Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, 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("6038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.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: | \(48.2136727404\) |
Analytic rank: | \(1\) |
Dimension: | \(57\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6038.1 |
$q$-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 | ||||||||
\(3\) | −1.71541 | −0.990394 | −0.495197 | − | 0.868781i | \(-0.664904\pi\) | ||||
−0.495197 | + | 0.868781i | \(0.664904\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.06645 | 0.476929 | 0.238465 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238465 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(6\) | 1.71541 | 0.700314 | ||||||||
\(7\) | 4.85447 | 1.83482 | 0.917408 | − | 0.397947i | \(-0.130277\pi\) | ||||
0.917408 | + | 0.397947i | \(0.130277\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.0573586 | −0.0191195 | ||||||||
\(10\) | −1.06645 | −0.337240 | ||||||||
\(11\) | −4.21829 | −1.27186 | −0.635931 | − | 0.771746i | \(-0.719384\pi\) | ||||
−0.635931 | + | 0.771746i | \(0.719384\pi\) | |||||||
\(12\) | −1.71541 | −0.495197 | ||||||||
\(13\) | −5.04666 | −1.39969 | −0.699845 | − | 0.714294i | \(-0.746748\pi\) | ||||
−0.699845 | + | 0.714294i | \(0.746748\pi\) | |||||||
\(14\) | −4.85447 | −1.29741 | ||||||||
\(15\) | −1.82940 | −0.472348 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.34566 | 1.29651 | 0.648257 | − | 0.761422i | \(-0.275498\pi\) | ||||
0.648257 | + | 0.761422i | \(0.275498\pi\) | |||||||
\(18\) | 0.0573586 | 0.0135196 | ||||||||
\(19\) | −0.676346 | −0.155164 | −0.0775822 | − | 0.996986i | \(-0.524720\pi\) | ||||
−0.0775822 | + | 0.996986i | \(0.524720\pi\) | |||||||
\(20\) | 1.06645 | 0.238465 | ||||||||
\(21\) | −8.32742 | −1.81719 | ||||||||
\(22\) | 4.21829 | 0.899342 | ||||||||
\(23\) | 0.753052 | 0.157022 | 0.0785111 | − | 0.996913i | \(-0.474983\pi\) | ||||
0.0785111 | + | 0.996913i | \(0.474983\pi\) | |||||||
\(24\) | 1.71541 | 0.350157 | ||||||||
\(25\) | −3.86269 | −0.772538 | ||||||||
\(26\) | 5.04666 | 0.989731 | ||||||||
\(27\) | 5.24463 | 1.00933 | ||||||||
\(28\) | 4.85447 | 0.917408 | ||||||||
\(29\) | −0.420186 | −0.0780267 | −0.0390133 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390133 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(30\) | 1.82940 | 0.334000 | ||||||||
\(31\) | −1.39465 | −0.250487 | −0.125244 | − | 0.992126i | \(-0.539971\pi\) | ||||
−0.125244 | + | 0.992126i | \(0.539971\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.23610 | 1.25964 | ||||||||
\(34\) | −5.34566 | −0.916773 | ||||||||
\(35\) | 5.17703 | 0.875078 | ||||||||
\(36\) | −0.0573586 | −0.00955977 | ||||||||
\(37\) | 3.97072 | 0.652782 | 0.326391 | − | 0.945235i | \(-0.394167\pi\) | ||||
0.326391 | + | 0.945235i | \(0.394167\pi\) | |||||||
\(38\) | 0.676346 | 0.109718 | ||||||||
\(39\) | 8.65710 | 1.38625 | ||||||||
\(40\) | −1.06645 | −0.168620 | ||||||||
\(41\) | −2.34182 | −0.365731 | −0.182866 | − | 0.983138i | \(-0.558537\pi\) | ||||
−0.182866 | + | 0.983138i | \(0.558537\pi\) | |||||||
\(42\) | 8.32742 | 1.28495 | ||||||||
\(43\) | −2.53027 | −0.385863 | −0.192932 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192932 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(44\) | −4.21829 | −0.635931 | ||||||||
\(45\) | −0.0611699 | −0.00911867 | ||||||||
\(46\) | −0.753052 | −0.111031 | ||||||||
\(47\) | 4.58870 | 0.669331 | 0.334666 | − | 0.942337i | \(-0.391377\pi\) | ||||
0.334666 | + | 0.942337i | \(0.391377\pi\) | |||||||
\(48\) | −1.71541 | −0.247599 | ||||||||
\(49\) | 16.5659 | 2.36655 | ||||||||
\(50\) | 3.86269 | 0.546267 | ||||||||
\(51\) | −9.17001 | −1.28406 | ||||||||
\(52\) | −5.04666 | −0.699845 | ||||||||
\(53\) | 9.68212 | 1.32994 | 0.664971 | − | 0.746869i | \(-0.268444\pi\) | ||||
0.664971 | + | 0.746869i | \(0.268444\pi\) | |||||||
\(54\) | −5.24463 | −0.713704 | ||||||||
\(55\) | −4.49858 | −0.606588 | ||||||||
\(56\) | −4.85447 | −0.648706 | ||||||||
\(57\) | 1.16021 | 0.153674 | ||||||||
\(58\) | 0.420186 | 0.0551732 | ||||||||
\(59\) | −1.30045 | −0.169305 | −0.0846523 | − | 0.996411i | \(-0.526978\pi\) | ||||
−0.0846523 | + | 0.996411i | \(0.526978\pi\) | |||||||
\(60\) | −1.82940 | −0.236174 | ||||||||
\(61\) | −5.12051 | −0.655614 | −0.327807 | − | 0.944745i | \(-0.606310\pi\) | ||||
−0.327807 | + | 0.944745i | \(0.606310\pi\) | |||||||
\(62\) | 1.39465 | 0.177121 | ||||||||
\(63\) | −0.278446 | −0.0350809 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.38199 | −0.667554 | ||||||||
\(66\) | −7.23610 | −0.890703 | ||||||||
\(67\) | −13.3698 | −1.63338 | −0.816692 | − | 0.577073i | \(-0.804195\pi\) | ||||
−0.816692 | + | 0.577073i | \(0.804195\pi\) | |||||||
\(68\) | 5.34566 | 0.648257 | ||||||||
\(69\) | −1.29180 | −0.155514 | ||||||||
\(70\) | −5.17703 | −0.618774 | ||||||||
\(71\) | −10.3650 | −1.23010 | −0.615050 | − | 0.788488i | \(-0.710864\pi\) | ||||
−0.615050 | + | 0.788488i | \(0.710864\pi\) | |||||||
\(72\) | 0.0573586 | 0.00675978 | ||||||||
\(73\) | −2.60917 | −0.305380 | −0.152690 | − | 0.988274i | \(-0.548794\pi\) | ||||
−0.152690 | + | 0.988274i | \(0.548794\pi\) | |||||||
\(74\) | −3.97072 | −0.461587 | ||||||||
\(75\) | 6.62611 | 0.765117 | ||||||||
\(76\) | −0.676346 | −0.0775822 | ||||||||
\(77\) | −20.4775 | −2.33363 | ||||||||
\(78\) | −8.65710 | −0.980224 | ||||||||
\(79\) | 5.09822 | 0.573594 | 0.286797 | − | 0.957991i | \(-0.407409\pi\) | ||||
0.286797 | + | 0.957991i | \(0.407409\pi\) | |||||||
\(80\) | 1.06645 | 0.119232 | ||||||||
\(81\) | −8.82463 | −0.980515 | ||||||||
\(82\) | 2.34182 | 0.258611 | ||||||||
\(83\) | 2.00273 | 0.219829 | 0.109914 | − | 0.993941i | \(-0.464942\pi\) | ||||
0.109914 | + | 0.993941i | \(0.464942\pi\) | |||||||
\(84\) | −8.32742 | −0.908596 | ||||||||
\(85\) | 5.70086 | 0.618345 | ||||||||
\(86\) | 2.53027 | 0.272846 | ||||||||
\(87\) | 0.720793 | 0.0772771 | ||||||||
\(88\) | 4.21829 | 0.449671 | ||||||||
\(89\) | −2.27995 | −0.241674 | −0.120837 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120837 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(90\) | 0.0611699 | 0.00644787 | ||||||||
\(91\) | −24.4988 | −2.56818 | ||||||||
\(92\) | 0.753052 | 0.0785111 | ||||||||
\(93\) | 2.39241 | 0.248081 | ||||||||
\(94\) | −4.58870 | −0.473289 | ||||||||
\(95\) | −0.721286 | −0.0740024 | ||||||||
\(96\) | 1.71541 | 0.175079 | ||||||||
\(97\) | 2.01635 | 0.204730 | 0.102365 | − | 0.994747i | \(-0.467359\pi\) | ||||
0.102365 | + | 0.994747i | \(0.467359\pi\) | |||||||
\(98\) | −16.5659 | −1.67341 | ||||||||
\(99\) | 0.241955 | 0.0243174 | ||||||||
\(100\) | −3.86269 | −0.386269 | ||||||||
\(101\) | −12.5909 | −1.25284 | −0.626419 | − | 0.779487i | \(-0.715480\pi\) | ||||
−0.626419 | + | 0.779487i | \(0.715480\pi\) | |||||||
\(102\) | 9.17001 | 0.907967 | ||||||||
\(103\) | 3.46163 | 0.341085 | 0.170542 | − | 0.985350i | \(-0.445448\pi\) | ||||
0.170542 | + | 0.985350i | \(0.445448\pi\) | |||||||
\(104\) | 5.04666 | 0.494865 | ||||||||
\(105\) | −8.88075 | −0.866672 | ||||||||
\(106\) | −9.68212 | −0.940411 | ||||||||
\(107\) | 5.76801 | 0.557614 | 0.278807 | − | 0.960347i | \(-0.410061\pi\) | ||||
0.278807 | + | 0.960347i | \(0.410061\pi\) | |||||||
\(108\) | 5.24463 | 0.504665 | ||||||||
\(109\) | −6.09862 | −0.584142 | −0.292071 | − | 0.956397i | \(-0.594344\pi\) | ||||
−0.292071 | + | 0.956397i | \(0.594344\pi\) | |||||||
\(110\) | 4.49858 | 0.428923 | ||||||||
\(111\) | −6.81142 | −0.646512 | ||||||||
\(112\) | 4.85447 | 0.458704 | ||||||||
\(113\) | 6.82556 | 0.642094 | 0.321047 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321047 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(114\) | −1.16021 | −0.108664 | ||||||||
\(115\) | 0.803090 | 0.0748885 | ||||||||
\(116\) | −0.420186 | −0.0390133 | ||||||||
\(117\) | 0.289469 | 0.0267614 | ||||||||
\(118\) | 1.30045 | 0.119716 | ||||||||
\(119\) | 25.9503 | 2.37886 | ||||||||
\(120\) | 1.82940 | 0.167000 | ||||||||
\(121\) | 6.79395 | 0.617632 | ||||||||
\(122\) | 5.12051 | 0.463589 | ||||||||
\(123\) | 4.01719 | 0.362218 | ||||||||
\(124\) | −1.39465 | −0.125244 | ||||||||
\(125\) | −9.45159 | −0.845376 | ||||||||
\(126\) | 0.278446 | 0.0248059 | ||||||||
\(127\) | 0.516288 | 0.0458132 | 0.0229066 | − | 0.999738i | \(-0.492708\pi\) | ||||
0.0229066 | + | 0.999738i | \(0.492708\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.34046 | 0.382157 | ||||||||
\(130\) | 5.38199 | 0.472032 | ||||||||
\(131\) | −5.82134 | −0.508613 | −0.254306 | − | 0.967124i | \(-0.581847\pi\) | ||||
−0.254306 | + | 0.967124i | \(0.581847\pi\) | |||||||
\(132\) | 7.23610 | 0.629822 | ||||||||
\(133\) | −3.28330 | −0.284698 | ||||||||
\(134\) | 13.3698 | 1.15498 | ||||||||
\(135\) | 5.59312 | 0.481379 | ||||||||
\(136\) | −5.34566 | −0.458387 | ||||||||
\(137\) | −15.3616 | −1.31243 | −0.656214 | − | 0.754575i | \(-0.727843\pi\) | ||||
−0.656214 | + | 0.754575i | \(0.727843\pi\) | |||||||
\(138\) | 1.29180 | 0.109965 | ||||||||
\(139\) | −5.49046 | −0.465695 | −0.232847 | − | 0.972513i | \(-0.574804\pi\) | ||||
−0.232847 | + | 0.972513i | \(0.574804\pi\) | |||||||
\(140\) | 5.17703 | 0.437539 | ||||||||
\(141\) | −7.87152 | −0.662901 | ||||||||
\(142\) | 10.3650 | 0.869811 | ||||||||
\(143\) | 21.2882 | 1.78021 | ||||||||
\(144\) | −0.0573586 | −0.00477989 | ||||||||
\(145\) | −0.448106 | −0.0372132 | ||||||||
\(146\) | 2.60917 | 0.215937 | ||||||||
\(147\) | −28.4173 | −2.34382 | ||||||||
\(148\) | 3.97072 | 0.326391 | ||||||||
\(149\) | −19.3454 | −1.58484 | −0.792419 | − | 0.609977i | \(-0.791179\pi\) | ||||
−0.792419 | + | 0.609977i | \(0.791179\pi\) | |||||||
\(150\) | −6.62611 | −0.541020 | ||||||||
\(151\) | −11.0070 | −0.895736 | −0.447868 | − | 0.894100i | \(-0.647817\pi\) | ||||
−0.447868 | + | 0.894100i | \(0.647817\pi\) | |||||||
\(152\) | 0.676346 | 0.0548589 | ||||||||
\(153\) | −0.306620 | −0.0247887 | ||||||||
\(154\) | 20.4775 | 1.65013 | ||||||||
\(155\) | −1.48732 | −0.119465 | ||||||||
\(156\) | 8.65710 | 0.693123 | ||||||||
\(157\) | 1.45541 | 0.116154 | 0.0580771 | − | 0.998312i | \(-0.481503\pi\) | ||||
0.0580771 | + | 0.998312i | \(0.481503\pi\) | |||||||
\(158\) | −5.09822 | −0.405592 | ||||||||
\(159\) | −16.6088 | −1.31717 | ||||||||
\(160\) | −1.06645 | −0.0843100 | ||||||||
\(161\) | 3.65567 | 0.288107 | ||||||||
\(162\) | 8.82463 | 0.693329 | ||||||||
\(163\) | −10.5625 | −0.827320 | −0.413660 | − | 0.910431i | \(-0.635750\pi\) | ||||
−0.413660 | + | 0.910431i | \(0.635750\pi\) | |||||||
\(164\) | −2.34182 | −0.182866 | ||||||||
\(165\) | 7.71692 | 0.600761 | ||||||||
\(166\) | −2.00273 | −0.155442 | ||||||||
\(167\) | 20.2343 | 1.56578 | 0.782890 | − | 0.622161i | \(-0.213745\pi\) | ||||
0.782890 | + | 0.622161i | \(0.213745\pi\) | |||||||
\(168\) | 8.32742 | 0.642474 | ||||||||
\(169\) | 12.4687 | 0.959134 | ||||||||
\(170\) | −5.70086 | −0.437236 | ||||||||
\(171\) | 0.0387943 | 0.00296667 | ||||||||
\(172\) | −2.53027 | −0.192932 | ||||||||
\(173\) | −6.68271 | −0.508077 | −0.254038 | − | 0.967194i | \(-0.581759\pi\) | ||||
−0.254038 | + | 0.967194i | \(0.581759\pi\) | |||||||
\(174\) | −0.720793 | −0.0546432 | ||||||||
\(175\) | −18.7513 | −1.41747 | ||||||||
\(176\) | −4.21829 | −0.317965 | ||||||||
\(177\) | 2.23081 | 0.167678 | ||||||||
\(178\) | 2.27995 | 0.170890 | ||||||||
\(179\) | 1.20167 | 0.0898170 | 0.0449085 | − | 0.998991i | \(-0.485700\pi\) | ||||
0.0449085 | + | 0.998991i | \(0.485700\pi\) | |||||||
\(180\) | −0.0611699 | −0.00455933 | ||||||||
\(181\) | 12.9017 | 0.958973 | 0.479486 | − | 0.877549i | \(-0.340823\pi\) | ||||
0.479486 | + | 0.877549i | \(0.340823\pi\) | |||||||
\(182\) | 24.4988 | 1.81597 | ||||||||
\(183\) | 8.78378 | 0.649316 | ||||||||
\(184\) | −0.753052 | −0.0555157 | ||||||||
\(185\) | 4.23456 | 0.311331 | ||||||||
\(186\) | −2.39241 | −0.175420 | ||||||||
\(187\) | −22.5495 | −1.64899 | ||||||||
\(188\) | 4.58870 | 0.334666 | ||||||||
\(189\) | 25.4599 | 1.85194 | ||||||||
\(190\) | 0.721286 | 0.0523276 | ||||||||
\(191\) | −3.79391 | −0.274518 | −0.137259 | − | 0.990535i | \(-0.543829\pi\) | ||||
−0.137259 | + | 0.990535i | \(0.543829\pi\) | |||||||
\(192\) | −1.71541 | −0.123799 | ||||||||
\(193\) | 4.03902 | 0.290735 | 0.145368 | − | 0.989378i | \(-0.453564\pi\) | ||||
0.145368 | + | 0.989378i | \(0.453564\pi\) | |||||||
\(194\) | −2.01635 | −0.144766 | ||||||||
\(195\) | 9.23233 | 0.661141 | ||||||||
\(196\) | 16.5659 | 1.18328 | ||||||||
\(197\) | 24.0088 | 1.71056 | 0.855278 | − | 0.518169i | \(-0.173386\pi\) | ||||
0.855278 | + | 0.518169i | \(0.173386\pi\) | |||||||
\(198\) | −0.241955 | −0.0171950 | ||||||||
\(199\) | −13.6434 | −0.967153 | −0.483577 | − | 0.875302i | \(-0.660663\pi\) | ||||
−0.483577 | + | 0.875302i | \(0.660663\pi\) | |||||||
\(200\) | 3.86269 | 0.273134 | ||||||||
\(201\) | 22.9348 | 1.61769 | ||||||||
\(202\) | 12.5909 | 0.885890 | ||||||||
\(203\) | −2.03978 | −0.143165 | ||||||||
\(204\) | −9.17001 | −0.642029 | ||||||||
\(205\) | −2.49743 | −0.174428 | ||||||||
\(206\) | −3.46163 | −0.241183 | ||||||||
\(207\) | −0.0431940 | −0.00300219 | ||||||||
\(208\) | −5.04666 | −0.349923 | ||||||||
\(209\) | 2.85302 | 0.197348 | ||||||||
\(210\) | 8.88075 | 0.612830 | ||||||||
\(211\) | 17.8142 | 1.22638 | 0.613189 | − | 0.789936i | \(-0.289886\pi\) | ||||
0.613189 | + | 0.789936i | \(0.289886\pi\) | |||||||
\(212\) | 9.68212 | 0.664971 | ||||||||
\(213\) | 17.7803 | 1.21828 | ||||||||
\(214\) | −5.76801 | −0.394293 | ||||||||
\(215\) | −2.69840 | −0.184029 | ||||||||
\(216\) | −5.24463 | −0.356852 | ||||||||
\(217\) | −6.77030 | −0.459598 | ||||||||
\(218\) | 6.09862 | 0.413051 | ||||||||
\(219\) | 4.47581 | 0.302447 | ||||||||
\(220\) | −4.49858 | −0.303294 | ||||||||
\(221\) | −26.9777 | −1.81472 | ||||||||
\(222\) | 6.81142 | 0.457153 | ||||||||
\(223\) | 0.669557 | 0.0448369 | 0.0224184 | − | 0.999749i | \(-0.492863\pi\) | ||||
0.0224184 | + | 0.999749i | \(0.492863\pi\) | |||||||
\(224\) | −4.85447 | −0.324353 | ||||||||
\(225\) | 0.221559 | 0.0147706 | ||||||||
\(226\) | −6.82556 | −0.454029 | ||||||||
\(227\) | −2.56221 | −0.170060 | −0.0850301 | − | 0.996378i | \(-0.527099\pi\) | ||||
−0.0850301 | + | 0.996378i | \(0.527099\pi\) | |||||||
\(228\) | 1.16021 | 0.0768369 | ||||||||
\(229\) | −17.6117 | −1.16381 | −0.581907 | − | 0.813255i | \(-0.697693\pi\) | ||||
−0.581907 | + | 0.813255i | \(0.697693\pi\) | |||||||
\(230\) | −0.803090 | −0.0529542 | ||||||||
\(231\) | 35.1274 | 2.31122 | ||||||||
\(232\) | 0.420186 | 0.0275866 | ||||||||
\(233\) | −6.50828 | −0.426372 | −0.213186 | − | 0.977012i | \(-0.568384\pi\) | ||||
−0.213186 | + | 0.977012i | \(0.568384\pi\) | |||||||
\(234\) | −0.289469 | −0.0189232 | ||||||||
\(235\) | 4.89361 | 0.319224 | ||||||||
\(236\) | −1.30045 | −0.0846523 | ||||||||
\(237\) | −8.74555 | −0.568084 | ||||||||
\(238\) | −25.9503 | −1.68211 | ||||||||
\(239\) | −16.0562 | −1.03859 | −0.519296 | − | 0.854594i | \(-0.673806\pi\) | ||||
−0.519296 | + | 0.854594i | \(0.673806\pi\) | |||||||
\(240\) | −1.82940 | −0.118087 | ||||||||
\(241\) | 2.88780 | 0.186020 | 0.0930099 | − | 0.995665i | \(-0.470351\pi\) | ||||
0.0930099 | + | 0.995665i | \(0.470351\pi\) | |||||||
\(242\) | −6.79395 | −0.436732 | ||||||||
\(243\) | −0.596006 | −0.0382338 | ||||||||
\(244\) | −5.12051 | −0.327807 | ||||||||
\(245\) | 17.6666 | 1.12868 | ||||||||
\(246\) | −4.01719 | −0.256127 | ||||||||
\(247\) | 3.41328 | 0.217182 | ||||||||
\(248\) | 1.39465 | 0.0885606 | ||||||||
\(249\) | −3.43551 | −0.217717 | ||||||||
\(250\) | 9.45159 | 0.597771 | ||||||||
\(251\) | 20.4942 | 1.29358 | 0.646791 | − | 0.762667i | \(-0.276111\pi\) | ||||
0.646791 | + | 0.762667i | \(0.276111\pi\) | |||||||
\(252\) | −0.278446 | −0.0175404 | ||||||||
\(253\) | −3.17659 | −0.199711 | ||||||||
\(254\) | −0.516288 | −0.0323948 | ||||||||
\(255\) | −9.77933 | −0.612405 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.0589 | 1.68789 | 0.843943 | − | 0.536433i | \(-0.180229\pi\) | ||||
0.843943 | + | 0.536433i | \(0.180229\pi\) | |||||||
\(258\) | −4.34046 | −0.270225 | ||||||||
\(259\) | 19.2757 | 1.19774 | ||||||||
\(260\) | −5.38199 | −0.333777 | ||||||||
\(261\) | 0.0241013 | 0.00149183 | ||||||||
\(262\) | 5.82134 | 0.359644 | ||||||||
\(263\) | 13.8185 | 0.852083 | 0.426041 | − | 0.904704i | \(-0.359908\pi\) | ||||
0.426041 | + | 0.904704i | \(0.359908\pi\) | |||||||
\(264\) | −7.23610 | −0.445351 | ||||||||
\(265\) | 10.3255 | 0.634288 | ||||||||
\(266\) | 3.28330 | 0.201312 | ||||||||
\(267\) | 3.91106 | 0.239353 | ||||||||
\(268\) | −13.3698 | −0.816692 | ||||||||
\(269\) | 12.2615 | 0.747599 | 0.373799 | − | 0.927510i | \(-0.378055\pi\) | ||||
0.373799 | + | 0.927510i | \(0.378055\pi\) | |||||||
\(270\) | −5.59312 | −0.340386 | ||||||||
\(271\) | −25.3154 | −1.53780 | −0.768900 | − | 0.639368i | \(-0.779196\pi\) | ||||
−0.768900 | + | 0.639368i | \(0.779196\pi\) | |||||||
\(272\) | 5.34566 | 0.324128 | ||||||||
\(273\) | 42.0256 | 2.54351 | ||||||||
\(274\) | 15.3616 | 0.928027 | ||||||||
\(275\) | 16.2939 | 0.982562 | ||||||||
\(276\) | −1.29180 | −0.0777570 | ||||||||
\(277\) | −20.8507 | −1.25280 | −0.626400 | − | 0.779502i | \(-0.715472\pi\) | ||||
−0.626400 | + | 0.779502i | \(0.715472\pi\) | |||||||
\(278\) | 5.49046 | 0.329296 | ||||||||
\(279\) | 0.0799954 | 0.00478920 | ||||||||
\(280\) | −5.17703 | −0.309387 | ||||||||
\(281\) | 10.1921 | 0.608007 | 0.304003 | − | 0.952671i | \(-0.401677\pi\) | ||||
0.304003 | + | 0.952671i | \(0.401677\pi\) | |||||||
\(282\) | 7.87152 | 0.468742 | ||||||||
\(283\) | 19.4740 | 1.15761 | 0.578805 | − | 0.815466i | \(-0.303519\pi\) | ||||
0.578805 | + | 0.815466i | \(0.303519\pi\) | |||||||
\(284\) | −10.3650 | −0.615050 | ||||||||
\(285\) | 1.23730 | 0.0732916 | ||||||||
\(286\) | −21.2882 | −1.25880 | ||||||||
\(287\) | −11.3683 | −0.671050 | ||||||||
\(288\) | 0.0573586 | 0.00337989 | ||||||||
\(289\) | 11.5761 | 0.680946 | ||||||||
\(290\) | 0.448106 | 0.0263137 | ||||||||
\(291\) | −3.45888 | −0.202763 | ||||||||
\(292\) | −2.60917 | −0.152690 | ||||||||
\(293\) | 7.93518 | 0.463578 | 0.231789 | − | 0.972766i | \(-0.425542\pi\) | ||||
0.231789 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(294\) | 28.4173 | 1.65733 | ||||||||
\(295\) | −1.38686 | −0.0807463 | ||||||||
\(296\) | −3.97072 | −0.230793 | ||||||||
\(297\) | −22.1234 | −1.28373 | ||||||||
\(298\) | 19.3454 | 1.12065 | ||||||||
\(299\) | −3.80040 | −0.219783 | ||||||||
\(300\) | 6.62611 | 0.382559 | ||||||||
\(301\) | −12.2831 | −0.707988 | ||||||||
\(302\) | 11.0070 | 0.633381 | ||||||||
\(303\) | 21.5985 | 1.24080 | ||||||||
\(304\) | −0.676346 | −0.0387911 | ||||||||
\(305\) | −5.46075 | −0.312681 | ||||||||
\(306\) | 0.306620 | 0.0175283 | ||||||||
\(307\) | −30.0031 | −1.71236 | −0.856182 | − | 0.516674i | \(-0.827170\pi\) | ||||
−0.856182 | + | 0.516674i | \(0.827170\pi\) | |||||||
\(308\) | −20.4775 | −1.16682 | ||||||||
\(309\) | −5.93813 | −0.337808 | ||||||||
\(310\) | 1.48732 | 0.0844743 | ||||||||
\(311\) | 1.96136 | 0.111219 | 0.0556093 | − | 0.998453i | \(-0.482290\pi\) | ||||
0.0556093 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(312\) | −8.65710 | −0.490112 | ||||||||
\(313\) | −12.3828 | −0.699917 | −0.349958 | − | 0.936765i | \(-0.613804\pi\) | ||||
−0.349958 | + | 0.936765i | \(0.613804\pi\) | |||||||
\(314\) | −1.45541 | −0.0821335 | ||||||||
\(315\) | −0.296947 | −0.0167311 | ||||||||
\(316\) | 5.09822 | 0.286797 | ||||||||
\(317\) | −18.8305 | −1.05763 | −0.528814 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528814 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(318\) | 16.6088 | 0.931377 | ||||||||
\(319\) | 1.77247 | 0.0992391 | ||||||||
\(320\) | 1.06645 | 0.0596162 | ||||||||
\(321\) | −9.89451 | −0.552258 | ||||||||
\(322\) | −3.65567 | −0.203722 | ||||||||
\(323\) | −3.61551 | −0.201173 | ||||||||
\(324\) | −8.82463 | −0.490257 | ||||||||
\(325\) | 19.4937 | 1.08131 | ||||||||
\(326\) | 10.5625 | 0.585003 | ||||||||
\(327\) | 10.4617 | 0.578531 | ||||||||
\(328\) | 2.34182 | 0.129306 | ||||||||
\(329\) | 22.2757 | 1.22810 | ||||||||
\(330\) | −7.71692 | −0.424802 | ||||||||
\(331\) | −14.2211 | −0.781660 | −0.390830 | − | 0.920463i | \(-0.627812\pi\) | ||||
−0.390830 | + | 0.920463i | \(0.627812\pi\) | |||||||
\(332\) | 2.00273 | 0.109914 | ||||||||
\(333\) | −0.227755 | −0.0124809 | ||||||||
\(334\) | −20.2343 | −1.10717 | ||||||||
\(335\) | −14.2582 | −0.779009 | ||||||||
\(336\) | −8.32742 | −0.454298 | ||||||||
\(337\) | −33.4181 | −1.82040 | −0.910200 | − | 0.414168i | \(-0.864073\pi\) | ||||
−0.910200 | + | 0.414168i | \(0.864073\pi\) | |||||||
\(338\) | −12.4687 | −0.678210 | ||||||||
\(339\) | −11.7086 | −0.635926 | ||||||||
\(340\) | 5.70086 | 0.309173 | ||||||||
\(341\) | 5.88305 | 0.318585 | ||||||||
\(342\) | −0.0387943 | −0.00209775 | ||||||||
\(343\) | 46.4372 | 2.50737 | ||||||||
\(344\) | 2.53027 | 0.136423 | ||||||||
\(345\) | −1.37763 | −0.0741691 | ||||||||
\(346\) | 6.68271 | 0.359265 | ||||||||
\(347\) | −23.5597 | −1.26475 | −0.632375 | − | 0.774662i | \(-0.717920\pi\) | ||||
−0.632375 | + | 0.774662i | \(0.717920\pi\) | |||||||
\(348\) | 0.720793 | 0.0386386 | ||||||||
\(349\) | −6.89121 | −0.368878 | −0.184439 | − | 0.982844i | \(-0.559047\pi\) | ||||
−0.184439 | + | 0.982844i | \(0.559047\pi\) | |||||||
\(350\) | 18.7513 | 1.00230 | ||||||||
\(351\) | −26.4679 | −1.41275 | ||||||||
\(352\) | 4.21829 | 0.224835 | ||||||||
\(353\) | −0.682518 | −0.0363268 | −0.0181634 | − | 0.999835i | \(-0.505782\pi\) | ||||
−0.0181634 | + | 0.999835i | \(0.505782\pi\) | |||||||
\(354\) | −2.23081 | −0.118566 | ||||||||
\(355\) | −11.0537 | −0.586670 | ||||||||
\(356\) | −2.27995 | −0.120837 | ||||||||
\(357\) | −44.5155 | −2.35601 | ||||||||
\(358\) | −1.20167 | −0.0635102 | ||||||||
\(359\) | 30.7878 | 1.62492 | 0.812458 | − | 0.583019i | \(-0.198129\pi\) | ||||
0.812458 | + | 0.583019i | \(0.198129\pi\) | |||||||
\(360\) | 0.0611699 | 0.00322394 | ||||||||
\(361\) | −18.5426 | −0.975924 | ||||||||
\(362\) | −12.9017 | −0.678096 | ||||||||
\(363\) | −11.6544 | −0.611699 | ||||||||
\(364\) | −24.4988 | −1.28409 | ||||||||
\(365\) | −2.78254 | −0.145645 | ||||||||
\(366\) | −8.78378 | −0.459136 | ||||||||
\(367\) | −28.0131 | −1.46227 | −0.731137 | − | 0.682231i | \(-0.761010\pi\) | ||||
−0.731137 | + | 0.682231i | \(0.761010\pi\) | |||||||
\(368\) | 0.753052 | 0.0392556 | ||||||||
\(369\) | 0.134324 | 0.00699261 | ||||||||
\(370\) | −4.23456 | −0.220144 | ||||||||
\(371\) | 47.0016 | 2.44020 | ||||||||
\(372\) | 2.39241 | 0.124041 | ||||||||
\(373\) | 9.91937 | 0.513605 | 0.256803 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256803 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(374\) | 22.5495 | 1.16601 | ||||||||
\(375\) | 16.2134 | 0.837255 | ||||||||
\(376\) | −4.58870 | −0.236644 | ||||||||
\(377\) | 2.12054 | 0.109213 | ||||||||
\(378\) | −25.4599 | −1.30952 | ||||||||
\(379\) | −10.7029 | −0.549772 | −0.274886 | − | 0.961477i | \(-0.588640\pi\) | ||||
−0.274886 | + | 0.961477i | \(0.588640\pi\) | |||||||
\(380\) | −0.721286 | −0.0370012 | ||||||||
\(381\) | −0.885647 | −0.0453731 | ||||||||
\(382\) | 3.79391 | 0.194113 | ||||||||
\(383\) | −14.6152 | −0.746803 | −0.373401 | − | 0.927670i | \(-0.621809\pi\) | ||||
−0.373401 | + | 0.927670i | \(0.621809\pi\) | |||||||
\(384\) | 1.71541 | 0.0875393 | ||||||||
\(385\) | −21.8382 | −1.11298 | ||||||||
\(386\) | −4.03902 | −0.205581 | ||||||||
\(387\) | 0.145133 | 0.00737753 | ||||||||
\(388\) | 2.01635 | 0.102365 | ||||||||
\(389\) | −28.0460 | −1.42199 | −0.710995 | − | 0.703197i | \(-0.751755\pi\) | ||||
−0.710995 | + | 0.703197i | \(0.751755\pi\) | |||||||
\(390\) | −9.23233 | −0.467497 | ||||||||
\(391\) | 4.02556 | 0.203581 | ||||||||
\(392\) | −16.5659 | −0.836703 | ||||||||
\(393\) | 9.98600 | 0.503727 | ||||||||
\(394\) | −24.0088 | −1.20955 | ||||||||
\(395\) | 5.43698 | 0.273564 | ||||||||
\(396\) | 0.241955 | 0.0121587 | ||||||||
\(397\) | −19.2393 | −0.965595 | −0.482797 | − | 0.875732i | \(-0.660379\pi\) | ||||
−0.482797 | + | 0.875732i | \(0.660379\pi\) | |||||||
\(398\) | 13.6434 | 0.683881 | ||||||||
\(399\) | 5.63221 | 0.281963 | ||||||||
\(400\) | −3.86269 | −0.193135 | ||||||||
\(401\) | −30.6769 | −1.53193 | −0.765965 | − | 0.642882i | \(-0.777738\pi\) | ||||
−0.765965 | + | 0.642882i | \(0.777738\pi\) | |||||||
\(402\) | −22.9348 | −1.14388 | ||||||||
\(403\) | 7.03834 | 0.350605 | ||||||||
\(404\) | −12.5909 | −0.626419 | ||||||||
\(405\) | −9.41100 | −0.467636 | ||||||||
\(406\) | 2.03978 | 0.101233 | ||||||||
\(407\) | −16.7496 | −0.830249 | ||||||||
\(408\) | 9.17001 | 0.453983 | ||||||||
\(409\) | 2.90316 | 0.143552 | 0.0717760 | − | 0.997421i | \(-0.477133\pi\) | ||||
0.0717760 | + | 0.997421i | \(0.477133\pi\) | |||||||
\(410\) | 2.49743 | 0.123339 | ||||||||
\(411\) | 26.3515 | 1.29982 | ||||||||
\(412\) | 3.46163 | 0.170542 | ||||||||
\(413\) | −6.31301 | −0.310643 | ||||||||
\(414\) | 0.0431940 | 0.00212287 | ||||||||
\(415\) | 2.13581 | 0.104843 | ||||||||
\(416\) | 5.04666 | 0.247433 | ||||||||
\(417\) | 9.41841 | 0.461222 | ||||||||
\(418\) | −2.85302 | −0.139546 | ||||||||
\(419\) | 23.3752 | 1.14196 | 0.570978 | − | 0.820966i | \(-0.306564\pi\) | ||||
0.570978 | + | 0.820966i | \(0.306564\pi\) | |||||||
\(420\) | −8.88075 | −0.433336 | ||||||||
\(421\) | −10.5146 | −0.512448 | −0.256224 | − | 0.966617i | \(-0.582478\pi\) | ||||
−0.256224 | + | 0.966617i | \(0.582478\pi\) | |||||||
\(422\) | −17.8142 | −0.867180 | ||||||||
\(423\) | −0.263202 | −0.0127973 | ||||||||
\(424\) | −9.68212 | −0.470205 | ||||||||
\(425\) | −20.6486 | −1.00161 | ||||||||
\(426\) | −17.7803 | −0.861456 | ||||||||
\(427\) | −24.8573 | −1.20293 | ||||||||
\(428\) | 5.76801 | 0.278807 | ||||||||
\(429\) | −36.5181 | −1.76311 | ||||||||
\(430\) | 2.69840 | 0.130128 | ||||||||
\(431\) | 28.1981 | 1.35826 | 0.679128 | − | 0.734020i | \(-0.262358\pi\) | ||||
0.679128 | + | 0.734020i | \(0.262358\pi\) | |||||||
\(432\) | 5.24463 | 0.252332 | ||||||||
\(433\) | −17.3077 | −0.831757 | −0.415879 | − | 0.909420i | \(-0.636526\pi\) | ||||
−0.415879 | + | 0.909420i | \(0.636526\pi\) | |||||||
\(434\) | 6.77030 | 0.324985 | ||||||||
\(435\) | 0.768687 | 0.0368557 | ||||||||
\(436\) | −6.09862 | −0.292071 | ||||||||
\(437\) | −0.509324 | −0.0243643 | ||||||||
\(438\) | −4.47581 | −0.213862 | ||||||||
\(439\) | −29.3119 | −1.39898 | −0.699490 | − | 0.714643i | \(-0.746589\pi\) | ||||
−0.699490 | + | 0.714643i | \(0.746589\pi\) | |||||||
\(440\) | 4.49858 | 0.214461 | ||||||||
\(441\) | −0.950195 | −0.0452474 | ||||||||
\(442\) | 26.9777 | 1.28320 | ||||||||
\(443\) | 6.42674 | 0.305344 | 0.152672 | − | 0.988277i | \(-0.451212\pi\) | ||||
0.152672 | + | 0.988277i | \(0.451212\pi\) | |||||||
\(444\) | −6.81142 | −0.323256 | ||||||||
\(445\) | −2.43145 | −0.115262 | ||||||||
\(446\) | −0.669557 | −0.0317045 | ||||||||
\(447\) | 33.1854 | 1.56962 | ||||||||
\(448\) | 4.85447 | 0.229352 | ||||||||
\(449\) | −18.8315 | −0.888715 | −0.444358 | − | 0.895849i | \(-0.646568\pi\) | ||||
−0.444358 | + | 0.895849i | \(0.646568\pi\) | |||||||
\(450\) | −0.221559 | −0.0104444 | ||||||||
\(451\) | 9.87848 | 0.465159 | ||||||||
\(452\) | 6.82556 | 0.321047 | ||||||||
\(453\) | 18.8815 | 0.887132 | ||||||||
\(454\) | 2.56221 | 0.120251 | ||||||||
\(455\) | −26.1267 | −1.22484 | ||||||||
\(456\) | −1.16021 | −0.0543319 | ||||||||
\(457\) | −15.4594 | −0.723162 | −0.361581 | − | 0.932341i | \(-0.617763\pi\) | ||||
−0.361581 | + | 0.932341i | \(0.617763\pi\) | |||||||
\(458\) | 17.6117 | 0.822941 | ||||||||
\(459\) | 28.0360 | 1.30861 | ||||||||
\(460\) | 0.803090 | 0.0374443 | ||||||||
\(461\) | −25.4778 | −1.18662 | −0.593309 | − | 0.804975i | \(-0.702179\pi\) | ||||
−0.593309 | + | 0.804975i | \(0.702179\pi\) | |||||||
\(462\) | −35.1274 | −1.63428 | ||||||||
\(463\) | 4.48763 | 0.208558 | 0.104279 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104279 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(464\) | −0.420186 | −0.0195067 | ||||||||
\(465\) | 2.55137 | 0.118317 | ||||||||
\(466\) | 6.50828 | 0.301490 | ||||||||
\(467\) | −7.61059 | −0.352176 | −0.176088 | − | 0.984374i | \(-0.556344\pi\) | ||||
−0.176088 | + | 0.984374i | \(0.556344\pi\) | |||||||
\(468\) | 0.289469 | 0.0133807 | ||||||||
\(469\) | −64.9034 | −2.99696 | ||||||||
\(470\) | −4.89361 | −0.225725 | ||||||||
\(471\) | −2.49663 | −0.115038 | ||||||||
\(472\) | 1.30045 | 0.0598582 | ||||||||
\(473\) | 10.6734 | 0.490764 | ||||||||
\(474\) | 8.74555 | 0.401696 | ||||||||
\(475\) | 2.61252 | 0.119870 | ||||||||
\(476\) | 25.9503 | 1.18943 | ||||||||
\(477\) | −0.555353 | −0.0254279 | ||||||||
\(478\) | 16.0562 | 0.734396 | ||||||||
\(479\) | −2.50044 | −0.114248 | −0.0571240 | − | 0.998367i | \(-0.518193\pi\) | ||||
−0.0571240 | + | 0.998367i | \(0.518193\pi\) | |||||||
\(480\) | 1.82940 | 0.0835001 | ||||||||
\(481\) | −20.0389 | −0.913693 | ||||||||
\(482\) | −2.88780 | −0.131536 | ||||||||
\(483\) | −6.27098 | −0.285340 | ||||||||
\(484\) | 6.79395 | 0.308816 | ||||||||
\(485\) | 2.15033 | 0.0976415 | ||||||||
\(486\) | 0.596006 | 0.0270354 | ||||||||
\(487\) | −5.05372 | −0.229006 | −0.114503 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114503 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(488\) | 5.12051 | 0.231794 | ||||||||
\(489\) | 18.1191 | 0.819373 | ||||||||
\(490\) | −17.6666 | −0.798096 | ||||||||
\(491\) | −25.8437 | −1.16631 | −0.583155 | − | 0.812361i | \(-0.698182\pi\) | ||||
−0.583155 | + | 0.812361i | \(0.698182\pi\) | |||||||
\(492\) | 4.01719 | 0.181109 | ||||||||
\(493\) | −2.24617 | −0.101163 | ||||||||
\(494\) | −3.41328 | −0.153571 | ||||||||
\(495\) | 0.258032 | 0.0115977 | ||||||||
\(496\) | −1.39465 | −0.0626218 | ||||||||
\(497\) | −50.3166 | −2.25701 | ||||||||
\(498\) | 3.43551 | 0.153949 | ||||||||
\(499\) | −19.1158 | −0.855742 | −0.427871 | − | 0.903840i | \(-0.640736\pi\) | ||||
−0.427871 | + | 0.903840i | \(0.640736\pi\) | |||||||
\(500\) | −9.45159 | −0.422688 | ||||||||
\(501\) | −34.7102 | −1.55074 | ||||||||
\(502\) | −20.4942 | −0.914701 | ||||||||
\(503\) | 13.1739 | 0.587395 | 0.293697 | − | 0.955898i | \(-0.405114\pi\) | ||||
0.293697 | + | 0.955898i | \(0.405114\pi\) | |||||||
\(504\) | 0.278446 | 0.0124030 | ||||||||
\(505\) | −13.4275 | −0.597515 | ||||||||
\(506\) | 3.17659 | 0.141217 | ||||||||
\(507\) | −21.3890 | −0.949921 | ||||||||
\(508\) | 0.516288 | 0.0229066 | ||||||||
\(509\) | −11.4676 | −0.508292 | −0.254146 | − | 0.967166i | \(-0.581794\pi\) | ||||
−0.254146 | + | 0.967166i | \(0.581794\pi\) | |||||||
\(510\) | 9.77933 | 0.433036 | ||||||||
\(511\) | −12.6661 | −0.560317 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.54718 | −0.156612 | ||||||||
\(514\) | −27.0589 | −1.19352 | ||||||||
\(515\) | 3.69164 | 0.162673 | ||||||||
\(516\) | 4.34046 | 0.191078 | ||||||||
\(517\) | −19.3565 | −0.851296 | ||||||||
\(518\) | −19.2757 | −0.846927 | ||||||||
\(519\) | 11.4636 | 0.503196 | ||||||||
\(520\) | 5.38199 | 0.236016 | ||||||||
\(521\) | 26.1402 | 1.14522 | 0.572611 | − | 0.819827i | \(-0.305930\pi\) | ||||
0.572611 | + | 0.819827i | \(0.305930\pi\) | |||||||
\(522\) | −0.0241013 | −0.00105489 | ||||||||
\(523\) | −4.93397 | −0.215747 | −0.107874 | − | 0.994165i | \(-0.534404\pi\) | ||||
−0.107874 | + | 0.994165i | \(0.534404\pi\) | |||||||
\(524\) | −5.82134 | −0.254306 | ||||||||
\(525\) | 32.1663 | 1.40385 | ||||||||
\(526\) | −13.8185 | −0.602514 | ||||||||
\(527\) | −7.45534 | −0.324760 | ||||||||
\(528\) | 7.23610 | 0.314911 | ||||||||
\(529\) | −22.4329 | −0.975344 | ||||||||
\(530\) | −10.3255 | −0.448509 | ||||||||
\(531\) | 0.0745922 | 0.00323702 | ||||||||
\(532\) | −3.28330 | −0.142349 | ||||||||
\(533\) | 11.8184 | 0.511911 | ||||||||
\(534\) | −3.91106 | −0.169248 | ||||||||
\(535\) | 6.15127 | 0.265943 | ||||||||
\(536\) | 13.3698 | 0.577489 | ||||||||
\(537\) | −2.06136 | −0.0889543 | ||||||||
\(538\) | −12.2615 | −0.528632 | ||||||||
\(539\) | −69.8796 | −3.00993 | ||||||||
\(540\) | 5.59312 | 0.240690 | ||||||||
\(541\) | −29.5794 | −1.27172 | −0.635860 | − | 0.771805i | \(-0.719354\pi\) | ||||
−0.635860 | + | 0.771805i | \(0.719354\pi\) | |||||||
\(542\) | 25.3154 | 1.08739 | ||||||||
\(543\) | −22.1317 | −0.949761 | ||||||||
\(544\) | −5.34566 | −0.229193 | ||||||||
\(545\) | −6.50386 | −0.278595 | ||||||||
\(546\) | −42.0256 | −1.79853 | ||||||||
\(547\) | 11.7861 | 0.503936 | 0.251968 | − | 0.967736i | \(-0.418922\pi\) | ||||
0.251968 | + | 0.967736i | \(0.418922\pi\) | |||||||
\(548\) | −15.3616 | −0.656214 | ||||||||
\(549\) | 0.293705 | 0.0125350 | ||||||||
\(550\) | −16.2939 | −0.694776 | ||||||||
\(551\) | 0.284191 | 0.0121070 | ||||||||
\(552\) | 1.29180 | 0.0549825 | ||||||||
\(553\) | 24.7491 | 1.05244 | ||||||||
\(554\) | 20.8507 | 0.885863 | ||||||||
\(555\) | −7.26402 | −0.308340 | ||||||||
\(556\) | −5.49046 | −0.232847 | ||||||||
\(557\) | −19.8784 | −0.842276 | −0.421138 | − | 0.906997i | \(-0.638369\pi\) | ||||
−0.421138 | + | 0.906997i | \(0.638369\pi\) | |||||||
\(558\) | −0.0799954 | −0.00338648 | ||||||||
\(559\) | 12.7694 | 0.540089 | ||||||||
\(560\) | 5.17703 | 0.218769 | ||||||||
\(561\) | 38.6818 | 1.63315 | ||||||||
\(562\) | −10.1921 | −0.429926 | ||||||||
\(563\) | 16.5885 | 0.699123 | 0.349562 | − | 0.936913i | \(-0.386331\pi\) | ||||
0.349562 | + | 0.936913i | \(0.386331\pi\) | |||||||
\(564\) | −7.87152 | −0.331451 | ||||||||
\(565\) | 7.27909 | 0.306234 | ||||||||
\(566\) | −19.4740 | −0.818553 | ||||||||
\(567\) | −42.8389 | −1.79907 | ||||||||
\(568\) | 10.3650 | 0.434906 | ||||||||
\(569\) | 19.3599 | 0.811607 | 0.405804 | − | 0.913960i | \(-0.366992\pi\) | ||||
0.405804 | + | 0.913960i | \(0.366992\pi\) | |||||||
\(570\) | −1.23730 | −0.0518250 | ||||||||
\(571\) | 38.8137 | 1.62430 | 0.812151 | − | 0.583447i | \(-0.198296\pi\) | ||||
0.812151 | + | 0.583447i | \(0.198296\pi\) | |||||||
\(572\) | 21.2882 | 0.890106 | ||||||||
\(573\) | 6.50812 | 0.271881 | ||||||||
\(574\) | 11.3683 | 0.474504 | ||||||||
\(575\) | −2.90881 | −0.121306 | ||||||||
\(576\) | −0.0573586 | −0.00238994 | ||||||||
\(577\) | −13.8479 | −0.576494 | −0.288247 | − | 0.957556i | \(-0.593072\pi\) | ||||
−0.288247 | + | 0.957556i | \(0.593072\pi\) | |||||||
\(578\) | −11.5761 | −0.481502 | ||||||||
\(579\) | −6.92859 | −0.287942 | ||||||||
\(580\) | −0.448106 | −0.0186066 | ||||||||
\(581\) | 9.72220 | 0.403345 | ||||||||
\(582\) | 3.45888 | 0.143375 | ||||||||
\(583\) | −40.8420 | −1.69150 | ||||||||
\(584\) | 2.60917 | 0.107968 | ||||||||
\(585\) | 0.308703 | 0.0127633 | ||||||||
\(586\) | −7.93518 | −0.327799 | ||||||||
\(587\) | −22.3606 | −0.922921 | −0.461460 | − | 0.887161i | \(-0.652674\pi\) | ||||
−0.461460 | + | 0.887161i | \(0.652674\pi\) | |||||||
\(588\) | −28.4173 | −1.17191 | ||||||||
\(589\) | 0.943268 | 0.0388667 | ||||||||
\(590\) | 1.38686 | 0.0570963 | ||||||||
\(591\) | −41.1850 | −1.69412 | ||||||||
\(592\) | 3.97072 | 0.163196 | ||||||||
\(593\) | 25.7391 | 1.05698 | 0.528490 | − | 0.848939i | \(-0.322758\pi\) | ||||
0.528490 | + | 0.848939i | \(0.322758\pi\) | |||||||
\(594\) | 22.1234 | 0.907733 | ||||||||
\(595\) | 27.6746 | 1.13455 | ||||||||
\(596\) | −19.3454 | −0.792419 | ||||||||
\(597\) | 23.4040 | 0.957863 | ||||||||
\(598\) | 3.80040 | 0.155410 | ||||||||
\(599\) | 22.8937 | 0.935411 | 0.467706 | − | 0.883884i | \(-0.345081\pi\) | ||||
0.467706 | + | 0.883884i | \(0.345081\pi\) | |||||||
\(600\) | −6.62611 | −0.270510 | ||||||||
\(601\) | 5.89293 | 0.240378 | 0.120189 | − | 0.992751i | \(-0.461650\pi\) | ||||
0.120189 | + | 0.992751i | \(0.461650\pi\) | |||||||
\(602\) | 12.2831 | 0.500623 | ||||||||
\(603\) | 0.766875 | 0.0312296 | ||||||||
\(604\) | −11.0070 | −0.447868 | ||||||||
\(605\) | 7.24538 | 0.294567 | ||||||||
\(606\) | −21.5985 | −0.877380 | ||||||||
\(607\) | 25.1247 | 1.01978 | 0.509889 | − | 0.860240i | \(-0.329686\pi\) | ||||
0.509889 | + | 0.860240i | \(0.329686\pi\) | |||||||
\(608\) | 0.676346 | 0.0274294 | ||||||||
\(609\) | 3.49907 | 0.141789 | ||||||||
\(610\) | 5.46075 | 0.221099 | ||||||||
\(611\) | −23.1576 | −0.936856 | ||||||||
\(612\) | −0.306620 | −0.0123944 | ||||||||
\(613\) | −41.1397 | −1.66162 | −0.830809 | − | 0.556558i | \(-0.812122\pi\) | ||||
−0.830809 | + | 0.556558i | \(0.812122\pi\) | |||||||
\(614\) | 30.0031 | 1.21082 | ||||||||
\(615\) | 4.28412 | 0.172752 | ||||||||
\(616\) | 20.4775 | 0.825064 | ||||||||
\(617\) | −15.0568 | −0.606165 | −0.303082 | − | 0.952964i | \(-0.598016\pi\) | ||||
−0.303082 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(618\) | 5.93813 | 0.238866 | ||||||||
\(619\) | −4.83852 | −0.194477 | −0.0972383 | − | 0.995261i | \(-0.531001\pi\) | ||||
−0.0972383 | + | 0.995261i | \(0.531001\pi\) | |||||||
\(620\) | −1.48732 | −0.0597323 | ||||||||
\(621\) | 3.94948 | 0.158487 | ||||||||
\(622\) | −1.96136 | −0.0786434 | ||||||||
\(623\) | −11.0680 | −0.443428 | ||||||||
\(624\) | 8.65710 | 0.346561 | ||||||||
\(625\) | 9.23385 | 0.369354 | ||||||||
\(626\) | 12.3828 | 0.494916 | ||||||||
\(627\) | −4.89411 | −0.195452 | ||||||||
\(628\) | 1.45541 | 0.0580771 | ||||||||
\(629\) | 21.2261 | 0.846341 | ||||||||
\(630\) | 0.296947 | 0.0118307 | ||||||||
\(631\) | 29.4899 | 1.17398 | 0.586988 | − | 0.809596i | \(-0.300314\pi\) | ||||
0.586988 | + | 0.809596i | \(0.300314\pi\) | |||||||
\(632\) | −5.09822 | −0.202796 | ||||||||
\(633\) | −30.5586 | −1.21460 | ||||||||
\(634\) | 18.8305 | 0.747856 | ||||||||
\(635\) | 0.550594 | 0.0218496 | ||||||||
\(636\) | −16.6088 | −0.658583 | ||||||||
\(637\) | −83.6022 | −3.31244 | ||||||||
\(638\) | −1.77247 | −0.0701726 | ||||||||
\(639\) | 0.594522 | 0.0235189 | ||||||||
\(640\) | −1.06645 | −0.0421550 | ||||||||
\(641\) | 12.7863 | 0.505028 | 0.252514 | − | 0.967593i | \(-0.418743\pi\) | ||||
0.252514 | + | 0.967593i | \(0.418743\pi\) | |||||||
\(642\) | 9.89451 | 0.390505 | ||||||||
\(643\) | −23.1913 | −0.914576 | −0.457288 | − | 0.889319i | \(-0.651179\pi\) | ||||
−0.457288 | + | 0.889319i | \(0.651179\pi\) | |||||||
\(644\) | 3.65567 | 0.144054 | ||||||||
\(645\) | 4.62887 | 0.182262 | ||||||||
\(646\) | 3.61551 | 0.142251 | ||||||||
\(647\) | 17.9749 | 0.706667 | 0.353334 | − | 0.935497i | \(-0.385048\pi\) | ||||
0.353334 | + | 0.935497i | \(0.385048\pi\) | |||||||
\(648\) | 8.82463 | 0.346664 | ||||||||
\(649\) | 5.48568 | 0.215332 | ||||||||
\(650\) | −19.4937 | −0.764605 | ||||||||
\(651\) | 11.6139 | 0.455183 | ||||||||
\(652\) | −10.5625 | −0.413660 | ||||||||
\(653\) | 19.9684 | 0.781425 | 0.390713 | − | 0.920513i | \(-0.372229\pi\) | ||||
0.390713 | + | 0.920513i | \(0.372229\pi\) | |||||||
\(654\) | −10.4617 | −0.409083 | ||||||||
\(655\) | −6.20815 | −0.242572 | ||||||||
\(656\) | −2.34182 | −0.0914328 | ||||||||
\(657\) | 0.149659 | 0.00583873 | ||||||||
\(658\) | −22.2757 | −0.868398 | ||||||||
\(659\) | −6.94174 | −0.270412 | −0.135206 | − | 0.990818i | \(-0.543170\pi\) | ||||
−0.135206 | + | 0.990818i | \(0.543170\pi\) | |||||||
\(660\) | 7.71692 | 0.300381 | ||||||||
\(661\) | 5.56753 | 0.216552 | 0.108276 | − | 0.994121i | \(-0.465467\pi\) | ||||
0.108276 | + | 0.994121i | \(0.465467\pi\) | |||||||
\(662\) | 14.2211 | 0.552717 | ||||||||
\(663\) | 46.2779 | 1.79729 | ||||||||
\(664\) | −2.00273 | −0.0777211 | ||||||||
\(665\) | −3.50146 | −0.135781 | ||||||||
\(666\) | 0.227755 | 0.00882533 | ||||||||
\(667\) | −0.316422 | −0.0122519 | ||||||||
\(668\) | 20.2343 | 0.782890 | ||||||||
\(669\) | −1.14857 | −0.0444062 | ||||||||
\(670\) | 14.2582 | 0.550843 | ||||||||
\(671\) | 21.5998 | 0.833850 | ||||||||
\(672\) | 8.32742 | 0.321237 | ||||||||
\(673\) | 6.69109 | 0.257922 | 0.128961 | − | 0.991650i | \(-0.458836\pi\) | ||||
0.128961 | + | 0.991650i | \(0.458836\pi\) | |||||||
\(674\) | 33.4181 | 1.28722 | ||||||||
\(675\) | −20.2584 | −0.779746 | ||||||||
\(676\) | 12.4687 | 0.479567 | ||||||||
\(677\) | −11.1374 | −0.428046 | −0.214023 | − | 0.976829i | \(-0.568657\pi\) | ||||
−0.214023 | + | 0.976829i | \(0.568657\pi\) | |||||||
\(678\) | 11.7086 | 0.449668 | ||||||||
\(679\) | 9.78832 | 0.375641 | ||||||||
\(680\) | −5.70086 | −0.218618 | ||||||||
\(681\) | 4.39526 | 0.168427 | ||||||||
\(682\) | −5.88305 | −0.225274 | ||||||||
\(683\) | −25.5392 | −0.977230 | −0.488615 | − | 0.872500i | \(-0.662498\pi\) | ||||
−0.488615 | + | 0.872500i | \(0.662498\pi\) | |||||||
\(684\) | 0.0387943 | 0.00148334 | ||||||||
\(685\) | −16.3823 | −0.625936 | ||||||||
\(686\) | −46.4372 | −1.77298 | ||||||||
\(687\) | 30.2114 | 1.15263 | ||||||||
\(688\) | −2.53027 | −0.0964658 | ||||||||
\(689\) | −48.8623 | −1.86151 | ||||||||
\(690\) | 1.37763 | 0.0524455 | ||||||||
\(691\) | 34.5098 | 1.31281 | 0.656407 | − | 0.754407i | \(-0.272076\pi\) | ||||
0.656407 | + | 0.754407i | \(0.272076\pi\) | |||||||
\(692\) | −6.68271 | −0.254038 | ||||||||
\(693\) | 1.17456 | 0.0446180 | ||||||||
\(694\) | 23.5597 | 0.894313 | ||||||||
\(695\) | −5.85528 | −0.222104 | ||||||||
\(696\) | −0.720793 | −0.0273216 | ||||||||
\(697\) | −12.5186 | −0.474175 | ||||||||
\(698\) | 6.89121 | 0.260836 | ||||||||
\(699\) | 11.1644 | 0.422276 | ||||||||
\(700\) | −18.7513 | −0.708733 | ||||||||
\(701\) | −29.1673 | −1.10163 | −0.550817 | − | 0.834626i | \(-0.685684\pi\) | ||||
−0.550817 | + | 0.834626i | \(0.685684\pi\) | |||||||
\(702\) | 26.4679 | 0.998965 | ||||||||
\(703\) | −2.68558 | −0.101289 | ||||||||
\(704\) | −4.21829 | −0.158983 | ||||||||
\(705\) | −8.39455 | −0.316157 | ||||||||
\(706\) | 0.682518 | 0.0256869 | ||||||||
\(707\) | −61.1219 | −2.29873 | ||||||||
\(708\) | 2.23081 | 0.0838391 | ||||||||
\(709\) | 8.08103 | 0.303489 | 0.151745 | − | 0.988420i | \(-0.451511\pi\) | ||||
0.151745 | + | 0.988420i | \(0.451511\pi\) | |||||||
\(710\) | 11.0537 | 0.414839 | ||||||||
\(711\) | −0.292427 | −0.0109669 | ||||||||
\(712\) | 2.27995 | 0.0854448 | ||||||||
\(713\) | −1.05025 | −0.0393321 | ||||||||
\(714\) | 44.5155 | 1.66595 | ||||||||
\(715\) | 22.7028 | 0.849036 | ||||||||
\(716\) | 1.20167 | 0.0449085 | ||||||||
\(717\) | 27.5431 | 1.02862 | ||||||||
\(718\) | −30.7878 | −1.14899 | ||||||||
\(719\) | −8.48912 | −0.316591 | −0.158295 | − | 0.987392i | \(-0.550600\pi\) | ||||
−0.158295 | + | 0.987392i | \(0.550600\pi\) | |||||||
\(720\) | −0.0611699 | −0.00227967 | ||||||||
\(721\) | 16.8044 | 0.625828 | ||||||||
\(722\) | 18.5426 | 0.690082 | ||||||||
\(723\) | −4.95378 | −0.184233 | ||||||||
\(724\) | 12.9017 | 0.479486 | ||||||||
\(725\) | 1.62305 | 0.0602786 | ||||||||
\(726\) | 11.6544 | 0.432536 | ||||||||
\(727\) | 23.8775 | 0.885566 | 0.442783 | − | 0.896629i | \(-0.353991\pi\) | ||||
0.442783 | + | 0.896629i | \(0.353991\pi\) | |||||||
\(728\) | 24.4988 | 0.907987 | ||||||||
\(729\) | 27.4963 | 1.01838 | ||||||||
\(730\) | 2.78254 | 0.102987 | ||||||||
\(731\) | −13.5260 | −0.500277 | ||||||||
\(732\) | 8.78378 | 0.324658 | ||||||||
\(733\) | −4.68120 | −0.172904 | −0.0864520 | − | 0.996256i | \(-0.527553\pi\) | ||||
−0.0864520 | + | 0.996256i | \(0.527553\pi\) | |||||||
\(734\) | 28.0131 | 1.03398 | ||||||||
\(735\) | −30.3055 | −1.11784 | ||||||||
\(736\) | −0.753052 | −0.0277579 | ||||||||
\(737\) | 56.3978 | 2.07744 | ||||||||
\(738\) | −0.134324 | −0.00494452 | ||||||||
\(739\) | 14.7968 | 0.544310 | 0.272155 | − | 0.962253i | \(-0.412264\pi\) | ||||
0.272155 | + | 0.962253i | \(0.412264\pi\) | |||||||
\(740\) | 4.23456 | 0.155665 | ||||||||
\(741\) | −5.85519 | −0.215096 | ||||||||
\(742\) | −47.0016 | −1.72548 | ||||||||
\(743\) | 28.3088 | 1.03855 | 0.519274 | − | 0.854608i | \(-0.326202\pi\) | ||||
0.519274 | + | 0.854608i | \(0.326202\pi\) | |||||||
\(744\) | −2.39241 | −0.0877099 | ||||||||
\(745\) | −20.6309 | −0.755856 | ||||||||
\(746\) | −9.91937 | −0.363174 | ||||||||
\(747\) | −0.114874 | −0.00420302 | ||||||||
\(748\) | −22.5495 | −0.824493 | ||||||||
\(749\) | 28.0006 | 1.02312 | ||||||||
\(750\) | −16.2134 | −0.592029 | ||||||||
\(751\) | 45.7904 | 1.67092 | 0.835458 | − | 0.549555i | \(-0.185203\pi\) | ||||
0.835458 | + | 0.549555i | \(0.185203\pi\) | |||||||
\(752\) | 4.58870 | 0.167333 | ||||||||
\(753\) | −35.1560 | −1.28116 | ||||||||
\(754\) | −2.12054 | −0.0772254 | ||||||||
\(755\) | −11.7384 | −0.427203 | ||||||||
\(756\) | 25.4599 | 0.925968 | ||||||||
\(757\) | −0.164561 | −0.00598108 | −0.00299054 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299054 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(758\) | 10.7029 | 0.388748 | ||||||||
\(759\) | 5.44916 | 0.197792 | ||||||||
\(760\) | 0.721286 | 0.0261638 | ||||||||
\(761\) | 16.2532 | 0.589179 | 0.294590 | − | 0.955624i | \(-0.404817\pi\) | ||||
0.294590 | + | 0.955624i | \(0.404817\pi\) | |||||||
\(762\) | 0.885647 | 0.0320836 | ||||||||
\(763\) | −29.6056 | −1.07179 | ||||||||
\(764\) | −3.79391 | −0.137259 | ||||||||
\(765\) | −0.326993 | −0.0118225 | ||||||||
\(766\) | 14.6152 | 0.528069 | ||||||||
\(767\) | 6.56294 | 0.236974 | ||||||||
\(768\) | −1.71541 | −0.0618996 | ||||||||
\(769\) | −4.46011 | −0.160836 | −0.0804179 | − | 0.996761i | \(-0.525625\pi\) | ||||
−0.0804179 | + | 0.996761i | \(0.525625\pi\) | |||||||
\(770\) | 21.8382 | 0.786994 | ||||||||
\(771\) | −46.4171 | −1.67167 | ||||||||
\(772\) | 4.03902 | 0.145368 | ||||||||
\(773\) | −17.9538 | −0.645752 | −0.322876 | − | 0.946441i | \(-0.604650\pi\) | ||||
−0.322876 | + | 0.946441i | \(0.604650\pi\) | |||||||
\(774\) | −0.145133 | −0.00521670 | ||||||||
\(775\) | 5.38712 | 0.193511 | ||||||||
\(776\) | −2.01635 | −0.0723828 | ||||||||
\(777\) | −33.0658 | −1.18623 | ||||||||
\(778\) | 28.0460 | 1.00550 | ||||||||
\(779\) | 1.58388 | 0.0567484 | ||||||||
\(780\) | 9.23233 | 0.330571 | ||||||||
\(781\) | 43.7225 | 1.56452 | ||||||||
\(782\) | −4.02556 | −0.143954 | ||||||||
\(783\) | −2.20372 | −0.0787546 | ||||||||
\(784\) | 16.5659 | 0.591638 | ||||||||
\(785\) | 1.55212 | 0.0553974 | ||||||||
\(786\) | −9.98600 | −0.356189 | ||||||||
\(787\) | 37.3990 | 1.33313 | 0.666565 | − | 0.745447i | \(-0.267764\pi\) | ||||
0.666565 | + | 0.745447i | \(0.267764\pi\) | |||||||
\(788\) | 24.0088 | 0.855278 | ||||||||
\(789\) | −23.7044 | −0.843898 | ||||||||
\(790\) | −5.43698 | −0.193439 | ||||||||
\(791\) | 33.1344 | 1.17813 | ||||||||
\(792\) | −0.241955 | −0.00859750 | ||||||||
\(793\) | 25.8414 | 0.917657 | ||||||||
\(794\) | 19.2393 | 0.682779 | ||||||||
\(795\) | −17.7124 | −0.628195 | ||||||||
\(796\) | −13.6434 | −0.483577 | ||||||||
\(797\) | 42.6720 | 1.51152 | 0.755761 | − | 0.654848i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654848i | \(0.227267\pi\) | |||||||
\(798\) | −5.63221 | −0.199378 | ||||||||
\(799\) | 24.5296 | 0.867796 | ||||||||
\(800\) | 3.86269 | 0.136567 | ||||||||
\(801\) | 0.130775 | 0.00462070 | ||||||||
\(802\) | 30.6769 | 1.08324 | ||||||||
\(803\) | 11.0062 | 0.388402 | ||||||||
\(804\) | 22.9348 | 0.808847 | ||||||||
\(805\) | 3.89857 | 0.137407 | ||||||||
\(806\) | −7.03834 | −0.247915 | ||||||||
\(807\) | −21.0336 | −0.740417 | ||||||||
\(808\) | 12.5909 | 0.442945 | ||||||||
\(809\) | −21.4279 | −0.753364 | −0.376682 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376682 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(810\) | 9.41100 | 0.330669 | ||||||||
\(811\) | −43.0765 | −1.51262 | −0.756311 | − | 0.654212i | \(-0.773000\pi\) | ||||
−0.756311 | + | 0.654212i | \(0.773000\pi\) | |||||||
\(812\) | −2.03978 | −0.0715823 | ||||||||
\(813\) | 43.4264 | 1.52303 | ||||||||
\(814\) | 16.7496 | 0.587074 | ||||||||
\(815\) | −11.2644 | −0.394573 | ||||||||
\(816\) | −9.17001 | −0.321015 | ||||||||
\(817\) | 1.71134 | 0.0598722 | ||||||||
\(818\) | −2.90316 | −0.101507 | ||||||||
\(819\) | 1.40522 | 0.0491023 | ||||||||
\(820\) | −2.49743 | −0.0872140 | ||||||||
\(821\) | −37.0210 | −1.29204 | −0.646021 | − | 0.763319i | \(-0.723568\pi\) | ||||
−0.646021 | + | 0.763319i | \(0.723568\pi\) | |||||||
\(822\) | −26.3515 | −0.919113 | ||||||||
\(823\) | −9.21511 | −0.321219 | −0.160609 | − | 0.987018i | \(-0.551346\pi\) | ||||
−0.160609 | + | 0.987018i | \(0.551346\pi\) | |||||||
\(824\) | −3.46163 | −0.120592 | ||||||||
\(825\) | −27.9508 | −0.973124 | ||||||||
\(826\) | 6.31301 | 0.219658 | ||||||||
\(827\) | 32.7345 | 1.13829 | 0.569145 | − | 0.822237i | \(-0.307274\pi\) | ||||
0.569145 | + | 0.822237i | \(0.307274\pi\) | |||||||
\(828\) | −0.0431940 | −0.00150110 | ||||||||
\(829\) | −0.407045 | −0.0141373 | −0.00706863 | − | 0.999975i | \(-0.502250\pi\) | ||||
−0.00706863 | + | 0.999975i | \(0.502250\pi\) | |||||||
\(830\) | −2.13581 | −0.0741350 | ||||||||
\(831\) | 35.7676 | 1.24076 | ||||||||
\(832\) | −5.04666 | −0.174961 | ||||||||
\(833\) | 88.5555 | 3.06827 | ||||||||
\(834\) | −9.41841 | −0.326133 | ||||||||
\(835\) | 21.5788 | 0.746766 | ||||||||
\(836\) | 2.85302 | 0.0986738 | ||||||||
\(837\) | −7.31445 | −0.252824 | ||||||||
\(838\) | −23.3752 | −0.807484 | ||||||||
\(839\) | 13.4307 | 0.463678 | 0.231839 | − | 0.972754i | \(-0.425526\pi\) | ||||
0.231839 | + | 0.972754i | \(0.425526\pi\) | |||||||
\(840\) | 8.88075 | 0.306415 | ||||||||
\(841\) | −28.8234 | −0.993912 | ||||||||
\(842\) | 10.5146 | 0.362355 | ||||||||
\(843\) | −17.4836 | −0.602166 | ||||||||
\(844\) | 17.8142 | 0.613189 | ||||||||
\(845\) | 13.2972 | 0.457439 | ||||||||
\(846\) | 0.263202 | 0.00904906 | ||||||||
\(847\) | 32.9810 | 1.13324 | ||||||||
\(848\) | 9.68212 | 0.332485 | ||||||||
\(849\) | −33.4060 | −1.14649 | ||||||||
\(850\) | 20.6486 | 0.708242 | ||||||||
\(851\) | 2.99016 | 0.102501 | ||||||||
\(852\) | 17.7803 | 0.609141 | ||||||||
\(853\) | −45.9317 | −1.57267 | −0.786336 | − | 0.617800i | \(-0.788024\pi\) | ||||
−0.786336 | + | 0.617800i | \(0.788024\pi\) | |||||||
\(854\) | 24.8573 | 0.850601 | ||||||||
\(855\) | 0.0413720 | 0.00141489 | ||||||||
\(856\) | −5.76801 | −0.197146 | ||||||||
\(857\) | 15.4284 | 0.527023 | 0.263512 | − | 0.964656i | \(-0.415119\pi\) | ||||
0.263512 | + | 0.964656i | \(0.415119\pi\) | |||||||
\(858\) | 36.5181 | 1.24671 | ||||||||
\(859\) | 41.1838 | 1.40517 | 0.702586 | − | 0.711598i | \(-0.252028\pi\) | ||||
0.702586 | + | 0.711598i | \(0.252028\pi\) | |||||||
\(860\) | −2.69840 | −0.0920147 | ||||||||
\(861\) | 19.5013 | 0.664604 | ||||||||
\(862\) | −28.1981 | −0.960432 | ||||||||
\(863\) | 54.5160 | 1.85575 | 0.927874 | − | 0.372895i | \(-0.121635\pi\) | ||||
0.927874 | + | 0.372895i | \(0.121635\pi\) | |||||||
\(864\) | −5.24463 | −0.178426 | ||||||||
\(865\) | −7.12675 | −0.242317 | ||||||||
\(866\) | 17.3077 | 0.588141 | ||||||||
\(867\) | −19.8578 | −0.674405 | ||||||||
\(868\) | −6.77030 | −0.229799 | ||||||||
\(869\) | −21.5058 | −0.729533 | ||||||||
\(870\) | −0.768687 | −0.0260609 | ||||||||
\(871\) | 67.4729 | 2.28623 | ||||||||
\(872\) | 6.09862 | 0.206525 | ||||||||
\(873\) | −0.115655 | −0.00391433 | ||||||||
\(874\) | 0.509324 | 0.0172281 | ||||||||
\(875\) | −45.8824 | −1.55111 | ||||||||
\(876\) | 4.47581 | 0.151224 | ||||||||
\(877\) | −10.0843 | −0.340523 | −0.170261 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170261 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(878\) | 29.3119 | 0.989228 | ||||||||
\(879\) | −13.6121 | −0.459125 | ||||||||
\(880\) | −4.49858 | −0.151647 | ||||||||
\(881\) | −10.4814 | −0.353128 | −0.176564 | − | 0.984289i | \(-0.556498\pi\) | ||||
−0.176564 | + | 0.984289i | \(0.556498\pi\) | |||||||
\(882\) | 0.950195 | 0.0319947 | ||||||||
\(883\) | −41.5097 | −1.39691 | −0.698456 | − | 0.715653i | \(-0.746129\pi\) | ||||
−0.698456 | + | 0.715653i | \(0.746129\pi\) | |||||||
\(884\) | −26.9777 | −0.907359 | ||||||||
\(885\) | 2.37904 | 0.0799707 | ||||||||
\(886\) | −6.42674 | −0.215911 | ||||||||
\(887\) | 55.1685 | 1.85238 | 0.926189 | − | 0.377060i | \(-0.123065\pi\) | ||||
0.926189 | + | 0.377060i | \(0.123065\pi\) | |||||||
\(888\) | 6.81142 | 0.228576 | ||||||||
\(889\) | 2.50630 | 0.0840588 | ||||||||
\(890\) | 2.43145 | 0.0815023 | ||||||||
\(891\) | 37.2248 | 1.24708 | ||||||||
\(892\) | 0.669557 | 0.0224184 | ||||||||
\(893\) | −3.10355 | −0.103856 | ||||||||
\(894\) | −33.1854 | −1.10989 | ||||||||
\(895\) | 1.28152 | 0.0428364 | ||||||||
\(896\) | −4.85447 | −0.162176 | ||||||||
\(897\) | 6.51925 | 0.217671 | ||||||||
\(898\) | 18.8315 | 0.628417 | ||||||||
\(899\) | 0.586015 | 0.0195447 | ||||||||
\(900\) | 0.221559 | 0.00738529 | ||||||||
\(901\) | 51.7573 | 1.72429 | ||||||||
\(902\) | −9.87848 | −0.328917 | ||||||||
\(903\) | 21.0706 | 0.701187 | ||||||||
\(904\) | −6.82556 | −0.227015 | ||||||||
\(905\) | 13.7589 | 0.457362 | ||||||||
\(906\) | −18.8815 | −0.627297 | ||||||||
\(907\) | −30.2264 | −1.00365 | −0.501826 | − | 0.864968i | \(-0.667338\pi\) | ||||
−0.501826 | + | 0.864968i | \(0.667338\pi\) | |||||||
\(908\) | −2.56221 | −0.0850301 | ||||||||
\(909\) | 0.722194 | 0.0239537 | ||||||||
\(910\) | 26.1267 | 0.866092 | ||||||||
\(911\) | −49.5086 | −1.64029 | −0.820146 | − | 0.572154i | \(-0.806108\pi\) | ||||
−0.820146 | + | 0.572154i | \(0.806108\pi\) | |||||||
\(912\) | 1.16021 | 0.0384185 | ||||||||
\(913\) | −8.44810 | −0.279591 | ||||||||
\(914\) | 15.4594 | 0.511353 | ||||||||
\(915\) | 9.36744 | 0.309678 | ||||||||
\(916\) | −17.6117 | −0.581907 | ||||||||
\(917\) | −28.2595 | −0.933211 | ||||||||
\(918\) | −28.0360 | −0.925327 | ||||||||
\(919\) | 25.0822 | 0.827385 | 0.413692 | − | 0.910417i | \(-0.364239\pi\) | ||||
0.413692 | + | 0.910417i | \(0.364239\pi\) | |||||||
\(920\) | −0.803090 | −0.0264771 | ||||||||
\(921\) | 51.4676 | 1.69592 | ||||||||
\(922\) | 25.4778 | 0.839065 | ||||||||
\(923\) | 52.3086 | 1.72176 | ||||||||
\(924\) | 35.1274 | 1.15561 | ||||||||
\(925\) | −15.3377 | −0.504299 | ||||||||
\(926\) | −4.48763 | −0.147473 | ||||||||
\(927\) | −0.198554 | −0.00652138 | ||||||||
\(928\) | 0.420186 | 0.0137933 | ||||||||
\(929\) | 5.47667 | 0.179684 | 0.0898419 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898419 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(930\) | −2.55137 | −0.0836628 | ||||||||
\(931\) | −11.2043 | −0.367205 | ||||||||
\(932\) | −6.50828 | −0.213186 | ||||||||
\(933\) | −3.36454 | −0.110150 | ||||||||
\(934\) | 7.61059 | 0.249026 | ||||||||
\(935\) | −24.0479 | −0.786449 | ||||||||
\(936\) | −0.289469 | −0.00946160 | ||||||||
\(937\) | 15.4936 | 0.506153 | 0.253077 | − | 0.967446i | \(-0.418557\pi\) | ||||
0.253077 | + | 0.967446i | \(0.418557\pi\) | |||||||
\(938\) | 64.9034 | 2.11917 | ||||||||
\(939\) | 21.2416 | 0.693193 | ||||||||
\(940\) | 4.89361 | 0.159612 | ||||||||
\(941\) | −28.0298 | −0.913744 | −0.456872 | − | 0.889532i | \(-0.651030\pi\) | ||||
−0.456872 | + | 0.889532i | \(0.651030\pi\) | |||||||
\(942\) | 2.49663 | 0.0813445 | ||||||||
\(943\) | −1.76351 | −0.0574279 | ||||||||
\(944\) | −1.30045 | −0.0423261 | ||||||||
\(945\) | 27.1516 | 0.883242 | ||||||||
\(946\) | −10.6734 | −0.347023 | ||||||||
\(947\) | −19.3105 | −0.627508 | −0.313754 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313754 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(948\) | −8.74555 | −0.284042 | ||||||||
\(949\) | 13.1676 | 0.427438 | ||||||||
\(950\) | −2.61252 | −0.0847612 | ||||||||
\(951\) | 32.3022 | 1.04747 | ||||||||
\(952\) | −25.9503 | −0.841055 | ||||||||
\(953\) | 4.18686 | 0.135626 | 0.0678129 | − | 0.997698i | \(-0.478398\pi\) | ||||
0.0678129 | + | 0.997698i | \(0.478398\pi\) | |||||||
\(954\) | 0.555353 | 0.0179802 | ||||||||
\(955\) | −4.04600 | −0.130925 | ||||||||
\(956\) | −16.0562 | −0.519296 | ||||||||
\(957\) | −3.04051 | −0.0982858 | ||||||||
\(958\) | 2.50044 | 0.0807855 | ||||||||
\(959\) | −74.5723 | −2.40807 | ||||||||
\(960\) | −1.82940 | −0.0590435 | ||||||||
\(961\) | −29.0549 | −0.937256 | ||||||||
\(962\) | 20.0389 | 0.646079 | ||||||||
\(963\) | −0.330845 | −0.0106613 | ||||||||
\(964\) | 2.88780 | 0.0930099 | ||||||||
\(965\) | 4.30740 | 0.138660 | ||||||||
\(966\) | 6.27098 | 0.201766 | ||||||||
\(967\) | −21.9010 | −0.704289 | −0.352145 | − | 0.935946i | \(-0.614547\pi\) | ||||
−0.352145 | + | 0.935946i | \(0.614547\pi\) | |||||||
\(968\) | −6.79395 | −0.218366 | ||||||||
\(969\) | 6.20210 | 0.199240 | ||||||||
\(970\) | −2.15033 | −0.0690430 | ||||||||
\(971\) | −48.3128 | −1.55043 | −0.775216 | − | 0.631697i | \(-0.782359\pi\) | ||||
−0.775216 | + | 0.631697i | \(0.782359\pi\) | |||||||
\(972\) | −0.596006 | −0.0191169 | ||||||||
\(973\) | −26.6533 | −0.854465 | ||||||||
\(974\) | 5.05372 | 0.161932 | ||||||||
\(975\) | −33.4397 | −1.07093 | ||||||||
\(976\) | −5.12051 | −0.163903 | ||||||||
\(977\) | −33.1039 | −1.05909 | −0.529544 | − | 0.848283i | \(-0.677637\pi\) | ||||
−0.529544 | + | 0.848283i | \(0.677637\pi\) | |||||||
\(978\) | −18.1191 | −0.579384 | ||||||||
\(979\) | 9.61749 | 0.307376 | ||||||||
\(980\) | 17.6666 | 0.564339 | ||||||||
\(981\) | 0.349809 | 0.0111685 | ||||||||
\(982\) | 25.8437 | 0.824706 | ||||||||
\(983\) | −49.5933 | −1.58178 | −0.790890 | − | 0.611958i | \(-0.790382\pi\) | ||||
−0.790890 | + | 0.611958i | \(0.790382\pi\) | |||||||
\(984\) | −4.01719 | −0.128063 | ||||||||
\(985\) | 25.6041 | 0.815814 | ||||||||
\(986\) | 2.24617 | 0.0715327 | ||||||||
\(987\) | −38.2120 | −1.21630 | ||||||||
\(988\) | 3.41328 | 0.108591 | ||||||||
\(989\) | −1.90543 | −0.0605891 | ||||||||
\(990\) | −0.258032 | −0.00820080 | ||||||||
\(991\) | 4.91020 | 0.155978 | 0.0779888 | − | 0.996954i | \(-0.475150\pi\) | ||||
0.0779888 | + | 0.996954i | \(0.475150\pi\) | |||||||
\(992\) | 1.39465 | 0.0442803 | ||||||||
\(993\) | 24.3950 | 0.774152 | ||||||||
\(994\) | 50.3166 | 1.59594 | ||||||||
\(995\) | −14.5499 | −0.461264 | ||||||||
\(996\) | −3.43551 | −0.108858 | ||||||||
\(997\) | −45.2065 | −1.43170 | −0.715851 | − | 0.698253i | \(-0.753961\pi\) | ||||
−0.715851 | + | 0.698253i | \(0.753961\pi\) | |||||||
\(998\) | 19.1158 | 0.605101 | ||||||||
\(999\) | 20.8250 | 0.658873 |
(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 | 6038.2.a.c.1.15 | ✓ | 57 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6038.2.a.c.1.15 | ✓ | 57 | 1.1 | even | 1 | trivial |