Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.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: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.10070523904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 24x^{5} + 30x^{4} - 16x^{3} - 20x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.536630\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-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 | ||||||||
\(5\) | 3.36028 | 1.50276 | 0.751382 | − | 0.659867i | \(-0.229388\pi\) | ||||
0.751382 | + | 0.659867i | \(0.229388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64575 | 1.37796 | 0.688982 | − | 0.724778i | \(-0.258058\pi\) | ||||
0.688982 | + | 0.724778i | \(0.258058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19038 | 0.358912 | 0.179456 | − | 0.983766i | \(-0.442566\pi\) | ||||
0.179456 | + | 0.983766i | \(0.442566\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74166 | 1.03775 | 0.518875 | − | 0.854850i | \(-0.326351\pi\) | ||||
0.518875 | + | 0.854850i | \(0.326351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06871 | −0.744272 | −0.372136 | − | 0.928178i | \(-0.621375\pi\) | ||||
−0.372136 | + | 0.928178i | \(0.621375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.32744 | 0.533952 | 0.266976 | − | 0.963703i | \(-0.413976\pi\) | ||||
0.266976 | + | 0.963703i | \(0.413976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.82087 | −1.63076 | −0.815382 | − | 0.578923i | \(-0.803473\pi\) | ||||
−0.815382 | + | 0.578923i | \(0.803473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.29150 | 1.25830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.979531 | −0.181894 | −0.0909472 | − | 0.995856i | \(-0.528989\pi\) | ||||
−0.0909472 | + | 0.995856i | \(0.528989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.354249 | 0.0636249 | 0.0318125 | − | 0.999494i | \(-0.489872\pi\) | ||||
0.0318125 | + | 0.999494i | \(0.489872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.2508 | 2.07076 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.57008 | −1.08012 | −0.540058 | − | 0.841628i | \(-0.681598\pi\) | ||||
−0.540058 | + | 0.841628i | \(0.681598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.43560 | −1.00507 | −0.502536 | − | 0.864556i | \(-0.667600\pi\) | ||||
−0.502536 | + | 0.864556i | \(0.667600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.98430 | 1.21759 | 0.608797 | − | 0.793326i | \(-0.291652\pi\) | ||||
0.608797 | + | 0.793326i | \(0.291652\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1878 | 1.63190 | 0.815951 | − | 0.578121i | \(-0.196214\pi\) | ||||
0.815951 | + | 0.578121i | \(0.196214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.29150 | 0.898786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.70010 | −1.05769 | −0.528845 | − | 0.848719i | \(-0.677375\pi\) | ||||
−0.528845 | + | 0.848719i | \(0.677375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0604 | 1.43994 | 0.719969 | − | 0.694006i | \(-0.244156\pi\) | ||||
0.719969 | + | 0.694006i | \(0.244156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.57008 | 0.841213 | 0.420607 | − | 0.907243i | \(-0.361817\pi\) | ||||
0.420607 | + | 0.907243i | \(0.361817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.5730 | 1.55949 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.36689 | −0.399577 | −0.199788 | − | 0.979839i | \(-0.564025\pi\) | ||||
−0.199788 | + | 0.979839i | \(0.564025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29150 | 0.853406 | 0.426703 | − | 0.904392i | \(-0.359675\pi\) | ||||
0.426703 | + | 0.904392i | \(0.359675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.33981 | 0.494568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.35425 | 0.489891 | 0.244946 | − | 0.969537i | \(-0.421230\pi\) | ||||
0.244946 | + | 0.969537i | \(0.421230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.19038 | 0.130661 | 0.0653304 | − | 0.997864i | \(-0.479190\pi\) | ||||
0.0653304 | + | 0.997864i | \(0.479190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3117 | −1.11847 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.50432 | 1.00746 | 0.503728 | − | 0.863862i | \(-0.331961\pi\) | ||||
0.503728 | + | 0.863862i | \(0.331961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6412 | 1.42998 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.82087 | 0.802404 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5830 | 1.07454 | 0.537271 | − | 0.843410i | \(-0.319455\pi\) | ||||
0.537271 | + | 0.843410i | \(0.319455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36028 | 0.334361 | 0.167180 | − | 0.985926i | \(-0.446534\pi\) | ||||
0.167180 | + | 0.985926i | \(0.446534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.06275 | 0.104715 | 0.0523577 | − | 0.998628i | \(-0.483326\pi\) | ||||
0.0523577 | + | 0.998628i | \(0.483326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4411 | 1.29940 | 0.649702 | − | 0.760189i | \(-0.274894\pi\) | ||||
0.649702 | + | 0.760189i | \(0.274894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91520 | 0.183443 | 0.0917213 | − | 0.995785i | \(-0.470763\pi\) | ||||
0.0917213 | + | 0.995785i | \(0.470763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.2803 | −2.45065 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.1878 | −1.02558 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.58301 | −0.871182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.33981 | 0.388165 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9373 | 1.32547 | 0.662733 | − | 0.748855i | \(-0.269396\pi\) | ||||
0.662733 | + | 0.748855i | \(0.269396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.38075 | 0.208007 | 0.104004 | − | 0.994577i | \(-0.466835\pi\) | ||||
0.104004 | + | 0.994577i | \(0.466835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.48528 | 0.735767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9399 | 1.36184 | 0.680920 | − | 0.732358i | \(-0.261580\pi\) | ||||
0.680920 | + | 0.732358i | \(0.261580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.30978 | −0.789645 | −0.394822 | − | 0.918757i | \(-0.629194\pi\) | ||||
−0.394822 | + | 0.918757i | \(0.629194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.45398 | 0.372460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.29150 | −0.273344 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.31935 | 0.435778 | 0.217889 | − | 0.975974i | \(-0.430083\pi\) | ||||
0.217889 | + | 0.975974i | \(0.430083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6458 | 1.27323 | 0.636617 | − | 0.771180i | \(-0.280333\pi\) | ||||
0.636617 | + | 0.771180i | \(0.280333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.19038 | 0.0956133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.91520 | −0.152849 | −0.0764247 | − | 0.997075i | \(-0.524350\pi\) | ||||
−0.0764247 | + | 0.997075i | \(0.524350\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.5129 | −2.24714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.98626 | −0.703859 | −0.351929 | − | 0.936027i | \(-0.614474\pi\) | ||||
−0.351929 | + | 0.936027i | \(0.614474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.45398 | −0.344659 | −0.172330 | − | 0.985039i | \(-0.555129\pi\) | ||||
−0.172330 | + | 0.985039i | \(0.555129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.70010 | −0.585428 | −0.292714 | − | 0.956200i | \(-0.594558\pi\) | ||||
−0.292714 | + | 0.956200i | \(0.594558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.9373 | 1.73389 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4411 | 1.00464 | 0.502319 | − | 0.864683i | \(-0.332480\pi\) | ||||
0.502319 | + | 0.864683i | \(0.332480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.57008 | 0.488351 | 0.244175 | − | 0.969731i | \(-0.421483\pi\) | ||||
0.244175 | + | 0.969731i | \(0.421483\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.0773 | −1.62316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.65292 | −0.267128 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1878 | 0.809518 | 0.404759 | − | 0.914423i | \(-0.367355\pi\) | ||||
0.404759 | + | 0.914423i | \(0.367355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8745 | −1.43060 | −0.715299 | − | 0.698818i | \(-0.753710\pi\) | ||||
−0.715299 | + | 0.698818i | \(0.753710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4616 | −0.887852 | −0.443926 | − | 0.896063i | \(-0.646415\pi\) | ||||
−0.443926 | + | 0.896063i | \(0.646415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.35425 | 0.592217 | 0.296108 | − | 0.955154i | \(-0.404311\pi\) | ||||
0.296108 | + | 0.955154i | \(0.404311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.57113 | −0.250644 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.6255 | −1.51039 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.77053 | 0.191642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30978 | 0.640911 | 0.320456 | − | 0.947264i | \(-0.396164\pi\) | ||||
0.320456 | + | 0.947264i | \(0.396164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.8295 | 1.82976 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29150 | 0.0876729 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4821 | −0.772368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6458 | 1.31558 | 0.657788 | − | 0.753203i | \(-0.271492\pi\) | ||||
0.657788 | + | 0.753203i | \(0.271492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.6919 | −1.70523 | −0.852615 | − | 0.522539i | \(-0.824985\pi\) | ||||
−0.852615 | + | 0.522539i | \(0.824985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.91716 | −0.192772 | −0.0963858 | − | 0.995344i | \(-0.530728\pi\) | ||||
−0.0963858 | + | 0.995344i | \(0.530728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.7792 | −1.42680 | −0.713400 | − | 0.700757i | \(-0.752846\pi\) | ||||
−0.713400 | + | 0.700757i | \(0.752846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.5940 | 2.45237 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.4626 | −1.51767 | −0.758835 | − | 0.651283i | \(-0.774231\pi\) | ||||
−0.758835 | + | 0.651283i | \(0.774231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.29150 | −0.598518 | −0.299259 | − | 0.954172i | \(-0.596740\pi\) | ||||
−0.299259 | + | 0.954172i | \(0.596740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.1412 | 1.35066 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.70850 | 0.554108 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5496 | −1.17084 | −0.585421 | − | 0.810729i | \(-0.699071\pi\) | ||||
−0.585421 | + | 0.810729i | \(0.699071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.30978 | −0.585301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.2381 | 1.01290 | 0.506452 | − | 0.862268i | \(-0.330957\pi\) | ||||
0.506452 | + | 0.862268i | \(0.330957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9529 | −1.48836 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6417 | −0.964511 | −0.482256 | − | 0.876031i | \(-0.660182\pi\) | ||||
−0.482256 | + | 0.876031i | \(0.660182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.8745 | −1.58946 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0399 | −0.734086 | −0.367043 | − | 0.930204i | \(-0.619630\pi\) | ||||
−0.367043 | + | 0.930204i | \(0.619630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6458 | 0.707429 | 0.353715 | − | 0.935353i | \(-0.384918\pi\) | ||||
0.353715 | + | 0.935353i | \(0.384918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.48925 | 0.451619 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.0200 | 1.74364 | 0.871822 | − | 0.489822i | \(-0.162938\pi\) | ||||
0.871822 | + | 0.489822i | \(0.162938\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50432 | 0.566980 | 0.283490 | − | 0.958975i | \(-0.408508\pi\) | ||||
0.283490 | + | 0.958975i | \(0.408508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2803 | 1.56220 | 0.781102 | − | 0.624403i | \(-0.214658\pi\) | ||||
0.781102 | + | 0.624403i | \(0.214658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.4626 | −1.38495 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.58301 | −0.446059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.1412 | −1.23508 | −0.617542 | − | 0.786538i | \(-0.711871\pi\) | ||||
−0.617542 | + | 0.786538i | \(0.711871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.1660 | 2.16389 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.2630 | −1.69232 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.1088 | 1.67780 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.0773 | 1.26415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.2843 | −1.61427 | −0.807134 | − | 0.590368i | \(-0.798983\pi\) | ||||
−0.807134 | + | 0.590368i | \(0.798983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6417 | 0.886962 | 0.443481 | − | 0.896284i | \(-0.353743\pi\) | ||||
0.443481 | + | 0.896284i | \(0.353743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.29150 | 0.0730000 | 0.0365000 | − | 0.999334i | \(-0.488379\pi\) | ||||
0.0365000 | + | 0.999334i | \(0.488379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.36028 | 0.188732 | 0.0943662 | − | 0.995538i | \(-0.469918\pi\) | ||||
0.0943662 | + | 0.995538i | \(0.469918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.16601 | −0.0652841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.14226 | −0.397406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.5406 | 1.30580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.7878 | 2.24870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3137 | 0.621858 | 0.310929 | − | 0.950433i | \(-0.399360\pi\) | ||||
0.310929 | + | 0.950433i | \(0.399360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.0086 | −1.03855 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.2915 | −0.832981 | −0.416491 | − | 0.909140i | \(-0.636740\pi\) | ||||
−0.416491 | + | 0.909140i | \(0.636740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.421689 | 0.0228357 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.58301 | −0.139469 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.19038 | −0.0639027 | −0.0319514 | − | 0.999489i | \(-0.510172\pi\) | ||||
−0.0319514 | + | 0.999489i | \(0.510172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.8504 | −1.75844 | −0.879221 | − | 0.476413i | \(-0.841937\pi\) | ||||
−0.879221 | + | 0.476413i | \(0.841937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.5129 | −1.51759 | −0.758796 | − | 0.651329i | \(-0.774212\pi\) | ||||
−0.758796 | + | 0.651329i | \(0.774212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3137 | −0.600469 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.0086 | 1.00324 | 0.501619 | − | 0.865089i | \(-0.332738\pi\) | ||||
0.501619 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5830 | −0.714895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.5015 | 1.28247 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8118 | −0.668769 | −0.334384 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334384 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0726 | −1.45746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.56812 | −0.288306 | −0.144153 | − | 0.989555i | \(-0.546046\pi\) | ||||
−0.144153 | + | 0.989555i | \(0.546046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.66507 | −0.188761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2980 | 0.991272 | 0.495636 | − | 0.868530i | \(-0.334935\pi\) | ||||
0.495636 | + | 0.868530i | \(0.334935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1878 | −0.571668 | −0.285834 | − | 0.958279i | \(-0.592271\pi\) | ||||
−0.285834 | + | 0.958279i | \(0.592271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5830 | 0.743219 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5025 | 0.532500 | 0.266250 | − | 0.963904i | \(-0.414215\pi\) | ||||
0.266250 | + | 0.963904i | \(0.414215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.6315 | 0.736191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.8524 | −1.69900 | −0.849501 | − | 0.527586i | \(-0.823097\pi\) | ||||
−0.849501 | + | 0.527586i | \(0.823097\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.20614 | −0.459733 | −0.229866 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229866 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.32548 | 0.0660267 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.82087 | −0.387666 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.1660 | −0.848805 | −0.424402 | − | 0.905474i | \(-0.639516\pi\) | ||||
−0.424402 | + | 0.905474i | \(0.639516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.3234 | 1.98418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.5496 | −0.906209 | −0.453104 | − | 0.891457i | \(-0.649684\pi\) | ||||
−0.453104 | + | 0.891457i | \(0.649684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.5406 | −1.14730 | −0.573650 | − | 0.819100i | \(-0.694473\pi\) | ||||
−0.573650 | + | 0.819100i | \(0.694473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.3068 | −0.936518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.9529 | 1.15916 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.08709 | 0.0523632 | 0.0261816 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261816 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.2026 | −0.870750 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.5203 | 1.79074 | 0.895372 | − | 0.445319i | \(-0.146910\pi\) | ||||
0.895372 | + | 0.445319i | \(0.146910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.8341 | −1.56000 | −0.779999 | − | 0.625781i | \(-0.784780\pi\) | ||||
−0.779999 | + | 0.625781i | \(0.784780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.9372 | 1.51397 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.7191 | 1.78007 | 0.890037 | − | 0.455889i | \(-0.150678\pi\) | ||||
0.890037 | + | 0.455889i | \(0.150678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.66079 | −0.360732 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.8381 | 2.14892 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5830 | 1.24350 | 0.621750 | − | 0.783216i | \(-0.286422\pi\) | ||||
0.621750 | + | 0.783216i | \(0.286422\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.4616 | 0.580395 | 0.290197 | − | 0.956967i | \(-0.406279\pi\) | ||||
0.290197 | + | 0.956967i | \(0.406279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9373 | 1.43778 | 0.718888 | − | 0.695126i | \(-0.244651\pi\) | ||||
0.718888 | + | 0.695126i | \(0.244651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1689 | −0.748207 | −0.374103 | − | 0.927387i | \(-0.622049\pi\) | ||||
−0.374103 | + | 0.927387i | \(0.622049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.6235 | −0.952304 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.50432 | 0.437009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6431 | 0.671872 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.2748 | 0.560852 | 0.280426 | − | 0.959876i | \(-0.409524\pi\) | ||||
0.280426 | + | 0.959876i | \(0.409524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.5830 | −1.12089 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.5619 | 1.61478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2288 | −0.826024 | −0.413012 | − | 0.910726i | \(-0.635523\pi\) | ||||
−0.413012 | + | 0.910726i | \(0.635523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7400 | −0.890854 | −0.445427 | − | 0.895318i | \(-0.646948\pi\) | ||||
−0.445427 | + | 0.895318i | \(0.646948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00590 | 0.135379 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.2748 | −0.550602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9666 | −0.669998 | −0.334999 | − | 0.942218i | \(-0.608736\pi\) | ||||
−0.334999 | + | 0.942218i | \(0.608736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7424 | 1.14780 | 0.573899 | − | 0.818926i | \(-0.305430\pi\) | ||||
0.573899 | + | 0.818926i | \(0.305430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2915 | 0.502465 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.5005 | −1.70650 | −0.853252 | − | 0.521499i | \(-0.825373\pi\) | ||||
−0.853252 | + | 0.521499i | \(0.825373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.5830 | 1.17596 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.57113 | 0.157363 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3176 | 0.585709 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7105 | −0.819720 | −0.409860 | − | 0.912148i | \(-0.634422\pi\) | ||||
−0.409860 | + | 0.912148i | \(0.634422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.33138 | 0.189398 | 0.0946989 | − | 0.995506i | \(-0.469811\pi\) | ||||
0.0946989 | + | 0.995506i | \(0.469811\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.08709 | −0.0473543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.1660 | 1.65939 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0798 | −1.04301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.1660 | 1.95270 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.48925 | 0.322585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0495 | 0.518047 | 0.259024 | − | 0.965871i | \(-0.416599\pi\) | ||||
0.259024 | + | 0.965871i | \(0.416599\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.43560 | 0.275671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.32548 | 0.0566733 | 0.0283367 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283367 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.27980 | −0.0971229 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.8745 | 0.675053 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.0041 | −1.48317 | −0.741585 | − | 0.670859i | \(-0.765925\pi\) | ||||
−0.741585 | + | 0.670859i | \(0.765925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8745 | 1.26356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3111 | −0.982447 | −0.491224 | − | 0.871033i | \(-0.663450\pi\) | ||||
−0.491224 | + | 0.871033i | \(0.663450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.9767 | −0.502088 | −0.251044 | − | 0.967976i | \(-0.580774\pi\) | ||||
−0.251044 | + | 0.967976i | \(0.580774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.65685 | 0.236732 | 0.118366 | − | 0.992970i | \(-0.462234\pi\) | ||||
0.118366 | + | 0.992970i | \(0.462234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −49.2050 | −2.05199 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0405 | 1.45876 | 0.729378 | − | 0.684111i | \(-0.239810\pi\) | ||||
0.729378 | + | 0.684111i | \(0.239810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.33981 | 0.180046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.16601 | −0.379617 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.8823 | −1.10955 | −0.554775 | − | 0.832000i | \(-0.687196\pi\) | ||||
−0.554775 | + | 0.832000i | \(0.687196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.824494 | 0.0339727 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2748 | −0.504068 | −0.252034 | − | 0.967718i | \(-0.581099\pi\) | ||||
−0.252034 | + | 0.967718i | \(0.581099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.5940 | −1.54121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1964 | −1.23379 | −0.616896 | − | 0.787045i | \(-0.711610\pi\) | ||||
−0.616896 | + | 0.787045i | \(0.711610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.29150 | −0.297427 | −0.148713 | − | 0.988880i | \(-0.547513\pi\) | ||||
−0.148713 | + | 0.988880i | \(0.547513\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.2016 | −1.30918 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.1033 | 1.79010 | 0.895048 | − | 0.445970i | \(-0.147141\pi\) | ||||
0.895048 | + | 0.445970i | \(0.147141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.8608 | 1.69351 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.1995 | −1.21975 | −0.609873 | − | 0.792500i | \(-0.708779\pi\) | ||||
−0.609873 | + | 0.792500i | \(0.708779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.7424 | −1.03635 | −0.518175 | − | 0.855274i | \(-0.673389\pi\) | ||||
−0.518175 | + | 0.855274i | \(0.673389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9333 | −1.20312 | −0.601560 | − | 0.798828i | \(-0.705454\pi\) | ||||
−0.601560 | + | 0.798828i | \(0.705454\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.6504 | 1.38824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.8745 | −0.674980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.1617 | 0.803900 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2288 | −0.725675 | −0.362838 | − | 0.931852i | \(-0.618192\pi\) | ||||
−0.362838 | + | 0.931852i | \(0.618192\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.1934 | 1.99186 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.5406 | 0.932714 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.20614 | 0.363621 | 0.181810 | − | 0.983334i | \(-0.441804\pi\) | ||||
0.181810 | + | 0.983334i | \(0.441804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.32744 | −0.0917854 | −0.0458927 | − | 0.998946i | \(-0.514613\pi\) | ||||
−0.0458927 | + | 0.998946i | \(0.514613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.82087 | 0.307470 | 0.153735 | − | 0.988112i | \(-0.450870\pi\) | ||||
0.153735 | + | 0.988112i | \(0.450870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1660 | 0.516811 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.5025 | −0.410996 | −0.205498 | − | 0.978658i | \(-0.565881\pi\) | ||||
−0.205498 | + | 0.978658i | \(0.565881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.0245 | −1.32541 | −0.662704 | − | 0.748882i | \(-0.730591\pi\) | ||||
−0.662704 | + | 0.748882i | \(0.730591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.3357 | −1.60777 | −0.803886 | − | 0.594783i | \(-0.797238\pi\) | ||||
−0.803886 | + | 0.594783i | \(0.797238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.5129 | 1.10568 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.66079 | 0.296627 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.82087 | 0.301921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.12179 | −0.312146 | −0.156073 | − | 0.987746i | \(-0.549883\pi\) | ||||
−0.156073 | + | 0.987746i | \(0.549883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.5830 | 1.48068 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.1934 | 1.92060 | 0.960299 | − | 0.278974i | \(-0.0899944\pi\) | ||||
0.960299 | + | 0.278974i | \(0.0899944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.5626 | 2.04652 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.8111 | −1.09762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32744 | 0.0885401 | 0.0442701 | − | 0.999020i | \(-0.485904\pi\) | ||||
0.0442701 | + | 0.999020i | \(0.485904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.2835 | −1.18665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7490 | 0.748047 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.5220 | 0.888413 | 0.444206 | − | 0.895924i | \(-0.353486\pi\) | ||||
0.444206 | + | 0.895924i | \(0.353486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.2915 | −0.576730 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2508 | 0.460737 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.8210 | 1.87107 | 0.935533 | − | 0.353239i | \(-0.114920\pi\) | ||||
0.935533 | + | 0.353239i | \(0.114920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.77053 | −0.103757 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.9666 | 0.559720 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1007 | 0.376692 | 0.188346 | − | 0.982103i | \(-0.439687\pi\) | ||||
0.188346 | + | 0.982103i | \(0.439687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.87451 | 0.144294 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.16272 | −0.228878 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.3948 | −1.31272 | −0.656360 | − | 0.754448i | \(-0.727905\pi\) | ||||
−0.656360 | + | 0.754448i | \(0.727905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.5015 | −0.906221 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.4005 | −0.384150 | −0.192075 | − | 0.981380i | \(-0.561522\pi\) | ||||
−0.192075 | + | 0.981380i | \(0.561522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.73378 | −0.248042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.9038 | −1.72538 | −0.862692 | − | 0.505729i | \(-0.831224\pi\) | ||||
−0.862692 | + | 0.505729i | \(0.831224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.5547 | −0.533958 | −0.266979 | − | 0.963702i | \(-0.586026\pi\) | ||||
−0.266979 | + | 0.963702i | \(0.586026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.8745 | 0.654871 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.0030 | 1.79053 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.93725 | −0.107182 | −0.0535910 | − | 0.998563i | \(-0.517067\pi\) | ||||
−0.0535910 | + | 0.998563i | \(0.517067\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 52.5742 | 1.91337 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.1936 | 0.988367 | 0.494184 | − | 0.869358i | \(-0.335467\pi\) | ||||
0.494184 | + | 0.869358i | \(0.335467\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.43560 | 0.233290 | 0.116645 | − | 0.993174i | \(-0.462786\pi\) | ||||
0.116645 | + | 0.993174i | \(0.462786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.98233 | 0.252777 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.3842 | 1.49430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.70850 | 0.241915 | 0.120957 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120957 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.7195 | 0.745230 | 0.372615 | − | 0.927986i | \(-0.378461\pi\) | ||||
0.372615 | + | 0.927986i | \(0.378461\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22876 | 0.0800593 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.9785 | −0.536661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00787 | −0.143413 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.43560 | −0.229697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.6078 | −1.01976 | −0.509879 | − | 0.860246i | \(-0.670310\pi\) | ||||
−0.509879 | + | 0.860246i | \(0.670310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5830 | 0.872968 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.7195 | 0.733924 | 0.366962 | − | 0.930236i | \(-0.380398\pi\) | ||||
0.366962 | + | 0.930236i | \(0.380398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3320 | −1.21458 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.67963 | 0.306297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −95.8116 | −3.37691 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.4529 | 1.56288 | 0.781440 | − | 0.623981i | \(-0.214486\pi\) | ||||
0.781440 | + | 0.623981i | \(0.214486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6431 | 0.514189 | 0.257095 | − | 0.966386i | \(-0.417235\pi\) | ||||
0.257095 | + | 0.966386i | \(0.417235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.1964 | −1.05773 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5830 | 0.650137 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.6837 | −1.52457 | −0.762285 | − | 0.647241i | \(-0.775923\pi\) | ||||
−0.762285 | + | 0.647241i | \(0.775923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.77124 | 0.201173 | 0.100586 | − | 0.994928i | \(-0.467928\pi\) | ||||
0.100586 | + | 0.994928i | \(0.467928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.0604 | 0.384607 | 0.192304 | − | 0.981335i | \(-0.438404\pi\) | ||||
0.192304 | + | 0.981335i | \(0.438404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2289 | 0.459459 | 0.229729 | − | 0.973255i | \(-0.426216\pi\) | ||||
0.229729 | + | 0.973255i | \(0.426216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.3068 | −0.668941 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9666 | −0.517942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.1914 | −1.38756 | −0.693781 | − | 0.720186i | \(-0.744057\pi\) | ||||
−0.693781 | + | 0.720186i | \(0.744057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0405 | −0.966914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.36028 | 0.115597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.9373 | −1.20046 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.3838 | 1.76141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.56812 | −0.190649 | −0.0953244 | − | 0.995446i | \(-0.530389\pi\) | ||||
−0.0953244 | + | 0.995446i | \(0.530389\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.9399 | −0.544497 | −0.272249 | − | 0.962227i | \(-0.587767\pi\) | ||||
−0.272249 | + | 0.962227i | \(0.587767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.5783 | −1.55511 | −0.777557 | − | 0.628813i | \(-0.783541\pi\) | ||||
−0.777557 | + | 0.628813i | \(0.783541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.3619 | −0.454846 | −0.227423 | − | 0.973796i | \(-0.573030\pi\) | ||||
−0.227423 | + | 0.973796i | \(0.573030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.8745 | −0.879760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.18319 | 0.175828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.1660 | −0.717183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.8219 | 0.534877 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.57402 | 0.289524 | 0.144762 | − | 0.989467i | \(-0.453758\pi\) | ||||
0.144762 | + | 0.989467i | \(0.453758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.7878 | 1.37418 | 0.687088 | − | 0.726574i | \(-0.258889\pi\) | ||||
0.687088 | + | 0.726574i | \(0.258889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.2273 | 1.58933 | 0.794663 | − | 0.607051i | \(-0.207648\pi\) | ||||
0.794663 | + | 0.607051i | \(0.207648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0086 | −0.638247 | −0.319124 | − | 0.947713i | \(-0.603389\pi\) | ||||
−0.319124 | + | 0.947713i | \(0.603389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.4575 | 1.82645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.0389 | 0.871358 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.1660 | 1.50973 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.346998 | −0.0115730 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.6294 | 0.787209 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0773 | 0.733876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.5430 | 1.97709 | 0.988547 | − | 0.150916i | \(-0.0482224\pi\) | ||||
0.988547 | + | 0.150916i | \(0.0482224\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.8381 | 1.51869 | 0.759343 | − | 0.650691i | \(-0.225521\pi\) | ||||
0.759343 | + | 0.650691i | \(0.225521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.41699 | 0.0468957 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.67963 | 0.286627 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.1033 | 0.531198 | 0.265599 | − | 0.964084i | \(-0.414430\pi\) | ||||
0.265599 | + | 0.964084i | \(0.414430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.5978 | −0.414660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.3357 | −1.35911 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.3068 | 0.633436 | 0.316718 | − | 0.948520i | \(-0.397419\pi\) | ||||
0.316718 | + | 0.948520i | \(0.397419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.6431 | 0.479909 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.2748 | −0.401430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1660 | −0.364778 | −0.182389 | − | 0.983226i | \(-0.558383\pi\) | ||||
−0.182389 | + | 0.983226i | \(0.558383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.5414 | −1.19122 | −0.595608 | − | 0.803275i | \(-0.703089\pi\) | ||||
−0.595608 | + | 0.803275i | \(0.703089\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.3320 | 1.63904 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.4411 | 0.436778 | 0.218389 | − | 0.975862i | \(-0.429920\pi\) | ||||
0.218389 | + | 0.975862i | \(0.429920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.2823 | 0.885621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.8479 | 0.804902 | 0.402451 | − | 0.915442i | \(-0.368158\pi\) | ||||
0.402451 | + | 0.915442i | \(0.368158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.5940 | 1.21651 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.1130 | 1.87657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8745 | −0.995952 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −66.7840 | −2.14985 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3948 | 0.752325 | 0.376162 | − | 0.926554i | \(-0.377243\pi\) | ||||
0.376162 | + | 0.926554i | \(0.377243\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.0511 | 1.38158 | 0.690789 | − | 0.723057i | \(-0.257264\pi\) | ||||
0.690789 | + | 0.723057i | \(0.257264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.9411 | −1.08810 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.8565 | 1.40309 | 0.701547 | − | 0.712623i | \(-0.252493\pi\) | ||||
0.701547 | + | 0.712623i | \(0.252493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3137 | 0.361588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.73378 | −0.214774 | −0.107387 | − | 0.994217i | \(-0.534248\pi\) | ||||
−0.107387 | + | 0.994217i | \(0.534248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.8745 | −1.33423 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.4442 | −1.98561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9373 | −0.601562 | −0.300781 | − | 0.953693i | \(-0.597247\pi\) | ||||
−0.300781 | + | 0.953693i | \(0.597247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.0726 | 0.889963 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.735758 | 0.0233017 | 0.0116508 | − | 0.999932i | \(-0.496291\pi\) | ||||
0.0116508 | + | 0.999932i | \(0.496291\pi\) | |||||||
\(998\) | 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 | 9216.2.a.bt.1.8 | 8 | ||
3.2 | odd | 2 | inner | 9216.2.a.bt.1.2 | 8 | ||
4.3 | odd | 2 | 9216.2.a.bq.1.8 | 8 | |||
8.3 | odd | 2 | 9216.2.a.bq.1.1 | 8 | |||
8.5 | even | 2 | inner | 9216.2.a.bt.1.1 | 8 | ||
12.11 | even | 2 | 9216.2.a.bq.1.2 | 8 | |||
24.5 | odd | 2 | inner | 9216.2.a.bt.1.7 | 8 | ||
24.11 | even | 2 | 9216.2.a.bq.1.7 | 8 | |||
32.3 | odd | 8 | 144.2.k.c.109.2 | yes | 8 | ||
32.5 | even | 8 | 1152.2.k.d.865.4 | 8 | |||
32.11 | odd | 8 | 144.2.k.c.37.2 | ✓ | 8 | ||
32.13 | even | 8 | 1152.2.k.d.289.4 | 8 | |||
32.19 | odd | 8 | 1152.2.k.e.289.4 | 8 | |||
32.21 | even | 8 | 576.2.k.c.433.1 | 8 | |||
32.27 | odd | 8 | 1152.2.k.e.865.4 | 8 | |||
32.29 | even | 8 | 576.2.k.c.145.1 | 8 | |||
96.5 | odd | 8 | 1152.2.k.d.865.1 | 8 | |||
96.11 | even | 8 | 144.2.k.c.37.3 | yes | 8 | ||
96.29 | odd | 8 | 576.2.k.c.145.4 | 8 | |||
96.35 | even | 8 | 144.2.k.c.109.3 | yes | 8 | ||
96.53 | odd | 8 | 576.2.k.c.433.4 | 8 | |||
96.59 | even | 8 | 1152.2.k.e.865.1 | 8 | |||
96.77 | odd | 8 | 1152.2.k.d.289.1 | 8 | |||
96.83 | even | 8 | 1152.2.k.e.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.2 | ✓ | 8 | 32.11 | odd | 8 | ||
144.2.k.c.37.3 | yes | 8 | 96.11 | even | 8 | ||
144.2.k.c.109.2 | yes | 8 | 32.3 | odd | 8 | ||
144.2.k.c.109.3 | yes | 8 | 96.35 | even | 8 | ||
576.2.k.c.145.1 | 8 | 32.29 | even | 8 | |||
576.2.k.c.145.4 | 8 | 96.29 | odd | 8 | |||
576.2.k.c.433.1 | 8 | 32.21 | even | 8 | |||
576.2.k.c.433.4 | 8 | 96.53 | odd | 8 | |||
1152.2.k.d.289.1 | 8 | 96.77 | odd | 8 | |||
1152.2.k.d.289.4 | 8 | 32.13 | even | 8 | |||
1152.2.k.d.865.1 | 8 | 96.5 | odd | 8 | |||
1152.2.k.d.865.4 | 8 | 32.5 | even | 8 | |||
1152.2.k.e.289.1 | 8 | 96.83 | even | 8 | |||
1152.2.k.e.289.4 | 8 | 32.19 | odd | 8 | |||
1152.2.k.e.865.1 | 8 | 96.59 | even | 8 | |||
1152.2.k.e.865.4 | 8 | 32.27 | odd | 8 | |||
9216.2.a.bq.1.1 | 8 | 8.3 | odd | 2 | |||
9216.2.a.bq.1.2 | 8 | 12.11 | even | 2 | |||
9216.2.a.bq.1.7 | 8 | 24.11 | even | 2 | |||
9216.2.a.bq.1.8 | 8 | 4.3 | odd | 2 | |||
9216.2.a.bt.1.1 | 8 | 8.5 | even | 2 | inner | ||
9216.2.a.bt.1.2 | 8 | 3.2 | odd | 2 | inner | ||
9216.2.a.bt.1.7 | 8 | 24.5 | odd | 2 | inner | ||
9216.2.a.bt.1.8 | 8 | 1.1 | even | 1 | trivial |