Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, 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("3240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.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: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.37228 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37228 | 0.715270 | 0.357635 | − | 0.933862i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933862i | \(0.383583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.37228 | −0.935303 | −0.467651 | − | 0.883913i | \(-0.654900\pi\) | ||||
−0.467651 | + | 0.883913i | \(0.654900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.74456 | −1.63580 | −0.817898 | − | 0.575363i | \(-0.804861\pi\) | ||||
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.37228 | 1.12020 | 0.560099 | − | 0.828426i | \(-0.310763\pi\) | ||||
0.560099 | + | 0.828426i | \(0.310763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.37228 | 0.440522 | 0.220261 | − | 0.975441i | \(-0.429309\pi\) | ||||
0.220261 | + | 0.975441i | \(0.429309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.1168 | 1.99664 | 0.998322 | − | 0.0579057i | \(-0.0184423\pi\) | ||||
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.255437 | 0.0398926 | 0.0199463 | − | 0.999801i | \(-0.493650\pi\) | ||||
0.0199463 | + | 0.999801i | \(0.493650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.74456 | −0.723539 | −0.361770 | − | 0.932268i | \(-0.617827\pi\) | ||||
−0.361770 | + | 0.932268i | \(0.617827\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.37228 | −1.36709 | −0.683544 | − | 0.729909i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729909i | \(0.739562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1168 | 1.38966 | 0.694828 | − | 0.719176i | \(-0.255481\pi\) | ||||
0.694828 | + | 0.719176i | \(0.255481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | 0.650945 | 0.325472 | − | 0.945552i | \(-0.394477\pi\) | ||||
0.325472 | + | 0.945552i | \(0.394477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7446 | 1.63177 | 0.815887 | − | 0.578211i | \(-0.196249\pi\) | ||||
0.815887 | + | 0.578211i | \(0.196249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.37228 | −0.418280 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.744563 | −0.0909628 | −0.0454814 | − | 0.998965i | \(-0.514482\pi\) | ||||
−0.0454814 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.37228 | −0.518894 | −0.259447 | − | 0.965757i | \(-0.583540\pi\) | ||||
−0.259447 | + | 0.965757i | \(0.583540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7446 | 1.72572 | 0.862860 | − | 0.505443i | \(-0.168671\pi\) | ||||
0.862860 | + | 0.505443i | \(0.168671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | 0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.74456 | −0.308787 | −0.154394 | − | 0.988009i | \(-0.549342\pi\) | ||||
−0.154394 | + | 0.988009i | \(0.549342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0000 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.74456 | −0.731551 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.37228 | −0.463461 | −0.231730 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231730 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3723 | −1.19214 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.74456 | −0.481737 | −0.240869 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240869 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.8614 | −1.57827 | −0.789134 | − | 0.614220i | \(-0.789471\pi\) | ||||
−0.789134 | + | 0.614220i | \(0.789471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.116844 | −0.0115130 | −0.00575649 | − | 0.999983i | \(-0.501832\pi\) | ||||
−0.00575649 | + | 0.999983i | \(0.501832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.883156 | 0.0845910 | 0.0422955 | − | 0.999105i | \(-0.486533\pi\) | ||||
0.0422955 | + | 0.999105i | \(0.486533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7446 | 1.38705 | 0.693526 | − | 0.720432i | \(-0.256056\pi\) | ||||
0.693526 | + | 0.720432i | \(0.256056\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.37228 | 0.500968 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.7446 | −2.08499 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8614 | −1.14127 | −0.570633 | − | 0.821205i | \(-0.693302\pi\) | ||||
−0.570633 | + | 0.821205i | \(0.693302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.25544 | 0.546540 | 0.273270 | − | 0.961937i | \(-0.411895\pi\) | ||||
0.273270 | + | 0.961937i | \(0.411895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.37228 | 0.292414 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.25544 | −0.449002 | −0.224501 | − | 0.974474i | \(-0.572075\pi\) | ||||
−0.224501 | + | 0.974474i | \(0.572075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0000 | 1.27228 | 0.636142 | − | 0.771572i | \(-0.280529\pi\) | ||||
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.37228 | 0.197007 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.4891 | 1.59661 | 0.798306 | − | 0.602252i | \(-0.205730\pi\) | ||||
0.798306 | + | 0.602252i | \(0.205730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.3723 | 1.98339 | 0.991694 | − | 0.128619i | \(-0.0410545\pi\) | ||||
0.991694 | + | 0.128619i | \(0.0410545\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1168 | 0.892926 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.8614 | 1.82454 | 0.912269 | − | 0.409591i | \(-0.134328\pi\) | ||||
0.912269 | + | 0.409591i | \(0.134328\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.1168 | 1.42781 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.48913 | 0.743246 | 0.371623 | − | 0.928384i | \(-0.378801\pi\) | ||||
0.371623 | + | 0.928384i | \(0.378801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.62772 | −0.125209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8614 | 1.12989 | 0.564946 | − | 0.825128i | \(-0.308897\pi\) | ||||
0.564946 | + | 0.825128i | \(0.308897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.37228 | 0.254921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.25544 | −0.318066 | −0.159033 | − | 0.987273i | \(-0.550838\pi\) | ||||
−0.159033 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8614 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0000 | −1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.62772 | −0.407207 | −0.203604 | − | 0.979053i | \(-0.565265\pi\) | ||||
−0.203604 | + | 0.979053i | \(0.565265\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.744563 | 0.0535948 | 0.0267974 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267974 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.627719 | −0.0447231 | −0.0223616 | − | 0.999750i | \(-0.507118\pi\) | ||||
−0.0223616 | + | 0.999750i | \(0.507118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4891 | 0.956219 | 0.478109 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478109 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.255437 | 0.0178405 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.37228 | 0.164094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.74456 | −0.323576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.4891 | 2.54493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.7446 | 1.52996 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4891 | 1.70688 | 0.853439 | − | 0.521193i | \(-0.174513\pi\) | ||||
0.853439 | + | 0.521193i | \(0.174513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4891 | −1.16079 | −0.580397 | − | 0.814334i | \(-0.697103\pi\) | ||||
−0.580397 | + | 0.814334i | \(0.697103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.7446 | −1.10651 | −0.553256 | − | 0.833011i | \(-0.686615\pi\) | ||||
−0.553256 | + | 0.833011i | \(0.686615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.2337 | −0.932480 | −0.466240 | − | 0.884658i | \(-0.654392\pi\) | ||||
−0.466240 | + | 0.884658i | \(0.654392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.37228 | −0.611380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.2337 | −1.30881 | −0.654404 | − | 0.756145i | \(-0.727081\pi\) | ||||
−0.654404 | + | 0.756145i | \(0.727081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.6060 | −0.683191 | −0.341595 | − | 0.939847i | \(-0.610967\pi\) | ||||
−0.341595 | + | 0.939847i | \(0.610967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.37228 | −0.214573 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.8614 | −0.811805 | −0.405902 | − | 0.913916i | \(-0.633043\pi\) | ||||
−0.405902 | + | 0.913916i | \(0.633043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7446 | 0.801244 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.510875 | 0.0318675 | 0.0159337 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159337 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.2337 | 1.25726 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.11684 | 0.253855 | 0.126928 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126928 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1168 | 0.621473 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.11684 | −0.311979 | −0.155990 | − | 0.987759i | \(-0.549857\pi\) | ||||
−0.155990 | + | 0.987759i | \(0.549857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.25544 | −0.562228 | −0.281114 | − | 0.959674i | \(-0.590704\pi\) | ||||
−0.281114 | + | 0.959674i | \(0.590704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.37228 | 0.143054 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.116844 | 0.00702047 | 0.00351024 | − | 0.999994i | \(-0.498883\pi\) | ||||
0.00351024 | + | 0.999994i | \(0.498883\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3723 | 1.03634 | 0.518172 | − | 0.855277i | \(-0.326613\pi\) | ||||
0.518172 | + | 0.855277i | \(0.326613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.7446 | 0.995361 | 0.497680 | − | 0.867360i | \(-0.334185\pi\) | ||||
0.497680 | + | 0.867360i | \(0.334185\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.861407 | 0.0508472 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.4891 | 1.67583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.8614 | −0.868213 | −0.434106 | − | 0.900862i | \(-0.642936\pi\) | ||||
−0.434106 | + | 0.900862i | \(0.642936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.00000 | 0.291111 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1168 | −1.04772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.7446 | 0.729752 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.744563 | 0.0424944 | 0.0212472 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212472 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8614 | 1.01283 | 0.506414 | − | 0.862291i | \(-0.330971\pi\) | ||||
0.506414 | + | 0.862291i | \(0.330971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | −0.226093 | −0.113047 | − | 0.993590i | \(-0.536061\pi\) | ||||
−0.113047 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6277 | −0.596912 | −0.298456 | − | 0.954423i | \(-0.596472\pi\) | ||||
−0.298456 | + | 0.954423i | \(0.596472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.62772 | 0.315092 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.74456 | −0.375278 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.37228 | −0.187061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.6060 | −1.74249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6277 | 0.749047 | 0.374524 | − | 0.927217i | \(-0.377806\pi\) | ||||
0.374524 | + | 0.927217i | \(0.377806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.744563 | −0.0406798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.7446 | −0.585294 | −0.292647 | − | 0.956221i | \(-0.594536\pi\) | ||||
−0.292647 | + | 0.956221i | \(0.594536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.3723 | 1.42814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.23369 | 0.227276 | 0.113638 | − | 0.993522i | \(-0.463750\pi\) | ||||
0.113638 | + | 0.993522i | \(0.463750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6277 | −1.05065 | −0.525324 | − | 0.850902i | \(-0.676056\pi\) | ||||
−0.525324 | + | 0.850902i | \(0.676056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.9783 | −1.11656 | −0.558280 | − | 0.829653i | \(-0.688538\pi\) | ||||
−0.558280 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.37228 | −0.232057 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.3723 | −0.864096 | −0.432048 | − | 0.901851i | \(-0.642209\pi\) | ||||
−0.432048 | + | 0.901851i | \(0.642209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7446 | 0.771766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.2337 | −1.57819 | −0.789093 | − | 0.614274i | \(-0.789449\pi\) | ||||
−0.789093 | + | 0.614274i | \(0.789449\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.1168 | 1.77126 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7446 | −0.556332 | −0.278166 | − | 0.960533i | \(-0.589727\pi\) | ||||
−0.278166 | + | 0.960533i | \(0.589727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.3505 | −1.35354 | −0.676768 | − | 0.736196i | \(-0.736620\pi\) | ||||
−0.676768 | + | 0.736196i | \(0.736620\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3723 | −0.989877 | −0.494939 | − | 0.868928i | \(-0.664809\pi\) | ||||
−0.494939 | + | 0.868928i | \(0.664809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | 0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.7446 | 1.05179 | 0.525896 | − | 0.850549i | \(-0.323730\pi\) | ||||
0.525896 | + | 0.850549i | \(0.323730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.2337 | −1.83242 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.74456 | −0.138094 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0000 | 1.70641 | 0.853206 | − | 0.521575i | \(-0.174655\pi\) | ||||
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.3505 | 1.81526 | 0.907629 | − | 0.419772i | \(-0.137890\pi\) | ||||
0.907629 | + | 0.419772i | \(0.137890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.4891 | −1.86747 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.2337 | 0.705538 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3723 | −1.05679 | −0.528396 | − | 0.848998i | \(-0.677206\pi\) | ||||
−0.528396 | + | 0.848998i | \(0.677206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.8614 | 0.829696 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | −0.490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.9783 | 1.70880 | 0.854400 | − | 0.519616i | \(-0.173925\pi\) | ||||
0.854400 | + | 0.519616i | \(0.173925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3723 | 1.38278 | 0.691390 | − | 0.722482i | \(-0.256999\pi\) | ||||
0.691390 | + | 0.722482i | \(0.256999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.74456 | −0.327159 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.9783 | 2.07986 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.62772 | 0.463751 | 0.231875 | − | 0.972745i | \(-0.425514\pi\) | ||||
0.231875 | + | 0.972745i | \(0.425514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.2119 | −1.98052 | −0.990260 | − | 0.139233i | \(-0.955536\pi\) | ||||
−0.990260 | + | 0.139233i | \(0.955536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.37228 | 0.256991 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0951 | −1.53182 | −0.765908 | − | 0.642951i | \(-0.777710\pi\) | ||||
−0.765908 | + | 0.642951i | \(0.777710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.9783 | −1.37680 | −0.688399 | − | 0.725332i | \(-0.741686\pi\) | ||||
−0.688399 | + | 0.725332i | \(0.741686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.37228 | −0.207266 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.7228 | 1.63867 | 0.819335 | − | 0.573314i | \(-0.194343\pi\) | ||||
0.819335 | + | 0.573314i | \(0.194343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.605969 | 0.0285340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3723 | −0.533141 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.76631 | −0.269737 | −0.134868 | − | 0.990864i | \(-0.543061\pi\) | ||||
−0.134868 | + | 0.990864i | \(0.543061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1168 | 1.44926 | 0.724628 | − | 0.689140i | \(-0.242012\pi\) | ||||
0.724628 | + | 0.689140i | \(0.242012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.86141 | 0.318877 | 0.159438 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159438 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2337 | 0.751205 | 0.375603 | − | 0.926781i | \(-0.377436\pi\) | ||||
0.375603 | + | 0.926781i | \(0.377436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51087 | −0.115941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2554 | −0.517526 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.88316 | −0.314499 | −0.157250 | − | 0.987559i | \(-0.550263\pi\) | ||||
−0.157250 | + | 0.987559i | \(0.550263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.2337 | −0.922577 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.74456 | −0.215439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.6060 | 0.888431 | 0.444216 | − | 0.895920i | \(-0.353482\pi\) | ||||
0.444216 | + | 0.895920i | \(0.353482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9783 | −1.17238 | −0.586191 | − | 0.810173i | \(-0.699373\pi\) | ||||
−0.586191 | + | 0.810173i | \(0.699373\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0000 | −0.720604 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7446 | −0.661384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7446 | 0.883888 | 0.441944 | − | 0.897043i | \(-0.354289\pi\) | ||||
0.441944 | + | 0.897043i | \(0.354289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.9783 | 0.489496 | 0.244748 | − | 0.969587i | \(-0.421295\pi\) | ||||
0.244748 | + | 0.969587i | \(0.421295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8614 | −0.705823 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.0000 | −1.68432 | −0.842160 | − | 0.539227i | \(-0.818716\pi\) | ||||
−0.842160 | + | 0.539227i | \(0.818716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.7228 | 2.19961 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.116844 | −0.00514876 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.2337 | −0.977836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.116844 | −0.00511903 | −0.00255951 | − | 0.999997i | \(-0.500815\pi\) | ||||
−0.00255951 | + | 0.999997i | \(0.500815\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.2337 | −1.75930 | −0.879648 | − | 0.475625i | \(-0.842222\pi\) | ||||
−0.879648 | + | 0.475625i | \(0.842222\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −74.9783 | −3.26610 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.86141 | 0.254844 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.861407 | −0.0373117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | −0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3723 | 0.446766 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3505 | 0.573984 | 0.286992 | − | 0.957933i | \(-0.407345\pi\) | ||||
0.286992 | + | 0.957933i | \(0.407345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.883156 | 0.0378302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.0000 | −1.71028 | −0.855138 | − | 0.518400i | \(-0.826528\pi\) | ||||
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.37228 | 0.101063 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.25544 | −0.393581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.6060 | −1.33919 | −0.669594 | − | 0.742727i | \(-0.733532\pi\) | ||||
−0.669594 | + | 0.742727i | \(0.733532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.2337 | −0.431299 | −0.215649 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215649 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.7446 | 0.620308 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.76631 | 0.367503 | 0.183751 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183751 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.11684 | −0.130436 | −0.0652179 | − | 0.997871i | \(-0.520774\pi\) | ||||
−0.0652179 | + | 0.997871i | \(0.520774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.37228 | 0.224040 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.48913 | −0.395037 | −0.197519 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197519 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.7228 | −1.39906 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000 | 0.993978 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0000 | 1.23823 | 0.619116 | − | 0.785299i | \(-0.287491\pi\) | ||||
0.619116 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1168 | 0.458062 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9783 | −1.18999 | −0.594997 | − | 0.803728i | \(-0.702847\pi\) | ||||
−0.594997 | + | 0.803728i | \(0.702847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.7446 | −0.932436 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3505 | 0.627206 | 0.313603 | − | 0.949554i | \(-0.398464\pi\) | ||||
0.313603 | + | 0.949554i | \(0.398464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | 0.530281 | 0.265141 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265141 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.37228 | −0.218414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.7446 | −1.81613 | −0.908063 | − | 0.418834i | \(-0.862439\pi\) | ||||
−0.908063 | + | 0.418834i | \(0.862439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.6060 | 1.27864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.3505 | 0.741171 | 0.370586 | − | 0.928798i | \(-0.379157\pi\) | ||||
0.370586 | + | 0.928798i | \(0.379157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7228 | 0.552460 | 0.276230 | − | 0.961092i | \(-0.410915\pi\) | ||||
0.276230 | + | 0.961092i | \(0.410915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.6277 | −1.31142 | −0.655709 | − | 0.755013i | \(-0.727630\pi\) | ||||
−0.655709 | + | 0.755013i | \(0.727630\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.7446 | −0.590728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.4674 | −1.61354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3723 | −1.68681 | −0.843407 | − | 0.537275i | \(-0.819454\pi\) | ||||
−0.843407 | + | 0.537275i | \(0.819454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.8614 | −0.510389 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.7446 | −0.584201 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.6060 | 1.68283 | 0.841417 | − | 0.540386i | \(-0.181722\pi\) | ||||
0.841417 | + | 0.540386i | \(0.181722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.7446 | 1.29132 | 0.645660 | − | 0.763625i | \(-0.276582\pi\) | ||||
0.645660 | + | 0.763625i | \(0.276582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.7228 | −1.24715 | −0.623576 | − | 0.781763i | \(-0.714321\pi\) | ||||
−0.623576 | + | 0.781763i | \(0.714321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8614 | 0.465601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2554 | −0.518725 | −0.259363 | − | 0.965780i | \(-0.583512\pi\) | ||||
−0.259363 | + | 0.965780i | \(0.583512\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.25544 | 0.244420 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.5842 | 1.50303 | 0.751514 | − | 0.659717i | \(-0.229324\pi\) | ||||
0.751514 | + | 0.659717i | \(0.229324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0951 | 0.703818 | 0.351909 | − | 0.936034i | \(-0.385533\pi\) | ||||
0.351909 | + | 0.936034i | \(0.385533\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.37228 | 0.130771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7446 | 0.493471 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.2337 | 1.16716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.4891 | −0.905439 | −0.452720 | − | 0.891653i | \(-0.649546\pi\) | ||||
−0.452720 | + | 0.891653i | \(0.649546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.88316 | −0.149242 | −0.0746209 | − | 0.997212i | \(-0.523775\pi\) | ||||
−0.0746209 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | −0.614024 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.76631 | 0.144114 | 0.0720570 | − | 0.997401i | \(-0.477044\pi\) | ||||
0.0720570 | + | 0.997401i | \(0.477044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.25544 | −0.200800 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.1168 | −1.29975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.3505 | −0.393753 | −0.196876 | − | 0.980428i | \(-0.563080\pi\) | ||||
−0.196876 | + | 0.980428i | \(0.563080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0000 | 0.568982 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.72281 | −0.0652562 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.11684 | 0.344338 | 0.172169 | − | 0.985067i | \(-0.444922\pi\) | ||||
0.172169 | + | 0.985067i | \(0.444922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −53.4891 | −2.01167 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.4674 | −1.89534 | −0.947671 | − | 0.319248i | \(-0.896570\pi\) | ||||
−0.947671 | + | 0.319248i | \(0.896570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 59.7228 | 2.23664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.6060 | −1.88728 | −0.943642 | − | 0.330968i | \(-0.892625\pi\) | ||||
−0.943642 | + | 0.330968i | \(0.892625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.394031 | −0.0146745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.37228 | 0.0881043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.8832 | −1.10830 | −0.554152 | − | 0.832415i | \(-0.686958\pi\) | ||||
−0.554152 | + | 0.832415i | \(0.686958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9783 | 0.627106 | 0.313553 | − | 0.949571i | \(-0.398481\pi\) | ||||
0.313553 | + | 0.949571i | \(0.398481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.76631 | −0.0650629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.8614 | 0.583471 | 0.291736 | − | 0.956499i | \(-0.405767\pi\) | ||||
0.291736 | + | 0.956499i | \(0.405767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.51087 | −0.238861 | −0.119430 | − | 0.992843i | \(-0.538107\pi\) | ||||
−0.119430 | + | 0.992843i | \(0.538107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.4891 | 0.714026 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.2337 | −0.739323 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.76631 | −0.137435 | −0.0687173 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687173 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.3723 | 0.886998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.88316 | 0.359209 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2337 | 0.624721 | 0.312360 | − | 0.949964i | \(-0.398880\pi\) | ||||
0.312360 | + | 0.949964i | \(0.398880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.97825 | 0.107820 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.8614 | −0.608830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3505 | 0.697798 | 0.348899 | − | 0.937160i | \(-0.386556\pi\) | ||||
0.348899 | + | 0.937160i | \(0.386556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1168 | 0.399329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.255437 | 0.00915199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.3723 | −0.371149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.8614 | 0.815959 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.7228 | −1.48726 | −0.743629 | − | 0.668593i | \(-0.766897\pi\) | ||||
−0.743629 | + | 0.668593i | \(0.766897\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 49.7228 | 1.76794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.9783 | −1.52620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.2337 | −0.716714 | −0.358357 | − | 0.933585i | \(-0.616663\pi\) | ||||
−0.358357 | + | 0.933585i | \(0.616663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.2119 | 2.23628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.9783 | 1.23436 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.1168 | 0.638535 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.2119 | 1.62473 | 0.812363 | − | 0.583153i | \(-0.198181\pi\) | ||||
0.812363 | + | 0.583153i | \(0.198181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.3505 | −1.31155 | −0.655777 | − | 0.754954i | \(-0.727659\pi\) | ||||
−0.655777 | + | 0.754954i | \(0.727659\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.48913 | 0.332390 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.74456 | −0.165991 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.6277 | 1.24342 | 0.621708 | − | 0.783249i | \(-0.286439\pi\) | ||||
0.621708 | + | 0.783249i | \(0.286439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2554 | −0.810634 | −0.405317 | − | 0.914176i | \(-0.632839\pi\) | ||||
−0.405317 | + | 0.914176i | \(0.632839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.9565 | −1.59806 | −0.799032 | − | 0.601288i | \(-0.794654\pi\) | ||||
−0.799032 | + | 0.601288i | \(0.794654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.5842 | −1.51374 | −0.756871 | − | 0.653564i | \(-0.773273\pi\) | ||||
−0.756871 | + | 0.653564i | \(0.773273\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.4891 | −1.02174 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.6060 | −0.987588 | −0.493794 | − | 0.869579i | \(-0.664390\pi\) | ||||
−0.493794 | + | 0.869579i | \(0.664390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3723 | −0.805941 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.62772 | −0.0559952 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.1168 | −0.622502 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.2337 | 1.10496 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7446 | 0.367887 | 0.183943 | − | 0.982937i | \(-0.441114\pi\) | ||||
0.183943 | + | 0.982937i | \(0.441114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.2554 | −1.13598 | −0.567992 | − | 0.823034i | \(-0.692280\pi\) | ||||
−0.567992 | + | 0.823034i | \(0.692280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.35053 | −0.0460796 | −0.0230398 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230398 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.6060 | −1.75669 | −0.878344 | − | 0.478029i | \(-0.841351\pi\) | ||||
−0.878344 | + | 0.478029i | \(0.841351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.8614 | 0.505303 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.51087 | −0.220866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.51087 | 0.0850777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.37228 | 0.114004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1168 | 0.881903 | 0.440952 | − | 0.897531i | \(-0.354641\pi\) | ||||
0.440952 | + | 0.897531i | \(0.354641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6277 | 0.661275 | 0.330637 | − | 0.943758i | \(-0.392736\pi\) | ||||
0.330637 | + | 0.943758i | \(0.392736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2337 | 1.35397 | 0.676986 | − | 0.735996i | \(-0.263286\pi\) | ||||
0.676986 | + | 0.735996i | \(0.263286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.1386 | −0.441151 | −0.220575 | − | 0.975370i | \(-0.570794\pi\) | ||||
−0.220575 | + | 0.975370i | \(0.570794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.3723 | −1.45466 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.37228 | −0.313631 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.25544 | −0.142244 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3723 | 0.879565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −68.2337 | −2.27319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.8614 | −0.460769 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5109 | −0.415417 | −0.207708 | − | 0.978191i | \(-0.566601\pi\) | ||||
−0.207708 | + | 0.978191i | \(0.566601\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.0733 | −1.82466 | −0.912331 | − | 0.409454i | \(-0.865719\pi\) | ||||
−0.912331 | + | 0.409454i | \(0.865719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.7228 | −0.785111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.0951 | 0.696621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8832 | 0.820820 | 0.410410 | − | 0.911901i | \(-0.365386\pi\) | ||||
0.410410 | + | 0.911901i | \(0.365386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7446 | 0.485323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.8614 | 0.848485 | 0.424243 | − | 0.905549i | \(-0.360540\pi\) | ||||
0.424243 | + | 0.905549i | \(0.360540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.37228 | 0.143296 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.0000 | −0.523256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.2554 | 1.02107 | 0.510535 | − | 0.859857i | \(-0.329447\pi\) | ||||
0.510535 | + | 0.859857i | \(0.329447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.4674 | −1.38440 | −0.692198 | − | 0.721707i | \(-0.743358\pi\) | ||||
−0.692198 | + | 0.721707i | \(0.743358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37228 | 0.0446876 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.7446 | 1.58399 | 0.791993 | − | 0.610531i | \(-0.209044\pi\) | ||||
0.791993 | + | 0.610531i | \(0.209044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.7228 | −1.61407 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0000 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.62772 | −0.182109 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.7228 | −0.572299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 92.5842 | 2.98659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.744563 | 0.0239683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.4891 | −1.33420 | −0.667100 | − | 0.744968i | \(-0.732465\pi\) | ||||
−0.667100 | + | 0.744968i | \(0.732465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7228 | 1.56359 | 0.781795 | − | 0.623536i | \(-0.214304\pi\) | ||||
0.781795 | + | 0.623536i | \(0.214304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.5842 | 1.62166 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.2337 | 1.67110 | 0.835552 | − | 0.549412i | \(-0.185148\pi\) | ||||
0.835552 | + | 0.549412i | \(0.185148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3723 | −0.331500 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.4891 | 0.557816 | 0.278908 | − | 0.960318i | \(-0.410027\pi\) | ||||
0.278908 | + | 0.960318i | \(0.410027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.627719 | −0.0200008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.4891 | −0.810507 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.37228 | −0.0753580 | −0.0376790 | − | 0.999290i | \(-0.511996\pi\) | ||||
−0.0376790 | + | 0.999290i | \(0.511996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4891 | 0.427634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.3505 | −1.34125 | −0.670627 | − | 0.741794i | \(-0.733975\pi\) | ||||
−0.670627 | + | 0.741794i | \(0.733975\pi\) | |||||||
\(998\) | 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 | 3240.2.a.m.1.2 | yes | 2 | |
3.2 | odd | 2 | 3240.2.a.i.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 6480.2.a.bo.1.1 | 2 | |||
9.2 | odd | 6 | 3240.2.q.bd.1081.1 | 4 | |||
9.4 | even | 3 | 3240.2.q.ba.2161.1 | 4 | |||
9.5 | odd | 6 | 3240.2.q.bd.2161.1 | 4 | |||
9.7 | even | 3 | 3240.2.q.ba.1081.1 | 4 | |||
12.11 | even | 2 | 6480.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3240.2.a.i.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3240.2.a.m.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
3240.2.q.ba.1081.1 | 4 | 9.7 | even | 3 | |||
3240.2.q.ba.2161.1 | 4 | 9.4 | even | 3 | |||
3240.2.q.bd.1081.1 | 4 | 9.2 | odd | 6 | |||
3240.2.q.bd.2161.1 | 4 | 9.5 | odd | 6 | |||
6480.2.a.bd.1.1 | 2 | 12.11 | even | 2 | |||
6480.2.a.bo.1.1 | 2 | 4.3 | odd | 2 |