Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, 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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.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: | \(64.1358429035\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-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 | ||||||||
\(3\) | 1.12351 | 0.648660 | 0.324330 | − | 0.945944i | \(-0.394861\pi\) | ||||
0.324330 | + | 0.945944i | \(0.394861\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.837743 | 0.374650 | 0.187325 | − | 0.982298i | \(-0.440018\pi\) | ||||
0.187325 | + | 0.982298i | \(0.440018\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.914625 | 0.345696 | 0.172848 | − | 0.984949i | \(-0.444703\pi\) | ||||
0.172848 | + | 0.984949i | \(0.444703\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.73772 | −0.579241 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.68790 | −0.810431 | −0.405216 | − | 0.914221i | \(-0.632804\pi\) | ||||
−0.405216 | + | 0.914221i | \(0.632804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.48712 | 1.79920 | 0.899602 | − | 0.436710i | \(-0.143856\pi\) | ||||
0.899602 | + | 0.436710i | \(0.143856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.941213 | 0.243020 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64299 | −0.641019 | −0.320509 | − | 0.947245i | \(-0.603854\pi\) | ||||
−0.320509 | + | 0.947245i | \(0.603854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38001 | −0.546011 | −0.273005 | − | 0.962012i | \(-0.588018\pi\) | ||||
−0.273005 | + | 0.962012i | \(0.588018\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.02759 | 0.224239 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.02383 | 0.213483 | 0.106742 | − | 0.994287i | \(-0.465958\pi\) | ||||
0.106742 | + | 0.994287i | \(0.465958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29819 | −0.859637 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.32288 | −1.02439 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.24964 | −0.603443 | −0.301722 | − | 0.953396i | \(-0.597561\pi\) | ||||
−0.301722 | + | 0.953396i | \(0.597561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.564072 | −0.101310 | −0.0506552 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506552 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.01988 | −0.525694 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.766220 | 0.129515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.959245 | −0.157699 | −0.0788494 | − | 0.996887i | \(-0.525125\pi\) | ||||
−0.0788494 | + | 0.996887i | \(0.525125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.28836 | 1.16707 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.79287 | 0.748521 | 0.374261 | − | 0.927324i | \(-0.377897\pi\) | ||||
0.374261 | + | 0.927324i | \(0.377897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.94079 | −1.05846 | −0.529230 | − | 0.848478i | \(-0.677519\pi\) | ||||
−0.529230 | + | 0.848478i | \(0.677519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.45576 | −0.217013 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.03713 | −0.880605 | −0.440303 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440303 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16346 | −0.880494 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.96943 | −0.415803 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.79887 | −0.521816 | −0.260908 | − | 0.965364i | \(-0.584022\pi\) | ||||
−0.260908 | + | 0.965364i | \(0.584022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.25177 | −0.303628 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.67396 | −0.354175 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.91325 | −0.249084 | −0.124542 | − | 0.992214i | \(-0.539746\pi\) | ||||
−0.124542 | + | 0.992214i | \(0.539746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.45521 | 0.442394 | 0.221197 | − | 0.975229i | \(-0.429004\pi\) | ||||
0.221197 | + | 0.975229i | \(0.429004\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.58936 | −0.200241 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.43454 | 0.674072 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9343 | −1.70235 | −0.851173 | − | 0.524885i | \(-0.824108\pi\) | ||||
−0.851173 | + | 0.524885i | \(0.824108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.15029 | 0.138478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.544993 | −0.0646788 | −0.0323394 | − | 0.999477i | \(-0.510296\pi\) | ||||
−0.0323394 | + | 0.999477i | \(0.510296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.94039 | 0.695270 | 0.347635 | − | 0.937630i | \(-0.386985\pi\) | ||||
0.347635 | + | 0.937630i | \(0.386985\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.82906 | −0.557612 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.45842 | −0.280163 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.81781 | 0.429537 | 0.214768 | − | 0.976665i | \(-0.431100\pi\) | ||||
0.214768 | + | 0.976665i | \(0.431100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.767154 | −0.0852393 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.21857 | −0.463048 | −0.231524 | − | 0.972829i | \(-0.574371\pi\) | ||||
−0.231524 | + | 0.972829i | \(0.574371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.21414 | −0.240158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65101 | −0.391429 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.26471 | 0.346059 | 0.173030 | − | 0.984917i | \(-0.444644\pi\) | ||||
0.173030 | + | 0.984917i | \(0.444644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.93329 | 0.621977 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.633742 | −0.0657160 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.99383 | −0.204563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8133 | −1.19946 | −0.599729 | − | 0.800203i | \(-0.704725\pi\) | ||||
−0.599729 | + | 0.800203i | \(0.704725\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.67082 | 0.469435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.27857 | 0.624741 | 0.312370 | − | 0.949960i | \(-0.398877\pi\) | ||||
0.312370 | + | 0.949960i | \(0.398877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.57362 | 0.549185 | 0.274593 | − | 0.961561i | \(-0.411457\pi\) | ||||
0.274593 | + | 0.961561i | \(0.411457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.860857 | 0.0840111 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0677 | 1.26330 | 0.631652 | − | 0.775252i | \(-0.282377\pi\) | ||||
0.631652 | + | 0.775252i | \(0.282377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2936 | −1.36908 | −0.684538 | − | 0.728977i | \(-0.739996\pi\) | ||||
−0.684538 | + | 0.728977i | \(0.739996\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.07772 | −0.102293 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0354 | −0.944050 | −0.472025 | − | 0.881585i | \(-0.656477\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.857707 | 0.0799815 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.2728 | −1.04217 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.41734 | −0.221598 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.77522 | −0.343201 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.38485 | 0.485535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.78949 | −0.696713 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8409 | 1.76060 | 0.880298 | − | 0.474421i | \(-0.157343\pi\) | ||||
0.880298 | + | 0.474421i | \(0.157343\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.79805 | −0.686580 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.0221 | −1.66197 | −0.830983 | − | 0.556298i | \(-0.812221\pi\) | ||||
−0.830983 | + | 0.556298i | \(0.812221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17681 | −0.188754 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.45921 | −0.383788 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9489 | 0.935427 | 0.467713 | − | 0.883880i | \(-0.345078\pi\) | ||||
0.467713 | + | 0.883880i | \(0.345078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.67341 | 0.311574 | 0.155787 | − | 0.987791i | \(-0.450209\pi\) | ||||
0.155787 | + | 0.987791i | \(0.450209\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.78278 | −0.571213 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.4367 | −1.45813 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.72236 | −0.226080 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.92472 | −0.571141 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4910 | 1.02331 | 0.511653 | − | 0.859192i | \(-0.329033\pi\) | ||||
0.511653 | + | 0.859192i | \(0.329033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0042 | −1.54654 | −0.773270 | − | 0.634077i | \(-0.781380\pi\) | ||||
−0.773270 | + | 0.634077i | \(0.781380\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.59278 | 0.371304 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.472548 | −0.0379559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.501496 | −0.0400238 | −0.0200119 | − | 0.999800i | \(-0.506370\pi\) | ||||
−0.0200119 | + | 0.999800i | \(0.506370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.26808 | −0.338481 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.936421 | 0.0738003 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.85208 | 0.536696 | 0.268348 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268348 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.52988 | −0.196951 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.1821 | −0.942677 | −0.471339 | − | 0.881952i | \(-0.656229\pi\) | ||||
−0.471339 | + | 0.881952i | \(0.656229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.0828 | 2.23714 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.13579 | 0.316272 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.28011 | 0.629525 | 0.314763 | − | 0.949170i | \(-0.398075\pi\) | ||||
0.314763 | + | 0.949170i | \(0.398075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.93123 | −0.297173 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.14956 | −0.161571 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.4551 | 0.856198 | 0.428099 | − | 0.903732i | \(-0.359183\pi\) | ||||
0.428099 | + | 0.903732i | \(0.359183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0757 | 0.748920 | 0.374460 | − | 0.927243i | \(-0.377828\pi\) | ||||
0.374460 | + | 0.927243i | \(0.377828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.88197 | 0.286963 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.803600 | −0.0590819 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.10408 | 0.519502 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.86844 | −0.354127 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3206 | −1.03620 | −0.518102 | − | 0.855319i | \(-0.673361\pi\) | ||||
−0.518102 | + | 0.855319i | \(0.673361\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.30349 | −0.669680 | −0.334840 | − | 0.942275i | \(-0.608682\pi\) | ||||
−0.334840 | + | 0.942275i | \(0.608682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.10577 | 0.437243 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.2639 | −1.51499 | −0.757495 | − | 0.652842i | \(-0.773577\pi\) | ||||
−0.757495 | + | 0.652842i | \(0.773577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0729 | 1.13938 | 0.569689 | − | 0.821861i | \(-0.307064\pi\) | ||||
0.569689 | + | 0.821861i | \(0.307064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.6553 | −1.10424 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.97220 | −0.208608 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.01519 | 0.280433 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.77913 | −0.123658 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.39721 | 0.442504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.53964 | −0.243679 | −0.121839 | − | 0.992550i | \(-0.538879\pi\) | ||||
−0.121839 | + | 0.992550i | \(0.538879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.612306 | −0.0419545 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.81459 | −0.396552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.515915 | −0.0350226 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.67409 | 0.450993 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.1454 | −1.15332 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.353039 | −0.0236412 | −0.0118206 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118206 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.46906 | 0.497937 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.8073 | −1.18191 | −0.590957 | − | 0.806703i | \(-0.701250\pi\) | ||||
−0.590957 | + | 0.806703i | \(0.701250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.42091 | 0.292142 | 0.146071 | − | 0.989274i | \(-0.453337\pi\) | ||||
0.146071 | + | 0.989274i | \(0.453337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.76206 | −0.181730 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.22980 | −0.211591 | −0.105796 | − | 0.994388i | \(-0.533739\pi\) | ||||
−0.105796 | + | 0.994388i | \(0.533739\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.05756 | −0.329919 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.28935 | 0.278623 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7997 | −1.34542 | −0.672710 | − | 0.739907i | \(-0.734870\pi\) | ||||
−0.672710 | + | 0.739907i | \(0.734870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.4909 | 1.83526 | 0.917631 | − | 0.397434i | \(-0.130099\pi\) | ||||
0.917631 | + | 0.397434i | \(0.130099\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1067 | 0.969098 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.16340 | −0.329877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.4394 | −0.982385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.73961 | −0.300361 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.75195 | −0.173014 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.48762 | −0.155781 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.70654 | 0.231208 | 0.115604 | − | 0.993295i | \(-0.463120\pi\) | ||||
0.115604 | + | 0.993295i | \(0.463120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.877349 | −0.0545158 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.64697 | 0.349539 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31.2731 | −1.92838 | −0.964190 | − | 0.265212i | \(-0.914558\pi\) | ||||
−0.964190 | + | 0.265212i | \(0.914558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.18248 | −0.195498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.66794 | 0.224475 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.82685 | −0.416240 | −0.208120 | − | 0.978103i | \(-0.566735\pi\) | ||||
−0.208120 | + | 0.978103i | \(0.566735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0054 | −1.70120 | −0.850602 | − | 0.525810i | \(-0.823762\pi\) | ||||
−0.850602 | + | 0.525810i | \(0.823762\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.66611 | 0.403452 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.5531 | 0.696677 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7310 | 0.764930 | 0.382465 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382465 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.980201 | 0.0586831 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4260 | −0.741273 | −0.370636 | − | 0.928778i | \(-0.620860\pi\) | ||||
−0.370636 | + | 0.928778i | \(0.620860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.9540 | −0.888924 | −0.444462 | − | 0.895798i | \(-0.646605\pi\) | ||||
−0.444462 | + | 0.895798i | \(0.646605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.24009 | −0.132692 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.38368 | 0.258761 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0146 | −0.589095 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.2724 | −0.778040 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.32019 | 0.0771261 | 0.0385630 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385630 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.60281 | −0.0933193 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.3074 | 0.830197 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.64172 | 0.384100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.34822 | −0.365905 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.05404 | 0.405244 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.89458 | 0.165743 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.14221 | −0.407628 | −0.203814 | − | 0.979010i | \(-0.565334\pi\) | ||||
−0.203814 | + | 0.979010i | \(0.565334\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.26203 | 0.356234 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.35571 | −0.303694 | −0.151847 | − | 0.988404i | \(-0.548522\pi\) | ||||
−0.151847 | + | 0.988404i | \(0.548522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2503 | 1.20114 | 0.600570 | − | 0.799572i | \(-0.294940\pi\) | ||||
0.600570 | + | 0.799572i | \(0.294940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.33148 | −0.0750203 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0012 | −0.842553 | −0.421276 | − | 0.906932i | \(-0.638418\pi\) | ||||
−0.421276 | + | 0.906932i | \(0.638418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.73470 | 0.489049 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6817 | 0.819454 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.29033 | 0.350003 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.8829 | −1.54666 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.0590 | −0.888064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.52171 | −0.304421 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.905269 | 0.0497581 | 0.0248790 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248790 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.66690 | 0.0913456 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6734 | −0.637784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.8204 | −0.698370 | −0.349185 | − | 0.937054i | \(-0.613541\pi\) | ||||
−0.349185 | + | 0.937054i | \(0.613541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.2749 | −0.612367 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.51617 | 0.0821051 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0396 | −0.650079 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.963643 | 0.0518808 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.09193 | 0.165984 | 0.0829919 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829919 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.4241 | 0.665049 | 0.332525 | − | 0.943095i | \(-0.392100\pi\) | ||||
0.332525 | + | 0.943095i | \(0.392100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34.5302 | −1.84309 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.28265 | 0.227943 | 0.113971 | − | 0.993484i | \(-0.463643\pi\) | ||||
0.113971 | + | 0.993484i | \(0.463643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.456564 | −0.0242319 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.71591 | −0.143741 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.6478 | −1.51197 | −0.755987 | − | 0.654587i | \(-0.772843\pi\) | ||||
−0.755987 | + | 0.654587i | \(0.772843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3356 | −0.701872 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.24150 | −0.222621 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.97652 | 0.260483 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.571150 | −0.0298138 | −0.0149069 | − | 0.999889i | \(-0.504745\pi\) | ||||
−0.0149069 | + | 0.999889i | \(0.504745\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.32868 | −0.433574 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.47455 | −0.180389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5845 | 0.806935 | 0.403468 | − | 0.914994i | \(-0.367805\pi\) | ||||
0.403468 | + | 0.914994i | \(0.367805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.75158 | −0.451930 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.0808 | −1.08572 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6281 | 1.11096 | 0.555480 | − | 0.831530i | \(-0.312534\pi\) | ||||
0.555480 | + | 0.831530i | \(0.312534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2915 | 1.14203 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.1681 | 0.928344 | 0.464172 | − | 0.885745i | \(-0.346352\pi\) | ||||
0.464172 | + | 0.885745i | \(0.346352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.05952 | −0.104963 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0612 | 0.613103 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.9755 | 1.87473 | 0.937367 | − | 0.348344i | \(-0.113256\pi\) | ||||
0.937367 | + | 0.348344i | \(0.113256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.70597 | −0.136847 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.3715 | −1.07805 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.19834 | 0.160926 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.75998 | −0.238896 | −0.119448 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119448 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.44567 | −0.122437 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.37072 | 0.268201 | 0.134100 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134100 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.65921 | −0.182278 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.642678 | −0.0319349 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.57835 | 0.127804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.0094 | 1.78055 | 0.890275 | − | 0.455423i | \(-0.150512\pi\) | ||||
0.890275 | + | 0.455423i | \(0.150512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3012 | 0.606773 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.74991 | −0.0861073 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.53408 | −0.173481 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.12712 | 0.202106 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.2585 | −1.62478 | −0.812392 | − | 0.583112i | \(-0.801835\pi\) | ||||
−0.812392 | + | 0.583112i | \(0.801835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.70553 | −0.229333 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.4908 | 0.510082 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.3601 | 0.551044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.16022 | 0.152934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.5903 | −0.945831 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.34678 | 0.161209 | 0.0806043 | − | 0.996746i | \(-0.474315\pi\) | ||||
0.0806043 | + | 0.996746i | \(0.474315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.9634 | 1.77635 | 0.888175 | − | 0.459506i | \(-0.151974\pi\) | ||||
0.888175 | + | 0.459506i | \(0.151974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.05861 | −0.146649 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.43672 | −0.116564 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.1004 | 1.05479 | 0.527396 | − | 0.849619i | \(-0.323168\pi\) | ||||
0.527396 | + | 0.849619i | \(0.323168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7104 | 0.510018 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2016 | 0.532206 | 0.266103 | − | 0.963945i | \(-0.414264\pi\) | ||||
0.266103 | + | 0.963945i | \(0.414264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.73499 | 0.129651 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0338 | 0.663777 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.575571 | −0.0271629 | −0.0135814 | − | 0.999908i | \(-0.504323\pi\) | ||||
−0.0135814 | + | 0.999908i | \(0.504323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8827 | −0.606625 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.3514 | −1.00318 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.97057 | 0.233024 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3518 | 0.624571 | 0.312286 | − | 0.949988i | \(-0.398905\pi\) | ||||
0.312286 | + | 0.949988i | \(0.398905\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0683 | 0.656653 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6167 | −0.541042 | −0.270521 | − | 0.962714i | \(-0.587196\pi\) | ||||
−0.270521 | + | 0.962714i | \(0.587196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2859 | 1.45398 | 0.726989 | − | 0.686649i | \(-0.240919\pi\) | ||||
0.726989 | + | 0.686649i | \(0.240919\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.530913 | −0.0246205 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7554 | −0.867897 | −0.433949 | − | 0.900938i | \(-0.642880\pi\) | ||||
−0.433949 | + | 0.900938i | \(0.642880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7447 | −0.588494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.563437 | −0.0259618 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6561 | 0.857809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2297 | 0.469371 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.60139 | 0.302257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.8888 | −0.863052 | −0.431526 | − | 0.902100i | \(-0.642025\pi\) | ||||
−0.431526 | + | 0.902100i | \(0.642025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.22274 | −0.283733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.05208 | 0.0478713 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.89650 | −0.449377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.5019 | −1.88063 | −0.940315 | − | 0.340306i | \(-0.889469\pi\) | ||||
−0.940315 | + | 0.340306i | \(0.889469\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.69839 | 0.348133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.75278 | −0.395007 | −0.197504 | − | 0.980302i | \(-0.563283\pi\) | ||||
−0.197504 | + | 0.980302i | \(0.563283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.58876 | 0.386818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.91294 | 0.175874 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.498464 | −0.0223592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.8347 | 1.38035 | 0.690176 | − | 0.723642i | \(-0.257533\pi\) | ||||
0.690176 | + | 0.723642i | \(0.257533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6867 | −0.611477 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5937 | −0.962815 | −0.481408 | − | 0.876497i | \(-0.659874\pi\) | ||||
−0.481408 | + | 0.876497i | \(0.659874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.25982 | 0.234059 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.6748 | 1.45114 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.236848 | 0.0104981 | 0.00524905 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00524905 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.43323 | 0.240352 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.6685 | 0.559328 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.66926 | 0.205752 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.2272 | 0.713670 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.30280 | 0.408348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.9509 | 0.917874 | 0.458937 | − | 0.888469i | \(-0.348230\pi\) | ||||
0.458937 | + | 0.888469i | \(0.348230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.6823 | −1.25419 | −0.627094 | − | 0.778944i | \(-0.715756\pi\) | ||||
−0.627094 | + | 0.778944i | \(0.715756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.41678 | −0.192764 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.49084 | 0.0649419 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9518 | −0.954425 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.32470 | 0.144280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.0920 | 1.34674 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9474 | 0.473297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.8700 | 0.555381 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5667 | 0.713580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1991 | 0.739446 | 0.369723 | − | 0.929142i | \(-0.379453\pi\) | ||||
0.369723 | + | 0.929142i | \(0.379453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.3201 | 0.485794 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.9743 | −0.512924 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1830 | 1.16226 | 0.581130 | − | 0.813811i | \(-0.302611\pi\) | ||||
0.581130 | + | 0.813811i | \(0.302611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00419 | −0.256253 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.73417 | 0.329487 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.49186 | 0.148489 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.902854 | −0.0383240 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5830 | 0.956872 | 0.478436 | − | 0.878122i | \(-0.341204\pi\) | ||||
0.478436 | + | 0.878122i | \(0.341204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −45.0257 | −1.90439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.98151 | 0.336980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.0940 | −1.22617 | −0.613083 | − | 0.790019i | \(-0.710071\pi\) | ||||
−0.613083 | + | 0.790019i | \(0.710071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.40707 | −0.353688 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.701658 | −0.0294669 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.7632 | −1.96041 | −0.980207 | − | 0.197977i | \(-0.936563\pi\) | ||||
−0.980207 | + | 0.197977i | \(0.936563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0896 | 0.966270 | 0.483135 | − | 0.875546i | \(-0.339498\pi\) | ||||
0.483135 | + | 0.875546i | \(0.339498\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0894 | −0.672144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.40061 | −0.183518 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.73647 | −0.155551 | −0.0777756 | − | 0.996971i | \(-0.524782\pi\) | ||||
−0.0777756 | + | 0.996971i | \(0.524782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.4526 | −0.434394 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.85841 | −0.160074 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2110 | 0.422896 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.44373 | −0.390450 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.5144 | −1.63094 | −0.815468 | − | 0.578803i | \(-0.803520\pi\) | ||||
−0.815468 | + | 0.578803i | \(0.803520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.34250 | 0.0553166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.8902 | −0.982712 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.8975 | −0.981353 | −0.490677 | − | 0.871342i | \(-0.663250\pi\) | ||||
−0.490677 | + | 0.871342i | \(0.663250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.02511 | −0.0830215 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.0581 | 0.739068 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.3427 | 0.504310 | 0.252155 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252155 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3314 | −0.625381 | −0.312690 | − | 0.949855i | \(-0.601230\pi\) | ||||
−0.312690 | + | 0.949855i | \(0.601230\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.2139 | 0.986068 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.16266 | −0.128580 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.95851 | 0.160671 | 0.0803354 | − | 0.996768i | \(-0.474401\pi\) | ||||
0.0803354 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.33930 | −0.135315 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.1636 | −1.58439 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.5554 | 1.47646 | 0.738229 | − | 0.674551i | \(-0.235663\pi\) | ||||
0.738229 | + | 0.674551i | \(0.235663\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.51112 | 0.181906 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8829 | 0.760196 | 0.380098 | − | 0.924946i | \(-0.375890\pi\) | ||||
0.380098 | + | 0.924946i | \(0.375890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.1093 | −1.37097 | −0.685485 | − | 0.728087i | \(-0.740410\pi\) | ||||
−0.685485 | + | 0.728087i | \(0.740410\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.44973 | −0.218690 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.98599 | 0.119631 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9653 | 0.598614 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.18734 | 0.287035 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.53527 | 0.101088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.5357 | −1.29523 | −0.647613 | − | 0.761970i | \(-0.724233\pi\) | ||||
−0.647613 | + | 0.761970i | \(0.724233\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.97682 | −0.158064 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.6216 | 0.659607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.9831 | −1.58419 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.947046 | 0.0374646 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.62567 | −0.340693 | −0.170347 | − | 0.985384i | \(-0.554489\pi\) | ||||
−0.170347 | + | 0.985384i | \(0.554489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9906 | 0.946099 | 0.473049 | − | 0.881036i | \(-0.343153\pi\) | ||||
0.473049 | + | 0.881036i | \(0.343153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.53276 | −0.257227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.5477 | −0.611244 | −0.305622 | − | 0.952153i | \(-0.598864\pi\) | ||||
−0.305622 | + | 0.952153i | \(0.598864\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.14262 | 0.201865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.579636 | −0.0227177 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.3626 | 0.640319 | 0.320159 | − | 0.947364i | \(-0.396264\pi\) | ||||
0.320159 | + | 0.947364i | \(0.396264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.9356 | −0.622656 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3227 | −0.402729 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2467 | 0.399153 | 0.199577 | − | 0.979882i | \(-0.436043\pi\) | ||||
0.199577 | + | 0.979882i | \(0.436043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.86675 | 0.150399 | 0.0751995 | − | 0.997169i | \(-0.476041\pi\) | ||||
0.0751995 | + | 0.997169i | \(0.476041\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.2630 | −0.748115 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.82361 | −0.0707165 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.32708 | −0.128825 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.396643 | −0.0153351 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.28724 | −0.358530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.5164 | −0.983583 | −0.491792 | − | 0.870713i | \(-0.663658\pi\) | ||||
−0.491792 | + | 0.870713i | \(0.663658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.8788 | 0.880604 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.7382 | −0.489569 | −0.244784 | − | 0.969578i | \(-0.578717\pi\) | ||||
−0.244784 | + | 0.969578i | \(0.578717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8047 | −0.414648 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0068 | −0.766660 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.5051 | 0.555021 | 0.277511 | − | 0.960723i | \(-0.410491\pi\) | ||||
0.277511 | + | 0.960723i | \(0.410491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.17235 | 0.350458 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.96694 | 0.189501 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.6438 | −0.938853 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.4368 | 1.04375 | 0.521873 | − | 0.853023i | \(-0.325233\pi\) | ||||
0.521873 | + | 0.853023i | \(0.325233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.27205 | 0.162282 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.07737 | 0.116731 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6675 | −0.479816 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.62872 | −0.137251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.45900 | 0.168414 | 0.0842070 | − | 0.996448i | \(-0.473164\pi\) | ||||
0.0842070 | + | 0.996448i | \(0.473164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.28301 | 0.0861053 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.68222 | −0.214005 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.74253 | 0.215970 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.8867 | −1.08486 | −0.542432 | − | 0.840100i | \(-0.682496\pi\) | ||||
−0.542432 | + | 0.840100i | \(0.682496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.63429 | −0.248805 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.577515 | −0.0216281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6075 | −0.546289 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.3687 | −0.872719 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5059 | 0.727446 | 0.363723 | − | 0.931507i | \(-0.381505\pi\) | ||||
0.363723 | + | 0.931507i | \(0.381505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.09777 | 0.189851 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.0099 | 1.19046 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.9676 | 0.518742 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.1180 | −1.30245 | −0.651227 | − | 0.758883i | \(-0.725746\pi\) | ||||
−0.651227 | + | 0.758883i | \(0.725746\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.2741 | 0.713854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3444 | 0.678493 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.30475 | 0.343679 | 0.171839 | − | 0.985125i | \(-0.445029\pi\) | ||||
0.171839 | + | 0.985125i | \(0.445029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.80113 | −0.213978 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.4540 | 1.37963 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50063 | −0.165558 | −0.0827792 | − | 0.996568i | \(-0.526380\pi\) | ||||
−0.0827792 | + | 0.996568i | \(0.526380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.3463 | −0.637234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0965 | 1.17751 | 0.588753 | − | 0.808313i | \(-0.299619\pi\) | ||||
0.588753 | + | 0.808313i | \(0.299619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.4643 | 0.383382 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.33070 | 0.268216 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9521 | 0.436719 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.2904 | 1.43373 | 0.716863 | − | 0.697214i | \(-0.245577\pi\) | ||||
0.716863 | + | 0.697214i | \(0.245577\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.12351 | −0.0409430 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.9206 | −0.579411 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.2225 | 1.75267 | 0.876337 | − | 0.481698i | \(-0.159980\pi\) | ||||
0.876337 | + | 0.481698i | \(0.159980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.09185 | −0.112227 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.1518 | −0.549253 | −0.274626 | − | 0.961551i | \(-0.588554\pi\) | ||||
−0.274626 | + | 0.961551i | \(0.588554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0733 | −0.473284 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.84757 | 0.139109 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.4115 | −0.448153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.6348 | −0.780171 | −0.390085 | − | 0.920779i | \(-0.627554\pi\) | ||||
−0.390085 | + | 0.920779i | \(0.627554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.16434 | 0.149975 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.56620 | 0.236170 | 0.118085 | − | 0.993004i | \(-0.462325\pi\) | ||||
0.118085 | + | 0.993004i | \(0.462325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.42449 | 0.0870902 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.985712 | −0.0353622 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4071 | −0.408701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.46488 | 0.0524177 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.2975 | 0.618161 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.420125 | −0.0149949 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.8098 | −0.884374 | −0.442187 | − | 0.896923i | \(-0.645797\pi\) | ||||
−0.442187 | + | 0.896923i | \(0.645797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.1356 | −1.25086 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.17861 | −0.326354 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4144 | 0.795958 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.57555 | −0.126812 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.0966 | 0.995232 | 0.497616 | − | 0.867397i | \(-0.334209\pi\) | ||||
0.497616 | + | 0.867397i | \(0.334209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9561 | 0.564485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.67317 | −0.200452 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.9671 | −0.563468 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.784480 | 0.0276493 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.67004 | −0.269998 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.74367 | −0.0964623 | −0.0482311 | − | 0.998836i | \(-0.515358\pi\) | ||||
−0.0482311 | + | 0.998836i | \(0.515358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.65863 | 0.268931 | 0.134465 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134465 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.4643 | −1.10350 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.74028 | 0.201073 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.5191 | 0.577931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.3104 | −0.360275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.3509 | −0.675352 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.8145 | −0.899839 | −0.449919 | − | 0.893069i | \(-0.648547\pi\) | ||||
−0.449919 | + | 0.893069i | \(0.648547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.9800 | 0.451906 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.30389 | −0.0453409 | −0.0226704 | − | 0.999743i | \(-0.507217\pi\) | ||||
−0.0226704 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.38214 | −0.256392 | −0.128196 | − | 0.991749i | \(-0.540919\pi\) | ||||
−0.128196 | + | 0.991749i | \(0.540919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3034 | 0.496179 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.2900 | 0.564414 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.2054 | −0.353174 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.00249 | 0.103781 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.1387 | −1.24765 | −0.623823 | − | 0.781565i | \(-0.714422\pi\) | ||||
−0.623823 | + | 0.781565i | \(0.714422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4398 | −0.635856 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9607 | −0.480834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.3639 | 0.838143 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.45291 | −0.118643 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8010 | −0.576609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.982104 | −0.0336661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.9567 | 0.751782 | 0.375891 | − | 0.926664i | \(-0.377337\pi\) | ||||
0.375891 | + | 0.926664i | \(0.377337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.46473 | 0.118491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.5956 | 1.42088 | 0.710439 | − | 0.703759i | \(-0.248496\pi\) | ||||
0.710439 | + | 0.703759i | \(0.248496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9788 | 1.05698 | 0.528491 | − | 0.848939i | \(-0.322758\pi\) | ||||
0.528491 | + | 0.848939i | \(0.322758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.92512 | 0.167847 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6703 | 0.499384 | 0.249692 | − | 0.968325i | \(-0.419671\pi\) | ||||
0.249692 | + | 0.968325i | \(0.419671\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.93661 | 0.235852 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.2515 | −0.382122 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2619 | −0.348110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −90.3936 | −3.06287 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.5282 | 0.694775 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.12446 | −0.240851 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.7697 | 0.431203 | 0.215601 | − | 0.976481i | \(-0.430829\pi\) | ||||
0.215601 | + | 0.976481i | \(0.430829\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.48324 | 0.0500286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6925 | −1.23620 | −0.618100 | − | 0.786099i | \(-0.712097\pi\) | ||||
−0.618100 | + | 0.786099i | \(0.712097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8974 | 0.400379 | 0.200189 | − | 0.979757i | \(-0.435844\pi\) | ||||
0.200189 | + | 0.979757i | \(0.435844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.80078 | −0.0605325 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1527 | 0.441624 | 0.220812 | − | 0.975316i | \(-0.429129\pi\) | ||||
0.220812 | + | 0.975316i | \(0.429129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.1470 | 0.608630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.06203 | 0.0690806 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.3684 | 0.480820 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.59647 | 0.320775 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.46204 | 0.249150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.83303 | 0.0611351 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0404 | 0.334494 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.13229 | −0.237348 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.44083 | 0.280583 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.3827 | −1.90536 | −0.952680 | − | 0.303975i | \(-0.901686\pi\) | ||||
−0.952680 | + | 0.303975i | \(0.901686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9104 | −0.361875 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1353 | −1.29661 | −0.648306 | − | 0.761380i | \(-0.724522\pi\) | ||||
−0.648306 | + | 0.761380i | \(0.724522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3391 | 0.375269 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.25209 | 0.107511 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3981 | −0.574535 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.2548 | 1.55879 | 0.779396 | − | 0.626532i | \(-0.215526\pi\) | ||||
0.779396 | + | 0.626532i | \(0.215526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.02436 | −0.264412 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.53544 | −0.116370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.12301 | 0.135564 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.68541 | −0.318111 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.5513 | −1.59292 | −0.796459 | − | 0.604693i | \(-0.793296\pi\) | ||||
−0.796459 | + | 0.604693i | \(0.793296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.6691 | 0.480760 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.01720 | −0.196994 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.95139 | 0.194631 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.1197 | 0.787957 | 0.393978 | − | 0.919120i | \(-0.371098\pi\) | ||||
0.393978 | + | 0.919120i | \(0.371098\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.8750 | 0.779131 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.2531 | 0.497237 | 0.248619 | − | 0.968601i | \(-0.420023\pi\) | ||||
0.248619 | + | 0.968601i | \(0.420023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.90709 | 0.159797 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.07850 | −0.132674 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.5900 | 0.929049 | 0.464525 | − | 0.885560i | \(-0.346225\pi\) | ||||
0.464525 | + | 0.885560i | \(0.346225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.5360 | 1.25093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8540 | −0.546530 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.02081 | −0.162640 | −0.0813200 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813200 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9970 | −0.388214 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.81353 | 0.317226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0141 | 0.323373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6818 | −0.989736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.7081 | −0.731757 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.79393 | −0.250895 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1791 | −0.584601 | −0.292300 | − | 0.956327i | \(-0.594421\pi\) | ||||
−0.292300 | + | 0.956327i | \(0.594421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.06726 | 0.227033 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5831 | 0.692634 | 0.346317 | − | 0.938118i | \(-0.387432\pi\) | ||||
0.346317 | + | 0.938118i | \(0.387432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.35979 | 0.107710 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31.3267 | −1.00326 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6723 | 0.469409 | 0.234705 | − | 0.972067i | \(-0.424588\pi\) | ||||
0.234705 | + | 0.972067i | \(0.424588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.77521 | −0.280457 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.8383 | 0.793025 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.66628 | 0.0531459 | 0.0265730 | − | 0.999647i | \(-0.491541\pi\) | ||||
0.0265730 | + | 0.999647i | \(0.491541\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8137 | −0.567591 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.20370 | −0.197466 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.10619 | −0.225964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.6294 | −1.83066 | −0.915329 | − | 0.402707i | \(-0.868069\pi\) | ||||
−0.915329 | + | 0.402707i | \(0.868069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.01708 | 0.0322761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4649 | 0.426868 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.5092 | 1.06125 | 0.530624 | − | 0.847607i | \(-0.321958\pi\) | ||||
0.530624 | + | 0.847607i | \(0.321958\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.10595 | 0.161545 |
(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 | 8032.2.a.h.1.20 | ✓ | 30 | |
4.3 | odd | 2 | 8032.2.a.i.1.11 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.h.1.20 | ✓ | 30 | 1.1 | even | 1 | trivial | |
8032.2.a.i.1.11 | yes | 30 | 4.3 | odd | 2 |