Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6930,2,Mod(1,6930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.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: | \(55.3363286007\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6930.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.12311 | −1.48527 | −0.742635 | − | 0.669696i | \(-0.766424\pi\) | ||||
−0.742635 | + | 0.669696i | \(0.766424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 8.24621 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.12311 | −1.27935 | −0.639674 | − | 0.768647i | \(-0.720931\pi\) | ||||
−0.639674 | + | 0.768647i | \(0.720931\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.12311 | 0.535608 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.12311 | 1.17103 | 0.585516 | − | 0.810661i | \(-0.300892\pi\) | ||||
0.585516 | + | 0.810661i | \(0.300892\pi\) | |||||||
\(38\) | −1.12311 | −0.182192 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.12311 | −1.42479 | −0.712395 | − | 0.701779i | \(-0.752389\pi\) | ||||
−0.712395 | + | 0.701779i | \(0.752389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.12311 | −0.781266 | −0.390633 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390633 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.12311 | 1.05024 | ||||||||
\(47\) | 11.3693 | 1.65839 | 0.829193 | − | 0.558963i | \(-0.188801\pi\) | ||||
0.829193 | + | 0.558963i | \(0.188801\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.24621 | −1.08278 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.12311 | 0.399873 | 0.199936 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(62\) | 7.12311 | 0.904635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.12311 | −1.11456 | −0.557282 | − | 0.830323i | \(-0.688156\pi\) | ||||
−0.557282 | + | 0.830323i | \(0.688156\pi\) | |||||||
\(68\) | −3.12311 | −0.378732 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 1.12311 | 0.133288 | 0.0666441 | − | 0.997777i | \(-0.478771\pi\) | ||||
0.0666441 | + | 0.997777i | \(0.478771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.246211 | −0.0288168 | −0.0144084 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144084 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(74\) | −7.12311 | −0.828044 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.12311 | 0.128829 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.12311 | 1.00748 | ||||||||
\(83\) | −11.1231 | −1.22092 | −0.610460 | − | 0.792047i | \(-0.709015\pi\) | ||||
−0.610460 | + | 0.792047i | \(0.709015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.12311 | −0.338748 | ||||||||
\(86\) | 5.12311 | 0.552439 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −8.24621 | −0.874097 | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | −7.12311 | −0.742635 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.3693 | −1.17266 | ||||||||
\(95\) | 1.12311 | 0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.87689 | −0.292104 | −0.146052 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146052 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.3693 | 1.13129 | 0.565645 | − | 0.824649i | \(-0.308627\pi\) | ||||
0.565645 | + | 0.824649i | \(0.308627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | −18.2462 | −1.76393 | −0.881964 | − | 0.471317i | \(-0.843779\pi\) | ||||
−0.881964 | + | 0.471317i | \(0.843779\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.12311 | −0.664233 | ||||||||
\(116\) | 8.24621 | 0.765641 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 3.12311 | 0.286295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.12311 | −0.282753 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.12311 | −0.639674 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.75379 | −0.155624 | −0.0778118 | − | 0.996968i | \(-0.524793\pi\) | ||||
−0.0778118 | + | 0.996968i | \(0.524793\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | −0.175412 | ||||||||
\(131\) | 5.75379 | 0.502711 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.12311 | −0.0973856 | ||||||||
\(134\) | 9.12311 | 0.788116 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.12311 | 0.267804 | ||||||||
\(137\) | −20.2462 | −1.72975 | −0.864875 | − | 0.501987i | \(-0.832603\pi\) | ||||
−0.864875 | + | 0.501987i | \(0.832603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.12311 | −0.773812 | −0.386906 | − | 0.922119i | \(-0.626456\pi\) | ||||
−0.386906 | + | 0.922119i | \(0.626456\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.12311 | −0.0942489 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.24621 | 0.684811 | ||||||||
\(146\) | 0.246211 | 0.0203766 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.12311 | 0.585516 | ||||||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8769 | 1.04791 | 0.523953 | − | 0.851747i | \(-0.324457\pi\) | ||||
0.523953 | + | 0.851747i | \(0.324457\pi\) | |||||||
\(152\) | −1.12311 | −0.0910959 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −7.12311 | −0.572142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.12311 | 0.408868 | 0.204434 | − | 0.978880i | \(-0.434465\pi\) | ||||
0.204434 | + | 0.978880i | \(0.434465\pi\) | |||||||
\(158\) | 3.12311 | 0.248461 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 7.12311 | 0.561379 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.36932 | 0.263905 | 0.131953 | − | 0.991256i | \(-0.457875\pi\) | ||||
0.131953 | + | 0.991256i | \(0.457875\pi\) | |||||||
\(164\) | −9.12311 | −0.712395 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1231 | 0.863320 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 3.12311 | 0.239531 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.12311 | −0.390633 | ||||||||
\(173\) | 4.24621 | 0.322833 | 0.161417 | − | 0.986886i | \(-0.448394\pi\) | ||||
0.161417 | + | 0.986886i | \(0.448394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.24621 | 0.618080 | ||||||||
\(179\) | −14.2462 | −1.06481 | −0.532406 | − | 0.846489i | \(-0.678712\pi\) | ||||
−0.532406 | + | 0.846489i | \(0.678712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.36932 | −0.399098 | −0.199549 | − | 0.979888i | \(-0.563948\pi\) | ||||
−0.199549 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(182\) | 2.00000 | 0.148250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.12311 | 0.525122 | ||||||||
\(185\) | 7.12311 | 0.523701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.12311 | −0.228384 | ||||||||
\(188\) | 11.3693 | 0.829193 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.12311 | −0.0814786 | ||||||||
\(191\) | −6.87689 | −0.497595 | −0.248797 | − | 0.968556i | \(-0.580035\pi\) | ||||
−0.248797 | + | 0.968556i | \(0.580035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.87689 | 0.207083 | 0.103542 | − | 0.994625i | \(-0.466982\pi\) | ||||
0.103542 | + | 0.994625i | \(0.466982\pi\) | |||||||
\(194\) | 2.87689 | 0.206549 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −22.4924 | −1.60252 | −0.801259 | − | 0.598317i | \(-0.795836\pi\) | ||||
−0.801259 | + | 0.598317i | \(0.795836\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.87689 | −0.345714 | −0.172857 | − | 0.984947i | \(-0.555300\pi\) | ||||
−0.172857 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.3693 | −0.799942 | ||||||||
\(203\) | −8.24621 | −0.578771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.12311 | −0.637185 | ||||||||
\(206\) | −14.2462 | −0.992581 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 1.12311 | 0.0776868 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.87689 | 0.611111 | 0.305555 | − | 0.952174i | \(-0.401158\pi\) | ||||
0.305555 | + | 0.952174i | \(0.401158\pi\) | |||||||
\(212\) | −10.0000 | −0.686803 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.2462 | 1.24729 | ||||||||
\(215\) | −5.12311 | −0.349393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.12311 | 0.483548 | ||||||||
\(218\) | −18.0000 | −1.21911 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −6.24621 | −0.420166 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.49242 | 0.300835 | 0.150417 | − | 0.988623i | \(-0.451938\pi\) | ||||
0.150417 | + | 0.988623i | \(0.451938\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | −21.3693 | −1.41833 | −0.709166 | − | 0.705042i | \(-0.750928\pi\) | ||||
−0.709166 | + | 0.705042i | \(0.750928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1231 | 0.735036 | 0.367518 | − | 0.930017i | \(-0.380208\pi\) | ||||
0.367518 | + | 0.930017i | \(0.380208\pi\) | |||||||
\(230\) | 7.12311 | 0.469684 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.24621 | −0.541390 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3693 | 0.741652 | ||||||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.12311 | −0.202441 | ||||||||
\(239\) | 7.36932 | 0.476681 | 0.238341 | − | 0.971182i | \(-0.423396\pi\) | ||||
0.238341 | + | 0.971182i | \(0.423396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4924 | 1.44886 | 0.724432 | − | 0.689346i | \(-0.242102\pi\) | ||||
0.724432 | + | 0.689346i | \(0.242102\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.12311 | 0.199936 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24621 | 0.142923 | ||||||||
\(248\) | 7.12311 | 0.452318 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −16.4924 | −1.04099 | −0.520496 | − | 0.853864i | \(-0.674253\pi\) | ||||
−0.520496 | + | 0.853864i | \(0.674253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.12311 | −0.447826 | ||||||||
\(254\) | 1.75379 | 0.110042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.6155 | 0.974070 | 0.487035 | − | 0.873382i | \(-0.338078\pi\) | ||||
0.487035 | + | 0.873382i | \(0.338078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.12311 | −0.442608 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.75379 | −0.355470 | ||||||||
\(263\) | 8.49242 | 0.523665 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 1.12311 | 0.0688620 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.12311 | −0.557282 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.2462 | 1.22312 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2462 | −0.615635 | −0.307818 | − | 0.951445i | \(-0.599599\pi\) | ||||
−0.307818 | + | 0.951445i | \(0.599599\pi\) | |||||||
\(278\) | 9.12311 | 0.547168 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −13.3693 | −0.797547 | −0.398773 | − | 0.917050i | \(-0.630564\pi\) | ||||
−0.398773 | + | 0.917050i | \(0.630564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2462 | 0.846849 | 0.423425 | − | 0.905931i | \(-0.360828\pi\) | ||||
0.423425 | + | 0.905931i | \(0.360828\pi\) | |||||||
\(284\) | 1.12311 | 0.0666441 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 9.12311 | 0.538520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | −8.24621 | −0.484234 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.246211 | −0.0144084 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | −7.12311 | −0.414022 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | −14.2462 | −0.823880 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.12311 | 0.295291 | ||||||||
\(302\) | −12.8769 | −0.740982 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.12311 | 0.0644145 | ||||||||
\(305\) | 3.12311 | 0.178829 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.7386 | −1.98264 | −0.991319 | − | 0.131477i | \(-0.958028\pi\) | ||||
−0.991319 | + | 0.131477i | \(0.958028\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.12311 | 0.404565 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.6155 | −0.995689 | −0.497844 | − | 0.867266i | \(-0.665875\pi\) | ||||
−0.497844 | + | 0.867266i | \(0.665875\pi\) | |||||||
\(314\) | −5.12311 | −0.289114 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.12311 | −0.175688 | ||||||||
\(317\) | 8.24621 | 0.463153 | 0.231577 | − | 0.972817i | \(-0.425612\pi\) | ||||
0.231577 | + | 0.972817i | \(0.425612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.24621 | 0.461699 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.12311 | −0.396955 | ||||||||
\(323\) | −3.50758 | −0.195167 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −3.36932 | −0.186609 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.12311 | 0.503739 | ||||||||
\(329\) | −11.3693 | −0.626811 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | −11.1231 | −0.610460 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | −9.12311 | −0.498449 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.6155 | 1.61326 | 0.806630 | − | 0.591056i | \(-0.201289\pi\) | ||||
0.806630 | + | 0.591056i | \(0.201289\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.12311 | −0.169374 | ||||||||
\(341\) | −7.12311 | −0.385738 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.12311 | 0.276219 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.24621 | −0.228278 | ||||||||
\(347\) | 30.7386 | 1.65014 | 0.825068 | − | 0.565033i | \(-0.191137\pi\) | ||||
0.825068 | + | 0.565033i | \(0.191137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.36932 | −0.287413 | −0.143706 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143706 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 15.6155 | 0.831131 | 0.415565 | − | 0.909563i | \(-0.363584\pi\) | ||||
0.415565 | + | 0.909563i | \(0.363584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.12311 | 0.0596083 | ||||||||
\(356\) | −8.24621 | −0.437048 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.2462 | 0.752936 | ||||||||
\(359\) | 7.36932 | 0.388938 | 0.194469 | − | 0.980909i | \(-0.437702\pi\) | ||||
0.194469 | + | 0.980909i | \(0.437702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 5.36932 | 0.282205 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | −0.246211 | −0.0128873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.4924 | −1.48729 | −0.743646 | − | 0.668573i | \(-0.766905\pi\) | ||||
−0.743646 | + | 0.668573i | \(0.766905\pi\) | |||||||
\(368\) | −7.12311 | −0.371318 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.12311 | −0.370313 | ||||||||
\(371\) | 10.0000 | 0.519174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.2462 | −1.15187 | −0.575933 | − | 0.817497i | \(-0.695361\pi\) | ||||
−0.575933 | + | 0.817497i | \(0.695361\pi\) | |||||||
\(374\) | 3.12311 | 0.161492 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.3693 | −0.586328 | ||||||||
\(377\) | 16.4924 | 0.849403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 1.12311 | 0.0576141 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.87689 | 0.351853 | ||||||||
\(383\) | −5.61553 | −0.286940 | −0.143470 | − | 0.989655i | \(-0.545826\pi\) | ||||
−0.143470 | + | 0.989655i | \(0.545826\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −2.87689 | −0.146430 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.87689 | −0.146052 | ||||||||
\(389\) | −11.3693 | −0.576447 | −0.288224 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288224 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.2462 | 1.12504 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.4924 | 1.13315 | ||||||||
\(395\) | −3.12311 | −0.157140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.3693 | −1.37363 | −0.686813 | − | 0.726834i | \(-0.740991\pi\) | ||||
−0.686813 | + | 0.726834i | \(0.740991\pi\) | |||||||
\(398\) | 4.87689 | 0.244457 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 32.0000 | 1.59800 | 0.799002 | − | 0.601329i | \(-0.205362\pi\) | ||||
0.799002 | + | 0.601329i | \(0.205362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.2462 | −0.709654 | ||||||||
\(404\) | 11.3693 | 0.565645 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.24621 | 0.409253 | ||||||||
\(407\) | 7.12311 | 0.353079 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2462 | 0.803323 | 0.401662 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401662 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(410\) | 9.12311 | 0.450558 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.2462 | 0.701860 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.1231 | −0.546012 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.12311 | −0.0549329 | ||||||||
\(419\) | 0.492423 | 0.0240564 | 0.0120282 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120282 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.24621 | −0.401896 | −0.200948 | − | 0.979602i | \(-0.564402\pi\) | ||||
−0.200948 | + | 0.979602i | \(0.564402\pi\) | |||||||
\(422\) | −8.87689 | −0.432120 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0000 | 0.485643 | ||||||||
\(425\) | −3.12311 | −0.151493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.12311 | −0.151138 | ||||||||
\(428\) | −18.2462 | −0.881964 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.12311 | 0.247058 | ||||||||
\(431\) | 17.6155 | 0.848510 | 0.424255 | − | 0.905543i | \(-0.360536\pi\) | ||||
0.424255 | + | 0.905543i | \(0.360536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.12311 | −0.0539730 | −0.0269865 | − | 0.999636i | \(-0.508591\pi\) | ||||
−0.0269865 | + | 0.999636i | \(0.508591\pi\) | |||||||
\(434\) | −7.12311 | −0.341920 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0000 | 0.862044 | ||||||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7386 | −1.08526 | −0.542628 | − | 0.839973i | \(-0.682571\pi\) | ||||
−0.542628 | + | 0.839973i | \(0.682571\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.24621 | 0.297102 | ||||||||
\(443\) | −27.6155 | −1.31205 | −0.656027 | − | 0.754738i | \(-0.727764\pi\) | ||||
−0.656027 | + | 0.754738i | \(0.727764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.24621 | −0.390908 | ||||||||
\(446\) | −4.49242 | −0.212722 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −30.7386 | −1.45065 | −0.725323 | − | 0.688409i | \(-0.758310\pi\) | ||||
−0.725323 | + | 0.688409i | \(0.758310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.12311 | −0.429590 | ||||||||
\(452\) | −2.00000 | −0.0940721 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.3693 | 1.00291 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3693 | 0.531834 | 0.265917 | − | 0.963996i | \(-0.414325\pi\) | ||||
0.265917 | + | 0.963996i | \(0.414325\pi\) | |||||||
\(458\) | −11.1231 | −0.519749 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.12311 | −0.332117 | ||||||||
\(461\) | 13.1231 | 0.611204 | 0.305602 | − | 0.952159i | \(-0.401142\pi\) | ||||
0.305602 | + | 0.952159i | \(0.401142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.7386 | 1.05675 | 0.528377 | − | 0.849010i | \(-0.322801\pi\) | ||||
0.528377 | + | 0.849010i | \(0.322801\pi\) | |||||||
\(464\) | 8.24621 | 0.382821 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 12.4924 | 0.578080 | 0.289040 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289040 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.12311 | 0.421266 | ||||||||
\(470\) | −11.3693 | −0.524427 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.00000 | 0.184115 | ||||||||
\(473\) | −5.12311 | −0.235561 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12311 | 0.0515316 | ||||||||
\(476\) | 3.12311 | 0.143147 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.36932 | −0.337065 | ||||||||
\(479\) | 16.4924 | 0.753558 | 0.376779 | − | 0.926303i | \(-0.377032\pi\) | ||||
0.376779 | + | 0.926303i | \(0.377032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2462 | 0.649571 | ||||||||
\(482\) | −22.4924 | −1.02450 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.87689 | −0.130633 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.49242 | 0.203571 | 0.101786 | − | 0.994806i | \(-0.467544\pi\) | ||||
0.101786 | + | 0.994806i | \(0.467544\pi\) | |||||||
\(488\) | −3.12311 | −0.141376 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −6.24621 | −0.281888 | −0.140944 | − | 0.990018i | \(-0.545014\pi\) | ||||
−0.140944 | + | 0.990018i | \(0.545014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.7538 | −1.15989 | ||||||||
\(494\) | −2.24621 | −0.101062 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.12311 | −0.319837 | ||||||||
\(497\) | −1.12311 | −0.0503782 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7386 | −0.838856 | −0.419428 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419428 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.4924 | 0.736093 | ||||||||
\(503\) | 0.246211 | 0.0109780 | 0.00548901 | − | 0.999985i | \(-0.498253\pi\) | ||||
0.00548901 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3693 | 0.505928 | ||||||||
\(506\) | 7.12311 | 0.316661 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.75379 | −0.0778118 | ||||||||
\(509\) | −40.2462 | −1.78388 | −0.891941 | − | 0.452152i | \(-0.850657\pi\) | ||||
−0.891941 | + | 0.452152i | \(0.850657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.246211 | 0.0108917 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.6155 | −0.688771 | ||||||||
\(515\) | 14.2462 | 0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3693 | 0.500022 | ||||||||
\(518\) | 7.12311 | 0.312971 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 12.2462 | 0.536516 | 0.268258 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268258 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.492423 | 0.0215321 | 0.0107661 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107661 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(524\) | 5.75379 | 0.251355 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.49242 | −0.370287 | ||||||||
\(527\) | 22.2462 | 0.969060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7386 | 1.20603 | ||||||||
\(530\) | 10.0000 | 0.434372 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.12311 | −0.0486928 | ||||||||
\(533\) | −18.2462 | −0.790331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.2462 | −0.788853 | ||||||||
\(536\) | 9.12311 | 0.394058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.7538 | −0.505335 | −0.252667 | − | 0.967553i | \(-0.581308\pi\) | ||||
−0.252667 | + | 0.967553i | \(0.581308\pi\) | |||||||
\(542\) | 12.0000 | 0.515444 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.12311 | 0.133902 | ||||||||
\(545\) | 18.0000 | 0.771035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.61553 | 0.240103 | 0.120051 | − | 0.992768i | \(-0.461694\pi\) | ||||
0.120051 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(548\) | −20.2462 | −0.864875 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 9.26137 | 0.394547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.12311 | 0.132808 | ||||||||
\(554\) | 10.2462 | 0.435320 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.12311 | −0.386906 | ||||||||
\(557\) | −32.7386 | −1.38718 | −0.693590 | − | 0.720370i | \(-0.743972\pi\) | ||||
−0.693590 | + | 0.720370i | \(0.743972\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2462 | −0.433369 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.3693 | 0.563951 | ||||||||
\(563\) | 31.1231 | 1.31168 | 0.655841 | − | 0.754899i | \(-0.272314\pi\) | ||||
0.655841 | + | 0.754899i | \(0.272314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | −14.2462 | −0.598813 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.12311 | −0.0471245 | ||||||||
\(569\) | −31.1231 | −1.30475 | −0.652374 | − | 0.757897i | \(-0.726227\pi\) | ||||
−0.652374 | + | 0.757897i | \(0.726227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6155 | 0.653490 | 0.326745 | − | 0.945113i | \(-0.394048\pi\) | ||||
0.326745 | + | 0.945113i | \(0.394048\pi\) | |||||||
\(572\) | 2.00000 | 0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.12311 | −0.380791 | ||||||||
\(575\) | −7.12311 | −0.297054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.8769 | −0.952378 | −0.476189 | − | 0.879343i | \(-0.657982\pi\) | ||||
−0.476189 | + | 0.879343i | \(0.657982\pi\) | |||||||
\(578\) | 7.24621 | 0.301403 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.24621 | 0.342405 | ||||||||
\(581\) | 11.1231 | 0.461464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | −0.414158 | ||||||||
\(584\) | 0.246211 | 0.0101883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0000 | −0.413096 | ||||||||
\(587\) | −20.9848 | −0.866137 | −0.433069 | − | 0.901361i | \(-0.642569\pi\) | ||||
−0.433069 | + | 0.901361i | \(0.642569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 4.00000 | 0.164677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.12311 | 0.292758 | ||||||||
\(593\) | 35.1231 | 1.44233 | 0.721167 | − | 0.692762i | \(-0.243606\pi\) | ||||
0.721167 | + | 0.692762i | \(0.243606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.12311 | 0.128035 | ||||||||
\(596\) | −2.00000 | −0.0819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.2462 | 0.582571 | ||||||||
\(599\) | −5.12311 | −0.209324 | −0.104662 | − | 0.994508i | \(-0.533376\pi\) | ||||
−0.104662 | + | 0.994508i | \(0.533376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9848 | 0.774408 | 0.387204 | − | 0.921994i | \(-0.373441\pi\) | ||||
0.387204 | + | 0.921994i | \(0.373441\pi\) | |||||||
\(602\) | −5.12311 | −0.208802 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.8769 | 0.523953 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9848 | −1.33881 | −0.669407 | − | 0.742896i | \(-0.733452\pi\) | ||||
−0.669407 | + | 0.742896i | \(0.733452\pi\) | |||||||
\(608\) | −1.12311 | −0.0455479 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.12311 | −0.126451 | ||||||||
\(611\) | 22.7386 | 0.919907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0000 | 0.969351 | 0.484675 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484675 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(614\) | 34.7386 | 1.40194 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −19.7538 | −0.795258 | −0.397629 | − | 0.917546i | \(-0.630167\pi\) | ||||
−0.397629 | + | 0.917546i | \(0.630167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | −0.562708 | −0.281354 | − | 0.959604i | \(-0.590783\pi\) | ||||
−0.281354 | + | 0.959604i | \(0.590783\pi\) | |||||||
\(620\) | −7.12311 | −0.286071 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.00000 | 0.320771 | ||||||||
\(623\) | 8.24621 | 0.330377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.6155 | 0.704058 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.12311 | 0.204434 | ||||||||
\(629\) | −22.2462 | −0.887015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4924 | −1.13427 | −0.567133 | − | 0.823626i | \(-0.691947\pi\) | ||||
−0.567133 | + | 0.823626i | \(0.691947\pi\) | |||||||
\(632\) | 3.12311 | 0.124230 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.24621 | −0.327499 | ||||||||
\(635\) | −1.75379 | −0.0695970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | −8.24621 | −0.326471 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −30.7386 | −1.21410 | −0.607052 | − | 0.794662i | \(-0.707648\pi\) | ||||
−0.607052 | + | 0.794662i | \(0.707648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.2462 | −1.50828 | −0.754142 | − | 0.656712i | \(-0.771947\pi\) | ||||
−0.754142 | + | 0.656712i | \(0.771947\pi\) | |||||||
\(644\) | 7.12311 | 0.280690 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.50758 | 0.138004 | ||||||||
\(647\) | −18.8769 | −0.742127 | −0.371064 | − | 0.928607i | \(-0.621007\pi\) | ||||
−0.371064 | + | 0.928607i | \(0.621007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.36932 | 0.131953 | ||||||||
\(653\) | −48.7386 | −1.90729 | −0.953645 | − | 0.300934i | \(-0.902702\pi\) | ||||
−0.953645 | + | 0.300934i | \(0.902702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.75379 | 0.224819 | ||||||||
\(656\) | −9.12311 | −0.356197 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.3693 | 0.443222 | ||||||||
\(659\) | −15.5076 | −0.604089 | −0.302045 | − | 0.953294i | \(-0.597669\pi\) | ||||
−0.302045 | + | 0.953294i | \(0.597669\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3693 | −0.831170 | −0.415585 | − | 0.909554i | \(-0.636423\pi\) | ||||
−0.415585 | + | 0.909554i | \(0.636423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.1231 | 0.431660 | ||||||||
\(665\) | −1.12311 | −0.0435522 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −58.7386 | −2.27437 | ||||||||
\(668\) | −14.0000 | −0.541676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.12311 | 0.352456 | ||||||||
\(671\) | 3.12311 | 0.120566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.8617 | −1.53656 | −0.768279 | − | 0.640116i | \(-0.778886\pi\) | ||||
−0.768279 | + | 0.640116i | \(0.778886\pi\) | |||||||
\(674\) | −29.6155 | −1.14075 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 14.0000 | 0.538064 | 0.269032 | − | 0.963131i | \(-0.413296\pi\) | ||||
0.269032 | + | 0.963131i | \(0.413296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.87689 | 0.110405 | ||||||||
\(680\) | 3.12311 | 0.119766 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.12311 | 0.272758 | ||||||||
\(683\) | −27.6155 | −1.05668 | −0.528339 | − | 0.849033i | \(-0.677185\pi\) | ||||
−0.528339 | + | 0.849033i | \(0.677185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.2462 | −0.773568 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.12311 | −0.195317 | ||||||||
\(689\) | −20.0000 | −0.761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | 0.0760836 | 0.0380418 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380418 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(692\) | 4.24621 | 0.161417 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.7386 | −1.16682 | ||||||||
\(695\) | −9.12311 | −0.346059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.4924 | 1.07923 | ||||||||
\(698\) | 5.36932 | 0.203232 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −9.50758 | −0.359096 | −0.179548 | − | 0.983749i | \(-0.557464\pi\) | ||||
−0.179548 | + | 0.983749i | \(0.557464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.6155 | −0.587698 | ||||||||
\(707\) | −11.3693 | −0.427587 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.9848 | 1.61433 | 0.807165 | − | 0.590326i | \(-0.201001\pi\) | ||||
0.807165 | + | 0.590326i | \(0.201001\pi\) | |||||||
\(710\) | −1.12311 | −0.0421494 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.24621 | 0.309040 | ||||||||
\(713\) | 50.7386 | 1.90018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | −14.2462 | −0.532406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.36932 | −0.275020 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2462 | −0.530557 | ||||||||
\(722\) | 17.7386 | 0.660164 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.36932 | −0.199549 | ||||||||
\(725\) | 8.24621 | 0.306257 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.2462 | −1.71518 | −0.857589 | − | 0.514336i | \(-0.828038\pi\) | ||||
−0.857589 | + | 0.514336i | \(0.828038\pi\) | |||||||
\(728\) | 2.00000 | 0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.246211 | 0.00911269 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.7386 | −0.618256 | −0.309128 | − | 0.951021i | \(-0.600037\pi\) | ||||
−0.309128 | + | 0.951021i | \(0.600037\pi\) | |||||||
\(734\) | 28.4924 | 1.05167 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.12311 | 0.262561 | ||||||||
\(737\) | −9.12311 | −0.336054 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8769 | 0.915111 | 0.457556 | − | 0.889181i | \(-0.348725\pi\) | ||||
0.457556 | + | 0.889181i | \(0.348725\pi\) | |||||||
\(740\) | 7.12311 | 0.261851 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.0000 | −0.367112 | ||||||||
\(743\) | −2.73863 | −0.100471 | −0.0502354 | − | 0.998737i | \(-0.515997\pi\) | ||||
−0.0502354 | + | 0.998737i | \(0.515997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | −0.0732743 | ||||||||
\(746\) | 22.2462 | 0.814492 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.12311 | −0.114192 | ||||||||
\(749\) | 18.2462 | 0.666702 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.2462 | −1.39562 | −0.697812 | − | 0.716281i | \(-0.745843\pi\) | ||||
−0.697812 | + | 0.716281i | \(0.745843\pi\) | |||||||
\(752\) | 11.3693 | 0.414596 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.4924 | −0.600619 | ||||||||
\(755\) | 12.8769 | 0.468638 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.8617 | −1.81226 | −0.906128 | − | 0.423004i | \(-0.860976\pi\) | ||||
−0.906128 | + | 0.423004i | \(0.860976\pi\) | |||||||
\(758\) | −16.0000 | −0.581146 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.12311 | −0.0407393 | ||||||||
\(761\) | 34.1080 | 1.23641 | 0.618206 | − | 0.786016i | \(-0.287860\pi\) | ||||
0.618206 | + | 0.786016i | \(0.287860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0000 | −0.651644 | ||||||||
\(764\) | −6.87689 | −0.248797 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.61553 | 0.202897 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0000 | −0.649097 | −0.324548 | − | 0.945869i | \(-0.605212\pi\) | ||||
−0.324548 | + | 0.945869i | \(0.605212\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.87689 | 0.103542 | ||||||||
\(773\) | −52.2462 | −1.87917 | −0.939583 | − | 0.342322i | \(-0.888787\pi\) | ||||
−0.939583 | + | 0.342322i | \(0.888787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.12311 | −0.255870 | ||||||||
\(776\) | 2.87689 | 0.103274 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.3693 | 0.407610 | ||||||||
\(779\) | −10.2462 | −0.367109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.12311 | 0.0401879 | ||||||||
\(782\) | −22.2462 | −0.795523 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 5.12311 | 0.182851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.24621 | −0.222653 | −0.111327 | − | 0.993784i | \(-0.535510\pi\) | ||||
−0.111327 | + | 0.993784i | \(0.535510\pi\) | |||||||
\(788\) | −22.4924 | −0.801259 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.12311 | 0.111115 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.24621 | 0.221809 | ||||||||
\(794\) | 27.3693 | 0.971301 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.87689 | −0.172857 | ||||||||
\(797\) | 7.75379 | 0.274653 | 0.137327 | − | 0.990526i | \(-0.456149\pi\) | ||||
0.137327 | + | 0.990526i | \(0.456149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.5076 | −1.25617 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.0000 | −1.12996 | ||||||||
\(803\) | −0.246211 | −0.00868861 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.12311 | 0.251056 | ||||||||
\(806\) | 14.2462 | 0.501801 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.3693 | −0.399971 | ||||||||
\(809\) | 7.12311 | 0.250435 | 0.125218 | − | 0.992129i | \(-0.460037\pi\) | ||||
0.125218 | + | 0.992129i | \(0.460037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.8617 | 1.39973 | 0.699867 | − | 0.714273i | \(-0.253242\pi\) | ||||
0.699867 | + | 0.714273i | \(0.253242\pi\) | |||||||
\(812\) | −8.24621 | −0.289385 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.12311 | −0.249665 | ||||||||
\(815\) | 3.36932 | 0.118022 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.75379 | −0.201300 | ||||||||
\(818\) | −16.2462 | −0.568035 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.12311 | −0.318593 | ||||||||
\(821\) | 42.9848 | 1.50018 | 0.750091 | − | 0.661335i | \(-0.230010\pi\) | ||||
0.750091 | + | 0.661335i | \(0.230010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.7538 | 0.758289 | 0.379145 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379145 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(824\) | −14.2462 | −0.496290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.00000 | −0.139178 | ||||||||
\(827\) | −29.7538 | −1.03464 | −0.517320 | − | 0.855792i | \(-0.673070\pi\) | ||||
−0.517320 | + | 0.855792i | \(0.673070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.3542 | 1.47102 | 0.735510 | − | 0.677513i | \(-0.236942\pi\) | ||||
0.735510 | + | 0.677513i | \(0.236942\pi\) | |||||||
\(830\) | 11.1231 | 0.386089 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −3.12311 | −0.108209 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | −0.484490 | ||||||||
\(836\) | 1.12311 | 0.0388434 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.492423 | −0.0170105 | ||||||||
\(839\) | −5.75379 | −0.198643 | −0.0993214 | − | 0.995055i | \(-0.531667\pi\) | ||||
−0.0993214 | + | 0.995055i | \(0.531667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 8.24621 | 0.284183 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.87689 | 0.305555 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −10.0000 | −0.343401 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.12311 | 0.107122 | ||||||||
\(851\) | −50.7386 | −1.73930 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.24621 | −0.145388 | −0.0726938 | − | 0.997354i | \(-0.523160\pi\) | ||||
−0.0726938 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(854\) | 3.12311 | 0.106870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.2462 | 0.623643 | ||||||||
\(857\) | 10.6307 | 0.363137 | 0.181569 | − | 0.983378i | \(-0.441883\pi\) | ||||
0.181569 | + | 0.983378i | \(0.441883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4924 | 0.494475 | 0.247238 | − | 0.968955i | \(-0.420477\pi\) | ||||
0.247238 | + | 0.968955i | \(0.420477\pi\) | |||||||
\(860\) | −5.12311 | −0.174696 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.6155 | −0.599987 | ||||||||
\(863\) | 42.3542 | 1.44175 | 0.720876 | − | 0.693064i | \(-0.243740\pi\) | ||||
0.720876 | + | 0.693064i | \(0.243740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.24621 | 0.144376 | ||||||||
\(866\) | 1.12311 | 0.0381647 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.12311 | 0.241774 | ||||||||
\(869\) | −3.12311 | −0.105944 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.2462 | −0.618249 | ||||||||
\(872\) | −18.0000 | −0.609557 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.00000 | 0.270604 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.7386 | −0.767829 | −0.383915 | − | 0.923369i | \(-0.625424\pi\) | ||||
−0.383915 | + | 0.923369i | \(0.625424\pi\) | |||||||
\(878\) | 22.7386 | 0.767392 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 30.4924 | 1.02732 | 0.513658 | − | 0.857995i | \(-0.328290\pi\) | ||||
0.513658 | + | 0.857995i | \(0.328290\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.6155 | −1.80431 | −0.902153 | − | 0.431416i | \(-0.858014\pi\) | ||||
−0.902153 | + | 0.431416i | \(0.858014\pi\) | |||||||
\(884\) | −6.24621 | −0.210083 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.6155 | 0.927762 | ||||||||
\(887\) | −38.9848 | −1.30898 | −0.654491 | − | 0.756069i | \(-0.727117\pi\) | ||||
−0.654491 | + | 0.756069i | \(0.727117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.75379 | 0.0588202 | ||||||||
\(890\) | 8.24621 | 0.276414 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.49242 | 0.150417 | ||||||||
\(893\) | 12.7689 | 0.427296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2462 | −0.476198 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.7386 | 1.02576 | ||||||||
\(899\) | −58.7386 | −1.95904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2311 | 1.04046 | ||||||||
\(902\) | 9.12311 | 0.303766 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | −5.36932 | −0.178482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.86174 | 0.261045 | 0.130522 | − | 0.991445i | \(-0.458335\pi\) | ||||
0.130522 | + | 0.991445i | \(0.458335\pi\) | |||||||
\(908\) | −21.3693 | −0.709166 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.00000 | 0.0662994 | ||||||||
\(911\) | −30.8769 | −1.02300 | −0.511499 | − | 0.859284i | \(-0.670909\pi\) | ||||
−0.511499 | + | 0.859284i | \(0.670909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1231 | −0.368121 | ||||||||
\(914\) | −11.3693 | −0.376064 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.1231 | 0.367518 | ||||||||
\(917\) | −5.75379 | −0.190007 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.6155 | 1.83459 | 0.917293 | − | 0.398212i | \(-0.130369\pi\) | ||||
0.917293 | + | 0.398212i | \(0.130369\pi\) | |||||||
\(920\) | 7.12311 | 0.234842 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.1231 | −0.432186 | ||||||||
\(923\) | 2.24621 | 0.0739349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.12311 | 0.234206 | ||||||||
\(926\) | −22.7386 | −0.747238 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.24621 | −0.270695 | ||||||||
\(929\) | 52.7386 | 1.73030 | 0.865149 | − | 0.501515i | \(-0.167224\pi\) | ||||
0.865149 | + | 0.501515i | \(0.167224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12311 | 0.0368083 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.4924 | −0.408765 | ||||||||
\(935\) | −3.12311 | −0.102136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2311 | 0.824263 | 0.412131 | − | 0.911124i | \(-0.364784\pi\) | ||||
0.412131 | + | 0.911124i | \(0.364784\pi\) | |||||||
\(938\) | −9.12311 | −0.297880 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.3693 | 0.370826 | ||||||||
\(941\) | −32.3542 | −1.05472 | −0.527358 | − | 0.849643i | \(-0.676817\pi\) | ||||
−0.527358 | + | 0.849643i | \(0.676817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.9848 | 2.11620 | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.12311 | 0.166567 | ||||||||
\(947\) | −9.86174 | −0.320463 | −0.160232 | − | 0.987079i | \(-0.551224\pi\) | ||||
−0.160232 | + | 0.987079i | \(0.551224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.492423 | −0.0159847 | ||||||||
\(950\) | −1.12311 | −0.0364384 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.12311 | −0.101220 | ||||||||
\(953\) | 18.9848 | 0.614979 | 0.307490 | − | 0.951551i | \(-0.400511\pi\) | ||||
0.307490 | + | 0.951551i | \(0.400511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.87689 | −0.222531 | ||||||||
\(956\) | 7.36932 | 0.238341 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.4924 | −0.532846 | ||||||||
\(959\) | 20.2462 | 0.653784 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7386 | 0.636730 | ||||||||
\(962\) | −14.2462 | −0.459316 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.4924 | 0.724432 | ||||||||
\(965\) | 2.87689 | 0.0926105 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.4924 | −1.68804 | −0.844021 | − | 0.536310i | \(-0.819818\pi\) | ||||
−0.844021 | + | 0.536310i | \(0.819818\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.87689 | 0.0923715 | ||||||||
\(971\) | −4.00000 | −0.128366 | −0.0641831 | − | 0.997938i | \(-0.520444\pi\) | ||||
−0.0641831 | + | 0.997938i | \(0.520444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.12311 | 0.292473 | ||||||||
\(974\) | −4.49242 | −0.143947 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.12311 | 0.0999682 | ||||||||
\(977\) | 45.2311 | 1.44707 | 0.723535 | − | 0.690288i | \(-0.242516\pi\) | ||||
0.723535 | + | 0.690288i | \(0.242516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.24621 | −0.263550 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.24621 | 0.199325 | ||||||||
\(983\) | −19.8617 | −0.633491 | −0.316746 | − | 0.948511i | \(-0.602590\pi\) | ||||
−0.316746 | + | 0.948511i | \(0.602590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.4924 | −0.716668 | ||||||||
\(986\) | 25.7538 | 0.820168 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.24621 | 0.0714615 | ||||||||
\(989\) | 36.4924 | 1.16039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.4773 | −1.69876 | −0.849381 | − | 0.527781i | \(-0.823024\pi\) | ||||
−0.849381 | + | 0.527781i | \(0.823024\pi\) | |||||||
\(992\) | 7.12311 | 0.226159 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.12311 | 0.0356227 | ||||||||
\(995\) | −4.87689 | −0.154608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.7386 | −1.54357 | −0.771784 | − | 0.635885i | \(-0.780635\pi\) | ||||
−0.771784 | + | 0.635885i | \(0.780635\pi\) | |||||||
\(998\) | 18.7386 | 0.593161 | ||||||||
\(999\) | 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 | 6930.2.a.bs.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 6930.2.a.bx.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6930.2.a.bs.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6930.2.a.bx.1.2 | yes | 2 | 3.2 | odd | 2 |