Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30742 | −1.63159 | −0.815796 | − | 0.578339i | \(-0.803701\pi\) | ||||
−0.815796 | + | 0.578339i | \(0.803701\pi\) | |||||||
\(3\) | −2.51530 | −1.45221 | −0.726105 | − | 0.687584i | \(-0.758671\pi\) | ||||
−0.726105 | + | 0.687584i | \(0.758671\pi\) | |||||||
\(4\) | 3.32419 | 1.66209 | ||||||||
\(5\) | −4.19325 | −1.87528 | −0.937639 | − | 0.347609i | \(-0.886994\pi\) | ||||
−0.937639 | + | 0.347609i | \(0.886994\pi\) | |||||||
\(6\) | 5.80386 | 2.36941 | ||||||||
\(7\) | 2.00418 | 0.757509 | 0.378755 | − | 0.925497i | \(-0.376352\pi\) | ||||
0.378755 | + | 0.925497i | \(0.376352\pi\) | |||||||
\(8\) | −3.05546 | −1.08027 | ||||||||
\(9\) | 3.32673 | 1.10891 | ||||||||
\(10\) | 9.67559 | 3.05969 | ||||||||
\(11\) | 4.40006 | 1.32667 | 0.663335 | − | 0.748323i | \(-0.269141\pi\) | ||||
0.663335 | + | 0.748323i | \(0.269141\pi\) | |||||||
\(12\) | −8.36134 | −2.41371 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.62449 | −1.23595 | ||||||||
\(15\) | 10.5473 | 2.72330 | ||||||||
\(16\) | 0.401859 | 0.100465 | ||||||||
\(17\) | 0.837810 | 0.203199 | 0.101599 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101599 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(18\) | −7.67618 | −1.80929 | ||||||||
\(19\) | 2.59581 | 0.595519 | 0.297759 | − | 0.954641i | \(-0.403761\pi\) | ||||
0.297759 | + | 0.954641i | \(0.403761\pi\) | |||||||
\(20\) | −13.9392 | −3.11689 | ||||||||
\(21\) | −5.04112 | −1.10006 | ||||||||
\(22\) | −10.1528 | −2.16458 | ||||||||
\(23\) | −5.88386 | −1.22687 | −0.613435 | − | 0.789745i | \(-0.710213\pi\) | ||||
−0.613435 | + | 0.789745i | \(0.710213\pi\) | |||||||
\(24\) | 7.68541 | 1.56878 | ||||||||
\(25\) | 12.5834 | 2.51667 | ||||||||
\(26\) | 2.30742 | 0.452522 | ||||||||
\(27\) | −0.821837 | −0.158163 | ||||||||
\(28\) | 6.66228 | 1.25905 | ||||||||
\(29\) | 6.24966 | 1.16053 | 0.580267 | − | 0.814427i | \(-0.302948\pi\) | ||||
0.580267 | + | 0.814427i | \(0.302948\pi\) | |||||||
\(30\) | −24.3370 | −4.44331 | ||||||||
\(31\) | 5.84018 | 1.04893 | 0.524464 | − | 0.851433i | \(-0.324266\pi\) | ||||
0.524464 | + | 0.851433i | \(0.324266\pi\) | |||||||
\(32\) | 5.18367 | 0.916352 | ||||||||
\(33\) | −11.0675 | −1.92660 | ||||||||
\(34\) | −1.93318 | −0.331538 | ||||||||
\(35\) | −8.40403 | −1.42054 | ||||||||
\(36\) | 11.0587 | 1.84312 | ||||||||
\(37\) | −9.01297 | −1.48172 | −0.740861 | − | 0.671658i | \(-0.765582\pi\) | ||||
−0.740861 | + | 0.671658i | \(0.765582\pi\) | |||||||
\(38\) | −5.98962 | −0.971644 | ||||||||
\(39\) | 2.51530 | 0.402770 | ||||||||
\(40\) | 12.8123 | 2.02581 | ||||||||
\(41\) | 2.59430 | 0.405162 | 0.202581 | − | 0.979265i | \(-0.435067\pi\) | ||||
0.202581 | + | 0.979265i | \(0.435067\pi\) | |||||||
\(42\) | 11.6320 | 1.79485 | ||||||||
\(43\) | 6.27715 | 0.957256 | 0.478628 | − | 0.878018i | \(-0.341134\pi\) | ||||
0.478628 | + | 0.878018i | \(0.341134\pi\) | |||||||
\(44\) | 14.6266 | 2.20505 | ||||||||
\(45\) | −13.9498 | −2.07952 | ||||||||
\(46\) | 13.5765 | 2.00175 | ||||||||
\(47\) | −1.11510 | −0.162655 | −0.0813273 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813273 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(48\) | −1.01080 | −0.145896 | ||||||||
\(49\) | −2.98326 | −0.426180 | ||||||||
\(50\) | −29.0351 | −4.10618 | ||||||||
\(51\) | −2.10734 | −0.295087 | ||||||||
\(52\) | −3.32419 | −0.460982 | ||||||||
\(53\) | −6.18217 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(54\) | 1.89632 | 0.258057 | ||||||||
\(55\) | −18.4506 | −2.48787 | ||||||||
\(56\) | −6.12370 | −0.818314 | ||||||||
\(57\) | −6.52923 | −0.864818 | ||||||||
\(58\) | −14.4206 | −1.89352 | ||||||||
\(59\) | −4.91759 | −0.640216 | −0.320108 | − | 0.947381i | \(-0.603719\pi\) | ||||
−0.320108 | + | 0.947381i | \(0.603719\pi\) | |||||||
\(60\) | 35.0612 | 4.52638 | ||||||||
\(61\) | 11.9123 | 1.52521 | 0.762604 | − | 0.646866i | \(-0.223921\pi\) | ||||
0.762604 | + | 0.646866i | \(0.223921\pi\) | |||||||
\(62\) | −13.4758 | −1.71142 | ||||||||
\(63\) | 6.66738 | 0.840011 | ||||||||
\(64\) | −12.7646 | −1.59558 | ||||||||
\(65\) | 4.19325 | 0.520109 | ||||||||
\(66\) | 25.5373 | 3.14343 | ||||||||
\(67\) | −1.37117 | −0.167516 | −0.0837578 | − | 0.996486i | \(-0.526692\pi\) | ||||
−0.0837578 | + | 0.996486i | \(0.526692\pi\) | |||||||
\(68\) | 2.78504 | 0.337736 | ||||||||
\(69\) | 14.7997 | 1.78167 | ||||||||
\(70\) | 19.3916 | 2.31774 | ||||||||
\(71\) | 7.30611 | 0.867076 | 0.433538 | − | 0.901135i | \(-0.357265\pi\) | ||||
0.433538 | + | 0.901135i | \(0.357265\pi\) | |||||||
\(72\) | −10.1647 | −1.19792 | ||||||||
\(73\) | −5.14693 | −0.602402 | −0.301201 | − | 0.953561i | \(-0.597388\pi\) | ||||
−0.301201 | + | 0.953561i | \(0.597388\pi\) | |||||||
\(74\) | 20.7967 | 2.41757 | ||||||||
\(75\) | −31.6509 | −3.65473 | ||||||||
\(76\) | 8.62895 | 0.989809 | ||||||||
\(77\) | 8.81852 | 1.00496 | ||||||||
\(78\) | −5.80386 | −0.657157 | ||||||||
\(79\) | −11.6248 | −1.30789 | −0.653947 | − | 0.756540i | \(-0.726888\pi\) | ||||
−0.653947 | + | 0.756540i | \(0.726888\pi\) | |||||||
\(80\) | −1.68510 | −0.188399 | ||||||||
\(81\) | −7.91304 | −0.879227 | ||||||||
\(82\) | −5.98615 | −0.661060 | ||||||||
\(83\) | −12.7465 | −1.39911 | −0.699557 | − | 0.714577i | \(-0.746619\pi\) | ||||
−0.699557 | + | 0.714577i | \(0.746619\pi\) | |||||||
\(84\) | −16.7576 | −1.82841 | ||||||||
\(85\) | −3.51315 | −0.381054 | ||||||||
\(86\) | −14.4840 | −1.56185 | ||||||||
\(87\) | −15.7198 | −1.68534 | ||||||||
\(88\) | −13.4442 | −1.43316 | ||||||||
\(89\) | −15.8100 | −1.67585 | −0.837927 | − | 0.545783i | \(-0.816232\pi\) | ||||
−0.837927 | + | 0.545783i | \(0.816232\pi\) | |||||||
\(90\) | 32.1881 | 3.39293 | ||||||||
\(91\) | −2.00418 | −0.210095 | ||||||||
\(92\) | −19.5591 | −2.03918 | ||||||||
\(93\) | −14.6898 | −1.52326 | ||||||||
\(94\) | 2.57301 | 0.265386 | ||||||||
\(95\) | −10.8849 | −1.11676 | ||||||||
\(96\) | −13.0385 | −1.33073 | ||||||||
\(97\) | −15.2479 | −1.54819 | −0.774096 | − | 0.633068i | \(-0.781795\pi\) | ||||
−0.774096 | + | 0.633068i | \(0.781795\pi\) | |||||||
\(98\) | 6.88363 | 0.695352 | ||||||||
\(99\) | 14.6378 | 1.47116 | ||||||||
\(100\) | 41.8295 | 4.18295 | ||||||||
\(101\) | −16.0749 | −1.59951 | −0.799757 | − | 0.600324i | \(-0.795038\pi\) | ||||
−0.799757 | + | 0.600324i | \(0.795038\pi\) | |||||||
\(102\) | 4.86253 | 0.481462 | ||||||||
\(103\) | −1.59614 | −0.157272 | −0.0786360 | − | 0.996903i | \(-0.525056\pi\) | ||||
−0.0786360 | + | 0.996903i | \(0.525056\pi\) | |||||||
\(104\) | 3.05546 | 0.299613 | ||||||||
\(105\) | 21.1387 | 2.06292 | ||||||||
\(106\) | 14.2649 | 1.38553 | ||||||||
\(107\) | −0.938871 | −0.0907641 | −0.0453821 | − | 0.998970i | \(-0.514451\pi\) | ||||
−0.0453821 | + | 0.998970i | \(0.514451\pi\) | |||||||
\(108\) | −2.73194 | −0.262881 | ||||||||
\(109\) | 19.4836 | 1.86619 | 0.933096 | − | 0.359627i | \(-0.117096\pi\) | ||||
0.933096 | + | 0.359627i | \(0.117096\pi\) | |||||||
\(110\) | 42.5732 | 4.05920 | ||||||||
\(111\) | 22.6703 | 2.15177 | ||||||||
\(112\) | 0.805398 | 0.0761030 | ||||||||
\(113\) | −2.27989 | −0.214474 | −0.107237 | − | 0.994233i | \(-0.534200\pi\) | ||||
−0.107237 | + | 0.994233i | \(0.534200\pi\) | |||||||
\(114\) | 15.0657 | 1.41103 | ||||||||
\(115\) | 24.6725 | 2.30072 | ||||||||
\(116\) | 20.7751 | 1.92892 | ||||||||
\(117\) | −3.32673 | −0.307557 | ||||||||
\(118\) | 11.3470 | 1.04457 | ||||||||
\(119\) | 1.67912 | 0.153925 | ||||||||
\(120\) | −32.2268 | −2.94189 | ||||||||
\(121\) | 8.36056 | 0.760051 | ||||||||
\(122\) | −27.4866 | −2.48852 | ||||||||
\(123\) | −6.52545 | −0.588380 | ||||||||
\(124\) | 19.4139 | 1.74342 | ||||||||
\(125\) | −31.7989 | −2.84418 | ||||||||
\(126\) | −15.3844 | −1.37056 | ||||||||
\(127\) | 4.10817 | 0.364541 | 0.182271 | − | 0.983248i | \(-0.441655\pi\) | ||||
0.182271 | + | 0.983248i | \(0.441655\pi\) | |||||||
\(128\) | 19.0860 | 1.68698 | ||||||||
\(129\) | −15.7889 | −1.39014 | ||||||||
\(130\) | −9.67559 | −0.848606 | ||||||||
\(131\) | −20.6051 | −1.80027 | −0.900136 | − | 0.435608i | \(-0.856533\pi\) | ||||
−0.900136 | + | 0.435608i | \(0.856533\pi\) | |||||||
\(132\) | −36.7904 | −3.20219 | ||||||||
\(133\) | 5.20246 | 0.451111 | ||||||||
\(134\) | 3.16387 | 0.273317 | ||||||||
\(135\) | 3.44617 | 0.296599 | ||||||||
\(136\) | −2.55990 | −0.219509 | ||||||||
\(137\) | 13.7361 | 1.17355 | 0.586775 | − | 0.809750i | \(-0.300397\pi\) | ||||
0.586775 | + | 0.809750i | \(0.300397\pi\) | |||||||
\(138\) | −34.1491 | −2.90696 | ||||||||
\(139\) | 17.8883 | 1.51726 | 0.758631 | − | 0.651521i | \(-0.225869\pi\) | ||||
0.758631 | + | 0.651521i | \(0.225869\pi\) | |||||||
\(140\) | −27.9366 | −2.36107 | ||||||||
\(141\) | 2.80482 | 0.236209 | ||||||||
\(142\) | −16.8583 | −1.41472 | ||||||||
\(143\) | −4.40006 | −0.367952 | ||||||||
\(144\) | 1.33688 | 0.111407 | ||||||||
\(145\) | −26.2064 | −2.17632 | ||||||||
\(146\) | 11.8761 | 0.982875 | ||||||||
\(147\) | 7.50379 | 0.618902 | ||||||||
\(148\) | −29.9608 | −2.46276 | ||||||||
\(149\) | 21.9430 | 1.79764 | 0.898819 | − | 0.438320i | \(-0.144426\pi\) | ||||
0.898819 | + | 0.438320i | \(0.144426\pi\) | |||||||
\(150\) | 73.0320 | 5.96304 | ||||||||
\(151\) | −0.607759 | −0.0494587 | −0.0247294 | − | 0.999694i | \(-0.507872\pi\) | ||||
−0.0247294 | + | 0.999694i | \(0.507872\pi\) | |||||||
\(152\) | −7.93139 | −0.643321 | ||||||||
\(153\) | 2.78717 | 0.225329 | ||||||||
\(154\) | −20.3480 | −1.63969 | ||||||||
\(155\) | −24.4894 | −1.96703 | ||||||||
\(156\) | 8.36134 | 0.669443 | ||||||||
\(157\) | 19.4281 | 1.55053 | 0.775266 | − | 0.631635i | \(-0.217616\pi\) | ||||
0.775266 | + | 0.631635i | \(0.217616\pi\) | |||||||
\(158\) | 26.8234 | 2.13395 | ||||||||
\(159\) | 15.5500 | 1.23320 | ||||||||
\(160\) | −21.7364 | −1.71842 | ||||||||
\(161\) | −11.7923 | −0.929366 | ||||||||
\(162\) | 18.2587 | 1.43454 | ||||||||
\(163\) | −0.334974 | −0.0262372 | −0.0131186 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131186 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(164\) | 8.62396 | 0.673418 | ||||||||
\(165\) | 46.4087 | 3.61291 | ||||||||
\(166\) | 29.4116 | 2.28278 | ||||||||
\(167\) | 1.75686 | 0.135950 | 0.0679749 | − | 0.997687i | \(-0.478346\pi\) | ||||
0.0679749 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(168\) | 15.4029 | 1.18836 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 8.10631 | 0.621726 | ||||||||
\(171\) | 8.63556 | 0.660378 | ||||||||
\(172\) | 20.8664 | 1.59105 | ||||||||
\(173\) | 9.19355 | 0.698973 | 0.349486 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349486 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(174\) | 36.2721 | 2.74978 | ||||||||
\(175\) | 25.2193 | 1.90640 | ||||||||
\(176\) | 1.76821 | 0.133283 | ||||||||
\(177\) | 12.3692 | 0.929728 | ||||||||
\(178\) | 36.4803 | 2.73431 | ||||||||
\(179\) | −23.9686 | −1.79150 | −0.895748 | − | 0.444562i | \(-0.853359\pi\) | ||||
−0.895748 | + | 0.444562i | \(0.853359\pi\) | |||||||
\(180\) | −46.3719 | −3.45636 | ||||||||
\(181\) | −3.26090 | −0.242381 | −0.121190 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121190 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(182\) | 4.62449 | 0.342790 | ||||||||
\(183\) | −29.9629 | −2.21492 | ||||||||
\(184\) | 17.9779 | 1.32535 | ||||||||
\(185\) | 37.7936 | 2.77864 | ||||||||
\(186\) | 33.8956 | 2.48534 | ||||||||
\(187\) | 3.68642 | 0.269578 | ||||||||
\(188\) | −3.70682 | −0.270347 | ||||||||
\(189\) | −1.64711 | −0.119810 | ||||||||
\(190\) | 25.1160 | 1.82210 | ||||||||
\(191\) | −17.4760 | −1.26452 | −0.632261 | − | 0.774756i | \(-0.717873\pi\) | ||||
−0.632261 | + | 0.774756i | \(0.717873\pi\) | |||||||
\(192\) | 32.1069 | 2.31711 | ||||||||
\(193\) | 26.3480 | 1.89657 | 0.948285 | − | 0.317419i | \(-0.102816\pi\) | ||||
0.948285 | + | 0.317419i | \(0.102816\pi\) | |||||||
\(194\) | 35.1834 | 2.52602 | ||||||||
\(195\) | −10.5473 | −0.755307 | ||||||||
\(196\) | −9.91692 | −0.708351 | ||||||||
\(197\) | −21.9987 | −1.56735 | −0.783673 | − | 0.621174i | \(-0.786656\pi\) | ||||
−0.783673 | + | 0.621174i | \(0.786656\pi\) | |||||||
\(198\) | −33.7757 | −2.40033 | ||||||||
\(199\) | 27.0569 | 1.91802 | 0.959008 | − | 0.283379i | \(-0.0914555\pi\) | ||||
0.959008 | + | 0.283379i | \(0.0914555\pi\) | |||||||
\(200\) | −38.4480 | −2.71868 | ||||||||
\(201\) | 3.44891 | 0.243268 | ||||||||
\(202\) | 37.0916 | 2.60975 | ||||||||
\(203\) | 12.5255 | 0.879114 | ||||||||
\(204\) | −7.00521 | −0.490463 | ||||||||
\(205\) | −10.8786 | −0.759792 | ||||||||
\(206\) | 3.68296 | 0.256604 | ||||||||
\(207\) | −19.5741 | −1.36049 | ||||||||
\(208\) | −0.401859 | −0.0278639 | ||||||||
\(209\) | 11.4217 | 0.790056 | ||||||||
\(210\) | −48.7758 | −3.36585 | ||||||||
\(211\) | 16.4545 | 1.13278 | 0.566388 | − | 0.824139i | \(-0.308340\pi\) | ||||
0.566388 | + | 0.824139i | \(0.308340\pi\) | |||||||
\(212\) | −20.5507 | −1.41143 | ||||||||
\(213\) | −18.3771 | −1.25918 | ||||||||
\(214\) | 2.16637 | 0.148090 | ||||||||
\(215\) | −26.3216 | −1.79512 | ||||||||
\(216\) | 2.51109 | 0.170858 | ||||||||
\(217\) | 11.7048 | 0.794572 | ||||||||
\(218\) | −44.9569 | −3.04487 | ||||||||
\(219\) | 12.9461 | 0.874814 | ||||||||
\(220\) | −61.3332 | −4.13508 | ||||||||
\(221\) | −0.837810 | −0.0563572 | ||||||||
\(222\) | −52.3099 | −3.51081 | ||||||||
\(223\) | −6.80781 | −0.455885 | −0.227942 | − | 0.973675i | \(-0.573200\pi\) | ||||
−0.227942 | + | 0.973675i | \(0.573200\pi\) | |||||||
\(224\) | 10.3890 | 0.694145 | ||||||||
\(225\) | 41.8615 | 2.79077 | ||||||||
\(226\) | 5.26067 | 0.349935 | ||||||||
\(227\) | 2.76864 | 0.183761 | 0.0918804 | − | 0.995770i | \(-0.470712\pi\) | ||||
0.0918804 | + | 0.995770i | \(0.470712\pi\) | |||||||
\(228\) | −21.7044 | −1.43741 | ||||||||
\(229\) | 16.6874 | 1.10273 | 0.551366 | − | 0.834264i | \(-0.314107\pi\) | ||||
0.551366 | + | 0.834264i | \(0.314107\pi\) | |||||||
\(230\) | −56.9299 | −3.75384 | ||||||||
\(231\) | −22.1812 | −1.45942 | ||||||||
\(232\) | −19.0956 | −1.25369 | ||||||||
\(233\) | 22.5749 | 1.47893 | 0.739464 | − | 0.673196i | \(-0.235079\pi\) | ||||
0.739464 | + | 0.673196i | \(0.235079\pi\) | |||||||
\(234\) | 7.67618 | 0.501807 | ||||||||
\(235\) | 4.67591 | 0.305023 | ||||||||
\(236\) | −16.3470 | −1.06410 | ||||||||
\(237\) | 29.2399 | 1.89934 | ||||||||
\(238\) | −3.87444 | −0.251143 | ||||||||
\(239\) | −7.73348 | −0.500237 | −0.250119 | − | 0.968215i | \(-0.580470\pi\) | ||||
−0.250119 | + | 0.968215i | \(0.580470\pi\) | |||||||
\(240\) | 4.23852 | 0.273595 | ||||||||
\(241\) | 1.37304 | 0.0884450 | 0.0442225 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442225 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(242\) | −19.2913 | −1.24009 | ||||||||
\(243\) | 22.3692 | 1.43498 | ||||||||
\(244\) | 39.5986 | 2.53504 | ||||||||
\(245\) | 12.5096 | 0.799206 | ||||||||
\(246\) | 15.0570 | 0.959997 | ||||||||
\(247\) | −2.59581 | −0.165167 | ||||||||
\(248\) | −17.8445 | −1.13312 | ||||||||
\(249\) | 32.0614 | 2.03181 | ||||||||
\(250\) | 73.3735 | 4.64055 | ||||||||
\(251\) | −6.34159 | −0.400278 | −0.200139 | − | 0.979768i | \(-0.564139\pi\) | ||||
−0.200139 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(252\) | 22.1636 | 1.39618 | ||||||||
\(253\) | −25.8894 | −1.62765 | ||||||||
\(254\) | −9.47928 | −0.594783 | ||||||||
\(255\) | 8.83662 | 0.553371 | ||||||||
\(256\) | −18.5102 | −1.15689 | ||||||||
\(257\) | −27.3339 | −1.70504 | −0.852522 | − | 0.522691i | \(-0.824928\pi\) | ||||
−0.852522 | + | 0.522691i | \(0.824928\pi\) | |||||||
\(258\) | 36.4316 | 2.26814 | ||||||||
\(259\) | −18.0636 | −1.12242 | ||||||||
\(260\) | 13.9392 | 0.864470 | ||||||||
\(261\) | 20.7910 | 1.28693 | ||||||||
\(262\) | 47.5445 | 2.93731 | ||||||||
\(263\) | 0.297471 | 0.0183429 | 0.00917143 | − | 0.999958i | \(-0.497081\pi\) | ||||
0.00917143 | + | 0.999958i | \(0.497081\pi\) | |||||||
\(264\) | 33.8163 | 2.08125 | ||||||||
\(265\) | 25.9234 | 1.59246 | ||||||||
\(266\) | −12.0043 | −0.736029 | ||||||||
\(267\) | 39.7668 | 2.43369 | ||||||||
\(268\) | −4.55804 | −0.278427 | ||||||||
\(269\) | 29.5888 | 1.80406 | 0.902029 | − | 0.431675i | \(-0.142077\pi\) | ||||
0.902029 | + | 0.431675i | \(0.142077\pi\) | |||||||
\(270\) | −7.95176 | −0.483929 | ||||||||
\(271\) | 2.59118 | 0.157403 | 0.0787014 | − | 0.996898i | \(-0.474923\pi\) | ||||
0.0787014 | + | 0.996898i | \(0.474923\pi\) | |||||||
\(272\) | 0.336682 | 0.0204143 | ||||||||
\(273\) | 5.04112 | 0.305102 | ||||||||
\(274\) | −31.6949 | −1.91476 | ||||||||
\(275\) | 55.3676 | 3.33879 | ||||||||
\(276\) | 49.1970 | 2.96131 | ||||||||
\(277\) | 2.04608 | 0.122937 | 0.0614685 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614685 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(278\) | −41.2757 | −2.47555 | ||||||||
\(279\) | 19.4287 | 1.16317 | ||||||||
\(280\) | 25.6782 | 1.53457 | ||||||||
\(281\) | −32.6588 | −1.94826 | −0.974130 | − | 0.225988i | \(-0.927439\pi\) | ||||
−0.974130 | + | 0.225988i | \(0.927439\pi\) | |||||||
\(282\) | −6.47190 | −0.385396 | ||||||||
\(283\) | −4.86333 | −0.289095 | −0.144547 | − | 0.989498i | \(-0.546173\pi\) | ||||
−0.144547 | + | 0.989498i | \(0.546173\pi\) | |||||||
\(284\) | 24.2869 | 1.44116 | ||||||||
\(285\) | 27.3787 | 1.62177 | ||||||||
\(286\) | 10.1528 | 0.600347 | ||||||||
\(287\) | 5.19946 | 0.306914 | ||||||||
\(288\) | 17.2447 | 1.01615 | ||||||||
\(289\) | −16.2981 | −0.958710 | ||||||||
\(290\) | 60.4692 | 3.55087 | ||||||||
\(291\) | 38.3531 | 2.24830 | ||||||||
\(292\) | −17.1094 | −1.00125 | ||||||||
\(293\) | 10.0381 | 0.586432 | 0.293216 | − | 0.956046i | \(-0.405274\pi\) | ||||
0.293216 | + | 0.956046i | \(0.405274\pi\) | |||||||
\(294\) | −17.3144 | −1.00980 | ||||||||
\(295\) | 20.6207 | 1.20058 | ||||||||
\(296\) | 27.5388 | 1.60066 | ||||||||
\(297\) | −3.61613 | −0.209829 | ||||||||
\(298\) | −50.6317 | −2.93301 | ||||||||
\(299\) | 5.88386 | 0.340273 | ||||||||
\(300\) | −105.214 | −6.07451 | ||||||||
\(301\) | 12.5805 | 0.725130 | ||||||||
\(302\) | 1.40236 | 0.0806965 | ||||||||
\(303\) | 40.4332 | 2.32283 | ||||||||
\(304\) | 1.04315 | 0.0598287 | ||||||||
\(305\) | −49.9511 | −2.86019 | ||||||||
\(306\) | −6.43118 | −0.367646 | ||||||||
\(307\) | 24.1594 | 1.37885 | 0.689426 | − | 0.724356i | \(-0.257863\pi\) | ||||
0.689426 | + | 0.724356i | \(0.257863\pi\) | |||||||
\(308\) | 29.3144 | 1.67035 | ||||||||
\(309\) | 4.01476 | 0.228392 | ||||||||
\(310\) | 56.5072 | 3.20940 | ||||||||
\(311\) | −13.5451 | −0.768072 | −0.384036 | − | 0.923318i | \(-0.625466\pi\) | ||||
−0.384036 | + | 0.923318i | \(0.625466\pi\) | |||||||
\(312\) | −7.68541 | −0.435101 | ||||||||
\(313\) | −14.6200 | −0.826374 | −0.413187 | − | 0.910646i | \(-0.635584\pi\) | ||||
−0.413187 | + | 0.910646i | \(0.635584\pi\) | |||||||
\(314\) | −44.8288 | −2.52984 | ||||||||
\(315\) | −27.9580 | −1.57525 | ||||||||
\(316\) | −38.6431 | −2.17385 | ||||||||
\(317\) | 14.0975 | 0.791792 | 0.395896 | − | 0.918295i | \(-0.370434\pi\) | ||||
0.395896 | + | 0.918295i | \(0.370434\pi\) | |||||||
\(318\) | −35.8804 | −2.01207 | ||||||||
\(319\) | 27.4989 | 1.53964 | ||||||||
\(320\) | 53.5253 | 2.99215 | ||||||||
\(321\) | 2.36154 | 0.131808 | ||||||||
\(322\) | 27.2099 | 1.51635 | ||||||||
\(323\) | 2.17479 | 0.121009 | ||||||||
\(324\) | −26.3044 | −1.46136 | ||||||||
\(325\) | −12.5834 | −0.697999 | ||||||||
\(326\) | 0.772927 | 0.0428085 | ||||||||
\(327\) | −49.0072 | −2.71010 | ||||||||
\(328\) | −7.92680 | −0.437684 | ||||||||
\(329\) | −2.23487 | −0.123212 | ||||||||
\(330\) | −107.084 | −5.89480 | ||||||||
\(331\) | −19.3268 | −1.06230 | −0.531148 | − | 0.847279i | \(-0.678239\pi\) | ||||
−0.531148 | + | 0.847279i | \(0.678239\pi\) | |||||||
\(332\) | −42.3719 | −2.32546 | ||||||||
\(333\) | −29.9837 | −1.64310 | ||||||||
\(334\) | −4.05381 | −0.221815 | ||||||||
\(335\) | 5.74968 | 0.314138 | ||||||||
\(336\) | −2.02582 | −0.110517 | ||||||||
\(337\) | 16.1962 | 0.882262 | 0.441131 | − | 0.897443i | \(-0.354577\pi\) | ||||
0.441131 | + | 0.897443i | \(0.354577\pi\) | |||||||
\(338\) | −2.30742 | −0.125507 | ||||||||
\(339\) | 5.73462 | 0.311462 | ||||||||
\(340\) | −11.6784 | −0.633349 | ||||||||
\(341\) | 25.6972 | 1.39158 | ||||||||
\(342\) | −19.9259 | −1.07747 | ||||||||
\(343\) | −20.0083 | −1.08034 | ||||||||
\(344\) | −19.1796 | −1.03409 | ||||||||
\(345\) | −62.0588 | −3.34113 | ||||||||
\(346\) | −21.2134 | −1.14044 | ||||||||
\(347\) | −19.7790 | −1.06179 | −0.530897 | − | 0.847436i | \(-0.678145\pi\) | ||||
−0.530897 | + | 0.847436i | \(0.678145\pi\) | |||||||
\(348\) | −52.2555 | −2.80119 | ||||||||
\(349\) | −24.1406 | −1.29222 | −0.646109 | − | 0.763245i | \(-0.723605\pi\) | ||||
−0.646109 | + | 0.763245i | \(0.723605\pi\) | |||||||
\(350\) | −58.1916 | −3.11047 | ||||||||
\(351\) | 0.821837 | 0.0438664 | ||||||||
\(352\) | 22.8085 | 1.21570 | ||||||||
\(353\) | 12.2551 | 0.652272 | 0.326136 | − | 0.945323i | \(-0.394253\pi\) | ||||
0.326136 | + | 0.945323i | \(0.394253\pi\) | |||||||
\(354\) | −28.5410 | −1.51694 | ||||||||
\(355\) | −30.6364 | −1.62601 | ||||||||
\(356\) | −52.5553 | −2.78543 | ||||||||
\(357\) | −4.22350 | −0.223531 | ||||||||
\(358\) | 55.3056 | 2.92299 | ||||||||
\(359\) | −7.02540 | −0.370786 | −0.185393 | − | 0.982664i | \(-0.559356\pi\) | ||||
−0.185393 | + | 0.982664i | \(0.559356\pi\) | |||||||
\(360\) | 42.6232 | 2.24644 | ||||||||
\(361\) | −12.2618 | −0.645357 | ||||||||
\(362\) | 7.52427 | 0.395467 | ||||||||
\(363\) | −21.0293 | −1.10375 | ||||||||
\(364\) | −6.66228 | −0.349198 | ||||||||
\(365\) | 21.5824 | 1.12967 | ||||||||
\(366\) | 69.1370 | 3.61385 | ||||||||
\(367\) | −33.9945 | −1.77450 | −0.887250 | − | 0.461289i | \(-0.847387\pi\) | ||||
−0.887250 | + | 0.461289i | \(0.847387\pi\) | |||||||
\(368\) | −2.36448 | −0.123257 | ||||||||
\(369\) | 8.63056 | 0.449289 | ||||||||
\(370\) | −87.2058 | −4.53361 | ||||||||
\(371\) | −12.3902 | −0.643266 | ||||||||
\(372\) | −48.8317 | −2.53181 | ||||||||
\(373\) | −4.97998 | −0.257853 | −0.128927 | − | 0.991654i | \(-0.541153\pi\) | ||||
−0.128927 | + | 0.991654i | \(0.541153\pi\) | |||||||
\(374\) | −8.50611 | −0.439841 | ||||||||
\(375\) | 79.9838 | 4.13035 | ||||||||
\(376\) | 3.40716 | 0.175711 | ||||||||
\(377\) | −6.24966 | −0.321874 | ||||||||
\(378\) | 3.80057 | 0.195480 | ||||||||
\(379\) | 22.4150 | 1.15138 | 0.575690 | − | 0.817668i | \(-0.304734\pi\) | ||||
0.575690 | + | 0.817668i | \(0.304734\pi\) | |||||||
\(380\) | −36.1834 | −1.85617 | ||||||||
\(381\) | −10.3333 | −0.529390 | ||||||||
\(382\) | 40.3246 | 2.06318 | ||||||||
\(383\) | −30.2749 | −1.54697 | −0.773487 | − | 0.633812i | \(-0.781489\pi\) | ||||
−0.773487 | + | 0.633812i | \(0.781489\pi\) | |||||||
\(384\) | −48.0071 | −2.44985 | ||||||||
\(385\) | −36.9783 | −1.88459 | ||||||||
\(386\) | −60.7959 | −3.09443 | ||||||||
\(387\) | 20.8824 | 1.06151 | ||||||||
\(388\) | −50.6870 | −2.57324 | ||||||||
\(389\) | −9.64014 | −0.488774 | −0.244387 | − | 0.969678i | \(-0.578587\pi\) | ||||
−0.244387 | + | 0.969678i | \(0.578587\pi\) | |||||||
\(390\) | 24.3370 | 1.23235 | ||||||||
\(391\) | −4.92956 | −0.249299 | ||||||||
\(392\) | 9.11524 | 0.460389 | ||||||||
\(393\) | 51.8279 | 2.61437 | ||||||||
\(394\) | 50.7603 | 2.55727 | ||||||||
\(395\) | 48.7458 | 2.45267 | ||||||||
\(396\) | 48.6590 | 2.44521 | ||||||||
\(397\) | −26.0762 | −1.30873 | −0.654363 | − | 0.756180i | \(-0.727063\pi\) | ||||
−0.654363 | + | 0.756180i | \(0.727063\pi\) | |||||||
\(398\) | −62.4318 | −3.12942 | ||||||||
\(399\) | −13.0858 | −0.655107 | ||||||||
\(400\) | 5.05674 | 0.252837 | ||||||||
\(401\) | 36.0830 | 1.80190 | 0.900950 | − | 0.433924i | \(-0.142871\pi\) | ||||
0.900950 | + | 0.433924i | \(0.142871\pi\) | |||||||
\(402\) | −7.95809 | −0.396914 | ||||||||
\(403\) | −5.84018 | −0.290920 | ||||||||
\(404\) | −53.4361 | −2.65854 | ||||||||
\(405\) | 33.1814 | 1.64880 | ||||||||
\(406\) | −28.9015 | −1.43436 | ||||||||
\(407\) | −39.6576 | −1.96576 | ||||||||
\(408\) | 6.43891 | 0.318774 | ||||||||
\(409\) | −31.8928 | −1.57700 | −0.788498 | − | 0.615037i | \(-0.789141\pi\) | ||||
−0.788498 | + | 0.615037i | \(0.789141\pi\) | |||||||
\(410\) | 25.1014 | 1.23967 | ||||||||
\(411\) | −34.5503 | −1.70424 | ||||||||
\(412\) | −5.30586 | −0.261401 | ||||||||
\(413\) | −9.85575 | −0.484970 | ||||||||
\(414\) | 45.1656 | 2.21977 | ||||||||
\(415\) | 53.4494 | 2.62373 | ||||||||
\(416\) | −5.18367 | −0.254150 | ||||||||
\(417\) | −44.9943 | −2.20338 | ||||||||
\(418\) | −26.3547 | −1.28905 | ||||||||
\(419\) | 14.1428 | 0.690923 | 0.345462 | − | 0.938433i | \(-0.387722\pi\) | ||||
0.345462 | + | 0.938433i | \(0.387722\pi\) | |||||||
\(420\) | 70.2689 | 3.42877 | ||||||||
\(421\) | 5.07246 | 0.247217 | 0.123608 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123608 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(422\) | −37.9675 | −1.84823 | ||||||||
\(423\) | −3.70966 | −0.180370 | ||||||||
\(424\) | 18.8894 | 0.917350 | ||||||||
\(425\) | 10.5425 | 0.511384 | ||||||||
\(426\) | 42.4036 | 2.05446 | ||||||||
\(427\) | 23.8743 | 1.15536 | ||||||||
\(428\) | −3.12099 | −0.150859 | ||||||||
\(429\) | 11.0675 | 0.534343 | ||||||||
\(430\) | 60.7351 | 2.92891 | ||||||||
\(431\) | 16.8209 | 0.810233 | 0.405116 | − | 0.914265i | \(-0.367231\pi\) | ||||
0.405116 | + | 0.914265i | \(0.367231\pi\) | |||||||
\(432\) | −0.330262 | −0.0158898 | ||||||||
\(433\) | 15.9238 | 0.765249 | 0.382624 | − | 0.923904i | \(-0.375020\pi\) | ||||
0.382624 | + | 0.923904i | \(0.375020\pi\) | |||||||
\(434\) | −27.0079 | −1.29642 | ||||||||
\(435\) | 65.9170 | 3.16048 | ||||||||
\(436\) | 64.7673 | 3.10179 | ||||||||
\(437\) | −15.2734 | −0.730624 | ||||||||
\(438\) | −29.8720 | −1.42734 | ||||||||
\(439\) | −17.3955 | −0.830244 | −0.415122 | − | 0.909766i | \(-0.636261\pi\) | ||||
−0.415122 | + | 0.909766i | \(0.636261\pi\) | |||||||
\(440\) | 56.3750 | 2.68757 | ||||||||
\(441\) | −9.92451 | −0.472596 | ||||||||
\(442\) | 1.93318 | 0.0919520 | ||||||||
\(443\) | −14.0738 | −0.668664 | −0.334332 | − | 0.942455i | \(-0.608511\pi\) | ||||
−0.334332 | + | 0.942455i | \(0.608511\pi\) | |||||||
\(444\) | 75.3604 | 3.57645 | ||||||||
\(445\) | 66.2952 | 3.14269 | ||||||||
\(446\) | 15.7085 | 0.743818 | ||||||||
\(447\) | −55.1932 | −2.61055 | ||||||||
\(448\) | −25.5826 | −1.20866 | ||||||||
\(449\) | −19.3251 | −0.912007 | −0.456003 | − | 0.889978i | \(-0.650720\pi\) | ||||
−0.456003 | + | 0.889978i | \(0.650720\pi\) | |||||||
\(450\) | −96.5921 | −4.55339 | ||||||||
\(451\) | 11.4151 | 0.537516 | ||||||||
\(452\) | −7.57880 | −0.356477 | ||||||||
\(453\) | 1.52870 | 0.0718244 | ||||||||
\(454\) | −6.38841 | −0.299823 | ||||||||
\(455\) | 8.40403 | 0.393987 | ||||||||
\(456\) | 19.9498 | 0.934236 | ||||||||
\(457\) | 13.0933 | 0.612477 | 0.306238 | − | 0.951955i | \(-0.400930\pi\) | ||||
0.306238 | + | 0.951955i | \(0.400930\pi\) | |||||||
\(458\) | −38.5047 | −1.79921 | ||||||||
\(459\) | −0.688543 | −0.0321384 | ||||||||
\(460\) | 82.0161 | 3.82402 | ||||||||
\(461\) | 17.4314 | 0.811861 | 0.405930 | − | 0.913904i | \(-0.366948\pi\) | ||||
0.405930 | + | 0.913904i | \(0.366948\pi\) | |||||||
\(462\) | 51.1814 | 2.38118 | ||||||||
\(463\) | −15.9368 | −0.740644 | −0.370322 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370322 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(464\) | 2.51148 | 0.116593 | ||||||||
\(465\) | 61.5981 | 2.85654 | ||||||||
\(466\) | −52.0897 | −2.41301 | ||||||||
\(467\) | 31.3594 | 1.45114 | 0.725569 | − | 0.688149i | \(-0.241576\pi\) | ||||
0.725569 | + | 0.688149i | \(0.241576\pi\) | |||||||
\(468\) | −11.0587 | −0.511189 | ||||||||
\(469\) | −2.74808 | −0.126895 | ||||||||
\(470\) | −10.7893 | −0.497673 | ||||||||
\(471\) | −48.8675 | −2.25170 | ||||||||
\(472\) | 15.0255 | 0.691606 | ||||||||
\(473\) | 27.6198 | 1.26996 | ||||||||
\(474\) | −67.4688 | −3.09894 | ||||||||
\(475\) | 32.6639 | 1.49872 | ||||||||
\(476\) | 5.58172 | 0.255838 | ||||||||
\(477\) | −20.5664 | −0.941672 | ||||||||
\(478\) | 17.8444 | 0.816183 | ||||||||
\(479\) | −5.29035 | −0.241722 | −0.120861 | − | 0.992669i | \(-0.538566\pi\) | ||||
−0.120861 | + | 0.992669i | \(0.538566\pi\) | |||||||
\(480\) | 54.6736 | 2.49550 | ||||||||
\(481\) | 9.01297 | 0.410956 | ||||||||
\(482\) | −3.16817 | −0.144306 | ||||||||
\(483\) | 29.6612 | 1.34963 | ||||||||
\(484\) | 27.7921 | 1.26328 | ||||||||
\(485\) | 63.9384 | 2.90329 | ||||||||
\(486\) | −51.6151 | −2.34131 | ||||||||
\(487\) | −28.7874 | −1.30448 | −0.652240 | − | 0.758012i | \(-0.726171\pi\) | ||||
−0.652240 | + | 0.758012i | \(0.726171\pi\) | |||||||
\(488\) | −36.3975 | −1.64764 | ||||||||
\(489\) | 0.842561 | 0.0381019 | ||||||||
\(490\) | −28.8648 | −1.30398 | ||||||||
\(491\) | 9.24466 | 0.417205 | 0.208603 | − | 0.978000i | \(-0.433108\pi\) | ||||
0.208603 | + | 0.978000i | \(0.433108\pi\) | |||||||
\(492\) | −21.6918 | −0.977944 | ||||||||
\(493\) | 5.23603 | 0.235819 | ||||||||
\(494\) | 5.98962 | 0.269486 | ||||||||
\(495\) | −61.3802 | −2.75883 | ||||||||
\(496\) | 2.34693 | 0.105380 | ||||||||
\(497\) | 14.6428 | 0.656818 | ||||||||
\(498\) | −73.9790 | −3.31508 | ||||||||
\(499\) | 0.659907 | 0.0295415 | 0.0147708 | − | 0.999891i | \(-0.495298\pi\) | ||||
0.0147708 | + | 0.999891i | \(0.495298\pi\) | |||||||
\(500\) | −105.706 | −4.72730 | ||||||||
\(501\) | −4.41903 | −0.197428 | ||||||||
\(502\) | 14.6327 | 0.653090 | ||||||||
\(503\) | 12.6755 | 0.565170 | 0.282585 | − | 0.959242i | \(-0.408808\pi\) | ||||
0.282585 | + | 0.959242i | \(0.408808\pi\) | |||||||
\(504\) | −20.3719 | −0.907438 | ||||||||
\(505\) | 67.4061 | 2.99953 | ||||||||
\(506\) | 59.7377 | 2.65566 | ||||||||
\(507\) | −2.51530 | −0.111708 | ||||||||
\(508\) | 13.6563 | 0.605902 | ||||||||
\(509\) | 10.8954 | 0.482931 | 0.241466 | − | 0.970409i | \(-0.422372\pi\) | ||||
0.241466 | + | 0.970409i | \(0.422372\pi\) | |||||||
\(510\) | −20.3898 | −0.902876 | ||||||||
\(511\) | −10.3154 | −0.456325 | ||||||||
\(512\) | 4.53884 | 0.200590 | ||||||||
\(513\) | −2.13333 | −0.0941888 | ||||||||
\(514\) | 63.0709 | 2.78194 | ||||||||
\(515\) | 6.69300 | 0.294929 | ||||||||
\(516\) | −52.4853 | −2.31054 | ||||||||
\(517\) | −4.90653 | −0.215789 | ||||||||
\(518\) | 41.6804 | 1.83133 | ||||||||
\(519\) | −23.1245 | −1.01505 | ||||||||
\(520\) | −12.8123 | −0.561858 | ||||||||
\(521\) | 6.30000 | 0.276008 | 0.138004 | − | 0.990432i | \(-0.455931\pi\) | ||||
0.138004 | + | 0.990432i | \(0.455931\pi\) | |||||||
\(522\) | −47.9735 | −2.09974 | ||||||||
\(523\) | −4.69048 | −0.205100 | −0.102550 | − | 0.994728i | \(-0.532700\pi\) | ||||
−0.102550 | + | 0.994728i | \(0.532700\pi\) | |||||||
\(524\) | −68.4951 | −2.99222 | ||||||||
\(525\) | −63.4342 | −2.76849 | ||||||||
\(526\) | −0.686391 | −0.0299281 | ||||||||
\(527\) | 4.89296 | 0.213141 | ||||||||
\(528\) | −4.44757 | −0.193556 | ||||||||
\(529\) | 11.6198 | 0.505211 | ||||||||
\(530\) | −59.8161 | −2.59825 | ||||||||
\(531\) | −16.3595 | −0.709943 | ||||||||
\(532\) | 17.2940 | 0.749789 | ||||||||
\(533\) | −2.59430 | −0.112372 | ||||||||
\(534\) | −91.7588 | −3.97079 | ||||||||
\(535\) | 3.93692 | 0.170208 | ||||||||
\(536\) | 4.18957 | 0.180962 | ||||||||
\(537\) | 60.2882 | 2.60163 | ||||||||
\(538\) | −68.2737 | −2.94349 | ||||||||
\(539\) | −13.1265 | −0.565400 | ||||||||
\(540\) | 11.4557 | 0.492975 | ||||||||
\(541\) | 9.11956 | 0.392081 | 0.196040 | − | 0.980596i | \(-0.437192\pi\) | ||||
0.196040 | + | 0.980596i | \(0.437192\pi\) | |||||||
\(542\) | −5.97893 | −0.256817 | ||||||||
\(543\) | 8.20214 | 0.351988 | ||||||||
\(544\) | 4.34293 | 0.186202 | ||||||||
\(545\) | −81.6997 | −3.49963 | ||||||||
\(546\) | −11.6320 | −0.497803 | ||||||||
\(547\) | 16.9628 | 0.725275 | 0.362638 | − | 0.931930i | \(-0.381876\pi\) | ||||
0.362638 | + | 0.931930i | \(0.381876\pi\) | |||||||
\(548\) | 45.6613 | 1.95055 | ||||||||
\(549\) | 39.6289 | 1.69132 | ||||||||
\(550\) | −127.756 | −5.44754 | ||||||||
\(551\) | 16.2229 | 0.691119 | ||||||||
\(552\) | −45.2199 | −1.92469 | ||||||||
\(553\) | −23.2983 | −0.990742 | ||||||||
\(554\) | −4.72117 | −0.200583 | ||||||||
\(555\) | −95.0623 | −4.03517 | ||||||||
\(556\) | 59.4640 | 2.52183 | ||||||||
\(557\) | 0.459805 | 0.0194825 | 0.00974127 | − | 0.999953i | \(-0.496899\pi\) | ||||
0.00974127 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(558\) | −44.8303 | −1.89782 | ||||||||
\(559\) | −6.27715 | −0.265495 | ||||||||
\(560\) | −3.37724 | −0.142714 | ||||||||
\(561\) | −9.27245 | −0.391483 | ||||||||
\(562\) | 75.3576 | 3.17877 | ||||||||
\(563\) | 14.8643 | 0.626458 | 0.313229 | − | 0.949678i | \(-0.398589\pi\) | ||||
0.313229 | + | 0.949678i | \(0.398589\pi\) | |||||||
\(564\) | 9.32376 | 0.392601 | ||||||||
\(565\) | 9.56016 | 0.402199 | ||||||||
\(566\) | 11.2217 | 0.471685 | ||||||||
\(567\) | −15.8592 | −0.666022 | ||||||||
\(568\) | −22.3236 | −0.936676 | ||||||||
\(569\) | 31.3976 | 1.31626 | 0.658128 | − | 0.752906i | \(-0.271349\pi\) | ||||
0.658128 | + | 0.752906i | \(0.271349\pi\) | |||||||
\(570\) | −63.1742 | −2.64608 | ||||||||
\(571\) | −15.3776 | −0.643534 | −0.321767 | − | 0.946819i | \(-0.604277\pi\) | ||||
−0.321767 | + | 0.946819i | \(0.604277\pi\) | |||||||
\(572\) | −14.6266 | −0.611571 | ||||||||
\(573\) | 43.9575 | 1.83635 | ||||||||
\(574\) | −11.9973 | −0.500759 | ||||||||
\(575\) | −74.0387 | −3.08763 | ||||||||
\(576\) | −42.4645 | −1.76935 | ||||||||
\(577\) | −32.4485 | −1.35085 | −0.675424 | − | 0.737429i | \(-0.736039\pi\) | ||||
−0.675424 | + | 0.737429i | \(0.736039\pi\) | |||||||
\(578\) | 37.6065 | 1.56422 | ||||||||
\(579\) | −66.2731 | −2.75422 | ||||||||
\(580\) | −87.1151 | −3.61726 | ||||||||
\(581\) | −25.5464 | −1.05984 | ||||||||
\(582\) | −88.4967 | −3.66831 | ||||||||
\(583\) | −27.2019 | −1.12659 | ||||||||
\(584\) | 15.7262 | 0.650757 | ||||||||
\(585\) | 13.9498 | 0.576755 | ||||||||
\(586\) | −23.1621 | −0.956818 | ||||||||
\(587\) | −15.1447 | −0.625088 | −0.312544 | − | 0.949903i | \(-0.601181\pi\) | ||||
−0.312544 | + | 0.949903i | \(0.601181\pi\) | |||||||
\(588\) | 24.9440 | 1.02867 | ||||||||
\(589\) | 15.1600 | 0.624656 | ||||||||
\(590\) | −47.5806 | −1.95886 | ||||||||
\(591\) | 55.3334 | 2.27611 | ||||||||
\(592\) | −3.62194 | −0.148861 | ||||||||
\(593\) | −35.3234 | −1.45056 | −0.725279 | − | 0.688455i | \(-0.758289\pi\) | ||||
−0.725279 | + | 0.688455i | \(0.758289\pi\) | |||||||
\(594\) | 8.34394 | 0.342356 | ||||||||
\(595\) | −7.04098 | −0.288652 | ||||||||
\(596\) | 72.9426 | 2.98785 | ||||||||
\(597\) | −68.0563 | −2.78536 | ||||||||
\(598\) | −13.5765 | −0.555186 | ||||||||
\(599\) | 26.5482 | 1.08473 | 0.542364 | − | 0.840143i | \(-0.317529\pi\) | ||||
0.542364 | + | 0.840143i | \(0.317529\pi\) | |||||||
\(600\) | 96.7082 | 3.94810 | ||||||||
\(601\) | 13.0158 | 0.530924 | 0.265462 | − | 0.964121i | \(-0.414476\pi\) | ||||
0.265462 | + | 0.964121i | \(0.414476\pi\) | |||||||
\(602\) | −29.0286 | −1.18312 | ||||||||
\(603\) | −4.56153 | −0.185760 | ||||||||
\(604\) | −2.02031 | −0.0822051 | ||||||||
\(605\) | −35.0579 | −1.42531 | ||||||||
\(606\) | −93.2965 | −3.78991 | ||||||||
\(607\) | 29.0374 | 1.17859 | 0.589297 | − | 0.807917i | \(-0.299405\pi\) | ||||
0.589297 | + | 0.807917i | \(0.299405\pi\) | |||||||
\(608\) | 13.4558 | 0.545705 | ||||||||
\(609\) | −31.5053 | −1.27666 | ||||||||
\(610\) | 115.258 | 4.66667 | ||||||||
\(611\) | 1.11510 | 0.0451123 | ||||||||
\(612\) | 9.26509 | 0.374519 | ||||||||
\(613\) | 11.8500 | 0.478617 | 0.239308 | − | 0.970944i | \(-0.423079\pi\) | ||||
0.239308 | + | 0.970944i | \(0.423079\pi\) | |||||||
\(614\) | −55.7460 | −2.24973 | ||||||||
\(615\) | 27.3629 | 1.10338 | ||||||||
\(616\) | −26.9447 | −1.08563 | ||||||||
\(617\) | 37.5497 | 1.51169 | 0.755847 | − | 0.654749i | \(-0.227225\pi\) | ||||
0.755847 | + | 0.654749i | \(0.227225\pi\) | |||||||
\(618\) | −9.26374 | −0.372642 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | −81.4073 | −3.26939 | ||||||||
\(621\) | 4.83557 | 0.194045 | ||||||||
\(622\) | 31.2542 | 1.25318 | ||||||||
\(623\) | −31.6860 | −1.26947 | ||||||||
\(624\) | 1.01080 | 0.0404642 | ||||||||
\(625\) | 70.4240 | 2.81696 | ||||||||
\(626\) | 33.7346 | 1.34831 | ||||||||
\(627\) | −28.7290 | −1.14733 | ||||||||
\(628\) | 64.5827 | 2.57713 | ||||||||
\(629\) | −7.55115 | −0.301084 | ||||||||
\(630\) | 64.5108 | 2.57017 | ||||||||
\(631\) | 7.06177 | 0.281125 | 0.140562 | − | 0.990072i | \(-0.455109\pi\) | ||||
0.140562 | + | 0.990072i | \(0.455109\pi\) | |||||||
\(632\) | 35.5192 | 1.41288 | ||||||||
\(633\) | −41.3880 | −1.64503 | ||||||||
\(634\) | −32.5288 | −1.29188 | ||||||||
\(635\) | −17.2266 | −0.683616 | ||||||||
\(636\) | 51.6912 | 2.04969 | ||||||||
\(637\) | 2.98326 | 0.118201 | ||||||||
\(638\) | −63.4516 | −2.51207 | ||||||||
\(639\) | 24.3055 | 0.961511 | ||||||||
\(640\) | −80.0325 | −3.16356 | ||||||||
\(641\) | 48.5922 | 1.91928 | 0.959638 | − | 0.281237i | \(-0.0907446\pi\) | ||||
0.959638 | + | 0.281237i | \(0.0907446\pi\) | |||||||
\(642\) | −5.44907 | −0.215058 | ||||||||
\(643\) | −22.8077 | −0.899450 | −0.449725 | − | 0.893167i | \(-0.648478\pi\) | ||||
−0.449725 | + | 0.893167i | \(0.648478\pi\) | |||||||
\(644\) | −39.1999 | −1.54469 | ||||||||
\(645\) | 66.2068 | 2.60689 | ||||||||
\(646\) | −5.01816 | −0.197437 | ||||||||
\(647\) | 39.8494 | 1.56664 | 0.783320 | − | 0.621619i | \(-0.213525\pi\) | ||||
0.783320 | + | 0.621619i | \(0.213525\pi\) | |||||||
\(648\) | 24.1780 | 0.949802 | ||||||||
\(649\) | −21.6377 | −0.849355 | ||||||||
\(650\) | 29.0351 | 1.13885 | ||||||||
\(651\) | −29.4410 | −1.15389 | ||||||||
\(652\) | −1.11352 | −0.0436087 | ||||||||
\(653\) | 21.9504 | 0.858987 | 0.429494 | − | 0.903070i | \(-0.358692\pi\) | ||||
0.429494 | + | 0.903070i | \(0.358692\pi\) | |||||||
\(654\) | 113.080 | 4.42178 | ||||||||
\(655\) | 86.4022 | 3.37601 | ||||||||
\(656\) | 1.04254 | 0.0407045 | ||||||||
\(657\) | −17.1225 | −0.668011 | ||||||||
\(658\) | 5.15679 | 0.201032 | ||||||||
\(659\) | 49.2922 | 1.92015 | 0.960076 | − | 0.279740i | \(-0.0902483\pi\) | ||||
0.960076 | + | 0.279740i | \(0.0902483\pi\) | |||||||
\(660\) | 154.271 | 6.00501 | ||||||||
\(661\) | −31.3296 | −1.21858 | −0.609290 | − | 0.792948i | \(-0.708545\pi\) | ||||
−0.609290 | + | 0.792948i | \(0.708545\pi\) | |||||||
\(662\) | 44.5951 | 1.73324 | ||||||||
\(663\) | 2.10734 | 0.0818424 | ||||||||
\(664\) | 38.9466 | 1.51142 | ||||||||
\(665\) | −21.8152 | −0.845959 | ||||||||
\(666\) | 69.1851 | 2.68087 | ||||||||
\(667\) | −36.7722 | −1.42382 | ||||||||
\(668\) | 5.84013 | 0.225961 | ||||||||
\(669\) | 17.1237 | 0.662040 | ||||||||
\(670\) | −13.2669 | −0.512546 | ||||||||
\(671\) | 52.4147 | 2.02345 | ||||||||
\(672\) | −26.1315 | −1.00804 | ||||||||
\(673\) | −23.0839 | −0.889821 | −0.444910 | − | 0.895575i | \(-0.646764\pi\) | ||||
−0.444910 | + | 0.895575i | \(0.646764\pi\) | |||||||
\(674\) | −37.3714 | −1.43949 | ||||||||
\(675\) | −10.3415 | −0.398043 | ||||||||
\(676\) | 3.32419 | 0.127853 | ||||||||
\(677\) | −18.4307 | −0.708351 | −0.354175 | − | 0.935179i | \(-0.615238\pi\) | ||||
−0.354175 | + | 0.935179i | \(0.615238\pi\) | |||||||
\(678\) | −13.2322 | −0.508178 | ||||||||
\(679\) | −30.5596 | −1.17277 | ||||||||
\(680\) | 10.7343 | 0.411641 | ||||||||
\(681\) | −6.96395 | −0.266859 | ||||||||
\(682\) | −59.2942 | −2.27049 | ||||||||
\(683\) | 10.4717 | 0.400689 | 0.200345 | − | 0.979725i | \(-0.435794\pi\) | ||||
0.200345 | + | 0.979725i | \(0.435794\pi\) | |||||||
\(684\) | 28.7062 | 1.09761 | ||||||||
\(685\) | −57.5988 | −2.20074 | ||||||||
\(686\) | 46.1675 | 1.76268 | ||||||||
\(687\) | −41.9737 | −1.60140 | ||||||||
\(688\) | 2.52253 | 0.0961705 | ||||||||
\(689\) | 6.18217 | 0.235522 | ||||||||
\(690\) | 143.196 | 5.45137 | ||||||||
\(691\) | −48.1953 | −1.83344 | −0.916718 | − | 0.399535i | \(-0.869172\pi\) | ||||
−0.916718 | + | 0.399535i | \(0.869172\pi\) | |||||||
\(692\) | 30.5611 | 1.16176 | ||||||||
\(693\) | 29.3369 | 1.11442 | ||||||||
\(694\) | 45.6386 | 1.73242 | ||||||||
\(695\) | −75.0099 | −2.84529 | ||||||||
\(696\) | 48.0312 | 1.82062 | ||||||||
\(697\) | 2.17353 | 0.0823285 | ||||||||
\(698\) | 55.7026 | 2.10837 | ||||||||
\(699\) | −56.7826 | −2.14771 | ||||||||
\(700\) | 83.8338 | 3.16862 | ||||||||
\(701\) | 3.42573 | 0.129388 | 0.0646941 | − | 0.997905i | \(-0.479393\pi\) | ||||
0.0646941 | + | 0.997905i | \(0.479393\pi\) | |||||||
\(702\) | −1.89632 | −0.0715721 | ||||||||
\(703\) | −23.3959 | −0.882393 | ||||||||
\(704\) | −56.1651 | −2.11680 | ||||||||
\(705\) | −11.7613 | −0.442957 | ||||||||
\(706\) | −28.2776 | −1.06424 | ||||||||
\(707\) | −32.2170 | −1.21165 | ||||||||
\(708\) | 41.1177 | 1.54530 | ||||||||
\(709\) | 26.2834 | 0.987093 | 0.493546 | − | 0.869719i | \(-0.335700\pi\) | ||||
0.493546 | + | 0.869719i | \(0.335700\pi\) | |||||||
\(710\) | 70.6910 | 2.65299 | ||||||||
\(711\) | −38.6727 | −1.45034 | ||||||||
\(712\) | 48.3068 | 1.81037 | ||||||||
\(713\) | −34.3628 | −1.28690 | ||||||||
\(714\) | 9.74539 | 0.364712 | ||||||||
\(715\) | 18.4506 | 0.690012 | ||||||||
\(716\) | −79.6761 | −2.97764 | ||||||||
\(717\) | 19.4520 | 0.726449 | ||||||||
\(718\) | 16.2106 | 0.604972 | ||||||||
\(719\) | 1.00578 | 0.0375094 | 0.0187547 | − | 0.999824i | \(-0.494030\pi\) | ||||
0.0187547 | + | 0.999824i | \(0.494030\pi\) | |||||||
\(720\) | −5.60587 | −0.208918 | ||||||||
\(721\) | −3.19895 | −0.119135 | ||||||||
\(722\) | 28.2931 | 1.05296 | ||||||||
\(723\) | −3.45360 | −0.128441 | ||||||||
\(724\) | −10.8398 | −0.402860 | ||||||||
\(725\) | 78.6417 | 2.92068 | ||||||||
\(726\) | 48.5235 | 1.80088 | ||||||||
\(727\) | 15.7201 | 0.583027 | 0.291513 | − | 0.956567i | \(-0.405841\pi\) | ||||
0.291513 | + | 0.956567i | \(0.405841\pi\) | |||||||
\(728\) | 6.12370 | 0.226959 | ||||||||
\(729\) | −32.5261 | −1.20467 | ||||||||
\(730\) | −49.7996 | −1.84317 | ||||||||
\(731\) | 5.25905 | 0.194513 | ||||||||
\(732\) | −99.6024 | −3.68141 | ||||||||
\(733\) | −41.8845 | −1.54704 | −0.773519 | − | 0.633773i | \(-0.781506\pi\) | ||||
−0.773519 | + | 0.633773i | \(0.781506\pi\) | |||||||
\(734\) | 78.4397 | 2.89526 | ||||||||
\(735\) | −31.4653 | −1.16061 | ||||||||
\(736\) | −30.5000 | −1.12424 | ||||||||
\(737\) | −6.03325 | −0.222238 | ||||||||
\(738\) | −19.9143 | −0.733057 | ||||||||
\(739\) | −33.1751 | −1.22036 | −0.610182 | − | 0.792261i | \(-0.708904\pi\) | ||||
−0.610182 | + | 0.792261i | \(0.708904\pi\) | |||||||
\(740\) | 125.633 | 4.61837 | ||||||||
\(741\) | 6.52923 | 0.239857 | ||||||||
\(742\) | 28.5894 | 1.04955 | ||||||||
\(743\) | −28.3361 | −1.03955 | −0.519775 | − | 0.854303i | \(-0.673984\pi\) | ||||
−0.519775 | + | 0.854303i | \(0.673984\pi\) | |||||||
\(744\) | 44.8842 | 1.64553 | ||||||||
\(745\) | −92.0124 | −3.37107 | ||||||||
\(746\) | 11.4909 | 0.420712 | ||||||||
\(747\) | −42.4043 | −1.55149 | ||||||||
\(748\) | 12.2544 | 0.448063 | ||||||||
\(749\) | −1.88167 | −0.0687547 | ||||||||
\(750\) | −184.556 | −6.73904 | ||||||||
\(751\) | −29.2251 | −1.06644 | −0.533220 | − | 0.845977i | \(-0.679018\pi\) | ||||
−0.533220 | + | 0.845977i | \(0.679018\pi\) | |||||||
\(752\) | −0.448115 | −0.0163411 | ||||||||
\(753\) | 15.9510 | 0.581287 | ||||||||
\(754\) | 14.4206 | 0.525167 | ||||||||
\(755\) | 2.54849 | 0.0927489 | ||||||||
\(756\) | −5.47530 | −0.199135 | ||||||||
\(757\) | −3.60291 | −0.130950 | −0.0654750 | − | 0.997854i | \(-0.520856\pi\) | ||||
−0.0654750 | + | 0.997854i | \(0.520856\pi\) | |||||||
\(758\) | −51.7207 | −1.87858 | ||||||||
\(759\) | 65.1195 | 2.36369 | ||||||||
\(760\) | 33.2583 | 1.20641 | ||||||||
\(761\) | −19.0691 | −0.691253 | −0.345626 | − | 0.938372i | \(-0.612334\pi\) | ||||
−0.345626 | + | 0.938372i | \(0.612334\pi\) | |||||||
\(762\) | 23.8432 | 0.863749 | ||||||||
\(763\) | 39.0487 | 1.41366 | ||||||||
\(764\) | −58.0937 | −2.10175 | ||||||||
\(765\) | −11.6873 | −0.422556 | ||||||||
\(766\) | 69.8569 | 2.52403 | ||||||||
\(767\) | 4.91759 | 0.177564 | ||||||||
\(768\) | 46.5588 | 1.68004 | ||||||||
\(769\) | 3.33850 | 0.120389 | 0.0601947 | − | 0.998187i | \(-0.480828\pi\) | ||||
0.0601947 | + | 0.998187i | \(0.480828\pi\) | |||||||
\(770\) | 85.3244 | 3.07488 | ||||||||
\(771\) | 68.7531 | 2.47608 | ||||||||
\(772\) | 87.5858 | 3.15228 | ||||||||
\(773\) | −24.8408 | −0.893461 | −0.446730 | − | 0.894669i | \(-0.647412\pi\) | ||||
−0.446730 | + | 0.894669i | \(0.647412\pi\) | |||||||
\(774\) | −48.1845 | −1.73196 | ||||||||
\(775\) | 73.4891 | 2.63981 | ||||||||
\(776\) | 46.5895 | 1.67246 | ||||||||
\(777\) | 45.4354 | 1.62999 | ||||||||
\(778\) | 22.2438 | 0.797481 | ||||||||
\(779\) | 6.73431 | 0.241282 | ||||||||
\(780\) | −35.0612 | −1.25539 | ||||||||
\(781\) | 32.1474 | 1.15032 | ||||||||
\(782\) | 11.3746 | 0.406754 | ||||||||
\(783\) | −5.13620 | −0.183553 | ||||||||
\(784\) | −1.19885 | −0.0428161 | ||||||||
\(785\) | −81.4670 | −2.90768 | ||||||||
\(786\) | −119.589 | −4.26559 | ||||||||
\(787\) | −28.3371 | −1.01011 | −0.505054 | − | 0.863088i | \(-0.668527\pi\) | ||||
−0.505054 | + | 0.863088i | \(0.668527\pi\) | |||||||
\(788\) | −73.1280 | −2.60508 | ||||||||
\(789\) | −0.748230 | −0.0266377 | ||||||||
\(790\) | −112.477 | −4.00176 | ||||||||
\(791\) | −4.56932 | −0.162466 | ||||||||
\(792\) | −44.7254 | −1.58925 | ||||||||
\(793\) | −11.9123 | −0.423017 | ||||||||
\(794\) | 60.1687 | 2.13531 | ||||||||
\(795\) | −65.2051 | −2.31259 | ||||||||
\(796\) | 89.9424 | 3.18792 | ||||||||
\(797\) | 23.9952 | 0.849954 | 0.424977 | − | 0.905204i | \(-0.360282\pi\) | ||||
0.424977 | + | 0.905204i | \(0.360282\pi\) | |||||||
\(798\) | 30.1944 | 1.06887 | ||||||||
\(799\) | −0.934245 | −0.0330512 | ||||||||
\(800\) | 65.2279 | 2.30616 | ||||||||
\(801\) | −52.5956 | −1.85837 | ||||||||
\(802\) | −83.2587 | −2.93997 | ||||||||
\(803\) | −22.6468 | −0.799189 | ||||||||
\(804\) | 11.4648 | 0.404334 | ||||||||
\(805\) | 49.4482 | 1.74282 | ||||||||
\(806\) | 13.4758 | 0.474663 | ||||||||
\(807\) | −74.4246 | −2.61987 | ||||||||
\(808\) | 49.1163 | 1.72791 | ||||||||
\(809\) | −9.66366 | −0.339756 | −0.169878 | − | 0.985465i | \(-0.554337\pi\) | ||||
−0.169878 | + | 0.985465i | \(0.554337\pi\) | |||||||
\(810\) | −76.5634 | −2.69016 | ||||||||
\(811\) | −23.4690 | −0.824109 | −0.412055 | − | 0.911159i | \(-0.635189\pi\) | ||||
−0.412055 | + | 0.911159i | \(0.635189\pi\) | |||||||
\(812\) | 41.6370 | 1.46117 | ||||||||
\(813\) | −6.51758 | −0.228582 | ||||||||
\(814\) | 91.5068 | 3.20731 | ||||||||
\(815\) | 1.40463 | 0.0492021 | ||||||||
\(816\) | −0.846855 | −0.0296459 | ||||||||
\(817\) | 16.2943 | 0.570064 | ||||||||
\(818\) | 73.5901 | 2.57302 | ||||||||
\(819\) | −6.66738 | −0.232977 | ||||||||
\(820\) | −36.1624 | −1.26285 | ||||||||
\(821\) | −0.117516 | −0.00410135 | −0.00205068 | − | 0.999998i | \(-0.500653\pi\) | ||||
−0.00205068 | + | 0.999998i | \(0.500653\pi\) | |||||||
\(822\) | 79.7221 | 2.78063 | ||||||||
\(823\) | −18.1813 | −0.633759 | −0.316880 | − | 0.948466i | \(-0.602635\pi\) | ||||
−0.316880 | + | 0.948466i | \(0.602635\pi\) | |||||||
\(824\) | 4.87694 | 0.169896 | ||||||||
\(825\) | −139.266 | −4.84862 | ||||||||
\(826\) | 22.7414 | 0.791273 | ||||||||
\(827\) | −54.8879 | −1.90864 | −0.954319 | − | 0.298789i | \(-0.903417\pi\) | ||||
−0.954319 | + | 0.298789i | \(0.903417\pi\) | |||||||
\(828\) | −65.0679 | −2.26127 | ||||||||
\(829\) | 15.8018 | 0.548819 | 0.274409 | − | 0.961613i | \(-0.411518\pi\) | ||||
0.274409 | + | 0.961613i | \(0.411518\pi\) | |||||||
\(830\) | −123.330 | −4.28086 | ||||||||
\(831\) | −5.14651 | −0.178530 | ||||||||
\(832\) | 12.7646 | 0.442534 | ||||||||
\(833\) | −2.49940 | −0.0865992 | ||||||||
\(834\) | 103.821 | 3.59502 | ||||||||
\(835\) | −7.36695 | −0.254944 | ||||||||
\(836\) | 37.9679 | 1.31315 | ||||||||
\(837\) | −4.79968 | −0.165901 | ||||||||
\(838\) | −32.6335 | −1.12731 | ||||||||
\(839\) | 2.26113 | 0.0780630 | 0.0390315 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390315 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(840\) | −64.5884 | −2.22851 | ||||||||
\(841\) | 10.0583 | 0.346837 | ||||||||
\(842\) | −11.7043 | −0.403357 | ||||||||
\(843\) | 82.1467 | 2.82928 | ||||||||
\(844\) | 54.6979 | 1.88278 | ||||||||
\(845\) | −4.19325 | −0.144252 | ||||||||
\(846\) | 8.55974 | 0.294290 | ||||||||
\(847\) | 16.7561 | 0.575745 | ||||||||
\(848\) | −2.48436 | −0.0853133 | ||||||||
\(849\) | 12.2327 | 0.419826 | ||||||||
\(850\) | −24.3259 | −0.834371 | ||||||||
\(851\) | 53.0311 | 1.81788 | ||||||||
\(852\) | −61.0889 | −2.09287 | ||||||||
\(853\) | −0.161949 | −0.00554503 | −0.00277251 | − | 0.999996i | \(-0.500883\pi\) | ||||
−0.00277251 | + | 0.999996i | \(0.500883\pi\) | |||||||
\(854\) | −55.0881 | −1.88508 | ||||||||
\(855\) | −36.2111 | −1.23839 | ||||||||
\(856\) | 2.86869 | 0.0980497 | ||||||||
\(857\) | −3.34887 | −0.114395 | −0.0571976 | − | 0.998363i | \(-0.518217\pi\) | ||||
−0.0571976 | + | 0.998363i | \(0.518217\pi\) | |||||||
\(858\) | −25.5373 | −0.871830 | ||||||||
\(859\) | 22.6702 | 0.773497 | 0.386749 | − | 0.922185i | \(-0.373598\pi\) | ||||
0.386749 | + | 0.922185i | \(0.373598\pi\) | |||||||
\(860\) | −87.4982 | −2.98366 | ||||||||
\(861\) | −13.0782 | −0.445704 | ||||||||
\(862\) | −38.8128 | −1.32197 | ||||||||
\(863\) | 14.7355 | 0.501604 | 0.250802 | − | 0.968038i | \(-0.419306\pi\) | ||||
0.250802 | + | 0.968038i | \(0.419306\pi\) | |||||||
\(864\) | −4.26013 | −0.144933 | ||||||||
\(865\) | −38.5509 | −1.31077 | ||||||||
\(866\) | −36.7429 | −1.24857 | ||||||||
\(867\) | 40.9945 | 1.39225 | ||||||||
\(868\) | 38.9089 | 1.32065 | ||||||||
\(869\) | −51.1500 | −1.73514 | ||||||||
\(870\) | −152.098 | −5.15661 | ||||||||
\(871\) | 1.37117 | 0.0464605 | ||||||||
\(872\) | −59.5315 | −2.01599 | ||||||||
\(873\) | −50.7258 | −1.71681 | ||||||||
\(874\) | 35.2421 | 1.19208 | ||||||||
\(875\) | −63.7308 | −2.15449 | ||||||||
\(876\) | 43.0352 | 1.45402 | ||||||||
\(877\) | −13.4780 | −0.455120 | −0.227560 | − | 0.973764i | \(-0.573075\pi\) | ||||
−0.227560 | + | 0.973764i | \(0.573075\pi\) | |||||||
\(878\) | 40.1388 | 1.35462 | ||||||||
\(879\) | −25.2488 | −0.851622 | ||||||||
\(880\) | −7.41453 | −0.249944 | ||||||||
\(881\) | −30.3003 | −1.02084 | −0.510422 | − | 0.859924i | \(-0.670511\pi\) | ||||
−0.510422 | + | 0.859924i | \(0.670511\pi\) | |||||||
\(882\) | 22.9000 | 0.771084 | ||||||||
\(883\) | 31.8695 | 1.07249 | 0.536246 | − | 0.844061i | \(-0.319842\pi\) | ||||
0.536246 | + | 0.844061i | \(0.319842\pi\) | |||||||
\(884\) | −2.78504 | −0.0936710 | ||||||||
\(885\) | −51.8673 | −1.74350 | ||||||||
\(886\) | 32.4741 | 1.09099 | ||||||||
\(887\) | 14.0184 | 0.470692 | 0.235346 | − | 0.971912i | \(-0.424378\pi\) | ||||
0.235346 | + | 0.971912i | \(0.424378\pi\) | |||||||
\(888\) | −69.2683 | −2.32449 | ||||||||
\(889\) | 8.23352 | 0.276143 | ||||||||
\(890\) | −152.971 | −5.12759 | ||||||||
\(891\) | −34.8179 | −1.16644 | ||||||||
\(892\) | −22.6305 | −0.757724 | ||||||||
\(893\) | −2.89459 | −0.0968639 | ||||||||
\(894\) | 127.354 | 4.25935 | ||||||||
\(895\) | 100.506 | 3.35955 | ||||||||
\(896\) | 38.2518 | 1.27790 | ||||||||
\(897\) | −14.7997 | −0.494147 | ||||||||
\(898\) | 44.5911 | 1.48802 | ||||||||
\(899\) | 36.4992 | 1.21732 | ||||||||
\(900\) | 139.156 | 4.63852 | ||||||||
\(901\) | −5.17948 | −0.172554 | ||||||||
\(902\) | −26.3394 | −0.877008 | ||||||||
\(903\) | −31.6438 | −1.05304 | ||||||||
\(904\) | 6.96613 | 0.231690 | ||||||||
\(905\) | 13.6738 | 0.454531 | ||||||||
\(906\) | −3.52735 | −0.117188 | ||||||||
\(907\) | 11.4493 | 0.380169 | 0.190085 | − | 0.981768i | \(-0.439124\pi\) | ||||
0.190085 | + | 0.981768i | \(0.439124\pi\) | |||||||
\(908\) | 9.20347 | 0.305428 | ||||||||
\(909\) | −53.4770 | −1.77372 | ||||||||
\(910\) | −19.3916 | −0.642827 | ||||||||
\(911\) | 4.89970 | 0.162334 | 0.0811672 | − | 0.996701i | \(-0.474135\pi\) | ||||
0.0811672 | + | 0.996701i | \(0.474135\pi\) | |||||||
\(912\) | −2.62383 | −0.0868837 | ||||||||
\(913\) | −56.0856 | −1.85616 | ||||||||
\(914\) | −30.2117 | −0.999313 | ||||||||
\(915\) | 125.642 | 4.15359 | ||||||||
\(916\) | 55.4719 | 1.83284 | ||||||||
\(917\) | −41.2963 | −1.36372 | ||||||||
\(918\) | 1.58876 | 0.0524368 | ||||||||
\(919\) | 1.67117 | 0.0551267 | 0.0275633 | − | 0.999620i | \(-0.491225\pi\) | ||||
0.0275633 | + | 0.999620i | \(0.491225\pi\) | |||||||
\(920\) | −75.3860 | −2.48540 | ||||||||
\(921\) | −60.7682 | −2.00238 | ||||||||
\(922\) | −40.2215 | −1.32463 | ||||||||
\(923\) | −7.30611 | −0.240484 | ||||||||
\(924\) | −73.7346 | −2.42569 | ||||||||
\(925\) | −113.413 | −3.72901 | ||||||||
\(926\) | 36.7728 | 1.20843 | ||||||||
\(927\) | −5.30992 | −0.174401 | ||||||||
\(928\) | 32.3962 | 1.06346 | ||||||||
\(929\) | −42.5355 | −1.39555 | −0.697773 | − | 0.716319i | \(-0.745825\pi\) | ||||
−0.697773 | + | 0.716319i | \(0.745825\pi\) | |||||||
\(930\) | −142.133 | −4.66071 | ||||||||
\(931\) | −7.74396 | −0.253798 | ||||||||
\(932\) | 75.0432 | 2.45812 | ||||||||
\(933\) | 34.0700 | 1.11540 | ||||||||
\(934\) | −72.3593 | −2.36767 | ||||||||
\(935\) | −15.4581 | −0.505533 | ||||||||
\(936\) | 10.1647 | 0.332244 | ||||||||
\(937\) | 0.952489 | 0.0311164 | 0.0155582 | − | 0.999879i | \(-0.495047\pi\) | ||||
0.0155582 | + | 0.999879i | \(0.495047\pi\) | |||||||
\(938\) | 6.34098 | 0.207040 | ||||||||
\(939\) | 36.7738 | 1.20007 | ||||||||
\(940\) | 15.5436 | 0.506977 | ||||||||
\(941\) | −4.21856 | −0.137521 | −0.0687606 | − | 0.997633i | \(-0.521904\pi\) | ||||
−0.0687606 | + | 0.997633i | \(0.521904\pi\) | |||||||
\(942\) | 112.758 | 3.67385 | ||||||||
\(943\) | −15.2645 | −0.497082 | ||||||||
\(944\) | −1.97618 | −0.0643192 | ||||||||
\(945\) | 6.90674 | 0.224676 | ||||||||
\(946\) | −63.7306 | −2.07206 | ||||||||
\(947\) | −1.82244 | −0.0592212 | −0.0296106 | − | 0.999562i | \(-0.509427\pi\) | ||||
−0.0296106 | + | 0.999562i | \(0.509427\pi\) | |||||||
\(948\) | 97.1991 | 3.15688 | ||||||||
\(949\) | 5.14693 | 0.167076 | ||||||||
\(950\) | −75.3695 | −2.44531 | ||||||||
\(951\) | −35.4593 | −1.14985 | ||||||||
\(952\) | −5.13050 | −0.166280 | ||||||||
\(953\) | −5.69949 | −0.184625 | −0.0923124 | − | 0.995730i | \(-0.529426\pi\) | ||||
−0.0923124 | + | 0.995730i | \(0.529426\pi\) | |||||||
\(954\) | 47.4554 | 1.53643 | ||||||||
\(955\) | 73.2814 | 2.37133 | ||||||||
\(956\) | −25.7076 | −0.831442 | ||||||||
\(957\) | −69.1680 | −2.23588 | ||||||||
\(958\) | 12.2071 | 0.394392 | ||||||||
\(959\) | 27.5296 | 0.888976 | ||||||||
\(960\) | −134.632 | −4.34523 | ||||||||
\(961\) | 3.10773 | 0.100249 | ||||||||
\(962\) | −20.7967 | −0.670513 | ||||||||
\(963\) | −3.12338 | −0.100649 | ||||||||
\(964\) | 4.56423 | 0.147004 | ||||||||
\(965\) | −110.484 | −3.55660 | ||||||||
\(966\) | −68.4410 | −2.20205 | ||||||||
\(967\) | 46.0581 | 1.48113 | 0.740564 | − | 0.671986i | \(-0.234558\pi\) | ||||
0.740564 | + | 0.671986i | \(0.234558\pi\) | |||||||
\(968\) | −25.5454 | −0.821060 | ||||||||
\(969\) | −5.47026 | −0.175730 | ||||||||
\(970\) | −147.533 | −4.73699 | ||||||||
\(971\) | −22.5596 | −0.723972 | −0.361986 | − | 0.932183i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932183i | \(0.617901\pi\) | |||||||
\(972\) | 74.3594 | 2.38508 | ||||||||
\(973\) | 35.8513 | 1.14934 | ||||||||
\(974\) | 66.4246 | 2.12838 | ||||||||
\(975\) | 31.6509 | 1.01364 | ||||||||
\(976\) | 4.78705 | 0.153230 | ||||||||
\(977\) | −48.7202 | −1.55870 | −0.779349 | − | 0.626590i | \(-0.784450\pi\) | ||||
−0.779349 | + | 0.626590i | \(0.784450\pi\) | |||||||
\(978\) | −1.94414 | −0.0621668 | ||||||||
\(979\) | −69.5649 | −2.22330 | ||||||||
\(980\) | 41.5841 | 1.32836 | ||||||||
\(981\) | 64.8168 | 2.06944 | ||||||||
\(982\) | −21.3313 | −0.680709 | ||||||||
\(983\) | −60.9557 | −1.94419 | −0.972093 | − | 0.234597i | \(-0.924623\pi\) | ||||
−0.972093 | + | 0.234597i | \(0.924623\pi\) | |||||||
\(984\) | 19.9383 | 0.635609 | ||||||||
\(985\) | 92.2462 | 2.93921 | ||||||||
\(986\) | −12.0817 | −0.384760 | ||||||||
\(987\) | 5.62137 | 0.178930 | ||||||||
\(988\) | −8.62895 | −0.274524 | ||||||||
\(989\) | −36.9339 | −1.17443 | ||||||||
\(990\) | 141.630 | 4.50129 | ||||||||
\(991\) | 29.1645 | 0.926442 | 0.463221 | − | 0.886243i | \(-0.346694\pi\) | ||||
0.463221 | + | 0.886243i | \(0.346694\pi\) | |||||||
\(992\) | 30.2736 | 0.961187 | ||||||||
\(993\) | 48.6127 | 1.54268 | ||||||||
\(994\) | −33.7870 | −1.07166 | ||||||||
\(995\) | −113.457 | −3.59681 | ||||||||
\(996\) | 106.578 | 3.37705 | ||||||||
\(997\) | 41.4988 | 1.31428 | 0.657140 | − | 0.753768i | \(-0.271766\pi\) | ||||
0.657140 | + | 0.753768i | \(0.271766\pi\) | |||||||
\(998\) | −1.52268 | −0.0481997 | ||||||||
\(999\) | 7.40718 | 0.234353 |
(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 | 8047.2.a.c.1.18 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.c.1.18 | ✓ | 151 | 1.1 | even | 1 | trivial |