Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.100558 | 0.0580573 | 0.0290286 | − | 0.999579i | \(-0.490759\pi\) | ||||
0.0290286 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.02652 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(6\) | −0.100558 | −0.0410527 | ||||||||
\(7\) | 1.91249 | 0.722852 | 0.361426 | − | 0.932401i | \(-0.382290\pi\) | ||||
0.361426 | + | 0.932401i | \(0.382290\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.98989 | −0.996629 | ||||||||
\(10\) | −2.02652 | −0.640841 | ||||||||
\(11\) | −3.03504 | −0.915097 | −0.457549 | − | 0.889185i | \(-0.651272\pi\) | ||||
−0.457549 | + | 0.889185i | \(0.651272\pi\) | |||||||
\(12\) | 0.100558 | 0.0290286 | ||||||||
\(13\) | −1.59215 | −0.441582 | −0.220791 | − | 0.975321i | \(-0.570864\pi\) | ||||
−0.220791 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(14\) | −1.91249 | −0.511134 | ||||||||
\(15\) | 0.203783 | 0.0526165 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.83109 | 1.17171 | 0.585856 | − | 0.810415i | \(-0.300759\pi\) | ||||
0.585856 | + | 0.810415i | \(0.300759\pi\) | |||||||
\(18\) | 2.98989 | 0.704723 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.02652 | 0.453143 | ||||||||
\(21\) | 0.192316 | 0.0419668 | ||||||||
\(22\) | 3.03504 | 0.647072 | ||||||||
\(23\) | 2.15761 | 0.449893 | 0.224947 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224947 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(24\) | −0.100558 | −0.0205263 | ||||||||
\(25\) | −0.893223 | −0.178645 | ||||||||
\(26\) | 1.59215 | 0.312245 | ||||||||
\(27\) | −0.602332 | −0.115919 | ||||||||
\(28\) | 1.91249 | 0.361426 | ||||||||
\(29\) | −1.54555 | −0.287001 | −0.143501 | − | 0.989650i | \(-0.545836\pi\) | ||||
−0.143501 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(30\) | −0.203783 | −0.0372055 | ||||||||
\(31\) | −3.26259 | −0.585979 | −0.292990 | − | 0.956116i | \(-0.594650\pi\) | ||||
−0.292990 | + | 0.956116i | \(0.594650\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.305197 | −0.0531280 | ||||||||
\(34\) | −4.83109 | −0.828525 | ||||||||
\(35\) | 3.87569 | 0.655111 | ||||||||
\(36\) | −2.98989 | −0.498315 | ||||||||
\(37\) | −11.1692 | −1.83621 | −0.918103 | − | 0.396341i | \(-0.870280\pi\) | ||||
−0.918103 | + | 0.396341i | \(0.870280\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −0.160103 | −0.0256370 | ||||||||
\(40\) | −2.02652 | −0.320421 | ||||||||
\(41\) | −0.0525980 | −0.00821442 | −0.00410721 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410721 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(42\) | −0.192316 | −0.0296750 | ||||||||
\(43\) | 8.48995 | 1.29470 | 0.647352 | − | 0.762191i | \(-0.275876\pi\) | ||||
0.647352 | + | 0.762191i | \(0.275876\pi\) | |||||||
\(44\) | −3.03504 | −0.457549 | ||||||||
\(45\) | −6.05906 | −0.903232 | ||||||||
\(46\) | −2.15761 | −0.318123 | ||||||||
\(47\) | 11.3415 | 1.65433 | 0.827167 | − | 0.561956i | \(-0.189951\pi\) | ||||
0.827167 | + | 0.561956i | \(0.189951\pi\) | |||||||
\(48\) | 0.100558 | 0.0145143 | ||||||||
\(49\) | −3.34239 | −0.477485 | ||||||||
\(50\) | 0.893223 | 0.126321 | ||||||||
\(51\) | 0.485805 | 0.0680263 | ||||||||
\(52\) | −1.59215 | −0.220791 | ||||||||
\(53\) | −9.77354 | −1.34250 | −0.671250 | − | 0.741231i | \(-0.734242\pi\) | ||||
−0.671250 | + | 0.741231i | \(0.734242\pi\) | |||||||
\(54\) | 0.602332 | 0.0819670 | ||||||||
\(55\) | −6.15055 | −0.829341 | ||||||||
\(56\) | −1.91249 | −0.255567 | ||||||||
\(57\) | −0.100558 | −0.0133192 | ||||||||
\(58\) | 1.54555 | 0.202940 | ||||||||
\(59\) | 3.74947 | 0.488140 | 0.244070 | − | 0.969758i | \(-0.421517\pi\) | ||||
0.244070 | + | 0.969758i | \(0.421517\pi\) | |||||||
\(60\) | 0.203783 | 0.0263083 | ||||||||
\(61\) | 9.52357 | 1.21937 | 0.609684 | − | 0.792645i | \(-0.291296\pi\) | ||||
0.609684 | + | 0.792645i | \(0.291296\pi\) | |||||||
\(62\) | 3.26259 | 0.414350 | ||||||||
\(63\) | −5.71812 | −0.720416 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.22651 | −0.400199 | ||||||||
\(66\) | 0.305197 | 0.0375672 | ||||||||
\(67\) | 11.6242 | 1.42012 | 0.710058 | − | 0.704143i | \(-0.248669\pi\) | ||||
0.710058 | + | 0.704143i | \(0.248669\pi\) | |||||||
\(68\) | 4.83109 | 0.585856 | ||||||||
\(69\) | 0.216965 | 0.0261196 | ||||||||
\(70\) | −3.87569 | −0.463234 | ||||||||
\(71\) | −14.7569 | −1.75132 | −0.875658 | − | 0.482931i | \(-0.839572\pi\) | ||||
−0.875658 | + | 0.482931i | \(0.839572\pi\) | |||||||
\(72\) | 2.98989 | 0.352362 | ||||||||
\(73\) | 5.61699 | 0.657419 | 0.328710 | − | 0.944431i | \(-0.393386\pi\) | ||||
0.328710 | + | 0.944431i | \(0.393386\pi\) | |||||||
\(74\) | 11.1692 | 1.29839 | ||||||||
\(75\) | −0.0898209 | −0.0103716 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −5.80446 | −0.661480 | ||||||||
\(78\) | 0.160103 | 0.0181281 | ||||||||
\(79\) | −8.77091 | −0.986805 | −0.493402 | − | 0.869801i | \(-0.664247\pi\) | ||||
−0.493402 | + | 0.869801i | \(0.664247\pi\) | |||||||
\(80\) | 2.02652 | 0.226572 | ||||||||
\(81\) | 8.90909 | 0.989899 | ||||||||
\(82\) | 0.0525980 | 0.00580847 | ||||||||
\(83\) | −4.40132 | −0.483108 | −0.241554 | − | 0.970387i | \(-0.577657\pi\) | ||||
−0.241554 | + | 0.970387i | \(0.577657\pi\) | |||||||
\(84\) | 0.192316 | 0.0209834 | ||||||||
\(85\) | 9.79029 | 1.06191 | ||||||||
\(86\) | −8.48995 | −0.915494 | ||||||||
\(87\) | −0.155417 | −0.0166625 | ||||||||
\(88\) | 3.03504 | 0.323536 | ||||||||
\(89\) | −12.7448 | −1.35095 | −0.675473 | − | 0.737385i | \(-0.736061\pi\) | ||||
−0.675473 | + | 0.737385i | \(0.736061\pi\) | |||||||
\(90\) | 6.05906 | 0.638681 | ||||||||
\(91\) | −3.04496 | −0.319198 | ||||||||
\(92\) | 2.15761 | 0.224947 | ||||||||
\(93\) | −0.328080 | −0.0340204 | ||||||||
\(94\) | −11.3415 | −1.16979 | ||||||||
\(95\) | −2.02652 | −0.207916 | ||||||||
\(96\) | −0.100558 | −0.0102632 | ||||||||
\(97\) | 17.8613 | 1.81354 | 0.906769 | − | 0.421627i | \(-0.138541\pi\) | ||||
0.906769 | + | 0.421627i | \(0.138541\pi\) | |||||||
\(98\) | 3.34239 | 0.337633 | ||||||||
\(99\) | 9.07442 | 0.912013 | ||||||||
\(100\) | −0.893223 | −0.0893223 | ||||||||
\(101\) | −14.7941 | −1.47207 | −0.736035 | − | 0.676943i | \(-0.763304\pi\) | ||||
−0.736035 | + | 0.676943i | \(0.763304\pi\) | |||||||
\(102\) | −0.485805 | −0.0481019 | ||||||||
\(103\) | −1.75592 | −0.173016 | −0.0865080 | − | 0.996251i | \(-0.527571\pi\) | ||||
−0.0865080 | + | 0.996251i | \(0.527571\pi\) | |||||||
\(104\) | 1.59215 | 0.156123 | ||||||||
\(105\) | 0.389732 | 0.0380340 | ||||||||
\(106\) | 9.77354 | 0.949290 | ||||||||
\(107\) | −13.3976 | −1.29520 | −0.647598 | − | 0.761982i | \(-0.724227\pi\) | ||||
−0.647598 | + | 0.761982i | \(0.724227\pi\) | |||||||
\(108\) | −0.602332 | −0.0579594 | ||||||||
\(109\) | −6.12159 | −0.586342 | −0.293171 | − | 0.956060i | \(-0.594711\pi\) | ||||
−0.293171 | + | 0.956060i | \(0.594711\pi\) | |||||||
\(110\) | 6.15055 | 0.586432 | ||||||||
\(111\) | −1.12315 | −0.106605 | ||||||||
\(112\) | 1.91249 | 0.180713 | ||||||||
\(113\) | 10.1321 | 0.953147 | 0.476574 | − | 0.879135i | \(-0.341879\pi\) | ||||
0.476574 | + | 0.879135i | \(0.341879\pi\) | |||||||
\(114\) | 0.100558 | 0.00941813 | ||||||||
\(115\) | 4.37244 | 0.407732 | ||||||||
\(116\) | −1.54555 | −0.143501 | ||||||||
\(117\) | 4.76034 | 0.440093 | ||||||||
\(118\) | −3.74947 | −0.345167 | ||||||||
\(119\) | 9.23940 | 0.846974 | ||||||||
\(120\) | −0.203783 | −0.0186027 | ||||||||
\(121\) | −1.78856 | −0.162597 | ||||||||
\(122\) | −9.52357 | −0.862223 | ||||||||
\(123\) | −0.00528915 | −0.000476907 0 | ||||||||
\(124\) | −3.26259 | −0.292990 | ||||||||
\(125\) | −11.9427 | −1.06819 | ||||||||
\(126\) | 5.71812 | 0.509411 | ||||||||
\(127\) | −10.1667 | −0.902148 | −0.451074 | − | 0.892487i | \(-0.648959\pi\) | ||||
−0.451074 | + | 0.892487i | \(0.648959\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.853733 | 0.0751670 | ||||||||
\(130\) | 3.22651 | 0.282984 | ||||||||
\(131\) | 1.91916 | 0.167678 | 0.0838389 | − | 0.996479i | \(-0.473282\pi\) | ||||
0.0838389 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(132\) | −0.305197 | −0.0265640 | ||||||||
\(133\) | −1.91249 | −0.165834 | ||||||||
\(134\) | −11.6242 | −1.00417 | ||||||||
\(135\) | −1.22064 | −0.105056 | ||||||||
\(136\) | −4.83109 | −0.414263 | ||||||||
\(137\) | 0.917951 | 0.0784258 | 0.0392129 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392129 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(138\) | −0.216965 | −0.0184693 | ||||||||
\(139\) | 11.4651 | 0.972460 | 0.486230 | − | 0.873831i | \(-0.338372\pi\) | ||||
0.486230 | + | 0.873831i | \(0.338372\pi\) | |||||||
\(140\) | 3.87569 | 0.327556 | ||||||||
\(141\) | 1.14048 | 0.0960461 | ||||||||
\(142\) | 14.7569 | 1.23837 | ||||||||
\(143\) | 4.83222 | 0.404090 | ||||||||
\(144\) | −2.98989 | −0.249157 | ||||||||
\(145\) | −3.13208 | −0.260105 | ||||||||
\(146\) | −5.61699 | −0.464866 | ||||||||
\(147\) | −0.336105 | −0.0277215 | ||||||||
\(148\) | −11.1692 | −0.918103 | ||||||||
\(149\) | −12.1455 | −0.994995 | −0.497497 | − | 0.867466i | \(-0.665748\pi\) | ||||
−0.497497 | + | 0.867466i | \(0.665748\pi\) | |||||||
\(150\) | 0.0898209 | 0.00733384 | ||||||||
\(151\) | −7.48903 | −0.609448 | −0.304724 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304724 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −14.4444 | −1.16776 | ||||||||
\(154\) | 5.80446 | 0.467737 | ||||||||
\(155\) | −6.61171 | −0.531065 | ||||||||
\(156\) | −0.160103 | −0.0128185 | ||||||||
\(157\) | −10.1203 | −0.807690 | −0.403845 | − | 0.914827i | \(-0.632326\pi\) | ||||
−0.403845 | + | 0.914827i | \(0.632326\pi\) | |||||||
\(158\) | 8.77091 | 0.697776 | ||||||||
\(159\) | −0.982809 | −0.0779418 | ||||||||
\(160\) | −2.02652 | −0.160210 | ||||||||
\(161\) | 4.12641 | 0.325206 | ||||||||
\(162\) | −8.90909 | −0.699965 | ||||||||
\(163\) | 1.50702 | 0.118039 | 0.0590195 | − | 0.998257i | \(-0.481203\pi\) | ||||
0.0590195 | + | 0.998257i | \(0.481203\pi\) | |||||||
\(164\) | −0.0525980 | −0.00410721 | ||||||||
\(165\) | −0.618488 | −0.0481492 | ||||||||
\(166\) | 4.40132 | 0.341609 | ||||||||
\(167\) | −17.2871 | −1.33772 | −0.668858 | − | 0.743391i | \(-0.733216\pi\) | ||||
−0.668858 | + | 0.743391i | \(0.733216\pi\) | |||||||
\(168\) | −0.192316 | −0.0148375 | ||||||||
\(169\) | −10.4651 | −0.805006 | ||||||||
\(170\) | −9.79029 | −0.750881 | ||||||||
\(171\) | 2.98989 | 0.228642 | ||||||||
\(172\) | 8.48995 | 0.647352 | ||||||||
\(173\) | 15.6606 | 1.19065 | 0.595327 | − | 0.803484i | \(-0.297023\pi\) | ||||
0.595327 | + | 0.803484i | \(0.297023\pi\) | |||||||
\(174\) | 0.155417 | 0.0117822 | ||||||||
\(175\) | −1.70828 | −0.129134 | ||||||||
\(176\) | −3.03504 | −0.228774 | ||||||||
\(177\) | 0.377040 | 0.0283401 | ||||||||
\(178\) | 12.7448 | 0.955263 | ||||||||
\(179\) | 9.00762 | 0.673261 | 0.336631 | − | 0.941637i | \(-0.390713\pi\) | ||||
0.336631 | + | 0.941637i | \(0.390713\pi\) | |||||||
\(180\) | −6.05906 | −0.451616 | ||||||||
\(181\) | −22.7058 | −1.68771 | −0.843854 | − | 0.536573i | \(-0.819719\pi\) | ||||
−0.843854 | + | 0.536573i | \(0.819719\pi\) | |||||||
\(182\) | 3.04496 | 0.225707 | ||||||||
\(183\) | 0.957672 | 0.0707932 | ||||||||
\(184\) | −2.15761 | −0.159061 | ||||||||
\(185\) | −22.6346 | −1.66413 | ||||||||
\(186\) | 0.328080 | 0.0240560 | ||||||||
\(187\) | −14.6625 | −1.07223 | ||||||||
\(188\) | 11.3415 | 0.827167 | ||||||||
\(189\) | −1.15195 | −0.0837922 | ||||||||
\(190\) | 2.02652 | 0.147019 | ||||||||
\(191\) | −0.461537 | −0.0333956 | −0.0166978 | − | 0.999861i | \(-0.505315\pi\) | ||||
−0.0166978 | + | 0.999861i | \(0.505315\pi\) | |||||||
\(192\) | 0.100558 | 0.00725716 | ||||||||
\(193\) | −19.0090 | −1.36830 | −0.684149 | − | 0.729342i | \(-0.739826\pi\) | ||||
−0.684149 | + | 0.729342i | \(0.739826\pi\) | |||||||
\(194\) | −17.8613 | −1.28237 | ||||||||
\(195\) | −0.324452 | −0.0232345 | ||||||||
\(196\) | −3.34239 | −0.238742 | ||||||||
\(197\) | −11.1545 | −0.794727 | −0.397364 | − | 0.917661i | \(-0.630075\pi\) | ||||
−0.397364 | + | 0.917661i | \(0.630075\pi\) | |||||||
\(198\) | −9.07442 | −0.644891 | ||||||||
\(199\) | −25.3525 | −1.79719 | −0.898595 | − | 0.438779i | \(-0.855411\pi\) | ||||
−0.898595 | + | 0.438779i | \(0.855411\pi\) | |||||||
\(200\) | 0.893223 | 0.0631604 | ||||||||
\(201\) | 1.16890 | 0.0824481 | ||||||||
\(202\) | 14.7941 | 1.04091 | ||||||||
\(203\) | −2.95584 | −0.207459 | ||||||||
\(204\) | 0.485805 | 0.0340132 | ||||||||
\(205\) | −0.106591 | −0.00744462 | ||||||||
\(206\) | 1.75592 | 0.122341 | ||||||||
\(207\) | −6.45102 | −0.448377 | ||||||||
\(208\) | −1.59215 | −0.110395 | ||||||||
\(209\) | 3.03504 | 0.209938 | ||||||||
\(210\) | −0.389732 | −0.0268941 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −9.77354 | −0.671250 | ||||||||
\(213\) | −1.48392 | −0.101677 | ||||||||
\(214\) | 13.3976 | 0.915842 | ||||||||
\(215\) | 17.2050 | 1.17337 | ||||||||
\(216\) | 0.602332 | 0.0409835 | ||||||||
\(217\) | −6.23967 | −0.423576 | ||||||||
\(218\) | 6.12159 | 0.414606 | ||||||||
\(219\) | 0.564834 | 0.0381680 | ||||||||
\(220\) | −6.15055 | −0.414670 | ||||||||
\(221\) | −7.69180 | −0.517406 | ||||||||
\(222\) | 1.12315 | 0.0753812 | ||||||||
\(223\) | 9.91371 | 0.663871 | 0.331935 | − | 0.943302i | \(-0.392298\pi\) | ||||
0.331935 | + | 0.943302i | \(0.392298\pi\) | |||||||
\(224\) | −1.91249 | −0.127783 | ||||||||
\(225\) | 2.67064 | 0.178043 | ||||||||
\(226\) | −10.1321 | −0.673977 | ||||||||
\(227\) | −12.3604 | −0.820389 | −0.410194 | − | 0.911998i | \(-0.634539\pi\) | ||||
−0.410194 | + | 0.911998i | \(0.634539\pi\) | |||||||
\(228\) | −0.100558 | −0.00665962 | ||||||||
\(229\) | 7.65151 | 0.505626 | 0.252813 | − | 0.967515i | \(-0.418644\pi\) | ||||
0.252813 | + | 0.967515i | \(0.418644\pi\) | |||||||
\(230\) | −4.37244 | −0.288310 | ||||||||
\(231\) | −0.583686 | −0.0384037 | ||||||||
\(232\) | 1.54555 | 0.101470 | ||||||||
\(233\) | 24.2147 | 1.58635 | 0.793177 | − | 0.608991i | \(-0.208425\pi\) | ||||
0.793177 | + | 0.608991i | \(0.208425\pi\) | |||||||
\(234\) | −4.76034 | −0.311193 | ||||||||
\(235\) | 22.9838 | 1.49930 | ||||||||
\(236\) | 3.74947 | 0.244070 | ||||||||
\(237\) | −0.881986 | −0.0572912 | ||||||||
\(238\) | −9.23940 | −0.598901 | ||||||||
\(239\) | −27.6853 | −1.79081 | −0.895406 | − | 0.445250i | \(-0.853115\pi\) | ||||
−0.895406 | + | 0.445250i | \(0.853115\pi\) | |||||||
\(240\) | 0.203783 | 0.0131541 | ||||||||
\(241\) | 5.78747 | 0.372804 | 0.186402 | − | 0.982474i | \(-0.440317\pi\) | ||||
0.186402 | + | 0.982474i | \(0.440317\pi\) | |||||||
\(242\) | 1.78856 | 0.114973 | ||||||||
\(243\) | 2.70288 | 0.173390 | ||||||||
\(244\) | 9.52357 | 0.609684 | ||||||||
\(245\) | −6.77342 | −0.432738 | ||||||||
\(246\) | 0.00528915 | 0.000337224 0 | ||||||||
\(247\) | 1.59215 | 0.101306 | ||||||||
\(248\) | 3.26259 | 0.207175 | ||||||||
\(249\) | −0.442588 | −0.0280479 | ||||||||
\(250\) | 11.9427 | 0.755324 | ||||||||
\(251\) | −17.4127 | −1.09908 | −0.549540 | − | 0.835467i | \(-0.685197\pi\) | ||||
−0.549540 | + | 0.835467i | \(0.685197\pi\) | |||||||
\(252\) | −5.71812 | −0.360208 | ||||||||
\(253\) | −6.54843 | −0.411696 | ||||||||
\(254\) | 10.1667 | 0.637915 | ||||||||
\(255\) | 0.984493 | 0.0616514 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.30923 | 0.0816678 | 0.0408339 | − | 0.999166i | \(-0.486999\pi\) | ||||
0.0408339 | + | 0.999166i | \(0.486999\pi\) | |||||||
\(258\) | −0.853733 | −0.0531511 | ||||||||
\(259\) | −21.3610 | −1.32731 | ||||||||
\(260\) | −3.22651 | −0.200100 | ||||||||
\(261\) | 4.62102 | 0.286034 | ||||||||
\(262\) | −1.91916 | −0.118566 | ||||||||
\(263\) | −3.72047 | −0.229414 | −0.114707 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114707 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(264\) | 0.305197 | 0.0187836 | ||||||||
\(265\) | −19.8063 | −1.21669 | ||||||||
\(266\) | 1.91249 | 0.117262 | ||||||||
\(267\) | −1.28159 | −0.0784322 | ||||||||
\(268\) | 11.6242 | 0.710058 | ||||||||
\(269\) | 1.61281 | 0.0983349 | 0.0491675 | − | 0.998791i | \(-0.484343\pi\) | ||||
0.0491675 | + | 0.998791i | \(0.484343\pi\) | |||||||
\(270\) | 1.22064 | 0.0742856 | ||||||||
\(271\) | −23.8452 | −1.44849 | −0.724246 | − | 0.689541i | \(-0.757812\pi\) | ||||
−0.724246 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(272\) | 4.83109 | 0.292928 | ||||||||
\(273\) | −0.306195 | −0.0185318 | ||||||||
\(274\) | −0.917951 | −0.0554554 | ||||||||
\(275\) | 2.71096 | 0.163477 | ||||||||
\(276\) | 0.216965 | 0.0130598 | ||||||||
\(277\) | 19.3813 | 1.16451 | 0.582254 | − | 0.813007i | \(-0.302171\pi\) | ||||
0.582254 | + | 0.813007i | \(0.302171\pi\) | |||||||
\(278\) | −11.4651 | −0.687633 | ||||||||
\(279\) | 9.75479 | 0.584004 | ||||||||
\(280\) | −3.87569 | −0.231617 | ||||||||
\(281\) | 24.9138 | 1.48623 | 0.743116 | − | 0.669163i | \(-0.233347\pi\) | ||||
0.743116 | + | 0.669163i | \(0.233347\pi\) | |||||||
\(282\) | −1.14048 | −0.0679148 | ||||||||
\(283\) | 13.9472 | 0.829075 | 0.414538 | − | 0.910032i | \(-0.363943\pi\) | ||||
0.414538 | + | 0.910032i | \(0.363943\pi\) | |||||||
\(284\) | −14.7569 | −0.875658 | ||||||||
\(285\) | −0.203783 | −0.0120711 | ||||||||
\(286\) | −4.83222 | −0.285735 | ||||||||
\(287\) | −0.100593 | −0.00593781 | ||||||||
\(288\) | 2.98989 | 0.176181 | ||||||||
\(289\) | 6.33943 | 0.372908 | ||||||||
\(290\) | 3.13208 | 0.183922 | ||||||||
\(291\) | 1.79610 | 0.105289 | ||||||||
\(292\) | 5.61699 | 0.328710 | ||||||||
\(293\) | 2.74166 | 0.160170 | 0.0800848 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800848 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(294\) | 0.336105 | 0.0196020 | ||||||||
\(295\) | 7.59838 | 0.442395 | ||||||||
\(296\) | 11.1692 | 0.649197 | ||||||||
\(297\) | 1.82810 | 0.106077 | ||||||||
\(298\) | 12.1455 | 0.703567 | ||||||||
\(299\) | −3.43523 | −0.198665 | ||||||||
\(300\) | −0.0898209 | −0.00518581 | ||||||||
\(301\) | 16.2369 | 0.935880 | ||||||||
\(302\) | 7.48903 | 0.430945 | ||||||||
\(303\) | −1.48767 | −0.0854643 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 19.2997 | 1.10510 | ||||||||
\(306\) | 14.4444 | 0.825732 | ||||||||
\(307\) | 4.59553 | 0.262281 | 0.131140 | − | 0.991364i | \(-0.458136\pi\) | ||||
0.131140 | + | 0.991364i | \(0.458136\pi\) | |||||||
\(308\) | −5.80446 | −0.330740 | ||||||||
\(309\) | −0.176572 | −0.0100448 | ||||||||
\(310\) | 6.61171 | 0.375520 | ||||||||
\(311\) | −26.9363 | −1.52741 | −0.763707 | − | 0.645563i | \(-0.776623\pi\) | ||||
−0.763707 | + | 0.645563i | \(0.776623\pi\) | |||||||
\(312\) | 0.160103 | 0.00906405 | ||||||||
\(313\) | −10.1071 | −0.571288 | −0.285644 | − | 0.958336i | \(-0.592208\pi\) | ||||
−0.285644 | + | 0.958336i | \(0.592208\pi\) | |||||||
\(314\) | 10.1203 | 0.571123 | ||||||||
\(315\) | −11.5879 | −0.652903 | ||||||||
\(316\) | −8.77091 | −0.493402 | ||||||||
\(317\) | 21.9768 | 1.23434 | 0.617171 | − | 0.786829i | \(-0.288279\pi\) | ||||
0.617171 | + | 0.786829i | \(0.288279\pi\) | |||||||
\(318\) | 0.982809 | 0.0551132 | ||||||||
\(319\) | 4.69079 | 0.262634 | ||||||||
\(320\) | 2.02652 | 0.113286 | ||||||||
\(321\) | −1.34724 | −0.0751956 | ||||||||
\(322\) | −4.12641 | −0.229956 | ||||||||
\(323\) | −4.83109 | −0.268809 | ||||||||
\(324\) | 8.90909 | 0.494950 | ||||||||
\(325\) | 1.42214 | 0.0788862 | ||||||||
\(326\) | −1.50702 | −0.0834661 | ||||||||
\(327\) | −0.615576 | −0.0340414 | ||||||||
\(328\) | 0.0525980 | 0.00290424 | ||||||||
\(329\) | 21.6906 | 1.19584 | ||||||||
\(330\) | 0.618488 | 0.0340466 | ||||||||
\(331\) | 11.4471 | 0.629192 | 0.314596 | − | 0.949226i | \(-0.398131\pi\) | ||||
0.314596 | + | 0.949226i | \(0.398131\pi\) | |||||||
\(332\) | −4.40132 | −0.241554 | ||||||||
\(333\) | 33.3947 | 1.83002 | ||||||||
\(334\) | 17.2871 | 0.945907 | ||||||||
\(335\) | 23.5566 | 1.28703 | ||||||||
\(336\) | 0.192316 | 0.0104917 | ||||||||
\(337\) | −3.67206 | −0.200030 | −0.100015 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100015 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(338\) | 10.4651 | 0.569225 | ||||||||
\(339\) | 1.01886 | 0.0553371 | ||||||||
\(340\) | 9.79029 | 0.530953 | ||||||||
\(341\) | 9.90209 | 0.536228 | ||||||||
\(342\) | −2.98989 | −0.161675 | ||||||||
\(343\) | −19.7797 | −1.06800 | ||||||||
\(344\) | −8.48995 | −0.457747 | ||||||||
\(345\) | 0.439684 | 0.0236718 | ||||||||
\(346\) | −15.6606 | −0.841920 | ||||||||
\(347\) | −0.407595 | −0.0218808 | −0.0109404 | − | 0.999940i | \(-0.503483\pi\) | ||||
−0.0109404 | + | 0.999940i | \(0.503483\pi\) | |||||||
\(348\) | −0.155417 | −0.00833125 | ||||||||
\(349\) | −27.9617 | −1.49676 | −0.748378 | − | 0.663273i | \(-0.769167\pi\) | ||||
−0.748378 | + | 0.663273i | \(0.769167\pi\) | |||||||
\(350\) | 1.70828 | 0.0913113 | ||||||||
\(351\) | 0.959000 | 0.0511876 | ||||||||
\(352\) | 3.03504 | 0.161768 | ||||||||
\(353\) | 32.2883 | 1.71853 | 0.859267 | − | 0.511527i | \(-0.170920\pi\) | ||||
0.859267 | + | 0.511527i | \(0.170920\pi\) | |||||||
\(354\) | −0.377040 | −0.0200395 | ||||||||
\(355\) | −29.9050 | −1.58719 | ||||||||
\(356\) | −12.7448 | −0.675473 | ||||||||
\(357\) | 0.929096 | 0.0491730 | ||||||||
\(358\) | −9.00762 | −0.476067 | ||||||||
\(359\) | −25.7865 | −1.36096 | −0.680479 | − | 0.732767i | \(-0.738228\pi\) | ||||
−0.680479 | + | 0.732767i | \(0.738228\pi\) | |||||||
\(360\) | 6.05906 | 0.319341 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 22.7058 | 1.19339 | ||||||||
\(363\) | −0.179854 | −0.00943991 | ||||||||
\(364\) | −3.04496 | −0.159599 | ||||||||
\(365\) | 11.3829 | 0.595810 | ||||||||
\(366\) | −0.957672 | −0.0500583 | ||||||||
\(367\) | −6.43524 | −0.335917 | −0.167958 | − | 0.985794i | \(-0.553717\pi\) | ||||
−0.167958 | + | 0.985794i | \(0.553717\pi\) | |||||||
\(368\) | 2.15761 | 0.112473 | ||||||||
\(369\) | 0.157262 | 0.00818673 | ||||||||
\(370\) | 22.6346 | 1.17672 | ||||||||
\(371\) | −18.6918 | −0.970428 | ||||||||
\(372\) | −0.328080 | −0.0170102 | ||||||||
\(373\) | −31.7099 | −1.64188 | −0.820938 | − | 0.571017i | \(-0.806549\pi\) | ||||
−0.820938 | + | 0.571017i | \(0.806549\pi\) | |||||||
\(374\) | 14.6625 | 0.758181 | ||||||||
\(375\) | −1.20094 | −0.0620162 | ||||||||
\(376\) | −11.3415 | −0.584895 | ||||||||
\(377\) | 2.46074 | 0.126734 | ||||||||
\(378\) | 1.15195 | 0.0592500 | ||||||||
\(379\) | −18.2073 | −0.935244 | −0.467622 | − | 0.883929i | \(-0.654889\pi\) | ||||
−0.467622 | + | 0.883929i | \(0.654889\pi\) | |||||||
\(380\) | −2.02652 | −0.103958 | ||||||||
\(381\) | −1.02234 | −0.0523762 | ||||||||
\(382\) | 0.461537 | 0.0236143 | ||||||||
\(383\) | 33.1960 | 1.69624 | 0.848119 | − | 0.529806i | \(-0.177735\pi\) | ||||
0.848119 | + | 0.529806i | \(0.177735\pi\) | |||||||
\(384\) | −0.100558 | −0.00513158 | ||||||||
\(385\) | −11.7629 | −0.599491 | ||||||||
\(386\) | 19.0090 | 0.967533 | ||||||||
\(387\) | −25.3840 | −1.29034 | ||||||||
\(388\) | 17.8613 | 0.906769 | ||||||||
\(389\) | 31.0290 | 1.57323 | 0.786616 | − | 0.617442i | \(-0.211831\pi\) | ||||
0.786616 | + | 0.617442i | \(0.211831\pi\) | |||||||
\(390\) | 0.324452 | 0.0164293 | ||||||||
\(391\) | 10.4236 | 0.527145 | ||||||||
\(392\) | 3.34239 | 0.168816 | ||||||||
\(393\) | 0.192987 | 0.00973491 | ||||||||
\(394\) | 11.1545 | 0.561957 | ||||||||
\(395\) | −17.7744 | −0.894328 | ||||||||
\(396\) | 9.07442 | 0.456007 | ||||||||
\(397\) | 35.5304 | 1.78322 | 0.891611 | − | 0.452802i | \(-0.149576\pi\) | ||||
0.891611 | + | 0.452802i | \(0.149576\pi\) | |||||||
\(398\) | 25.3525 | 1.27081 | ||||||||
\(399\) | −0.192316 | −0.00962785 | ||||||||
\(400\) | −0.893223 | −0.0446612 | ||||||||
\(401\) | 2.06243 | 0.102993 | 0.0514965 | − | 0.998673i | \(-0.483601\pi\) | ||||
0.0514965 | + | 0.998673i | \(0.483601\pi\) | |||||||
\(402\) | −1.16890 | −0.0582996 | ||||||||
\(403\) | 5.19452 | 0.258758 | ||||||||
\(404\) | −14.7941 | −0.736035 | ||||||||
\(405\) | 18.0544 | 0.897133 | ||||||||
\(406\) | 2.95584 | 0.146696 | ||||||||
\(407\) | 33.8989 | 1.68031 | ||||||||
\(408\) | −0.485805 | −0.0240509 | ||||||||
\(409\) | −16.3714 | −0.809514 | −0.404757 | − | 0.914424i | \(-0.632644\pi\) | ||||
−0.404757 | + | 0.914424i | \(0.632644\pi\) | |||||||
\(410\) | 0.106591 | 0.00526414 | ||||||||
\(411\) | 0.0923074 | 0.00455319 | ||||||||
\(412\) | −1.75592 | −0.0865080 | ||||||||
\(413\) | 7.17082 | 0.352853 | ||||||||
\(414\) | 6.45102 | 0.317050 | ||||||||
\(415\) | −8.91936 | −0.437834 | ||||||||
\(416\) | 1.59215 | 0.0780613 | ||||||||
\(417\) | 1.15291 | 0.0564584 | ||||||||
\(418\) | −3.03504 | −0.148448 | ||||||||
\(419\) | 34.3311 | 1.67718 | 0.838591 | − | 0.544762i | \(-0.183380\pi\) | ||||
0.838591 | + | 0.544762i | \(0.183380\pi\) | |||||||
\(420\) | 0.389732 | 0.0190170 | ||||||||
\(421\) | −0.484634 | −0.0236196 | −0.0118098 | − | 0.999930i | \(-0.503759\pi\) | ||||
−0.0118098 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −33.9099 | −1.64876 | ||||||||
\(424\) | 9.77354 | 0.474645 | ||||||||
\(425\) | −4.31524 | −0.209320 | ||||||||
\(426\) | 1.48392 | 0.0718962 | ||||||||
\(427\) | 18.2137 | 0.881423 | ||||||||
\(428\) | −13.3976 | −0.647598 | ||||||||
\(429\) | 0.485919 | 0.0234604 | ||||||||
\(430\) | −17.2050 | −0.829700 | ||||||||
\(431\) | 39.1350 | 1.88507 | 0.942534 | − | 0.334111i | \(-0.108436\pi\) | ||||
0.942534 | + | 0.334111i | \(0.108436\pi\) | |||||||
\(432\) | −0.602332 | −0.0289797 | ||||||||
\(433\) | 8.60782 | 0.413665 | 0.206833 | − | 0.978376i | \(-0.433684\pi\) | ||||
0.206833 | + | 0.978376i | \(0.433684\pi\) | |||||||
\(434\) | 6.23967 | 0.299514 | ||||||||
\(435\) | −0.314956 | −0.0151010 | ||||||||
\(436\) | −6.12159 | −0.293171 | ||||||||
\(437\) | −2.15761 | −0.103213 | ||||||||
\(438\) | −0.564834 | −0.0269888 | ||||||||
\(439\) | −26.2639 | −1.25351 | −0.626753 | − | 0.779218i | \(-0.715616\pi\) | ||||
−0.626753 | + | 0.779218i | \(0.715616\pi\) | |||||||
\(440\) | 6.15055 | 0.293216 | ||||||||
\(441\) | 9.99338 | 0.475875 | ||||||||
\(442\) | 7.69180 | 0.365861 | ||||||||
\(443\) | 30.9679 | 1.47133 | 0.735664 | − | 0.677347i | \(-0.236870\pi\) | ||||
0.735664 | + | 0.677347i | \(0.236870\pi\) | |||||||
\(444\) | −1.12315 | −0.0533025 | ||||||||
\(445\) | −25.8276 | −1.22434 | ||||||||
\(446\) | −9.91371 | −0.469428 | ||||||||
\(447\) | −1.22132 | −0.0577667 | ||||||||
\(448\) | 1.91249 | 0.0903565 | ||||||||
\(449\) | 5.98084 | 0.282253 | 0.141127 | − | 0.989992i | \(-0.454928\pi\) | ||||
0.141127 | + | 0.989992i | \(0.454928\pi\) | |||||||
\(450\) | −2.67064 | −0.125895 | ||||||||
\(451\) | 0.159637 | 0.00751700 | ||||||||
\(452\) | 10.1321 | 0.476574 | ||||||||
\(453\) | −0.753082 | −0.0353829 | ||||||||
\(454\) | 12.3604 | 0.580103 | ||||||||
\(455\) | −6.17066 | −0.289285 | ||||||||
\(456\) | 0.100558 | 0.00470906 | ||||||||
\(457\) | −13.5583 | −0.634230 | −0.317115 | − | 0.948387i | \(-0.602714\pi\) | ||||
−0.317115 | + | 0.948387i | \(0.602714\pi\) | |||||||
\(458\) | −7.65151 | −0.357531 | ||||||||
\(459\) | −2.90992 | −0.135823 | ||||||||
\(460\) | 4.37244 | 0.203866 | ||||||||
\(461\) | 4.14128 | 0.192879 | 0.0964394 | − | 0.995339i | \(-0.469255\pi\) | ||||
0.0964394 | + | 0.995339i | \(0.469255\pi\) | |||||||
\(462\) | 0.583686 | 0.0271555 | ||||||||
\(463\) | −18.9491 | −0.880638 | −0.440319 | − | 0.897841i | \(-0.645135\pi\) | ||||
−0.440319 | + | 0.897841i | \(0.645135\pi\) | |||||||
\(464\) | −1.54555 | −0.0717503 | ||||||||
\(465\) | −0.664861 | −0.0308322 | ||||||||
\(466\) | −24.2147 | −1.12172 | ||||||||
\(467\) | −16.8398 | −0.779255 | −0.389628 | − | 0.920972i | \(-0.627396\pi\) | ||||
−0.389628 | + | 0.920972i | \(0.627396\pi\) | |||||||
\(468\) | 4.76034 | 0.220047 | ||||||||
\(469\) | 22.2310 | 1.02653 | ||||||||
\(470\) | −22.9838 | −1.06017 | ||||||||
\(471\) | −1.01768 | −0.0468922 | ||||||||
\(472\) | −3.74947 | −0.172584 | ||||||||
\(473\) | −25.7673 | −1.18478 | ||||||||
\(474\) | 0.881986 | 0.0405110 | ||||||||
\(475\) | 0.893223 | 0.0409839 | ||||||||
\(476\) | 9.23940 | 0.423487 | ||||||||
\(477\) | 29.2218 | 1.33797 | ||||||||
\(478\) | 27.6853 | 1.26630 | ||||||||
\(479\) | −29.7128 | −1.35761 | −0.678807 | − | 0.734317i | \(-0.737503\pi\) | ||||
−0.678807 | + | 0.734317i | \(0.737503\pi\) | |||||||
\(480\) | −0.203783 | −0.00930137 | ||||||||
\(481\) | 17.7830 | 0.810835 | ||||||||
\(482\) | −5.78747 | −0.263612 | ||||||||
\(483\) | 0.414944 | 0.0188806 | ||||||||
\(484\) | −1.78856 | −0.0812983 | ||||||||
\(485\) | 36.1962 | 1.64359 | ||||||||
\(486\) | −2.70288 | −0.122605 | ||||||||
\(487\) | −14.5662 | −0.660058 | −0.330029 | − | 0.943971i | \(-0.607059\pi\) | ||||
−0.330029 | + | 0.943971i | \(0.607059\pi\) | |||||||
\(488\) | −9.52357 | −0.431112 | ||||||||
\(489\) | 0.151543 | 0.00685302 | ||||||||
\(490\) | 6.77342 | 0.305992 | ||||||||
\(491\) | 30.5166 | 1.37719 | 0.688597 | − | 0.725144i | \(-0.258227\pi\) | ||||
0.688597 | + | 0.725144i | \(0.258227\pi\) | |||||||
\(492\) | −0.00528915 | −0.000238453 0 | ||||||||
\(493\) | −7.46668 | −0.336283 | ||||||||
\(494\) | −1.59215 | −0.0716340 | ||||||||
\(495\) | 18.3895 | 0.826545 | ||||||||
\(496\) | −3.26259 | −0.146495 | ||||||||
\(497\) | −28.2223 | −1.26594 | ||||||||
\(498\) | 0.442588 | 0.0198329 | ||||||||
\(499\) | −31.5212 | −1.41108 | −0.705540 | − | 0.708670i | \(-0.749296\pi\) | ||||
−0.705540 | + | 0.708670i | \(0.749296\pi\) | |||||||
\(500\) | −11.9427 | −0.534095 | ||||||||
\(501\) | −1.73836 | −0.0776641 | ||||||||
\(502\) | 17.4127 | 0.777167 | ||||||||
\(503\) | 1.84738 | 0.0823708 | 0.0411854 | − | 0.999152i | \(-0.486887\pi\) | ||||
0.0411854 | + | 0.999152i | \(0.486887\pi\) | |||||||
\(504\) | 5.71812 | 0.254705 | ||||||||
\(505\) | −29.9806 | −1.33412 | ||||||||
\(506\) | 6.54843 | 0.291113 | ||||||||
\(507\) | −1.05235 | −0.0467364 | ||||||||
\(508\) | −10.1667 | −0.451074 | ||||||||
\(509\) | −12.9404 | −0.573571 | −0.286786 | − | 0.957995i | \(-0.592587\pi\) | ||||
−0.286786 | + | 0.957995i | \(0.592587\pi\) | |||||||
\(510\) | −0.984493 | −0.0435941 | ||||||||
\(511\) | 10.7424 | 0.475217 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.602332 | 0.0265936 | ||||||||
\(514\) | −1.30923 | −0.0577478 | ||||||||
\(515\) | −3.55840 | −0.156802 | ||||||||
\(516\) | 0.853733 | 0.0375835 | ||||||||
\(517\) | −34.4220 | −1.51388 | ||||||||
\(518\) | 21.3610 | 0.938547 | ||||||||
\(519\) | 1.57480 | 0.0691261 | ||||||||
\(520\) | 3.22651 | 0.141492 | ||||||||
\(521\) | 3.52182 | 0.154294 | 0.0771470 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771470 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(522\) | −4.62102 | −0.202256 | ||||||||
\(523\) | −21.6922 | −0.948534 | −0.474267 | − | 0.880381i | \(-0.657287\pi\) | ||||
−0.474267 | + | 0.880381i | \(0.657287\pi\) | |||||||
\(524\) | 1.91916 | 0.0838389 | ||||||||
\(525\) | −0.171781 | −0.00749715 | ||||||||
\(526\) | 3.72047 | 0.162220 | ||||||||
\(527\) | −15.7619 | −0.686599 | ||||||||
\(528\) | −0.305197 | −0.0132820 | ||||||||
\(529\) | −18.3447 | −0.797596 | ||||||||
\(530\) | 19.8063 | 0.860329 | ||||||||
\(531\) | −11.2105 | −0.486495 | ||||||||
\(532\) | −1.91249 | −0.0829168 | ||||||||
\(533\) | 0.0837436 | 0.00362734 | ||||||||
\(534\) | 1.28159 | 0.0554599 | ||||||||
\(535\) | −27.1505 | −1.17382 | ||||||||
\(536\) | −11.6242 | −0.502087 | ||||||||
\(537\) | 0.905789 | 0.0390877 | ||||||||
\(538\) | −1.61281 | −0.0695333 | ||||||||
\(539\) | 10.1443 | 0.436945 | ||||||||
\(540\) | −1.22064 | −0.0525278 | ||||||||
\(541\) | 10.6975 | 0.459921 | 0.229960 | − | 0.973200i | \(-0.426140\pi\) | ||||
0.229960 | + | 0.973200i | \(0.426140\pi\) | |||||||
\(542\) | 23.8452 | 1.02424 | ||||||||
\(543\) | −2.28325 | −0.0979837 | ||||||||
\(544\) | −4.83109 | −0.207131 | ||||||||
\(545\) | −12.4055 | −0.531394 | ||||||||
\(546\) | 0.306195 | 0.0131039 | ||||||||
\(547\) | −18.0029 | −0.769748 | −0.384874 | − | 0.922969i | \(-0.625755\pi\) | ||||
−0.384874 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(548\) | 0.917951 | 0.0392129 | ||||||||
\(549\) | −28.4744 | −1.21526 | ||||||||
\(550\) | −2.71096 | −0.115596 | ||||||||
\(551\) | 1.54555 | 0.0658426 | ||||||||
\(552\) | −0.216965 | −0.00923466 | ||||||||
\(553\) | −16.7743 | −0.713314 | ||||||||
\(554\) | −19.3813 | −0.823432 | ||||||||
\(555\) | −2.27609 | −0.0966148 | ||||||||
\(556\) | 11.4651 | 0.486230 | ||||||||
\(557\) | 1.26638 | 0.0536584 | 0.0268292 | − | 0.999640i | \(-0.491459\pi\) | ||||
0.0268292 | + | 0.999640i | \(0.491459\pi\) | |||||||
\(558\) | −9.75479 | −0.412953 | ||||||||
\(559\) | −13.5172 | −0.571718 | ||||||||
\(560\) | 3.87569 | 0.163778 | ||||||||
\(561\) | −1.47444 | −0.0622507 | ||||||||
\(562\) | −24.9138 | −1.05092 | ||||||||
\(563\) | 12.0579 | 0.508179 | 0.254090 | − | 0.967181i | \(-0.418224\pi\) | ||||
0.254090 | + | 0.967181i | \(0.418224\pi\) | |||||||
\(564\) | 1.14048 | 0.0480230 | ||||||||
\(565\) | 20.5329 | 0.863824 | ||||||||
\(566\) | −13.9472 | −0.586245 | ||||||||
\(567\) | 17.0385 | 0.715551 | ||||||||
\(568\) | 14.7569 | 0.619184 | ||||||||
\(569\) | −4.47378 | −0.187551 | −0.0937753 | − | 0.995593i | \(-0.529894\pi\) | ||||
−0.0937753 | + | 0.995593i | \(0.529894\pi\) | |||||||
\(570\) | 0.203783 | 0.00853552 | ||||||||
\(571\) | 1.27084 | 0.0531829 | 0.0265914 | − | 0.999646i | \(-0.491535\pi\) | ||||
0.0265914 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(572\) | 4.83222 | 0.202045 | ||||||||
\(573\) | −0.0464113 | −0.00193886 | ||||||||
\(574\) | 0.100593 | 0.00419867 | ||||||||
\(575\) | −1.92723 | −0.0803710 | ||||||||
\(576\) | −2.98989 | −0.124579 | ||||||||
\(577\) | −3.27565 | −0.136367 | −0.0681836 | − | 0.997673i | \(-0.521720\pi\) | ||||
−0.0681836 | + | 0.997673i | \(0.521720\pi\) | |||||||
\(578\) | −6.33943 | −0.263686 | ||||||||
\(579\) | −1.91151 | −0.0794397 | ||||||||
\(580\) | −3.13208 | −0.130053 | ||||||||
\(581\) | −8.41747 | −0.349215 | ||||||||
\(582\) | −1.79610 | −0.0744506 | ||||||||
\(583\) | 29.6630 | 1.22852 | ||||||||
\(584\) | −5.61699 | −0.232433 | ||||||||
\(585\) | 9.64691 | 0.398851 | ||||||||
\(586\) | −2.74166 | −0.113257 | ||||||||
\(587\) | 6.38985 | 0.263737 | 0.131869 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131869 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(588\) | −0.336105 | −0.0138607 | ||||||||
\(589\) | 3.26259 | 0.134433 | ||||||||
\(590\) | −7.59838 | −0.312820 | ||||||||
\(591\) | −1.12168 | −0.0461397 | ||||||||
\(592\) | −11.1692 | −0.459052 | ||||||||
\(593\) | 4.34937 | 0.178607 | 0.0893036 | − | 0.996004i | \(-0.471536\pi\) | ||||
0.0893036 | + | 0.996004i | \(0.471536\pi\) | |||||||
\(594\) | −1.82810 | −0.0750078 | ||||||||
\(595\) | 18.7238 | 0.767601 | ||||||||
\(596\) | −12.1455 | −0.497497 | ||||||||
\(597\) | −2.54940 | −0.104340 | ||||||||
\(598\) | 3.43523 | 0.140477 | ||||||||
\(599\) | −15.4381 | −0.630785 | −0.315392 | − | 0.948961i | \(-0.602136\pi\) | ||||
−0.315392 | + | 0.948961i | \(0.602136\pi\) | |||||||
\(600\) | 0.0898209 | 0.00366692 | ||||||||
\(601\) | −36.6882 | −1.49654 | −0.748271 | − | 0.663393i | \(-0.769116\pi\) | ||||
−0.748271 | + | 0.663393i | \(0.769116\pi\) | |||||||
\(602\) | −16.2369 | −0.661767 | ||||||||
\(603\) | −34.7549 | −1.41533 | ||||||||
\(604\) | −7.48903 | −0.304724 | ||||||||
\(605\) | −3.62455 | −0.147359 | ||||||||
\(606\) | 1.48767 | 0.0604324 | ||||||||
\(607\) | 28.4521 | 1.15483 | 0.577417 | − | 0.816449i | \(-0.304061\pi\) | ||||
0.577417 | + | 0.816449i | \(0.304061\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −0.297234 | −0.0120445 | ||||||||
\(610\) | −19.2997 | −0.781422 | ||||||||
\(611\) | −18.0574 | −0.730524 | ||||||||
\(612\) | −14.4444 | −0.583881 | ||||||||
\(613\) | −41.7708 | −1.68711 | −0.843554 | − | 0.537045i | \(-0.819540\pi\) | ||||
−0.843554 | + | 0.537045i | \(0.819540\pi\) | |||||||
\(614\) | −4.59553 | −0.185461 | ||||||||
\(615\) | −0.0107186 | −0.000432214 0 | ||||||||
\(616\) | 5.80446 | 0.233869 | ||||||||
\(617\) | 25.5161 | 1.02724 | 0.513620 | − | 0.858018i | \(-0.328304\pi\) | ||||
0.513620 | + | 0.858018i | \(0.328304\pi\) | |||||||
\(618\) | 0.176572 | 0.00710277 | ||||||||
\(619\) | 19.2877 | 0.775239 | 0.387620 | − | 0.921819i | \(-0.373297\pi\) | ||||
0.387620 | + | 0.921819i | \(0.373297\pi\) | |||||||
\(620\) | −6.61171 | −0.265533 | ||||||||
\(621\) | −1.29960 | −0.0521511 | ||||||||
\(622\) | 26.9363 | 1.08005 | ||||||||
\(623\) | −24.3743 | −0.976534 | ||||||||
\(624\) | −0.160103 | −0.00640925 | ||||||||
\(625\) | −19.7360 | −0.789441 | ||||||||
\(626\) | 10.1071 | 0.403962 | ||||||||
\(627\) | 0.305197 | 0.0121884 | ||||||||
\(628\) | −10.1203 | −0.403845 | ||||||||
\(629\) | −53.9594 | −2.15150 | ||||||||
\(630\) | 11.5879 | 0.461672 | ||||||||
\(631\) | −17.7784 | −0.707746 | −0.353873 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353873 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(632\) | 8.77091 | 0.348888 | ||||||||
\(633\) | −0.100558 | −0.00399683 | ||||||||
\(634\) | −21.9768 | −0.872812 | ||||||||
\(635\) | −20.6030 | −0.817604 | ||||||||
\(636\) | −0.982809 | −0.0389709 | ||||||||
\(637\) | 5.32158 | 0.210849 | ||||||||
\(638\) | −4.69079 | −0.185710 | ||||||||
\(639\) | 44.1213 | 1.74541 | ||||||||
\(640\) | −2.02652 | −0.0801052 | ||||||||
\(641\) | 27.6669 | 1.09278 | 0.546389 | − | 0.837532i | \(-0.316002\pi\) | ||||
0.546389 | + | 0.837532i | \(0.316002\pi\) | |||||||
\(642\) | 1.34724 | 0.0531713 | ||||||||
\(643\) | −5.88810 | −0.232204 | −0.116102 | − | 0.993237i | \(-0.537040\pi\) | ||||
−0.116102 | + | 0.993237i | \(0.537040\pi\) | |||||||
\(644\) | 4.12641 | 0.162603 | ||||||||
\(645\) | 1.73011 | 0.0681228 | ||||||||
\(646\) | 4.83109 | 0.190077 | ||||||||
\(647\) | −39.8685 | −1.56739 | −0.783697 | − | 0.621143i | \(-0.786669\pi\) | ||||
−0.783697 | + | 0.621143i | \(0.786669\pi\) | |||||||
\(648\) | −8.90909 | −0.349982 | ||||||||
\(649\) | −11.3798 | −0.446696 | ||||||||
\(650\) | −1.42214 | −0.0557810 | ||||||||
\(651\) | −0.627449 | −0.0245917 | ||||||||
\(652\) | 1.50702 | 0.0590195 | ||||||||
\(653\) | −1.54468 | −0.0604481 | −0.0302240 | − | 0.999543i | \(-0.509622\pi\) | ||||
−0.0302240 | + | 0.999543i | \(0.509622\pi\) | |||||||
\(654\) | 0.615576 | 0.0240709 | ||||||||
\(655\) | 3.88921 | 0.151964 | ||||||||
\(656\) | −0.0525980 | −0.00205361 | ||||||||
\(657\) | −16.7942 | −0.655203 | ||||||||
\(658\) | −21.6906 | −0.845586 | ||||||||
\(659\) | 4.85462 | 0.189109 | 0.0945547 | − | 0.995520i | \(-0.469857\pi\) | ||||
0.0945547 | + | 0.995520i | \(0.469857\pi\) | |||||||
\(660\) | −0.618488 | −0.0240746 | ||||||||
\(661\) | 26.0039 | 1.01143 | 0.505717 | − | 0.862700i | \(-0.331228\pi\) | ||||
0.505717 | + | 0.862700i | \(0.331228\pi\) | |||||||
\(662\) | −11.4471 | −0.444906 | ||||||||
\(663\) | −0.773472 | −0.0300392 | ||||||||
\(664\) | 4.40132 | 0.170804 | ||||||||
\(665\) | −3.87569 | −0.150293 | ||||||||
\(666\) | −33.3947 | −1.29402 | ||||||||
\(667\) | −3.33469 | −0.129120 | ||||||||
\(668\) | −17.2871 | −0.668858 | ||||||||
\(669\) | 0.996904 | 0.0385425 | ||||||||
\(670\) | −23.5566 | −0.910069 | ||||||||
\(671\) | −28.9044 | −1.11584 | ||||||||
\(672\) | −0.192316 | −0.00741875 | ||||||||
\(673\) | −35.8428 | −1.38164 | −0.690820 | − | 0.723027i | \(-0.742750\pi\) | ||||
−0.690820 | + | 0.723027i | \(0.742750\pi\) | |||||||
\(674\) | 3.67206 | 0.141442 | ||||||||
\(675\) | 0.538017 | 0.0207083 | ||||||||
\(676\) | −10.4651 | −0.402503 | ||||||||
\(677\) | −14.4793 | −0.556484 | −0.278242 | − | 0.960511i | \(-0.589752\pi\) | ||||
−0.278242 | + | 0.960511i | \(0.589752\pi\) | |||||||
\(678\) | −1.01886 | −0.0391292 | ||||||||
\(679\) | 34.1595 | 1.31092 | ||||||||
\(680\) | −9.79029 | −0.375441 | ||||||||
\(681\) | −1.24294 | −0.0476295 | ||||||||
\(682\) | −9.90209 | −0.379171 | ||||||||
\(683\) | 27.4785 | 1.05143 | 0.525717 | − | 0.850659i | \(-0.323797\pi\) | ||||
0.525717 | + | 0.850659i | \(0.323797\pi\) | |||||||
\(684\) | 2.98989 | 0.114321 | ||||||||
\(685\) | 1.86024 | 0.0710763 | ||||||||
\(686\) | 19.7797 | 0.755192 | ||||||||
\(687\) | 0.769421 | 0.0293552 | ||||||||
\(688\) | 8.48995 | 0.323676 | ||||||||
\(689\) | 15.5609 | 0.592823 | ||||||||
\(690\) | −0.439684 | −0.0167385 | ||||||||
\(691\) | 5.39570 | 0.205262 | 0.102631 | − | 0.994719i | \(-0.467274\pi\) | ||||
0.102631 | + | 0.994719i | \(0.467274\pi\) | |||||||
\(692\) | 15.6606 | 0.595327 | ||||||||
\(693\) | 17.3547 | 0.659251 | ||||||||
\(694\) | 0.407595 | 0.0154721 | ||||||||
\(695\) | 23.2343 | 0.881328 | ||||||||
\(696\) | 0.155417 | 0.00589108 | ||||||||
\(697\) | −0.254106 | −0.00962493 | ||||||||
\(698\) | 27.9617 | 1.05837 | ||||||||
\(699\) | 2.43498 | 0.0920994 | ||||||||
\(700\) | −1.70828 | −0.0645668 | ||||||||
\(701\) | −6.60945 | −0.249635 | −0.124818 | − | 0.992180i | \(-0.539835\pi\) | ||||
−0.124818 | + | 0.992180i | \(0.539835\pi\) | |||||||
\(702\) | −0.959000 | −0.0361951 | ||||||||
\(703\) | 11.1692 | 0.421255 | ||||||||
\(704\) | −3.03504 | −0.114387 | ||||||||
\(705\) | 2.31121 | 0.0870453 | ||||||||
\(706\) | −32.2883 | −1.21519 | ||||||||
\(707\) | −28.2936 | −1.06409 | ||||||||
\(708\) | 0.377040 | 0.0141700 | ||||||||
\(709\) | 13.5222 | 0.507837 | 0.253918 | − | 0.967226i | \(-0.418281\pi\) | ||||
0.253918 | + | 0.967226i | \(0.418281\pi\) | |||||||
\(710\) | 29.9050 | 1.12232 | ||||||||
\(711\) | 26.2240 | 0.983478 | ||||||||
\(712\) | 12.7448 | 0.477632 | ||||||||
\(713\) | −7.03941 | −0.263628 | ||||||||
\(714\) | −0.929096 | −0.0347706 | ||||||||
\(715\) | 9.79258 | 0.366222 | ||||||||
\(716\) | 9.00762 | 0.336631 | ||||||||
\(717\) | −2.78398 | −0.103970 | ||||||||
\(718\) | 25.7865 | 0.962343 | ||||||||
\(719\) | −26.4079 | −0.984850 | −0.492425 | − | 0.870355i | \(-0.663889\pi\) | ||||
−0.492425 | + | 0.870355i | \(0.663889\pi\) | |||||||
\(720\) | −6.05906 | −0.225808 | ||||||||
\(721\) | −3.35817 | −0.125065 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0.581977 | 0.0216440 | ||||||||
\(724\) | −22.7058 | −0.843854 | ||||||||
\(725\) | 1.38052 | 0.0512712 | ||||||||
\(726\) | 0.179854 | 0.00667502 | ||||||||
\(727\) | −26.8667 | −0.996429 | −0.498215 | − | 0.867054i | \(-0.666011\pi\) | ||||
−0.498215 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(728\) | 3.04496 | 0.112854 | ||||||||
\(729\) | −26.4555 | −0.979833 | ||||||||
\(730\) | −11.3829 | −0.421302 | ||||||||
\(731\) | 41.0157 | 1.51702 | ||||||||
\(732\) | 0.957672 | 0.0353966 | ||||||||
\(733\) | 23.6822 | 0.874724 | 0.437362 | − | 0.899286i | \(-0.355913\pi\) | ||||
0.437362 | + | 0.899286i | \(0.355913\pi\) | |||||||
\(734\) | 6.43524 | 0.237529 | ||||||||
\(735\) | −0.681123 | −0.0251236 | ||||||||
\(736\) | −2.15761 | −0.0795306 | ||||||||
\(737\) | −35.2797 | −1.29955 | ||||||||
\(738\) | −0.157262 | −0.00578890 | ||||||||
\(739\) | 2.28553 | 0.0840747 | 0.0420373 | − | 0.999116i | \(-0.486615\pi\) | ||||
0.0420373 | + | 0.999116i | \(0.486615\pi\) | |||||||
\(740\) | −22.6346 | −0.832065 | ||||||||
\(741\) | 0.160103 | 0.00588153 | ||||||||
\(742\) | 18.6918 | 0.686197 | ||||||||
\(743\) | 40.4110 | 1.48253 | 0.741267 | − | 0.671210i | \(-0.234225\pi\) | ||||
0.741267 | + | 0.671210i | \(0.234225\pi\) | |||||||
\(744\) | 0.328080 | 0.0120280 | ||||||||
\(745\) | −24.6130 | −0.901750 | ||||||||
\(746\) | 31.7099 | 1.16098 | ||||||||
\(747\) | 13.1595 | 0.481479 | ||||||||
\(748\) | −14.6625 | −0.536115 | ||||||||
\(749\) | −25.6228 | −0.936236 | ||||||||
\(750\) | 1.20094 | 0.0438521 | ||||||||
\(751\) | −32.2569 | −1.17707 | −0.588535 | − | 0.808471i | \(-0.700295\pi\) | ||||
−0.588535 | + | 0.808471i | \(0.700295\pi\) | |||||||
\(752\) | 11.3415 | 0.413584 | ||||||||
\(753\) | −1.75099 | −0.0638096 | ||||||||
\(754\) | −2.46074 | −0.0896148 | ||||||||
\(755\) | −15.1767 | −0.552335 | ||||||||
\(756\) | −1.15195 | −0.0418961 | ||||||||
\(757\) | 14.3136 | 0.520236 | 0.260118 | − | 0.965577i | \(-0.416238\pi\) | ||||
0.260118 | + | 0.965577i | \(0.416238\pi\) | |||||||
\(758\) | 18.2073 | 0.661317 | ||||||||
\(759\) | −0.658498 | −0.0239019 | ||||||||
\(760\) | 2.02652 | 0.0735095 | ||||||||
\(761\) | −6.01324 | −0.217980 | −0.108990 | − | 0.994043i | \(-0.534762\pi\) | ||||
−0.108990 | + | 0.994043i | \(0.534762\pi\) | |||||||
\(762\) | 1.02234 | 0.0370356 | ||||||||
\(763\) | −11.7075 | −0.423839 | ||||||||
\(764\) | −0.461537 | −0.0166978 | ||||||||
\(765\) | −29.2719 | −1.05833 | ||||||||
\(766\) | −33.1960 | −1.19942 | ||||||||
\(767\) | −5.96971 | −0.215554 | ||||||||
\(768\) | 0.100558 | 0.00362858 | ||||||||
\(769\) | −18.0939 | −0.652482 | −0.326241 | − | 0.945287i | \(-0.605782\pi\) | ||||
−0.326241 | + | 0.945287i | \(0.605782\pi\) | |||||||
\(770\) | 11.7629 | 0.423904 | ||||||||
\(771\) | 0.131654 | 0.00474141 | ||||||||
\(772\) | −19.0090 | −0.684149 | ||||||||
\(773\) | −27.4909 | −0.988781 | −0.494390 | − | 0.869240i | \(-0.664609\pi\) | ||||
−0.494390 | + | 0.869240i | \(0.664609\pi\) | |||||||
\(774\) | 25.3840 | 0.912409 | ||||||||
\(775\) | 2.91423 | 0.104682 | ||||||||
\(776\) | −17.8613 | −0.641183 | ||||||||
\(777\) | −2.14802 | −0.0770597 | ||||||||
\(778\) | −31.0290 | −1.11244 | ||||||||
\(779\) | 0.0525980 | 0.00188452 | ||||||||
\(780\) | −0.324452 | −0.0116172 | ||||||||
\(781\) | 44.7876 | 1.60263 | ||||||||
\(782\) | −10.4236 | −0.372748 | ||||||||
\(783\) | 0.930933 | 0.0332688 | ||||||||
\(784\) | −3.34239 | −0.119371 | ||||||||
\(785\) | −20.5090 | −0.731998 | ||||||||
\(786\) | −0.192987 | −0.00688362 | ||||||||
\(787\) | −5.79504 | −0.206571 | −0.103285 | − | 0.994652i | \(-0.532936\pi\) | ||||
−0.103285 | + | 0.994652i | \(0.532936\pi\) | |||||||
\(788\) | −11.1545 | −0.397364 | ||||||||
\(789\) | −0.374124 | −0.0133192 | ||||||||
\(790\) | 17.7744 | 0.632385 | ||||||||
\(791\) | 19.3775 | 0.688984 | ||||||||
\(792\) | −9.07442 | −0.322445 | ||||||||
\(793\) | −15.1629 | −0.538451 | ||||||||
\(794\) | −35.5304 | −1.26093 | ||||||||
\(795\) | −1.99168 | −0.0706376 | ||||||||
\(796\) | −25.3525 | −0.898595 | ||||||||
\(797\) | −22.7299 | −0.805136 | −0.402568 | − | 0.915390i | \(-0.631882\pi\) | ||||
−0.402568 | + | 0.915390i | \(0.631882\pi\) | |||||||
\(798\) | 0.192316 | 0.00680791 | ||||||||
\(799\) | 54.7920 | 1.93840 | ||||||||
\(800\) | 0.893223 | 0.0315802 | ||||||||
\(801\) | 38.1055 | 1.34639 | ||||||||
\(802\) | −2.06243 | −0.0728270 | ||||||||
\(803\) | −17.0478 | −0.601603 | ||||||||
\(804\) | 1.16890 | 0.0412240 | ||||||||
\(805\) | 8.36224 | 0.294730 | ||||||||
\(806\) | −5.19452 | −0.182969 | ||||||||
\(807\) | 0.162181 | 0.00570906 | ||||||||
\(808\) | 14.7941 | 0.520455 | ||||||||
\(809\) | 1.42641 | 0.0501499 | 0.0250750 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250750 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(810\) | −18.0544 | −0.634368 | ||||||||
\(811\) | −9.03760 | −0.317353 | −0.158677 | − | 0.987331i | \(-0.550723\pi\) | ||||
−0.158677 | + | 0.987331i | \(0.550723\pi\) | |||||||
\(812\) | −2.95584 | −0.103730 | ||||||||
\(813\) | −2.39783 | −0.0840955 | ||||||||
\(814\) | −33.8989 | −1.18816 | ||||||||
\(815\) | 3.05400 | 0.106977 | ||||||||
\(816\) | 0.485805 | 0.0170066 | ||||||||
\(817\) | −8.48995 | −0.297026 | ||||||||
\(818\) | 16.3714 | 0.572413 | ||||||||
\(819\) | 9.10408 | 0.318122 | ||||||||
\(820\) | −0.106591 | −0.00372231 | ||||||||
\(821\) | −29.3903 | −1.02573 | −0.512864 | − | 0.858470i | \(-0.671415\pi\) | ||||
−0.512864 | + | 0.858470i | \(0.671415\pi\) | |||||||
\(822\) | −0.0923074 | −0.00321959 | ||||||||
\(823\) | −1.10514 | −0.0385227 | −0.0192613 | − | 0.999814i | \(-0.506131\pi\) | ||||
−0.0192613 | + | 0.999814i | \(0.506131\pi\) | |||||||
\(824\) | 1.75592 | 0.0611704 | ||||||||
\(825\) | 0.272609 | 0.00949104 | ||||||||
\(826\) | −7.17082 | −0.249505 | ||||||||
\(827\) | 5.12870 | 0.178342 | 0.0891711 | − | 0.996016i | \(-0.471578\pi\) | ||||
0.0891711 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(828\) | −6.45102 | −0.224188 | ||||||||
\(829\) | −5.21821 | −0.181236 | −0.0906180 | − | 0.995886i | \(-0.528884\pi\) | ||||
−0.0906180 | + | 0.995886i | \(0.528884\pi\) | |||||||
\(830\) | 8.91936 | 0.309595 | ||||||||
\(831\) | 1.94895 | 0.0676082 | ||||||||
\(832\) | −1.59215 | −0.0551977 | ||||||||
\(833\) | −16.1474 | −0.559474 | ||||||||
\(834\) | −1.15291 | −0.0399221 | ||||||||
\(835\) | −35.0326 | −1.21235 | ||||||||
\(836\) | 3.03504 | 0.104969 | ||||||||
\(837\) | 1.96516 | 0.0679260 | ||||||||
\(838\) | −34.3311 | −1.18595 | ||||||||
\(839\) | 16.7022 | 0.576625 | 0.288312 | − | 0.957536i | \(-0.406906\pi\) | ||||
0.288312 | + | 0.957536i | \(0.406906\pi\) | |||||||
\(840\) | −0.389732 | −0.0134470 | ||||||||
\(841\) | −26.6113 | −0.917630 | ||||||||
\(842\) | 0.484634 | 0.0167016 | ||||||||
\(843\) | 2.50528 | 0.0862865 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −21.2077 | −0.729566 | ||||||||
\(846\) | 33.9099 | 1.16585 | ||||||||
\(847\) | −3.42060 | −0.117533 | ||||||||
\(848\) | −9.77354 | −0.335625 | ||||||||
\(849\) | 1.40250 | 0.0481338 | ||||||||
\(850\) | 4.31524 | 0.148012 | ||||||||
\(851\) | −24.0988 | −0.826097 | ||||||||
\(852\) | −1.48392 | −0.0508383 | ||||||||
\(853\) | 45.7580 | 1.56672 | 0.783362 | − | 0.621566i | \(-0.213503\pi\) | ||||
0.783362 | + | 0.621566i | \(0.213503\pi\) | |||||||
\(854\) | −18.2137 | −0.623260 | ||||||||
\(855\) | 6.05906 | 0.207216 | ||||||||
\(856\) | 13.3976 | 0.457921 | ||||||||
\(857\) | 32.0857 | 1.09603 | 0.548013 | − | 0.836470i | \(-0.315385\pi\) | ||||
0.548013 | + | 0.836470i | \(0.315385\pi\) | |||||||
\(858\) | −0.485919 | −0.0165890 | ||||||||
\(859\) | −12.9492 | −0.441822 | −0.220911 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220911 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(860\) | 17.2050 | 0.586687 | ||||||||
\(861\) | −0.0101154 | −0.000344733 0 | ||||||||
\(862\) | −39.1350 | −1.33294 | ||||||||
\(863\) | 18.9698 | 0.645740 | 0.322870 | − | 0.946443i | \(-0.395352\pi\) | ||||
0.322870 | + | 0.946443i | \(0.395352\pi\) | |||||||
\(864\) | 0.602332 | 0.0204917 | ||||||||
\(865\) | 31.7365 | 1.07907 | ||||||||
\(866\) | −8.60782 | −0.292506 | ||||||||
\(867\) | 0.637481 | 0.0216500 | ||||||||
\(868\) | −6.23967 | −0.211788 | ||||||||
\(869\) | 26.6200 | 0.903022 | ||||||||
\(870\) | 0.314956 | 0.0106780 | ||||||||
\(871\) | −18.5073 | −0.627097 | ||||||||
\(872\) | 6.12159 | 0.207303 | ||||||||
\(873\) | −53.4032 | −1.80743 | ||||||||
\(874\) | 2.15761 | 0.0729823 | ||||||||
\(875\) | −22.8403 | −0.772143 | ||||||||
\(876\) | 0.564834 | 0.0190840 | ||||||||
\(877\) | 9.83788 | 0.332202 | 0.166101 | − | 0.986109i | \(-0.446882\pi\) | ||||
0.166101 | + | 0.986109i | \(0.446882\pi\) | |||||||
\(878\) | 26.2639 | 0.886362 | ||||||||
\(879\) | 0.275696 | 0.00929900 | ||||||||
\(880\) | −6.15055 | −0.207335 | ||||||||
\(881\) | 38.5919 | 1.30019 | 0.650097 | − | 0.759851i | \(-0.274728\pi\) | ||||
0.650097 | + | 0.759851i | \(0.274728\pi\) | |||||||
\(882\) | −9.99338 | −0.336495 | ||||||||
\(883\) | 39.8138 | 1.33984 | 0.669920 | − | 0.742433i | \(-0.266328\pi\) | ||||
0.669920 | + | 0.742433i | \(0.266328\pi\) | |||||||
\(884\) | −7.69180 | −0.258703 | ||||||||
\(885\) | 0.764079 | 0.0256842 | ||||||||
\(886\) | −30.9679 | −1.04039 | ||||||||
\(887\) | 13.0985 | 0.439805 | 0.219902 | − | 0.975522i | \(-0.429426\pi\) | ||||
0.219902 | + | 0.975522i | \(0.429426\pi\) | |||||||
\(888\) | 1.12315 | 0.0376906 | ||||||||
\(889\) | −19.4437 | −0.652119 | ||||||||
\(890\) | 25.8276 | 0.865742 | ||||||||
\(891\) | −27.0394 | −0.905854 | ||||||||
\(892\) | 9.91371 | 0.331935 | ||||||||
\(893\) | −11.3415 | −0.379530 | ||||||||
\(894\) | 1.22132 | 0.0408472 | ||||||||
\(895\) | 18.2541 | 0.610167 | ||||||||
\(896\) | −1.91249 | −0.0638917 | ||||||||
\(897\) | −0.345440 | −0.0115339 | ||||||||
\(898\) | −5.98084 | −0.199583 | ||||||||
\(899\) | 5.04250 | 0.168177 | ||||||||
\(900\) | 2.67064 | 0.0890213 | ||||||||
\(901\) | −47.2169 | −1.57302 | ||||||||
\(902\) | −0.159637 | −0.00531532 | ||||||||
\(903\) | 1.63275 | 0.0543346 | ||||||||
\(904\) | −10.1321 | −0.336988 | ||||||||
\(905\) | −46.0137 | −1.52955 | ||||||||
\(906\) | 0.753082 | 0.0250195 | ||||||||
\(907\) | −42.6908 | −1.41753 | −0.708763 | − | 0.705447i | \(-0.750746\pi\) | ||||
−0.708763 | + | 0.705447i | \(0.750746\pi\) | |||||||
\(908\) | −12.3604 | −0.410194 | ||||||||
\(909\) | 44.2328 | 1.46711 | ||||||||
\(910\) | 6.17066 | 0.204555 | ||||||||
\(911\) | −24.0607 | −0.797168 | −0.398584 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398584 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(912\) | −0.100558 | −0.00332981 | ||||||||
\(913\) | 13.3582 | 0.442091 | ||||||||
\(914\) | 13.5583 | 0.448468 | ||||||||
\(915\) | 1.94074 | 0.0641589 | ||||||||
\(916\) | 7.65151 | 0.252813 | ||||||||
\(917\) | 3.67037 | 0.121206 | ||||||||
\(918\) | 2.90992 | 0.0960416 | ||||||||
\(919\) | −10.1936 | −0.336257 | −0.168128 | − | 0.985765i | \(-0.553772\pi\) | ||||
−0.168128 | + | 0.985765i | \(0.553772\pi\) | |||||||
\(920\) | −4.37244 | −0.144155 | ||||||||
\(921\) | 0.462118 | 0.0152273 | ||||||||
\(922\) | −4.14128 | −0.136386 | ||||||||
\(923\) | 23.4951 | 0.773349 | ||||||||
\(924\) | −0.583686 | −0.0192019 | ||||||||
\(925\) | 9.97660 | 0.328029 | ||||||||
\(926\) | 18.9491 | 0.622705 | ||||||||
\(927\) | 5.25000 | 0.172433 | ||||||||
\(928\) | 1.54555 | 0.0507351 | ||||||||
\(929\) | −38.2130 | −1.25373 | −0.626864 | − | 0.779129i | \(-0.715662\pi\) | ||||
−0.626864 | + | 0.779129i | \(0.715662\pi\) | |||||||
\(930\) | 0.664861 | 0.0218016 | ||||||||
\(931\) | 3.34239 | 0.109543 | ||||||||
\(932\) | 24.2147 | 0.793177 | ||||||||
\(933\) | −2.70866 | −0.0886775 | ||||||||
\(934\) | 16.8398 | 0.551017 | ||||||||
\(935\) | −29.7139 | −0.971748 | ||||||||
\(936\) | −4.76034 | −0.155596 | ||||||||
\(937\) | 38.7253 | 1.26510 | 0.632550 | − | 0.774520i | \(-0.282008\pi\) | ||||
0.632550 | + | 0.774520i | \(0.282008\pi\) | |||||||
\(938\) | −22.2310 | −0.725869 | ||||||||
\(939\) | −1.01635 | −0.0331674 | ||||||||
\(940\) | 22.9838 | 0.749650 | ||||||||
\(941\) | −5.42669 | −0.176905 | −0.0884525 | − | 0.996080i | \(-0.528192\pi\) | ||||
−0.0884525 | + | 0.996080i | \(0.528192\pi\) | |||||||
\(942\) | 1.01768 | 0.0331578 | ||||||||
\(943\) | −0.113486 | −0.00369561 | ||||||||
\(944\) | 3.74947 | 0.122035 | ||||||||
\(945\) | −2.33445 | −0.0759397 | ||||||||
\(946\) | 25.7673 | 0.837767 | ||||||||
\(947\) | 36.2026 | 1.17643 | 0.588213 | − | 0.808706i | \(-0.299832\pi\) | ||||
0.588213 | + | 0.808706i | \(0.299832\pi\) | |||||||
\(948\) | −0.881986 | −0.0286456 | ||||||||
\(949\) | −8.94307 | −0.290304 | ||||||||
\(950\) | −0.893223 | −0.0289800 | ||||||||
\(951\) | 2.20995 | 0.0716625 | ||||||||
\(952\) | −9.23940 | −0.299451 | ||||||||
\(953\) | −40.2095 | −1.30251 | −0.651257 | − | 0.758857i | \(-0.725758\pi\) | ||||
−0.651257 | + | 0.758857i | \(0.725758\pi\) | |||||||
\(954\) | −29.2218 | −0.946091 | ||||||||
\(955\) | −0.935313 | −0.0302660 | ||||||||
\(956\) | −27.6853 | −0.895406 | ||||||||
\(957\) | 0.471697 | 0.0152478 | ||||||||
\(958\) | 29.7128 | 0.959978 | ||||||||
\(959\) | 1.75557 | 0.0566903 | ||||||||
\(960\) | 0.203783 | 0.00657706 | ||||||||
\(961\) | −20.3555 | −0.656628 | ||||||||
\(962\) | −17.7830 | −0.573347 | ||||||||
\(963\) | 40.0574 | 1.29083 | ||||||||
\(964\) | 5.78747 | 0.186402 | ||||||||
\(965\) | −38.5221 | −1.24007 | ||||||||
\(966\) | −0.414944 | −0.0133506 | ||||||||
\(967\) | −23.4551 | −0.754264 | −0.377132 | − | 0.926160i | \(-0.623090\pi\) | ||||
−0.377132 | + | 0.926160i | \(0.623090\pi\) | |||||||
\(968\) | 1.78856 | 0.0574866 | ||||||||
\(969\) | −0.485805 | −0.0156063 | ||||||||
\(970\) | −36.1962 | −1.16219 | ||||||||
\(971\) | 3.10786 | 0.0997360 | 0.0498680 | − | 0.998756i | \(-0.484120\pi\) | ||||
0.0498680 | + | 0.998756i | \(0.484120\pi\) | |||||||
\(972\) | 2.70288 | 0.0866948 | ||||||||
\(973\) | 21.9269 | 0.702945 | ||||||||
\(974\) | 14.5662 | 0.466732 | ||||||||
\(975\) | 0.143008 | 0.00457992 | ||||||||
\(976\) | 9.52357 | 0.304842 | ||||||||
\(977\) | 21.0039 | 0.671973 | 0.335987 | − | 0.941867i | \(-0.390930\pi\) | ||||
0.335987 | + | 0.941867i | \(0.390930\pi\) | |||||||
\(978\) | −0.151543 | −0.00484582 | ||||||||
\(979\) | 38.6809 | 1.23625 | ||||||||
\(980\) | −6.77342 | −0.216369 | ||||||||
\(981\) | 18.3029 | 0.584366 | ||||||||
\(982\) | −30.5166 | −0.973823 | ||||||||
\(983\) | −55.7287 | −1.77747 | −0.888734 | − | 0.458423i | \(-0.848414\pi\) | ||||
−0.888734 | + | 0.458423i | \(0.848414\pi\) | |||||||
\(984\) | 0.00528915 | 0.000168612 0 | ||||||||
\(985\) | −22.6049 | −0.720251 | ||||||||
\(986\) | 7.46668 | 0.237788 | ||||||||
\(987\) | 2.18116 | 0.0694271 | ||||||||
\(988\) | 1.59215 | 0.0506529 | ||||||||
\(989\) | 18.3180 | 0.582479 | ||||||||
\(990\) | −18.3895 | −0.584456 | ||||||||
\(991\) | −12.2353 | −0.388667 | −0.194333 | − | 0.980936i | \(-0.562254\pi\) | ||||
−0.194333 | + | 0.980936i | \(0.562254\pi\) | |||||||
\(992\) | 3.26259 | 0.103587 | ||||||||
\(993\) | 1.15110 | 0.0365291 | ||||||||
\(994\) | 28.2223 | 0.895157 | ||||||||
\(995\) | −51.3773 | −1.62877 | ||||||||
\(996\) | −0.442588 | −0.0140240 | ||||||||
\(997\) | 34.5312 | 1.09361 | 0.546807 | − | 0.837259i | \(-0.315843\pi\) | ||||
0.546807 | + | 0.837259i | \(0.315843\pi\) | |||||||
\(998\) | 31.5212 | 0.997785 | ||||||||
\(999\) | 6.72757 | 0.212851 |
(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 | 8018.2.a.f.1.20 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.20 | ✓ | 34 | 1.1 | even | 1 | trivial |