Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8025,2,Mod(1,8025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8025, 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("8025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8025 = 3 \cdot 5^{2} \cdot 107 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8025.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: | \(64.0799476221\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 9x^{5} + 24x^{4} + 13x^{3} - 47x^{2} + 19x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 321) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.83986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.726480 | 0.513699 | 0.256850 | − | 0.966451i | \(-0.417316\pi\) | ||||
0.256850 | + | 0.966451i | \(0.417316\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.47223 | −0.736113 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.726480 | 0.296584 | ||||||||
\(7\) | −3.04775 | −1.15194 | −0.575971 | − | 0.817470i | \(-0.695376\pi\) | ||||
−0.575971 | + | 0.817470i | \(0.695376\pi\) | |||||||
\(8\) | −2.52250 | −0.891840 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.61409 | −1.39120 | −0.695601 | − | 0.718429i | \(-0.744862\pi\) | ||||
−0.695601 | + | 0.718429i | \(0.744862\pi\) | |||||||
\(12\) | −1.47223 | −0.424995 | ||||||||
\(13\) | 0.527054 | 0.146179 | 0.0730893 | − | 0.997325i | \(-0.476714\pi\) | ||||
0.0730893 | + | 0.997325i | \(0.476714\pi\) | |||||||
\(14\) | −2.21413 | −0.591751 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.11190 | 0.277976 | ||||||||
\(17\) | −5.95072 | −1.44326 | −0.721630 | − | 0.692279i | \(-0.756607\pi\) | ||||
−0.721630 | + | 0.692279i | \(0.756607\pi\) | |||||||
\(18\) | 0.726480 | 0.171233 | ||||||||
\(19\) | 3.68708 | 0.845873 | 0.422937 | − | 0.906159i | \(-0.360999\pi\) | ||||
0.422937 | + | 0.906159i | \(0.360999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.04775 | −0.665074 | ||||||||
\(22\) | −3.35205 | −0.714659 | ||||||||
\(23\) | −7.43002 | −1.54927 | −0.774633 | − | 0.632411i | \(-0.782065\pi\) | ||||
−0.774633 | + | 0.632411i | \(0.782065\pi\) | |||||||
\(24\) | −2.52250 | −0.514904 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.382895 | 0.0750918 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.48698 | 0.847959 | ||||||||
\(29\) | 1.45296 | 0.269808 | 0.134904 | − | 0.990859i | \(-0.456927\pi\) | ||||
0.134904 | + | 0.990859i | \(0.456927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.38618 | −0.608176 | −0.304088 | − | 0.952644i | \(-0.598352\pi\) | ||||
−0.304088 | + | 0.952644i | \(0.598352\pi\) | |||||||
\(32\) | 5.85278 | 1.03464 | ||||||||
\(33\) | −4.61409 | −0.803210 | ||||||||
\(34\) | −4.32308 | −0.741402 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.47223 | −0.245371 | ||||||||
\(37\) | −5.96860 | −0.981232 | −0.490616 | − | 0.871376i | \(-0.663228\pi\) | ||||
−0.490616 | + | 0.871376i | \(0.663228\pi\) | |||||||
\(38\) | 2.67859 | 0.434524 | ||||||||
\(39\) | 0.527054 | 0.0843962 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.67325 | −0.729839 | −0.364919 | − | 0.931039i | \(-0.618903\pi\) | ||||
−0.364919 | + | 0.931039i | \(0.618903\pi\) | |||||||
\(42\) | −2.21413 | −0.341648 | ||||||||
\(43\) | −5.43062 | −0.828162 | −0.414081 | − | 0.910240i | \(-0.635897\pi\) | ||||
−0.414081 | + | 0.910240i | \(0.635897\pi\) | |||||||
\(44\) | 6.79299 | 1.02408 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.39776 | −0.795857 | ||||||||
\(47\) | 11.1597 | 1.62781 | 0.813904 | − | 0.580999i | \(-0.197338\pi\) | ||||
0.813904 | + | 0.580999i | \(0.197338\pi\) | |||||||
\(48\) | 1.11190 | 0.160489 | ||||||||
\(49\) | 2.28878 | 0.326968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.95072 | −0.833267 | ||||||||
\(52\) | −0.775943 | −0.107604 | ||||||||
\(53\) | −0.271205 | −0.0372529 | −0.0186265 | − | 0.999827i | \(-0.505929\pi\) | ||||
−0.0186265 | + | 0.999827i | \(0.505929\pi\) | |||||||
\(54\) | 0.726480 | 0.0988615 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.68796 | 1.02735 | ||||||||
\(57\) | 3.68708 | 0.488365 | ||||||||
\(58\) | 1.05555 | 0.138600 | ||||||||
\(59\) | 7.51794 | 0.978753 | 0.489376 | − | 0.872073i | \(-0.337224\pi\) | ||||
0.489376 | + | 0.872073i | \(0.337224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.61419 | 0.718823 | 0.359412 | − | 0.933179i | \(-0.382977\pi\) | ||||
0.359412 | + | 0.933179i | \(0.382977\pi\) | |||||||
\(62\) | −2.45999 | −0.312420 | ||||||||
\(63\) | −3.04775 | −0.383980 | ||||||||
\(64\) | 2.02813 | 0.253516 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.35205 | −0.412608 | ||||||||
\(67\) | 10.5410 | 1.28778 | 0.643892 | − | 0.765116i | \(-0.277318\pi\) | ||||
0.643892 | + | 0.765116i | \(0.277318\pi\) | |||||||
\(68\) | 8.76080 | 1.06240 | ||||||||
\(69\) | −7.43002 | −0.894469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4009 | 1.82775 | 0.913877 | − | 0.405990i | \(-0.133073\pi\) | ||||
0.913877 | + | 0.405990i | \(0.133073\pi\) | |||||||
\(72\) | −2.52250 | −0.297280 | ||||||||
\(73\) | 1.83822 | 0.215147 | 0.107574 | − | 0.994197i | \(-0.465692\pi\) | ||||
0.107574 | + | 0.994197i | \(0.465692\pi\) | |||||||
\(74\) | −4.33607 | −0.504058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.42821 | −0.622658 | ||||||||
\(77\) | 14.0626 | 1.60258 | ||||||||
\(78\) | 0.382895 | 0.0433543 | ||||||||
\(79\) | 7.04158 | 0.792240 | 0.396120 | − | 0.918199i | \(-0.370356\pi\) | ||||
0.396120 | + | 0.918199i | \(0.370356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.39502 | −0.374917 | ||||||||
\(83\) | −8.68125 | −0.952891 | −0.476446 | − | 0.879204i | \(-0.658075\pi\) | ||||
−0.476446 | + | 0.879204i | \(0.658075\pi\) | |||||||
\(84\) | 4.48698 | 0.489569 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.94524 | −0.425426 | ||||||||
\(87\) | 1.45296 | 0.155774 | ||||||||
\(88\) | 11.6391 | 1.24073 | ||||||||
\(89\) | 0.0613646 | 0.00650464 | 0.00325232 | − | 0.999995i | \(-0.498965\pi\) | ||||
0.00325232 | + | 0.999995i | \(0.498965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.60633 | −0.168389 | ||||||||
\(92\) | 10.9387 | 1.14044 | ||||||||
\(93\) | −3.38618 | −0.351131 | ||||||||
\(94\) | 8.10730 | 0.836204 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.85278 | 0.597347 | ||||||||
\(97\) | −4.65646 | −0.472792 | −0.236396 | − | 0.971657i | \(-0.575966\pi\) | ||||
−0.236396 | + | 0.971657i | \(0.575966\pi\) | |||||||
\(98\) | 1.66275 | 0.167963 | ||||||||
\(99\) | −4.61409 | −0.463734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.40708 | 0.936039 | 0.468020 | − | 0.883718i | \(-0.344968\pi\) | ||||
0.468020 | + | 0.883718i | \(0.344968\pi\) | |||||||
\(102\) | −4.32308 | −0.428049 | ||||||||
\(103\) | −15.4272 | −1.52008 | −0.760042 | − | 0.649874i | \(-0.774822\pi\) | ||||
−0.760042 | + | 0.649874i | \(0.774822\pi\) | |||||||
\(104\) | −1.32950 | −0.130368 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.197025 | −0.0191368 | ||||||||
\(107\) | −1.00000 | −0.0966736 | ||||||||
\(108\) | −1.47223 | −0.141665 | ||||||||
\(109\) | −9.22379 | −0.883479 | −0.441739 | − | 0.897143i | \(-0.645638\pi\) | ||||
−0.441739 | + | 0.897143i | \(0.645638\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.96860 | −0.566514 | ||||||||
\(112\) | −3.38880 | −0.320212 | ||||||||
\(113\) | −7.81945 | −0.735592 | −0.367796 | − | 0.929906i | \(-0.619888\pi\) | ||||
−0.367796 | + | 0.929906i | \(0.619888\pi\) | |||||||
\(114\) | 2.67859 | 0.250873 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.13909 | −0.198609 | ||||||||
\(117\) | 0.527054 | 0.0487262 | ||||||||
\(118\) | 5.46164 | 0.502784 | ||||||||
\(119\) | 18.1363 | 1.66255 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2898 | 0.935441 | ||||||||
\(122\) | 4.07860 | 0.369259 | ||||||||
\(123\) | −4.67325 | −0.421373 | ||||||||
\(124\) | 4.98523 | 0.447687 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.21413 | −0.197250 | ||||||||
\(127\) | −20.5133 | −1.82026 | −0.910131 | − | 0.414320i | \(-0.864019\pi\) | ||||
−0.910131 | + | 0.414320i | \(0.864019\pi\) | |||||||
\(128\) | −10.2322 | −0.904405 | ||||||||
\(129\) | −5.43062 | −0.478140 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.77818 | 0.679583 | 0.339791 | − | 0.940501i | \(-0.389644\pi\) | ||||
0.339791 | + | 0.940501i | \(0.389644\pi\) | |||||||
\(132\) | 6.79299 | 0.591254 | ||||||||
\(133\) | −11.2373 | −0.974396 | ||||||||
\(134\) | 7.65781 | 0.661534 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0107 | 1.28716 | ||||||||
\(137\) | 17.7918 | 1.52005 | 0.760027 | − | 0.649891i | \(-0.225186\pi\) | ||||
0.760027 | + | 0.649891i | \(0.225186\pi\) | |||||||
\(138\) | −5.39776 | −0.459488 | ||||||||
\(139\) | 2.45851 | 0.208528 | 0.104264 | − | 0.994550i | \(-0.466751\pi\) | ||||
0.104264 | + | 0.994550i | \(0.466751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1597 | 0.939816 | ||||||||
\(142\) | 11.1885 | 0.938916 | ||||||||
\(143\) | −2.43188 | −0.203364 | ||||||||
\(144\) | 1.11190 | 0.0926586 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.33543 | 0.110521 | ||||||||
\(147\) | 2.28878 | 0.188775 | ||||||||
\(148\) | 8.78713 | 0.722297 | ||||||||
\(149\) | 12.4010 | 1.01593 | 0.507966 | − | 0.861377i | \(-0.330398\pi\) | ||||
0.507966 | + | 0.861377i | \(0.330398\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2238 | −1.40165 | −0.700826 | − | 0.713332i | \(-0.747185\pi\) | ||||
−0.700826 | + | 0.713332i | \(0.747185\pi\) | |||||||
\(152\) | −9.30066 | −0.754383 | ||||||||
\(153\) | −5.95072 | −0.481087 | ||||||||
\(154\) | 10.2162 | 0.823245 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.775943 | −0.0621252 | ||||||||
\(157\) | 22.3958 | 1.78738 | 0.893689 | − | 0.448687i | \(-0.148108\pi\) | ||||
0.893689 | + | 0.448687i | \(0.148108\pi\) | |||||||
\(158\) | 5.11557 | 0.406973 | ||||||||
\(159\) | −0.271205 | −0.0215080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.6448 | 1.78466 | ||||||||
\(162\) | 0.726480 | 0.0570777 | ||||||||
\(163\) | 7.34210 | 0.575078 | 0.287539 | − | 0.957769i | \(-0.407163\pi\) | ||||
0.287539 | + | 0.957769i | \(0.407163\pi\) | |||||||
\(164\) | 6.88008 | 0.537244 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.30676 | −0.489499 | ||||||||
\(167\) | −0.0802501 | −0.00620994 | −0.00310497 | − | 0.999995i | \(-0.500988\pi\) | ||||
−0.00310497 | + | 0.999995i | \(0.500988\pi\) | |||||||
\(168\) | 7.68796 | 0.593139 | ||||||||
\(169\) | −12.7222 | −0.978632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.68708 | 0.281958 | ||||||||
\(172\) | 7.99511 | 0.609621 | ||||||||
\(173\) | 0.445106 | 0.0338408 | 0.0169204 | − | 0.999857i | \(-0.494614\pi\) | ||||
0.0169204 | + | 0.999857i | \(0.494614\pi\) | |||||||
\(174\) | 1.05555 | 0.0800208 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.13042 | −0.386720 | ||||||||
\(177\) | 7.51794 | 0.565083 | ||||||||
\(178\) | 0.0445802 | 0.00334143 | ||||||||
\(179\) | 16.6475 | 1.24430 | 0.622148 | − | 0.782900i | \(-0.286260\pi\) | ||||
0.622148 | + | 0.782900i | \(0.286260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5686 | −1.45452 | −0.727262 | − | 0.686360i | \(-0.759208\pi\) | ||||
−0.727262 | + | 0.686360i | \(0.759208\pi\) | |||||||
\(182\) | −1.16697 | −0.0865013 | ||||||||
\(183\) | 5.61419 | 0.415013 | ||||||||
\(184\) | 18.7423 | 1.38170 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.45999 | −0.180376 | ||||||||
\(187\) | 27.4572 | 2.00787 | ||||||||
\(188\) | −16.4296 | −1.19825 | ||||||||
\(189\) | −3.04775 | −0.221691 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.03205 | 0.508821 | 0.254411 | − | 0.967096i | \(-0.418119\pi\) | ||||
0.254411 | + | 0.967096i | \(0.418119\pi\) | |||||||
\(192\) | 2.02813 | 0.146367 | ||||||||
\(193\) | −9.41610 | −0.677785 | −0.338893 | − | 0.940825i | \(-0.610052\pi\) | ||||
−0.338893 | + | 0.940825i | \(0.610052\pi\) | |||||||
\(194\) | −3.38283 | −0.242873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.36960 | −0.240686 | ||||||||
\(197\) | 17.5470 | 1.25017 | 0.625087 | − | 0.780555i | \(-0.285064\pi\) | ||||
0.625087 | + | 0.780555i | \(0.285064\pi\) | |||||||
\(198\) | −3.35205 | −0.238220 | ||||||||
\(199\) | −11.0431 | −0.782824 | −0.391412 | − | 0.920215i | \(-0.628013\pi\) | ||||
−0.391412 | + | 0.920215i | \(0.628013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5410 | 0.743503 | ||||||||
\(202\) | 6.83406 | 0.480843 | ||||||||
\(203\) | −4.42826 | −0.310803 | ||||||||
\(204\) | 8.76080 | 0.613379 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2075 | −0.780866 | ||||||||
\(207\) | −7.43002 | −0.516422 | ||||||||
\(208\) | 0.586033 | 0.0406341 | ||||||||
\(209\) | −17.0125 | −1.17678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8907 | 1.09396 | 0.546980 | − | 0.837146i | \(-0.315778\pi\) | ||||
0.546980 | + | 0.837146i | \(0.315778\pi\) | |||||||
\(212\) | 0.399276 | 0.0274224 | ||||||||
\(213\) | 15.4009 | 1.05525 | ||||||||
\(214\) | −0.726480 | −0.0496612 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.52250 | −0.171635 | ||||||||
\(217\) | 10.3202 | 0.700583 | ||||||||
\(218\) | −6.70090 | −0.453842 | ||||||||
\(219\) | 1.83822 | 0.124215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.13635 | −0.210974 | ||||||||
\(222\) | −4.33607 | −0.291018 | ||||||||
\(223\) | 14.8139 | 0.992009 | 0.496004 | − | 0.868320i | \(-0.334800\pi\) | ||||
0.496004 | + | 0.868320i | \(0.334800\pi\) | |||||||
\(224\) | −17.8378 | −1.19184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.68068 | −0.377873 | ||||||||
\(227\) | −27.3563 | −1.81570 | −0.907849 | − | 0.419297i | \(-0.862277\pi\) | ||||
−0.907849 | + | 0.419297i | \(0.862277\pi\) | |||||||
\(228\) | −5.42821 | −0.359492 | ||||||||
\(229\) | 22.7405 | 1.50273 | 0.751367 | − | 0.659884i | \(-0.229395\pi\) | ||||
0.751367 | + | 0.659884i | \(0.229395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.0626 | 0.925251 | ||||||||
\(232\) | −3.66510 | −0.240626 | ||||||||
\(233\) | 14.0156 | 0.918191 | 0.459096 | − | 0.888387i | \(-0.348174\pi\) | ||||
0.459096 | + | 0.888387i | \(0.348174\pi\) | |||||||
\(234\) | 0.382895 | 0.0250306 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.0681 | −0.720473 | ||||||||
\(237\) | 7.04158 | 0.457400 | ||||||||
\(238\) | 13.1757 | 0.854051 | ||||||||
\(239\) | 23.8481 | 1.54260 | 0.771302 | − | 0.636470i | \(-0.219606\pi\) | ||||
0.771302 | + | 0.636470i | \(0.219606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.16373 | −0.525872 | −0.262936 | − | 0.964813i | \(-0.584691\pi\) | ||||
−0.262936 | + | 0.964813i | \(0.584691\pi\) | |||||||
\(242\) | 7.47537 | 0.480535 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.26536 | −0.529135 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.39502 | −0.216459 | ||||||||
\(247\) | 1.94329 | 0.123649 | ||||||||
\(248\) | 8.54166 | 0.542396 | ||||||||
\(249\) | −8.68125 | −0.550152 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.33147 | 0.525878 | 0.262939 | − | 0.964812i | \(-0.415308\pi\) | ||||
0.262939 | + | 0.964812i | \(0.415308\pi\) | |||||||
\(252\) | 4.48698 | 0.282653 | ||||||||
\(253\) | 34.2828 | 2.15534 | ||||||||
\(254\) | −14.9025 | −0.935067 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.4897 | −0.718108 | ||||||||
\(257\) | 21.9193 | 1.36729 | 0.683643 | − | 0.729817i | \(-0.260395\pi\) | ||||
0.683643 | + | 0.729817i | \(0.260395\pi\) | |||||||
\(258\) | −3.94524 | −0.245620 | ||||||||
\(259\) | 18.1908 | 1.13032 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.45296 | 0.0899360 | ||||||||
\(262\) | 5.65069 | 0.349101 | ||||||||
\(263\) | −22.0210 | −1.35787 | −0.678936 | − | 0.734198i | \(-0.737559\pi\) | ||||
−0.678936 | + | 0.734198i | \(0.737559\pi\) | |||||||
\(264\) | 11.6391 | 0.716335 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.16367 | −0.500547 | ||||||||
\(267\) | 0.0613646 | 0.00375545 | ||||||||
\(268\) | −15.5187 | −0.947955 | ||||||||
\(269\) | −20.8237 | −1.26965 | −0.634823 | − | 0.772658i | \(-0.718927\pi\) | ||||
−0.634823 | + | 0.772658i | \(0.718927\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4274 | 0.815656 | 0.407828 | − | 0.913059i | \(-0.366286\pi\) | ||||
0.407828 | + | 0.913059i | \(0.366286\pi\) | |||||||
\(272\) | −6.61662 | −0.401191 | ||||||||
\(273\) | −1.60633 | −0.0972195 | ||||||||
\(274\) | 12.9254 | 0.780850 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.9387 | 0.658431 | ||||||||
\(277\) | −30.2875 | −1.81980 | −0.909901 | − | 0.414826i | \(-0.863842\pi\) | ||||
−0.909901 | + | 0.414826i | \(0.863842\pi\) | |||||||
\(278\) | 1.78606 | 0.107121 | ||||||||
\(279\) | −3.38618 | −0.202725 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.98260 | −0.118272 | −0.0591361 | − | 0.998250i | \(-0.518835\pi\) | ||||
−0.0591361 | + | 0.998250i | \(0.518835\pi\) | |||||||
\(282\) | 8.10730 | 0.482783 | ||||||||
\(283\) | 16.9481 | 1.00746 | 0.503730 | − | 0.863861i | \(-0.331961\pi\) | ||||
0.503730 | + | 0.863861i | \(0.331961\pi\) | |||||||
\(284\) | −22.6737 | −1.34543 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.76671 | −0.104468 | ||||||||
\(287\) | 14.2429 | 0.840731 | ||||||||
\(288\) | 5.85278 | 0.344879 | ||||||||
\(289\) | 18.4110 | 1.08300 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.65646 | −0.272967 | ||||||||
\(292\) | −2.70627 | −0.158373 | ||||||||
\(293\) | −1.05078 | −0.0613872 | −0.0306936 | − | 0.999529i | \(-0.509772\pi\) | ||||
−0.0306936 | + | 0.999529i | \(0.509772\pi\) | |||||||
\(294\) | 1.66275 | 0.0969737 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.0558 | 0.875101 | ||||||||
\(297\) | −4.61409 | −0.267737 | ||||||||
\(298\) | 9.00910 | 0.521883 | ||||||||
\(299\) | −3.91602 | −0.226470 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.5512 | 0.953994 | ||||||||
\(302\) | −12.5127 | −0.720028 | ||||||||
\(303\) | 9.40708 | 0.540423 | ||||||||
\(304\) | 4.09967 | 0.235132 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.32308 | −0.247134 | ||||||||
\(307\) | 28.4381 | 1.62305 | 0.811525 | − | 0.584317i | \(-0.198638\pi\) | ||||
0.811525 | + | 0.584317i | \(0.198638\pi\) | |||||||
\(308\) | −20.7033 | −1.17968 | ||||||||
\(309\) | −15.4272 | −0.877621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3839 | −1.38268 | −0.691342 | − | 0.722528i | \(-0.742980\pi\) | ||||
−0.691342 | + | 0.722528i | \(0.742980\pi\) | |||||||
\(312\) | −1.32950 | −0.0752679 | ||||||||
\(313\) | 13.6663 | 0.772466 | 0.386233 | − | 0.922401i | \(-0.373776\pi\) | ||||
0.386233 | + | 0.922401i | \(0.373776\pi\) | |||||||
\(314\) | 16.2701 | 0.918175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.3668 | −0.583178 | ||||||||
\(317\) | 16.5706 | 0.930698 | 0.465349 | − | 0.885127i | \(-0.345929\pi\) | ||||
0.465349 | + | 0.885127i | \(0.345929\pi\) | |||||||
\(318\) | −0.197025 | −0.0110486 | ||||||||
\(319\) | −6.70409 | −0.375357 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | −0.0558146 | ||||||||
\(322\) | 16.4510 | 0.916780 | ||||||||
\(323\) | −21.9407 | −1.22082 | ||||||||
\(324\) | −1.47223 | −0.0817904 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.33389 | 0.295417 | ||||||||
\(327\) | −9.22379 | −0.510077 | ||||||||
\(328\) | 11.7883 | 0.650899 | ||||||||
\(329\) | −34.0120 | −1.87514 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.89673 | −0.104253 | −0.0521267 | − | 0.998640i | \(-0.516600\pi\) | ||||
−0.0521267 | + | 0.998640i | \(0.516600\pi\) | |||||||
\(332\) | 12.7808 | 0.701436 | ||||||||
\(333\) | −5.96860 | −0.327077 | ||||||||
\(334\) | −0.0583001 | −0.00319004 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.38880 | −0.184874 | ||||||||
\(337\) | −13.9796 | −0.761517 | −0.380759 | − | 0.924674i | \(-0.624337\pi\) | ||||
−0.380759 | + | 0.924674i | \(0.624337\pi\) | |||||||
\(338\) | −9.24244 | −0.502722 | ||||||||
\(339\) | −7.81945 | −0.424694 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6242 | 0.846096 | ||||||||
\(342\) | 2.67859 | 0.144841 | ||||||||
\(343\) | 14.3586 | 0.775293 | ||||||||
\(344\) | 13.6988 | 0.738588 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.323361 | 0.0173840 | ||||||||
\(347\) | 4.94636 | 0.265534 | 0.132767 | − | 0.991147i | \(-0.457614\pi\) | ||||
0.132767 | + | 0.991147i | \(0.457614\pi\) | |||||||
\(348\) | −2.13909 | −0.114667 | ||||||||
\(349\) | 21.4602 | 1.14874 | 0.574369 | − | 0.818596i | \(-0.305247\pi\) | ||||
0.574369 | + | 0.818596i | \(0.305247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.527054 | 0.0281321 | ||||||||
\(352\) | −27.0053 | −1.43939 | ||||||||
\(353\) | 12.6360 | 0.672547 | 0.336274 | − | 0.941764i | \(-0.390833\pi\) | ||||
0.336274 | + | 0.941764i | \(0.390833\pi\) | |||||||
\(354\) | 5.46164 | 0.290283 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0903426 | −0.00478815 | ||||||||
\(357\) | 18.1363 | 0.959874 | ||||||||
\(358\) | 12.0941 | 0.639193 | ||||||||
\(359\) | 20.5962 | 1.08703 | 0.543513 | − | 0.839401i | \(-0.317094\pi\) | ||||
0.543513 | + | 0.839401i | \(0.317094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.40547 | −0.284498 | ||||||||
\(362\) | −14.2162 | −0.747188 | ||||||||
\(363\) | 10.2898 | 0.540077 | ||||||||
\(364\) | 2.36488 | 0.123953 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.07860 | 0.213192 | ||||||||
\(367\) | 12.3694 | 0.645677 | 0.322839 | − | 0.946454i | \(-0.395363\pi\) | ||||
0.322839 | + | 0.946454i | \(0.395363\pi\) | |||||||
\(368\) | −8.26146 | −0.430658 | ||||||||
\(369\) | −4.67325 | −0.243280 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.826566 | 0.0429132 | ||||||||
\(372\) | 4.98523 | 0.258472 | ||||||||
\(373\) | −22.5057 | −1.16530 | −0.582650 | − | 0.812724i | \(-0.697984\pi\) | ||||
−0.582650 | + | 0.812724i | \(0.697984\pi\) | |||||||
\(374\) | 19.9471 | 1.03144 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −28.1504 | −1.45174 | ||||||||
\(377\) | 0.765789 | 0.0394401 | ||||||||
\(378\) | −2.21413 | −0.113883 | ||||||||
\(379\) | −8.34910 | −0.428864 | −0.214432 | − | 0.976739i | \(-0.568790\pi\) | ||||
−0.214432 | + | 0.976739i | \(0.568790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.5133 | −1.05093 | ||||||||
\(382\) | 5.10865 | 0.261381 | ||||||||
\(383\) | −26.5509 | −1.35669 | −0.678344 | − | 0.734744i | \(-0.737302\pi\) | ||||
−0.678344 | + | 0.734744i | \(0.737302\pi\) | |||||||
\(384\) | −10.2322 | −0.522158 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.84061 | −0.348178 | ||||||||
\(387\) | −5.43062 | −0.276054 | ||||||||
\(388\) | 6.85537 | 0.348029 | ||||||||
\(389\) | 10.9539 | 0.555385 | 0.277693 | − | 0.960670i | \(-0.410430\pi\) | ||||
0.277693 | + | 0.960670i | \(0.410430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.2139 | 2.23600 | ||||||||
\(392\) | −5.77345 | −0.291603 | ||||||||
\(393\) | 7.77818 | 0.392357 | ||||||||
\(394\) | 12.7476 | 0.642213 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.79299 | 0.341360 | ||||||||
\(397\) | 12.5411 | 0.629419 | 0.314709 | − | 0.949188i | \(-0.398093\pi\) | ||||
0.314709 | + | 0.949188i | \(0.398093\pi\) | |||||||
\(398\) | −8.02259 | −0.402136 | ||||||||
\(399\) | −11.2373 | −0.562568 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.7276 | −1.28478 | −0.642389 | − | 0.766379i | \(-0.722056\pi\) | ||||
−0.642389 | + | 0.766379i | \(0.722056\pi\) | |||||||
\(402\) | 7.65781 | 0.381937 | ||||||||
\(403\) | −1.78470 | −0.0889023 | ||||||||
\(404\) | −13.8494 | −0.689031 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.21704 | −0.159659 | ||||||||
\(407\) | 27.5397 | 1.36509 | ||||||||
\(408\) | 15.0107 | 0.743141 | ||||||||
\(409\) | 7.58380 | 0.374995 | 0.187497 | − | 0.982265i | \(-0.439962\pi\) | ||||
0.187497 | + | 0.982265i | \(0.439962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7918 | 0.877604 | ||||||||
\(412\) | 22.7123 | 1.11895 | ||||||||
\(413\) | −22.9128 | −1.12747 | ||||||||
\(414\) | −5.39776 | −0.265286 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.08473 | 0.151242 | ||||||||
\(417\) | 2.45851 | 0.120394 | ||||||||
\(418\) | −12.3593 | −0.604511 | ||||||||
\(419\) | −25.1281 | −1.22759 | −0.613794 | − | 0.789466i | \(-0.710357\pi\) | ||||
−0.613794 | + | 0.789466i | \(0.710357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8460 | 0.528604 | 0.264302 | − | 0.964440i | \(-0.414859\pi\) | ||||
0.264302 | + | 0.964440i | \(0.414859\pi\) | |||||||
\(422\) | 11.5443 | 0.561966 | ||||||||
\(423\) | 11.1597 | 0.542603 | ||||||||
\(424\) | 0.684116 | 0.0332236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.1885 | 0.542083 | ||||||||
\(427\) | −17.1106 | −0.828042 | ||||||||
\(428\) | 1.47223 | 0.0711627 | ||||||||
\(429\) | −2.43188 | −0.117412 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.2467 | 0.830746 | 0.415373 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415373 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(432\) | 1.11190 | 0.0534965 | ||||||||
\(433\) | 8.40039 | 0.403697 | 0.201849 | − | 0.979417i | \(-0.435305\pi\) | ||||
0.201849 | + | 0.979417i | \(0.435305\pi\) | |||||||
\(434\) | 7.49745 | 0.359889 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.5795 | 0.650340 | ||||||||
\(437\) | −27.3950 | −1.31048 | ||||||||
\(438\) | 1.33543 | 0.0638093 | ||||||||
\(439\) | −20.5888 | −0.982652 | −0.491326 | − | 0.870976i | \(-0.663488\pi\) | ||||
−0.491326 | + | 0.870976i | \(0.663488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.28878 | 0.108989 | ||||||||
\(442\) | −2.27850 | −0.108377 | ||||||||
\(443\) | 24.5763 | 1.16766 | 0.583828 | − | 0.811877i | \(-0.301554\pi\) | ||||
0.583828 | + | 0.811877i | \(0.301554\pi\) | |||||||
\(444\) | 8.78713 | 0.417019 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7620 | 0.509594 | ||||||||
\(447\) | 12.4010 | 0.586549 | ||||||||
\(448\) | −6.18122 | −0.292035 | ||||||||
\(449\) | 12.4259 | 0.586414 | 0.293207 | − | 0.956049i | \(-0.405277\pi\) | ||||
0.293207 | + | 0.956049i | \(0.405277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5628 | 1.01535 | ||||||||
\(452\) | 11.5120 | 0.541479 | ||||||||
\(453\) | −17.2238 | −0.809244 | ||||||||
\(454\) | −19.8738 | −0.932723 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.30066 | −0.435544 | ||||||||
\(457\) | −14.9004 | −0.697012 | −0.348506 | − | 0.937307i | \(-0.613311\pi\) | ||||
−0.348506 | + | 0.937307i | \(0.613311\pi\) | |||||||
\(458\) | 16.5205 | 0.771954 | ||||||||
\(459\) | −5.95072 | −0.277756 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652043 | 0.326022 | − | 0.945362i | \(-0.394292\pi\) | ||||
0.326022 | + | 0.945362i | \(0.394292\pi\) | |||||||
\(462\) | 10.2162 | 0.475301 | ||||||||
\(463\) | −33.9468 | −1.57764 | −0.788822 | − | 0.614622i | \(-0.789309\pi\) | ||||
−0.788822 | + | 0.614622i | \(0.789309\pi\) | |||||||
\(464\) | 1.61555 | 0.0750001 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.1820 | 0.471674 | ||||||||
\(467\) | 13.8914 | 0.642817 | 0.321409 | − | 0.946941i | \(-0.395844\pi\) | ||||
0.321409 | + | 0.946941i | \(0.395844\pi\) | |||||||
\(468\) | −0.775943 | −0.0358680 | ||||||||
\(469\) | −32.1262 | −1.48345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.3958 | 1.03194 | ||||||||
\(472\) | −18.9640 | −0.872891 | ||||||||
\(473\) | 25.0574 | 1.15214 | ||||||||
\(474\) | 5.11557 | 0.234966 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −26.7007 | −1.22383 | ||||||||
\(477\) | −0.271205 | −0.0124176 | ||||||||
\(478\) | 17.3252 | 0.792434 | ||||||||
\(479\) | −11.7271 | −0.535824 | −0.267912 | − | 0.963443i | \(-0.586334\pi\) | ||||
−0.267912 | + | 0.963443i | \(0.586334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.14578 | −0.143435 | ||||||||
\(482\) | −5.93079 | −0.270140 | ||||||||
\(483\) | 22.6448 | 1.03038 | ||||||||
\(484\) | −15.1490 | −0.688590 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.726480 | 0.0329538 | ||||||||
\(487\) | −9.82435 | −0.445184 | −0.222592 | − | 0.974912i | \(-0.571452\pi\) | ||||
−0.222592 | + | 0.974912i | \(0.571452\pi\) | |||||||
\(488\) | −14.1618 | −0.641075 | ||||||||
\(489\) | 7.34210 | 0.332021 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6602 | −0.842121 | −0.421061 | − | 0.907033i | \(-0.638342\pi\) | ||||
−0.421061 | + | 0.907033i | \(0.638342\pi\) | |||||||
\(492\) | 6.88008 | 0.310178 | ||||||||
\(493\) | −8.64616 | −0.389403 | ||||||||
\(494\) | 1.41176 | 0.0635181 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.76511 | −0.169058 | ||||||||
\(497\) | −46.9382 | −2.10547 | ||||||||
\(498\) | −6.30676 | −0.282613 | ||||||||
\(499\) | 19.9825 | 0.894540 | 0.447270 | − | 0.894399i | \(-0.352396\pi\) | ||||
0.447270 | + | 0.894399i | \(0.352396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0802501 | −0.00358531 | ||||||||
\(502\) | 6.05265 | 0.270143 | ||||||||
\(503\) | 4.02993 | 0.179686 | 0.0898428 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898428 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(504\) | 7.68796 | 0.342449 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.9058 | 1.10720 | ||||||||
\(507\) | −12.7222 | −0.565013 | ||||||||
\(508\) | 30.2002 | 1.33992 | ||||||||
\(509\) | 1.34049 | 0.0594160 | 0.0297080 | − | 0.999559i | \(-0.490542\pi\) | ||||
0.0297080 | + | 0.999559i | \(0.490542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.60243 | −0.247837 | ||||||||
\(512\) | 12.1173 | 0.535514 | ||||||||
\(513\) | 3.68708 | 0.162788 | ||||||||
\(514\) | 15.9239 | 0.702373 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.99511 | 0.351965 | ||||||||
\(517\) | −51.4919 | −2.26461 | ||||||||
\(518\) | 13.2153 | 0.580645 | ||||||||
\(519\) | 0.445106 | 0.0195380 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.45034 | −0.282594 | −0.141297 | − | 0.989967i | \(-0.545127\pi\) | ||||
−0.141297 | + | 0.989967i | \(0.545127\pi\) | |||||||
\(522\) | 1.05555 | 0.0462001 | ||||||||
\(523\) | −15.7561 | −0.688968 | −0.344484 | − | 0.938792i | \(-0.611946\pi\) | ||||
−0.344484 | + | 0.938792i | \(0.611946\pi\) | |||||||
\(524\) | −11.4512 | −0.500250 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.9978 | −0.697538 | ||||||||
\(527\) | 20.1502 | 0.877757 | ||||||||
\(528\) | −5.13042 | −0.223273 | ||||||||
\(529\) | 32.2052 | 1.40023 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.51794 | 0.326251 | ||||||||
\(532\) | 16.5438 | 0.717266 | ||||||||
\(533\) | −2.46306 | −0.106687 | ||||||||
\(534\) | 0.0445802 | 0.00192917 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.5896 | −1.14850 | ||||||||
\(537\) | 16.6475 | 0.718394 | ||||||||
\(538\) | −15.1280 | −0.652216 | ||||||||
\(539\) | −10.5606 | −0.454879 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5027 | −0.838485 | −0.419242 | − | 0.907874i | \(-0.637704\pi\) | ||||
−0.419242 | + | 0.907874i | \(0.637704\pi\) | |||||||
\(542\) | 9.75473 | 0.419002 | ||||||||
\(543\) | −19.5686 | −0.839770 | ||||||||
\(544\) | −34.8283 | −1.49325 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.16697 | −0.0499416 | ||||||||
\(547\) | −0.313021 | −0.0133838 | −0.00669192 | − | 0.999978i | \(-0.502130\pi\) | ||||
−0.00669192 | + | 0.999978i | \(0.502130\pi\) | |||||||
\(548\) | −26.1935 | −1.11893 | ||||||||
\(549\) | 5.61419 | 0.239608 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.35718 | 0.228223 | ||||||||
\(552\) | 18.7423 | 0.797723 | ||||||||
\(553\) | −21.4610 | −0.912614 | ||||||||
\(554\) | −22.0033 | −0.934830 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.61949 | −0.153501 | ||||||||
\(557\) | −26.0269 | −1.10280 | −0.551398 | − | 0.834243i | \(-0.685905\pi\) | ||||
−0.551398 | + | 0.834243i | \(0.685905\pi\) | |||||||
\(558\) | −2.45999 | −0.104140 | ||||||||
\(559\) | −2.86223 | −0.121060 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.4572 | 1.15924 | ||||||||
\(562\) | −1.44032 | −0.0607563 | ||||||||
\(563\) | −26.1472 | −1.10197 | −0.550986 | − | 0.834515i | \(-0.685748\pi\) | ||||
−0.550986 | + | 0.834515i | \(0.685748\pi\) | |||||||
\(564\) | −16.4296 | −0.691811 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.3125 | 0.517532 | ||||||||
\(567\) | −3.04775 | −0.127993 | ||||||||
\(568\) | −38.8489 | −1.63006 | ||||||||
\(569\) | −5.83479 | −0.244607 | −0.122304 | − | 0.992493i | \(-0.539028\pi\) | ||||
−0.122304 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.62287 | 0.193461 | 0.0967306 | − | 0.995311i | \(-0.469161\pi\) | ||||
0.0967306 | + | 0.995311i | \(0.469161\pi\) | |||||||
\(572\) | 3.58027 | 0.149699 | ||||||||
\(573\) | 7.03205 | 0.293768 | ||||||||
\(574\) | 10.3472 | 0.431883 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.02813 | 0.0845053 | ||||||||
\(577\) | −36.5940 | −1.52343 | −0.761713 | − | 0.647914i | \(-0.775642\pi\) | ||||
−0.761713 | + | 0.647914i | \(0.775642\pi\) | |||||||
\(578\) | 13.3752 | 0.556337 | ||||||||
\(579\) | −9.41610 | −0.391320 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.4583 | 1.09767 | ||||||||
\(582\) | −3.38283 | −0.140223 | ||||||||
\(583\) | 1.25137 | 0.0518263 | ||||||||
\(584\) | −4.63691 | −0.191877 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.763371 | −0.0315346 | ||||||||
\(587\) | 6.69597 | 0.276372 | 0.138186 | − | 0.990406i | \(-0.455873\pi\) | ||||
0.138186 | + | 0.990406i | \(0.455873\pi\) | |||||||
\(588\) | −3.36960 | −0.138960 | ||||||||
\(589\) | −12.4851 | −0.514440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.5470 | 0.721788 | ||||||||
\(592\) | −6.63650 | −0.272759 | ||||||||
\(593\) | 44.9423 | 1.84556 | 0.922780 | − | 0.385328i | \(-0.125912\pi\) | ||||
0.922780 | + | 0.385328i | \(0.125912\pi\) | |||||||
\(594\) | −3.35205 | −0.137536 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.2571 | −0.747841 | ||||||||
\(597\) | −11.0431 | −0.451964 | ||||||||
\(598\) | −2.84491 | −0.116337 | ||||||||
\(599\) | 41.6016 | 1.69979 | 0.849897 | − | 0.526948i | \(-0.176664\pi\) | ||||
0.849897 | + | 0.526948i | \(0.176664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9505 | −0.813796 | −0.406898 | − | 0.913474i | \(-0.633390\pi\) | ||||
−0.406898 | + | 0.913474i | \(0.633390\pi\) | |||||||
\(602\) | 12.0241 | 0.490066 | ||||||||
\(603\) | 10.5410 | 0.429262 | ||||||||
\(604\) | 25.3573 | 1.03177 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.83406 | 0.277615 | ||||||||
\(607\) | 38.5437 | 1.56444 | 0.782220 | − | 0.623003i | \(-0.214088\pi\) | ||||
0.782220 | + | 0.623003i | \(0.214088\pi\) | |||||||
\(608\) | 21.5797 | 0.875171 | ||||||||
\(609\) | −4.42826 | −0.179442 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.88176 | 0.237951 | ||||||||
\(612\) | 8.76080 | 0.354134 | ||||||||
\(613\) | −21.0071 | −0.848471 | −0.424235 | − | 0.905552i | \(-0.639457\pi\) | ||||
−0.424235 | + | 0.905552i | \(0.639457\pi\) | |||||||
\(614\) | 20.6598 | 0.833760 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.4730 | −1.42925 | ||||||||
\(617\) | −10.1623 | −0.409118 | −0.204559 | − | 0.978854i | \(-0.565576\pi\) | ||||
−0.204559 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(618\) | −11.2075 | −0.450833 | ||||||||
\(619\) | 38.9227 | 1.56444 | 0.782218 | − | 0.623004i | \(-0.214088\pi\) | ||||
0.782218 | + | 0.623004i | \(0.214088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.43002 | −0.298156 | ||||||||
\(622\) | −17.7144 | −0.710284 | ||||||||
\(623\) | −0.187024 | −0.00749296 | ||||||||
\(624\) | 0.586033 | 0.0234601 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.92831 | 0.396815 | ||||||||
\(627\) | −17.0125 | −0.679414 | ||||||||
\(628\) | −32.9717 | −1.31571 | ||||||||
\(629\) | 35.5174 | 1.41617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.1333 | −1.27921 | −0.639603 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639603 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(632\) | −17.7624 | −0.706551 | ||||||||
\(633\) | 15.8907 | 0.631598 | ||||||||
\(634\) | 12.0382 | 0.478099 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.399276 | 0.0158323 | ||||||||
\(637\) | 1.20631 | 0.0477958 | ||||||||
\(638\) | −4.87039 | −0.192821 | ||||||||
\(639\) | 15.4009 | 0.609252 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.7046 | −0.896776 | −0.448388 | − | 0.893839i | \(-0.648002\pi\) | ||||
−0.448388 | + | 0.893839i | \(0.648002\pi\) | |||||||
\(642\) | −0.726480 | −0.0286719 | ||||||||
\(643\) | 8.23270 | 0.324666 | 0.162333 | − | 0.986736i | \(-0.448098\pi\) | ||||
0.162333 | + | 0.986736i | \(0.448098\pi\) | |||||||
\(644\) | −33.3383 | −1.31371 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.9395 | −0.627132 | ||||||||
\(647\) | 47.5899 | 1.87095 | 0.935477 | − | 0.353388i | \(-0.114970\pi\) | ||||
0.935477 | + | 0.353388i | \(0.114970\pi\) | |||||||
\(648\) | −2.52250 | −0.0990933 | ||||||||
\(649\) | −34.6885 | −1.36164 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.3202 | 0.404482 | ||||||||
\(652\) | −10.8092 | −0.423322 | ||||||||
\(653\) | −36.9870 | −1.44741 | −0.723707 | − | 0.690107i | \(-0.757563\pi\) | ||||
−0.723707 | + | 0.690107i | \(0.757563\pi\) | |||||||
\(654\) | −6.70090 | −0.262026 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.19620 | −0.202877 | ||||||||
\(657\) | 1.83822 | 0.0717157 | ||||||||
\(658\) | −24.7090 | −0.963258 | ||||||||
\(659\) | 9.74467 | 0.379598 | 0.189799 | − | 0.981823i | \(-0.439216\pi\) | ||||
0.189799 | + | 0.981823i | \(0.439216\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1768 | 0.590308 | 0.295154 | − | 0.955450i | \(-0.404629\pi\) | ||||
0.295154 | + | 0.955450i | \(0.404629\pi\) | |||||||
\(662\) | −1.37793 | −0.0535549 | ||||||||
\(663\) | −3.13635 | −0.121806 | ||||||||
\(664\) | 21.8985 | 0.849826 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.33607 | −0.168019 | ||||||||
\(667\) | −10.7955 | −0.418004 | ||||||||
\(668\) | 0.118146 | 0.00457122 | ||||||||
\(669\) | 14.8139 | 0.572737 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.9044 | −1.00003 | ||||||||
\(672\) | −17.8378 | −0.688109 | ||||||||
\(673\) | 24.9994 | 0.963657 | 0.481828 | − | 0.876266i | \(-0.339973\pi\) | ||||
0.481828 | + | 0.876266i | \(0.339973\pi\) | |||||||
\(674\) | −10.1559 | −0.391191 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.7300 | 0.720384 | ||||||||
\(677\) | −14.2024 | −0.545842 | −0.272921 | − | 0.962037i | \(-0.587990\pi\) | ||||
−0.272921 | + | 0.962037i | \(0.587990\pi\) | |||||||
\(678\) | −5.68068 | −0.218165 | ||||||||
\(679\) | 14.1917 | 0.544629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.3563 | −1.04829 | ||||||||
\(682\) | 11.3506 | 0.434639 | ||||||||
\(683\) | 12.7506 | 0.487888 | 0.243944 | − | 0.969789i | \(-0.421559\pi\) | ||||
0.243944 | + | 0.969789i | \(0.421559\pi\) | |||||||
\(684\) | −5.42821 | −0.207553 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.4313 | 0.398267 | ||||||||
\(687\) | 22.7405 | 0.867604 | ||||||||
\(688\) | −6.03833 | −0.230209 | ||||||||
\(689\) | −0.142940 | −0.00544558 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1546 | −1.18517 | −0.592587 | − | 0.805506i | \(-0.701894\pi\) | ||||
−0.592587 | + | 0.805506i | \(0.701894\pi\) | |||||||
\(692\) | −0.655297 | −0.0249106 | ||||||||
\(693\) | 14.0626 | 0.534194 | ||||||||
\(694\) | 3.59343 | 0.136405 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.66510 | −0.138925 | ||||||||
\(697\) | 27.8092 | 1.05335 | ||||||||
\(698\) | 15.5904 | 0.590106 | ||||||||
\(699\) | 14.0156 | 0.530118 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2223 | 0.801556 | 0.400778 | − | 0.916175i | \(-0.368740\pi\) | ||||
0.400778 | + | 0.916175i | \(0.368740\pi\) | |||||||
\(702\) | 0.382895 | 0.0144514 | ||||||||
\(703\) | −22.0067 | −0.829997 | ||||||||
\(704\) | −9.35796 | −0.352691 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.17982 | 0.345487 | ||||||||
\(707\) | −28.6704 | −1.07826 | ||||||||
\(708\) | −11.0681 | −0.415965 | ||||||||
\(709\) | −3.65794 | −0.137377 | −0.0686883 | − | 0.997638i | \(-0.521881\pi\) | ||||
−0.0686883 | + | 0.997638i | \(0.521881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.04158 | 0.264080 | ||||||||
\(712\) | −0.154792 | −0.00580109 | ||||||||
\(713\) | 25.1594 | 0.942227 | ||||||||
\(714\) | 13.1757 | 0.493087 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.5089 | −0.915942 | ||||||||
\(717\) | 23.8481 | 0.890623 | ||||||||
\(718\) | 14.9627 | 0.558404 | ||||||||
\(719\) | 0.812002 | 0.0302826 | 0.0151413 | − | 0.999885i | \(-0.495180\pi\) | ||||
0.0151413 | + | 0.999885i | \(0.495180\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0182 | 1.75105 | ||||||||
\(722\) | −3.92697 | −0.146147 | ||||||||
\(723\) | −8.16373 | −0.303613 | ||||||||
\(724\) | 28.8095 | 1.07069 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.47537 | 0.277437 | ||||||||
\(727\) | −24.0101 | −0.890485 | −0.445242 | − | 0.895410i | \(-0.646882\pi\) | ||||
−0.445242 | + | 0.895410i | \(0.646882\pi\) | |||||||
\(728\) | 4.05197 | 0.150176 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.3161 | 1.19525 | ||||||||
\(732\) | −8.26536 | −0.305496 | ||||||||
\(733\) | −21.7704 | −0.804108 | −0.402054 | − | 0.915616i | \(-0.631704\pi\) | ||||
−0.402054 | + | 0.915616i | \(0.631704\pi\) | |||||||
\(734\) | 8.98612 | 0.331684 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.4863 | −1.60293 | ||||||||
\(737\) | −48.6370 | −1.79157 | ||||||||
\(738\) | −3.39502 | −0.124972 | ||||||||
\(739\) | 27.0058 | 0.993423 | 0.496711 | − | 0.867916i | \(-0.334541\pi\) | ||||
0.496711 | + | 0.867916i | \(0.334541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.94329 | 0.0713885 | ||||||||
\(742\) | 0.600484 | 0.0220445 | ||||||||
\(743\) | 16.2017 | 0.594383 | 0.297192 | − | 0.954818i | \(-0.403950\pi\) | ||||
0.297192 | + | 0.954818i | \(0.403950\pi\) | |||||||
\(744\) | 8.54166 | 0.313152 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.3499 | −0.598613 | ||||||||
\(747\) | −8.68125 | −0.317630 | ||||||||
\(748\) | −40.4231 | −1.47802 | ||||||||
\(749\) | 3.04775 | 0.111362 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.3599 | 0.378039 | 0.189019 | − | 0.981973i | \(-0.439469\pi\) | ||||
0.189019 | + | 0.981973i | \(0.439469\pi\) | |||||||
\(752\) | 12.4085 | 0.452491 | ||||||||
\(753\) | 8.33147 | 0.303616 | ||||||||
\(754\) | 0.556331 | 0.0202604 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.48698 | 0.163190 | ||||||||
\(757\) | 31.1950 | 1.13380 | 0.566901 | − | 0.823786i | \(-0.308142\pi\) | ||||
0.566901 | + | 0.823786i | \(0.308142\pi\) | |||||||
\(758\) | −6.06545 | −0.220307 | ||||||||
\(759\) | 34.2828 | 1.24439 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0943888 | 0.00342159 | 0.00171079 | − | 0.999999i | \(-0.499455\pi\) | ||||
0.00171079 | + | 0.999999i | \(0.499455\pi\) | |||||||
\(762\) | −14.9025 | −0.539861 | ||||||||
\(763\) | 28.1118 | 1.01772 | ||||||||
\(764\) | −10.3528 | −0.374550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.2887 | −0.696930 | ||||||||
\(767\) | 3.96236 | 0.143073 | ||||||||
\(768\) | −11.4897 | −0.414600 | ||||||||
\(769\) | −38.6683 | −1.39441 | −0.697207 | − | 0.716870i | \(-0.745574\pi\) | ||||
−0.697207 | + | 0.716870i | \(0.745574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.9193 | 0.789403 | ||||||||
\(772\) | 13.8626 | 0.498927 | ||||||||
\(773\) | 24.3242 | 0.874879 | 0.437439 | − | 0.899248i | \(-0.355885\pi\) | ||||
0.437439 | + | 0.899248i | \(0.355885\pi\) | |||||||
\(774\) | −3.94524 | −0.141809 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.7459 | 0.421655 | ||||||||
\(777\) | 18.1908 | 0.652591 | ||||||||
\(778\) | 7.95780 | 0.285301 | ||||||||
\(779\) | −17.2306 | −0.617351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.0613 | −2.54277 | ||||||||
\(782\) | 32.1206 | 1.14863 | ||||||||
\(783\) | 1.45296 | 0.0519246 | ||||||||
\(784\) | 2.54490 | 0.0908893 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.65069 | 0.201554 | ||||||||
\(787\) | 27.6147 | 0.984358 | 0.492179 | − | 0.870494i | \(-0.336201\pi\) | ||||
0.492179 | + | 0.870494i | \(0.336201\pi\) | |||||||
\(788\) | −25.8332 | −0.920269 | ||||||||
\(789\) | −22.0210 | −0.783968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.8317 | 0.847359 | ||||||||
\(792\) | 11.6391 | 0.413576 | ||||||||
\(793\) | 2.95898 | 0.105077 | ||||||||
\(794\) | 9.11085 | 0.323332 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.2579 | 0.576247 | ||||||||
\(797\) | 37.4117 | 1.32519 | 0.662594 | − | 0.748978i | \(-0.269455\pi\) | ||||
0.662594 | + | 0.748978i | \(0.269455\pi\) | |||||||
\(798\) | −8.16367 | −0.288991 | ||||||||
\(799\) | −66.4082 | −2.34935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0613646 | 0.00216821 | ||||||||
\(802\) | −18.6906 | −0.659989 | ||||||||
\(803\) | −8.48171 | −0.299313 | ||||||||
\(804\) | −15.5187 | −0.547302 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.29655 | −0.0456691 | ||||||||
\(807\) | −20.8237 | −0.733030 | ||||||||
\(808\) | −23.7294 | −0.834797 | ||||||||
\(809\) | 15.3385 | 0.539273 | 0.269636 | − | 0.962962i | \(-0.413097\pi\) | ||||
0.269636 | + | 0.962962i | \(0.413097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.81264 | 0.168995 | 0.0844974 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844974 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(812\) | 6.51940 | 0.228786 | ||||||||
\(813\) | 13.4274 | 0.470919 | ||||||||
\(814\) | 20.0070 | 0.701246 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.61662 | −0.231628 | ||||||||
\(817\) | −20.0231 | −0.700520 | ||||||||
\(818\) | 5.50948 | 0.192634 | ||||||||
\(819\) | −1.60633 | −0.0561297 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.7554 | −1.91098 | −0.955489 | − | 0.295027i | \(-0.904671\pi\) | ||||
−0.955489 | + | 0.295027i | \(0.904671\pi\) | |||||||
\(822\) | 12.9254 | 0.450824 | ||||||||
\(823\) | −15.9383 | −0.555573 | −0.277787 | − | 0.960643i | \(-0.589601\pi\) | ||||
−0.277787 | + | 0.960643i | \(0.589601\pi\) | |||||||
\(824\) | 38.9151 | 1.35567 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.6457 | −0.579178 | ||||||||
\(827\) | 25.3608 | 0.881882 | 0.440941 | − | 0.897536i | \(-0.354645\pi\) | ||||
0.440941 | + | 0.897536i | \(0.354645\pi\) | |||||||
\(828\) | 10.9387 | 0.380145 | ||||||||
\(829\) | 42.9249 | 1.49084 | 0.745422 | − | 0.666593i | \(-0.232248\pi\) | ||||
0.745422 | + | 0.666593i | \(0.232248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.2875 | −1.05066 | ||||||||
\(832\) | 1.06893 | 0.0370586 | ||||||||
\(833\) | −13.6199 | −0.471901 | ||||||||
\(834\) | 1.78606 | 0.0618463 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.0463 | 0.866243 | ||||||||
\(837\) | −3.38618 | −0.117044 | ||||||||
\(838\) | −18.2551 | −0.630611 | ||||||||
\(839\) | 33.1819 | 1.14557 | 0.572783 | − | 0.819707i | \(-0.305864\pi\) | ||||
0.572783 | + | 0.819707i | \(0.305864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8889 | −0.927204 | ||||||||
\(842\) | 7.87943 | 0.271543 | ||||||||
\(843\) | −1.98260 | −0.0682845 | ||||||||
\(844\) | −23.3947 | −0.805278 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.10730 | 0.278735 | ||||||||
\(847\) | −31.3609 | −1.07757 | ||||||||
\(848\) | −0.301554 | −0.0103554 | ||||||||
\(849\) | 16.9481 | 0.581658 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.3468 | 1.52019 | ||||||||
\(852\) | −22.6737 | −0.776787 | ||||||||
\(853\) | −36.0092 | −1.23293 | −0.616466 | − | 0.787381i | \(-0.711436\pi\) | ||||
−0.616466 | + | 0.787381i | \(0.711436\pi\) | |||||||
\(854\) | −12.4305 | −0.425364 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.52250 | 0.0862174 | ||||||||
\(857\) | 31.0229 | 1.05972 | 0.529861 | − | 0.848085i | \(-0.322244\pi\) | ||||
0.529861 | + | 0.848085i | \(0.322244\pi\) | |||||||
\(858\) | −1.76671 | −0.0603145 | ||||||||
\(859\) | 1.54856 | 0.0528362 | 0.0264181 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264181 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.2429 | 0.485396 | ||||||||
\(862\) | 12.5294 | 0.426754 | ||||||||
\(863\) | −3.60559 | −0.122736 | −0.0613679 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613679 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(864\) | 5.85278 | 0.199116 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.10272 | 0.207379 | ||||||||
\(867\) | 18.4110 | 0.625271 | ||||||||
\(868\) | −15.1937 | −0.515709 | ||||||||
\(869\) | −32.4905 | −1.10217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.55566 | 0.188247 | ||||||||
\(872\) | 23.2670 | 0.787922 | ||||||||
\(873\) | −4.65646 | −0.157597 | ||||||||
\(874\) | −19.9020 | −0.673194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.70627 | −0.0914365 | ||||||||
\(877\) | 40.2200 | 1.35813 | 0.679066 | − | 0.734077i | \(-0.262385\pi\) | ||||
0.679066 | + | 0.734077i | \(0.262385\pi\) | |||||||
\(878\) | −14.9574 | −0.504787 | ||||||||
\(879\) | −1.05078 | −0.0354419 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2869 | −0.851937 | −0.425968 | − | 0.904738i | \(-0.640067\pi\) | ||||
−0.425968 | + | 0.904738i | \(0.640067\pi\) | |||||||
\(882\) | 1.66275 | 0.0559878 | ||||||||
\(883\) | −25.1997 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(884\) | 4.61742 | 0.155301 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.8542 | 0.599824 | ||||||||
\(887\) | −10.8673 | −0.364887 | −0.182443 | − | 0.983216i | \(-0.558401\pi\) | ||||
−0.182443 | + | 0.983216i | \(0.558401\pi\) | |||||||
\(888\) | 15.0558 | 0.505240 | ||||||||
\(889\) | 62.5194 | 2.09684 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.61409 | −0.154578 | ||||||||
\(892\) | −21.8093 | −0.730231 | ||||||||
\(893\) | 41.1466 | 1.37692 | ||||||||
\(894\) | 9.00910 | 0.301310 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31.1851 | 1.04182 | ||||||||
\(897\) | −3.91602 | −0.130752 | ||||||||
\(898\) | 9.02717 | 0.301241 | ||||||||
\(899\) | −4.91999 | −0.164091 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.61387 | 0.0537657 | ||||||||
\(902\) | 15.6649 | 0.521586 | ||||||||
\(903\) | 16.5512 | 0.550789 | ||||||||
\(904\) | 19.7246 | 0.656030 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.5127 | −0.415708 | ||||||||
\(907\) | −7.18720 | −0.238647 | −0.119324 | − | 0.992855i | \(-0.538073\pi\) | ||||
−0.119324 | + | 0.992855i | \(0.538073\pi\) | |||||||
\(908\) | 40.2746 | 1.33656 | ||||||||
\(909\) | 9.40708 | 0.312013 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.7220 | −1.21665 | −0.608327 | − | 0.793686i | \(-0.708159\pi\) | ||||
−0.608327 | + | 0.793686i | \(0.708159\pi\) | |||||||
\(912\) | 4.09967 | 0.135754 | ||||||||
\(913\) | 40.0561 | 1.32566 | ||||||||
\(914\) | −10.8249 | −0.358054 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.4792 | −1.10618 | ||||||||
\(917\) | −23.7059 | −0.782839 | ||||||||
\(918\) | −4.32308 | −0.142683 | ||||||||
\(919\) | 23.6711 | 0.780837 | 0.390418 | − | 0.920638i | \(-0.372330\pi\) | ||||
0.390418 | + | 0.920638i | \(0.372330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.4381 | 0.937069 | ||||||||
\(922\) | 10.1707 | 0.334954 | ||||||||
\(923\) | 8.11713 | 0.267179 | ||||||||
\(924\) | −20.7033 | −0.681089 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.6617 | −0.810434 | ||||||||
\(927\) | −15.4272 | −0.506695 | ||||||||
\(928\) | 8.50386 | 0.279153 | ||||||||
\(929\) | −14.8209 | −0.486258 | −0.243129 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243129 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.43890 | 0.276574 | ||||||||
\(932\) | −20.6341 | −0.675893 | ||||||||
\(933\) | −24.3839 | −0.798293 | ||||||||
\(934\) | 10.0918 | 0.330215 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.32950 | −0.0434560 | ||||||||
\(937\) | −31.5111 | −1.02942 | −0.514712 | − | 0.857363i | \(-0.672101\pi\) | ||||
−0.514712 | + | 0.857363i | \(0.672101\pi\) | |||||||
\(938\) | −23.3391 | −0.762048 | ||||||||
\(939\) | 13.6663 | 0.445983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.9429 | 0.747916 | 0.373958 | − | 0.927446i | \(-0.378000\pi\) | ||||
0.373958 | + | 0.927446i | \(0.378000\pi\) | |||||||
\(942\) | 16.2701 | 0.530108 | ||||||||
\(943\) | 34.7223 | 1.13071 | ||||||||
\(944\) | 8.35922 | 0.272070 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.2037 | 0.591854 | ||||||||
\(947\) | −3.38995 | −0.110158 | −0.0550792 | − | 0.998482i | \(-0.517541\pi\) | ||||
−0.0550792 | + | 0.998482i | \(0.517541\pi\) | |||||||
\(948\) | −10.3668 | −0.336698 | ||||||||
\(949\) | 0.968841 | 0.0314499 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.5706 | 0.537339 | ||||||||
\(952\) | −45.7489 | −1.48273 | ||||||||
\(953\) | −33.1747 | −1.07463 | −0.537317 | − | 0.843380i | \(-0.680562\pi\) | ||||
−0.537317 | + | 0.843380i | \(0.680562\pi\) | |||||||
\(954\) | −0.197025 | −0.00637893 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.1098 | −1.13553 | ||||||||
\(957\) | −6.70409 | −0.216713 | ||||||||
\(958\) | −8.51949 | −0.275252 | ||||||||
\(959\) | −54.2249 | −1.75101 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5338 | −0.630122 | ||||||||
\(962\) | −2.28534 | −0.0736824 | ||||||||
\(963\) | −1.00000 | −0.0322245 | ||||||||
\(964\) | 12.0189 | 0.387102 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.4510 | 0.529303 | ||||||||
\(967\) | −30.1127 | −0.968359 | −0.484179 | − | 0.874969i | \(-0.660882\pi\) | ||||
−0.484179 | + | 0.874969i | \(0.660882\pi\) | |||||||
\(968\) | −25.9562 | −0.834263 | ||||||||
\(969\) | −21.9407 | −0.704838 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.5503 | 0.980407 | 0.490203 | − | 0.871608i | \(-0.336923\pi\) | ||||
0.490203 | + | 0.871608i | \(0.336923\pi\) | |||||||
\(972\) | −1.47223 | −0.0472217 | ||||||||
\(973\) | −7.49294 | −0.240212 | ||||||||
\(974\) | −7.13719 | −0.228690 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.24243 | 0.199815 | ||||||||
\(977\) | −39.0056 | −1.24790 | −0.623949 | − | 0.781465i | \(-0.714473\pi\) | ||||
−0.623949 | + | 0.781465i | \(0.714473\pi\) | |||||||
\(978\) | 5.33389 | 0.170559 | ||||||||
\(979\) | −0.283142 | −0.00904926 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.22379 | −0.294493 | ||||||||
\(982\) | −13.5562 | −0.432597 | ||||||||
\(983\) | −18.6052 | −0.593412 | −0.296706 | − | 0.954969i | \(-0.595888\pi\) | ||||
−0.296706 | + | 0.954969i | \(0.595888\pi\) | |||||||
\(984\) | 11.7883 | 0.375797 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.28126 | −0.200036 | ||||||||
\(987\) | −34.0120 | −1.08261 | ||||||||
\(988\) | −2.86096 | −0.0910193 | ||||||||
\(989\) | 40.3496 | 1.28304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.5712 | 1.35232 | 0.676159 | − | 0.736755i | \(-0.263643\pi\) | ||||
0.676159 | + | 0.736755i | \(0.263643\pi\) | |||||||
\(992\) | −19.8186 | −0.629241 | ||||||||
\(993\) | −1.89673 | −0.0601908 | ||||||||
\(994\) | −34.0997 | −1.08158 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.7808 | 0.404974 | ||||||||
\(997\) | −21.4879 | −0.680528 | −0.340264 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340264 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(998\) | 14.5169 | 0.459525 | ||||||||
\(999\) | −5.96860 | −0.188838 |
(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 | 8025.2.a.bb.1.5 | 7 | ||
5.4 | even | 2 | 321.2.a.d.1.3 | ✓ | 7 | ||
15.14 | odd | 2 | 963.2.a.e.1.5 | 7 | |||
20.19 | odd | 2 | 5136.2.a.bi.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
321.2.a.d.1.3 | ✓ | 7 | 5.4 | even | 2 | ||
963.2.a.e.1.5 | 7 | 15.14 | odd | 2 | |||
5136.2.a.bi.1.2 | 7 | 20.19 | odd | 2 | |||
8025.2.a.bb.1.5 | 7 | 1.1 | even | 1 | trivial |