403 | ||||||||
\(293\) | −16.5723 | −0.968164 | −0.484082 | − | 0.875023i | \(-0.660846\pi\) | ||||
−0.484082 | + | 0.875023i | \(0.660846\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.85914 | 0.515799 | ||||||||
\(296\) | 9.94239 | 0.577890 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.47751 | 0.143519 | ||||||||
\(299\) | 0.673470 | 0.0389478 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.8527 | 1.95124 | ||||||||
\(302\) | −2.22016 | −0.127756 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −31.8307 | −1.82562 | ||||||||
\(305\) | −2.16725 | −0.124097 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.88162 | −0.506901 | −0.253451 | − | 0.967348i | \(-0.581566\pi\) | ||||
−0.253451 | + | 0.967348i | \(0.581566\pi\) | |||||||
\(308\) | 1.06736 | 0.0608183 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.16976 | 0.236826 | ||||||||
\(311\) | 33.1230 | 1.87823 | 0.939117 | − | 0.343597i | \(-0.111645\pi\) | ||||
0.939117 | + | 0.343597i | \(0.111645\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.858895 | −0.0485476 | −0.0242738 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242738 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(314\) | 3.19804 | 0.180476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.44489 | −0.306299 | ||||||||
\(317\) | −18.1664 | −1.02033 | −0.510165 | − | 0.860077i | \(-0.670416\pi\) | ||||
−0.510165 | + | 0.860077i | \(0.670416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.99192 | −0.279494 | ||||||||
\(320\) | −13.1927 | −0.737495 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.74209 | 0.152810 | ||||||||
\(323\) | −48.0066 | −2.67116 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.338845 | −0.0187957 | ||||||||
\(326\) | −21.3327 | −1.18151 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.44024 | −0.189956 | ||||||||
\(329\) | 10.3156 | 0.568715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.83812 | 0.155997 | 0.0779987 | − | 0.996953i | \(-0.475147\pi\) | ||||
0.0779987 | + | 0.996953i | \(0.475147\pi\) | |||||||
\(332\) | −3.94231 | −0.216363 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.13793 | 0.390570 | ||||||||
\(335\) | 12.0625 | 0.659043 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.25080 | −0.340503 | −0.170251 | − | 0.985401i | \(-0.554458\pi\) | ||||
−0.170251 | + | 0.985401i | \(0.554458\pi\) | |||||||
\(338\) | −18.0505 | −0.981820 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.40397 | 0.293071 | ||||||||
\(341\) | −1.25237 | −0.0678195 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4605 | −0.834788 | ||||||||
\(344\) | −28.7765 | −1.55153 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.1106 | −1.51123 | ||||||||
\(347\) | 0.687843 | 0.0369254 | 0.0184627 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184627 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.99137 | −0.320711 | −0.160355 | − | 0.987059i | \(-0.551264\pi\) | ||||
−0.160355 | + | 0.987059i | \(0.551264\pi\) | |||||||
\(350\) | −1.37963 | −0.0737445 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.01388 | −0.107340 | ||||||||
\(353\) | 21.5599 | 1.14752 | 0.573758 | − | 0.819025i | \(-0.305485\pi\) | ||||
0.573758 | + | 0.819025i | \(0.305485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.0464 | 0.692429 | ||||||||
\(356\) | 1.29284 | 0.0685203 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.76538 | −0.0933034 | ||||||||
\(359\) | 9.54787 | 0.503917 | 0.251959 | − | 0.967738i | \(-0.418925\pi\) | ||||
0.251959 | + | 0.967738i | \(0.418925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0792 | 1.53048 | ||||||||
\(362\) | −21.9802 | −1.15525 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.19357 | 0.0625599 | ||||||||
\(365\) | −9.20745 | −0.481940 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2671 | 0.953537 | 0.476769 | − | 0.879029i | \(-0.341808\pi\) | ||||
0.476769 | + | 0.879029i | \(0.341808\pi\) | |||||||
\(368\) | −2.76471 | −0.144121 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.1400 | 0.683116 | ||||||||
\(371\) | −29.5513 | −1.53423 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4678 | −1.11156 | −0.555781 | − | 0.831329i | \(-0.687581\pi\) | ||||
−0.555781 | + | 0.831329i | \(0.687581\pi\) | |||||||
\(374\) | −10.6363 | −0.549992 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.76875 | −0.452214 | ||||||||
\(377\) | −5.58218 | −0.287497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3560 | −1.14835 | −0.574176 | − | 0.818732i | \(-0.694677\pi\) | ||||
−0.574176 | + | 0.818732i | \(0.694677\pi\) | |||||||
\(380\) | −5.41213 | −0.277636 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.51182 | 0.128516 | ||||||||
\(383\) | −31.2050 | −1.59450 | −0.797252 | − | 0.603647i | \(-0.793714\pi\) | ||||
−0.797252 | + | 0.603647i | \(0.793714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.42302 | −0.327347 | ||||||||
\(386\) | 35.5092 | 1.80737 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.71013 | −0.289888 | ||||||||
\(389\) | −31.3867 | −1.59137 | −0.795684 | − | 0.605712i | \(-0.792888\pi\) | ||||
−0.795684 | + | 0.605712i | \(0.792888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.16970 | −0.210871 | ||||||||
\(392\) | −4.49268 | −0.226915 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.3291 | 0.923408 | ||||||||
\(395\) | 32.7656 | 1.64862 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1105 | 1.10969 | 0.554847 | − | 0.831952i | \(-0.312777\pi\) | ||||
0.554847 | + | 0.831952i | \(0.312777\pi\) | |||||||
\(398\) | −5.46272 | −0.273821 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.39102 | 0.0695509 | ||||||||
\(401\) | −33.4242 | −1.66912 | −0.834562 | − | 0.550915i | \(-0.814279\pi\) | ||||
−0.834562 | + | 0.550915i | \(0.814279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.40045 | −0.0697615 | ||||||||
\(404\) | −0.598087 | −0.0297559 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.7283 | −1.12799 | ||||||||
\(407\) | −3.94654 | −0.195623 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.67708 | 0.478501 | 0.239250 | − | 0.970958i | \(-0.423098\pi\) | ||||
0.239250 | + | 0.970958i | \(0.423098\pi\) | |||||||
\(410\) | −4.54667 | −0.224544 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.20082 | −0.206959 | ||||||||
\(413\) | −12.1147 | −0.596123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.7236 | 1.16455 | ||||||||
\(416\) | −2.25201 | −0.110414 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.6524 | 0.521027 | ||||||||
\(419\) | 31.9454 | 1.56063 | 0.780317 | − | 0.625384i | \(-0.215058\pi\) | ||||
0.780317 | + | 0.625384i | \(0.215058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.9318 | 1.50753 | 0.753763 | − | 0.657146i | \(-0.228237\pi\) | ||||
0.753763 | + | 0.657146i | \(0.228237\pi\) | |||||||
\(422\) | −20.1382 | −0.980315 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.1201 | 1.21994 | ||||||||
\(425\) | 2.09791 | 0.101764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.96367 | 0.143422 | ||||||||
\(428\) | −1.80257 | −0.0871305 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −38.0315 | −1.83404 | ||||||||
\(431\) | 0.341449 | 0.0164470 | 0.00822351 | − | 0.999966i | \(-0.497382\pi\) | ||||
0.00822351 | + | 0.999966i | \(0.497382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.92341 | 0.140490 | 0.0702450 | − | 0.997530i | \(-0.477622\pi\) | ||||
0.0702450 | + | 0.997530i | \(0.477622\pi\) | |||||||
\(434\) | −5.70205 | −0.273707 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.98166 | 0.190687 | ||||||||
\(437\) | 4.17600 | 0.199765 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8788 | 1.56922 | 0.784609 | − | 0.619991i | \(-0.212864\pi\) | ||||
0.784609 | + | 0.619991i | \(0.212864\pi\) | |||||||
\(440\) | 5.45989 | 0.260290 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.8940 | −0.565741 | ||||||||
\(443\) | −23.6725 | −1.12471 | −0.562356 | − | 0.826895i | \(-0.690105\pi\) | ||||
−0.562356 | + | 0.826895i | \(0.690105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.77989 | −0.368802 | ||||||||
\(446\) | −36.0556 | −1.70728 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.0407 | 0.852344 | ||||||||
\(449\) | −23.9338 | −1.12950 | −0.564752 | − | 0.825261i | \(-0.691028\pi\) | ||||
−0.564752 | + | 0.825261i | \(0.691028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.36557 | 0.0643022 | ||||||||
\(452\) | 0.0123327 | 0.000580080 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −45.1187 | −2.11753 | ||||||||
\(455\) | −7.18250 | −0.336721 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7798 | 1.53337 | 0.766687 | − | 0.642022i | \(-0.221904\pi\) | ||||
0.766687 | + | 0.642022i | \(0.221904\pi\) | |||||||
\(458\) | −44.5228 | −2.08041 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.470080 | −0.0219176 | ||||||||
\(461\) | 27.3848 | 1.27544 | 0.637718 | − | 0.770270i | \(-0.279879\pi\) | ||||
0.637718 | + | 0.770270i | \(0.279879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.92457 | 0.182390 | 0.0911952 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911952 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(464\) | 22.9158 | 1.06384 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.3513 | 1.22070 | ||||||||
\(467\) | 10.0855 | 0.466701 | 0.233351 | − | 0.972393i | \(-0.425031\pi\) | ||||
0.233351 | + | 0.972393i | \(0.425031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4952 | −0.761675 | ||||||||
\(470\) | −11.5889 | −0.534556 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.2981 | 0.474007 | ||||||||
\(473\) | 11.4226 | 0.525211 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.10108 | −0.0964042 | ||||||||
\(476\) | −7.38980 | −0.338711 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 37.9401 | 1.73534 | ||||||||
\(479\) | 3.63175 | 0.165939 | 0.0829695 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829695 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41319 | −0.201224 | ||||||||
\(482\) | −25.6104 | −1.16652 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.360147 | 0.0163703 | ||||||||
\(485\) | 34.3617 | 1.56029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.40952 | −0.290443 | −0.145222 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145222 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(488\) | −2.51927 | −0.114042 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.93759 | −0.268233 | ||||||||
\(491\) | −15.8126 | −0.713613 | −0.356807 | − | 0.934178i | \(-0.616135\pi\) | ||||
−0.356807 | + | 0.934178i | \(0.616135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.5613 | 1.55656 | ||||||||
\(494\) | 11.9120 | 0.535946 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.74910 | 0.258142 | ||||||||
\(497\) | −17.8406 | −0.800260 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.57896 | −0.204982 | −0.102491 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102491 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(500\) | 4.13917 | 0.185109 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −34.6148 | −1.54493 | ||||||||
\(503\) | 9.30226 | 0.414767 | 0.207384 | − | 0.978260i | \(-0.433505\pi\) | ||||
0.207384 | + | 0.978260i | \(0.433505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.59910 | 0.160158 | ||||||||
\(506\) | 0.925234 | 0.0411317 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.61316 | 0.204676 | ||||||||
\(509\) | −33.7782 | −1.49719 | −0.748596 | − | 0.663026i | \(-0.769272\pi\) | ||||
−0.748596 | + | 0.663026i | \(0.769272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5910 | 0.556992 | ||||||||
\(512\) | −13.8849 | −0.613634 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.9294 | 0.967262 | ||||||||
\(515\) | 25.2792 | 1.11393 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.48067 | 0.153080 | ||||||||
\(518\) | −17.9687 | −0.789497 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.10549 | 0.267743 | ||||||||
\(521\) | 27.0350 | 1.18442 | 0.592212 | − | 0.805782i | \(-0.298255\pi\) | ||||
0.592212 | + | 0.805782i | \(0.298255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.3914 | 1.63501 | 0.817507 | − | 0.575919i | \(-0.195356\pi\) | ||||
0.817507 | + | 0.575919i | \(0.195356\pi\) | |||||||
\(524\) | −0.824382 | −0.0360133 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8264 | 0.777267 | ||||||||
\(527\) | 8.67071 | 0.377702 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6373 | −0.984230 | ||||||||
\(530\) | 33.1991 | 1.44208 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.40096 | 0.320872 | ||||||||
\(533\) | 1.52704 | 0.0661435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8473 | 0.468969 | ||||||||
\(536\) | 14.0217 | 0.605646 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.9927 | 1.76732 | ||||||||
\(539\) | 1.78333 | 0.0768133 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7680 | 1.62377 | 0.811886 | − | 0.583815i | \(-0.198441\pi\) | ||||
0.811886 | + | 0.583815i | \(0.198441\pi\) | |||||||
\(542\) | −30.0834 | −1.29219 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.9430 | 0.597801 | ||||||||
\(545\) | −23.9604 | −1.02635 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.32281 | −0.270344 | −0.135172 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135172 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(548\) | −4.62190 | −0.197438 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.465515 | −0.0198496 | ||||||||
\(551\) | −34.6135 | −1.47459 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.8062 | −1.90535 | ||||||||
\(554\) | 8.52286 | 0.362101 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.18169 | −0.219752 | ||||||||
\(557\) | 33.1235 | 1.40349 | 0.701744 | − | 0.712430i | \(-0.252405\pi\) | ||||
0.701744 | + | 0.712430i | \(0.252405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.7732 | 0.540250 | ||||||||
\(560\) | 29.4854 | 1.24599 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.55320 | 0.318612 | ||||||||
\(563\) | 9.13968 | 0.385192 | 0.192596 | − | 0.981278i | \(-0.438309\pi\) | ||||
0.192596 | + | 0.981278i | \(0.438309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0742140 | −0.00312221 | ||||||||
\(566\) | 26.3828 | 1.10895 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.1654 | 0.636326 | ||||||||
\(569\) | −43.1897 | −1.81061 | −0.905304 | − | 0.424764i | \(-0.860357\pi\) | ||||
−0.905304 | + | 0.424764i | \(0.860357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.63115 | 0.319353 | 0.159677 | − | 0.987169i | \(-0.448955\pi\) | ||||
0.159677 | + | 0.987169i | \(0.448955\pi\) | |||||||
\(572\) | 0.402733 | 0.0168391 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.21747 | 0.259512 | ||||||||
\(575\) | −0.182493 | −0.00761049 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.0501 | 1.66731 | 0.833654 | − | 0.552287i | \(-0.186245\pi\) | ||||
0.833654 | + | 0.552287i | \(0.186245\pi\) | |||||||
\(578\) | 47.5235 | 1.97672 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.89634 | 0.161787 | ||||||||
\(581\) | −32.4415 | −1.34590 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.97119 | −0.412964 | ||||||||
\(584\) | −10.7030 | −0.442892 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.4596 | −1.05173 | ||||||||
\(587\) | 44.4272 | 1.83371 | 0.916854 | − | 0.399223i | \(-0.130720\pi\) | ||||
0.916854 | + | 0.399223i | \(0.130720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.68381 | −0.357810 | ||||||||
\(590\) | 13.6101 | 0.560318 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.1169 | 0.744602 | ||||||||
\(593\) | −9.39583 | −0.385840 | −0.192920 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192920 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.4694 | 1.82307 | ||||||||
\(596\) | 0.580800 | 0.0237905 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.03464 | 0.0423095 | ||||||||
\(599\) | 6.52995 | 0.266807 | 0.133403 | − | 0.991062i | \(-0.457409\pi\) | ||||
0.133403 | + | 0.991062i | \(0.457409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5451 | −0.634099 | −0.317050 | − | 0.948409i | \(-0.602692\pi\) | ||||
−0.317050 | + | 0.948409i | \(0.602692\pi\) | |||||||
\(602\) | 52.0072 | 2.11965 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.520469 | −0.0211776 | ||||||||
\(605\) | −2.16725 | −0.0881114 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.8074 | 0.479249 | 0.239625 | − | 0.970866i | \(-0.422976\pi\) | ||||
0.239625 | + | 0.970866i | \(0.422976\pi\) | |||||||
\(608\) | −13.9641 | −0.566318 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.32950 | −0.134808 | ||||||||
\(611\) | 3.89224 | 0.157463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1209 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(614\) | −13.6446 | −0.550653 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.46627 | −0.300825 | ||||||||
\(617\) | −18.1856 | −0.732124 | −0.366062 | − | 0.930591i | \(-0.619294\pi\) | ||||
−0.366062 | + | 0.930591i | \(0.619294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.6887 | 1.51484 | 0.757419 | − | 0.652929i | \(-0.226460\pi\) | ||||
0.757419 | + | 0.652929i | \(0.226460\pi\) | |||||||
\(620\) | 0.977511 | 0.0392578 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 50.8861 | 2.04035 | ||||||||
\(623\) | 10.6388 | 0.426235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3931 | −0.935724 | ||||||||
\(626\) | −1.31950 | −0.0527379 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.749712 | 0.0299168 | ||||||||
\(629\) | 27.3237 | 1.08947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.98191 | 0.118708 | 0.0593540 | − | 0.998237i | \(-0.481096\pi\) | ||||
0.0593540 | + | 0.998237i | \(0.481096\pi\) | |||||||
\(632\) | 38.0875 | 1.51504 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.9087 | −1.10840 | ||||||||
\(635\) | −27.7606 | −1.10164 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.99419 | 0.0790129 | ||||||||
\(638\) | −7.66897 | −0.303617 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.9968 | −1.14620 | ||||||||
\(641\) | 1.83933 | 0.0726491 | 0.0363246 | − | 0.999340i | \(-0.488435\pi\) | ||||
0.0363246 | + | 0.999340i | \(0.488435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0684 | 0.594239 | 0.297119 | − | 0.954840i | \(-0.403974\pi\) | ||||
0.297119 | + | 0.954840i | \(0.403974\pi\) | |||||||
\(644\) | 0.642824 | 0.0253308 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −73.7515 | −2.90171 | ||||||||
\(647\) | −9.19964 | −0.361675 | −0.180838 | − | 0.983513i | \(-0.557881\pi\) | ||||
−0.180838 | + | 0.983513i | \(0.557881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.08773 | −0.160457 | ||||||||
\(650\) | −0.520560 | −0.0204180 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00099 | −0.195854 | ||||||||
\(653\) | −29.7910 | −1.16581 | −0.582906 | − | 0.812540i | \(-0.698084\pi\) | ||||
−0.582906 | + | 0.812540i | \(0.698084\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.96087 | 0.193837 | ||||||||
\(656\) | −6.26878 | −0.244755 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.8476 | 0.617802 | ||||||||
\(659\) | −14.7506 | −0.574601 | −0.287301 | − | 0.957840i | \(-0.592758\pi\) | ||||
−0.287301 | + | 0.957840i | \(0.592758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0393 | −0.701648 | −0.350824 | − | 0.936442i | \(-0.614098\pi\) | ||||
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(662\) | 4.36014 | 0.169462 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.5769 | 1.07019 | ||||||||
\(665\) | −44.5366 | −1.72706 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.00642 | −0.116409 | ||||||||
\(668\) | 1.67334 | 0.0647433 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.5313 | 0.715927 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.65379 | 0.256485 | 0.128242 | − | 0.991743i | \(-0.459066\pi\) | ||||
0.128242 | + | 0.991743i | \(0.459066\pi\) | |||||||
\(674\) | −9.60296 | −0.369892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.23156 | −0.162752 | ||||||||
\(677\) | 23.5492 | 0.905070 | 0.452535 | − | 0.891747i | \(-0.350520\pi\) | ||||
0.452535 | + | 0.891747i | \(0.350520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.9889 | −1.80327 | ||||||||
\(680\) | −37.8013 | −1.44961 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.92398 | −0.0736731 | ||||||||
\(683\) | −38.8826 | −1.48780 | −0.743901 | − | 0.668290i | \(-0.767027\pi\) | ||||
−0.743901 | + | 0.668290i | \(0.767027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.8131 | 1.06268 | ||||||||
\(686\) | −23.7516 | −0.906840 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −52.4364 | −1.99912 | ||||||||
\(689\) | −11.1502 | −0.424790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.93629 | 0.339953 | 0.169976 | − | 0.985448i | \(-0.445631\pi\) | ||||
0.169976 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(692\) | −6.58993 | −0.250512 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.05672 | 0.0401125 | ||||||||
\(695\) | 31.1817 | 1.18279 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.45447 | −0.358113 | ||||||||
\(698\) | −9.20441 | −0.348392 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.323425 | −0.0122243 | ||||||||
\(701\) | 29.3901 | 1.11005 | 0.555025 | − | 0.831834i | \(-0.312709\pi\) | ||||
0.555025 | + | 0.831834i | \(0.312709\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.3650 | −1.03209 | ||||||||
\(704\) | 6.08730 | 0.229424 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.1219 | 1.24656 | ||||||||
\(707\) | −4.92168 | −0.185099 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4876 | 1.06987 | 0.534936 | − | 0.844892i | \(-0.320336\pi\) | ||||
0.534936 | + | 0.844892i | \(0.320336\pi\) | |||||||
\(710\) | 20.0428 | 0.752194 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.04354 | −0.338921 | ||||||||
\(713\) | −0.754247 | −0.0282468 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.42352 | −0.0906344 | ||||||||
\(716\) | −0.413856 | −0.0154665 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.6682 | 0.547412 | ||||||||
\(719\) | 44.8105 | 1.67115 | 0.835574 | − | 0.549378i | \(-0.185135\pi\) | ||||
0.835574 | + | 0.549378i | \(0.185135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.5687 | −1.28740 | ||||||||
\(722\) | 44.6736 | 1.66258 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.15278 | −0.191502 | ||||||||
\(725\) | 1.51263 | 0.0561775 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.3792 | −1.38632 | −0.693158 | − | 0.720785i | \(-0.743781\pi\) | ||||
−0.693158 | + | 0.720785i | \(0.743781\pi\) | |||||||
\(728\) | −8.34912 | −0.309439 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.1452 | −0.523537 | ||||||||
\(731\) | −79.0837 | −2.92502 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.9355 | 0.736334 | 0.368167 | − | 0.929760i | \(-0.379985\pi\) | ||||
0.368167 | + | 0.929760i | \(0.379985\pi\) | |||||||
\(734\) | 28.0634 | 1.03584 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.21287 | −0.0447071 | ||||||||
\(737\) | −5.56579 | −0.205019 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9077 | 0.953029 | 0.476514 | − | 0.879167i | \(-0.341900\pi\) | ||||
0.476514 | + | 0.879167i | \(0.341900\pi\) | |||||||
\(740\) | 3.08039 | 0.113238 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45.3990 | −1.66665 | ||||||||
\(743\) | 53.6023 | 1.96648 | 0.983239 | − | 0.182324i | \(-0.0583620\pi\) | ||||
0.983239 | + | 0.182324i | \(0.0583620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.49507 | −0.128050 | ||||||||
\(746\) | −32.9805 | −1.20750 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.49346 | −0.0911700 | ||||||||
\(749\) | −14.8334 | −0.542001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.9819 | −1.82387 | −0.911933 | − | 0.410339i | \(-0.865410\pi\) | ||||
−0.911933 | + | 0.410339i | \(0.865410\pi\) | |||||||
\(752\) | −15.9783 | −0.582670 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.57578 | −0.312311 | ||||||||
\(755\) | 3.13202 | 0.113986 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9641 | −0.580225 | −0.290113 | − | 0.956993i | \(-0.593693\pi\) | ||||
−0.290113 | + | 0.956993i | \(0.593693\pi\) | |||||||
\(758\) | −34.3451 | −1.24747 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 37.8584 | 1.37327 | ||||||||
\(761\) | 23.6666 | 0.857912 | 0.428956 | − | 0.903325i | \(-0.358882\pi\) | ||||
0.428956 | + | 0.903325i | \(0.358882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.7653 | 1.18618 | ||||||||
\(764\) | 0.588843 | 0.0213036 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47.9396 | −1.73213 | ||||||||
\(767\) | −4.57107 | −0.165052 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.05401 | 0.0740696 | 0.0370348 | − | 0.999314i | \(-0.488209\pi\) | ||||
0.0370348 | + | 0.999314i | \(0.488209\pi\) | |||||||
\(770\) | −9.86753 | −0.355601 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.32437 | 0.299601 | ||||||||
\(773\) | 40.4222 | 1.45389 | 0.726944 | − | 0.686697i | \(-0.240940\pi\) | ||||
0.726944 | + | 0.686697i | \(0.240940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.379486 | 0.0136316 | ||||||||
\(776\) | 39.9429 | 1.43387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48.2186 | −1.72872 | ||||||||
\(779\) | 9.46875 | 0.339253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.01977 | −0.215404 | ||||||||
\(782\) | −6.40581 | −0.229071 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.18652 | −0.292376 | ||||||||
\(785\) | −4.51153 | −0.161023 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3124 | 0.581473 | 0.290736 | − | 0.956803i | \(-0.406100\pi\) | ||||
0.290736 | + | 0.956803i | \(0.406100\pi\) | |||||||
\(788\) | 4.29687 | 0.153070 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 50.3370 | 1.79091 | ||||||||
\(791\) | 0.101486 | 0.00360843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.11824 | 0.0397100 | ||||||||
\(794\) | 33.9678 | 1.20547 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.28062 | −0.0453903 | ||||||||
\(797\) | 4.40506 | 0.156035 | 0.0780176 | − | 0.996952i | \(-0.475141\pi\) | ||||
0.0780176 | + | 0.996952i | \(0.475141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0983 | −0.852536 | ||||||||
\(800\) | 0.610236 | 0.0215751 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −51.3488 | −1.81319 | ||||||||
\(803\) | 4.24844 | 0.149924 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86831 | −0.136340 | ||||||||
\(806\) | −2.15148 | −0.0757828 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.18368 | 0.147181 | ||||||||
\(809\) | −14.1528 | −0.497586 | −0.248793 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248793 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.7568 | 1.74720 | 0.873598 | − | 0.486648i | \(-0.161781\pi\) | ||||
0.873598 | + | 0.486648i | \(0.161781\pi\) | |||||||
\(812\) | −5.32816 | −0.186982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.06298 | −0.212507 | ||||||||
\(815\) | 30.0944 | 1.05416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 79.2032 | 2.77097 | ||||||||
\(818\) | 14.8667 | 0.519801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.06587 | −0.0372218 | ||||||||
\(821\) | −4.12520 | −0.143971 | −0.0719853 | − | 0.997406i | \(-0.522933\pi\) | ||||
−0.0719853 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.13671 | −0.0744809 | −0.0372405 | − | 0.999306i | \(-0.511857\pi\) | ||||
−0.0372405 | + | 0.999306i | \(0.511857\pi\) | |||||||
\(824\) | 29.3851 | 1.02368 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.6115 | −0.647576 | ||||||||
\(827\) | 15.4530 | 0.537353 | 0.268676 | − | 0.963231i | \(-0.413414\pi\) | ||||
0.268676 | + | 0.963231i | \(0.413414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3229 | 0.601651 | 0.300825 | − | 0.953679i | \(-0.402738\pi\) | ||||
0.300825 | + | 0.953679i | \(0.402738\pi\) | |||||||
\(830\) | 36.4460 | 1.26506 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.80709 | 0.235993 | ||||||||
\(833\) | −12.3468 | −0.427790 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0696 | −0.348473 | ||||||||
\(836\) | 2.49723 | 0.0863686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.0770 | 1.69534 | ||||||||
\(839\) | −23.7300 | −0.819250 | −0.409625 | − | 0.912254i | \(-0.634340\pi\) | ||||
−0.409625 | + | 0.912254i | \(0.634340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.08076 | −0.140716 | ||||||||
\(842\) | 47.5199 | 1.63764 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.72098 | −0.162503 | ||||||||
\(845\) | 25.4642 | 0.875995 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.96367 | 0.101833 | ||||||||
\(848\) | 45.7736 | 1.57187 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.22297 | 0.110547 | ||||||||
\(851\) | −2.37683 | −0.0814767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.60379 | −0.191870 | −0.0959350 | − | 0.995388i | \(-0.530584\pi\) | ||||
−0.0959350 | + | 0.995388i | \(0.530584\pi\) | |||||||
\(854\) | 4.55302 | 0.155801 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.6092 | 0.430972 | ||||||||
\(857\) | −20.2530 | −0.691829 | −0.345915 | − | 0.938266i | \(-0.612431\pi\) | ||||
−0.345915 | + | 0.938266i | \(0.612431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.5525 | −0.769483 | −0.384741 | − | 0.923024i | \(-0.625709\pi\) | ||||
−0.384741 | + | 0.923024i | \(0.625709\pi\) | |||||||
\(860\) | −8.91567 | −0.304022 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.524560 | 0.0178666 | ||||||||
\(863\) | −12.8191 | −0.436366 | −0.218183 | − | 0.975908i | \(-0.570013\pi\) | ||||
−0.218183 | + | 0.975908i | \(0.570013\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.6561 | 1.34835 | ||||||||
\(866\) | 4.49117 | 0.152616 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.33672 | −0.0453714 | ||||||||
\(869\) | −15.1185 | −0.512860 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.22391 | −0.210889 | ||||||||
\(872\) | −27.8521 | −0.943192 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.41549 | 0.217007 | ||||||||
\(875\) | 34.0614 | 1.15148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.58171 | 0.120946 | 0.0604729 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604729 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(878\) | 50.5109 | 1.70466 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.94897 | 0.335380 | ||||||||
\(881\) | −36.6210 | −1.23379 | −0.616896 | − | 0.787045i | \(-0.711610\pi\) | ||||
−0.616896 | + | 0.787045i | \(0.711610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.9528 | −1.34452 | −0.672260 | − | 0.740315i | \(-0.734676\pi\) | ||||
−0.672260 | + | 0.740315i | \(0.734676\pi\) | |||||||
\(884\) | −2.78830 | −0.0937807 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.3675 | −1.22179 | ||||||||
\(887\) | 35.7841 | 1.20151 | 0.600756 | − | 0.799433i | \(-0.294866\pi\) | ||||
0.600756 | + | 0.799433i | \(0.294866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.9619 | 1.27320 | ||||||||
\(890\) | −11.9521 | −0.400634 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.45247 | −0.283010 | ||||||||
\(893\) | 24.1347 | 0.807637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.49046 | 0.0832468 | ||||||||
\(896\) | 39.6525 | 1.32470 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.7689 | −1.22699 | ||||||||
\(899\) | 6.25171 | 0.208506 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69.0350 | 2.29989 | ||||||||
\(902\) | 2.09790 | 0.0698523 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0862682 | −0.00286924 | ||||||||
\(905\) | 31.0078 | 1.03073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.5669 | 0.583301 | 0.291650 | − | 0.956525i | \(-0.405796\pi\) | ||||
0.291650 | + | 0.956525i | \(0.405796\pi\) | |||||||
\(908\) | −10.5771 | −0.351014 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.0343 | −0.365784 | ||||||||
\(911\) | −48.1419 | −1.59501 | −0.797506 | − | 0.603312i | \(-0.793848\pi\) | ||||
−0.797506 | + | 0.603312i | \(0.793848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.9464 | −0.362273 | ||||||||
\(914\) | 50.3588 | 1.66572 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.4374 | −0.344862 | ||||||||
\(917\) | −6.78387 | −0.224023 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.75158 | 0.321675 | 0.160838 | − | 0.986981i | \(-0.448580\pi\) | ||||
0.160838 | + | 0.986981i | \(0.448580\pi\) | |||||||
\(920\) | 3.28826 | 0.108411 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.0706 | 1.38552 | ||||||||
\(923\) | −6.73157 | −0.221572 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.19586 | 0.0393197 | ||||||||
\(926\) | 6.02923 | 0.198133 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.0531 | 0.330010 | ||||||||
\(929\) | −19.2963 | −0.633090 | −0.316545 | − | 0.948577i | \(-0.602523\pi\) | ||||
−0.316545 | + | 0.948577i | \(0.602523\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3654 | 0.405261 | ||||||||
\(932\) | 6.17750 | 0.202351 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.4941 | 0.506983 | ||||||||
\(935\) | 15.0049 | 0.490712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.7671 | 1.26647 | 0.633234 | − | 0.773961i | \(-0.281727\pi\) | ||||
0.633234 | + | 0.773961i | \(0.281727\pi\) | |||||||
\(938\) | −25.3411 | −0.827417 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.71677 | −0.0886113 | ||||||||
\(941\) | −11.5036 | −0.375008 | −0.187504 | − | 0.982264i | \(-0.560040\pi\) | ||||
−0.187504 | + | 0.982264i | \(0.560040\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.822425 | 0.0267818 | ||||||||
\(944\) | 18.7651 | 0.610751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.5482 | 0.570543 | ||||||||
\(947\) | 36.2501 | 1.17797 | 0.588985 | − | 0.808144i | \(-0.299528\pi\) | ||||
0.588985 | + | 0.808144i | \(0.299528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.75079 | 0.154217 | ||||||||
\(950\) | −3.22784 | −0.104725 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 51.6924 | 1.67536 | ||||||||
\(953\) | −17.5362 | −0.568053 | −0.284026 | − | 0.958817i | \(-0.591670\pi\) | ||||
−0.284026 | + | 0.958817i | \(0.591670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.54347 | −0.114664 | ||||||||
\(956\) | 8.89424 | 0.287660 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.57938 | 0.180262 | ||||||||
\(959\) | −38.0338 | −1.22817 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4316 | −0.949406 | ||||||||
\(962\) | −6.77989 | −0.218592 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.00382 | −0.193370 | ||||||||
\(965\) | −50.0934 | −1.61256 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.1752 | −0.455844 | −0.227922 | − | 0.973679i | \(-0.573193\pi\) | ||||
−0.227922 | + | 0.973679i | \(0.573193\pi\) | |||||||
\(968\) | −2.51927 | −0.0809723 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 52.7891 | 1.69496 | ||||||||
\(971\) | −29.6419 | −0.951255 | −0.475627 | − | 0.879647i | \(-0.657779\pi\) | ||||
−0.475627 | + | 0.879647i | \(0.657779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.6403 | −1.36699 | ||||||||
\(974\) | −9.84681 | −0.315512 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.59059 | −0.146941 | ||||||||
\(977\) | 9.22781 | 0.295224 | 0.147612 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147612 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.58975 | 0.114729 | ||||||||
\(980\) | −1.39194 | −0.0444639 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.2926 | −0.775207 | ||||||||
\(983\) | 39.2361 | 1.25144 | 0.625718 | − | 0.780049i | \(-0.284806\pi\) | ||||
0.625718 | + | 0.780049i | \(0.284806\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8572 | −0.823879 | ||||||||
\(986\) | 53.0957 | 1.69091 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.79251 | 0.0888417 | ||||||||
\(989\) | 6.87933 | 0.218750 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0776 | −0.701317 | −0.350659 | − | 0.936503i | \(-0.614042\pi\) | ||||
−0.350659 | + | 0.936503i | \(0.614042\pi\) | |||||||
\(992\) | 2.52212 | 0.0800773 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27.4081 | −0.869332 | ||||||||
\(995\) | 7.70636 | 0.244308 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.8055 | 1.51401 | 0.757007 | − | 0.653407i | \(-0.226661\pi\) | ||||
0.757007 | + | 0.653407i | \(0.226661\pi\) | |||||||
\(998\) | −7.03455 | −0.222675 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.m.1.20 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.p.1.6 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.20 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.p.1.6 | yes | 25 | 3.2 | odd | 2 |