Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.823496 | −0.475446 | −0.237723 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237723 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12271 | −0.949304 | −0.474652 | − | 0.880174i | \(-0.657426\pi\) | ||||
−0.474652 | + | 0.880174i | \(0.657426\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.15456 | −1.57027 | −0.785137 | − | 0.619322i | \(-0.787408\pi\) | ||||
−0.785137 | + | 0.619322i | \(0.787408\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.32185 | −0.773951 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.347254 | −0.104701 | −0.0523505 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523505 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.83770 | 1.06439 | 0.532193 | − | 0.846623i | \(-0.321368\pi\) | ||||
0.532193 | + | 0.846623i | \(0.321368\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.74804 | 0.451343 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.72831 | −1.63185 | −0.815927 | − | 0.578154i | \(-0.803773\pi\) | ||||
−0.815927 | + | 0.578154i | \(0.803773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.76295 | 1.55153 | 0.775763 | − | 0.631024i | \(-0.217365\pi\) | ||||
0.775763 | + | 0.631024i | \(0.217365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.42126 | 0.746580 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.816344 | −0.170219 | −0.0851097 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851097 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.494108 | −0.0988217 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.38253 | 0.843418 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.71507 | 0.318480 | 0.159240 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159240 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.32959 | −0.418406 | −0.209203 | − | 0.977872i | \(-0.567087\pi\) | ||||
−0.209203 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.285962 | 0.0497797 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.81891 | 1.49067 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.48996 | 0.902544 | 0.451272 | − | 0.892386i | \(-0.350970\pi\) | ||||
0.451272 | + | 0.892386i | \(0.350970\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.16033 | −0.506058 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.70345 | −0.266035 | −0.133017 | − | 0.991114i | \(-0.542467\pi\) | ||||
−0.133017 | + | 0.991114i | \(0.542467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51038 | 0.840325 | 0.420163 | − | 0.907449i | \(-0.361973\pi\) | ||||
0.420163 | + | 0.907449i | \(0.361973\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.92862 | 0.734715 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.07376 | 0.885949 | 0.442974 | − | 0.896534i | \(-0.353923\pi\) | ||||
0.442974 | + | 0.896534i | \(0.353923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.2603 | 1.46576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.54074 | 0.775858 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.81786 | 0.524424 | 0.262212 | − | 0.965010i | \(-0.415548\pi\) | ||||
0.262212 | + | 0.965010i | \(0.415548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.737119 | 0.0993931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.56926 | −0.737667 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.10272 | 1.05488 | 0.527442 | − | 0.849591i | \(-0.323151\pi\) | ||||
0.527442 | + | 0.849591i | \(0.323151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.2931 | −1.95808 | −0.979039 | − | 0.203674i | \(-0.934712\pi\) | ||||
−0.979039 | + | 0.203674i | \(0.934712\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.64627 | 1.21532 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.14632 | −1.01043 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.22250 | 0.882368 | 0.441184 | − | 0.897417i | \(-0.354559\pi\) | ||||
0.441184 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.672256 | 0.0809301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48015 | 1.00641 | 0.503204 | − | 0.864167i | \(-0.332154\pi\) | ||||
0.503204 | + | 0.864167i | \(0.332154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.46685 | −0.522806 | −0.261403 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261403 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.406896 | 0.0469843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.44269 | 0.164409 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.7094 | −1.31741 | −0.658703 | − | 0.752403i | \(-0.728895\pi\) | ||||
−0.658703 | + | 0.752403i | \(0.728895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.35657 | 0.372952 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00287 | 0.110079 | 0.0550394 | − | 0.998484i | \(-0.482472\pi\) | ||||
0.0550394 | + | 0.998484i | \(0.482472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2822 | 1.54913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41235 | −0.151420 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.30368 | −0.880188 | −0.440094 | − | 0.897952i | \(-0.645055\pi\) | ||||
−0.440094 | + | 0.897952i | \(0.645055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.9439 | −1.67138 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.91841 | 0.198929 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.3558 | −1.47287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0445 | 1.52753 | 0.763767 | − | 0.645492i | \(-0.223348\pi\) | ||||
0.763767 | + | 0.645492i | \(0.223348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.806273 | 0.0810335 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6568 | 1.35890 | 0.679452 | − | 0.733720i | \(-0.262218\pi\) | ||||
0.679452 | + | 0.733720i | \(0.262218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5941 | −1.14240 | −0.571202 | − | 0.820809i | \(-0.693523\pi\) | ||||
−0.571202 | + | 0.820809i | \(0.693523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.26234 | −0.708732 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.824365 | 0.0796943 | 0.0398472 | − | 0.999206i | \(-0.487313\pi\) | ||||
0.0398472 | + | 0.999206i | \(0.487313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.67512 | −0.735144 | −0.367572 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367572 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.52096 | −0.429111 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.59341 | 0.149895 | 0.0749475 | − | 0.997187i | \(-0.476121\pi\) | ||||
0.0749475 | + | 0.997187i | \(0.476121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.73286 | 0.161590 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.91058 | −0.823783 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.9531 | 2.56246 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8794 | −0.989038 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.40279 | 0.126485 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6624 | 1.04312 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7093 | 1.39397 | 0.696987 | − | 0.717083i | \(-0.254523\pi\) | ||||
0.696987 | + | 0.717083i | \(0.254523\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.53778 | −0.399529 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7398 | 1.72468 | 0.862339 | − | 0.506332i | \(-0.168999\pi\) | ||||
0.862339 | + | 0.506332i | \(0.168999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.0971 | −2.43632 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.30283 | −0.800660 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.120001 | −0.0102524 | −0.00512618 | − | 0.999987i | \(-0.501632\pi\) | ||||
−0.00512618 | + | 0.999987i | \(0.501632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.83196 | −0.240204 | −0.120102 | − | 0.992762i | \(-0.538322\pi\) | ||||
−0.120102 | + | 0.992762i | \(0.538322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00172 | −0.421220 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.33266 | −0.111442 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.64059 | −0.302335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.44934 | −0.696890 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.31380 | −0.681093 | −0.340546 | − | 0.940228i | \(-0.610612\pi\) | ||||
−0.340546 | + | 0.940228i | \(0.610612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.69855 | −0.463742 | −0.231871 | − | 0.972747i | \(-0.574485\pi\) | ||||
−0.231871 | + | 0.972747i | \(0.574485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.6222 | 1.26298 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.94503 | 0.397195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.49199 | −0.198883 | −0.0994413 | − | 0.995043i | \(-0.531706\pi\) | ||||
−0.0994413 | + | 0.995043i | \(0.531706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.14400 | −0.249335 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.39155 | 0.267291 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.83664 | −0.692139 | −0.346070 | − | 0.938209i | \(-0.612484\pi\) | ||||
−0.346070 | + | 0.938209i | \(0.612484\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.607015 | −0.0472560 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.457582 | −0.0354088 | −0.0177044 | − | 0.999843i | \(-0.505636\pi\) | ||||
−0.0177044 | + | 0.999843i | \(0.505636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.72794 | 0.132918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.7026 | −1.20081 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9072 | 1.28543 | 0.642717 | − | 0.766104i | \(-0.277807\pi\) | ||||
0.642717 | + | 0.766104i | \(0.277807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.05280 | 0.155177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.67256 | −0.501540 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.81648 | 0.285257 | 0.142628 | − | 0.989776i | \(-0.454445\pi\) | ||||
0.142628 | + | 0.989776i | \(0.454445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4118 | 1.07122 | 0.535611 | − | 0.844465i | \(-0.320081\pi\) | ||||
0.535611 | + | 0.844465i | \(0.320081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5938 | 0.930960 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6536 | −0.856789 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.33643 | 0.170857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.2074 | −1.32440 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.5386 | 1.34140 | 0.670701 | − | 0.741728i | \(-0.265993\pi\) | ||||
0.670701 | + | 0.741728i | \(0.265993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.7549 | −1.78190 | −0.890949 | − | 0.454103i | \(-0.849960\pi\) | ||||
−0.890949 | + | 0.454103i | \(0.849960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.70846 | 0.480403 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.0824 | −1.50206 | −0.751030 | − | 0.660268i | \(-0.770443\pi\) | ||||
−0.751030 | + | 0.660268i | \(0.770443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.5709 | −1.74179 | −0.870893 | − | 0.491472i | \(-0.836459\pi\) | ||||
−0.870893 | + | 0.491472i | \(0.836459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.94770 | −0.419518 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.12535 | −0.500102 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.61594 | 0.252548 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.89543 | 0.131742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.34846 | −0.162447 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.17275 | 0.287264 | 0.143632 | − | 0.989631i | \(-0.454122\pi\) | ||||
0.143632 | + | 0.989631i | \(0.454122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.98337 | −0.478493 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6969 | −0.797724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.67840 | 0.657013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.67844 | 0.248566 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.8212 | −1.73692 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7125 | −0.851293 | −0.425646 | − | 0.904890i | \(-0.639953\pi\) | ||||
−0.425646 | + | 0.904890i | \(0.639953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.14725 | 0.0764832 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.68166 | 0.111616 | 0.0558079 | − | 0.998442i | \(-0.482227\pi\) | ||||
0.0558079 | + | 0.998442i | \(0.482227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5569 | −1.35844 | −0.679218 | − | 0.733937i | \(-0.737681\pi\) | ||||
−0.679218 | + | 0.733937i | \(0.737681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.18805 | −0.0781677 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.2247 | −1.39047 | −0.695237 | − | 0.718780i | \(-0.744701\pi\) | ||||
−0.695237 | + | 0.718780i | \(0.744701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8928 | −0.841035 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.64262 | 0.626355 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0093 | 1.61772 | 0.808859 | − | 0.588003i | \(-0.200086\pi\) | ||||
0.808859 | + | 0.588003i | \(0.200086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.373029 | 0.0240289 | 0.0120145 | − | 0.999928i | \(-0.496176\pi\) | ||||
0.0120145 | + | 0.999928i | \(0.496176\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9117 | −1.02074 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.7797 | −1.39145 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.9542 | 1.65142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.825856 | −0.0523365 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.81990 | 0.241110 | 0.120555 | − | 0.992707i | \(-0.461533\pi\) | ||||
0.120555 | + | 0.992707i | \(0.461533\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.283479 | 0.0178222 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.7614 | −0.736526 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.7329 | −1.35566 | −0.677831 | − | 0.735218i | \(-0.737080\pi\) | ||||
−0.677831 | + | 0.735218i | \(0.737080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8084 | −1.41724 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.98214 | −0.246488 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00331 | 0.185192 | 0.0925961 | − | 0.995704i | \(-0.470483\pi\) | ||||
0.0925961 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.10421 | −0.497838 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.83805 | 0.418482 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.97821 | 0.486440 | 0.243220 | − | 0.969971i | \(-0.421796\pi\) | ||||
0.243220 | + | 0.969971i | \(0.421796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.9565 | −1.21227 | −0.606137 | − | 0.795360i | \(-0.707282\pi\) | ||||
−0.606137 | + | 0.795360i | \(0.707282\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.1298 | 0.794650 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.171581 | 0.0103467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8065 | −1.55056 | −0.775281 | − | 0.631616i | \(-0.782392\pi\) | ||||
−0.775281 | + | 0.631616i | \(0.782392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.40896 | 0.323826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.93470 | −0.175070 | −0.0875348 | − | 0.996161i | \(-0.527899\pi\) | ||||
−0.0875348 | + | 0.996161i | \(0.527899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3900 | 1.27151 | 0.635753 | − | 0.771893i | \(-0.280690\pi\) | ||||
0.635753 | + | 0.771893i | \(0.280690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.8219 | 0.700270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.07710 | 0.417748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.2702 | 1.66295 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.3891 | −0.726260 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.3928 | −1.48346 | −0.741731 | − | 0.670697i | \(-0.765995\pi\) | ||||
−0.741731 | + | 0.670697i | \(0.765995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.1997 | −1.00141 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.52185 | −0.0883067 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.13288 | −0.181179 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.8932 | −1.31954 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.2463 | −0.646085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.4627 | 1.85881 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6838 | −0.609757 | −0.304879 | − | 0.952391i | \(-0.598616\pi\) | ||||
−0.304879 | + | 0.952391i | \(0.598616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.54773 | 0.543151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.3607 | −1.09785 | −0.548923 | − | 0.835873i | \(-0.684962\pi\) | ||||
−0.548923 | + | 0.835873i | \(0.684962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.47721 | 0.422637 | 0.211318 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211318 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.4762 | −1.15370 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.9433 | −1.56945 | −0.784726 | − | 0.619843i | \(-0.787196\pi\) | ||||
−0.784726 | + | 0.619843i | \(0.787196\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.595565 | −0.0333452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.678861 | −0.0378903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.5032 | −2.53187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.89624 | −0.105184 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.32044 | 0.349521 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.2338 | −1.39118 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.06821 | 0.443469 | 0.221735 | − | 0.975107i | \(-0.428828\pi\) | ||||
0.221735 | + | 0.975107i | \(0.428828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.7469 | −0.698525 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.3313 | −0.837636 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1703 | 0.554013 | 0.277007 | − | 0.960868i | \(-0.410658\pi\) | ||||
0.277007 | + | 0.960868i | \(0.410658\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.31216 | −0.0712669 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.808959 | 0.0438076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.5452 | −0.731374 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.42700 | −0.0768273 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.9374 | 1.87554 | 0.937768 | − | 0.347263i | \(-0.112889\pi\) | ||||
0.937768 | + | 0.347263i | \(0.112889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.37287 | 0.0734880 | 0.0367440 | − | 0.999325i | \(-0.488301\pi\) | ||||
0.0367440 | + | 0.999325i | \(0.488301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.8188 | 0.897722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.0396 | 1.65207 | 0.826035 | − | 0.563619i | \(-0.190591\pi\) | ||||
0.826035 | + | 0.563619i | \(0.190591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0009 | −0.955388 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.0193 | −1.21831 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.8881 | 0.627431 | 0.313715 | − | 0.949517i | \(-0.398426\pi\) | ||||
0.313715 | + | 0.949517i | \(0.398426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.7375 | 1.40724 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.95916 | 0.470234 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.48183 | 0.496302 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.16528 | −0.478424 | −0.239212 | − | 0.970967i | \(-0.576889\pi\) | ||||
−0.239212 | + | 0.970967i | \(0.576889\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.95517 | 0.205898 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.8615 | −0.823489 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7199 | −0.762166 | −0.381083 | − | 0.924541i | \(-0.624449\pi\) | ||||
−0.381083 | + | 0.924541i | \(0.624449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.60393 | −0.495945 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.58192 | 0.338986 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.82369 | −0.401876 | −0.200938 | − | 0.979604i | \(-0.564399\pi\) | ||||
−0.200938 | + | 0.979604i | \(0.564399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9365 | −0.662759 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.55131 | −0.232561 | −0.116280 | − | 0.993216i | \(-0.537097\pi\) | ||||
−0.116280 | + | 0.993216i | \(0.537097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.06240 | −0.156075 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.7943 | −0.650371 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.8205 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239228\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.49261 | 0.277773 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.2557 | −0.819991 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.8556 | 1.25062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9789 | −0.551013 | −0.275506 | − | 0.961299i | \(-0.588846\pi\) | ||||
−0.275506 | + | 0.961299i | \(0.588846\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.1378 | 1.15834 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.07798 | 0.403395 | 0.201697 | − | 0.979448i | \(-0.435354\pi\) | ||||
0.201697 | + | 0.979448i | \(0.435354\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.94026 | −0.445346 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.12502 | −0.354045 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.90641 | −0.0944973 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3101 | 0.608695 | 0.304348 | − | 0.952561i | \(-0.401562\pi\) | ||||
0.304348 | + | 0.952561i | \(0.401562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0988202 | 0.00487444 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.6632 | −1.65646 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.12879 | −0.104498 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.33211 | 0.114204 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.56527 | −0.223028 | −0.111514 | − | 0.993763i | \(-0.535570\pi\) | ||||
−0.111514 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55210 | −0.319330 | −0.159665 | − | 0.987171i | \(-0.551041\pi\) | ||||
−0.159665 | + | 0.987171i | \(0.551041\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.1024 | −0.685681 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.32451 | 0.161263 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 63.5359 | 3.07472 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.09744 | 0.0529848 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2823 | 1.36231 | 0.681155 | − | 0.732140i | \(-0.261478\pi\) | ||||
0.681155 | + | 0.732140i | \(0.261478\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.34310 | 0.208716 | 0.104358 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104358 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.99801 | 0.143744 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.52089 | −0.264100 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.3827 | −1.68872 | −0.844362 | − | 0.535773i | \(-0.820020\pi\) | ||||
−0.844362 | + | 0.535773i | \(0.820020\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.8230 | −1.13443 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.2931 | −1.62932 | −0.814658 | − | 0.579942i | \(-0.803075\pi\) | ||||
−0.814658 | + | 0.579942i | \(0.803075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.6263 | 0.835566 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.84638 | 0.323823 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0109 | 1.46350 | 0.731748 | − | 0.681575i | \(-0.238705\pi\) | ||||
0.731748 | + | 0.681575i | \(0.238705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.591531 | 0.0278541 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.69273 | 0.220484 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.8443 | 1.58665 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3168 | 0.903600 | 0.451800 | − | 0.892119i | \(-0.350782\pi\) | ||||
0.451800 | + | 0.892119i | \(0.350782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.4870 | −1.37634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.8254 | 1.85485 | 0.927427 | − | 0.374004i | \(-0.122015\pi\) | ||||
0.927427 | + | 0.374004i | \(0.122015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.4088 | −1.92443 | −0.962216 | − | 0.272287i | \(-0.912220\pi\) | ||||
−0.962216 | + | 0.272287i | \(0.912220\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.07222 | −0.188845 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.5289 | 1.32016 | 0.660080 | − | 0.751195i | \(-0.270522\pi\) | ||||
0.660080 | + | 0.751195i | \(0.270522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0063 | −1.38556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.05215 | 0.0945579 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.91350 | −0.0879829 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.34163 | −0.153324 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.86452 | −0.405879 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.6159 | −1.21611 | −0.608056 | − | 0.793894i | \(-0.708050\pi\) | ||||
−0.608056 | + | 0.793894i | \(0.708050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.0688 | 0.960656 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.79292 | −0.127082 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.9350 | −1.45009 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.0051 | −1.67686 | −0.838430 | − | 0.545010i | \(-0.816526\pi\) | ||||
−0.838430 | + | 0.545010i | \(0.816526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.27694 | 0.329075 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0755 | −0.770605 | −0.385302 | − | 0.922790i | \(-0.625903\pi\) | ||||
−0.385302 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.5395 | −0.519714 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.71148 | −0.0769255 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.2313 | −1.58034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.3453 | −1.31367 | −0.656837 | − | 0.754033i | \(-0.728106\pi\) | ||||
−0.656837 | + | 0.754033i | \(0.728106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.376817 | 0.0168350 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.9894 | −1.29001 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.42295 | −0.0631955 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3858 | −0.460343 | −0.230171 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230171 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.5578 | 0.820949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.6388 | 1.30859 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6110 | 1.08449 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.10914 | −0.0927598 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.9230 | −0.611154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.5151 | −1.16165 | −0.580823 | − | 0.814030i | \(-0.697269\pi\) | ||||
−0.580823 | + | 0.814030i | \(0.697269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.8472 | 1.65494 | 0.827472 | − | 0.561507i | \(-0.189778\pi\) | ||||
0.827472 | + | 0.561507i | \(0.189778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.69047 | −0.0737783 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6742 | 0.682778 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3336 | −0.971025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.8133 | −0.816429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.53735 | −0.283164 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.74989 | −0.0756542 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.14285 | −0.135624 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.56294 | −0.153467 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.7987 | 1.92605 | 0.963024 | − | 0.269417i | \(-0.0868308\pi\) | ||||
0.963024 | + | 0.269417i | \(0.0868308\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.8681 | −0.509308 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.2921 | 0.697875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3039 | 0.782618 | 0.391309 | − | 0.920259i | \(-0.372022\pi\) | ||||
0.391309 | + | 0.920259i | \(0.372022\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.5083 | 1.51546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5989 | 0.494131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.6472 | 2.06869 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.59669 | 0.407357 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.3695 | −1.15968 | −0.579841 | − | 0.814730i | \(-0.696885\pi\) | ||||
−0.579841 | + | 0.814730i | \(0.696885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.1472 | 0.894431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.92404 | −0.0812332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.85582 | 0.162504 | 0.0812518 | − | 0.996694i | \(-0.474108\pi\) | ||||
0.0812518 | + | 0.996694i | \(0.474108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.38234 | −0.142296 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.9451 | −0.585637 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.22012 | 0.302683 | 0.151342 | − | 0.988482i | \(-0.451641\pi\) | ||||
0.151342 | + | 0.988482i | \(0.451641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.96941 | 0.124266 | 0.0621330 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621330 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2664 | −0.637764 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.403362 | 0.0168214 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8412 | −0.784370 | −0.392185 | − | 0.919886i | \(-0.628281\pi\) | ||||
−0.392185 | + | 0.919886i | \(0.628281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.3856 | 0.847196 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.16646 | −0.172854 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.32577 | −0.0549077 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.9146 | 0.782021 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.88738 | 0.366821 | 0.183411 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183411 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.7549 | −0.649169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.3613 | 0.714148 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.62411 | 0.395215 | 0.197607 | − | 0.980281i | \(-0.436683\pi\) | ||||
0.197607 | + | 0.980281i | \(0.436683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59.3364 | −2.43255 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.2341 | 0.828125 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.0832 | −1.10659 | −0.553294 | − | 0.832986i | \(-0.686629\pi\) | ||||
−0.553294 | + | 0.832986i | \(0.686629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6676 | 1.00621 | 0.503107 | − | 0.864224i | \(-0.332190\pi\) | ||||
0.503107 | + | 0.864224i | \(0.332190\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.7696 | −0.682910 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.0938 | 0.938898 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.40644 | 0.260030 | 0.130015 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130015 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.86770 | 0.237771 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3093 | 0.942992 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.516185 | 0.0208485 | 0.0104243 | − | 0.999946i | \(-0.496682\pi\) | ||||
0.0104243 | + | 0.999946i | \(0.496682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.97771 | −0.120073 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.1430 | 0.730409 | 0.365204 | − | 0.930927i | \(-0.380999\pi\) | ||||
0.365204 | + | 0.930927i | \(0.380999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.354113 | −0.0142330 | −0.00711650 | − | 0.999975i | \(-0.502265\pi\) | ||||
−0.00711650 | + | 0.999975i | \(0.502265\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.57765 | −0.143566 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.4981 | 1.38214 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.2853 | −0.891413 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.93395 | 0.0772345 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.9382 | −1.47282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9039 | 1.70798 | 0.853989 | − | 0.520291i | \(-0.174176\pi\) | ||||
0.853989 | + | 0.520291i | \(0.174176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.43625 | −0.136579 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.3463 | −1.32331 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.3761 | 1.56014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.6897 | −0.778912 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2037 | 1.15348 | 0.576739 | − | 0.816928i | \(-0.304325\pi\) | ||||
0.576739 | + | 0.816928i | \(0.304325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9413 | −1.02303 | −0.511513 | − | 0.859275i | \(-0.670915\pi\) | ||||
−0.511513 | + | 0.859275i | \(0.670915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.63238 | 0.379274 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.2575 | −1.50406 | −0.752029 | − | 0.659130i | \(-0.770925\pi\) | ||||
−0.752029 | + | 0.659130i | \(0.770925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.81370 | −0.110447 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.97012 | −0.312374 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4300 | −0.603824 | −0.301912 | − | 0.953336i | \(-0.597625\pi\) | ||||
−0.301912 | + | 0.953336i | \(0.597625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.9019 | −1.63724 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3714 | 0.404626 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.7609 | 1.66573 | 0.832864 | − | 0.553478i | \(-0.186700\pi\) | ||||
0.832864 | + | 0.553478i | \(0.186700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3138 | 0.867906 | 0.433953 | − | 0.900936i | \(-0.357118\pi\) | ||||
0.433953 | + | 0.900936i | \(0.357118\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.2637 | 0.825813 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 59.6418 | 2.31281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.40009 | −0.0542115 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.4687 | 0.404743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.31058 | 0.205013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9712 | −1.03966 | −0.519832 | − | 0.854268i | \(-0.674006\pi\) | ||||
−0.519832 | + | 0.854268i | \(0.674006\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.16544 | −0.0833479 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.23350 | −0.162706 | −0.0813532 | − | 0.996685i | \(-0.525924\pi\) | ||||
−0.0813532 | + | 0.996685i | \(0.525924\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −62.5031 | −2.39865 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.38484 | −0.0530673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.7643 | −0.985842 | −0.492921 | − | 0.870074i | \(-0.664071\pi\) | ||||
−0.492921 | + | 0.870074i | \(0.664071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.254727 | 0.00973261 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9285 | 0.645863 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.6518 | 0.558190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.35519 | 0.241763 | 0.120881 | − | 0.992667i | \(-0.461428\pi\) | ||||
0.120881 | + | 0.992667i | \(0.461428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.34971 | −0.127245 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.01144 | 0.228027 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4614 | 0.434130 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.4784 | 0.661095 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.91157 | −0.185507 | −0.0927537 | − | 0.995689i | \(-0.529567\pi\) | ||||
−0.0927537 | + | 0.995689i | \(0.529567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.1283 | 1.40032 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.6172 | 0.399866 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −56.7380 | −2.13385 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.9150 | 1.79948 | 0.899742 | − | 0.436421i | \(-0.143754\pi\) | ||||
0.899742 | + | 0.436421i | \(0.143754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.1874 | 1.01961 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.90174 | 0.0712209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82884 | 0.105793 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.5951 | −0.769137 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.628068 | 0.0234230 | 0.0117115 | − | 0.999931i | \(-0.496272\pi\) | ||||
0.0117115 | + | 0.999931i | \(0.496272\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.1685 | 1.79389 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.307188 | −0.0114244 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.847430 | −0.0314728 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.77808 | 0.288473 | 0.144236 | − | 0.989543i | \(-0.453927\pi\) | ||||
0.144236 | + | 0.989543i | \(0.453927\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.03352 | 0.112352 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.0755 | −1.37129 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.2134 | −0.894341 | −0.447170 | − | 0.894449i | \(-0.647568\pi\) | ||||
−0.447170 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.9355 | 0.661561 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.50804 | −0.0923849 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5972 | 0.757679 | 0.378840 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378840 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3732 | −0.785163 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.6514 | −1.85822 | −0.929109 | − | 0.369805i | \(-0.879424\pi\) | ||||
−0.929109 | + | 0.369805i | \(0.879424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6478 | 0.646564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.32851 | −0.0851957 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.42487 | −0.125142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.54226 | 0.348202 | 0.174101 | − | 0.984728i | \(-0.444298\pi\) | ||||
0.174101 | + | 0.984728i | \(0.444298\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.14568 | −0.114635 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0964 | 0.440232 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0891 | −0.911877 | −0.455939 | − | 0.890011i | \(-0.650696\pi\) | ||||
−0.455939 | + | 0.890011i | \(0.650696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.233444 | −0.00847347 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.1210 | −0.584387 | −0.292193 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292193 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.8867 | 1.15438 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.1613 | −1.19895 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.0958 | 1.12280 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.70242 | −0.133513 | −0.0667563 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667563 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.8970 | 0.644543 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6202 | −0.561820 | −0.280910 | − | 0.959734i | \(-0.590636\pi\) | ||||
−0.280910 | + | 0.959734i | \(0.590636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.15107 | 0.0413476 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.7826 | 0.673822 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5204 | −0.412760 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.94477 | −0.105372 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.51634 | 0.268612 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.28977 | 0.188800 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.9804 | −0.819162 | −0.409581 | − | 0.912274i | \(-0.634325\pi\) | ||||
−0.409581 | + | 0.912274i | \(0.634325\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.47322 | −0.0880488 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.61989 | −0.235376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.6902 | −2.08415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.67379 | 0.236695 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.0389 | −1.02861 | −0.514304 | − | 0.857608i | \(-0.671950\pi\) | ||||
−0.514304 | + | 0.857608i | \(0.671950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.8661 | −1.44574 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.2799 | 0.681223 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.55113 | 0.0547383 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.19926 | −0.253741 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.57002 | −0.231276 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.4110 | 1.91299 | 0.956495 | − | 0.291749i | \(-0.0942373\pi\) | ||||
0.956495 | + | 0.291749i | \(0.0942373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.15103 | −0.0755329 | −0.0377665 | − | 0.999287i | \(-0.512024\pi\) | ||||
−0.0377665 | + | 0.999287i | \(0.512024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4341 | 0.576370 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.7576 | 0.657051 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.2664 | 1.30379 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.0195 | 1.29357 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.22999 | 0.0429270 | 0.0214635 | − | 0.999770i | \(-0.493167\pi\) | ||||
0.0214635 | + | 0.999770i | \(0.493167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.62689 | −0.230999 | −0.115499 | − | 0.993308i | \(-0.536847\pi\) | ||||
−0.115499 | + | 0.993308i | \(0.536847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.141296 | −0.00491931 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.2468 | −1.53861 | −0.769306 | − | 0.638880i | \(-0.779398\pi\) | ||||
−0.769306 | + | 0.638880i | \(0.779398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.0928 | 1.84399 | 0.921995 | − | 0.387202i | \(-0.126558\pi\) | ||||
0.921995 | + | 0.387202i | \(0.126558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.2516 | 0.737208 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −69.0347 | −2.39191 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.971314 | 0.0336137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.2095 | −0.352891 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.79163 | −0.234473 | −0.117237 | − | 0.993104i | \(-0.537404\pi\) | ||||
−0.117237 | + | 0.993104i | \(0.537404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0585 | −0.898570 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.41671 | 0.0832361 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.66791 | −0.126180 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45.1991 | 1.55306 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6146 | −0.604532 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.48170 | −0.153631 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.2136 | 0.829057 | 0.414528 | − | 0.910036i | \(-0.363947\pi\) | ||||
0.414528 | + | 0.910036i | \(0.363947\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.3320 | 1.13993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.5641 | −0.429183 | −0.214591 | − | 0.976704i | \(-0.568842\pi\) | ||||
−0.214591 | + | 0.976704i | \(0.568842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0971 | 0.856301 | 0.428151 | − | 0.903707i | \(-0.359165\pi\) | ||||
0.428151 | + | 0.903707i | \(0.359165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.82796 | −0.198616 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.28070 | −0.315919 | −0.157959 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157959 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.8891 | −1.22027 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.2804 | −0.790643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.06612 | 0.137934 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7178 | 0.939181 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.9311 | −1.18224 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48.4521 | −1.63798 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.0652 | −1.38667 | −0.693336 | − | 0.720614i | \(-0.743860\pi\) | ||||
−0.693336 | + | 0.720614i | \(0.743860\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.9109 | 0.705306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.4251 | 1.73256 | 0.866278 | − | 0.499563i | \(-0.166506\pi\) | ||||
0.866278 | + | 0.499563i | \(0.166506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.524245 | −0.0176422 | −0.00882112 | − | 0.999961i | \(-0.502808\pi\) | ||||
−0.00882112 | + | 0.999961i | \(0.502808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1639 | 0.476114 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.0210 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.2651 | −2.18892 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16558 | −0.0390485 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.0765 | 1.37457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.10127 | −0.270796 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.57992 | 0.0861409 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.99540 | −0.133254 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.6878 | −0.855784 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.8524 | 0.627370 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.5921 | −1.01692 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.0731 | 0.766128 | 0.383064 | − | 0.923722i | \(-0.374869\pi\) | ||||
0.383064 | + | 0.923722i | \(0.374869\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.7091 | −1.05172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.7313 | −0.985040 | −0.492520 | − | 0.870301i | \(-0.663924\pi\) | ||||
−0.492520 | + | 0.870301i | \(0.663924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.348249 | −0.0115254 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.7329 | −0.883764 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −82.0103 | −2.70822 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8975 | 0.656357 | 0.328179 | − | 0.944616i | \(-0.393565\pi\) | ||||
0.328179 | + | 0.944616i | \(0.393565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.79808 | 0.289907 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.5443 | 1.07121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.71264 | −0.0891909 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.9199 | 0.884165 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4312 | −0.834372 | −0.417186 | − | 0.908821i | \(-0.636984\pi\) | ||||
−0.417186 | + | 0.908821i | \(0.636984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 69.3901 | 2.27417 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.9435 | 0.521967 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.95957 | −0.162195 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.2627 | 1.87069 | 0.935345 | − | 0.353737i | \(-0.115089\pi\) | ||||
0.935345 | + | 0.353737i | \(0.115089\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.15745 | −0.200941 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.1114 | 1.34019 | 0.670096 | − | 0.742274i | \(-0.266253\pi\) | ||||
0.670096 | + | 0.742274i | \(0.266253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.39060 | 0.0452843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.6491 | 1.25726 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.6839 | −1.48453 | −0.742263 | − | 0.670109i | \(-0.766247\pi\) | ||||
−0.742263 | + | 0.670109i | \(0.766247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1424 | −0.556467 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0112 | 0.746189 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.4998 | −1.60346 | −0.801728 | − | 0.597689i | \(-0.796086\pi\) | ||||
−0.801728 | + | 0.597689i | \(0.796086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.3519 | −1.27340 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.490445 | 0.0158538 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.498550 | 0.0160990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5730 | −0.824936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.91405 | −0.0616795 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.5475 | 1.69156 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.74494 | −0.120429 | −0.0602146 | − | 0.998185i | \(-0.519178\pi\) | ||||
−0.0602146 | + | 0.998185i | \(0.519178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.4717 | 1.20377 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.5625 | −1.33380 | −0.666901 | − | 0.745146i | \(-0.732380\pi\) | ||||
−0.666901 | + | 0.745146i | \(0.732380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7656 | 0.377186 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.56155 | 0.0500095 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.4357 | 1.00572 | 0.502859 | − | 0.864368i | \(-0.332281\pi\) | ||||
0.502859 | + | 0.864368i | \(0.332281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.88349 | 0.0921566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.8205 | 0.568965 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.3372 | 1.12708 | 0.563540 | − | 0.826089i | \(-0.309439\pi\) | ||||
0.563540 | + | 0.826089i | \(0.309439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.7518 | 1.42591 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.7799 | 0.661432 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.49836 | −0.143040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2922 | −0.549304 | −0.274652 | − | 0.961544i | \(-0.588563\pi\) | ||||
−0.274652 | + | 0.961544i | \(0.588563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.64414 | −0.210846 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.1569 | 1.65349 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2403 | 0.324312 | 0.162156 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162156 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0599 | 0.761222 |
(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 | 8048.2.a.v.1.11 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.18 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.18 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.11 | 28 | 1.1 | even | 1 | trivial |