Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5472,2,Mod(1,5472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5472, 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("5472.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5472.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: | \(43.6941399860\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.69353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5472.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.64453 | −1.18267 | −0.591335 | − | 0.806426i | \(-0.701399\pi\) | ||||
−0.591335 | + | 0.806426i | \(0.701399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.180969 | 0.0683997 | 0.0341998 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341998 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.644529 | −0.194333 | −0.0971664 | − | 0.995268i | \(-0.530978\pi\) | ||||
−0.0971664 | + | 0.995268i | \(0.530978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.94860 | −1.09515 | −0.547573 | − | 0.836758i | \(-0.684448\pi\) | ||||
−0.547573 | + | 0.836758i | \(0.684448\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.56802 | −1.35044 | −0.675221 | − | 0.737615i | \(-0.735952\pi\) | ||||
−0.675221 | + | 0.737615i | \(0.735952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.46356 | −0.930717 | −0.465358 | − | 0.885122i | \(-0.654075\pi\) | ||||
−0.465358 | + | 0.885122i | \(0.654075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.99353 | 0.398707 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.94860 | 0.733237 | 0.366619 | − | 0.930371i | \(-0.380515\pi\) | ||||
0.366619 | + | 0.930371i | \(0.380515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.48504 | 0.985143 | 0.492571 | − | 0.870272i | \(-0.336057\pi\) | ||||
0.492571 | + | 0.870272i | \(0.336057\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.478577 | −0.0808942 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.48504 | 1.23053 | 0.615267 | − | 0.788319i | \(-0.289048\pi\) | ||||
0.615267 | + | 0.788319i | \(0.289048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.41216 | −1.31376 | −0.656880 | − | 0.753995i | \(-0.728124\pi\) | ||||
−0.656880 | + | 0.753995i | \(0.728124\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.76763 | 0.879556 | 0.439778 | − | 0.898107i | \(-0.355057\pi\) | ||||
0.439778 | + | 0.898107i | \(0.355057\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2527 | −1.64137 | −0.820686 | − | 0.571380i | \(-0.806408\pi\) | ||||
−0.820686 | + | 0.571380i | \(0.806408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96725 | −0.995321 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.58667 | −1.04211 | −0.521054 | − | 0.853523i | \(-0.674461\pi\) | ||||
−0.521054 | + | 0.853523i | \(0.674461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70448 | 0.229831 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.8506 | 1.54282 | 0.771409 | − | 0.636340i | \(-0.219552\pi\) | ||||
0.771409 | + | 0.636340i | \(0.219552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.47858 | −0.317349 | −0.158675 | − | 0.987331i | \(-0.550722\pi\) | ||||
−0.158675 | + | 0.987331i | \(0.550722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4422 | 1.29519 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.97372 | 1.09631 | 0.548157 | − | 0.836375i | \(-0.315330\pi\) | ||||
0.548157 | + | 0.836375i | \(0.315330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.63806 | −0.906471 | −0.453236 | − | 0.891391i | \(-0.649730\pi\) | ||||
−0.453236 | + | 0.891391i | \(0.649730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6911 | 1.25130 | 0.625651 | − | 0.780103i | \(-0.284834\pi\) | ||||
0.625651 | + | 0.780103i | \(0.284834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.116639 | −0.0132923 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6081 | −1.19351 | −0.596755 | − | 0.802424i | \(-0.703544\pi\) | ||||
−0.596755 | + | 0.802424i | \(0.703544\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.65100 | 0.620277 | 0.310139 | − | 0.950691i | \(-0.399625\pi\) | ||||
0.310139 | + | 0.950691i | \(0.399625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7248 | 1.59713 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.1733 | 1.82037 | 0.910185 | − | 0.414202i | \(-0.135939\pi\) | ||||
0.910185 | + | 0.414202i | \(0.135939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.714573 | −0.0749076 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.64453 | 0.271323 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.28906 | 0.333953 | 0.166977 | − | 0.985961i | \(-0.446600\pi\) | ||||
0.166977 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4122 | −1.42007 | −0.710036 | − | 0.704165i | \(-0.751322\pi\) | ||||
−0.710036 | + | 0.704165i | \(0.751322\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.69759 | 0.937501 | 0.468751 | − | 0.883330i | \(-0.344704\pi\) | ||||
0.468751 | + | 0.883330i | \(0.344704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.4839 | 1.86622 | 0.933108 | − | 0.359596i | \(-0.117085\pi\) | ||||
0.933108 | + | 0.359596i | \(0.117085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.28906 | 0.685697 | 0.342848 | − | 0.939391i | \(-0.388608\pi\) | ||||
0.342848 | + | 0.939391i | \(0.388608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.8040 | 1.10073 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00764 | −0.0923699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5846 | −0.962235 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.95069 | 0.711131 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.595216 | 0.0528169 | 0.0264084 | − | 0.999651i | \(-0.491593\pi\) | ||||
0.0264084 | + | 0.999651i | \(0.491593\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.7806 | −1.37875 | −0.689377 | − | 0.724403i | \(-0.742116\pi\) | ||||
−0.689377 | + | 0.724403i | \(0.742116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.180969 | −0.0156920 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9802 | 1.36528 | 0.682640 | − | 0.730755i | \(-0.260832\pi\) | ||||
0.682640 | + | 0.730755i | \(0.260832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.47858 | −0.379868 | −0.189934 | − | 0.981797i | \(-0.560827\pi\) | ||||
−0.189934 | + | 0.981797i | \(0.560827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.54499 | 0.212823 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4422 | −0.867177 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3758 | −0.850017 | −0.425009 | − | 0.905189i | \(-0.639729\pi\) | ||||
−0.425009 | + | 0.905189i | \(0.639729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.6584 | 1.35564 | 0.677820 | − | 0.735228i | \(-0.262925\pi\) | ||||
0.677820 | + | 0.735228i | \(0.262925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5054 | −1.16510 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0203 | −0.879517 | −0.439758 | − | 0.898116i | \(-0.644936\pi\) | ||||
−0.439758 | + | 0.898116i | \(0.644936\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.807764 | −0.0636607 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.80402 | 0.611258 | 0.305629 | − | 0.952151i | \(-0.401133\pi\) | ||||
0.305629 | + | 0.952151i | \(0.401133\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.2462 | −0.792876 | −0.396438 | − | 0.918062i | \(-0.629754\pi\) | ||||
−0.396438 | + | 0.918062i | \(0.629754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.59147 | 0.199344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.80402 | 0.137157 | 0.0685784 | − | 0.997646i | \(-0.478154\pi\) | ||||
0.0685784 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.360767 | 0.0272714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.75379 | 0.131084 | 0.0655422 | − | 0.997850i | \(-0.479122\pi\) | ||||
0.0655422 | + | 0.997850i | \(0.479122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.52789 | 0.485214 | 0.242607 | − | 0.970125i | \(-0.421997\pi\) | ||||
0.242607 | + | 0.970125i | \(0.421997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.7944 | −1.45531 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.58875 | 0.262435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.45709 | −0.539576 | −0.269788 | − | 0.962920i | \(-0.586954\pi\) | ||||
−0.269788 | + | 0.962920i | \(0.586954\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0203 | 1.36911 | 0.684556 | − | 0.728960i | \(-0.259996\pi\) | ||||
0.684556 | + | 0.728960i | \(0.259996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.153020 | −0.0109022 | −0.00545112 | − | 0.999985i | \(-0.501735\pi\) | ||||
−0.00545112 | + | 0.999985i | \(0.501735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3672 | −1.51468 | −0.757341 | − | 0.653019i | \(-0.773502\pi\) | ||||
−0.757341 | + | 0.653019i | \(0.773502\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.714573 | 0.0501532 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.2462 | 1.55374 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.644529 | 0.0445830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.82070 | −0.469556 | −0.234778 | − | 0.972049i | \(-0.575436\pi\) | ||||
−0.234778 | + | 0.972049i | \(0.575436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.2527 | −1.04022 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.992620 | 0.0673835 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.9859 | 1.47893 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.42510 | 0.564186 | 0.282093 | − | 0.959387i | \(-0.408971\pi\) | ||||
0.282093 | + | 0.959387i | \(0.408971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3859 | 1.55218 | 0.776088 | − | 0.630625i | \(-0.217201\pi\) | ||||
0.776088 | + | 0.630625i | \(0.217201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.37567 | −0.223070 | −0.111535 | − | 0.993760i | \(-0.535577\pi\) | ||||
−0.111535 | + | 0.993760i | \(0.535577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8308 | 1.03711 | 0.518555 | − | 0.855044i | \(-0.326470\pi\) | ||||
0.518555 | + | 0.855044i | \(0.326470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.7580 | 1.94120 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.39715 | 0.155059 | 0.0775293 | − | 0.996990i | \(-0.475297\pi\) | ||||
0.0775293 | + | 0.996990i | \(0.475297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.44208 | 0.350555 | 0.175278 | − | 0.984519i | \(-0.443918\pi\) | ||||
0.175278 | + | 0.984519i | \(0.443918\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.4251 | 1.17714 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.94860 | 0.251244 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8405 | 0.810486 | 0.405243 | − | 0.914209i | \(-0.367187\pi\) | ||||
0.405243 | + | 0.914209i | \(0.367187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.87689 | 0.180869 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1863 | 1.19681 | 0.598403 | − | 0.801195i | \(-0.295802\pi\) | ||||
0.598403 | + | 0.801195i | \(0.295802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.35456 | 0.0841681 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.2098 | 1.24619 | 0.623096 | − | 0.782146i | \(-0.285875\pi\) | ||||
0.623096 | + | 0.782146i | \(0.285875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0632 | 1.23247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.4422 | −1.00250 | −0.501249 | − | 0.865303i | \(-0.667126\pi\) | ||||
−0.501249 | + | 0.865303i | \(0.667126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.02886 | −0.487719 | −0.243859 | − | 0.969811i | \(-0.578414\pi\) | ||||
−0.243859 | + | 0.969811i | \(0.578414\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.28489 | −0.0774818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.68738 | 0.582058 | 0.291029 | − | 0.956714i | \(-0.406002\pi\) | ||||
0.291029 | + | 0.956714i | \(0.406002\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.15302 | 0.486368 | 0.243184 | − | 0.969980i | \(-0.421808\pi\) | ||||
0.243184 | + | 0.969980i | \(0.421808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.9742 | −1.66289 | −0.831447 | − | 0.555604i | \(-0.812487\pi\) | ||||
−0.831447 | + | 0.555604i | \(0.812487\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.52234 | −0.0898607 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0028 | 0.823696 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.5438 | 0.732818 | 0.366409 | − | 0.930454i | \(-0.380587\pi\) | ||||
0.366409 | + | 0.930454i | \(0.380587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.3393 | −1.82464 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.6248 | 1.01927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.04376 | 0.0601614 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.55467 | 0.375319 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9572 | 0.739504 | 0.369752 | − | 0.929131i | \(-0.379443\pi\) | ||||
0.369752 | + | 0.929131i | \(0.379443\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.8467 | 1.80586 | 0.902931 | − | 0.429786i | \(-0.141411\pi\) | ||||
0.902931 | + | 0.429786i | \(0.141411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2628 | 0.919226 | 0.459613 | − | 0.888119i | \(-0.347988\pi\) | ||||
0.459613 | + | 0.888119i | \(0.347988\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.88866 | 0.386905 | 0.193453 | − | 0.981110i | \(-0.438031\pi\) | ||||
0.193453 | + | 0.981110i | \(0.438031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.54499 | −0.142492 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.56802 | 0.309813 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.87167 | −0.436642 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.03638 | −0.112269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6976 | −1.41247 | −0.706234 | − | 0.707979i | \(-0.749607\pi\) | ||||
−0.706234 | + | 0.707979i | \(0.749607\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.7313 | −1.29658 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.78382 | 0.424012 | 0.212006 | − | 0.977268i | \(-0.432000\pi\) | ||||
0.212006 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.53527 | −0.191446 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.52763 | −0.136479 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.3758 | −1.73802 | −0.869012 | − | 0.494792i | \(-0.835244\pi\) | ||||
−0.869012 | + | 0.494792i | \(0.835244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0567 | 1.34125 | 0.670627 | − | 0.741795i | \(-0.266025\pi\) | ||||
0.670627 | + | 0.741795i | \(0.266025\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.70731 | 0.144096 | 0.0720478 | − | 0.997401i | \(-0.477047\pi\) | ||||
0.0720478 | + | 0.997401i | \(0.477047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.1991 | 1.07206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.6862 | −1.46122 | −0.730611 | − | 0.682794i | \(-0.760765\pi\) | ||||
−0.730611 | + | 0.682794i | \(0.760765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2730 | −1.47988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.3020 | −0.798757 | −0.399379 | − | 0.916786i | \(-0.630774\pi\) | ||||
−0.399379 | + | 0.916786i | \(0.630774\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.37295 | −0.0712799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.2506 | 1.41098 | 0.705491 | − | 0.708719i | \(-0.250726\pi\) | ||||
0.705491 | + | 0.708719i | \(0.250726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.5915 | −0.803001 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0968 | −1.54597 | −0.772985 | − | 0.634424i | \(-0.781237\pi\) | ||||
−0.772985 | + | 0.634424i | \(0.781237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.8146 | 1.93224 | 0.966118 | − | 0.258100i | \(-0.0830966\pi\) | ||||
0.966118 | + | 0.258100i | \(0.0830966\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.308457 | 0.0157204 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.44128 | −0.123778 | −0.0618890 | − | 0.998083i | \(-0.519712\pi\) | ||||
−0.0618890 | + | 0.998083i | \(0.519712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.8532 | 1.25688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.0536 | 1.41153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4260 | 0.824398 | 0.412199 | − | 0.911094i | \(-0.364761\pi\) | ||||
0.412199 | + | 0.911094i | \(0.364761\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0932 | 1.50278 | 0.751391 | − | 0.659857i | \(-0.229383\pi\) | ||||
0.751391 | + | 0.659857i | \(0.229383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.6583 | −1.07887 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.82433 | −0.239133 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.4454 | −1.95045 | −0.975225 | − | 0.221216i | \(-0.928998\pi\) | ||||
−0.975225 | + | 0.221216i | \(0.928998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.14459 | 0.105528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9442 | −0.733583 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3522 | 0.652298 | 0.326149 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326149 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8587 | 1.06533 | 0.532665 | − | 0.846326i | \(-0.321191\pi\) | ||||
0.532665 | + | 0.846326i | \(0.321191\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1000 | −0.538431 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.448544 | −0.0217066 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3490 | −0.691167 | −0.345584 | − | 0.938388i | \(-0.612319\pi\) | ||||
−0.345584 | + | 0.938388i | \(0.612319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.2536 | 0.925269 | 0.462634 | − | 0.886549i | \(-0.346904\pi\) | ||||
0.462634 | + | 0.886549i | \(0.346904\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.46356 | 0.213521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.3020 | 0.921234 | 0.460617 | − | 0.887599i | \(-0.347628\pi\) | ||||
0.460617 | + | 0.887599i | \(0.347628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.61866 | 0.219439 | 0.109720 | − | 0.993963i | \(-0.465005\pi\) | ||||
0.109720 | + | 0.993963i | \(0.465005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −45.4154 | −2.15290 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.54082 | −0.403066 | −0.201533 | − | 0.979482i | \(-0.564592\pi\) | ||||
−0.201533 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.42188 | 0.255307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.88971 | 0.0885909 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7340 | 1.20378 | 0.601892 | − | 0.798577i | \(-0.294414\pi\) | ||||
0.601892 | + | 0.798577i | \(0.294414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3629 | 0.575795 | 0.287898 | − | 0.957661i | \(-0.407044\pi\) | ||||
0.287898 | + | 0.957661i | \(0.407044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.1069 | 0.980922 | 0.490461 | − | 0.871463i | \(-0.336828\pi\) | ||||
0.490461 | + | 0.871463i | \(0.336828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2729 | 1.16949 | 0.584745 | − | 0.811218i | \(-0.301195\pi\) | ||||
0.584745 | + | 0.811218i | \(0.301195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.62396 | 0.0749875 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.71741 | −0.170927 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.99353 | −0.0914696 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.27613 | 0.149690 | 0.0748450 | − | 0.997195i | \(-0.476154\pi\) | ||||
0.0748450 | + | 0.997195i | \(0.476154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.5555 | −1.34761 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.69801 | −0.394956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0202 | 0.635316 | 0.317658 | − | 0.948205i | \(-0.397104\pi\) | ||||
0.317658 | + | 0.948205i | \(0.397104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.6487 | −0.976990 | −0.488495 | − | 0.872567i | \(-0.662454\pi\) | ||||
−0.488495 | + | 0.872567i | \(0.662454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.9859 | −0.990195 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.38225 | −0.0620023 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.4187 | 1.54079 | 0.770397 | − | 0.637564i | \(-0.220058\pi\) | ||||
0.770397 | + | 0.637564i | \(0.220058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.3178 | −0.638399 | −0.319200 | − | 0.947687i | \(-0.603414\pi\) | ||||
−0.319200 | + | 0.947687i | \(0.603414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.651113 | 0.0289741 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3393 | −0.768550 | −0.384275 | − | 0.923219i | \(-0.625549\pi\) | ||||
−0.384275 | + | 0.923219i | \(0.625549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.93476 | 0.0855886 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.1134 | 1.67948 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.25268 | 0.318972 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.5856 | −1.33998 | −0.669990 | − | 0.742370i | \(-0.733702\pi\) | ||||
−0.669990 | + | 0.742370i | \(0.733702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.7275 | −0.993804 | −0.496902 | − | 0.867807i | \(-0.665529\pi\) | ||||
−0.496902 | + | 0.867807i | \(0.665529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.5408 | −1.33038 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.07663 | −0.133766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.2163 | 1.43876 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.6456 | −1.10875 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.49060 | 0.193424 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.9913 | −1.37541 | −0.687707 | − | 0.725988i | \(-0.741383\pi\) | ||||
−0.687707 | + | 0.725988i | \(0.741383\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.5257 | −2.20712 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1005 | 0.688406 | 0.344203 | − | 0.938895i | \(-0.388149\pi\) | ||||
0.344203 | + | 0.938895i | \(0.388149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.94860 | −0.168216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.91974 | −0.0816357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3126 | 0.606445 | 0.303223 | − | 0.952920i | \(-0.401937\pi\) | ||||
0.303223 | + | 0.952920i | \(0.401937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.7741 | −0.963242 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.9143 | 0.586418 | 0.293209 | − | 0.956048i | \(-0.405277\pi\) | ||||
0.293209 | + | 0.956048i | \(0.405277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2761 | −0.810953 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.71415 | 0.323394 | 0.161697 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161697 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.42188 | 0.394294 | 0.197147 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197147 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.89826 | −0.371083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.3851 | −0.432337 | −0.216168 | − | 0.976356i | \(-0.569356\pi\) | ||||
−0.216168 | + | 0.976356i | \(0.569356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.02265 | 0.0424268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.88983 | 0.202516 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.8866 | −1.60502 | −0.802510 | − | 0.596638i | \(-0.796503\pi\) | ||||
−0.802510 | + | 0.596638i | \(0.796503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.48504 | −0.226007 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.1304 | −0.785590 | −0.392795 | − | 0.919626i | \(-0.628492\pi\) | ||||
−0.392795 | + | 0.919626i | \(0.628492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.66472 | 0.109243 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.5353 | −1.12506 | −0.562530 | − | 0.826777i | \(-0.690172\pi\) | ||||
−0.562530 | + | 0.826777i | \(0.690172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.73669 | −0.234004 | −0.117002 | − | 0.993132i | \(-0.537328\pi\) | ||||
−0.117002 | + | 0.993132i | \(0.537328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.9912 | 1.13801 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.3191 | −1.02767 | −0.513835 | − | 0.857889i | \(-0.671776\pi\) | ||||
−0.513835 | + | 0.857889i | \(0.671776\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.4324 | 1.79754 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.55872 | 0.0629560 | 0.0314780 | − | 0.999504i | \(-0.489979\pi\) | ||||
0.0314780 | + | 0.999504i | \(0.489979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.6317 | 0.468275 | 0.234138 | − | 0.972203i | \(-0.424773\pi\) | ||||
0.234138 | + | 0.972203i | \(0.424773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.6754 | −0.630046 | −0.315023 | − | 0.949084i | \(-0.602012\pi\) | ||||
−0.315023 | + | 0.949084i | \(0.602012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.10783 | 0.124513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9935 | −1.23974 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.6769 | −1.66177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.63171 | 0.383432 | 0.191716 | − | 0.981450i | \(-0.438595\pi\) | ||||
0.191716 | + | 0.981450i | \(0.438595\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.57407 | −0.0624649 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.5109 | 1.09002 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5150 | 0.652302 | 0.326151 | − | 0.945318i | \(-0.394248\pi\) | ||||
0.326151 | + | 0.945318i | \(0.394248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3887 | 0.725180 | 0.362590 | − | 0.931949i | \(-0.381893\pi\) | ||||
0.362590 | + | 0.931949i | \(0.381893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3414 | 0.681760 | 0.340880 | − | 0.940107i | \(-0.389275\pi\) | ||||
0.340880 | + | 0.940107i | \(0.389275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.63806 | −0.299820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.46886 | 0.135747 | 0.0678734 | − | 0.997694i | \(-0.478379\pi\) | ||||
0.0678734 | + | 0.997694i | \(0.478379\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.7322 | 1.63061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.6677 | 1.42837 | 0.714185 | − | 0.699957i | \(-0.246798\pi\) | ||||
0.714185 | + | 0.699957i | \(0.246798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.6960 | −1.89405 | −0.947027 | − | 0.321153i | \(-0.895930\pi\) | ||||
−0.947027 | + | 0.321153i | \(0.895930\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.478577 | 0.0185584 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.6248 | −0.682436 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.59751 | 0.0616714 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.2535 | 0.934903 | 0.467451 | − | 0.884019i | \(-0.345172\pi\) | ||||
0.467451 | + | 0.884019i | \(0.345172\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.7471 | −0.643642 | −0.321821 | − | 0.946801i | \(-0.604295\pi\) | ||||
−0.321821 | + | 0.946801i | \(0.604295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.595216 | 0.0228423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.0299 | 0.651632 | 0.325816 | − | 0.945433i | \(-0.394361\pi\) | ||||
0.325816 | + | 0.945433i | \(0.394361\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.2601 | −1.61467 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.9567 | 1.14126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8811 | −1.47911 | −0.739554 | − | 0.673097i | \(-0.764964\pi\) | ||||
−0.739554 | + | 0.673097i | \(0.764964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8437 | 0.449258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.8391 | 1.77416 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.17888 | 0.308912 | 0.154456 | − | 0.988000i | \(-0.450637\pi\) | ||||
0.154456 | + | 0.988000i | \(0.450637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.48504 | −0.282304 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0445565 | −0.00167572 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.3522 | 0.877011 | 0.438505 | − | 0.898729i | \(-0.355508\pi\) | ||||
0.438505 | + | 0.898729i | \(0.355508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.4828 | −0.916889 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.73030 | −0.251699 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1810 | −0.901798 | −0.450899 | − | 0.892575i | \(-0.648897\pi\) | ||||
−0.450899 | + | 0.892575i | \(0.648897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.60815 | −0.0971325 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.87167 | 0.292347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.3503 | −0.383870 | −0.191935 | − | 0.981408i | \(-0.561476\pi\) | ||||
−0.191935 | + | 0.981408i | \(0.561476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.1143 | −1.18779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.81128 | −0.0669011 | −0.0334505 | − | 0.999440i | \(-0.510650\pi\) | ||||
−0.0334505 | + | 0.999440i | \(0.510650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.78382 | −0.213050 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0342 | 0.626612 | 0.313306 | − | 0.949652i | \(-0.398564\pi\) | ||||
0.313306 | + | 0.949652i | \(0.398564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.992620 | 0.0364157 | 0.0182079 | − | 0.999834i | \(-0.494204\pi\) | ||||
0.0182079 | + | 0.999834i | \(0.494204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.4391 | 1.00529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.75496 | 0.0641248 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.1263 | −1.46423 | −0.732115 | − | 0.681181i | \(-0.761467\pi\) | ||||
−0.732115 | + | 0.681181i | \(0.761467\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.0536 | −1.60327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.8810 | −1.52219 | −0.761096 | − | 0.648640i | \(-0.775338\pi\) | ||||
−0.761096 | + | 0.648640i | \(0.775338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.8142 | −0.863265 | −0.431633 | − | 0.902050i | \(-0.642062\pi\) | ||||
−0.431633 | + | 0.902050i | \(0.642062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.52597 | 0.127649 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.7934 | −1.68961 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.5828 | −1.71588 | −0.857939 | − | 0.513751i | \(-0.828256\pi\) | ||||
−0.857939 | + | 0.513751i | \(0.828256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.4240 | −1.20218 | −0.601090 | − | 0.799182i | \(-0.705267\pi\) | ||||
−0.601090 | + | 0.799182i | \(0.705267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9346 | 0.392783 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.41216 | 0.301397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.92295 | 0.176157 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.1435 | 1.04018 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.315342 | −0.0112407 | −0.00562036 | − | 0.999984i | \(-0.501789\pi\) | ||||
−0.00562036 | + | 0.999984i | \(0.501789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.31909 | 0.0469015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.78692 | 0.347544 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.0942 | −0.392978 | −0.196489 | − | 0.980506i | \(-0.562954\pi\) | ||||
−0.196489 | + | 0.980506i | \(0.562954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.6551 | 2.21658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.89074 | −0.243169 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.13616 | 0.0752896 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.4021 | −0.611824 | −0.305912 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305912 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.2703 | 1.55454 | 0.777270 | − | 0.629167i | \(-0.216604\pi\) | ||||
0.777270 | + | 0.629167i | \(0.216604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.6379 | −0.722916 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.76763 | −0.201784 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.12402 | −0.178830 | −0.0894148 | − | 0.995994i | \(-0.528500\pi\) | ||||
−0.0894148 | + | 0.995994i | \(0.528500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.29435 | −0.219407 | −0.109704 | − | 0.993964i | \(-0.534990\pi\) | ||||
−0.109704 | + | 0.993964i | \(0.534990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9996 | −1.00841 | −0.504207 | − | 0.863583i | \(-0.668215\pi\) | ||||
−0.504207 | + | 0.863583i | \(0.668215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0215 | −0.382792 | −0.191396 | − | 0.981513i | \(-0.561301\pi\) | ||||
−0.191396 | + | 0.981513i | \(0.561301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.7938 | 1.34412 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.0964 | 0.937710 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.8727 | 0.513464 | 0.256732 | − | 0.966483i | \(-0.417354\pi\) | ||||
0.256732 | + | 0.966483i | \(0.417354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4085 | −0.462363 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.85321 | −0.235758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.91548 | −0.0658166 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.4099 | −1.14528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.8801 | 0.680682 | 0.340341 | − | 0.940302i | \(-0.389458\pi\) | ||||
0.340341 | + | 0.940302i | \(0.389458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.9474 | 0.818029 | 0.409014 | − | 0.912528i | \(-0.365873\pi\) | ||||
0.409014 | + | 0.912528i | \(0.365873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.5394 | 1.51966 | 0.759832 | − | 0.650119i | \(-0.225281\pi\) | ||||
0.759832 | + | 0.650119i | \(0.225281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.47937 | −0.254601 | −0.127300 | − | 0.991864i | \(-0.540631\pi\) | ||||
−0.127300 | + | 0.991864i | \(0.540631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.77077 | −0.162211 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.83726 | 0.231938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.4336 | −1.20062 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.43882 | 0.0486411 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.0919 | 1.45511 | 0.727555 | − | 0.686049i | \(-0.240657\pi\) | ||||
0.727555 | + | 0.686049i | \(0.240657\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.4283 | −0.418722 | −0.209361 | − | 0.977838i | \(-0.567138\pi\) | ||||
−0.209361 | + | 0.977838i | \(0.567138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0244 | −1.14501 | −0.572507 | − | 0.819900i | \(-0.694029\pi\) | ||||
−0.572507 | + | 0.819900i | \(0.694029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.2609 | 1.51971 | 0.759855 | − | 0.650092i | \(-0.225270\pi\) | ||||
0.759855 | + | 0.650092i | \(0.225270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.107715 | 0.00361266 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.2527 | 0.376556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.63795 | −0.155029 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.6583 | 0.722343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.2427 | 1.40731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.2632 | −0.573848 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.7681 | −0.822412 | −0.411206 | − | 0.911542i | \(-0.634892\pi\) | ||||
−0.411206 | + | 0.911542i | \(0.634892\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8875 | 0.426981 | 0.213491 | − | 0.976945i | \(-0.431517\pi\) | ||||
0.213491 | + | 0.976945i | \(0.431517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.64223 | −0.120540 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.85579 | −0.0943064 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.0846 | 1.09136 | 0.545681 | − | 0.837993i | \(-0.316271\pi\) | ||||
0.545681 | + | 0.837993i | \(0.316271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.1597 | 0.992718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.9217 | 0.490622 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.0572 | −1.57671 | −0.788353 | − | 0.615224i | \(-0.789066\pi\) | ||||
−0.788353 | + | 0.615224i | \(0.789066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.96725 | 0.228342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.49055 | −0.310374 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.71132 | −0.153912 | −0.0769560 | − | 0.997034i | \(-0.524520\pi\) | ||||
−0.0769560 | + | 0.997034i | \(0.524520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.0727 | 1.79532 | 0.897659 | − | 0.440690i | \(-0.145266\pi\) | ||||
0.897659 | + | 0.440690i | \(0.145266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.5482 | 1.22274 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.5984 | 0.766846 | 0.383423 | − | 0.923573i | \(-0.374745\pi\) | ||||
0.383423 | + | 0.923573i | \(0.374745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.2150 | −1.37036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.4123 | −1.14712 | −0.573558 | − | 0.819165i | \(-0.694437\pi\) | ||||
−0.573558 | + | 0.819165i | \(0.694437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7205 | 0.638140 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.89191 | 0.0933847 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.914306 | −0.0294938 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −50.2998 | −1.61921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.6786 | −1.88698 | −0.943488 | − | 0.331407i | \(-0.892477\pi\) | ||||
−0.943488 | + | 0.331407i | \(0.892477\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.7839 | −0.666988 | −0.333494 | − | 0.942752i | \(-0.608228\pi\) | ||||
−0.333494 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.810482 | −0.0259828 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.7111 | −0.374670 | −0.187335 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187335 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.0687 | −0.353758 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.7921 | −1.77949 | −0.889745 | − | 0.456457i | \(-0.849118\pi\) | ||||
−0.889745 | + | 0.456457i | \(0.849118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.404666 | 0.0128937 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.7442 | −0.818617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.1167 | 1.65554 | 0.827771 | − | 0.561066i | \(-0.189609\pi\) | ||||
0.827771 | + | 0.561066i | \(0.189609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 56.5063 | 1.79137 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.9871 | −1.13972 | −0.569862 | − | 0.821740i | \(-0.693003\pi\) | ||||
−0.569862 | + | 0.821740i | \(0.693003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5472.2.a.bt.1.2 | 4 | ||
3.2 | odd | 2 | 608.2.a.i.1.2 | ✓ | 4 | ||
4.3 | odd | 2 | 5472.2.a.bs.1.2 | 4 | |||
12.11 | even | 2 | 608.2.a.j.1.4 | yes | 4 | ||
24.5 | odd | 2 | 1216.2.a.x.1.3 | 4 | |||
24.11 | even | 2 | 1216.2.a.w.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.i.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
608.2.a.j.1.4 | yes | 4 | 12.11 | even | 2 | ||
1216.2.a.w.1.1 | 4 | 24.11 | even | 2 | |||
1216.2.a.x.1.3 | 4 | 24.5 | odd | 2 | |||
5472.2.a.bs.1.2 | 4 | 4.3 | odd | 2 | |||
5472.2.a.bt.1.2 | 4 | 1.1 | even | 1 | trivial |