Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.82604 | −1.63161 | −0.815807 | − | 0.578325i | \(-0.803707\pi\) | ||||
−0.815807 | + | 0.578325i | \(0.803707\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.06326 | 1.36993 | 0.684965 | − | 0.728576i | \(-0.259817\pi\) | ||||
0.684965 | + | 0.728576i | \(0.259817\pi\) | |||||||
\(6\) | 2.82604 | 1.15372 | ||||||||
\(7\) | 0.692372 | 0.261692 | 0.130846 | − | 0.991403i | \(-0.458231\pi\) | ||||
0.130846 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.98649 | 1.66216 | ||||||||
\(10\) | −3.06326 | −0.968687 | ||||||||
\(11\) | 2.28019 | 0.687503 | 0.343751 | − | 0.939061i | \(-0.388302\pi\) | ||||
0.343751 | + | 0.939061i | \(0.388302\pi\) | |||||||
\(12\) | −2.82604 | −0.815807 | ||||||||
\(13\) | −1.07870 | −0.299176 | −0.149588 | − | 0.988748i | \(-0.547795\pi\) | ||||
−0.149588 | + | 0.988748i | \(0.547795\pi\) | |||||||
\(14\) | −0.692372 | −0.185044 | ||||||||
\(15\) | −8.65688 | −2.23520 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.85289 | 0.691927 | 0.345963 | − | 0.938248i | \(-0.387552\pi\) | ||||
0.345963 | + | 0.938248i | \(0.387552\pi\) | |||||||
\(18\) | −4.98649 | −1.17533 | ||||||||
\(19\) | 0.175144 | 0.0401809 | 0.0200904 | − | 0.999798i | \(-0.493605\pi\) | ||||
0.0200904 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(20\) | 3.06326 | 0.684965 | ||||||||
\(21\) | −1.95667 | −0.426980 | ||||||||
\(22\) | −2.28019 | −0.486138 | ||||||||
\(23\) | 1.51008 | 0.314874 | 0.157437 | − | 0.987529i | \(-0.449677\pi\) | ||||
0.157437 | + | 0.987529i | \(0.449677\pi\) | |||||||
\(24\) | 2.82604 | 0.576862 | ||||||||
\(25\) | 4.38355 | 0.876711 | ||||||||
\(26\) | 1.07870 | 0.211550 | ||||||||
\(27\) | −5.61389 | −1.08039 | ||||||||
\(28\) | 0.692372 | 0.130846 | ||||||||
\(29\) | 2.35314 | 0.436967 | 0.218484 | − | 0.975841i | \(-0.429889\pi\) | ||||
0.218484 | + | 0.975841i | \(0.429889\pi\) | |||||||
\(30\) | 8.65688 | 1.58052 | ||||||||
\(31\) | −6.93214 | −1.24505 | −0.622524 | − | 0.782601i | \(-0.713893\pi\) | ||||
−0.622524 | + | 0.782601i | \(0.713893\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.44390 | −1.12174 | ||||||||
\(34\) | −2.85289 | −0.489266 | ||||||||
\(35\) | 2.12092 | 0.358500 | ||||||||
\(36\) | 4.98649 | 0.831081 | ||||||||
\(37\) | −4.30129 | −0.707127 | −0.353564 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353564 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(38\) | −0.175144 | −0.0284122 | ||||||||
\(39\) | 3.04844 | 0.488140 | ||||||||
\(40\) | −3.06326 | −0.484344 | ||||||||
\(41\) | −12.1707 | −1.90074 | −0.950371 | − | 0.311118i | \(-0.899296\pi\) | ||||
−0.950371 | + | 0.311118i | \(0.899296\pi\) | |||||||
\(42\) | 1.95667 | 0.301921 | ||||||||
\(43\) | 12.1281 | 1.84952 | 0.924758 | − | 0.380555i | \(-0.124267\pi\) | ||||
0.924758 | + | 0.380555i | \(0.124267\pi\) | |||||||
\(44\) | 2.28019 | 0.343751 | ||||||||
\(45\) | 15.2749 | 2.27705 | ||||||||
\(46\) | −1.51008 | −0.222650 | ||||||||
\(47\) | −2.04189 | −0.297841 | −0.148920 | − | 0.988849i | \(-0.547580\pi\) | ||||
−0.148920 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(48\) | −2.82604 | −0.407903 | ||||||||
\(49\) | −6.52062 | −0.931517 | ||||||||
\(50\) | −4.38355 | −0.619928 | ||||||||
\(51\) | −8.06237 | −1.12896 | ||||||||
\(52\) | −1.07870 | −0.149588 | ||||||||
\(53\) | −5.37863 | −0.738812 | −0.369406 | − | 0.929268i | \(-0.620439\pi\) | ||||
−0.369406 | + | 0.929268i | \(0.620439\pi\) | |||||||
\(54\) | 5.61389 | 0.763953 | ||||||||
\(55\) | 6.98481 | 0.941831 | ||||||||
\(56\) | −0.692372 | −0.0925222 | ||||||||
\(57\) | −0.494964 | −0.0655596 | ||||||||
\(58\) | −2.35314 | −0.308983 | ||||||||
\(59\) | 2.13087 | 0.277415 | 0.138708 | − | 0.990333i | \(-0.455705\pi\) | ||||
0.138708 | + | 0.990333i | \(0.455705\pi\) | |||||||
\(60\) | −8.65688 | −1.11760 | ||||||||
\(61\) | −4.45670 | −0.570622 | −0.285311 | − | 0.958435i | \(-0.592097\pi\) | ||||
−0.285311 | + | 0.958435i | \(0.592097\pi\) | |||||||
\(62\) | 6.93214 | 0.880382 | ||||||||
\(63\) | 3.45251 | 0.434975 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.30433 | −0.409851 | ||||||||
\(66\) | 6.44390 | 0.793189 | ||||||||
\(67\) | 0.879153 | 0.107406 | 0.0537028 | − | 0.998557i | \(-0.482898\pi\) | ||||
0.0537028 | + | 0.998557i | \(0.482898\pi\) | |||||||
\(68\) | 2.85289 | 0.345963 | ||||||||
\(69\) | −4.26756 | −0.513753 | ||||||||
\(70\) | −2.12092 | −0.253498 | ||||||||
\(71\) | −10.9737 | −1.30233 | −0.651167 | − | 0.758935i | \(-0.725720\pi\) | ||||
−0.651167 | + | 0.758935i | \(0.725720\pi\) | |||||||
\(72\) | −4.98649 | −0.587663 | ||||||||
\(73\) | −11.3514 | −1.32858 | −0.664289 | − | 0.747476i | \(-0.731266\pi\) | ||||
−0.664289 | + | 0.747476i | \(0.731266\pi\) | |||||||
\(74\) | 4.30129 | 0.500014 | ||||||||
\(75\) | −12.3881 | −1.43045 | ||||||||
\(76\) | 0.175144 | 0.0200904 | ||||||||
\(77\) | 1.57874 | 0.179914 | ||||||||
\(78\) | −3.04844 | −0.345167 | ||||||||
\(79\) | 12.1508 | 1.36708 | 0.683538 | − | 0.729915i | \(-0.260440\pi\) | ||||
0.683538 | + | 0.729915i | \(0.260440\pi\) | |||||||
\(80\) | 3.06326 | 0.342483 | ||||||||
\(81\) | 0.905589 | 0.100621 | ||||||||
\(82\) | 12.1707 | 1.34403 | ||||||||
\(83\) | 7.64282 | 0.838909 | 0.419454 | − | 0.907776i | \(-0.362221\pi\) | ||||
0.419454 | + | 0.907776i | \(0.362221\pi\) | |||||||
\(84\) | −1.95667 | −0.213490 | ||||||||
\(85\) | 8.73913 | 0.947892 | ||||||||
\(86\) | −12.1281 | −1.30781 | ||||||||
\(87\) | −6.65006 | −0.712962 | ||||||||
\(88\) | −2.28019 | −0.243069 | ||||||||
\(89\) | −10.2676 | −1.08836 | −0.544181 | − | 0.838968i | \(-0.683160\pi\) | ||||
−0.544181 | + | 0.838968i | \(0.683160\pi\) | |||||||
\(90\) | −15.2749 | −1.61012 | ||||||||
\(91\) | −0.746859 | −0.0782921 | ||||||||
\(92\) | 1.51008 | 0.157437 | ||||||||
\(93\) | 19.5905 | 2.03144 | ||||||||
\(94\) | 2.04189 | 0.210605 | ||||||||
\(95\) | 0.536512 | 0.0550450 | ||||||||
\(96\) | 2.82604 | 0.288431 | ||||||||
\(97\) | −12.3896 | −1.25797 | −0.628986 | − | 0.777417i | \(-0.716530\pi\) | ||||
−0.628986 | + | 0.777417i | \(0.716530\pi\) | |||||||
\(98\) | 6.52062 | 0.658682 | ||||||||
\(99\) | 11.3701 | 1.14274 | ||||||||
\(100\) | 4.38355 | 0.438355 | ||||||||
\(101\) | −5.22039 | −0.519449 | −0.259724 | − | 0.965683i | \(-0.583632\pi\) | ||||
−0.259724 | + | 0.965683i | \(0.583632\pi\) | |||||||
\(102\) | 8.06237 | 0.798293 | ||||||||
\(103\) | −3.35208 | −0.330290 | −0.165145 | − | 0.986269i | \(-0.552809\pi\) | ||||
−0.165145 | + | 0.986269i | \(0.552809\pi\) | |||||||
\(104\) | 1.07870 | 0.105775 | ||||||||
\(105\) | −5.99379 | −0.584934 | ||||||||
\(106\) | 5.37863 | 0.522419 | ||||||||
\(107\) | −17.2057 | −1.66333 | −0.831667 | − | 0.555274i | \(-0.812613\pi\) | ||||
−0.831667 | + | 0.555274i | \(0.812613\pi\) | |||||||
\(108\) | −5.61389 | −0.540196 | ||||||||
\(109\) | −11.8145 | −1.13163 | −0.565813 | − | 0.824534i | \(-0.691438\pi\) | ||||
−0.565813 | + | 0.824534i | \(0.691438\pi\) | |||||||
\(110\) | −6.98481 | −0.665975 | ||||||||
\(111\) | 12.1556 | 1.15376 | ||||||||
\(112\) | 0.692372 | 0.0654230 | ||||||||
\(113\) | −19.1814 | −1.80444 | −0.902219 | − | 0.431279i | \(-0.858063\pi\) | ||||
−0.902219 | + | 0.431279i | \(0.858063\pi\) | |||||||
\(114\) | 0.494964 | 0.0463577 | ||||||||
\(115\) | 4.62578 | 0.431356 | ||||||||
\(116\) | 2.35314 | 0.218484 | ||||||||
\(117\) | −5.37890 | −0.497280 | ||||||||
\(118\) | −2.13087 | −0.196162 | ||||||||
\(119\) | 1.97526 | 0.181072 | ||||||||
\(120\) | 8.65688 | 0.790262 | ||||||||
\(121\) | −5.80074 | −0.527340 | ||||||||
\(122\) | 4.45670 | 0.403491 | ||||||||
\(123\) | 34.3948 | 3.10128 | ||||||||
\(124\) | −6.93214 | −0.622524 | ||||||||
\(125\) | −1.88833 | −0.168898 | ||||||||
\(126\) | −3.45251 | −0.307574 | ||||||||
\(127\) | −2.46955 | −0.219138 | −0.109569 | − | 0.993979i | \(-0.534947\pi\) | ||||
−0.109569 | + | 0.993979i | \(0.534947\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −34.2744 | −3.01770 | ||||||||
\(130\) | 3.30433 | 0.289809 | ||||||||
\(131\) | −7.50843 | −0.656014 | −0.328007 | − | 0.944675i | \(-0.606377\pi\) | ||||
−0.328007 | + | 0.944675i | \(0.606377\pi\) | |||||||
\(132\) | −6.44390 | −0.560869 | ||||||||
\(133\) | 0.121265 | 0.0105150 | ||||||||
\(134\) | −0.879153 | −0.0759473 | ||||||||
\(135\) | −17.1968 | −1.48006 | ||||||||
\(136\) | −2.85289 | −0.244633 | ||||||||
\(137\) | −7.67740 | −0.655925 | −0.327962 | − | 0.944691i | \(-0.606362\pi\) | ||||
−0.327962 | + | 0.944691i | \(0.606362\pi\) | |||||||
\(138\) | 4.26756 | 0.363279 | ||||||||
\(139\) | 7.67615 | 0.651083 | 0.325541 | − | 0.945528i | \(-0.394453\pi\) | ||||
0.325541 | + | 0.945528i | \(0.394453\pi\) | |||||||
\(140\) | 2.12092 | 0.179250 | ||||||||
\(141\) | 5.77047 | 0.485961 | ||||||||
\(142\) | 10.9737 | 0.920889 | ||||||||
\(143\) | −2.45963 | −0.205685 | ||||||||
\(144\) | 4.98649 | 0.415541 | ||||||||
\(145\) | 7.20828 | 0.598615 | ||||||||
\(146\) | 11.3514 | 0.939447 | ||||||||
\(147\) | 18.4275 | 1.51988 | ||||||||
\(148\) | −4.30129 | −0.353564 | ||||||||
\(149\) | −7.37986 | −0.604582 | −0.302291 | − | 0.953216i | \(-0.597751\pi\) | ||||
−0.302291 | + | 0.953216i | \(0.597751\pi\) | |||||||
\(150\) | 12.3881 | 1.01148 | ||||||||
\(151\) | −3.03501 | −0.246986 | −0.123493 | − | 0.992345i | \(-0.539410\pi\) | ||||
−0.123493 | + | 0.992345i | \(0.539410\pi\) | |||||||
\(152\) | −0.175144 | −0.0142061 | ||||||||
\(153\) | 14.2259 | 1.15009 | ||||||||
\(154\) | −1.57874 | −0.127218 | ||||||||
\(155\) | −21.2349 | −1.70563 | ||||||||
\(156\) | 3.04844 | 0.244070 | ||||||||
\(157\) | 12.1397 | 0.968855 | 0.484428 | − | 0.874831i | \(-0.339028\pi\) | ||||
0.484428 | + | 0.874831i | \(0.339028\pi\) | |||||||
\(158\) | −12.1508 | −0.966668 | ||||||||
\(159\) | 15.2002 | 1.20546 | ||||||||
\(160\) | −3.06326 | −0.242172 | ||||||||
\(161\) | 1.04554 | 0.0824002 | ||||||||
\(162\) | −0.905589 | −0.0711498 | ||||||||
\(163\) | 2.37411 | 0.185955 | 0.0929775 | − | 0.995668i | \(-0.470362\pi\) | ||||
0.0929775 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(164\) | −12.1707 | −0.950371 | ||||||||
\(165\) | −19.7393 | −1.53670 | ||||||||
\(166\) | −7.64282 | −0.593198 | ||||||||
\(167\) | −3.88661 | −0.300755 | −0.150377 | − | 0.988629i | \(-0.548049\pi\) | ||||
−0.150377 | + | 0.988629i | \(0.548049\pi\) | |||||||
\(168\) | 1.95667 | 0.150960 | ||||||||
\(169\) | −11.8364 | −0.910493 | ||||||||
\(170\) | −8.73913 | −0.670261 | ||||||||
\(171\) | 0.873355 | 0.0667871 | ||||||||
\(172\) | 12.1281 | 0.924758 | ||||||||
\(173\) | 16.9311 | 1.28725 | 0.643623 | − | 0.765343i | \(-0.277430\pi\) | ||||
0.643623 | + | 0.765343i | \(0.277430\pi\) | |||||||
\(174\) | 6.65006 | 0.504140 | ||||||||
\(175\) | 3.03505 | 0.229428 | ||||||||
\(176\) | 2.28019 | 0.171876 | ||||||||
\(177\) | −6.02191 | −0.452634 | ||||||||
\(178\) | 10.2676 | 0.769588 | ||||||||
\(179\) | 2.74384 | 0.205084 | 0.102542 | − | 0.994729i | \(-0.467302\pi\) | ||||
0.102542 | + | 0.994729i | \(0.467302\pi\) | |||||||
\(180\) | 15.2749 | 1.13852 | ||||||||
\(181\) | 19.9339 | 1.48168 | 0.740838 | − | 0.671684i | \(-0.234429\pi\) | ||||
0.740838 | + | 0.671684i | \(0.234429\pi\) | |||||||
\(182\) | 0.746859 | 0.0553609 | ||||||||
\(183\) | 12.5948 | 0.931034 | ||||||||
\(184\) | −1.51008 | −0.111325 | ||||||||
\(185\) | −13.1760 | −0.968715 | ||||||||
\(186\) | −19.5905 | −1.43644 | ||||||||
\(187\) | 6.50512 | 0.475702 | ||||||||
\(188\) | −2.04189 | −0.148920 | ||||||||
\(189\) | −3.88690 | −0.282730 | ||||||||
\(190\) | −0.536512 | −0.0389227 | ||||||||
\(191\) | 3.88094 | 0.280815 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(192\) | −2.82604 | −0.203952 | ||||||||
\(193\) | −14.3698 | −1.03436 | −0.517179 | − | 0.855877i | \(-0.673018\pi\) | ||||
−0.517179 | + | 0.855877i | \(0.673018\pi\) | |||||||
\(194\) | 12.3896 | 0.889520 | ||||||||
\(195\) | 9.33815 | 0.668719 | ||||||||
\(196\) | −6.52062 | −0.465759 | ||||||||
\(197\) | −5.03581 | −0.358786 | −0.179393 | − | 0.983777i | \(-0.557413\pi\) | ||||
−0.179393 | + | 0.983777i | \(0.557413\pi\) | |||||||
\(198\) | −11.3701 | −0.808040 | ||||||||
\(199\) | 21.6518 | 1.53486 | 0.767429 | − | 0.641134i | \(-0.221536\pi\) | ||||
0.767429 | + | 0.641134i | \(0.221536\pi\) | |||||||
\(200\) | −4.38355 | −0.309964 | ||||||||
\(201\) | −2.48452 | −0.175245 | ||||||||
\(202\) | 5.22039 | 0.367306 | ||||||||
\(203\) | 1.62925 | 0.114351 | ||||||||
\(204\) | −8.06237 | −0.564478 | ||||||||
\(205\) | −37.2820 | −2.60389 | ||||||||
\(206\) | 3.35208 | 0.233551 | ||||||||
\(207\) | 7.53002 | 0.523372 | ||||||||
\(208\) | −1.07870 | −0.0747941 | ||||||||
\(209\) | 0.399362 | 0.0276245 | ||||||||
\(210\) | 5.99379 | 0.413611 | ||||||||
\(211\) | −18.3389 | −1.26250 | −0.631251 | − | 0.775578i | \(-0.717458\pi\) | ||||
−0.631251 | + | 0.775578i | \(0.717458\pi\) | |||||||
\(212\) | −5.37863 | −0.369406 | ||||||||
\(213\) | 31.0120 | 2.12490 | ||||||||
\(214\) | 17.2057 | 1.17616 | ||||||||
\(215\) | 37.1515 | 2.53371 | ||||||||
\(216\) | 5.61389 | 0.381976 | ||||||||
\(217\) | −4.79962 | −0.325819 | ||||||||
\(218\) | 11.8145 | 0.800181 | ||||||||
\(219\) | 32.0794 | 2.16773 | ||||||||
\(220\) | 6.98481 | 0.470916 | ||||||||
\(221\) | −3.07740 | −0.207008 | ||||||||
\(222\) | −12.1556 | −0.815830 | ||||||||
\(223\) | 11.4755 | 0.768458 | 0.384229 | − | 0.923238i | \(-0.374467\pi\) | ||||
0.384229 | + | 0.923238i | \(0.374467\pi\) | |||||||
\(224\) | −0.692372 | −0.0462611 | ||||||||
\(225\) | 21.8585 | 1.45724 | ||||||||
\(226\) | 19.1814 | 1.27593 | ||||||||
\(227\) | −6.74186 | −0.447473 | −0.223736 | − | 0.974650i | \(-0.571825\pi\) | ||||
−0.223736 | + | 0.974650i | \(0.571825\pi\) | |||||||
\(228\) | −0.494964 | −0.0327798 | ||||||||
\(229\) | 17.7376 | 1.17213 | 0.586065 | − | 0.810264i | \(-0.300676\pi\) | ||||
0.586065 | + | 0.810264i | \(0.300676\pi\) | |||||||
\(230\) | −4.62578 | −0.305015 | ||||||||
\(231\) | −4.46158 | −0.293550 | ||||||||
\(232\) | −2.35314 | −0.154491 | ||||||||
\(233\) | 23.5701 | 1.54413 | 0.772063 | − | 0.635546i | \(-0.219225\pi\) | ||||
0.772063 | + | 0.635546i | \(0.219225\pi\) | |||||||
\(234\) | 5.37890 | 0.351630 | ||||||||
\(235\) | −6.25485 | −0.408021 | ||||||||
\(236\) | 2.13087 | 0.138708 | ||||||||
\(237\) | −34.3387 | −2.23054 | ||||||||
\(238\) | −1.97526 | −0.128037 | ||||||||
\(239\) | −8.59370 | −0.555880 | −0.277940 | − | 0.960598i | \(-0.589652\pi\) | ||||
−0.277940 | + | 0.960598i | \(0.589652\pi\) | |||||||
\(240\) | −8.65688 | −0.558799 | ||||||||
\(241\) | 14.8029 | 0.953540 | 0.476770 | − | 0.879028i | \(-0.341808\pi\) | ||||
0.476770 | + | 0.879028i | \(0.341808\pi\) | |||||||
\(242\) | 5.80074 | 0.372886 | ||||||||
\(243\) | 14.2824 | 0.916218 | ||||||||
\(244\) | −4.45670 | −0.285311 | ||||||||
\(245\) | −19.9743 | −1.27611 | ||||||||
\(246\) | −34.3948 | −2.19293 | ||||||||
\(247\) | −0.188927 | −0.0120212 | ||||||||
\(248\) | 6.93214 | 0.440191 | ||||||||
\(249\) | −21.5989 | −1.36877 | ||||||||
\(250\) | 1.88833 | 0.119429 | ||||||||
\(251\) | −9.70408 | −0.612516 | −0.306258 | − | 0.951949i | \(-0.599077\pi\) | ||||
−0.306258 | + | 0.951949i | \(0.599077\pi\) | |||||||
\(252\) | 3.45251 | 0.217487 | ||||||||
\(253\) | 3.44328 | 0.216477 | ||||||||
\(254\) | 2.46955 | 0.154954 | ||||||||
\(255\) | −24.6971 | −1.54659 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.86077 | 0.303207 | 0.151603 | − | 0.988441i | \(-0.451556\pi\) | ||||
0.151603 | + | 0.988441i | \(0.451556\pi\) | |||||||
\(258\) | 34.2744 | 2.13383 | ||||||||
\(259\) | −2.97809 | −0.185050 | ||||||||
\(260\) | −3.30433 | −0.204926 | ||||||||
\(261\) | 11.7339 | 0.726311 | ||||||||
\(262\) | 7.50843 | 0.463872 | ||||||||
\(263\) | 24.4920 | 1.51024 | 0.755119 | − | 0.655587i | \(-0.227579\pi\) | ||||
0.755119 | + | 0.655587i | \(0.227579\pi\) | |||||||
\(264\) | 6.44390 | 0.396595 | ||||||||
\(265\) | −16.4762 | −1.01212 | ||||||||
\(266\) | −0.121265 | −0.00743524 | ||||||||
\(267\) | 29.0166 | 1.77579 | ||||||||
\(268\) | 0.879153 | 0.0537028 | ||||||||
\(269\) | −6.53813 | −0.398637 | −0.199318 | − | 0.979935i | \(-0.563873\pi\) | ||||
−0.199318 | + | 0.979935i | \(0.563873\pi\) | |||||||
\(270\) | 17.1968 | 1.04656 | ||||||||
\(271\) | −21.0283 | −1.27738 | −0.638688 | − | 0.769466i | \(-0.720523\pi\) | ||||
−0.638688 | + | 0.769466i | \(0.720523\pi\) | |||||||
\(272\) | 2.85289 | 0.172982 | ||||||||
\(273\) | 2.11065 | 0.127743 | ||||||||
\(274\) | 7.67740 | 0.463809 | ||||||||
\(275\) | 9.99533 | 0.602741 | ||||||||
\(276\) | −4.26756 | −0.256877 | ||||||||
\(277\) | −2.57394 | −0.154653 | −0.0773264 | − | 0.997006i | \(-0.524638\pi\) | ||||
−0.0773264 | + | 0.997006i | \(0.524638\pi\) | |||||||
\(278\) | −7.67615 | −0.460385 | ||||||||
\(279\) | −34.5670 | −2.06947 | ||||||||
\(280\) | −2.12092 | −0.126749 | ||||||||
\(281\) | 24.1639 | 1.44150 | 0.720749 | − | 0.693196i | \(-0.243798\pi\) | ||||
0.720749 | + | 0.693196i | \(0.243798\pi\) | |||||||
\(282\) | −5.77047 | −0.343626 | ||||||||
\(283\) | −18.1926 | −1.08144 | −0.540719 | − | 0.841203i | \(-0.681848\pi\) | ||||
−0.540719 | + | 0.841203i | \(0.681848\pi\) | |||||||
\(284\) | −10.9737 | −0.651167 | ||||||||
\(285\) | −1.51620 | −0.0898122 | ||||||||
\(286\) | 2.45963 | 0.145441 | ||||||||
\(287\) | −8.42665 | −0.497409 | ||||||||
\(288\) | −4.98649 | −0.293832 | ||||||||
\(289\) | −8.86104 | −0.521237 | ||||||||
\(290\) | −7.20828 | −0.423285 | ||||||||
\(291\) | 35.0134 | 2.05252 | ||||||||
\(292\) | −11.3514 | −0.664289 | ||||||||
\(293\) | 24.0869 | 1.40717 | 0.703586 | − | 0.710610i | \(-0.251581\pi\) | ||||
0.703586 | + | 0.710610i | \(0.251581\pi\) | |||||||
\(294\) | −18.4275 | −1.07471 | ||||||||
\(295\) | 6.52740 | 0.380040 | ||||||||
\(296\) | 4.30129 | 0.250007 | ||||||||
\(297\) | −12.8007 | −0.742773 | ||||||||
\(298\) | 7.37986 | 0.427504 | ||||||||
\(299\) | −1.62892 | −0.0942030 | ||||||||
\(300\) | −12.3881 | −0.715227 | ||||||||
\(301\) | 8.39716 | 0.484004 | ||||||||
\(302\) | 3.03501 | 0.174645 | ||||||||
\(303\) | 14.7530 | 0.847539 | ||||||||
\(304\) | 0.175144 | 0.0100452 | ||||||||
\(305\) | −13.6520 | −0.781713 | ||||||||
\(306\) | −14.2259 | −0.813240 | ||||||||
\(307\) | 4.26161 | 0.243223 | 0.121611 | − | 0.992578i | \(-0.461194\pi\) | ||||
0.121611 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(308\) | 1.57874 | 0.0899570 | ||||||||
\(309\) | 9.47311 | 0.538906 | ||||||||
\(310\) | 21.2349 | 1.20606 | ||||||||
\(311\) | 30.9074 | 1.75260 | 0.876299 | − | 0.481767i | \(-0.160005\pi\) | ||||
0.876299 | + | 0.481767i | \(0.160005\pi\) | |||||||
\(312\) | −3.04844 | −0.172584 | ||||||||
\(313\) | 28.2680 | 1.59780 | 0.798901 | − | 0.601463i | \(-0.205415\pi\) | ||||
0.798901 | + | 0.601463i | \(0.205415\pi\) | |||||||
\(314\) | −12.1397 | −0.685084 | ||||||||
\(315\) | 10.5759 | 0.595885 | ||||||||
\(316\) | 12.1508 | 0.683538 | ||||||||
\(317\) | 11.8780 | 0.667133 | 0.333567 | − | 0.942727i | \(-0.391748\pi\) | ||||
0.333567 | + | 0.942727i | \(0.391748\pi\) | |||||||
\(318\) | −15.2002 | −0.852386 | ||||||||
\(319\) | 5.36561 | 0.300416 | ||||||||
\(320\) | 3.06326 | 0.171241 | ||||||||
\(321\) | 48.6239 | 2.71392 | ||||||||
\(322\) | −1.04554 | −0.0582657 | ||||||||
\(323\) | 0.499667 | 0.0278022 | ||||||||
\(324\) | 0.905589 | 0.0503105 | ||||||||
\(325\) | −4.72852 | −0.262291 | ||||||||
\(326\) | −2.37411 | −0.131490 | ||||||||
\(327\) | 33.3883 | 1.84638 | ||||||||
\(328\) | 12.1707 | 0.672014 | ||||||||
\(329\) | −1.41375 | −0.0779426 | ||||||||
\(330\) | 19.7393 | 1.08661 | ||||||||
\(331\) | 5.74696 | 0.315882 | 0.157941 | − | 0.987449i | \(-0.449514\pi\) | ||||
0.157941 | + | 0.987449i | \(0.449514\pi\) | |||||||
\(332\) | 7.64282 | 0.419454 | ||||||||
\(333\) | −21.4483 | −1.17536 | ||||||||
\(334\) | 3.88661 | 0.212666 | ||||||||
\(335\) | 2.69307 | 0.147138 | ||||||||
\(336\) | −1.95667 | −0.106745 | ||||||||
\(337\) | 25.2914 | 1.37771 | 0.688854 | − | 0.724900i | \(-0.258114\pi\) | ||||
0.688854 | + | 0.724900i | \(0.258114\pi\) | |||||||
\(338\) | 11.8364 | 0.643816 | ||||||||
\(339\) | 54.2074 | 2.94414 | ||||||||
\(340\) | 8.73913 | 0.473946 | ||||||||
\(341\) | −15.8066 | −0.855974 | ||||||||
\(342\) | −0.873355 | −0.0472256 | ||||||||
\(343\) | −9.36130 | −0.505463 | ||||||||
\(344\) | −12.1281 | −0.653903 | ||||||||
\(345\) | −13.0726 | −0.703807 | ||||||||
\(346\) | −16.9311 | −0.910221 | ||||||||
\(347\) | −0.377875 | −0.0202854 | −0.0101427 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101427 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(348\) | −6.65006 | −0.356481 | ||||||||
\(349\) | −27.0247 | −1.44660 | −0.723301 | − | 0.690533i | \(-0.757376\pi\) | ||||
−0.723301 | + | 0.690533i | \(0.757376\pi\) | |||||||
\(350\) | −3.03505 | −0.162230 | ||||||||
\(351\) | 6.05568 | 0.323228 | ||||||||
\(352\) | −2.28019 | −0.121534 | ||||||||
\(353\) | −2.06081 | −0.109686 | −0.0548429 | − | 0.998495i | \(-0.517466\pi\) | ||||
−0.0548429 | + | 0.998495i | \(0.517466\pi\) | |||||||
\(354\) | 6.02191 | 0.320061 | ||||||||
\(355\) | −33.6151 | −1.78411 | ||||||||
\(356\) | −10.2676 | −0.544181 | ||||||||
\(357\) | −5.58216 | −0.295439 | ||||||||
\(358\) | −2.74384 | −0.145016 | ||||||||
\(359\) | −15.3163 | −0.808363 | −0.404181 | − | 0.914679i | \(-0.632444\pi\) | ||||
−0.404181 | + | 0.914679i | \(0.632444\pi\) | |||||||
\(360\) | −15.2749 | −0.805058 | ||||||||
\(361\) | −18.9693 | −0.998385 | ||||||||
\(362\) | −19.9339 | −1.04770 | ||||||||
\(363\) | 16.3931 | 0.860415 | ||||||||
\(364\) | −0.746859 | −0.0391461 | ||||||||
\(365\) | −34.7722 | −1.82006 | ||||||||
\(366\) | −12.5948 | −0.658341 | ||||||||
\(367\) | 3.85655 | 0.201310 | 0.100655 | − | 0.994921i | \(-0.467906\pi\) | ||||
0.100655 | + | 0.994921i | \(0.467906\pi\) | |||||||
\(368\) | 1.51008 | 0.0787186 | ||||||||
\(369\) | −60.6890 | −3.15934 | ||||||||
\(370\) | 13.1760 | 0.684985 | ||||||||
\(371\) | −3.72402 | −0.193341 | ||||||||
\(372\) | 19.5905 | 1.01572 | ||||||||
\(373\) | −17.7945 | −0.921363 | −0.460681 | − | 0.887566i | \(-0.652395\pi\) | ||||
−0.460681 | + | 0.887566i | \(0.652395\pi\) | |||||||
\(374\) | −6.50512 | −0.336372 | ||||||||
\(375\) | 5.33650 | 0.275575 | ||||||||
\(376\) | 2.04189 | 0.105303 | ||||||||
\(377\) | −2.53832 | −0.130730 | ||||||||
\(378\) | 3.88690 | 0.199921 | ||||||||
\(379\) | −13.0418 | −0.669913 | −0.334956 | − | 0.942234i | \(-0.608722\pi\) | ||||
−0.334956 | + | 0.942234i | \(0.608722\pi\) | |||||||
\(380\) | 0.536512 | 0.0275225 | ||||||||
\(381\) | 6.97905 | 0.357548 | ||||||||
\(382\) | −3.88094 | −0.198566 | ||||||||
\(383\) | 13.8945 | 0.709977 | 0.354988 | − | 0.934871i | \(-0.384485\pi\) | ||||
0.354988 | + | 0.934871i | \(0.384485\pi\) | |||||||
\(384\) | 2.82604 | 0.144216 | ||||||||
\(385\) | 4.83609 | 0.246470 | ||||||||
\(386\) | 14.3698 | 0.731401 | ||||||||
\(387\) | 60.4766 | 3.07420 | ||||||||
\(388\) | −12.3896 | −0.628986 | ||||||||
\(389\) | 13.5860 | 0.688838 | 0.344419 | − | 0.938816i | \(-0.388076\pi\) | ||||
0.344419 | + | 0.938816i | \(0.388076\pi\) | |||||||
\(390\) | −9.33815 | −0.472855 | ||||||||
\(391\) | 4.30810 | 0.217870 | ||||||||
\(392\) | 6.52062 | 0.329341 | ||||||||
\(393\) | 21.2191 | 1.07036 | ||||||||
\(394\) | 5.03581 | 0.253700 | ||||||||
\(395\) | 37.2211 | 1.87280 | ||||||||
\(396\) | 11.3701 | 0.571371 | ||||||||
\(397\) | 11.8815 | 0.596316 | 0.298158 | − | 0.954517i | \(-0.403628\pi\) | ||||
0.298158 | + | 0.954517i | \(0.403628\pi\) | |||||||
\(398\) | −21.6518 | −1.08531 | ||||||||
\(399\) | −0.342700 | −0.0171564 | ||||||||
\(400\) | 4.38355 | 0.219178 | ||||||||
\(401\) | −30.0049 | −1.49837 | −0.749186 | − | 0.662359i | \(-0.769555\pi\) | ||||
−0.749186 | + | 0.662359i | \(0.769555\pi\) | |||||||
\(402\) | 2.48452 | 0.123917 | ||||||||
\(403\) | 7.47767 | 0.372489 | ||||||||
\(404\) | −5.22039 | −0.259724 | ||||||||
\(405\) | 2.77405 | 0.137844 | ||||||||
\(406\) | −1.62925 | −0.0808583 | ||||||||
\(407\) | −9.80774 | −0.486152 | ||||||||
\(408\) | 8.06237 | 0.399147 | ||||||||
\(409\) | −3.71049 | −0.183472 | −0.0917359 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917359 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(410\) | 37.2820 | 1.84123 | ||||||||
\(411\) | 21.6966 | 1.07022 | ||||||||
\(412\) | −3.35208 | −0.165145 | ||||||||
\(413\) | 1.47535 | 0.0725974 | ||||||||
\(414\) | −7.53002 | −0.370080 | ||||||||
\(415\) | 23.4119 | 1.14925 | ||||||||
\(416\) | 1.07870 | 0.0528874 | ||||||||
\(417\) | −21.6931 | −1.06232 | ||||||||
\(418\) | −0.399362 | −0.0195334 | ||||||||
\(419\) | −19.8018 | −0.967379 | −0.483690 | − | 0.875240i | \(-0.660704\pi\) | ||||
−0.483690 | + | 0.875240i | \(0.660704\pi\) | |||||||
\(420\) | −5.99379 | −0.292467 | ||||||||
\(421\) | −26.0484 | −1.26952 | −0.634761 | − | 0.772708i | \(-0.718902\pi\) | ||||
−0.634761 | + | 0.772708i | \(0.718902\pi\) | |||||||
\(422\) | 18.3389 | 0.892724 | ||||||||
\(423\) | −10.1819 | −0.495060 | ||||||||
\(424\) | 5.37863 | 0.261210 | ||||||||
\(425\) | 12.5058 | 0.606620 | ||||||||
\(426\) | −31.0120 | −1.50253 | ||||||||
\(427\) | −3.08570 | −0.149327 | ||||||||
\(428\) | −17.2057 | −0.831667 | ||||||||
\(429\) | 6.95101 | 0.335598 | ||||||||
\(430\) | −37.1515 | −1.79160 | ||||||||
\(431\) | −21.3389 | −1.02786 | −0.513929 | − | 0.857832i | \(-0.671811\pi\) | ||||
−0.513929 | + | 0.857832i | \(0.671811\pi\) | |||||||
\(432\) | −5.61389 | −0.270098 | ||||||||
\(433\) | −34.7279 | −1.66892 | −0.834458 | − | 0.551072i | \(-0.814219\pi\) | ||||
−0.834458 | + | 0.551072i | \(0.814219\pi\) | |||||||
\(434\) | 4.79962 | 0.230389 | ||||||||
\(435\) | −20.3709 | −0.976708 | ||||||||
\(436\) | −11.8145 | −0.565813 | ||||||||
\(437\) | 0.264483 | 0.0126519 | ||||||||
\(438\) | −32.0794 | −1.53281 | ||||||||
\(439\) | 35.0226 | 1.67154 | 0.835768 | − | 0.549082i | \(-0.185023\pi\) | ||||
0.835768 | + | 0.549082i | \(0.185023\pi\) | |||||||
\(440\) | −6.98481 | −0.332988 | ||||||||
\(441\) | −32.5150 | −1.54833 | ||||||||
\(442\) | 3.07740 | 0.146377 | ||||||||
\(443\) | −34.5796 | −1.64293 | −0.821464 | − | 0.570261i | \(-0.806842\pi\) | ||||
−0.821464 | + | 0.570261i | \(0.806842\pi\) | |||||||
\(444\) | 12.1556 | 0.576879 | ||||||||
\(445\) | −31.4523 | −1.49098 | ||||||||
\(446\) | −11.4755 | −0.543382 | ||||||||
\(447\) | 20.8558 | 0.986443 | ||||||||
\(448\) | 0.692372 | 0.0327115 | ||||||||
\(449\) | 27.6957 | 1.30704 | 0.653519 | − | 0.756910i | \(-0.273292\pi\) | ||||
0.653519 | + | 0.756910i | \(0.273292\pi\) | |||||||
\(450\) | −21.8585 | −1.03042 | ||||||||
\(451\) | −27.7515 | −1.30677 | ||||||||
\(452\) | −19.1814 | −0.902219 | ||||||||
\(453\) | 8.57706 | 0.402985 | ||||||||
\(454\) | 6.74186 | 0.316411 | ||||||||
\(455\) | −2.28782 | −0.107255 | ||||||||
\(456\) | 0.494964 | 0.0231788 | ||||||||
\(457\) | 5.23659 | 0.244957 | 0.122479 | − | 0.992471i | \(-0.460916\pi\) | ||||
0.122479 | + | 0.992471i | \(0.460916\pi\) | |||||||
\(458\) | −17.7376 | −0.828821 | ||||||||
\(459\) | −16.0158 | −0.747553 | ||||||||
\(460\) | 4.62578 | 0.215678 | ||||||||
\(461\) | −5.04783 | −0.235101 | −0.117550 | − | 0.993067i | \(-0.537504\pi\) | ||||
−0.117550 | + | 0.993067i | \(0.537504\pi\) | |||||||
\(462\) | 4.46158 | 0.207571 | ||||||||
\(463\) | −3.00114 | −0.139475 | −0.0697374 | − | 0.997565i | \(-0.522216\pi\) | ||||
−0.0697374 | + | 0.997565i | \(0.522216\pi\) | |||||||
\(464\) | 2.35314 | 0.109242 | ||||||||
\(465\) | 60.0107 | 2.78293 | ||||||||
\(466\) | −23.5701 | −1.09186 | ||||||||
\(467\) | −19.7214 | −0.912599 | −0.456300 | − | 0.889826i | \(-0.650826\pi\) | ||||
−0.456300 | + | 0.889826i | \(0.650826\pi\) | |||||||
\(468\) | −5.37890 | −0.248640 | ||||||||
\(469\) | 0.608701 | 0.0281072 | ||||||||
\(470\) | 6.25485 | 0.288515 | ||||||||
\(471\) | −34.3073 | −1.58080 | ||||||||
\(472\) | −2.13087 | −0.0980811 | ||||||||
\(473\) | 27.6543 | 1.27155 | ||||||||
\(474\) | 34.3387 | 1.57723 | ||||||||
\(475\) | 0.767755 | 0.0352270 | ||||||||
\(476\) | 1.97526 | 0.0905359 | ||||||||
\(477\) | −26.8205 | −1.22803 | ||||||||
\(478\) | 8.59370 | 0.393067 | ||||||||
\(479\) | −17.6085 | −0.804554 | −0.402277 | − | 0.915518i | \(-0.631781\pi\) | ||||
−0.402277 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(480\) | 8.65688 | 0.395131 | ||||||||
\(481\) | 4.63978 | 0.211556 | ||||||||
\(482\) | −14.8029 | −0.674254 | ||||||||
\(483\) | −2.95474 | −0.134445 | ||||||||
\(484\) | −5.80074 | −0.263670 | ||||||||
\(485\) | −37.9525 | −1.72333 | ||||||||
\(486\) | −14.2824 | −0.647864 | ||||||||
\(487\) | 34.0021 | 1.54078 | 0.770390 | − | 0.637573i | \(-0.220062\pi\) | ||||
0.770390 | + | 0.637573i | \(0.220062\pi\) | |||||||
\(488\) | 4.45670 | 0.201745 | ||||||||
\(489\) | −6.70933 | −0.303407 | ||||||||
\(490\) | 19.9743 | 0.902349 | ||||||||
\(491\) | −26.3016 | −1.18697 | −0.593487 | − | 0.804844i | \(-0.702249\pi\) | ||||
−0.593487 | + | 0.804844i | \(0.702249\pi\) | |||||||
\(492\) | 34.3948 | 1.55064 | ||||||||
\(493\) | 6.71325 | 0.302349 | ||||||||
\(494\) | 0.188927 | 0.00850025 | ||||||||
\(495\) | 34.8297 | 1.56548 | ||||||||
\(496\) | −6.93214 | −0.311262 | ||||||||
\(497\) | −7.59786 | −0.340810 | ||||||||
\(498\) | 21.5989 | 0.967870 | ||||||||
\(499\) | −32.1334 | −1.43849 | −0.719244 | − | 0.694758i | \(-0.755511\pi\) | ||||
−0.719244 | + | 0.694758i | \(0.755511\pi\) | |||||||
\(500\) | −1.88833 | −0.0844488 | ||||||||
\(501\) | 10.9837 | 0.490716 | ||||||||
\(502\) | 9.70408 | 0.433114 | ||||||||
\(503\) | −14.5127 | −0.647089 | −0.323544 | − | 0.946213i | \(-0.604874\pi\) | ||||
−0.323544 | + | 0.946213i | \(0.604874\pi\) | |||||||
\(504\) | −3.45251 | −0.153787 | ||||||||
\(505\) | −15.9914 | −0.711609 | ||||||||
\(506\) | −3.44328 | −0.153072 | ||||||||
\(507\) | 33.4501 | 1.48557 | ||||||||
\(508\) | −2.46955 | −0.109569 | ||||||||
\(509\) | −12.1659 | −0.539245 | −0.269623 | − | 0.962966i | \(-0.586899\pi\) | ||||
−0.269623 | + | 0.962966i | \(0.586899\pi\) | |||||||
\(510\) | 24.6971 | 1.09361 | ||||||||
\(511\) | −7.85938 | −0.347679 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.983240 | −0.0434111 | ||||||||
\(514\) | −4.86077 | −0.214400 | ||||||||
\(515\) | −10.2683 | −0.452475 | ||||||||
\(516\) | −34.2744 | −1.50885 | ||||||||
\(517\) | −4.65590 | −0.204766 | ||||||||
\(518\) | 2.97809 | 0.130850 | ||||||||
\(519\) | −47.8479 | −2.10029 | ||||||||
\(520\) | 3.30433 | 0.144904 | ||||||||
\(521\) | 5.94487 | 0.260449 | 0.130225 | − | 0.991485i | \(-0.458430\pi\) | ||||
0.130225 | + | 0.991485i | \(0.458430\pi\) | |||||||
\(522\) | −11.7339 | −0.513579 | ||||||||
\(523\) | 30.0528 | 1.31412 | 0.657059 | − | 0.753839i | \(-0.271800\pi\) | ||||
0.657059 | + | 0.753839i | \(0.271800\pi\) | |||||||
\(524\) | −7.50843 | −0.328007 | ||||||||
\(525\) | −8.57717 | −0.374338 | ||||||||
\(526\) | −24.4920 | −1.06790 | ||||||||
\(527\) | −19.7766 | −0.861482 | ||||||||
\(528\) | −6.44390 | −0.280435 | ||||||||
\(529\) | −20.7196 | −0.900854 | ||||||||
\(530\) | 16.4762 | 0.715678 | ||||||||
\(531\) | 10.6255 | 0.461109 | ||||||||
\(532\) | 0.121265 | 0.00525751 | ||||||||
\(533\) | 13.1285 | 0.568657 | ||||||||
\(534\) | −29.0166 | −1.25567 | ||||||||
\(535\) | −52.7054 | −2.27865 | ||||||||
\(536\) | −0.879153 | −0.0379736 | ||||||||
\(537\) | −7.75419 | −0.334618 | ||||||||
\(538\) | 6.53813 | 0.281879 | ||||||||
\(539\) | −14.8682 | −0.640421 | ||||||||
\(540\) | −17.1968 | −0.740032 | ||||||||
\(541\) | −40.6866 | −1.74926 | −0.874628 | − | 0.484795i | \(-0.838894\pi\) | ||||
−0.874628 | + | 0.484795i | \(0.838894\pi\) | |||||||
\(542\) | 21.0283 | 0.903242 | ||||||||
\(543\) | −56.3340 | −2.41752 | ||||||||
\(544\) | −2.85289 | −0.122317 | ||||||||
\(545\) | −36.1909 | −1.55025 | ||||||||
\(546\) | −2.11065 | −0.0903276 | ||||||||
\(547\) | −13.5945 | −0.581260 | −0.290630 | − | 0.956836i | \(-0.593865\pi\) | ||||
−0.290630 | + | 0.956836i | \(0.593865\pi\) | |||||||
\(548\) | −7.67740 | −0.327962 | ||||||||
\(549\) | −22.2233 | −0.948466 | ||||||||
\(550\) | −9.99533 | −0.426202 | ||||||||
\(551\) | 0.412139 | 0.0175577 | ||||||||
\(552\) | 4.26756 | 0.181639 | ||||||||
\(553\) | 8.41290 | 0.357753 | ||||||||
\(554\) | 2.57394 | 0.109356 | ||||||||
\(555\) | 37.2357 | 1.58057 | ||||||||
\(556\) | 7.67615 | 0.325541 | ||||||||
\(557\) | 26.5051 | 1.12306 | 0.561530 | − | 0.827457i | \(-0.310213\pi\) | ||||
0.561530 | + | 0.827457i | \(0.310213\pi\) | |||||||
\(558\) | 34.5670 | 1.46334 | ||||||||
\(559\) | −13.0825 | −0.553332 | ||||||||
\(560\) | 2.12092 | 0.0896251 | ||||||||
\(561\) | −18.3837 | −0.776161 | ||||||||
\(562\) | −24.1639 | −1.01929 | ||||||||
\(563\) | −30.4753 | −1.28438 | −0.642190 | − | 0.766546i | \(-0.721974\pi\) | ||||
−0.642190 | + | 0.766546i | \(0.721974\pi\) | |||||||
\(564\) | 5.77047 | 0.242981 | ||||||||
\(565\) | −58.7577 | −2.47195 | ||||||||
\(566\) | 18.1926 | 0.764693 | ||||||||
\(567\) | 0.627004 | 0.0263317 | ||||||||
\(568\) | 10.9737 | 0.460444 | ||||||||
\(569\) | −6.29771 | −0.264014 | −0.132007 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132007 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(570\) | 1.51620 | 0.0635068 | ||||||||
\(571\) | −42.2290 | −1.76723 | −0.883615 | − | 0.468214i | \(-0.844898\pi\) | ||||
−0.883615 | + | 0.468214i | \(0.844898\pi\) | |||||||
\(572\) | −2.45963 | −0.102842 | ||||||||
\(573\) | −10.9677 | −0.458182 | ||||||||
\(574\) | 8.42665 | 0.351722 | ||||||||
\(575\) | 6.61954 | 0.276054 | ||||||||
\(576\) | 4.98649 | 0.207770 | ||||||||
\(577\) | 11.4691 | 0.477463 | 0.238732 | − | 0.971086i | \(-0.423268\pi\) | ||||
0.238732 | + | 0.971086i | \(0.423268\pi\) | |||||||
\(578\) | 8.86104 | 0.368570 | ||||||||
\(579\) | 40.6095 | 1.68767 | ||||||||
\(580\) | 7.20828 | 0.299308 | ||||||||
\(581\) | 5.29168 | 0.219536 | ||||||||
\(582\) | −35.0134 | −1.45135 | ||||||||
\(583\) | −12.2643 | −0.507936 | ||||||||
\(584\) | 11.3514 | 0.469723 | ||||||||
\(585\) | −16.4770 | −0.681239 | ||||||||
\(586\) | −24.0869 | −0.995022 | ||||||||
\(587\) | −1.98876 | −0.0820847 | −0.0410424 | − | 0.999157i | \(-0.513068\pi\) | ||||
−0.0410424 | + | 0.999157i | \(0.513068\pi\) | |||||||
\(588\) | 18.4275 | 0.759938 | ||||||||
\(589\) | −1.21412 | −0.0500271 | ||||||||
\(590\) | −6.52740 | −0.268729 | ||||||||
\(591\) | 14.2314 | 0.585401 | ||||||||
\(592\) | −4.30129 | −0.176782 | ||||||||
\(593\) | 42.5772 | 1.74844 | 0.874219 | − | 0.485532i | \(-0.161374\pi\) | ||||
0.874219 | + | 0.485532i | \(0.161374\pi\) | |||||||
\(594\) | 12.8007 | 0.525220 | ||||||||
\(595\) | 6.05073 | 0.248056 | ||||||||
\(596\) | −7.37986 | −0.302291 | ||||||||
\(597\) | −61.1889 | −2.50429 | ||||||||
\(598\) | 1.62892 | 0.0666116 | ||||||||
\(599\) | −6.94414 | −0.283730 | −0.141865 | − | 0.989886i | \(-0.545310\pi\) | ||||
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(600\) | 12.3881 | 0.505742 | ||||||||
\(601\) | 43.2980 | 1.76616 | 0.883082 | − | 0.469219i | \(-0.155464\pi\) | ||||
0.883082 | + | 0.469219i | \(0.155464\pi\) | |||||||
\(602\) | −8.39716 | −0.342243 | ||||||||
\(603\) | 4.38389 | 0.178526 | ||||||||
\(604\) | −3.03501 | −0.123493 | ||||||||
\(605\) | −17.7692 | −0.722419 | ||||||||
\(606\) | −14.7530 | −0.599301 | ||||||||
\(607\) | 4.23105 | 0.171733 | 0.0858665 | − | 0.996307i | \(-0.472634\pi\) | ||||
0.0858665 | + | 0.996307i | \(0.472634\pi\) | |||||||
\(608\) | −0.175144 | −0.00710304 | ||||||||
\(609\) | −4.60432 | −0.186576 | ||||||||
\(610\) | 13.6520 | 0.552754 | ||||||||
\(611\) | 2.20258 | 0.0891070 | ||||||||
\(612\) | 14.2259 | 0.575047 | ||||||||
\(613\) | −3.81497 | −0.154085 | −0.0770425 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770425 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(614\) | −4.26161 | −0.171985 | ||||||||
\(615\) | 105.360 | 4.24853 | ||||||||
\(616\) | −1.57874 | −0.0636092 | ||||||||
\(617\) | 7.93363 | 0.319396 | 0.159698 | − | 0.987166i | \(-0.448948\pi\) | ||||
0.159698 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(618\) | −9.47311 | −0.381064 | ||||||||
\(619\) | 31.4615 | 1.26454 | 0.632272 | − | 0.774747i | \(-0.282123\pi\) | ||||
0.632272 | + | 0.774747i | \(0.282123\pi\) | |||||||
\(620\) | −21.2349 | −0.852815 | ||||||||
\(621\) | −8.47744 | −0.340188 | ||||||||
\(622\) | −30.9074 | −1.23927 | ||||||||
\(623\) | −7.10900 | −0.284816 | ||||||||
\(624\) | 3.04844 | 0.122035 | ||||||||
\(625\) | −27.7022 | −1.10809 | ||||||||
\(626\) | −28.2680 | −1.12982 | ||||||||
\(627\) | −1.12861 | −0.0450724 | ||||||||
\(628\) | 12.1397 | 0.484428 | ||||||||
\(629\) | −12.2711 | −0.489280 | ||||||||
\(630\) | −10.5759 | −0.421355 | ||||||||
\(631\) | 12.7590 | 0.507929 | 0.253964 | − | 0.967214i | \(-0.418265\pi\) | ||||
0.253964 | + | 0.967214i | \(0.418265\pi\) | |||||||
\(632\) | −12.1508 | −0.483334 | ||||||||
\(633\) | 51.8264 | 2.05992 | ||||||||
\(634\) | −11.8780 | −0.471735 | ||||||||
\(635\) | −7.56489 | −0.300203 | ||||||||
\(636\) | 15.2002 | 0.602728 | ||||||||
\(637\) | 7.03377 | 0.278688 | ||||||||
\(638\) | −5.36561 | −0.212426 | ||||||||
\(639\) | −54.7200 | −2.16469 | ||||||||
\(640\) | −3.06326 | −0.121086 | ||||||||
\(641\) | 22.9302 | 0.905687 | 0.452843 | − | 0.891590i | \(-0.350410\pi\) | ||||
0.452843 | + | 0.891590i | \(0.350410\pi\) | |||||||
\(642\) | −48.6239 | −1.91903 | ||||||||
\(643\) | −26.9601 | −1.06320 | −0.531602 | − | 0.846994i | \(-0.678410\pi\) | ||||
−0.531602 | + | 0.846994i | \(0.678410\pi\) | |||||||
\(644\) | 1.04554 | 0.0412001 | ||||||||
\(645\) | −104.991 | −4.13404 | ||||||||
\(646\) | −0.499667 | −0.0196591 | ||||||||
\(647\) | 33.7313 | 1.32611 | 0.663057 | − | 0.748569i | \(-0.269259\pi\) | ||||
0.663057 | + | 0.748569i | \(0.269259\pi\) | |||||||
\(648\) | −0.905589 | −0.0355749 | ||||||||
\(649\) | 4.85878 | 0.190724 | ||||||||
\(650\) | 4.72852 | 0.185468 | ||||||||
\(651\) | 13.5639 | 0.531611 | ||||||||
\(652\) | 2.37411 | 0.0929775 | ||||||||
\(653\) | −30.7541 | −1.20350 | −0.601750 | − | 0.798685i | \(-0.705530\pi\) | ||||
−0.601750 | + | 0.798685i | \(0.705530\pi\) | |||||||
\(654\) | −33.3883 | −1.30559 | ||||||||
\(655\) | −23.0003 | −0.898694 | ||||||||
\(656\) | −12.1707 | −0.475186 | ||||||||
\(657\) | −56.6035 | −2.20831 | ||||||||
\(658\) | 1.41375 | 0.0551137 | ||||||||
\(659\) | 36.4077 | 1.41824 | 0.709122 | − | 0.705086i | \(-0.249092\pi\) | ||||
0.709122 | + | 0.705086i | \(0.249092\pi\) | |||||||
\(660\) | −19.7393 | −0.768352 | ||||||||
\(661\) | 29.6229 | 1.15220 | 0.576098 | − | 0.817380i | \(-0.304574\pi\) | ||||
0.576098 | + | 0.817380i | \(0.304574\pi\) | |||||||
\(662\) | −5.74696 | −0.223362 | ||||||||
\(663\) | 8.69684 | 0.337757 | ||||||||
\(664\) | −7.64282 | −0.296599 | ||||||||
\(665\) | 0.371466 | 0.0144048 | ||||||||
\(666\) | 21.4483 | 0.831105 | ||||||||
\(667\) | 3.55344 | 0.137590 | ||||||||
\(668\) | −3.88661 | −0.150377 | ||||||||
\(669\) | −32.4303 | −1.25383 | ||||||||
\(670\) | −2.69307 | −0.104043 | ||||||||
\(671\) | −10.1621 | −0.392304 | ||||||||
\(672\) | 1.95667 | 0.0754802 | ||||||||
\(673\) | 16.4415 | 0.633772 | 0.316886 | − | 0.948464i | \(-0.397363\pi\) | ||||
0.316886 | + | 0.948464i | \(0.397363\pi\) | |||||||
\(674\) | −25.2914 | −0.974187 | ||||||||
\(675\) | −24.6088 | −0.947192 | ||||||||
\(676\) | −11.8364 | −0.455247 | ||||||||
\(677\) | 10.0655 | 0.386850 | 0.193425 | − | 0.981115i | \(-0.438040\pi\) | ||||
0.193425 | + | 0.981115i | \(0.438040\pi\) | |||||||
\(678\) | −54.2074 | −2.08182 | ||||||||
\(679\) | −8.57821 | −0.329201 | ||||||||
\(680\) | −8.73913 | −0.335130 | ||||||||
\(681\) | 19.0527 | 0.730103 | ||||||||
\(682\) | 15.8066 | 0.605265 | ||||||||
\(683\) | 37.0427 | 1.41740 | 0.708701 | − | 0.705509i | \(-0.249282\pi\) | ||||
0.708701 | + | 0.705509i | \(0.249282\pi\) | |||||||
\(684\) | 0.873355 | 0.0333936 | ||||||||
\(685\) | −23.5179 | −0.898571 | ||||||||
\(686\) | 9.36130 | 0.357416 | ||||||||
\(687\) | −50.1270 | −1.91246 | ||||||||
\(688\) | 12.1281 | 0.462379 | ||||||||
\(689\) | 5.80191 | 0.221035 | ||||||||
\(690\) | 13.0726 | 0.497666 | ||||||||
\(691\) | −14.3120 | −0.544452 | −0.272226 | − | 0.962233i | \(-0.587760\pi\) | ||||
−0.272226 | + | 0.962233i | \(0.587760\pi\) | |||||||
\(692\) | 16.9311 | 0.643623 | ||||||||
\(693\) | 7.87236 | 0.299046 | ||||||||
\(694\) | 0.377875 | 0.0143439 | ||||||||
\(695\) | 23.5140 | 0.891939 | ||||||||
\(696\) | 6.65006 | 0.252070 | ||||||||
\(697\) | −34.7216 | −1.31517 | ||||||||
\(698\) | 27.0247 | 1.02290 | ||||||||
\(699\) | −66.6099 | −2.51942 | ||||||||
\(700\) | 3.03505 | 0.114714 | ||||||||
\(701\) | 51.5426 | 1.94674 | 0.973368 | − | 0.229246i | \(-0.0736261\pi\) | ||||
0.973368 | + | 0.229246i | \(0.0736261\pi\) | |||||||
\(702\) | −6.05568 | −0.228557 | ||||||||
\(703\) | −0.753346 | −0.0284130 | ||||||||
\(704\) | 2.28019 | 0.0859379 | ||||||||
\(705\) | 17.6764 | 0.665733 | ||||||||
\(706\) | 2.06081 | 0.0775596 | ||||||||
\(707\) | −3.61446 | −0.135936 | ||||||||
\(708\) | −6.02191 | −0.226317 | ||||||||
\(709\) | −33.7053 | −1.26583 | −0.632915 | − | 0.774221i | \(-0.718142\pi\) | ||||
−0.632915 | + | 0.774221i | \(0.718142\pi\) | |||||||
\(710\) | 33.6151 | 1.26155 | ||||||||
\(711\) | 60.5900 | 2.27230 | ||||||||
\(712\) | 10.2676 | 0.384794 | ||||||||
\(713\) | −10.4681 | −0.392034 | ||||||||
\(714\) | 5.58216 | 0.208907 | ||||||||
\(715\) | −7.53449 | −0.281774 | ||||||||
\(716\) | 2.74384 | 0.102542 | ||||||||
\(717\) | 24.2861 | 0.906981 | ||||||||
\(718\) | 15.3163 | 0.571599 | ||||||||
\(719\) | 7.18676 | 0.268021 | 0.134011 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134011 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(720\) | 15.2749 | 0.569262 | ||||||||
\(721\) | −2.32089 | −0.0864344 | ||||||||
\(722\) | 18.9693 | 0.705965 | ||||||||
\(723\) | −41.8336 | −1.55581 | ||||||||
\(724\) | 19.9339 | 0.740838 | ||||||||
\(725\) | 10.3151 | 0.383094 | ||||||||
\(726\) | −16.3931 | −0.608405 | ||||||||
\(727\) | 17.7029 | 0.656566 | 0.328283 | − | 0.944579i | \(-0.393530\pi\) | ||||
0.328283 | + | 0.944579i | \(0.393530\pi\) | |||||||
\(728\) | 0.746859 | 0.0276805 | ||||||||
\(729\) | −43.0794 | −1.59553 | ||||||||
\(730\) | 34.7722 | 1.28698 | ||||||||
\(731\) | 34.6001 | 1.27973 | ||||||||
\(732\) | 12.5948 | 0.465517 | ||||||||
\(733\) | 52.4546 | 1.93746 | 0.968728 | − | 0.248127i | \(-0.0798149\pi\) | ||||
0.968728 | + | 0.248127i | \(0.0798149\pi\) | |||||||
\(734\) | −3.85655 | −0.142348 | ||||||||
\(735\) | 56.4483 | 2.08213 | ||||||||
\(736\) | −1.51008 | −0.0556625 | ||||||||
\(737\) | 2.00464 | 0.0738417 | ||||||||
\(738\) | 60.6890 | 2.23399 | ||||||||
\(739\) | −22.4648 | −0.826382 | −0.413191 | − | 0.910644i | \(-0.635586\pi\) | ||||
−0.413191 | + | 0.910644i | \(0.635586\pi\) | |||||||
\(740\) | −13.1760 | −0.484358 | ||||||||
\(741\) | 0.533916 | 0.0196139 | ||||||||
\(742\) | 3.72402 | 0.136713 | ||||||||
\(743\) | −18.9166 | −0.693983 | −0.346992 | − | 0.937868i | \(-0.612797\pi\) | ||||
−0.346992 | + | 0.937868i | \(0.612797\pi\) | |||||||
\(744\) | −19.5905 | −0.718222 | ||||||||
\(745\) | −22.6064 | −0.828235 | ||||||||
\(746\) | 17.7945 | 0.651502 | ||||||||
\(747\) | 38.1108 | 1.39440 | ||||||||
\(748\) | 6.50512 | 0.237851 | ||||||||
\(749\) | −11.9127 | −0.435282 | ||||||||
\(750\) | −5.33650 | −0.194861 | ||||||||
\(751\) | −35.4191 | −1.29246 | −0.646230 | − | 0.763143i | \(-0.723655\pi\) | ||||
−0.646230 | + | 0.763143i | \(0.723655\pi\) | |||||||
\(752\) | −2.04189 | −0.0744602 | ||||||||
\(753\) | 27.4241 | 0.999389 | ||||||||
\(754\) | 2.53832 | 0.0924403 | ||||||||
\(755\) | −9.29703 | −0.338354 | ||||||||
\(756\) | −3.88690 | −0.141365 | ||||||||
\(757\) | 9.65546 | 0.350934 | 0.175467 | − | 0.984485i | \(-0.443857\pi\) | ||||
0.175467 | + | 0.984485i | \(0.443857\pi\) | |||||||
\(758\) | 13.0418 | 0.473700 | ||||||||
\(759\) | −9.73083 | −0.353207 | ||||||||
\(760\) | −0.536512 | −0.0194613 | ||||||||
\(761\) | −40.9691 | −1.48513 | −0.742564 | − | 0.669775i | \(-0.766391\pi\) | ||||
−0.742564 | + | 0.669775i | \(0.766391\pi\) | |||||||
\(762\) | −6.97905 | −0.252824 | ||||||||
\(763\) | −8.18005 | −0.296138 | ||||||||
\(764\) | 3.88094 | 0.140408 | ||||||||
\(765\) | 43.5776 | 1.57555 | ||||||||
\(766\) | −13.8945 | −0.502029 | ||||||||
\(767\) | −2.29856 | −0.0829961 | ||||||||
\(768\) | −2.82604 | −0.101976 | ||||||||
\(769\) | 6.75488 | 0.243587 | 0.121794 | − | 0.992555i | \(-0.461135\pi\) | ||||
0.121794 | + | 0.992555i | \(0.461135\pi\) | |||||||
\(770\) | −4.83609 | −0.174281 | ||||||||
\(771\) | −13.7367 | −0.494716 | ||||||||
\(772\) | −14.3698 | −0.517179 | ||||||||
\(773\) | 2.53775 | 0.0912765 | 0.0456383 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456383 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(774\) | −60.4766 | −2.17379 | ||||||||
\(775\) | −30.3874 | −1.09155 | ||||||||
\(776\) | 12.3896 | 0.444760 | ||||||||
\(777\) | 8.41620 | 0.301929 | ||||||||
\(778\) | −13.5860 | −0.487082 | ||||||||
\(779\) | −2.13163 | −0.0763735 | ||||||||
\(780\) | 9.33815 | 0.334359 | ||||||||
\(781\) | −25.0220 | −0.895358 | ||||||||
\(782\) | −4.30810 | −0.154057 | ||||||||
\(783\) | −13.2103 | −0.472096 | ||||||||
\(784\) | −6.52062 | −0.232879 | ||||||||
\(785\) | 37.1871 | 1.32726 | ||||||||
\(786\) | −21.2191 | −0.756860 | ||||||||
\(787\) | −2.30590 | −0.0821964 | −0.0410982 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410982 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(788\) | −5.03581 | −0.179393 | ||||||||
\(789\) | −69.2152 | −2.46413 | ||||||||
\(790\) | −37.2211 | −1.32427 | ||||||||
\(791\) | −13.2807 | −0.472207 | ||||||||
\(792\) | −11.3701 | −0.404020 | ||||||||
\(793\) | 4.80742 | 0.170717 | ||||||||
\(794\) | −11.8815 | −0.421659 | ||||||||
\(795\) | 46.5622 | 1.65139 | ||||||||
\(796\) | 21.6518 | 0.767429 | ||||||||
\(797\) | −26.5242 | −0.939536 | −0.469768 | − | 0.882790i | \(-0.655662\pi\) | ||||
−0.469768 | + | 0.882790i | \(0.655662\pi\) | |||||||
\(798\) | 0.342700 | 0.0121314 | ||||||||
\(799\) | −5.82529 | −0.206084 | ||||||||
\(800\) | −4.38355 | −0.154982 | ||||||||
\(801\) | −51.1992 | −1.80903 | ||||||||
\(802\) | 30.0049 | 1.05951 | ||||||||
\(803\) | −25.8833 | −0.913401 | ||||||||
\(804\) | −2.48452 | −0.0876223 | ||||||||
\(805\) | 3.20276 | 0.112883 | ||||||||
\(806\) | −7.47767 | −0.263390 | ||||||||
\(807\) | 18.4770 | 0.650421 | ||||||||
\(808\) | 5.22039 | 0.183653 | ||||||||
\(809\) | 48.5854 | 1.70817 | 0.854085 | − | 0.520133i | \(-0.174118\pi\) | ||||
0.854085 | + | 0.520133i | \(0.174118\pi\) | |||||||
\(810\) | −2.77405 | −0.0974703 | ||||||||
\(811\) | 6.75928 | 0.237351 | 0.118675 | − | 0.992933i | \(-0.462135\pi\) | ||||
0.118675 | + | 0.992933i | \(0.462135\pi\) | |||||||
\(812\) | 1.62925 | 0.0571755 | ||||||||
\(813\) | 59.4267 | 2.08418 | ||||||||
\(814\) | 9.80774 | 0.343761 | ||||||||
\(815\) | 7.27253 | 0.254745 | ||||||||
\(816\) | −8.06237 | −0.282239 | ||||||||
\(817\) | 2.12417 | 0.0743152 | ||||||||
\(818\) | 3.71049 | 0.129734 | ||||||||
\(819\) | −3.72420 | −0.130134 | ||||||||
\(820\) | −37.2820 | −1.30194 | ||||||||
\(821\) | 3.04521 | 0.106278 | 0.0531392 | − | 0.998587i | \(-0.483077\pi\) | ||||
0.0531392 | + | 0.998587i | \(0.483077\pi\) | |||||||
\(822\) | −21.6966 | −0.756756 | ||||||||
\(823\) | −9.31957 | −0.324860 | −0.162430 | − | 0.986720i | \(-0.551933\pi\) | ||||
−0.162430 | + | 0.986720i | \(0.551933\pi\) | |||||||
\(824\) | 3.35208 | 0.116775 | ||||||||
\(825\) | −28.2472 | −0.983441 | ||||||||
\(826\) | −1.47535 | −0.0513341 | ||||||||
\(827\) | 13.7049 | 0.476567 | 0.238284 | − | 0.971196i | \(-0.423415\pi\) | ||||
0.238284 | + | 0.971196i | \(0.423415\pi\) | |||||||
\(828\) | 7.53002 | 0.261686 | ||||||||
\(829\) | −37.5301 | −1.30347 | −0.651737 | − | 0.758445i | \(-0.725959\pi\) | ||||
−0.651737 | + | 0.758445i | \(0.725959\pi\) | |||||||
\(830\) | −23.4119 | −0.812640 | ||||||||
\(831\) | 7.27404 | 0.252334 | ||||||||
\(832\) | −1.07870 | −0.0373971 | ||||||||
\(833\) | −18.6026 | −0.644542 | ||||||||
\(834\) | 21.6931 | 0.751170 | ||||||||
\(835\) | −11.9057 | −0.412014 | ||||||||
\(836\) | 0.399362 | 0.0138122 | ||||||||
\(837\) | 38.9162 | 1.34514 | ||||||||
\(838\) | 19.8018 | 0.684041 | ||||||||
\(839\) | −43.1783 | −1.49068 | −0.745341 | − | 0.666684i | \(-0.767713\pi\) | ||||
−0.745341 | + | 0.666684i | \(0.767713\pi\) | |||||||
\(840\) | 5.99379 | 0.206805 | ||||||||
\(841\) | −23.4627 | −0.809060 | ||||||||
\(842\) | 26.0484 | 0.897688 | ||||||||
\(843\) | −68.2881 | −2.35197 | ||||||||
\(844\) | −18.3389 | −0.631251 | ||||||||
\(845\) | −36.2580 | −1.24731 | ||||||||
\(846\) | 10.1819 | 0.350060 | ||||||||
\(847\) | −4.01627 | −0.138001 | ||||||||
\(848\) | −5.37863 | −0.184703 | ||||||||
\(849\) | 51.4130 | 1.76449 | ||||||||
\(850\) | −12.5058 | −0.428945 | ||||||||
\(851\) | −6.49531 | −0.222656 | ||||||||
\(852\) | 31.0120 | 1.06245 | ||||||||
\(853\) | 1.79446 | 0.0614413 | 0.0307206 | − | 0.999528i | \(-0.490220\pi\) | ||||
0.0307206 | + | 0.999528i | \(0.490220\pi\) | |||||||
\(854\) | 3.08570 | 0.105590 | ||||||||
\(855\) | 2.67531 | 0.0914937 | ||||||||
\(856\) | 17.2057 | 0.588078 | ||||||||
\(857\) | 51.4351 | 1.75699 | 0.878495 | − | 0.477751i | \(-0.158548\pi\) | ||||
0.878495 | + | 0.477751i | \(0.158548\pi\) | |||||||
\(858\) | −6.95101 | −0.237304 | ||||||||
\(859\) | 0.953473 | 0.0325321 | 0.0162660 | − | 0.999868i | \(-0.494822\pi\) | ||||
0.0162660 | + | 0.999868i | \(0.494822\pi\) | |||||||
\(860\) | 37.1515 | 1.26686 | ||||||||
\(861\) | 23.8140 | 0.811580 | ||||||||
\(862\) | 21.3389 | 0.726806 | ||||||||
\(863\) | −51.6708 | −1.75889 | −0.879447 | − | 0.475997i | \(-0.842087\pi\) | ||||
−0.879447 | + | 0.475997i | \(0.842087\pi\) | |||||||
\(864\) | 5.61389 | 0.190988 | ||||||||
\(865\) | 51.8643 | 1.76344 | ||||||||
\(866\) | 34.7279 | 1.18010 | ||||||||
\(867\) | 25.0416 | 0.850458 | ||||||||
\(868\) | −4.79962 | −0.162910 | ||||||||
\(869\) | 27.7062 | 0.939868 | ||||||||
\(870\) | 20.3709 | 0.690637 | ||||||||
\(871\) | −0.948339 | −0.0321332 | ||||||||
\(872\) | 11.8145 | 0.400090 | ||||||||
\(873\) | −61.7805 | −2.09095 | ||||||||
\(874\) | −0.264483 | −0.00894626 | ||||||||
\(875\) | −1.30743 | −0.0441992 | ||||||||
\(876\) | 32.0794 | 1.08386 | ||||||||
\(877\) | 44.9707 | 1.51855 | 0.759277 | − | 0.650768i | \(-0.225553\pi\) | ||||
0.759277 | + | 0.650768i | \(0.225553\pi\) | |||||||
\(878\) | −35.0226 | −1.18196 | ||||||||
\(879\) | −68.0705 | −2.29596 | ||||||||
\(880\) | 6.98481 | 0.235458 | ||||||||
\(881\) | 31.6458 | 1.06617 | 0.533087 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533087 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(882\) | 32.5150 | 1.09484 | ||||||||
\(883\) | −26.8434 | −0.903353 | −0.451676 | − | 0.892182i | \(-0.649174\pi\) | ||||
−0.451676 | + | 0.892182i | \(0.649174\pi\) | |||||||
\(884\) | −3.07740 | −0.103504 | ||||||||
\(885\) | −18.4467 | −0.620078 | ||||||||
\(886\) | 34.5796 | 1.16172 | ||||||||
\(887\) | 32.6200 | 1.09527 | 0.547636 | − | 0.836717i | \(-0.315528\pi\) | ||||
0.547636 | + | 0.836717i | \(0.315528\pi\) | |||||||
\(888\) | −12.1556 | −0.407915 | ||||||||
\(889\) | −1.70985 | −0.0573466 | ||||||||
\(890\) | 31.4523 | 1.05428 | ||||||||
\(891\) | 2.06491 | 0.0691772 | ||||||||
\(892\) | 11.4755 | 0.384229 | ||||||||
\(893\) | −0.357626 | −0.0119675 | ||||||||
\(894\) | −20.8558 | −0.697521 | ||||||||
\(895\) | 8.40509 | 0.280951 | ||||||||
\(896\) | −0.692372 | −0.0231305 | ||||||||
\(897\) | 4.60340 | 0.153703 | ||||||||
\(898\) | −27.6957 | −0.924216 | ||||||||
\(899\) | −16.3123 | −0.544045 | ||||||||
\(900\) | 21.8585 | 0.728618 | ||||||||
\(901\) | −15.3446 | −0.511204 | ||||||||
\(902\) | 27.7515 | 0.924023 | ||||||||
\(903\) | −23.7307 | −0.789707 | ||||||||
\(904\) | 19.1814 | 0.637965 | ||||||||
\(905\) | 61.0627 | 2.02979 | ||||||||
\(906\) | −8.57706 | −0.284954 | ||||||||
\(907\) | −18.0937 | −0.600792 | −0.300396 | − | 0.953815i | \(-0.597119\pi\) | ||||
−0.300396 | + | 0.953815i | \(0.597119\pi\) | |||||||
\(908\) | −6.74186 | −0.223736 | ||||||||
\(909\) | −26.0314 | −0.863408 | ||||||||
\(910\) | 2.28782 | 0.0758406 | ||||||||
\(911\) | −42.4198 | −1.40543 | −0.702716 | − | 0.711470i | \(-0.748030\pi\) | ||||
−0.702716 | + | 0.711470i | \(0.748030\pi\) | |||||||
\(912\) | −0.494964 | −0.0163899 | ||||||||
\(913\) | 17.4271 | 0.576752 | ||||||||
\(914\) | −5.23659 | −0.173211 | ||||||||
\(915\) | 38.5811 | 1.27545 | ||||||||
\(916\) | 17.7376 | 0.586065 | ||||||||
\(917\) | −5.19863 | −0.171674 | ||||||||
\(918\) | 16.0158 | 0.528600 | ||||||||
\(919\) | 33.8856 | 1.11778 | 0.558891 | − | 0.829241i | \(-0.311227\pi\) | ||||
0.558891 | + | 0.829241i | \(0.311227\pi\) | |||||||
\(920\) | −4.62578 | −0.152507 | ||||||||
\(921\) | −12.0435 | −0.396846 | ||||||||
\(922\) | 5.04783 | 0.166241 | ||||||||
\(923\) | 11.8372 | 0.389628 | ||||||||
\(924\) | −4.46158 | −0.146775 | ||||||||
\(925\) | −18.8549 | −0.619946 | ||||||||
\(926\) | 3.00114 | 0.0986236 | ||||||||
\(927\) | −16.7151 | −0.548996 | ||||||||
\(928\) | −2.35314 | −0.0772456 | ||||||||
\(929\) | −52.3693 | −1.71818 | −0.859091 | − | 0.511823i | \(-0.828970\pi\) | ||||
−0.859091 | + | 0.511823i | \(0.828970\pi\) | |||||||
\(930\) | −60.0107 | −1.96783 | ||||||||
\(931\) | −1.14205 | −0.0374292 | ||||||||
\(932\) | 23.5701 | 0.772063 | ||||||||
\(933\) | −87.3455 | −2.85956 | ||||||||
\(934\) | 19.7214 | 0.645305 | ||||||||
\(935\) | 19.9269 | 0.651678 | ||||||||
\(936\) | 5.37890 | 0.175815 | ||||||||
\(937\) | −37.9481 | −1.23971 | −0.619856 | − | 0.784716i | \(-0.712809\pi\) | ||||
−0.619856 | + | 0.784716i | \(0.712809\pi\) | |||||||
\(938\) | −0.608701 | −0.0198748 | ||||||||
\(939\) | −79.8864 | −2.60699 | ||||||||
\(940\) | −6.25485 | −0.204011 | ||||||||
\(941\) | −11.7081 | −0.381672 | −0.190836 | − | 0.981622i | \(-0.561120\pi\) | ||||
−0.190836 | + | 0.981622i | \(0.561120\pi\) | |||||||
\(942\) | 34.3073 | 1.11779 | ||||||||
\(943\) | −18.3788 | −0.598495 | ||||||||
\(944\) | 2.13087 | 0.0693538 | ||||||||
\(945\) | −11.9066 | −0.387321 | ||||||||
\(946\) | −27.6543 | −0.899120 | ||||||||
\(947\) | 16.9802 | 0.551784 | 0.275892 | − | 0.961189i | \(-0.411027\pi\) | ||||
0.275892 | + | 0.961189i | \(0.411027\pi\) | |||||||
\(948\) | −34.3387 | −1.11527 | ||||||||
\(949\) | 12.2447 | 0.397479 | ||||||||
\(950\) | −0.767755 | −0.0249092 | ||||||||
\(951\) | −33.5676 | −1.08850 | ||||||||
\(952\) | −1.97526 | −0.0640186 | ||||||||
\(953\) | −12.1950 | −0.395034 | −0.197517 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197517 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(954\) | 26.8205 | 0.868345 | ||||||||
\(955\) | 11.8883 | 0.384697 | ||||||||
\(956\) | −8.59370 | −0.277940 | ||||||||
\(957\) | −15.1634 | −0.490163 | ||||||||
\(958\) | 17.6085 | 0.568906 | ||||||||
\(959\) | −5.31562 | −0.171650 | ||||||||
\(960\) | −8.65688 | −0.279400 | ||||||||
\(961\) | 17.0545 | 0.550145 | ||||||||
\(962\) | −4.63978 | −0.149593 | ||||||||
\(963\) | −85.7958 | −2.76473 | ||||||||
\(964\) | 14.8029 | 0.476770 | ||||||||
\(965\) | −44.0183 | −1.41700 | ||||||||
\(966\) | 2.95474 | 0.0950671 | ||||||||
\(967\) | −52.7236 | −1.69548 | −0.847738 | − | 0.530415i | \(-0.822036\pi\) | ||||
−0.847738 | + | 0.530415i | \(0.822036\pi\) | |||||||
\(968\) | 5.80074 | 0.186443 | ||||||||
\(969\) | −1.41208 | −0.0453625 | ||||||||
\(970\) | 37.9525 | 1.21858 | ||||||||
\(971\) | 25.3702 | 0.814169 | 0.407085 | − | 0.913390i | \(-0.366545\pi\) | ||||
0.407085 | + | 0.913390i | \(0.366545\pi\) | |||||||
\(972\) | 14.2824 | 0.458109 | ||||||||
\(973\) | 5.31476 | 0.170383 | ||||||||
\(974\) | −34.0021 | −1.08950 | ||||||||
\(975\) | 13.3630 | 0.427958 | ||||||||
\(976\) | −4.45670 | −0.142655 | ||||||||
\(977\) | −7.93350 | −0.253815 | −0.126908 | − | 0.991915i | \(-0.540505\pi\) | ||||
−0.126908 | + | 0.991915i | \(0.540505\pi\) | |||||||
\(978\) | 6.70933 | 0.214541 | ||||||||
\(979\) | −23.4120 | −0.748252 | ||||||||
\(980\) | −19.9743 | −0.638057 | ||||||||
\(981\) | −58.9130 | −1.88095 | ||||||||
\(982\) | 26.3016 | 0.839318 | ||||||||
\(983\) | 49.3450 | 1.57386 | 0.786930 | − | 0.617042i | \(-0.211669\pi\) | ||||
0.786930 | + | 0.617042i | \(0.211669\pi\) | |||||||
\(984\) | −34.3948 | −1.09647 | ||||||||
\(985\) | −15.4260 | −0.491513 | ||||||||
\(986\) | −6.71325 | −0.213793 | ||||||||
\(987\) | 3.99531 | 0.127172 | ||||||||
\(988\) | −0.188927 | −0.00601058 | ||||||||
\(989\) | 18.3145 | 0.582366 | ||||||||
\(990\) | −34.8297 | −1.10696 | ||||||||
\(991\) | 5.03328 | 0.159887 | 0.0799437 | − | 0.996799i | \(-0.474526\pi\) | ||||
0.0799437 | + | 0.996799i | \(0.474526\pi\) | |||||||
\(992\) | 6.93214 | 0.220096 | ||||||||
\(993\) | −16.2411 | −0.515397 | ||||||||
\(994\) | 7.59786 | 0.240989 | ||||||||
\(995\) | 66.3251 | 2.10265 | ||||||||
\(996\) | −21.5989 | −0.684387 | ||||||||
\(997\) | 23.5351 | 0.745363 | 0.372681 | − | 0.927959i | \(-0.378438\pi\) | ||||
0.372681 | + | 0.927959i | \(0.378438\pi\) | |||||||
\(998\) | 32.1334 | 1.01716 | ||||||||
\(999\) | 24.1469 | 0.763975 |
(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 | 8006.2.a.b.1.6 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.b.1.6 | ✓ | 75 | 1.1 | even | 1 | trivial |