Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2x^{8} - 12x^{7} + 21x^{6} + 48x^{5} - 68x^{4} - 73x^{3} + 66x^{2} + 40x - 10 \) |
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 | 1.1 | ||
Root | \(-2.21081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21081 | −1.56328 | −0.781638 | − | 0.623733i | \(-0.785615\pi\) | ||||
−0.781638 | + | 0.623733i | \(0.785615\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.88766 | 1.44383 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.31646 | 0.497576 | 0.248788 | − | 0.968558i | \(-0.419968\pi\) | ||||
0.248788 | + | 0.968558i | \(0.419968\pi\) | |||||||
\(8\) | −1.96245 | −0.693830 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29189 | 1.29405 | 0.647027 | − | 0.762467i | \(-0.276012\pi\) | ||||
0.647027 | + | 0.762467i | \(0.276012\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.97543 | 0.825235 | 0.412617 | − | 0.910904i | \(-0.364615\pi\) | ||||
0.412617 | + | 0.910904i | \(0.364615\pi\) | |||||||
\(14\) | −2.91044 | −0.777849 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.43674 | −0.359184 | ||||||||
\(17\) | 0.642441 | 0.155815 | 0.0779074 | − | 0.996961i | \(-0.475176\pi\) | ||||
0.0779074 | + | 0.996961i | \(0.475176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.07923 | −1.16525 | −0.582627 | − | 0.812740i | \(-0.697975\pi\) | ||||
−0.582627 | + | 0.812740i | \(0.697975\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.48853 | −2.02296 | ||||||||
\(23\) | 8.84038 | 1.84335 | 0.921674 | − | 0.387966i | \(-0.126822\pi\) | ||||
0.921674 | + | 0.387966i | \(0.126822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.57809 | −1.29007 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.80150 | 0.718416 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.27016 | −1.12615 | −0.563077 | − | 0.826404i | \(-0.690383\pi\) | ||||
−0.563077 | + | 0.826404i | \(0.690383\pi\) | |||||||
\(32\) | 7.10123 | 1.25533 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.42031 | −0.243582 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.934054 | −0.153558 | −0.0767788 | − | 0.997048i | \(-0.524464\pi\) | ||||
−0.0767788 | + | 0.997048i | \(0.524464\pi\) | |||||||
\(38\) | 11.2292 | 1.82161 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0792 | 1.73028 | 0.865139 | − | 0.501533i | \(-0.167230\pi\) | ||||
0.865139 | + | 0.501533i | \(0.167230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.03981 | −0.311068 | −0.155534 | − | 0.987831i | \(-0.549710\pi\) | ||||
−0.155534 | + | 0.987831i | \(0.549710\pi\) | |||||||
\(44\) | 12.3935 | 1.86839 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −19.5444 | −2.88166 | ||||||||
\(47\) | 9.57178 | 1.39619 | 0.698094 | − | 0.716006i | \(-0.254032\pi\) | ||||
0.698094 | + | 0.716006i | \(0.254032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.26692 | −0.752418 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.59203 | 1.19150 | ||||||||
\(53\) | −13.0891 | −1.79792 | −0.898960 | − | 0.438030i | \(-0.855676\pi\) | ||||
−0.898960 | + | 0.438030i | \(0.855676\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.58349 | −0.345233 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.21081 | 0.290293 | ||||||||
\(59\) | −2.55069 | −0.332071 | −0.166036 | − | 0.986120i | \(-0.553097\pi\) | ||||
−0.166036 | + | 0.986120i | \(0.553097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.46575 | 1.08393 | 0.541964 | − | 0.840402i | \(-0.317681\pi\) | ||||
0.541964 | + | 0.840402i | \(0.317681\pi\) | |||||||
\(62\) | 13.8621 | 1.76049 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8260 | −1.60325 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9808 | 1.58586 | 0.792930 | − | 0.609313i | \(-0.208555\pi\) | ||||
0.792930 | + | 0.609313i | \(0.208555\pi\) | |||||||
\(68\) | 1.85515 | 0.224970 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.10419 | 0.605756 | 0.302878 | − | 0.953029i | \(-0.402053\pi\) | ||||
0.302878 | + | 0.953029i | \(0.402053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0007 | 1.87274 | 0.936372 | − | 0.351009i | \(-0.114161\pi\) | ||||
0.936372 | + | 0.351009i | \(0.114161\pi\) | |||||||
\(74\) | 2.06501 | 0.240053 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.6671 | −1.68243 | ||||||||
\(77\) | 5.65012 | 0.643890 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.30518 | −0.371861 | −0.185931 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185931 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24.4939 | −2.70490 | ||||||||
\(83\) | 5.24640 | 0.575867 | 0.287934 | − | 0.957650i | \(-0.407032\pi\) | ||||
0.287934 | + | 0.957650i | \(0.407032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.50962 | 0.486284 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.42260 | −0.897853 | ||||||||
\(89\) | −5.05088 | −0.535392 | −0.267696 | − | 0.963503i | \(-0.586262\pi\) | ||||
−0.267696 | + | 0.963503i | \(0.586262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.91704 | 0.410617 | ||||||||
\(92\) | 25.5280 | 2.66148 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.1614 | −2.18263 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.04414 | 0.207551 | 0.103776 | − | 0.994601i | \(-0.466908\pi\) | ||||
0.103776 | + | 0.994601i | \(0.466908\pi\) | |||||||
\(98\) | 11.6441 | 1.17624 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4871 | −1.24251 | −0.621255 | − | 0.783609i | \(-0.713377\pi\) | ||||
−0.621255 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6723 | 1.05157 | 0.525785 | − | 0.850617i | \(-0.323772\pi\) | ||||
0.525785 | + | 0.850617i | \(0.323772\pi\) | |||||||
\(104\) | −5.83912 | −0.572572 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.9374 | 2.81065 | ||||||||
\(107\) | −4.85956 | −0.469791 | −0.234896 | − | 0.972021i | \(-0.575475\pi\) | ||||
−0.234896 | + | 0.972021i | \(0.575475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3415 | 1.46945 | 0.734723 | − | 0.678367i | \(-0.237312\pi\) | ||||
0.734723 | + | 0.678367i | \(0.237312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.89141 | −0.178721 | ||||||||
\(113\) | 4.32180 | 0.406560 | 0.203280 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203280 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.88766 | −0.268113 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.63908 | 0.519119 | ||||||||
\(119\) | 0.845750 | 0.0775298 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.42032 | 0.674575 | ||||||||
\(122\) | −18.7161 | −1.69448 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.1061 | −1.62598 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5809 | −1.91500 | −0.957498 | − | 0.288440i | \(-0.906863\pi\) | ||||
−0.957498 | + | 0.288440i | \(0.906863\pi\) | |||||||
\(128\) | 14.1533 | 1.25098 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.25658 | 0.808751 | 0.404376 | − | 0.914593i | \(-0.367489\pi\) | ||||
0.404376 | + | 0.914593i | \(0.367489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.68661 | −0.579803 | ||||||||
\(134\) | −28.6981 | −2.47914 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.26076 | −0.108109 | ||||||||
\(137\) | −0.843767 | −0.0720879 | −0.0360439 | − | 0.999350i | \(-0.511476\pi\) | ||||
−0.0360439 | + | 0.999350i | \(0.511476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9777 | −1.18557 | −0.592785 | − | 0.805361i | \(-0.701972\pi\) | ||||
−0.592785 | + | 0.805361i | \(0.701972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.2844 | −0.946964 | ||||||||
\(143\) | 12.7702 | 1.06790 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −35.3745 | −2.92762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.69723 | −0.221711 | ||||||||
\(149\) | 19.6274 | 1.60794 | 0.803971 | − | 0.594669i | \(-0.202717\pi\) | ||||
0.803971 | + | 0.594669i | \(0.202717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7559 | −0.875301 | −0.437650 | − | 0.899145i | \(-0.644189\pi\) | ||||
−0.437650 | + | 0.899145i | \(0.644189\pi\) | |||||||
\(152\) | 9.96771 | 0.808488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.4913 | −1.00658 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.5513 | −1.87960 | −0.939800 | − | 0.341724i | \(-0.888989\pi\) | ||||
−0.939800 | + | 0.341724i | \(0.888989\pi\) | |||||||
\(158\) | 7.30710 | 0.581322 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6380 | 0.917206 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50148 | −0.744213 | −0.372107 | − | 0.928190i | \(-0.621364\pi\) | ||||
−0.372107 | + | 0.928190i | \(0.621364\pi\) | |||||||
\(164\) | 31.9929 | 2.49823 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5988 | −0.900239 | ||||||||
\(167\) | −1.82786 | −0.141444 | −0.0707220 | − | 0.997496i | \(-0.522530\pi\) | ||||
−0.0707220 | + | 0.997496i | \(0.522530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.14683 | −0.318987 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.89027 | −0.449129 | ||||||||
\(173\) | 5.50734 | 0.418715 | 0.209358 | − | 0.977839i | \(-0.432863\pi\) | ||||
0.209358 | + | 0.977839i | \(0.432863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.16631 | −0.464803 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.1665 | 0.836966 | ||||||||
\(179\) | 9.36470 | 0.699950 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6019 | 1.90297 | 0.951487 | − | 0.307688i | \(-0.0995552\pi\) | ||||
0.951487 | + | 0.307688i | \(0.0995552\pi\) | |||||||
\(182\) | −8.65981 | −0.641908 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.3488 | −1.27897 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.75729 | 0.201633 | ||||||||
\(188\) | 27.6401 | 2.01586 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.3658 | −0.894756 | −0.447378 | − | 0.894345i | \(-0.647642\pi\) | ||||
−0.447378 | + | 0.894345i | \(0.647642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.7223 | 1.13172 | 0.565859 | − | 0.824502i | \(-0.308545\pi\) | ||||
0.565859 | + | 0.824502i | \(0.308545\pi\) | |||||||
\(194\) | −4.51920 | −0.324459 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15.2091 | −1.08636 | ||||||||
\(197\) | 21.6728 | 1.54412 | 0.772061 | − | 0.635549i | \(-0.219226\pi\) | ||||
0.772061 | + | 0.635549i | \(0.219226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.23732 | −0.0877116 | −0.0438558 | − | 0.999038i | \(-0.513964\pi\) | ||||
−0.0438558 | + | 0.999038i | \(0.513964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27.6065 | 1.94238 | ||||||||
\(203\) | −1.31646 | −0.0923976 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.5943 | −1.64389 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.27490 | −0.296411 | ||||||||
\(209\) | −21.7995 | −1.50790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.05346 | −0.347895 | −0.173947 | − | 0.984755i | \(-0.555652\pi\) | ||||
−0.173947 | + | 0.984755i | \(0.555652\pi\) | |||||||
\(212\) | −37.7968 | −2.59589 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.7435 | 0.734413 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.25444 | −0.560348 | ||||||||
\(218\) | −33.9170 | −2.29715 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.91154 | 0.128584 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2248 | 1.08649 | 0.543245 | − | 0.839574i | \(-0.317195\pi\) | ||||
0.543245 | + | 0.839574i | \(0.317195\pi\) | |||||||
\(224\) | 9.34851 | 0.624624 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.55465 | −0.635566 | ||||||||
\(227\) | 6.82690 | 0.453117 | 0.226559 | − | 0.973998i | \(-0.427253\pi\) | ||||
0.226559 | + | 0.973998i | \(0.427253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.87121 | −0.387980 | −0.193990 | − | 0.981003i | \(-0.562143\pi\) | ||||
−0.193990 | + | 0.981003i | \(0.562143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.96245 | 0.128841 | ||||||||
\(233\) | −14.1453 | −0.926692 | −0.463346 | − | 0.886178i | \(-0.653351\pi\) | ||||
−0.463346 | + | 0.886178i | \(0.653351\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.36553 | −0.479455 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.86979 | −0.121200 | ||||||||
\(239\) | −20.6920 | −1.33845 | −0.669226 | − | 0.743059i | \(-0.733374\pi\) | ||||
−0.669226 | + | 0.743059i | \(0.733374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.90845 | −0.509428 | −0.254714 | − | 0.967016i | \(-0.581981\pi\) | ||||
−0.254714 | + | 0.967016i | \(0.581981\pi\) | |||||||
\(242\) | −16.4049 | −1.05455 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.4462 | 1.56501 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1129 | −0.961609 | ||||||||
\(248\) | 12.3049 | 0.781359 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8140 | 0.745691 | 0.372846 | − | 0.927893i | \(-0.378382\pi\) | ||||
0.372846 | + | 0.927893i | \(0.378382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.9420 | 2.38539 | ||||||||
\(254\) | 47.7112 | 2.99367 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.63818 | −0.352386 | ||||||||
\(257\) | −4.35440 | −0.271620 | −0.135810 | − | 0.990735i | \(-0.543364\pi\) | ||||
−0.135810 | + | 0.990735i | \(0.543364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.22965 | −0.0764066 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.4645 | −1.26430 | ||||||||
\(263\) | 27.6727 | 1.70637 | 0.853187 | − | 0.521605i | \(-0.174666\pi\) | ||||
0.853187 | + | 0.521605i | \(0.174666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.7828 | 0.906392 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 37.4842 | 2.28971 | ||||||||
\(269\) | −6.32037 | −0.385360 | −0.192680 | − | 0.981262i | \(-0.561718\pi\) | ||||
−0.192680 | + | 0.981262i | \(0.561718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.37191 | 0.265575 | 0.132787 | − | 0.991145i | \(-0.457607\pi\) | ||||
0.132787 | + | 0.991145i | \(0.457607\pi\) | |||||||
\(272\) | −0.923018 | −0.0559662 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.86540 | 0.112693 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.01638 | 0.241321 | 0.120660 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120660 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(278\) | 30.9019 | 1.85337 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6990 | −0.817215 | −0.408607 | − | 0.912710i | \(-0.633985\pi\) | ||||
−0.408607 | + | 0.912710i | \(0.633985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8058 | 0.880114 | 0.440057 | − | 0.897970i | \(-0.354958\pi\) | ||||
0.440057 | + | 0.897970i | \(0.354958\pi\) | |||||||
\(284\) | 14.7392 | 0.874609 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.2324 | −1.66942 | ||||||||
\(287\) | 14.5853 | 0.860945 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5873 | −0.975722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 46.2047 | 2.70393 | ||||||||
\(293\) | −16.6890 | −0.974983 | −0.487492 | − | 0.873128i | \(-0.662088\pi\) | ||||
−0.487492 | + | 0.873128i | \(0.662088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.83303 | 0.106543 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −43.3924 | −2.51366 | ||||||||
\(299\) | 26.3039 | 1.52119 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.68533 | −0.154780 | ||||||||
\(302\) | 23.7792 | 1.36834 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.29750 | 0.418540 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.97073 | −0.283695 | −0.141847 | − | 0.989889i | \(-0.545304\pi\) | ||||
−0.141847 | + | 0.989889i | \(0.545304\pi\) | |||||||
\(308\) | 16.3156 | 0.929669 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0786 | −1.19526 | −0.597629 | − | 0.801773i | \(-0.703890\pi\) | ||||
−0.597629 | + | 0.801773i | \(0.703890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3744 | −1.37772 | −0.688860 | − | 0.724894i | \(-0.741889\pi\) | ||||
−0.688860 | + | 0.724894i | \(0.741889\pi\) | |||||||
\(314\) | 52.0674 | 2.93833 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.54423 | −0.536905 | ||||||||
\(317\) | −13.4102 | −0.753194 | −0.376597 | − | 0.926377i | \(-0.622906\pi\) | ||||
−0.376597 | + | 0.926377i | \(0.622906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.29189 | −0.240300 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25.7294 | −1.43385 | ||||||||
\(323\) | −3.26310 | −0.181564 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.0059 | 1.16341 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.7423 | −1.20052 | ||||||||
\(329\) | 12.6009 | 0.694710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4187 | 1.28721 | 0.643603 | − | 0.765360i | \(-0.277439\pi\) | ||||
0.643603 | + | 0.765360i | \(0.277439\pi\) | |||||||
\(332\) | 15.1498 | 0.831455 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.04104 | 0.221116 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.7865 | −1.24126 | −0.620631 | − | 0.784103i | \(-0.713123\pi\) | ||||
−0.620631 | + | 0.784103i | \(0.713123\pi\) | |||||||
\(338\) | 9.16784 | 0.498665 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.9108 | −1.45730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1490 | −0.871962 | ||||||||
\(344\) | 4.00301 | 0.215828 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.1757 | −0.654567 | ||||||||
\(347\) | 4.98513 | 0.267616 | 0.133808 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133808 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.6783 | 1.37453 | 0.687264 | − | 0.726407i | \(-0.258811\pi\) | ||||
0.687264 | + | 0.726407i | \(0.258811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30.4777 | 1.62447 | ||||||||
\(353\) | 20.3160 | 1.08131 | 0.540656 | − | 0.841244i | \(-0.318176\pi\) | ||||
0.540656 | + | 0.841244i | \(0.318176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.5852 | −0.773016 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.7035 | −1.09422 | ||||||||
\(359\) | −9.68907 | −0.511370 | −0.255685 | − | 0.966760i | \(-0.582301\pi\) | ||||
−0.255685 | + | 0.966760i | \(0.582301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.79854 | 0.357818 | ||||||||
\(362\) | −56.6008 | −2.97487 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.3111 | 0.592862 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.16319 | −0.478315 | −0.239157 | − | 0.970981i | \(-0.576871\pi\) | ||||
−0.239157 | + | 0.970981i | \(0.576871\pi\) | |||||||
\(368\) | −12.7013 | −0.662101 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.2313 | −0.894603 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5773 | 0.703007 | 0.351504 | − | 0.936186i | \(-0.385670\pi\) | ||||
0.351504 | + | 0.936186i | \(0.385670\pi\) | |||||||
\(374\) | −6.09582 | −0.315208 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.7841 | −0.968717 | ||||||||
\(377\) | −2.97543 | −0.153242 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0601424 | 0.00308931 | 0.00154465 | − | 0.999999i | \(-0.499508\pi\) | ||||
0.00154465 | + | 0.999999i | \(0.499508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 27.3383 | 1.39875 | ||||||||
\(383\) | −9.71642 | −0.496486 | −0.248243 | − | 0.968698i | \(-0.579853\pi\) | ||||
−0.248243 | + | 0.968698i | \(0.579853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.7590 | −1.76919 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.90279 | 0.299669 | ||||||||
\(389\) | 5.68991 | 0.288490 | 0.144245 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144245 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.67943 | 0.287221 | ||||||||
\(392\) | 10.3361 | 0.522050 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −47.9143 | −2.41389 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.80729 | −0.341648 | −0.170824 | − | 0.985302i | \(-0.554643\pi\) | ||||
−0.170824 | + | 0.985302i | \(0.554643\pi\) | |||||||
\(398\) | 2.73548 | 0.137117 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7255 | 0.585543 | 0.292771 | − | 0.956182i | \(-0.405422\pi\) | ||||
0.292771 | + | 0.956182i | \(0.405422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6564 | −0.929342 | ||||||||
\(404\) | −36.0584 | −1.79397 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.91044 | 0.144443 | ||||||||
\(407\) | −4.00886 | −0.198712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.2665 | −1.10101 | −0.550505 | − | 0.834832i | \(-0.685565\pi\) | ||||
−0.550505 | + | 0.834832i | \(0.685565\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.8179 | 1.51829 | ||||||||
\(413\) | −3.35789 | −0.165231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.1292 | 1.03594 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 48.1944 | 2.35727 | ||||||||
\(419\) | −28.2149 | −1.37839 | −0.689194 | − | 0.724577i | \(-0.742035\pi\) | ||||
−0.689194 | + | 0.724577i | \(0.742035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.5167 | −1.68224 | −0.841121 | − | 0.540847i | \(-0.818104\pi\) | ||||
−0.841121 | + | 0.540847i | \(0.818104\pi\) | |||||||
\(422\) | 11.1722 | 0.543855 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.6866 | 1.24745 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1449 | 0.539337 | ||||||||
\(428\) | −14.0328 | −0.678299 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.0678 | 1.11114 | 0.555568 | − | 0.831471i | \(-0.312501\pi\) | ||||
0.555568 | + | 0.831471i | \(0.312501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.8519 | 0.857908 | 0.428954 | − | 0.903326i | \(-0.358882\pi\) | ||||
0.428954 | + | 0.903326i | \(0.358882\pi\) | |||||||
\(434\) | 18.2490 | 0.875978 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 44.3010 | 2.12163 | ||||||||
\(437\) | −44.9023 | −2.14797 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.31655 | −0.158290 | −0.0791452 | − | 0.996863i | \(-0.525219\pi\) | ||||
−0.0791452 | + | 0.996863i | \(0.525219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.22604 | −0.201012 | ||||||||
\(443\) | 29.8818 | 1.41973 | 0.709863 | − | 0.704340i | \(-0.248757\pi\) | ||||
0.709863 | + | 0.704340i | \(0.248757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −35.8698 | −1.69848 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.8849 | −0.797738 | ||||||||
\(449\) | 8.89198 | 0.419639 | 0.209819 | − | 0.977740i | \(-0.432712\pi\) | ||||
0.209819 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.5506 | 2.23907 | ||||||||
\(452\) | 12.4799 | 0.587004 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.0929 | −0.708347 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8853 | 0.930194 | 0.465097 | − | 0.885260i | \(-0.346019\pi\) | ||||
0.465097 | + | 0.885260i | \(0.346019\pi\) | |||||||
\(458\) | 12.9801 | 0.606520 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5776 | −0.632372 | −0.316186 | − | 0.948697i | \(-0.602402\pi\) | ||||
−0.316186 | + | 0.948697i | \(0.602402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.7645 | −1.38328 | −0.691638 | − | 0.722244i | \(-0.743111\pi\) | ||||
−0.691638 | + | 0.722244i | \(0.743111\pi\) | |||||||
\(464\) | 1.43674 | 0.0666988 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 31.2726 | 1.44867 | ||||||||
\(467\) | 6.56767 | 0.303915 | 0.151958 | − | 0.988387i | \(-0.451442\pi\) | ||||
0.151958 | + | 0.988387i | \(0.451442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.0888 | 0.789086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.00559 | 0.230401 | ||||||||
\(473\) | −8.75463 | −0.402538 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.44224 | 0.111940 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 45.7459 | 2.09237 | ||||||||
\(479\) | 36.9147 | 1.68668 | 0.843338 | − | 0.537383i | \(-0.180587\pi\) | ||||
0.843338 | + | 0.537383i | \(0.180587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.77921 | −0.126721 | ||||||||
\(482\) | 17.4840 | 0.796376 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.4274 | 0.973972 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.4257 | −1.10684 | −0.553418 | − | 0.832904i | \(-0.686677\pi\) | ||||
−0.553418 | + | 0.832904i | \(0.686677\pi\) | |||||||
\(488\) | −16.6136 | −0.752062 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.828059 | −0.0373698 | −0.0186849 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186849 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.642441 | −0.0289341 | ||||||||
\(494\) | 33.4116 | 1.50326 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.00856 | 0.404496 | ||||||||
\(497\) | 6.71948 | 0.301410 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.7413 | 1.46570 | 0.732850 | − | 0.680390i | \(-0.238189\pi\) | ||||
0.732850 | + | 0.680390i | \(0.238189\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.1184 | −1.16572 | ||||||||
\(503\) | 3.04972 | 0.135980 | 0.0679901 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679901 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −83.8823 | −3.72902 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −62.3183 | −2.76493 | ||||||||
\(509\) | 11.2666 | 0.499384 | 0.249692 | − | 0.968325i | \(-0.419671\pi\) | ||||
0.249692 | + | 0.968325i | \(0.419671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.0644 | 0.931833 | ||||||||
\(512\) | −15.8416 | −0.700107 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.62673 | 0.424617 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.0810 | 1.80674 | ||||||||
\(518\) | 2.71851 | 0.119445 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.39366 | −0.0610573 | −0.0305287 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305287 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6212 | 0.464434 | 0.232217 | − | 0.972664i | \(-0.425402\pi\) | ||||
0.232217 | + | 0.972664i | \(0.425402\pi\) | |||||||
\(524\) | 26.7299 | 1.16770 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −61.1791 | −2.66753 | ||||||||
\(527\) | −4.02821 | −0.175472 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.1524 | 2.39793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.3087 | −0.837137 | ||||||||
\(533\) | 32.9653 | 1.42789 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.4742 | −1.10032 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.9731 | 0.602424 | ||||||||
\(539\) | −22.6051 | −0.973669 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1071 | 1.33740 | 0.668698 | − | 0.743534i | \(-0.266852\pi\) | ||||
0.668698 | + | 0.743534i | \(0.266852\pi\) | |||||||
\(542\) | −9.66544 | −0.415166 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.56212 | 0.195599 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0828 | 0.730408 | 0.365204 | − | 0.930927i | \(-0.380999\pi\) | ||||
0.365204 | + | 0.930927i | \(0.380999\pi\) | |||||||
\(548\) | −2.43651 | −0.104083 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.07923 | 0.216382 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.35114 | −0.185029 | ||||||||
\(554\) | −8.87942 | −0.377251 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.3628 | −1.71176 | ||||||||
\(557\) | −15.1831 | −0.643329 | −0.321665 | − | 0.946854i | \(-0.604242\pi\) | ||||
−0.321665 | + | 0.946854i | \(0.604242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.06930 | −0.256704 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.2859 | 1.27753 | ||||||||
\(563\) | −34.9344 | −1.47231 | −0.736154 | − | 0.676814i | \(-0.763360\pi\) | ||||
−0.736154 | + | 0.676814i | \(0.763360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.7328 | −1.37586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.0167 | −0.420291 | ||||||||
\(569\) | −2.51836 | −0.105575 | −0.0527875 | − | 0.998606i | \(-0.516811\pi\) | ||||
−0.0527875 | + | 0.998606i | \(0.516811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.9130 | 0.791485 | 0.395742 | − | 0.918362i | \(-0.370487\pi\) | ||||
0.395742 | + | 0.918362i | \(0.370487\pi\) | |||||||
\(572\) | 36.8760 | 1.54186 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.2453 | −1.34589 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.64049 | 0.193186 | 0.0965930 | − | 0.995324i | \(-0.469205\pi\) | ||||
0.0965930 | + | 0.995324i | \(0.469205\pi\) | |||||||
\(578\) | 36.6712 | 1.52532 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.90669 | 0.286538 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −56.1768 | −2.32661 | ||||||||
\(584\) | −31.4006 | −1.29937 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.8962 | 1.52417 | ||||||||
\(587\) | 25.7669 | 1.06351 | 0.531756 | − | 0.846897i | \(-0.321532\pi\) | ||||
0.531756 | + | 0.846897i | \(0.321532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.8476 | 1.31226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.34199 | 0.0551554 | ||||||||
\(593\) | −3.02524 | −0.124232 | −0.0621158 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621158 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 56.6774 | 2.32160 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −58.1529 | −2.37805 | ||||||||
\(599\) | 0.521774 | 0.0213191 | 0.0106596 | − | 0.999943i | \(-0.496607\pi\) | ||||
0.0106596 | + | 0.999943i | \(0.496607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.7237 | −1.41641 | −0.708204 | − | 0.706008i | \(-0.750494\pi\) | ||||
−0.708204 | + | 0.706008i | \(0.750494\pi\) | |||||||
\(602\) | 5.93674 | 0.241964 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.0593 | −1.26379 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0480 | −0.570190 | −0.285095 | − | 0.958499i | \(-0.592025\pi\) | ||||
−0.285095 | + | 0.958499i | \(0.592025\pi\) | |||||||
\(608\) | −36.0688 | −1.46278 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.4801 | 1.15218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3819 | 0.621269 | 0.310635 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310635 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(614\) | 10.9893 | 0.443493 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0880 | −0.446750 | ||||||||
\(617\) | 15.6734 | 0.630988 | 0.315494 | − | 0.948928i | \(-0.397830\pi\) | ||||
0.315494 | + | 0.948928i | \(0.397830\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.1380 | 1.45251 | 0.726254 | − | 0.687427i | \(-0.241260\pi\) | ||||
0.726254 | + | 0.687427i | \(0.241260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.6007 | 1.86852 | ||||||||
\(623\) | −6.64930 | −0.266399 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 53.8870 | 2.15376 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −68.0083 | −2.71383 | ||||||||
\(629\) | −0.600075 | −0.0239265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.20523 | −0.207217 | −0.103608 | − | 0.994618i | \(-0.533039\pi\) | ||||
−0.103608 | + | 0.994618i | \(0.533039\pi\) | |||||||
\(632\) | 6.48623 | 0.258008 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.6474 | 1.17745 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6714 | −0.620921 | ||||||||
\(638\) | 9.48853 | 0.375655 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.6342 | 1.13098 | 0.565492 | − | 0.824754i | \(-0.308686\pi\) | ||||
0.565492 | + | 0.824754i | \(0.308686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.6717 | −1.40676 | −0.703378 | − | 0.710816i | \(-0.748326\pi\) | ||||
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(644\) | 33.6067 | 1.32429 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.21409 | 0.283834 | ||||||||
\(647\) | 6.14445 | 0.241563 | 0.120782 | − | 0.992679i | \(-0.461460\pi\) | ||||
0.120782 | + | 0.992679i | \(0.461460\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9473 | −0.429718 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.4371 | −1.07452 | ||||||||
\(653\) | 8.62982 | 0.337711 | 0.168855 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168855 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.9178 | −0.621488 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.8581 | −1.08602 | ||||||||
\(659\) | −35.4336 | −1.38030 | −0.690148 | − | 0.723668i | \(-0.742455\pi\) | ||||
−0.690148 | + | 0.723668i | \(0.742455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7938 | 0.497622 | 0.248811 | − | 0.968552i | \(-0.419960\pi\) | ||||
0.248811 | + | 0.968552i | \(0.419960\pi\) | |||||||
\(662\) | −51.7741 | −2.01226 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.2958 | −0.399554 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.84038 | −0.342301 | ||||||||
\(668\) | −5.27824 | −0.204221 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.3341 | 1.40266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.0602 | 1.50566 | 0.752830 | − | 0.658215i | \(-0.228688\pi\) | ||||
0.752830 | + | 0.658215i | \(0.228688\pi\) | |||||||
\(674\) | 50.3766 | 1.94043 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.9747 | −0.460564 | ||||||||
\(677\) | 51.8790 | 1.99387 | 0.996936 | − | 0.0782187i | \(-0.0249233\pi\) | ||||
0.996936 | + | 0.0782187i | \(0.0249233\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.69104 | 0.103272 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 59.4946 | 2.27817 | ||||||||
\(683\) | 27.2220 | 1.04162 | 0.520811 | − | 0.853672i | \(-0.325630\pi\) | ||||
0.520811 | + | 0.853672i | \(0.325630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.7022 | 1.36312 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.93066 | 0.111730 | ||||||||
\(689\) | −38.9455 | −1.48371 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.7474 | 0.827309 | 0.413655 | − | 0.910434i | \(-0.364252\pi\) | ||||
0.413655 | + | 0.910434i | \(0.364252\pi\) | |||||||
\(692\) | 15.9033 | 0.604554 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.0212 | −0.418357 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.11772 | 0.269603 | ||||||||
\(698\) | −56.7698 | −2.14877 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.4994 | 1.34079 | 0.670397 | − | 0.742003i | \(-0.266124\pi\) | ||||
0.670397 | + | 0.742003i | \(0.266124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.74427 | 0.178934 | ||||||||
\(704\) | −55.0477 | −2.07469 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −44.9148 | −1.69039 | ||||||||
\(707\) | −16.4388 | −0.618243 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.4325 | 1.25558 | 0.627792 | − | 0.778381i | \(-0.283959\pi\) | ||||
0.627792 | + | 0.778381i | \(0.283959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.91208 | 0.371471 | ||||||||
\(713\) | −55.4306 | −2.07589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.0421 | 1.01061 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.4207 | 0.799412 | ||||||||
\(719\) | 44.5343 | 1.66085 | 0.830425 | − | 0.557130i | \(-0.188098\pi\) | ||||
0.830425 | + | 0.557130i | \(0.188098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0497 | 0.523237 | ||||||||
\(722\) | −15.0302 | −0.559368 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 73.9296 | 2.74757 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.6700 | −0.581170 | −0.290585 | − | 0.956849i | \(-0.593850\pi\) | ||||
−0.290585 | + | 0.956849i | \(0.593850\pi\) | |||||||
\(728\) | −7.68698 | −0.284898 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.31046 | −0.0484689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.7350 | −1.09829 | −0.549143 | − | 0.835728i | \(-0.685046\pi\) | ||||
−0.549143 | + | 0.835728i | \(0.685046\pi\) | |||||||
\(734\) | 20.2580 | 0.747738 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.7776 | 2.31401 | ||||||||
\(737\) | 55.7123 | 2.05219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.9178 | 1.57876 | 0.789379 | − | 0.613906i | \(-0.210403\pi\) | ||||
0.789379 | + | 0.613906i | \(0.210403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 38.0950 | 1.39851 | ||||||||
\(743\) | 10.9064 | 0.400117 | 0.200058 | − | 0.979784i | \(-0.435887\pi\) | ||||
0.200058 | + | 0.979784i | \(0.435887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.0168 | −1.09899 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.96211 | 0.291124 | ||||||||
\(749\) | −6.39743 | −0.233757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.2977 | 1.72592 | 0.862960 | − | 0.505273i | \(-0.168608\pi\) | ||||
0.862960 | + | 0.505273i | \(0.168608\pi\) | |||||||
\(752\) | −13.7521 | −0.501488 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.57809 | 0.239560 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.3406 | −1.21179 | −0.605893 | − | 0.795546i | \(-0.707184\pi\) | ||||
−0.605893 | + | 0.795546i | \(0.707184\pi\) | |||||||
\(758\) | −0.132963 | −0.00482944 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.9707 | −1.66644 | −0.833219 | − | 0.552944i | \(-0.813504\pi\) | ||||
−0.833219 | + | 0.552944i | \(0.813504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.1965 | 0.731162 | ||||||||
\(764\) | −35.7082 | −1.29188 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.4811 | 0.776144 | ||||||||
\(767\) | −7.58939 | −0.274037 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.21048 | −0.332138 | −0.166069 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166069 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 45.4007 | 1.63401 | ||||||||
\(773\) | 28.6595 | 1.03081 | 0.515405 | − | 0.856947i | \(-0.327642\pi\) | ||||
0.515405 | + | 0.856947i | \(0.327642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.01152 | −0.144005 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5793 | −0.450989 | ||||||||
\(779\) | −56.2737 | −2.01621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.9066 | 0.783881 | ||||||||
\(782\) | −12.5561 | −0.449005 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.56718 | 0.270256 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.8195 | −0.742136 | −0.371068 | − | 0.928606i | \(-0.621008\pi\) | ||||
−0.371068 | + | 0.928606i | \(0.621008\pi\) | |||||||
\(788\) | 62.5837 | 2.22945 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.68948 | 0.202295 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.1892 | 0.894496 | ||||||||
\(794\) | 15.0496 | 0.534090 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.57298 | −0.126641 | ||||||||
\(797\) | 44.8656 | 1.58922 | 0.794610 | − | 0.607120i | \(-0.207675\pi\) | ||||
0.794610 | + | 0.607120i | \(0.207675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.14931 | 0.217547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.9228 | −0.915365 | ||||||||
\(803\) | 68.6734 | 2.42343 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 41.2457 | 1.45282 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.5052 | 0.862090 | ||||||||
\(809\) | −26.6975 | −0.938633 | −0.469317 | − | 0.883030i | \(-0.655500\pi\) | ||||
−0.469317 | + | 0.883030i | \(0.655500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6414 | −0.759934 | −0.379967 | − | 0.925000i | \(-0.624065\pi\) | ||||
−0.379967 | + | 0.925000i | \(0.624065\pi\) | |||||||
\(812\) | −3.80150 | −0.133406 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.86281 | 0.310641 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3606 | 0.362473 | ||||||||
\(818\) | 49.2270 | 1.72118 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.0374 | 1.25771 | 0.628857 | − | 0.777521i | \(-0.283523\pi\) | ||||
0.628857 | + | 0.777521i | \(0.283523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.4577 | 0.817684 | 0.408842 | − | 0.912605i | \(-0.365933\pi\) | ||||
0.408842 | + | 0.912605i | \(0.365933\pi\) | |||||||
\(824\) | −20.9438 | −0.729611 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.42364 | 0.258301 | ||||||||
\(827\) | −14.7623 | −0.513334 | −0.256667 | − | 0.966500i | \(-0.582624\pi\) | ||||
−0.256667 | + | 0.966500i | \(0.582624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.63801 | 0.195816 | 0.0979081 | − | 0.995195i | \(-0.468785\pi\) | ||||
0.0979081 | + | 0.995195i | \(0.468785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38.1628 | −1.32306 | ||||||||
\(833\) | −3.38369 | −0.117238 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −62.9495 | −2.17715 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 62.3776 | 2.15480 | ||||||||
\(839\) | −56.4632 | −1.94932 | −0.974662 | − | 0.223681i | \(-0.928193\pi\) | ||||
−0.974662 | + | 0.223681i | \(0.928193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 76.3098 | 2.62981 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.5927 | −0.502301 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.76858 | 0.335652 | ||||||||
\(848\) | 18.8055 | 0.645784 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.25740 | −0.283060 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.2731 | −1.31045 | −0.655223 | − | 0.755436i | \(-0.727425\pi\) | ||||
−0.655223 | + | 0.755436i | \(0.727425\pi\) | |||||||
\(854\) | −24.6391 | −0.843133 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.53663 | 0.325955 | ||||||||
\(857\) | 47.5891 | 1.62561 | 0.812806 | − | 0.582534i | \(-0.197939\pi\) | ||||
0.812806 | + | 0.582534i | \(0.197939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4348 | −0.663108 | −0.331554 | − | 0.943436i | \(-0.607573\pi\) | ||||
−0.331554 | + | 0.943436i | \(0.607573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −50.9984 | −1.73701 | ||||||||
\(863\) | 24.3695 | 0.829546 | 0.414773 | − | 0.909925i | \(-0.363861\pi\) | ||||
0.414773 | + | 0.909925i | \(0.363861\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.4671 | −1.34115 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.8360 | −0.809047 | ||||||||
\(869\) | −14.1855 | −0.481209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.6235 | 1.30871 | ||||||||
\(872\) | −30.1068 | −1.01955 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 99.2703 | 3.35787 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.4009 | −0.790193 | −0.395097 | − | 0.918640i | \(-0.629289\pi\) | ||||
−0.395097 | + | 0.918640i | \(0.629289\pi\) | |||||||
\(878\) | 7.33225 | 0.247451 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.1434 | 1.65568 | 0.827841 | − | 0.560963i | \(-0.189569\pi\) | ||||
0.827841 | + | 0.560963i | \(0.189569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0245 | 1.41424 | 0.707118 | − | 0.707095i | \(-0.249995\pi\) | ||||
0.707118 | + | 0.707095i | \(0.249995\pi\) | |||||||
\(884\) | 5.51987 | 0.185653 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −66.0628 | −2.21942 | ||||||||
\(887\) | 38.7280 | 1.30036 | 0.650179 | − | 0.759781i | \(-0.274694\pi\) | ||||
0.650179 | + | 0.759781i | \(0.274694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4105 | −0.952857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.8516 | 1.56871 | ||||||||
\(893\) | −48.6173 | −1.62691 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.6323 | 0.622460 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.6584 | −0.656011 | ||||||||
\(899\) | 6.27016 | 0.209122 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.40895 | −0.280143 | ||||||||
\(902\) | −105.125 | −3.50029 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.48129 | −0.282084 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7366 | −0.754956 | −0.377478 | − | 0.926019i | \(-0.623209\pi\) | ||||
−0.377478 | + | 0.926019i | \(0.623209\pi\) | |||||||
\(908\) | 19.7138 | 0.654224 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.74791 | 0.190437 | 0.0952183 | − | 0.995456i | \(-0.469645\pi\) | ||||
0.0952183 | + | 0.995456i | \(0.469645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5170 | 0.745203 | ||||||||
\(914\) | −43.9625 | −1.45415 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.9541 | −0.560178 | ||||||||
\(917\) | 12.1859 | 0.402415 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.1835 | 1.72137 | 0.860687 | − | 0.509135i | \(-0.170035\pi\) | ||||
0.860687 | + | 0.509135i | \(0.170035\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.0175 | 0.988572 | ||||||||
\(923\) | 15.1871 | 0.499891 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 65.8036 | 2.16244 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.10123 | −0.233109 | ||||||||
\(929\) | −4.61899 | −0.151544 | −0.0757721 | − | 0.997125i | \(-0.524142\pi\) | ||||
−0.0757721 | + | 0.997125i | \(0.524142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.7519 | 0.876758 | ||||||||
\(932\) | −40.8469 | −1.33799 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.5198 | −0.475104 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.8991 | 0.748082 | 0.374041 | − | 0.927412i | \(-0.377972\pi\) | ||||
0.374041 | + | 0.927412i | \(0.377972\pi\) | |||||||
\(938\) | −37.7800 | −1.23356 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.1297 | 0.786604 | 0.393302 | − | 0.919409i | \(-0.371333\pi\) | ||||
0.393302 | + | 0.919409i | \(0.371333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 97.9442 | 3.18950 | ||||||||
\(944\) | 3.66466 | 0.119275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3548 | 0.629278 | ||||||||
\(947\) | −13.6427 | −0.443329 | −0.221665 | − | 0.975123i | \(-0.571149\pi\) | ||||
−0.221665 | + | 0.975123i | \(0.571149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.6090 | 1.54545 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.65974 | −0.0537925 | ||||||||
\(953\) | −45.3303 | −1.46839 | −0.734196 | − | 0.678937i | \(-0.762441\pi\) | ||||
−0.734196 | + | 0.678937i | \(0.762441\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −59.7514 | −1.93250 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −81.6113 | −2.63674 | ||||||||
\(959\) | −1.11079 | −0.0358692 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.31492 | 0.268223 | ||||||||
\(962\) | 6.14429 | 0.198100 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.8369 | −0.735528 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2638 | 1.45558 | 0.727792 | − | 0.685798i | \(-0.240547\pi\) | ||||
0.727792 | + | 0.685798i | \(0.240547\pi\) | |||||||
\(968\) | −14.5620 | −0.468040 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.1089 | −1.51180 | −0.755899 | − | 0.654688i | \(-0.772800\pi\) | ||||
−0.755899 | + | 0.654688i | \(0.772800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4011 | −0.589912 | ||||||||
\(974\) | 54.0006 | 1.73029 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.1630 | −0.389330 | ||||||||
\(977\) | 2.89922 | 0.0927542 | 0.0463771 | − | 0.998924i | \(-0.485232\pi\) | ||||
0.0463771 | + | 0.998924i | \(0.485232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.6778 | −0.692826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.83068 | 0.0584193 | ||||||||
\(983\) | −37.0610 | −1.18206 | −0.591031 | − | 0.806649i | \(-0.701279\pi\) | ||||
−0.591031 | + | 0.806649i | \(0.701279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.42031 | 0.0452320 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.6408 | −1.38840 | ||||||||
\(989\) | −18.0327 | −0.573406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4669 | 0.554854 | 0.277427 | − | 0.960747i | \(-0.410518\pi\) | ||||
0.277427 | + | 0.960747i | \(0.410518\pi\) | |||||||
\(992\) | −44.5259 | −1.41370 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.8555 | −0.471187 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4726 | 0.616703 | 0.308352 | − | 0.951272i | \(-0.400223\pi\) | ||||
0.308352 | + | 0.951272i | \(0.400223\pi\) | |||||||
\(998\) | −72.3846 | −2.29129 | ||||||||
\(999\) | 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 | 6525.2.a.cc.1.1 | yes | 9 | |
3.2 | odd | 2 | 6525.2.a.ca.1.9 | ✓ | 9 | ||
5.4 | even | 2 | 6525.2.a.cb.1.9 | yes | 9 | ||
15.14 | odd | 2 | 6525.2.a.cd.1.1 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6525.2.a.ca.1.9 | ✓ | 9 | 3.2 | odd | 2 | ||
6525.2.a.cb.1.9 | yes | 9 | 5.4 | even | 2 | ||
6525.2.a.cc.1.1 | yes | 9 | 1.1 | even | 1 | trivial | |
6525.2.a.cd.1.1 | yes | 9 | 15.14 | odd | 2 |