Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57149 | −1.81832 | −0.909160 | − | 0.416447i | \(-0.863275\pi\) | ||||
−0.909160 | + | 0.416447i | \(0.863275\pi\) | |||||||
\(3\) | −0.285863 | −0.165043 | −0.0825216 | − | 0.996589i | \(-0.526297\pi\) | ||||
−0.0825216 | + | 0.996589i | \(0.526297\pi\) | |||||||
\(4\) | 4.61257 | 2.30629 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.735095 | 0.300101 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −6.71821 | −2.37525 | ||||||||
\(9\) | −2.91828 | −0.972761 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.14192 | 1.85186 | 0.925930 | − | 0.377696i | \(-0.123283\pi\) | ||||
0.925930 | + | 0.377696i | \(0.123283\pi\) | |||||||
\(12\) | −1.31856 | −0.380637 | ||||||||
\(13\) | −1.02339 | −0.283838 | −0.141919 | − | 0.989878i | \(-0.545327\pi\) | ||||
−0.141919 | + | 0.989878i | \(0.545327\pi\) | |||||||
\(14\) | 2.57149 | 0.687260 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.05068 | 2.01267 | ||||||||
\(17\) | −0.880458 | −0.213543 | −0.106771 | − | 0.994284i | \(-0.534051\pi\) | ||||
−0.106771 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(18\) | 7.50434 | 1.76879 | ||||||||
\(19\) | −3.91439 | −0.898024 | −0.449012 | − | 0.893526i | \(-0.648224\pi\) | ||||
−0.449012 | + | 0.893526i | \(0.648224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.285863 | 0.0623804 | ||||||||
\(22\) | −15.7939 | −3.36727 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.92049 | 0.392018 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.63165 | 0.516109 | ||||||||
\(27\) | 1.69182 | 0.325591 | ||||||||
\(28\) | −4.61257 | −0.871694 | ||||||||
\(29\) | 6.92254 | 1.28548 | 0.642742 | − | 0.766083i | \(-0.277797\pi\) | ||||
0.642742 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.390474 | 0.0701312 | 0.0350656 | − | 0.999385i | \(-0.488836\pi\) | ||||
0.0350656 | + | 0.999385i | \(0.488836\pi\) | |||||||
\(32\) | −7.26584 | −1.28443 | ||||||||
\(33\) | −1.75575 | −0.305637 | ||||||||
\(34\) | 2.26409 | 0.388289 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.4608 | −2.24346 | ||||||||
\(37\) | 3.09439 | 0.508714 | 0.254357 | − | 0.967110i | \(-0.418136\pi\) | ||||
0.254357 | + | 0.967110i | \(0.418136\pi\) | |||||||
\(38\) | 10.0658 | 1.63289 | ||||||||
\(39\) | 0.292551 | 0.0468456 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.45816 | −0.540074 | −0.270037 | − | 0.962850i | \(-0.587036\pi\) | ||||
−0.270037 | + | 0.962850i | \(0.587036\pi\) | |||||||
\(42\) | −0.735095 | −0.113428 | ||||||||
\(43\) | −0.0871065 | −0.0132836 | −0.00664181 | − | 0.999978i | \(-0.502114\pi\) | ||||
−0.00664181 | + | 0.999978i | \(0.502114\pi\) | |||||||
\(44\) | 28.3301 | 4.27092 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.57149 | 0.379146 | ||||||||
\(47\) | −6.66651 | −0.972410 | −0.486205 | − | 0.873845i | \(-0.661619\pi\) | ||||
−0.486205 | + | 0.873845i | \(0.661619\pi\) | |||||||
\(48\) | −2.30139 | −0.332177 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.251691 | 0.0352437 | ||||||||
\(52\) | −4.72048 | −0.654613 | ||||||||
\(53\) | −10.9506 | −1.50418 | −0.752090 | − | 0.659060i | \(-0.770954\pi\) | ||||
−0.752090 | + | 0.659060i | \(0.770954\pi\) | |||||||
\(54\) | −4.35050 | −0.592028 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.71821 | 0.897759 | ||||||||
\(57\) | 1.11898 | 0.148213 | ||||||||
\(58\) | −17.8013 | −2.33742 | ||||||||
\(59\) | 14.1936 | 1.84784 | 0.923922 | − | 0.382581i | \(-0.124965\pi\) | ||||
0.923922 | + | 0.382581i | \(0.124965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.74679 | −0.735801 | −0.367900 | − | 0.929865i | \(-0.619923\pi\) | ||||
−0.367900 | + | 0.929865i | \(0.619923\pi\) | |||||||
\(62\) | −1.00410 | −0.127521 | ||||||||
\(63\) | 2.91828 | 0.367669 | ||||||||
\(64\) | 2.58269 | 0.322837 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.51490 | 0.555745 | ||||||||
\(67\) | 3.65650 | 0.446712 | 0.223356 | − | 0.974737i | \(-0.428299\pi\) | ||||
0.223356 | + | 0.974737i | \(0.428299\pi\) | |||||||
\(68\) | −4.06118 | −0.492490 | ||||||||
\(69\) | 0.285863 | 0.0344139 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9617 | −1.77563 | −0.887814 | − | 0.460202i | \(-0.847777\pi\) | ||||
−0.887814 | + | 0.460202i | \(0.847777\pi\) | |||||||
\(72\) | 19.6056 | 2.31055 | ||||||||
\(73\) | 14.5236 | 1.69986 | 0.849930 | − | 0.526896i | \(-0.176644\pi\) | ||||
0.849930 | + | 0.526896i | \(0.176644\pi\) | |||||||
\(74\) | −7.95720 | −0.925005 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.0554 | −2.07110 | ||||||||
\(77\) | −6.14192 | −0.699937 | ||||||||
\(78\) | −0.752291 | −0.0851802 | ||||||||
\(79\) | 3.40561 | 0.383161 | 0.191580 | − | 0.981477i | \(-0.438639\pi\) | ||||
0.191580 | + | 0.981477i | \(0.438639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.27122 | 0.919024 | ||||||||
\(82\) | 8.89263 | 0.982027 | ||||||||
\(83\) | −1.88029 | −0.206389 | −0.103195 | − | 0.994661i | \(-0.532906\pi\) | ||||
−0.103195 | + | 0.994661i | \(0.532906\pi\) | |||||||
\(84\) | 1.31856 | 0.143867 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.223994 | 0.0241539 | ||||||||
\(87\) | −1.97890 | −0.212160 | ||||||||
\(88\) | −41.2627 | −4.39862 | ||||||||
\(89\) | −13.2126 | −1.40053 | −0.700266 | − | 0.713882i | \(-0.746935\pi\) | ||||
−0.700266 | + | 0.713882i | \(0.746935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.02339 | 0.107281 | ||||||||
\(92\) | −4.61257 | −0.480894 | ||||||||
\(93\) | −0.111622 | −0.0115747 | ||||||||
\(94\) | 17.1429 | 1.76815 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.07704 | 0.211987 | ||||||||
\(97\) | 16.5891 | 1.68436 | 0.842182 | − | 0.539194i | \(-0.181271\pi\) | ||||
0.842182 | + | 0.539194i | \(0.181271\pi\) | |||||||
\(98\) | −2.57149 | −0.259760 | ||||||||
\(99\) | −17.9239 | −1.80142 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0659 | 1.49911 | 0.749556 | − | 0.661941i | \(-0.230267\pi\) | ||||
0.749556 | + | 0.661941i | \(0.230267\pi\) | |||||||
\(102\) | −0.647220 | −0.0640844 | ||||||||
\(103\) | 13.5684 | 1.33694 | 0.668469 | − | 0.743740i | \(-0.266950\pi\) | ||||
0.668469 | + | 0.743740i | \(0.266950\pi\) | |||||||
\(104\) | 6.87537 | 0.674186 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.1594 | 2.73508 | ||||||||
\(107\) | −5.01686 | −0.484999 | −0.242499 | − | 0.970152i | \(-0.577967\pi\) | ||||
−0.242499 | + | 0.970152i | \(0.577967\pi\) | |||||||
\(108\) | 7.80364 | 0.750905 | ||||||||
\(109\) | 0.946819 | 0.0906888 | 0.0453444 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453444 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.884572 | −0.0839598 | ||||||||
\(112\) | −8.05068 | −0.760718 | ||||||||
\(113\) | −13.9764 | −1.31479 | −0.657393 | − | 0.753548i | \(-0.728341\pi\) | ||||
−0.657393 | + | 0.753548i | \(0.728341\pi\) | |||||||
\(114\) | −2.87745 | −0.269498 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 31.9307 | 2.96469 | ||||||||
\(117\) | 2.98655 | 0.276107 | ||||||||
\(118\) | −36.4986 | −3.35997 | ||||||||
\(119\) | 0.880458 | 0.0807115 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.7232 | 2.42938 | ||||||||
\(122\) | 14.7778 | 1.33792 | ||||||||
\(123\) | 0.988560 | 0.0891355 | ||||||||
\(124\) | 1.80109 | 0.161743 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.50434 | −0.668540 | ||||||||
\(127\) | 7.83418 | 0.695171 | 0.347586 | − | 0.937648i | \(-0.387002\pi\) | ||||
0.347586 | + | 0.937648i | \(0.387002\pi\) | |||||||
\(128\) | 7.89030 | 0.697411 | ||||||||
\(129\) | 0.0249005 | 0.00219237 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3276 | −0.989694 | −0.494847 | − | 0.868980i | \(-0.664776\pi\) | ||||
−0.494847 | + | 0.868980i | \(0.664776\pi\) | |||||||
\(132\) | −8.09852 | −0.704886 | ||||||||
\(133\) | 3.91439 | 0.339421 | ||||||||
\(134\) | −9.40266 | −0.812266 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.91510 | 0.507216 | ||||||||
\(137\) | −7.03539 | −0.601074 | −0.300537 | − | 0.953770i | \(-0.597166\pi\) | ||||
−0.300537 | + | 0.953770i | \(0.597166\pi\) | |||||||
\(138\) | −0.735095 | −0.0625754 | ||||||||
\(139\) | 13.3584 | 1.13304 | 0.566522 | − | 0.824047i | \(-0.308289\pi\) | ||||
0.566522 | + | 0.824047i | \(0.308289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.90571 | 0.160490 | ||||||||
\(142\) | 38.4739 | 3.22866 | ||||||||
\(143\) | −6.28561 | −0.525629 | ||||||||
\(144\) | −23.4942 | −1.95785 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −37.3473 | −3.09089 | ||||||||
\(147\) | −0.285863 | −0.0235776 | ||||||||
\(148\) | 14.2731 | 1.17324 | ||||||||
\(149\) | −0.0962328 | −0.00788370 | −0.00394185 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394185 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1272 | −0.905518 | −0.452759 | − | 0.891633i | \(-0.649560\pi\) | ||||
−0.452759 | + | 0.891633i | \(0.649560\pi\) | |||||||
\(152\) | 26.2977 | 2.13303 | ||||||||
\(153\) | 2.56943 | 0.207726 | ||||||||
\(154\) | 15.7939 | 1.27271 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.34941 | 0.108039 | ||||||||
\(157\) | 6.74396 | 0.538227 | 0.269113 | − | 0.963109i | \(-0.413269\pi\) | ||||
0.269113 | + | 0.963109i | \(0.413269\pi\) | |||||||
\(158\) | −8.75749 | −0.696708 | ||||||||
\(159\) | 3.13037 | 0.248255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −21.2694 | −1.67108 | ||||||||
\(163\) | 0.364094 | 0.0285181 | 0.0142590 | − | 0.999898i | \(-0.495461\pi\) | ||||
0.0142590 | + | 0.999898i | \(0.495461\pi\) | |||||||
\(164\) | −15.9510 | −1.24556 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.83516 | 0.375281 | ||||||||
\(167\) | 5.07724 | 0.392888 | 0.196444 | − | 0.980515i | \(-0.437061\pi\) | ||||
0.196444 | + | 0.980515i | \(0.437061\pi\) | |||||||
\(168\) | −1.92049 | −0.148169 | ||||||||
\(169\) | −11.9527 | −0.919436 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4233 | 0.873562 | ||||||||
\(172\) | −0.401785 | −0.0306358 | ||||||||
\(173\) | 16.0673 | 1.22157 | 0.610787 | − | 0.791795i | \(-0.290853\pi\) | ||||
0.610787 | + | 0.791795i | \(0.290853\pi\) | |||||||
\(174\) | 5.08872 | 0.385775 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 49.4467 | 3.72718 | ||||||||
\(177\) | −4.05741 | −0.304974 | ||||||||
\(178\) | 33.9761 | 2.54661 | ||||||||
\(179\) | −5.22849 | −0.390796 | −0.195398 | − | 0.980724i | \(-0.562600\pi\) | ||||
−0.195398 | + | 0.980724i | \(0.562600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.20868 | 0.610146 | 0.305073 | − | 0.952329i | \(-0.401319\pi\) | ||||
0.305073 | + | 0.952329i | \(0.401319\pi\) | |||||||
\(182\) | −2.63165 | −0.195071 | ||||||||
\(183\) | 1.64279 | 0.121439 | ||||||||
\(184\) | 6.71821 | 0.495273 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.287035 | 0.0210465 | ||||||||
\(187\) | −5.40771 | −0.395451 | ||||||||
\(188\) | −30.7498 | −2.24266 | ||||||||
\(189\) | −1.69182 | −0.123062 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.49029 | −0.252548 | −0.126274 | − | 0.991995i | \(-0.540302\pi\) | ||||
−0.126274 | + | 0.991995i | \(0.540302\pi\) | |||||||
\(192\) | −0.738297 | −0.0532820 | ||||||||
\(193\) | −18.8099 | −1.35396 | −0.676982 | − | 0.735999i | \(-0.736713\pi\) | ||||
−0.676982 | + | 0.735999i | \(0.736713\pi\) | |||||||
\(194\) | −42.6586 | −3.06271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.61257 | 0.329469 | ||||||||
\(197\) | −2.55570 | −0.182086 | −0.0910431 | − | 0.995847i | \(-0.529020\pi\) | ||||
−0.0910431 | + | 0.995847i | \(0.529020\pi\) | |||||||
\(198\) | 46.0911 | 3.27555 | ||||||||
\(199\) | 5.01832 | 0.355739 | 0.177870 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177870 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.04526 | −0.0737268 | ||||||||
\(202\) | −38.7418 | −2.72587 | ||||||||
\(203\) | −6.92254 | −0.485867 | ||||||||
\(204\) | 1.16094 | 0.0812821 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −34.8911 | −2.43098 | ||||||||
\(207\) | 2.91828 | 0.202835 | ||||||||
\(208\) | −8.23902 | −0.571273 | ||||||||
\(209\) | −24.0419 | −1.66301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2291 | −0.979571 | −0.489786 | − | 0.871843i | \(-0.662925\pi\) | ||||
−0.489786 | + | 0.871843i | \(0.662925\pi\) | |||||||
\(212\) | −50.5104 | −3.46907 | ||||||||
\(213\) | 4.27700 | 0.293055 | ||||||||
\(214\) | 12.9008 | 0.881882 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.3660 | −0.773358 | ||||||||
\(217\) | −0.390474 | −0.0265071 | ||||||||
\(218\) | −2.43474 | −0.164901 | ||||||||
\(219\) | −4.15176 | −0.280550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.901056 | 0.0606116 | ||||||||
\(222\) | 2.27467 | 0.152666 | ||||||||
\(223\) | 21.1228 | 1.41449 | 0.707245 | − | 0.706969i | \(-0.249938\pi\) | ||||
0.707245 | + | 0.706969i | \(0.249938\pi\) | |||||||
\(224\) | 7.26584 | 0.485469 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.9401 | 2.39070 | ||||||||
\(227\) | −25.6431 | −1.70199 | −0.850995 | − | 0.525174i | \(-0.824000\pi\) | ||||
−0.850995 | + | 0.525174i | \(0.824000\pi\) | |||||||
\(228\) | 5.16138 | 0.341821 | ||||||||
\(229\) | 10.3514 | 0.684041 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.75575 | 0.115520 | ||||||||
\(232\) | −46.5071 | −3.05334 | ||||||||
\(233\) | −15.0916 | −0.988683 | −0.494341 | − | 0.869268i | \(-0.664591\pi\) | ||||
−0.494341 | + | 0.869268i | \(0.664591\pi\) | |||||||
\(234\) | −7.67990 | −0.502051 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 65.4688 | 4.26166 | ||||||||
\(237\) | −0.973537 | −0.0632380 | ||||||||
\(238\) | −2.26409 | −0.146759 | ||||||||
\(239\) | −6.86382 | −0.443984 | −0.221992 | − | 0.975049i | \(-0.571256\pi\) | ||||
−0.221992 | + | 0.975049i | \(0.571256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.66803 | −0.493941 | −0.246971 | − | 0.969023i | \(-0.579435\pi\) | ||||
−0.246971 | + | 0.969023i | \(0.579435\pi\) | |||||||
\(242\) | −68.7186 | −4.41740 | ||||||||
\(243\) | −7.43989 | −0.477269 | ||||||||
\(244\) | −26.5075 | −1.69697 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.54208 | −0.162077 | ||||||||
\(247\) | 4.00597 | 0.254894 | ||||||||
\(248\) | −2.62329 | −0.166579 | ||||||||
\(249\) | 0.537507 | 0.0340631 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.2661 | 0.711110 | 0.355555 | − | 0.934655i | \(-0.384292\pi\) | ||||
0.355555 | + | 0.934655i | \(0.384292\pi\) | |||||||
\(252\) | 13.4608 | 0.847950 | ||||||||
\(253\) | −6.14192 | −0.386139 | ||||||||
\(254\) | −20.1455 | −1.26404 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −25.4552 | −1.59095 | ||||||||
\(257\) | 20.6164 | 1.28601 | 0.643007 | − | 0.765860i | \(-0.277687\pi\) | ||||
0.643007 | + | 0.765860i | \(0.277687\pi\) | |||||||
\(258\) | −0.0640316 | −0.00398643 | ||||||||
\(259\) | −3.09439 | −0.192276 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.2019 | −1.25047 | ||||||||
\(262\) | 29.1287 | 1.79958 | ||||||||
\(263\) | 11.4258 | 0.704543 | 0.352272 | − | 0.935898i | \(-0.385409\pi\) | ||||
0.352272 | + | 0.935898i | \(0.385409\pi\) | |||||||
\(264\) | 11.7955 | 0.725962 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.0658 | −0.617176 | ||||||||
\(267\) | 3.77699 | 0.231148 | ||||||||
\(268\) | 16.8659 | 1.03025 | ||||||||
\(269\) | 19.7562 | 1.20455 | 0.602277 | − | 0.798287i | \(-0.294260\pi\) | ||||
0.602277 | + | 0.798287i | \(0.294260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.40553 | −0.571345 | −0.285673 | − | 0.958327i | \(-0.592217\pi\) | ||||
−0.285673 | + | 0.958327i | \(0.592217\pi\) | |||||||
\(272\) | −7.08829 | −0.429791 | ||||||||
\(273\) | −0.292551 | −0.0177060 | ||||||||
\(274\) | 18.0915 | 1.09295 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.31856 | 0.0793682 | ||||||||
\(277\) | 26.4727 | 1.59059 | 0.795295 | − | 0.606223i | \(-0.207316\pi\) | ||||
0.795295 | + | 0.606223i | \(0.207316\pi\) | |||||||
\(278\) | −34.3510 | −2.06023 | ||||||||
\(279\) | −1.13951 | −0.0682209 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.60606 | 0.453740 | 0.226870 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226870 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(282\) | −4.90051 | −0.291821 | ||||||||
\(283\) | −1.27335 | −0.0756930 | −0.0378465 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378465 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(284\) | −69.0120 | −4.09511 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.1634 | 0.955761 | ||||||||
\(287\) | 3.45816 | 0.204129 | ||||||||
\(288\) | 21.2038 | 1.24944 | ||||||||
\(289\) | −16.2248 | −0.954400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.74220 | −0.277993 | ||||||||
\(292\) | 66.9912 | 3.92036 | ||||||||
\(293\) | 2.64891 | 0.154751 | 0.0773755 | − | 0.997002i | \(-0.475346\pi\) | ||||
0.0773755 | + | 0.997002i | \(0.475346\pi\) | |||||||
\(294\) | 0.735095 | 0.0428716 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.7888 | −1.20832 | ||||||||
\(297\) | 10.3910 | 0.602948 | ||||||||
\(298\) | 0.247462 | 0.0143351 | ||||||||
\(299\) | 1.02339 | 0.0591844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0871065 | 0.00502074 | ||||||||
\(302\) | 28.6135 | 1.64652 | ||||||||
\(303\) | −4.30678 | −0.247418 | ||||||||
\(304\) | −31.5135 | −1.80743 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.60726 | −0.377712 | ||||||||
\(307\) | 32.1809 | 1.83666 | 0.918330 | − | 0.395816i | \(-0.129538\pi\) | ||||
0.918330 | + | 0.395816i | \(0.129538\pi\) | |||||||
\(308\) | −28.3301 | −1.61426 | ||||||||
\(309\) | −3.87872 | −0.220652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1772 | −0.633799 | −0.316899 | − | 0.948459i | \(-0.602642\pi\) | ||||
−0.316899 | + | 0.948459i | \(0.602642\pi\) | |||||||
\(312\) | −1.96542 | −0.111270 | ||||||||
\(313\) | −24.6707 | −1.39447 | −0.697234 | − | 0.716844i | \(-0.745586\pi\) | ||||
−0.697234 | + | 0.716844i | \(0.745586\pi\) | |||||||
\(314\) | −17.3420 | −0.978668 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.7086 | 0.883678 | ||||||||
\(317\) | 33.4901 | 1.88099 | 0.940496 | − | 0.339805i | \(-0.110361\pi\) | ||||
0.940496 | + | 0.339805i | \(0.110361\pi\) | |||||||
\(318\) | −8.04973 | −0.451406 | ||||||||
\(319\) | 42.5177 | 2.38054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.43414 | 0.0800457 | ||||||||
\(322\) | −2.57149 | −0.143304 | ||||||||
\(323\) | 3.44646 | 0.191766 | ||||||||
\(324\) | 38.1516 | 2.11953 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.936265 | −0.0518549 | ||||||||
\(327\) | −0.270661 | −0.0149676 | ||||||||
\(328\) | 23.2326 | 1.28281 | ||||||||
\(329\) | 6.66651 | 0.367536 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2541 | 1.27816 | 0.639079 | − | 0.769141i | \(-0.279316\pi\) | ||||
0.639079 | + | 0.769141i | \(0.279316\pi\) | |||||||
\(332\) | −8.67300 | −0.475992 | ||||||||
\(333\) | −9.03030 | −0.494857 | ||||||||
\(334\) | −13.0561 | −0.714397 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.30139 | 0.125551 | ||||||||
\(337\) | −17.1987 | −0.936874 | −0.468437 | − | 0.883497i | \(-0.655183\pi\) | ||||
−0.468437 | + | 0.883497i | \(0.655183\pi\) | |||||||
\(338\) | 30.7362 | 1.67183 | ||||||||
\(339\) | 3.99533 | 0.216997 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.39826 | 0.129873 | ||||||||
\(342\) | −29.3749 | −1.58842 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.585200 | 0.0315519 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −41.3170 | −2.22121 | ||||||||
\(347\) | 14.7588 | 0.792293 | 0.396146 | − | 0.918187i | \(-0.370347\pi\) | ||||
0.396146 | + | 0.918187i | \(0.370347\pi\) | |||||||
\(348\) | −9.12782 | −0.489302 | ||||||||
\(349\) | −0.697509 | −0.0373368 | −0.0186684 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186684 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.73140 | −0.0924151 | ||||||||
\(352\) | −44.6262 | −2.37859 | ||||||||
\(353\) | 32.3083 | 1.71960 | 0.859799 | − | 0.510633i | \(-0.170589\pi\) | ||||
0.859799 | + | 0.510633i | \(0.170589\pi\) | |||||||
\(354\) | 10.4336 | 0.554540 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −60.9440 | −3.23003 | ||||||||
\(357\) | −0.251691 | −0.0133209 | ||||||||
\(358\) | 13.4450 | 0.710592 | ||||||||
\(359\) | −25.1633 | −1.32807 | −0.664033 | − | 0.747703i | \(-0.731157\pi\) | ||||
−0.664033 | + | 0.747703i | \(0.731157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.67752 | −0.193553 | ||||||||
\(362\) | −21.1086 | −1.10944 | ||||||||
\(363\) | −7.63918 | −0.400953 | ||||||||
\(364\) | 4.72048 | 0.247420 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.22443 | −0.220815 | ||||||||
\(367\) | 30.3693 | 1.58526 | 0.792632 | − | 0.609701i | \(-0.208710\pi\) | ||||
0.792632 | + | 0.609701i | \(0.208710\pi\) | |||||||
\(368\) | −8.05068 | −0.419671 | ||||||||
\(369\) | 10.0919 | 0.525363 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.9506 | 0.568527 | ||||||||
\(372\) | −0.514865 | −0.0266945 | ||||||||
\(373\) | 9.88041 | 0.511588 | 0.255794 | − | 0.966731i | \(-0.417663\pi\) | ||||
0.255794 | + | 0.966731i | \(0.417663\pi\) | |||||||
\(374\) | 13.9059 | 0.719056 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 44.7870 | 2.30971 | ||||||||
\(377\) | −7.08449 | −0.364870 | ||||||||
\(378\) | 4.35050 | 0.223765 | ||||||||
\(379\) | 6.61691 | 0.339888 | 0.169944 | − | 0.985454i | \(-0.445641\pi\) | ||||
0.169944 | + | 0.985454i | \(0.445641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.23950 | −0.114733 | ||||||||
\(382\) | 8.97525 | 0.459214 | ||||||||
\(383\) | 5.53793 | 0.282975 | 0.141487 | − | 0.989940i | \(-0.454812\pi\) | ||||
0.141487 | + | 0.989940i | \(0.454812\pi\) | |||||||
\(384\) | −2.25555 | −0.115103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 48.3695 | 2.46194 | ||||||||
\(387\) | 0.254201 | 0.0129218 | ||||||||
\(388\) | 76.5182 | 3.88462 | ||||||||
\(389\) | 32.5784 | 1.65179 | 0.825896 | − | 0.563823i | \(-0.190670\pi\) | ||||
0.825896 | + | 0.563823i | \(0.190670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.880458 | 0.0445267 | ||||||||
\(392\) | −6.71821 | −0.339321 | ||||||||
\(393\) | 3.23813 | 0.163342 | ||||||||
\(394\) | 6.57197 | 0.331091 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −82.6751 | −4.15458 | ||||||||
\(397\) | 22.7575 | 1.14217 | 0.571083 | − | 0.820892i | \(-0.306523\pi\) | ||||
0.571083 | + | 0.820892i | \(0.306523\pi\) | |||||||
\(398\) | −12.9046 | −0.646848 | ||||||||
\(399\) | −1.11898 | −0.0560191 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.3464 | 1.41555 | 0.707775 | − | 0.706438i | \(-0.249699\pi\) | ||||
0.707775 | + | 0.706438i | \(0.249699\pi\) | |||||||
\(402\) | 2.68787 | 0.134059 | ||||||||
\(403\) | −0.399609 | −0.0199059 | ||||||||
\(404\) | 69.4925 | 3.45738 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.8013 | 0.883462 | ||||||||
\(407\) | 19.0055 | 0.942068 | ||||||||
\(408\) | −1.69091 | −0.0837125 | ||||||||
\(409\) | −7.89846 | −0.390554 | −0.195277 | − | 0.980748i | \(-0.562561\pi\) | ||||
−0.195277 | + | 0.980748i | \(0.562561\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.01116 | 0.0992032 | ||||||||
\(412\) | 62.5854 | 3.08336 | ||||||||
\(413\) | −14.1936 | −0.698419 | ||||||||
\(414\) | −7.50434 | −0.368818 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.43582 | 0.364571 | ||||||||
\(417\) | −3.81867 | −0.187001 | ||||||||
\(418\) | 61.8236 | 3.02389 | ||||||||
\(419\) | 13.0465 | 0.637363 | 0.318682 | − | 0.947862i | \(-0.396760\pi\) | ||||
0.318682 | + | 0.947862i | \(0.396760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8242 | 0.868697 | 0.434349 | − | 0.900745i | \(-0.356979\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356979\pi\) | |||||||
\(422\) | 36.5900 | 1.78117 | ||||||||
\(423\) | 19.4548 | 0.945922 | ||||||||
\(424\) | 73.5684 | 3.57280 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.9983 | −0.532868 | ||||||||
\(427\) | 5.74679 | 0.278107 | ||||||||
\(428\) | −23.1406 | −1.11855 | ||||||||
\(429\) | 1.79682 | 0.0867514 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.69718 | 0.322592 | 0.161296 | − | 0.986906i | \(-0.448433\pi\) | ||||
0.161296 | + | 0.986906i | \(0.448433\pi\) | |||||||
\(432\) | 13.6203 | 0.655306 | ||||||||
\(433\) | 15.5526 | 0.747412 | 0.373706 | − | 0.927547i | \(-0.378087\pi\) | ||||
0.373706 | + | 0.927547i | \(0.378087\pi\) | |||||||
\(434\) | 1.00410 | 0.0481984 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.36727 | 0.209154 | ||||||||
\(437\) | 3.91439 | 0.187251 | ||||||||
\(438\) | 10.6762 | 0.510130 | ||||||||
\(439\) | −16.6090 | −0.792704 | −0.396352 | − | 0.918099i | \(-0.629724\pi\) | ||||
−0.396352 | + | 0.918099i | \(0.629724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.91828 | −0.138966 | ||||||||
\(442\) | −2.31706 | −0.110211 | ||||||||
\(443\) | 11.6526 | 0.553630 | 0.276815 | − | 0.960923i | \(-0.410721\pi\) | ||||
0.276815 | + | 0.960923i | \(0.410721\pi\) | |||||||
\(444\) | −4.08015 | −0.193635 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −54.3172 | −2.57199 | ||||||||
\(447\) | 0.0275094 | 0.00130115 | ||||||||
\(448\) | −2.58269 | −0.122021 | ||||||||
\(449\) | 16.1924 | 0.764168 | 0.382084 | − | 0.924128i | \(-0.375206\pi\) | ||||
0.382084 | + | 0.924128i | \(0.375206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.2398 | −1.00014 | ||||||||
\(452\) | −64.4670 | −3.03227 | ||||||||
\(453\) | 3.18085 | 0.149450 | ||||||||
\(454\) | 65.9409 | 3.09476 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.51755 | −0.352041 | ||||||||
\(457\) | 9.47239 | 0.443100 | 0.221550 | − | 0.975149i | \(-0.428888\pi\) | ||||
0.221550 | + | 0.975149i | \(0.428888\pi\) | |||||||
\(458\) | −26.6186 | −1.24380 | ||||||||
\(459\) | −1.48958 | −0.0695274 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.80775 | 0.317068 | 0.158534 | − | 0.987353i | \(-0.449323\pi\) | ||||
0.158534 | + | 0.987353i | \(0.449323\pi\) | |||||||
\(462\) | −4.51490 | −0.210052 | ||||||||
\(463\) | 12.2442 | 0.569039 | 0.284519 | − | 0.958670i | \(-0.408166\pi\) | ||||
0.284519 | + | 0.958670i | \(0.408166\pi\) | |||||||
\(464\) | 55.7312 | 2.58725 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 38.8079 | 1.79774 | ||||||||
\(467\) | 7.11405 | 0.329199 | 0.164600 | − | 0.986360i | \(-0.447367\pi\) | ||||
0.164600 | + | 0.986360i | \(0.447367\pi\) | |||||||
\(468\) | 13.7757 | 0.636781 | ||||||||
\(469\) | −3.65650 | −0.168841 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.92785 | −0.0888306 | ||||||||
\(472\) | −95.3553 | −4.38908 | ||||||||
\(473\) | −0.535002 | −0.0245994 | ||||||||
\(474\) | 2.50344 | 0.114987 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.06118 | 0.186144 | ||||||||
\(477\) | 31.9569 | 1.46321 | ||||||||
\(478\) | 17.6503 | 0.807304 | ||||||||
\(479\) | 13.0420 | 0.595905 | 0.297952 | − | 0.954581i | \(-0.403696\pi\) | ||||
0.297952 | + | 0.954581i | \(0.403696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.16678 | −0.144393 | ||||||||
\(482\) | 19.7183 | 0.898143 | ||||||||
\(483\) | −0.285863 | −0.0130072 | ||||||||
\(484\) | 123.263 | 5.60285 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.1316 | 0.867828 | ||||||||
\(487\) | −17.6809 | −0.801200 | −0.400600 | − | 0.916253i | \(-0.631198\pi\) | ||||
−0.400600 | + | 0.916253i | \(0.631198\pi\) | |||||||
\(488\) | 38.6081 | 1.74771 | ||||||||
\(489\) | −0.104081 | −0.00470671 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4923 | 1.33097 | 0.665484 | − | 0.746412i | \(-0.268225\pi\) | ||||
0.665484 | + | 0.746412i | \(0.268225\pi\) | |||||||
\(492\) | 4.55981 | 0.205572 | ||||||||
\(493\) | −6.09501 | −0.274505 | ||||||||
\(494\) | −10.3013 | −0.463478 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.14358 | 0.141151 | ||||||||
\(497\) | 14.9617 | 0.671125 | ||||||||
\(498\) | −1.38219 | −0.0619376 | ||||||||
\(499\) | −11.0638 | −0.495284 | −0.247642 | − | 0.968852i | \(-0.579656\pi\) | ||||
−0.247642 | + | 0.968852i | \(0.579656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.45139 | −0.0648435 | ||||||||
\(502\) | −28.9707 | −1.29302 | ||||||||
\(503\) | −27.0098 | −1.20431 | −0.602155 | − | 0.798379i | \(-0.705691\pi\) | ||||
−0.602155 | + | 0.798379i | \(0.705691\pi\) | |||||||
\(504\) | −19.6056 | −0.873304 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.7939 | 0.702125 | ||||||||
\(507\) | 3.41683 | 0.151747 | ||||||||
\(508\) | 36.1357 | 1.60326 | ||||||||
\(509\) | 31.4405 | 1.39358 | 0.696789 | − | 0.717277i | \(-0.254612\pi\) | ||||
0.696789 | + | 0.717277i | \(0.254612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5236 | −0.642486 | ||||||||
\(512\) | 49.6774 | 2.19545 | ||||||||
\(513\) | −6.62244 | −0.292388 | ||||||||
\(514\) | −53.0149 | −2.33839 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.114856 | 0.00505623 | ||||||||
\(517\) | −40.9452 | −1.80077 | ||||||||
\(518\) | 7.95720 | 0.349619 | ||||||||
\(519\) | −4.59305 | −0.201613 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.6660 | −1.47493 | −0.737467 | − | 0.675383i | \(-0.763978\pi\) | ||||
−0.737467 | + | 0.675383i | \(0.763978\pi\) | |||||||
\(522\) | 51.9491 | 2.27375 | ||||||||
\(523\) | 20.6357 | 0.902335 | 0.451168 | − | 0.892439i | \(-0.351008\pi\) | ||||
0.451168 | + | 0.892439i | \(0.351008\pi\) | |||||||
\(524\) | −52.2492 | −2.28252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.3813 | −1.28108 | ||||||||
\(527\) | −0.343796 | −0.0149760 | ||||||||
\(528\) | −14.1350 | −0.615146 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −41.4208 | −1.79751 | ||||||||
\(532\) | 18.0554 | 0.782802 | ||||||||
\(533\) | 3.53906 | 0.153294 | ||||||||
\(534\) | −9.71250 | −0.420301 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.5651 | −1.06105 | ||||||||
\(537\) | 1.49463 | 0.0644981 | ||||||||
\(538\) | −50.8028 | −2.19026 | ||||||||
\(539\) | 6.14192 | 0.264551 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.09344 | 0.347964 | 0.173982 | − | 0.984749i | \(-0.444337\pi\) | ||||
0.173982 | + | 0.984749i | \(0.444337\pi\) | |||||||
\(542\) | 24.1863 | 1.03889 | ||||||||
\(543\) | −2.34656 | −0.100700 | ||||||||
\(544\) | 6.39727 | 0.274281 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.752291 | 0.0321951 | ||||||||
\(547\) | 25.7441 | 1.10074 | 0.550369 | − | 0.834921i | \(-0.314487\pi\) | ||||
0.550369 | + | 0.834921i | \(0.314487\pi\) | |||||||
\(548\) | −32.4513 | −1.38625 | ||||||||
\(549\) | 16.7708 | 0.715758 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.0976 | −1.15439 | ||||||||
\(552\) | −1.92049 | −0.0817414 | ||||||||
\(553\) | −3.40561 | −0.144821 | ||||||||
\(554\) | −68.0743 | −2.89220 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 61.6165 | 2.61312 | ||||||||
\(557\) | −15.9396 | −0.675383 | −0.337692 | − | 0.941257i | \(-0.609646\pi\) | ||||
−0.337692 | + | 0.941257i | \(0.609646\pi\) | |||||||
\(558\) | 2.93025 | 0.124047 | ||||||||
\(559\) | 0.0891443 | 0.00377040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.54586 | 0.0652664 | ||||||||
\(562\) | −19.5589 | −0.825044 | ||||||||
\(563\) | 12.9073 | 0.543977 | 0.271989 | − | 0.962300i | \(-0.412319\pi\) | ||||
0.271989 | + | 0.962300i | \(0.412319\pi\) | |||||||
\(564\) | 8.79022 | 0.370135 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.27442 | 0.137634 | ||||||||
\(567\) | −8.27122 | −0.347359 | ||||||||
\(568\) | 100.516 | 4.21756 | ||||||||
\(569\) | 25.8495 | 1.08367 | 0.541834 | − | 0.840485i | \(-0.317730\pi\) | ||||
0.541834 | + | 0.840485i | \(0.317730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.65336 | 0.111040 | 0.0555199 | − | 0.998458i | \(-0.482318\pi\) | ||||
0.0555199 | + | 0.998458i | \(0.482318\pi\) | |||||||
\(572\) | −28.9928 | −1.21225 | ||||||||
\(573\) | 0.997744 | 0.0416814 | ||||||||
\(574\) | −8.89263 | −0.371171 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.53703 | −0.314043 | ||||||||
\(577\) | −12.8442 | −0.534710 | −0.267355 | − | 0.963598i | \(-0.586150\pi\) | ||||
−0.267355 | + | 0.963598i | \(0.586150\pi\) | |||||||
\(578\) | 41.7219 | 1.73540 | ||||||||
\(579\) | 5.37705 | 0.223463 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88029 | 0.0780078 | ||||||||
\(582\) | 12.1945 | 0.505479 | ||||||||
\(583\) | −67.2578 | −2.78553 | ||||||||
\(584\) | −97.5726 | −4.03758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.81166 | −0.281387 | ||||||||
\(587\) | −9.91770 | −0.409347 | −0.204674 | − | 0.978830i | \(-0.565613\pi\) | ||||
−0.204674 | + | 0.978830i | \(0.565613\pi\) | |||||||
\(588\) | −1.31856 | −0.0543767 | ||||||||
\(589\) | −1.52847 | −0.0629795 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.730581 | 0.0300521 | ||||||||
\(592\) | 24.9119 | 1.02387 | ||||||||
\(593\) | 31.1527 | 1.27929 | 0.639644 | − | 0.768671i | \(-0.279082\pi\) | ||||
0.639644 | + | 0.768671i | \(0.279082\pi\) | |||||||
\(594\) | −26.7204 | −1.09635 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.443881 | −0.0181821 | ||||||||
\(597\) | −1.43455 | −0.0587123 | ||||||||
\(598\) | −2.63165 | −0.107616 | ||||||||
\(599\) | −40.6804 | −1.66216 | −0.831079 | − | 0.556155i | \(-0.812276\pi\) | ||||
−0.831079 | + | 0.556155i | \(0.812276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.1729 | 0.822869 | 0.411435 | − | 0.911439i | \(-0.365028\pi\) | ||||
0.411435 | + | 0.911439i | \(0.365028\pi\) | |||||||
\(602\) | −0.223994 | −0.00912931 | ||||||||
\(603\) | −10.6707 | −0.434544 | ||||||||
\(604\) | −51.3250 | −2.08838 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.0749 | 0.449885 | ||||||||
\(607\) | −6.08065 | −0.246806 | −0.123403 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123403 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(608\) | 28.4414 | 1.15345 | ||||||||
\(609\) | 1.97890 | 0.0801890 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.82246 | 0.276007 | ||||||||
\(612\) | 11.8517 | 0.479075 | ||||||||
\(613\) | −37.2909 | −1.50617 | −0.753084 | − | 0.657925i | \(-0.771434\pi\) | ||||
−0.753084 | + | 0.657925i | \(0.771434\pi\) | |||||||
\(614\) | −82.7529 | −3.33963 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41.2627 | 1.66252 | ||||||||
\(617\) | −41.6439 | −1.67652 | −0.838261 | − | 0.545270i | \(-0.816427\pi\) | ||||
−0.838261 | + | 0.545270i | \(0.816427\pi\) | |||||||
\(618\) | 9.97409 | 0.401217 | ||||||||
\(619\) | 15.6115 | 0.627480 | 0.313740 | − | 0.949509i | \(-0.398418\pi\) | ||||
0.313740 | + | 0.949509i | \(0.398418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.69182 | −0.0678903 | ||||||||
\(622\) | 28.7420 | 1.15245 | ||||||||
\(623\) | 13.2126 | 0.529351 | ||||||||
\(624\) | 2.35523 | 0.0942847 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 63.4404 | 2.53559 | ||||||||
\(627\) | 6.87269 | 0.274469 | ||||||||
\(628\) | 31.1070 | 1.24130 | ||||||||
\(629\) | −2.72448 | −0.108632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.3500 | 1.04898 | 0.524488 | − | 0.851418i | \(-0.324257\pi\) | ||||
0.524488 | + | 0.851418i | \(0.324257\pi\) | |||||||
\(632\) | −22.8796 | −0.910101 | ||||||||
\(633\) | 4.06757 | 0.161672 | ||||||||
\(634\) | −86.1195 | −3.42024 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.4391 | 0.572546 | ||||||||
\(637\) | −1.02339 | −0.0405483 | ||||||||
\(638\) | −109.334 | −4.32857 | ||||||||
\(639\) | 43.6625 | 1.72726 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.38344 | −0.370623 | −0.185312 | − | 0.982680i | \(-0.559329\pi\) | ||||
−0.185312 | + | 0.982680i | \(0.559329\pi\) | |||||||
\(642\) | −3.68787 | −0.145549 | ||||||||
\(643\) | 44.1627 | 1.74161 | 0.870803 | − | 0.491632i | \(-0.163600\pi\) | ||||
0.870803 | + | 0.491632i | \(0.163600\pi\) | |||||||
\(644\) | 4.61257 | 0.181761 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.86255 | −0.348692 | ||||||||
\(647\) | −26.7049 | −1.04988 | −0.524939 | − | 0.851140i | \(-0.675912\pi\) | ||||
−0.524939 | + | 0.851140i | \(0.675912\pi\) | |||||||
\(648\) | −55.5678 | −2.18291 | ||||||||
\(649\) | 87.1758 | 3.42195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.111622 | 0.00437482 | ||||||||
\(652\) | 1.67941 | 0.0657708 | ||||||||
\(653\) | 40.8546 | 1.59876 | 0.799382 | − | 0.600823i | \(-0.205160\pi\) | ||||
0.799382 | + | 0.600823i | \(0.205160\pi\) | |||||||
\(654\) | 0.696001 | 0.0272158 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.8405 | −1.08699 | ||||||||
\(657\) | −42.3840 | −1.65356 | ||||||||
\(658\) | −17.1429 | −0.668299 | ||||||||
\(659\) | −3.67292 | −0.143077 | −0.0715383 | − | 0.997438i | \(-0.522791\pi\) | ||||
−0.0715383 | + | 0.997438i | \(0.522791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1813 | 1.67956 | 0.839779 | − | 0.542928i | \(-0.182684\pi\) | ||||
0.839779 | + | 0.542928i | \(0.182684\pi\) | |||||||
\(662\) | −59.7976 | −2.32410 | ||||||||
\(663\) | −0.257579 | −0.0100035 | ||||||||
\(664\) | 12.6322 | 0.490225 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.2213 | 0.899809 | ||||||||
\(667\) | −6.92254 | −0.268042 | ||||||||
\(668\) | 23.4191 | 0.906113 | ||||||||
\(669\) | −6.03824 | −0.233452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.2963 | −1.36260 | ||||||||
\(672\) | −2.07704 | −0.0801234 | ||||||||
\(673\) | 1.47909 | 0.0570148 | 0.0285074 | − | 0.999594i | \(-0.490925\pi\) | ||||
0.0285074 | + | 0.999594i | \(0.490925\pi\) | |||||||
\(674\) | 44.2264 | 1.70354 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −55.1325 | −2.12048 | ||||||||
\(677\) | 3.13956 | 0.120663 | 0.0603316 | − | 0.998178i | \(-0.480784\pi\) | ||||
0.0603316 | + | 0.998178i | \(0.480784\pi\) | |||||||
\(678\) | −10.2740 | −0.394569 | ||||||||
\(679\) | −16.5891 | −0.636630 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.33040 | 0.280902 | ||||||||
\(682\) | −6.16711 | −0.236151 | ||||||||
\(683\) | −0.168666 | −0.00645381 | −0.00322690 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322690 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(684\) | 52.6908 | 2.01468 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.57149 | 0.0981800 | ||||||||
\(687\) | −2.95909 | −0.112896 | ||||||||
\(688\) | −0.701267 | −0.0267355 | ||||||||
\(689\) | 11.2068 | 0.426944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.8940 | 1.66981 | 0.834903 | − | 0.550397i | \(-0.185524\pi\) | ||||
0.834903 | + | 0.550397i | \(0.185524\pi\) | |||||||
\(692\) | 74.1116 | 2.81730 | ||||||||
\(693\) | 17.9239 | 0.680871 | ||||||||
\(694\) | −37.9521 | −1.44064 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.2947 | 0.503933 | ||||||||
\(697\) | 3.04477 | 0.115329 | ||||||||
\(698\) | 1.79364 | 0.0678903 | ||||||||
\(699\) | 4.31413 | 0.163175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.91383 | −0.0722843 | −0.0361421 | − | 0.999347i | \(-0.511507\pi\) | ||||
−0.0361421 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(702\) | 4.45227 | 0.168040 | ||||||||
\(703\) | −12.1127 | −0.456838 | ||||||||
\(704\) | 15.8627 | 0.597848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −83.0805 | −3.12678 | ||||||||
\(707\) | −15.0659 | −0.566611 | ||||||||
\(708\) | −18.7151 | −0.703357 | ||||||||
\(709\) | −9.18131 | −0.344811 | −0.172406 | − | 0.985026i | \(-0.555154\pi\) | ||||
−0.172406 | + | 0.985026i | \(0.555154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.93852 | −0.372724 | ||||||||
\(712\) | 88.7649 | 3.32661 | ||||||||
\(713\) | −0.390474 | −0.0146234 | ||||||||
\(714\) | 0.647220 | 0.0242216 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.1168 | −0.901287 | ||||||||
\(717\) | 1.96211 | 0.0732765 | ||||||||
\(718\) | 64.7071 | 2.41485 | ||||||||
\(719\) | 38.6304 | 1.44067 | 0.720335 | − | 0.693626i | \(-0.243988\pi\) | ||||
0.720335 | + | 0.693626i | \(0.243988\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5684 | −0.505315 | ||||||||
\(722\) | 9.45670 | 0.351942 | ||||||||
\(723\) | 2.19201 | 0.0815216 | ||||||||
\(724\) | 37.8631 | 1.40717 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.6441 | 0.729061 | ||||||||
\(727\) | 45.2391 | 1.67782 | 0.838912 | − | 0.544267i | \(-0.183192\pi\) | ||||
0.838912 | + | 0.544267i | \(0.183192\pi\) | |||||||
\(728\) | −6.87537 | −0.254818 | ||||||||
\(729\) | −22.6869 | −0.840254 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0766937 | 0.00283662 | ||||||||
\(732\) | 7.57751 | 0.280073 | ||||||||
\(733\) | −6.31250 | −0.233157 | −0.116579 | − | 0.993181i | \(-0.537193\pi\) | ||||
−0.116579 | + | 0.993181i | \(0.537193\pi\) | |||||||
\(734\) | −78.0944 | −2.88252 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.26584 | 0.267822 | ||||||||
\(737\) | 22.4579 | 0.827248 | ||||||||
\(738\) | −25.9512 | −0.955277 | ||||||||
\(739\) | 33.8666 | 1.24580 | 0.622902 | − | 0.782300i | \(-0.285953\pi\) | ||||
0.622902 | + | 0.782300i | \(0.285953\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.14516 | −0.0420684 | ||||||||
\(742\) | −28.1594 | −1.03376 | ||||||||
\(743\) | 42.9413 | 1.57536 | 0.787682 | − | 0.616082i | \(-0.211281\pi\) | ||||
0.787682 | + | 0.616082i | \(0.211281\pi\) | |||||||
\(744\) | 0.749901 | 0.0274927 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.4074 | −0.930231 | ||||||||
\(747\) | 5.48723 | 0.200767 | ||||||||
\(748\) | −24.9434 | −0.912023 | ||||||||
\(749\) | 5.01686 | 0.183312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.829615 | −0.0302731 | −0.0151365 | − | 0.999885i | \(-0.504818\pi\) | ||||
−0.0151365 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(752\) | −53.6699 | −1.95714 | ||||||||
\(753\) | −3.22056 | −0.117364 | ||||||||
\(754\) | 18.2177 | 0.663450 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.80364 | −0.283815 | ||||||||
\(757\) | 24.2753 | 0.882300 | 0.441150 | − | 0.897434i | \(-0.354571\pi\) | ||||
0.441150 | + | 0.897434i | \(0.354571\pi\) | |||||||
\(758\) | −17.0153 | −0.618024 | ||||||||
\(759\) | 1.75575 | 0.0637297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.5478 | −1.21611 | −0.608053 | − | 0.793896i | \(-0.708049\pi\) | ||||
−0.608053 | + | 0.793896i | \(0.708049\pi\) | |||||||
\(762\) | 5.75886 | 0.208622 | ||||||||
\(763\) | −0.946819 | −0.0342771 | ||||||||
\(764\) | −16.0992 | −0.582449 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.2407 | −0.514539 | ||||||||
\(767\) | −14.5256 | −0.524489 | ||||||||
\(768\) | 7.27671 | 0.262576 | ||||||||
\(769\) | −35.7498 | −1.28917 | −0.644586 | − | 0.764532i | \(-0.722970\pi\) | ||||
−0.644586 | + | 0.764532i | \(0.722970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.89346 | −0.212248 | ||||||||
\(772\) | −86.7619 | −3.12263 | ||||||||
\(773\) | −14.7661 | −0.531101 | −0.265551 | − | 0.964097i | \(-0.585554\pi\) | ||||
−0.265551 | + | 0.964097i | \(0.585554\pi\) | |||||||
\(774\) | −0.653677 | −0.0234959 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −111.449 | −4.00078 | ||||||||
\(777\) | 0.884572 | 0.0317338 | ||||||||
\(778\) | −83.7752 | −3.00348 | ||||||||
\(779\) | 13.5366 | 0.484999 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −91.8937 | −3.28822 | ||||||||
\(782\) | −2.26409 | −0.0809638 | ||||||||
\(783\) | 11.7117 | 0.418541 | ||||||||
\(784\) | 8.05068 | 0.287524 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.32683 | −0.297008 | ||||||||
\(787\) | −51.8562 | −1.84847 | −0.924236 | − | 0.381821i | \(-0.875297\pi\) | ||||
−0.924236 | + | 0.381821i | \(0.875297\pi\) | |||||||
\(788\) | −11.7884 | −0.419943 | ||||||||
\(789\) | −3.26621 | −0.116280 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.9764 | 0.496943 | ||||||||
\(792\) | 120.416 | 4.27881 | ||||||||
\(793\) | 5.88123 | 0.208849 | ||||||||
\(794\) | −58.5207 | −2.07682 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.1474 | 0.820437 | ||||||||
\(797\) | −6.03809 | −0.213880 | −0.106940 | − | 0.994265i | \(-0.534105\pi\) | ||||
−0.106940 | + | 0.994265i | \(0.534105\pi\) | |||||||
\(798\) | 2.87745 | 0.101861 | ||||||||
\(799\) | 5.86958 | 0.207651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.5581 | 1.36238 | ||||||||
\(802\) | −72.8924 | −2.57392 | ||||||||
\(803\) | 89.2029 | 3.14790 | ||||||||
\(804\) | −4.82133 | −0.170035 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.02759 | 0.0361953 | ||||||||
\(807\) | −5.64756 | −0.198803 | ||||||||
\(808\) | −101.216 | −3.56076 | ||||||||
\(809\) | −31.8270 | −1.11898 | −0.559489 | − | 0.828838i | \(-0.689003\pi\) | ||||
−0.559489 | + | 0.828838i | \(0.689003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7616 | 0.764154 | 0.382077 | − | 0.924130i | \(-0.375209\pi\) | ||||
0.382077 | + | 0.924130i | \(0.375209\pi\) | |||||||
\(812\) | −31.9307 | −1.12055 | ||||||||
\(813\) | 2.68869 | 0.0942966 | ||||||||
\(814\) | −48.8725 | −1.71298 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.02628 | 0.0709340 | ||||||||
\(817\) | 0.340969 | 0.0119290 | ||||||||
\(818\) | 20.3108 | 0.710152 | ||||||||
\(819\) | −2.98655 | −0.104359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.1303 | 1.50526 | 0.752630 | − | 0.658444i | \(-0.228785\pi\) | ||||
0.752630 | + | 0.658444i | \(0.228785\pi\) | |||||||
\(822\) | −5.17168 | −0.180383 | ||||||||
\(823\) | 8.91338 | 0.310701 | 0.155350 | − | 0.987859i | \(-0.450349\pi\) | ||||
0.155350 | + | 0.987859i | \(0.450349\pi\) | |||||||
\(824\) | −91.1556 | −3.17556 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.4986 | 1.26995 | ||||||||
\(827\) | −39.3167 | −1.36718 | −0.683588 | − | 0.729868i | \(-0.739581\pi\) | ||||
−0.683588 | + | 0.729868i | \(0.739581\pi\) | |||||||
\(828\) | 13.4608 | 0.467795 | ||||||||
\(829\) | 9.43997 | 0.327864 | 0.163932 | − | 0.986472i | \(-0.447582\pi\) | ||||
0.163932 | + | 0.986472i | \(0.447582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.56757 | −0.262516 | ||||||||
\(832\) | −2.64311 | −0.0916334 | ||||||||
\(833\) | −0.880458 | −0.0305061 | ||||||||
\(834\) | 9.81967 | 0.340028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −110.895 | −3.83539 | ||||||||
\(837\) | 0.660611 | 0.0228341 | ||||||||
\(838\) | −33.5490 | −1.15893 | ||||||||
\(839\) | 34.0428 | 1.17529 | 0.587644 | − | 0.809120i | \(-0.300056\pi\) | ||||
0.587644 | + | 0.809120i | \(0.300056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9216 | 0.652468 | ||||||||
\(842\) | −45.8347 | −1.57957 | ||||||||
\(843\) | −2.17429 | −0.0748866 | ||||||||
\(844\) | −65.6327 | −2.25917 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −50.0277 | −1.71999 | ||||||||
\(847\) | −26.7232 | −0.918221 | ||||||||
\(848\) | −88.1598 | −3.02742 | ||||||||
\(849\) | 0.364005 | 0.0124926 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.09439 | −0.106074 | ||||||||
\(852\) | 19.7280 | 0.675870 | ||||||||
\(853\) | −10.6161 | −0.363490 | −0.181745 | − | 0.983346i | \(-0.558175\pi\) | ||||
−0.181745 | + | 0.983346i | \(0.558175\pi\) | |||||||
\(854\) | −14.7778 | −0.505687 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.7043 | 1.15199 | ||||||||
\(857\) | 13.1582 | 0.449474 | 0.224737 | − | 0.974419i | \(-0.427848\pi\) | ||||
0.224737 | + | 0.974419i | \(0.427848\pi\) | |||||||
\(858\) | −4.62052 | −0.157742 | ||||||||
\(859\) | 27.5047 | 0.938447 | 0.469224 | − | 0.883079i | \(-0.344534\pi\) | ||||
0.469224 | + | 0.883079i | \(0.344534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.988560 | −0.0336900 | ||||||||
\(862\) | −17.2217 | −0.586575 | ||||||||
\(863\) | −55.1862 | −1.87856 | −0.939280 | − | 0.343151i | \(-0.888506\pi\) | ||||
−0.939280 | + | 0.343151i | \(0.888506\pi\) | |||||||
\(864\) | −12.2925 | −0.418199 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.9935 | −1.35903 | ||||||||
\(867\) | 4.63807 | 0.157517 | ||||||||
\(868\) | −1.80109 | −0.0611330 | ||||||||
\(869\) | 20.9170 | 0.709560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.74204 | −0.126794 | ||||||||
\(872\) | −6.36093 | −0.215408 | ||||||||
\(873\) | −48.4115 | −1.63848 | ||||||||
\(874\) | −10.0658 | −0.340482 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.1503 | −0.647029 | ||||||||
\(877\) | −26.8565 | −0.906880 | −0.453440 | − | 0.891287i | \(-0.649803\pi\) | ||||
−0.453440 | + | 0.891287i | \(0.649803\pi\) | |||||||
\(878\) | 42.7099 | 1.44139 | ||||||||
\(879\) | −0.757226 | −0.0255406 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0482 | 0.709131 | 0.354566 | − | 0.935031i | \(-0.384629\pi\) | ||||
0.354566 | + | 0.935031i | \(0.384629\pi\) | |||||||
\(882\) | 7.50434 | 0.252684 | ||||||||
\(883\) | −40.7345 | −1.37083 | −0.685413 | − | 0.728155i | \(-0.740378\pi\) | ||||
−0.685413 | + | 0.728155i | \(0.740378\pi\) | |||||||
\(884\) | 4.15618 | 0.139788 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.9645 | −1.00668 | ||||||||
\(887\) | −32.8883 | −1.10428 | −0.552141 | − | 0.833751i | \(-0.686189\pi\) | ||||
−0.552141 | + | 0.833751i | \(0.686189\pi\) | |||||||
\(888\) | 5.94274 | 0.199425 | ||||||||
\(889\) | −7.83418 | −0.262750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.8012 | 1.70190 | ||||||||
\(892\) | 97.4306 | 3.26222 | ||||||||
\(893\) | 26.0953 | 0.873247 | ||||||||
\(894\) | −0.0707402 | −0.00236591 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.89030 | −0.263597 | ||||||||
\(897\) | −0.292551 | −0.00976798 | ||||||||
\(898\) | −41.6387 | −1.38950 | ||||||||
\(899\) | 2.70307 | 0.0901525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64155 | 0.321207 | ||||||||
\(902\) | 54.6179 | 1.81858 | ||||||||
\(903\) | −0.0249005 | −0.000828638 0 | ||||||||
\(904\) | 93.8962 | 3.12294 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.17954 | −0.271747 | ||||||||
\(907\) | 57.5807 | 1.91193 | 0.955967 | − | 0.293473i | \(-0.0948111\pi\) | ||||
0.955967 | + | 0.293473i | \(0.0948111\pi\) | |||||||
\(908\) | −118.280 | −3.92528 | ||||||||
\(909\) | −43.9665 | −1.45828 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.25171 | 0.107734 | 0.0538669 | − | 0.998548i | \(-0.482845\pi\) | ||||
0.0538669 | + | 0.998548i | \(0.482845\pi\) | |||||||
\(912\) | 9.00856 | 0.298303 | ||||||||
\(913\) | −11.5486 | −0.382204 | ||||||||
\(914\) | −24.3582 | −0.805697 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.7467 | 1.57759 | ||||||||
\(917\) | 11.3276 | 0.374069 | ||||||||
\(918\) | 3.83043 | 0.126423 | ||||||||
\(919\) | 43.5898 | 1.43790 | 0.718948 | − | 0.695064i | \(-0.244624\pi\) | ||||
0.718948 | + | 0.695064i | \(0.244624\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.19932 | −0.303128 | ||||||||
\(922\) | −17.5061 | −0.576532 | ||||||||
\(923\) | 15.3117 | 0.503992 | ||||||||
\(924\) | 8.09852 | 0.266422 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.4860 | −1.03469 | ||||||||
\(927\) | −39.5965 | −1.30052 | ||||||||
\(928\) | −50.2981 | −1.65112 | ||||||||
\(929\) | −30.8853 | −1.01331 | −0.506656 | − | 0.862148i | \(-0.669119\pi\) | ||||
−0.506656 | + | 0.862148i | \(0.669119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.91439 | −0.128289 | ||||||||
\(932\) | −69.6110 | −2.28019 | ||||||||
\(933\) | 3.19514 | 0.104604 | ||||||||
\(934\) | −18.2937 | −0.598589 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −20.0643 | −0.655822 | ||||||||
\(937\) | 26.1035 | 0.852763 | 0.426381 | − | 0.904543i | \(-0.359788\pi\) | ||||
0.426381 | + | 0.904543i | \(0.359788\pi\) | |||||||
\(938\) | 9.40266 | 0.307008 | ||||||||
\(939\) | 7.05243 | 0.230147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.9368 | −0.812915 | −0.406458 | − | 0.913670i | \(-0.633236\pi\) | ||||
−0.406458 | + | 0.913670i | \(0.633236\pi\) | |||||||
\(942\) | 4.95745 | 0.161522 | ||||||||
\(943\) | 3.45816 | 0.112613 | ||||||||
\(944\) | 114.268 | 3.71910 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37575 | 0.0447296 | ||||||||
\(947\) | 7.66115 | 0.248954 | 0.124477 | − | 0.992222i | \(-0.460275\pi\) | ||||
0.124477 | + | 0.992222i | \(0.460275\pi\) | |||||||
\(948\) | −4.49051 | −0.145845 | ||||||||
\(949\) | −14.8634 | −0.482485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.57358 | −0.310445 | ||||||||
\(952\) | −5.91510 | −0.191710 | ||||||||
\(953\) | 11.1554 | 0.361360 | 0.180680 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180680 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(954\) | −82.1770 | −2.66058 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31.6599 | −1.02395 | ||||||||
\(957\) | −12.1542 | −0.392891 | ||||||||
\(958\) | −33.5374 | −1.08354 | ||||||||
\(959\) | 7.03539 | 0.227185 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8475 | −0.995082 | ||||||||
\(962\) | 8.14335 | 0.262552 | ||||||||
\(963\) | 14.6406 | 0.471788 | ||||||||
\(964\) | −35.3693 | −1.13917 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.735095 | 0.0236513 | ||||||||
\(967\) | −3.29023 | −0.105807 | −0.0529034 | − | 0.998600i | \(-0.516848\pi\) | ||||
−0.0529034 | + | 0.998600i | \(0.516848\pi\) | |||||||
\(968\) | −179.532 | −5.77038 | ||||||||
\(969\) | −0.985216 | −0.0316497 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.2428 | 1.61237 | 0.806184 | − | 0.591665i | \(-0.201529\pi\) | ||||
0.806184 | + | 0.591665i | \(0.201529\pi\) | |||||||
\(972\) | −34.3170 | −1.10072 | ||||||||
\(973\) | −13.3584 | −0.428250 | ||||||||
\(974\) | 45.4664 | 1.45684 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.2656 | −1.48092 | ||||||||
\(977\) | 13.4807 | 0.431286 | 0.215643 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215643 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(978\) | 0.267644 | 0.00855830 | ||||||||
\(979\) | −81.1507 | −2.59359 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.76308 | −0.0882185 | ||||||||
\(982\) | −75.8392 | −2.42013 | ||||||||
\(983\) | 30.4473 | 0.971118 | 0.485559 | − | 0.874204i | \(-0.338616\pi\) | ||||
0.485559 | + | 0.874204i | \(0.338616\pi\) | |||||||
\(984\) | −6.64136 | −0.211719 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.6733 | 0.499139 | ||||||||
\(987\) | −1.90571 | −0.0606594 | ||||||||
\(988\) | 18.4778 | 0.587858 | ||||||||
\(989\) | 0.0871065 | 0.00276983 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.16595 | −0.100570 | −0.0502849 | − | 0.998735i | \(-0.516013\pi\) | ||||
−0.0502849 | + | 0.998735i | \(0.516013\pi\) | |||||||
\(992\) | −2.83712 | −0.0900787 | ||||||||
\(993\) | −6.64748 | −0.210951 | ||||||||
\(994\) | −38.4739 | −1.22032 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.47929 | 0.0785593 | ||||||||
\(997\) | −49.5209 | −1.56834 | −0.784171 | − | 0.620545i | \(-0.786911\pi\) | ||||
−0.784171 | + | 0.620545i | \(0.786911\pi\) | |||||||
\(998\) | 28.4505 | 0.900585 | ||||||||
\(999\) | 5.23514 | 0.165633 |
(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 | 4025.2.a.bd.1.3 | 21 | ||
5.2 | odd | 4 | 805.2.c.c.484.5 | ✓ | 42 | ||
5.3 | odd | 4 | 805.2.c.c.484.38 | yes | 42 | ||
5.4 | even | 2 | 4025.2.a.be.1.19 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.c.484.5 | ✓ | 42 | 5.2 | odd | 4 | ||
805.2.c.c.484.38 | yes | 42 | 5.3 | odd | 4 | ||
4025.2.a.bd.1.3 | 21 | 1.1 | even | 1 | trivial | ||
4025.2.a.be.1.19 | 21 | 5.4 | even | 2 |