Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.446590 | −0.315787 | −0.157894 | − | 0.987456i | \(-0.550470\pi\) | ||||
−0.157894 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(3\) | 1.08482 | 0.626323 | 0.313162 | − | 0.949700i | \(-0.398612\pi\) | ||||
0.313162 | + | 0.949700i | \(0.398612\pi\) | |||||||
\(4\) | −1.80056 | −0.900279 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.484472 | −0.197785 | ||||||||
\(7\) | 4.20380 | 1.58889 | 0.794444 | − | 0.607337i | \(-0.207762\pi\) | ||||
0.794444 | + | 0.607337i | \(0.207762\pi\) | |||||||
\(8\) | 1.69729 | 0.600083 | ||||||||
\(9\) | −1.82316 | −0.607719 | ||||||||
\(10\) | −0.446590 | −0.141224 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.95329 | −0.563865 | ||||||||
\(13\) | −2.82350 | −0.783097 | −0.391548 | − | 0.920158i | \(-0.628060\pi\) | ||||
−0.391548 | + | 0.920158i | \(0.628060\pi\) | |||||||
\(14\) | −1.87738 | −0.501750 | ||||||||
\(15\) | 1.08482 | 0.280100 | ||||||||
\(16\) | 2.84312 | 0.710780 | ||||||||
\(17\) | 4.54365 | 1.10200 | 0.550999 | − | 0.834506i | \(-0.314247\pi\) | ||||
0.550999 | + | 0.834506i | \(0.314247\pi\) | |||||||
\(18\) | 0.814205 | 0.191910 | ||||||||
\(19\) | −4.76704 | −1.09364 | −0.546818 | − | 0.837252i | \(-0.684161\pi\) | ||||
−0.546818 | + | 0.837252i | \(0.684161\pi\) | |||||||
\(20\) | −1.80056 | −0.402617 | ||||||||
\(21\) | 4.56039 | 0.995158 | ||||||||
\(22\) | −0.446590 | −0.0952134 | ||||||||
\(23\) | 2.76248 | 0.576017 | 0.288008 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288008 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(24\) | 1.84126 | 0.375846 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.26095 | 0.247292 | ||||||||
\(27\) | −5.23228 | −1.00695 | ||||||||
\(28\) | −7.56919 | −1.43044 | ||||||||
\(29\) | −2.06610 | −0.383665 | −0.191832 | − | 0.981428i | \(-0.561443\pi\) | ||||
−0.191832 | + | 0.981428i | \(0.561443\pi\) | |||||||
\(30\) | −0.484472 | −0.0884521 | ||||||||
\(31\) | 7.10845 | 1.27672 | 0.638358 | − | 0.769740i | \(-0.279614\pi\) | ||||
0.638358 | + | 0.769740i | \(0.279614\pi\) | |||||||
\(32\) | −4.66429 | −0.824539 | ||||||||
\(33\) | 1.08482 | 0.188844 | ||||||||
\(34\) | −2.02915 | −0.347997 | ||||||||
\(35\) | 4.20380 | 0.710572 | ||||||||
\(36\) | 3.28270 | 0.547116 | ||||||||
\(37\) | −5.06844 | −0.833247 | −0.416624 | − | 0.909079i | \(-0.636787\pi\) | ||||
−0.416624 | + | 0.909079i | \(0.636787\pi\) | |||||||
\(38\) | 2.12892 | 0.345356 | ||||||||
\(39\) | −3.06299 | −0.490472 | ||||||||
\(40\) | 1.69729 | 0.268365 | ||||||||
\(41\) | 9.63406 | 1.50459 | 0.752294 | − | 0.658828i | \(-0.228947\pi\) | ||||
0.752294 | + | 0.658828i | \(0.228947\pi\) | |||||||
\(42\) | −2.03662 | −0.314258 | ||||||||
\(43\) | 11.0577 | 1.68628 | 0.843141 | − | 0.537693i | \(-0.180704\pi\) | ||||
0.843141 | + | 0.537693i | \(0.180704\pi\) | |||||||
\(44\) | −1.80056 | −0.271444 | ||||||||
\(45\) | −1.82316 | −0.271780 | ||||||||
\(46\) | −1.23370 | −0.181899 | ||||||||
\(47\) | −0.673225 | −0.0981999 | −0.0491000 | − | 0.998794i | \(-0.515635\pi\) | ||||
−0.0491000 | + | 0.998794i | \(0.515635\pi\) | |||||||
\(48\) | 3.08428 | 0.445178 | ||||||||
\(49\) | 10.6720 | 1.52457 | ||||||||
\(50\) | −0.446590 | −0.0631574 | ||||||||
\(51\) | 4.92906 | 0.690207 | ||||||||
\(52\) | 5.08386 | 0.705005 | ||||||||
\(53\) | 12.9970 | 1.78528 | 0.892639 | − | 0.450772i | \(-0.148851\pi\) | ||||
0.892639 | + | 0.450772i | \(0.148851\pi\) | |||||||
\(54\) | 2.33668 | 0.317982 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 7.13508 | 0.953466 | ||||||||
\(57\) | −5.17140 | −0.684969 | ||||||||
\(58\) | 0.922700 | 0.121156 | ||||||||
\(59\) | −14.0926 | −1.83471 | −0.917353 | − | 0.398076i | \(-0.869678\pi\) | ||||
−0.917353 | + | 0.398076i | \(0.869678\pi\) | |||||||
\(60\) | −1.95329 | −0.252168 | ||||||||
\(61\) | 1.12602 | 0.144172 | 0.0720858 | − | 0.997398i | \(-0.477034\pi\) | ||||
0.0720858 | + | 0.997398i | \(0.477034\pi\) | |||||||
\(62\) | −3.17457 | −0.403170 | ||||||||
\(63\) | −7.66420 | −0.965598 | ||||||||
\(64\) | −3.60321 | −0.450401 | ||||||||
\(65\) | −2.82350 | −0.350212 | ||||||||
\(66\) | −0.484472 | −0.0596344 | ||||||||
\(67\) | 7.73434 | 0.944900 | 0.472450 | − | 0.881358i | \(-0.343370\pi\) | ||||
0.472450 | + | 0.881358i | \(0.343370\pi\) | |||||||
\(68\) | −8.18111 | −0.992105 | ||||||||
\(69\) | 2.99680 | 0.360773 | ||||||||
\(70\) | −1.87738 | −0.224390 | ||||||||
\(71\) | −15.4056 | −1.82831 | −0.914155 | − | 0.405364i | \(-0.867145\pi\) | ||||
−0.914155 | + | 0.405364i | \(0.867145\pi\) | |||||||
\(72\) | −3.09443 | −0.364682 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 2.26352 | 0.263129 | ||||||||
\(75\) | 1.08482 | 0.125265 | ||||||||
\(76\) | 8.58334 | 0.984576 | ||||||||
\(77\) | 4.20380 | 0.479068 | ||||||||
\(78\) | 1.36790 | 0.154885 | ||||||||
\(79\) | −3.88009 | −0.436544 | −0.218272 | − | 0.975888i | \(-0.570042\pi\) | ||||
−0.218272 | + | 0.975888i | \(0.570042\pi\) | |||||||
\(80\) | 2.84312 | 0.317870 | ||||||||
\(81\) | −0.206625 | −0.0229583 | ||||||||
\(82\) | −4.30248 | −0.475129 | ||||||||
\(83\) | 3.76371 | 0.413121 | 0.206560 | − | 0.978434i | \(-0.433773\pi\) | ||||
0.206560 | + | 0.978434i | \(0.433773\pi\) | |||||||
\(84\) | −8.21123 | −0.895919 | ||||||||
\(85\) | 4.54365 | 0.492829 | ||||||||
\(86\) | −4.93826 | −0.532506 | ||||||||
\(87\) | −2.24135 | −0.240298 | ||||||||
\(88\) | 1.69729 | 0.180932 | ||||||||
\(89\) | 3.77803 | 0.400470 | 0.200235 | − | 0.979748i | \(-0.435829\pi\) | ||||
0.200235 | + | 0.979748i | \(0.435829\pi\) | |||||||
\(90\) | 0.814205 | 0.0858247 | ||||||||
\(91\) | −11.8694 | −1.24425 | ||||||||
\(92\) | −4.97400 | −0.518576 | ||||||||
\(93\) | 7.71142 | 0.799637 | ||||||||
\(94\) | 0.300656 | 0.0310103 | ||||||||
\(95\) | −4.76704 | −0.489088 | ||||||||
\(96\) | −5.05994 | −0.516428 | ||||||||
\(97\) | 14.3786 | 1.45992 | 0.729961 | − | 0.683489i | \(-0.239538\pi\) | ||||
0.729961 | + | 0.683489i | \(0.239538\pi\) | |||||||
\(98\) | −4.76600 | −0.481438 | ||||||||
\(99\) | −1.82316 | −0.183234 | ||||||||
\(100\) | −1.80056 | −0.180056 | ||||||||
\(101\) | −13.3707 | −1.33044 | −0.665219 | − | 0.746649i | \(-0.731662\pi\) | ||||
−0.665219 | + | 0.746649i | \(0.731662\pi\) | |||||||
\(102\) | −2.20127 | −0.217958 | ||||||||
\(103\) | 14.1322 | 1.39249 | 0.696244 | − | 0.717805i | \(-0.254853\pi\) | ||||
0.696244 | + | 0.717805i | \(0.254853\pi\) | |||||||
\(104\) | −4.79230 | −0.469923 | ||||||||
\(105\) | 4.56039 | 0.445048 | ||||||||
\(106\) | −5.80434 | −0.563768 | ||||||||
\(107\) | 6.98899 | 0.675651 | 0.337826 | − | 0.941209i | \(-0.390309\pi\) | ||||
0.337826 | + | 0.941209i | \(0.390309\pi\) | |||||||
\(108\) | 9.42101 | 0.906537 | ||||||||
\(109\) | −6.80765 | −0.652054 | −0.326027 | − | 0.945360i | \(-0.605710\pi\) | ||||
−0.326027 | + | 0.945360i | \(0.605710\pi\) | |||||||
\(110\) | −0.446590 | −0.0425807 | ||||||||
\(111\) | −5.49837 | −0.521882 | ||||||||
\(112\) | 11.9519 | 1.12935 | ||||||||
\(113\) | 18.0038 | 1.69366 | 0.846829 | − | 0.531865i | \(-0.178509\pi\) | ||||
0.846829 | + | 0.531865i | \(0.178509\pi\) | |||||||
\(114\) | 2.30950 | 0.216304 | ||||||||
\(115\) | 2.76248 | 0.257603 | ||||||||
\(116\) | 3.72013 | 0.345405 | ||||||||
\(117\) | 5.14768 | 0.475903 | ||||||||
\(118\) | 6.29364 | 0.579376 | ||||||||
\(119\) | 19.1006 | 1.75095 | ||||||||
\(120\) | 1.84126 | 0.168084 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.502868 | −0.0455275 | ||||||||
\(123\) | 10.4513 | 0.942358 | ||||||||
\(124\) | −12.7992 | −1.14940 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.42276 | 0.304923 | ||||||||
\(127\) | 6.65081 | 0.590164 | 0.295082 | − | 0.955472i | \(-0.404653\pi\) | ||||
0.295082 | + | 0.955472i | \(0.404653\pi\) | |||||||
\(128\) | 10.9377 | 0.966769 | ||||||||
\(129\) | 11.9956 | 1.05616 | ||||||||
\(130\) | 1.26095 | 0.110592 | ||||||||
\(131\) | −15.2775 | −1.33480 | −0.667401 | − | 0.744698i | \(-0.732593\pi\) | ||||
−0.667401 | + | 0.744698i | \(0.732593\pi\) | |||||||
\(132\) | −1.95329 | −0.170012 | ||||||||
\(133\) | −20.0397 | −1.73766 | ||||||||
\(134\) | −3.45408 | −0.298387 | ||||||||
\(135\) | −5.23228 | −0.450323 | ||||||||
\(136\) | 7.71191 | 0.661291 | ||||||||
\(137\) | −12.9074 | −1.10275 | −0.551375 | − | 0.834257i | \(-0.685897\pi\) | ||||
−0.551375 | + | 0.834257i | \(0.685897\pi\) | |||||||
\(138\) | −1.33834 | −0.113927 | ||||||||
\(139\) | −1.39769 | −0.118551 | −0.0592753 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592753 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(140\) | −7.56919 | −0.639713 | ||||||||
\(141\) | −0.730330 | −0.0615049 | ||||||||
\(142\) | 6.88000 | 0.577357 | ||||||||
\(143\) | −2.82350 | −0.236113 | ||||||||
\(144\) | −5.18345 | −0.431955 | ||||||||
\(145\) | −2.06610 | −0.171580 | ||||||||
\(146\) | −0.446590 | −0.0369601 | ||||||||
\(147\) | 11.5772 | 0.954871 | ||||||||
\(148\) | 9.12602 | 0.750155 | ||||||||
\(149\) | −3.27780 | −0.268528 | −0.134264 | − | 0.990946i | \(-0.542867\pi\) | ||||
−0.134264 | + | 0.990946i | \(0.542867\pi\) | |||||||
\(150\) | −0.484472 | −0.0395570 | ||||||||
\(151\) | −6.18263 | −0.503135 | −0.251568 | − | 0.967840i | \(-0.580946\pi\) | ||||
−0.251568 | + | 0.967840i | \(0.580946\pi\) | |||||||
\(152\) | −8.09107 | −0.656272 | ||||||||
\(153\) | −8.28380 | −0.669705 | ||||||||
\(154\) | −1.87738 | −0.151283 | ||||||||
\(155\) | 7.10845 | 0.570965 | ||||||||
\(156\) | 5.51510 | 0.441561 | ||||||||
\(157\) | −8.67135 | −0.692049 | −0.346024 | − | 0.938226i | \(-0.612469\pi\) | ||||
−0.346024 | + | 0.938226i | \(0.612469\pi\) | |||||||
\(158\) | 1.73281 | 0.137855 | ||||||||
\(159\) | 14.0995 | 1.11816 | ||||||||
\(160\) | −4.66429 | −0.368745 | ||||||||
\(161\) | 11.6129 | 0.915227 | ||||||||
\(162\) | 0.0922767 | 0.00724994 | ||||||||
\(163\) | 17.7477 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(164\) | −17.3467 | −1.35455 | ||||||||
\(165\) | 1.08482 | 0.0844534 | ||||||||
\(166\) | −1.68084 | −0.130458 | ||||||||
\(167\) | 20.4600 | 1.58324 | 0.791621 | − | 0.611012i | \(-0.209237\pi\) | ||||
0.791621 | + | 0.611012i | \(0.209237\pi\) | |||||||
\(168\) | 7.74031 | 0.597178 | ||||||||
\(169\) | −5.02787 | −0.386759 | ||||||||
\(170\) | −2.02915 | −0.155629 | ||||||||
\(171\) | 8.69107 | 0.664623 | ||||||||
\(172\) | −19.9100 | −1.51812 | ||||||||
\(173\) | −22.2156 | −1.68902 | −0.844510 | − | 0.535540i | \(-0.820108\pi\) | ||||
−0.844510 | + | 0.535540i | \(0.820108\pi\) | |||||||
\(174\) | 1.00097 | 0.0758831 | ||||||||
\(175\) | 4.20380 | 0.317778 | ||||||||
\(176\) | 2.84312 | 0.214308 | ||||||||
\(177\) | −15.2880 | −1.14912 | ||||||||
\(178\) | −1.68723 | −0.126463 | ||||||||
\(179\) | 5.94621 | 0.444440 | 0.222220 | − | 0.974997i | \(-0.428670\pi\) | ||||
0.222220 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(180\) | 3.28270 | 0.244678 | ||||||||
\(181\) | 4.15122 | 0.308558 | 0.154279 | − | 0.988027i | \(-0.450695\pi\) | ||||
0.154279 | + | 0.988027i | \(0.450695\pi\) | |||||||
\(182\) | 5.30077 | 0.392919 | ||||||||
\(183\) | 1.22153 | 0.0902980 | ||||||||
\(184\) | 4.68874 | 0.345658 | ||||||||
\(185\) | −5.06844 | −0.372639 | ||||||||
\(186\) | −3.44385 | −0.252515 | ||||||||
\(187\) | 4.54365 | 0.332265 | ||||||||
\(188\) | 1.21218 | 0.0884073 | ||||||||
\(189\) | −21.9955 | −1.59993 | ||||||||
\(190\) | 2.12892 | 0.154448 | ||||||||
\(191\) | 8.77712 | 0.635090 | 0.317545 | − | 0.948243i | \(-0.397142\pi\) | ||||
0.317545 | + | 0.948243i | \(0.397142\pi\) | |||||||
\(192\) | −3.90885 | −0.282097 | ||||||||
\(193\) | −12.5672 | −0.904608 | −0.452304 | − | 0.891864i | \(-0.649398\pi\) | ||||
−0.452304 | + | 0.891864i | \(0.649398\pi\) | |||||||
\(194\) | −6.42132 | −0.461024 | ||||||||
\(195\) | −3.06299 | −0.219346 | ||||||||
\(196\) | −19.2155 | −1.37253 | ||||||||
\(197\) | −4.61568 | −0.328853 | −0.164427 | − | 0.986389i | \(-0.552577\pi\) | ||||
−0.164427 | + | 0.986389i | \(0.552577\pi\) | |||||||
\(198\) | 0.814205 | 0.0578630 | ||||||||
\(199\) | 9.01902 | 0.639341 | 0.319671 | − | 0.947529i | \(-0.396428\pi\) | ||||
0.319671 | + | 0.947529i | \(0.396428\pi\) | |||||||
\(200\) | 1.69729 | 0.120017 | ||||||||
\(201\) | 8.39039 | 0.591813 | ||||||||
\(202\) | 5.97124 | 0.420135 | ||||||||
\(203\) | −8.68547 | −0.609601 | ||||||||
\(204\) | −8.87506 | −0.621379 | ||||||||
\(205\) | 9.63406 | 0.672872 | ||||||||
\(206\) | −6.31131 | −0.439730 | ||||||||
\(207\) | −5.03644 | −0.350057 | ||||||||
\(208\) | −8.02754 | −0.556609 | ||||||||
\(209\) | −4.76704 | −0.329743 | ||||||||
\(210\) | −2.03662 | −0.140540 | ||||||||
\(211\) | 14.9813 | 1.03135 | 0.515676 | − | 0.856783i | \(-0.327541\pi\) | ||||
0.515676 | + | 0.856783i | \(0.327541\pi\) | |||||||
\(212\) | −23.4019 | −1.60725 | ||||||||
\(213\) | −16.7124 | −1.14511 | ||||||||
\(214\) | −3.12122 | −0.213362 | ||||||||
\(215\) | 11.0577 | 0.754128 | ||||||||
\(216\) | −8.88070 | −0.604255 | ||||||||
\(217\) | 29.8825 | 2.02856 | ||||||||
\(218\) | 3.04023 | 0.205910 | ||||||||
\(219\) | 1.08482 | 0.0733056 | ||||||||
\(220\) | −1.80056 | −0.121394 | ||||||||
\(221\) | −12.8290 | −0.862971 | ||||||||
\(222\) | 2.45552 | 0.164804 | ||||||||
\(223\) | −11.7986 | −0.790094 | −0.395047 | − | 0.918661i | \(-0.629272\pi\) | ||||
−0.395047 | + | 0.918661i | \(0.629272\pi\) | |||||||
\(224\) | −19.6078 | −1.31010 | ||||||||
\(225\) | −1.82316 | −0.121544 | ||||||||
\(226\) | −8.04034 | −0.534836 | ||||||||
\(227\) | 23.0051 | 1.52690 | 0.763451 | − | 0.645865i | \(-0.223503\pi\) | ||||
0.763451 | + | 0.645865i | \(0.223503\pi\) | |||||||
\(228\) | 9.31141 | 0.616663 | ||||||||
\(229\) | 18.0829 | 1.19495 | 0.597476 | − | 0.801887i | \(-0.296170\pi\) | ||||
0.597476 | + | 0.801887i | \(0.296170\pi\) | |||||||
\(230\) | −1.23370 | −0.0813476 | ||||||||
\(231\) | 4.56039 | 0.300051 | ||||||||
\(232\) | −3.50677 | −0.230231 | ||||||||
\(233\) | 20.0859 | 1.31587 | 0.657935 | − | 0.753075i | \(-0.271430\pi\) | ||||
0.657935 | + | 0.753075i | \(0.271430\pi\) | |||||||
\(234\) | −2.29890 | −0.150284 | ||||||||
\(235\) | −0.673225 | −0.0439163 | ||||||||
\(236\) | 25.3746 | 1.65175 | ||||||||
\(237\) | −4.20921 | −0.273418 | ||||||||
\(238\) | −8.53016 | −0.552928 | ||||||||
\(239\) | 16.4634 | 1.06493 | 0.532464 | − | 0.846453i | \(-0.321266\pi\) | ||||
0.532464 | + | 0.846453i | \(0.321266\pi\) | |||||||
\(240\) | 3.08428 | 0.199090 | ||||||||
\(241\) | 11.6755 | 0.752085 | 0.376042 | − | 0.926602i | \(-0.377285\pi\) | ||||
0.376042 | + | 0.926602i | \(0.377285\pi\) | |||||||
\(242\) | −0.446590 | −0.0287079 | ||||||||
\(243\) | 15.4727 | 0.992573 | ||||||||
\(244\) | −2.02746 | −0.129795 | ||||||||
\(245\) | 10.6720 | 0.681807 | ||||||||
\(246\) | −4.66743 | −0.297585 | ||||||||
\(247\) | 13.4597 | 0.856422 | ||||||||
\(248\) | 12.0651 | 0.766136 | ||||||||
\(249\) | 4.08296 | 0.258747 | ||||||||
\(250\) | −0.446590 | −0.0282449 | ||||||||
\(251\) | 30.0465 | 1.89652 | 0.948260 | − | 0.317496i | \(-0.102842\pi\) | ||||
0.948260 | + | 0.317496i | \(0.102842\pi\) | |||||||
\(252\) | 13.7998 | 0.869307 | ||||||||
\(253\) | 2.76248 | 0.173676 | ||||||||
\(254\) | −2.97019 | −0.186366 | ||||||||
\(255\) | 4.92906 | 0.308670 | ||||||||
\(256\) | 2.32173 | 0.145108 | ||||||||
\(257\) | 12.6649 | 0.790013 | 0.395007 | − | 0.918678i | \(-0.370742\pi\) | ||||
0.395007 | + | 0.918678i | \(0.370742\pi\) | |||||||
\(258\) | −5.35714 | −0.333521 | ||||||||
\(259\) | −21.3067 | −1.32394 | ||||||||
\(260\) | 5.08386 | 0.315288 | ||||||||
\(261\) | 3.76682 | 0.233161 | ||||||||
\(262\) | 6.82279 | 0.421513 | ||||||||
\(263\) | 23.5086 | 1.44960 | 0.724801 | − | 0.688958i | \(-0.241932\pi\) | ||||
0.724801 | + | 0.688958i | \(0.241932\pi\) | |||||||
\(264\) | 1.84126 | 0.113322 | ||||||||
\(265\) | 12.9970 | 0.798401 | ||||||||
\(266\) | 8.94955 | 0.548732 | ||||||||
\(267\) | 4.09850 | 0.250824 | ||||||||
\(268\) | −13.9261 | −0.850673 | ||||||||
\(269\) | −8.05493 | −0.491118 | −0.245559 | − | 0.969382i | \(-0.578971\pi\) | ||||
−0.245559 | + | 0.969382i | \(0.578971\pi\) | |||||||
\(270\) | 2.33668 | 0.142206 | ||||||||
\(271\) | −3.40895 | −0.207079 | −0.103539 | − | 0.994625i | \(-0.533017\pi\) | ||||
−0.103539 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(272\) | 12.9182 | 0.783278 | ||||||||
\(273\) | −12.8762 | −0.779305 | ||||||||
\(274\) | 5.76430 | 0.348234 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −5.39592 | −0.324796 | ||||||||
\(277\) | −13.0712 | −0.785374 | −0.392687 | − | 0.919672i | \(-0.628454\pi\) | ||||
−0.392687 | + | 0.919672i | \(0.628454\pi\) | |||||||
\(278\) | 0.624196 | 0.0374368 | ||||||||
\(279\) | −12.9598 | −0.775885 | ||||||||
\(280\) | 7.13508 | 0.426403 | ||||||||
\(281\) | −24.9860 | −1.49054 | −0.745270 | − | 0.666763i | \(-0.767679\pi\) | ||||
−0.745270 | + | 0.666763i | \(0.767679\pi\) | |||||||
\(282\) | 0.326158 | 0.0194225 | ||||||||
\(283\) | −28.4917 | −1.69366 | −0.846829 | − | 0.531866i | \(-0.821491\pi\) | ||||
−0.846829 | + | 0.531866i | \(0.821491\pi\) | |||||||
\(284\) | 27.7387 | 1.64599 | ||||||||
\(285\) | −5.17140 | −0.306328 | ||||||||
\(286\) | 1.26095 | 0.0745613 | ||||||||
\(287\) | 40.4997 | 2.39062 | ||||||||
\(288\) | 8.50374 | 0.501088 | ||||||||
\(289\) | 3.64479 | 0.214400 | ||||||||
\(290\) | 0.922700 | 0.0541828 | ||||||||
\(291\) | 15.5982 | 0.914383 | ||||||||
\(292\) | −1.80056 | −0.105370 | ||||||||
\(293\) | 19.5783 | 1.14378 | 0.571889 | − | 0.820331i | \(-0.306211\pi\) | ||||
0.571889 | + | 0.820331i | \(0.306211\pi\) | |||||||
\(294\) | −5.17027 | −0.301536 | ||||||||
\(295\) | −14.0926 | −0.820505 | ||||||||
\(296\) | −8.60263 | −0.500018 | ||||||||
\(297\) | −5.23228 | −0.303607 | ||||||||
\(298\) | 1.46384 | 0.0847977 | ||||||||
\(299\) | −7.79985 | −0.451077 | ||||||||
\(300\) | −1.95329 | −0.112773 | ||||||||
\(301\) | 46.4843 | 2.67931 | ||||||||
\(302\) | 2.76110 | 0.158884 | ||||||||
\(303\) | −14.5049 | −0.833284 | ||||||||
\(304\) | −13.5533 | −0.777334 | ||||||||
\(305\) | 1.12602 | 0.0644755 | ||||||||
\(306\) | 3.69946 | 0.211484 | ||||||||
\(307\) | 3.33865 | 0.190547 | 0.0952733 | − | 0.995451i | \(-0.469627\pi\) | ||||
0.0952733 | + | 0.995451i | \(0.469627\pi\) | |||||||
\(308\) | −7.56919 | −0.431295 | ||||||||
\(309\) | 15.3310 | 0.872148 | ||||||||
\(310\) | −3.17457 | −0.180303 | ||||||||
\(311\) | −25.6738 | −1.45583 | −0.727913 | − | 0.685669i | \(-0.759510\pi\) | ||||
−0.727913 | + | 0.685669i | \(0.759510\pi\) | |||||||
\(312\) | −5.19880 | −0.294324 | ||||||||
\(313\) | −32.0967 | −1.81421 | −0.907107 | − | 0.420901i | \(-0.861714\pi\) | ||||
−0.907107 | + | 0.420901i | \(0.861714\pi\) | |||||||
\(314\) | 3.87254 | 0.218540 | ||||||||
\(315\) | −7.66420 | −0.431828 | ||||||||
\(316\) | 6.98632 | 0.393011 | ||||||||
\(317\) | 18.3511 | 1.03070 | 0.515349 | − | 0.856980i | \(-0.327662\pi\) | ||||
0.515349 | + | 0.856980i | \(0.327662\pi\) | |||||||
\(318\) | −6.29669 | −0.353101 | ||||||||
\(319\) | −2.06610 | −0.115679 | ||||||||
\(320\) | −3.60321 | −0.201426 | ||||||||
\(321\) | 7.58182 | 0.423176 | ||||||||
\(322\) | −5.18622 | −0.289017 | ||||||||
\(323\) | −21.6598 | −1.20518 | ||||||||
\(324\) | 0.372040 | 0.0206689 | ||||||||
\(325\) | −2.82350 | −0.156619 | ||||||||
\(326\) | −7.92597 | −0.438979 | ||||||||
\(327\) | −7.38510 | −0.408397 | ||||||||
\(328\) | 16.3518 | 0.902878 | ||||||||
\(329\) | −2.83010 | −0.156029 | ||||||||
\(330\) | −0.484472 | −0.0266693 | ||||||||
\(331\) | −0.948328 | −0.0521248 | −0.0260624 | − | 0.999660i | \(-0.508297\pi\) | ||||
−0.0260624 | + | 0.999660i | \(0.508297\pi\) | |||||||
\(332\) | −6.77677 | −0.371924 | ||||||||
\(333\) | 9.24057 | 0.506380 | ||||||||
\(334\) | −9.13724 | −0.499967 | ||||||||
\(335\) | 7.73434 | 0.422572 | ||||||||
\(336\) | 12.9657 | 0.707338 | ||||||||
\(337\) | 0.499871 | 0.0272297 | 0.0136149 | − | 0.999907i | \(-0.495666\pi\) | ||||
0.0136149 | + | 0.999907i | \(0.495666\pi\) | |||||||
\(338\) | 2.24540 | 0.122134 | ||||||||
\(339\) | 19.5310 | 1.06078 | ||||||||
\(340\) | −8.18111 | −0.443683 | ||||||||
\(341\) | 7.10845 | 0.384944 | ||||||||
\(342\) | −3.88135 | −0.209879 | ||||||||
\(343\) | 15.4362 | 0.833477 | ||||||||
\(344\) | 18.7681 | 1.01191 | ||||||||
\(345\) | 2.99680 | 0.161343 | ||||||||
\(346\) | 9.92127 | 0.533371 | ||||||||
\(347\) | −18.3938 | −0.987431 | −0.493716 | − | 0.869623i | \(-0.664362\pi\) | ||||
−0.493716 | + | 0.869623i | \(0.664362\pi\) | |||||||
\(348\) | 4.03568 | 0.216335 | ||||||||
\(349\) | 25.8683 | 1.38470 | 0.692350 | − | 0.721562i | \(-0.256576\pi\) | ||||
0.692350 | + | 0.721562i | \(0.256576\pi\) | |||||||
\(350\) | −1.87738 | −0.100350 | ||||||||
\(351\) | 14.7733 | 0.788541 | ||||||||
\(352\) | −4.66429 | −0.248608 | ||||||||
\(353\) | 11.5289 | 0.613622 | 0.306811 | − | 0.951770i | \(-0.400738\pi\) | ||||
0.306811 | + | 0.951770i | \(0.400738\pi\) | |||||||
\(354\) | 6.82749 | 0.362877 | ||||||||
\(355\) | −15.4056 | −0.817645 | ||||||||
\(356\) | −6.80256 | −0.360535 | ||||||||
\(357\) | 20.7208 | 1.09666 | ||||||||
\(358\) | −2.65552 | −0.140349 | ||||||||
\(359\) | −13.3461 | −0.704378 | −0.352189 | − | 0.935929i | \(-0.614563\pi\) | ||||
−0.352189 | + | 0.935929i | \(0.614563\pi\) | |||||||
\(360\) | −3.09443 | −0.163091 | ||||||||
\(361\) | 3.72472 | 0.196038 | ||||||||
\(362\) | −1.85389 | −0.0974385 | ||||||||
\(363\) | 1.08482 | 0.0569385 | ||||||||
\(364\) | 21.3716 | 1.12017 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −0.545523 | −0.0285149 | ||||||||
\(367\) | −4.94953 | −0.258364 | −0.129182 | − | 0.991621i | \(-0.541235\pi\) | ||||
−0.129182 | + | 0.991621i | \(0.541235\pi\) | |||||||
\(368\) | 7.85406 | 0.409421 | ||||||||
\(369\) | −17.5644 | −0.914367 | ||||||||
\(370\) | 2.26352 | 0.117675 | ||||||||
\(371\) | 54.6369 | 2.83661 | ||||||||
\(372\) | −13.8848 | −0.719896 | ||||||||
\(373\) | 35.8998 | 1.85882 | 0.929411 | − | 0.369046i | \(-0.120315\pi\) | ||||
0.929411 | + | 0.369046i | \(0.120315\pi\) | |||||||
\(374\) | −2.02915 | −0.104925 | ||||||||
\(375\) | 1.08482 | 0.0560201 | ||||||||
\(376\) | −1.14266 | −0.0589281 | ||||||||
\(377\) | 5.83362 | 0.300447 | ||||||||
\(378\) | 9.82296 | 0.505239 | ||||||||
\(379\) | −24.6918 | −1.26833 | −0.634165 | − | 0.773197i | \(-0.718656\pi\) | ||||
−0.634165 | + | 0.773197i | \(0.718656\pi\) | |||||||
\(380\) | 8.58334 | 0.440316 | ||||||||
\(381\) | 7.21496 | 0.369634 | ||||||||
\(382\) | −3.91978 | −0.200553 | ||||||||
\(383\) | 17.0405 | 0.870729 | 0.435364 | − | 0.900254i | \(-0.356620\pi\) | ||||
0.435364 | + | 0.900254i | \(0.356620\pi\) | |||||||
\(384\) | 11.8655 | 0.605510 | ||||||||
\(385\) | 4.20380 | 0.214246 | ||||||||
\(386\) | 5.61240 | 0.285664 | ||||||||
\(387\) | −20.1599 | −1.02479 | ||||||||
\(388\) | −25.8894 | −1.31434 | ||||||||
\(389\) | −12.6850 | −0.643155 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(390\) | 1.36790 | 0.0692665 | ||||||||
\(391\) | 12.5518 | 0.634770 | ||||||||
\(392\) | 18.1134 | 0.914867 | ||||||||
\(393\) | −16.5734 | −0.836018 | ||||||||
\(394\) | 2.06132 | 0.103848 | ||||||||
\(395\) | −3.88009 | −0.195229 | ||||||||
\(396\) | 3.28270 | 0.164962 | ||||||||
\(397\) | 2.35417 | 0.118152 | 0.0590762 | − | 0.998253i | \(-0.481185\pi\) | ||||
0.0590762 | + | 0.998253i | \(0.481185\pi\) | |||||||
\(398\) | −4.02781 | −0.201896 | ||||||||
\(399\) | −21.7396 | −1.08834 | ||||||||
\(400\) | 2.84312 | 0.142156 | ||||||||
\(401\) | −26.1284 | −1.30479 | −0.652396 | − | 0.757878i | \(-0.726236\pi\) | ||||
−0.652396 | + | 0.757878i | \(0.726236\pi\) | |||||||
\(402\) | −3.74707 | −0.186887 | ||||||||
\(403\) | −20.0707 | −0.999792 | ||||||||
\(404\) | 24.0748 | 1.19776 | ||||||||
\(405\) | −0.206625 | −0.0102673 | ||||||||
\(406\) | 3.87885 | 0.192504 | ||||||||
\(407\) | −5.06844 | −0.251233 | ||||||||
\(408\) | 8.36606 | 0.414182 | ||||||||
\(409\) | −6.17352 | −0.305261 | −0.152630 | − | 0.988283i | \(-0.548774\pi\) | ||||
−0.152630 | + | 0.988283i | \(0.548774\pi\) | |||||||
\(410\) | −4.30248 | −0.212484 | ||||||||
\(411\) | −14.0022 | −0.690678 | ||||||||
\(412\) | −25.4458 | −1.25363 | ||||||||
\(413\) | −59.2427 | −2.91514 | ||||||||
\(414\) | 2.24922 | 0.110543 | ||||||||
\(415\) | 3.76371 | 0.184753 | ||||||||
\(416\) | 13.1696 | 0.645693 | ||||||||
\(417\) | −1.51625 | −0.0742511 | ||||||||
\(418\) | 2.12892 | 0.104129 | ||||||||
\(419\) | −12.6796 | −0.619437 | −0.309718 | − | 0.950828i | \(-0.600235\pi\) | ||||
−0.309718 | + | 0.950828i | \(0.600235\pi\) | |||||||
\(420\) | −8.21123 | −0.400667 | ||||||||
\(421\) | −9.82317 | −0.478752 | −0.239376 | − | 0.970927i | \(-0.576943\pi\) | ||||
−0.239376 | + | 0.970927i | \(0.576943\pi\) | |||||||
\(422\) | −6.69049 | −0.325688 | ||||||||
\(423\) | 1.22739 | 0.0596780 | ||||||||
\(424\) | 22.0597 | 1.07132 | ||||||||
\(425\) | 4.54365 | 0.220400 | ||||||||
\(426\) | 7.46359 | 0.361612 | ||||||||
\(427\) | 4.73355 | 0.229072 | ||||||||
\(428\) | −12.5841 | −0.608274 | ||||||||
\(429\) | −3.06299 | −0.147883 | ||||||||
\(430\) | −4.93826 | −0.238144 | ||||||||
\(431\) | 27.8242 | 1.34024 | 0.670122 | − | 0.742251i | \(-0.266242\pi\) | ||||
0.670122 | + | 0.742251i | \(0.266242\pi\) | |||||||
\(432\) | −14.8760 | −0.715721 | ||||||||
\(433\) | 1.89166 | 0.0909074 | 0.0454537 | − | 0.998966i | \(-0.485527\pi\) | ||||
0.0454537 | + | 0.998966i | \(0.485527\pi\) | |||||||
\(434\) | −13.3453 | −0.640593 | ||||||||
\(435\) | −2.24135 | −0.107465 | ||||||||
\(436\) | 12.2576 | 0.587030 | ||||||||
\(437\) | −13.1689 | −0.629952 | ||||||||
\(438\) | −0.484472 | −0.0231490 | ||||||||
\(439\) | −12.7924 | −0.610547 | −0.305274 | − | 0.952265i | \(-0.598748\pi\) | ||||
−0.305274 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(440\) | 1.69729 | 0.0809152 | ||||||||
\(441\) | −19.4567 | −0.926508 | ||||||||
\(442\) | 5.72930 | 0.272515 | ||||||||
\(443\) | 21.6744 | 1.02978 | 0.514891 | − | 0.857256i | \(-0.327832\pi\) | ||||
0.514891 | + | 0.857256i | \(0.327832\pi\) | |||||||
\(444\) | 9.90013 | 0.469839 | ||||||||
\(445\) | 3.77803 | 0.179096 | ||||||||
\(446\) | 5.26915 | 0.249502 | ||||||||
\(447\) | −3.55584 | −0.168185 | ||||||||
\(448\) | −15.1472 | −0.715637 | ||||||||
\(449\) | 21.0784 | 0.994750 | 0.497375 | − | 0.867536i | \(-0.334297\pi\) | ||||
0.497375 | + | 0.867536i | \(0.334297\pi\) | |||||||
\(450\) | 0.814205 | 0.0383820 | ||||||||
\(451\) | 9.63406 | 0.453650 | ||||||||
\(452\) | −32.4169 | −1.52476 | ||||||||
\(453\) | −6.70706 | −0.315125 | ||||||||
\(454\) | −10.2739 | −0.482176 | ||||||||
\(455\) | −11.8694 | −0.556447 | ||||||||
\(456\) | −8.77738 | −0.411039 | ||||||||
\(457\) | 24.7637 | 1.15839 | 0.579197 | − | 0.815187i | \(-0.303366\pi\) | ||||
0.579197 | + | 0.815187i | \(0.303366\pi\) | |||||||
\(458\) | −8.07565 | −0.377350 | ||||||||
\(459\) | −23.7737 | −1.10966 | ||||||||
\(460\) | −4.97400 | −0.231914 | ||||||||
\(461\) | −10.2398 | −0.476913 | −0.238457 | − | 0.971153i | \(-0.576641\pi\) | ||||
−0.238457 | + | 0.971153i | \(0.576641\pi\) | |||||||
\(462\) | −2.03662 | −0.0947524 | ||||||||
\(463\) | −3.21796 | −0.149551 | −0.0747756 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747756 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(464\) | −5.87417 | −0.272701 | ||||||||
\(465\) | 7.71142 | 0.357608 | ||||||||
\(466\) | −8.97016 | −0.415535 | ||||||||
\(467\) | 18.9161 | 0.875331 | 0.437665 | − | 0.899138i | \(-0.355805\pi\) | ||||
0.437665 | + | 0.899138i | \(0.355805\pi\) | |||||||
\(468\) | −9.26869 | −0.428445 | ||||||||
\(469\) | 32.5136 | 1.50134 | ||||||||
\(470\) | 0.300656 | 0.0138682 | ||||||||
\(471\) | −9.40688 | −0.433446 | ||||||||
\(472\) | −23.9193 | −1.10098 | ||||||||
\(473\) | 11.0577 | 0.508433 | ||||||||
\(474\) | 1.87979 | 0.0863418 | ||||||||
\(475\) | −4.76704 | −0.218727 | ||||||||
\(476\) | −34.3918 | −1.57634 | ||||||||
\(477\) | −23.6956 | −1.08495 | ||||||||
\(478\) | −7.35239 | −0.336290 | ||||||||
\(479\) | 2.25652 | 0.103103 | 0.0515515 | − | 0.998670i | \(-0.483583\pi\) | ||||
0.0515515 | + | 0.998670i | \(0.483583\pi\) | |||||||
\(480\) | −5.05994 | −0.230953 | ||||||||
\(481\) | 14.3107 | 0.652513 | ||||||||
\(482\) | −5.21416 | −0.237499 | ||||||||
\(483\) | 12.5980 | 0.573228 | ||||||||
\(484\) | −1.80056 | −0.0818435 | ||||||||
\(485\) | 14.3786 | 0.652897 | ||||||||
\(486\) | −6.90995 | −0.313442 | ||||||||
\(487\) | 10.7332 | 0.486367 | 0.243183 | − | 0.969980i | \(-0.421808\pi\) | ||||
0.243183 | + | 0.969980i | \(0.421808\pi\) | |||||||
\(488\) | 1.91118 | 0.0865149 | ||||||||
\(489\) | 19.2532 | 0.870658 | ||||||||
\(490\) | −4.76600 | −0.215306 | ||||||||
\(491\) | −9.76040 | −0.440481 | −0.220240 | − | 0.975446i | \(-0.570684\pi\) | ||||
−0.220240 | + | 0.975446i | \(0.570684\pi\) | |||||||
\(492\) | −18.8181 | −0.848385 | ||||||||
\(493\) | −9.38764 | −0.422798 | ||||||||
\(494\) | −6.01099 | −0.270447 | ||||||||
\(495\) | −1.82316 | −0.0819448 | ||||||||
\(496\) | 20.2102 | 0.907464 | ||||||||
\(497\) | −64.7622 | −2.90498 | ||||||||
\(498\) | −1.82341 | −0.0817090 | ||||||||
\(499\) | −8.19839 | −0.367010 | −0.183505 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183505 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(500\) | −1.80056 | −0.0805234 | ||||||||
\(501\) | 22.1955 | 0.991621 | ||||||||
\(502\) | −13.4185 | −0.598896 | ||||||||
\(503\) | 28.8451 | 1.28614 | 0.643071 | − | 0.765807i | \(-0.277660\pi\) | ||||
0.643071 | + | 0.765807i | \(0.277660\pi\) | |||||||
\(504\) | −13.0084 | −0.579439 | ||||||||
\(505\) | −13.3707 | −0.594990 | ||||||||
\(506\) | −1.23370 | −0.0548445 | ||||||||
\(507\) | −5.45436 | −0.242236 | ||||||||
\(508\) | −11.9752 | −0.531312 | ||||||||
\(509\) | −12.9788 | −0.575276 | −0.287638 | − | 0.957739i | \(-0.592870\pi\) | ||||
−0.287638 | + | 0.957739i | \(0.592870\pi\) | |||||||
\(510\) | −2.20127 | −0.0974740 | ||||||||
\(511\) | 4.20380 | 0.185965 | ||||||||
\(512\) | −22.9124 | −1.01259 | ||||||||
\(513\) | 24.9425 | 1.10124 | ||||||||
\(514\) | −5.65601 | −0.249476 | ||||||||
\(515\) | 14.1322 | 0.622739 | ||||||||
\(516\) | −21.5988 | −0.950836 | ||||||||
\(517\) | −0.673225 | −0.0296084 | ||||||||
\(518\) | 9.51539 | 0.418082 | ||||||||
\(519\) | −24.1000 | −1.05787 | ||||||||
\(520\) | −4.79230 | −0.210156 | ||||||||
\(521\) | −11.3429 | −0.496941 | −0.248470 | − | 0.968639i | \(-0.579928\pi\) | ||||
−0.248470 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(522\) | −1.68223 | −0.0736291 | ||||||||
\(523\) | −22.7127 | −0.993159 | −0.496579 | − | 0.867991i | \(-0.665411\pi\) | ||||
−0.496579 | + | 0.867991i | \(0.665411\pi\) | |||||||
\(524\) | 27.5080 | 1.20169 | ||||||||
\(525\) | 4.56039 | 0.199032 | ||||||||
\(526\) | −10.4987 | −0.457766 | ||||||||
\(527\) | 32.2984 | 1.40694 | ||||||||
\(528\) | 3.08428 | 0.134226 | ||||||||
\(529\) | −15.3687 | −0.668204 | ||||||||
\(530\) | −5.80434 | −0.252125 | ||||||||
\(531\) | 25.6931 | 1.11499 | ||||||||
\(532\) | 36.0827 | 1.56438 | ||||||||
\(533\) | −27.2017 | −1.17824 | ||||||||
\(534\) | −1.83035 | −0.0792069 | ||||||||
\(535\) | 6.98899 | 0.302160 | ||||||||
\(536\) | 13.1274 | 0.567019 | ||||||||
\(537\) | 6.45059 | 0.278363 | ||||||||
\(538\) | 3.59725 | 0.155089 | ||||||||
\(539\) | 10.6720 | 0.459674 | ||||||||
\(540\) | 9.42101 | 0.405416 | ||||||||
\(541\) | −33.8790 | −1.45657 | −0.728287 | − | 0.685273i | \(-0.759683\pi\) | ||||
−0.728287 | + | 0.685273i | \(0.759683\pi\) | |||||||
\(542\) | 1.52240 | 0.0653929 | ||||||||
\(543\) | 4.50334 | 0.193257 | ||||||||
\(544\) | −21.1929 | −0.908640 | ||||||||
\(545\) | −6.80765 | −0.291608 | ||||||||
\(546\) | 5.75040 | 0.246094 | ||||||||
\(547\) | −21.2530 | −0.908713 | −0.454357 | − | 0.890820i | \(-0.650131\pi\) | ||||
−0.454357 | + | 0.890820i | \(0.650131\pi\) | |||||||
\(548\) | 23.2404 | 0.992782 | ||||||||
\(549\) | −2.05290 | −0.0876158 | ||||||||
\(550\) | −0.446590 | −0.0190427 | ||||||||
\(551\) | 9.84919 | 0.419589 | ||||||||
\(552\) | 5.08645 | 0.216494 | ||||||||
\(553\) | −16.3111 | −0.693620 | ||||||||
\(554\) | 5.83749 | 0.248011 | ||||||||
\(555\) | −5.49837 | −0.233393 | ||||||||
\(556\) | 2.51662 | 0.106729 | ||||||||
\(557\) | 38.7154 | 1.64043 | 0.820213 | − | 0.572059i | \(-0.193855\pi\) | ||||
0.820213 | + | 0.572059i | \(0.193855\pi\) | |||||||
\(558\) | 5.78773 | 0.245014 | ||||||||
\(559\) | −31.2213 | −1.32052 | ||||||||
\(560\) | 11.9519 | 0.505061 | ||||||||
\(561\) | 4.92906 | 0.208105 | ||||||||
\(562\) | 11.1585 | 0.470693 | ||||||||
\(563\) | −29.8386 | −1.25755 | −0.628774 | − | 0.777588i | \(-0.716443\pi\) | ||||
−0.628774 | + | 0.777588i | \(0.716443\pi\) | |||||||
\(564\) | 1.31500 | 0.0553715 | ||||||||
\(565\) | 18.0038 | 0.757427 | ||||||||
\(566\) | 12.7241 | 0.534835 | ||||||||
\(567\) | −0.868610 | −0.0364782 | ||||||||
\(568\) | −26.1478 | −1.09714 | ||||||||
\(569\) | 3.16612 | 0.132731 | 0.0663654 | − | 0.997795i | \(-0.478860\pi\) | ||||
0.0663654 | + | 0.997795i | \(0.478860\pi\) | |||||||
\(570\) | 2.30950 | 0.0967343 | ||||||||
\(571\) | −6.67544 | −0.279359 | −0.139679 | − | 0.990197i | \(-0.544607\pi\) | ||||
−0.139679 | + | 0.990197i | \(0.544607\pi\) | |||||||
\(572\) | 5.08386 | 0.212567 | ||||||||
\(573\) | 9.52163 | 0.397772 | ||||||||
\(574\) | −18.0868 | −0.754928 | ||||||||
\(575\) | 2.76248 | 0.115203 | ||||||||
\(576\) | 6.56922 | 0.273717 | ||||||||
\(577\) | 24.4553 | 1.01809 | 0.509043 | − | 0.860741i | \(-0.329999\pi\) | ||||
0.509043 | + | 0.860741i | \(0.329999\pi\) | |||||||
\(578\) | −1.62773 | −0.0677047 | ||||||||
\(579\) | −13.6332 | −0.566577 | ||||||||
\(580\) | 3.72013 | 0.154470 | ||||||||
\(581\) | 15.8219 | 0.656403 | ||||||||
\(582\) | −6.96601 | −0.288750 | ||||||||
\(583\) | 12.9970 | 0.538282 | ||||||||
\(584\) | 1.69729 | 0.0702345 | ||||||||
\(585\) | 5.14768 | 0.212830 | ||||||||
\(586\) | −8.74350 | −0.361191 | ||||||||
\(587\) | −18.3362 | −0.756815 | −0.378408 | − | 0.925639i | \(-0.623528\pi\) | ||||
−0.378408 | + | 0.925639i | \(0.623528\pi\) | |||||||
\(588\) | −20.8454 | −0.859650 | ||||||||
\(589\) | −33.8863 | −1.39626 | ||||||||
\(590\) | 6.29364 | 0.259105 | ||||||||
\(591\) | −5.00719 | −0.205968 | ||||||||
\(592\) | −14.4102 | −0.592255 | ||||||||
\(593\) | −41.7703 | −1.71530 | −0.857650 | − | 0.514233i | \(-0.828077\pi\) | ||||
−0.857650 | + | 0.514233i | \(0.828077\pi\) | |||||||
\(594\) | 2.33668 | 0.0958753 | ||||||||
\(595\) | 19.1006 | 0.783049 | ||||||||
\(596\) | 5.90187 | 0.241750 | ||||||||
\(597\) | 9.78404 | 0.400434 | ||||||||
\(598\) | 3.48334 | 0.142444 | ||||||||
\(599\) | −17.8542 | −0.729501 | −0.364751 | − | 0.931105i | \(-0.618846\pi\) | ||||
−0.364751 | + | 0.931105i | \(0.618846\pi\) | |||||||
\(600\) | 1.84126 | 0.0751692 | ||||||||
\(601\) | 31.6467 | 1.29090 | 0.645448 | − | 0.763804i | \(-0.276671\pi\) | ||||
0.645448 | + | 0.763804i | \(0.276671\pi\) | |||||||
\(602\) | −20.7595 | −0.846093 | ||||||||
\(603\) | −14.1009 | −0.574234 | ||||||||
\(604\) | 11.1322 | 0.452962 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 6.47774 | 0.263140 | ||||||||
\(607\) | 39.3323 | 1.59645 | 0.798224 | − | 0.602361i | \(-0.205773\pi\) | ||||
0.798224 | + | 0.602361i | \(0.205773\pi\) | |||||||
\(608\) | 22.2349 | 0.901744 | ||||||||
\(609\) | −9.42221 | −0.381807 | ||||||||
\(610\) | −0.502868 | −0.0203605 | ||||||||
\(611\) | 1.90085 | 0.0769000 | ||||||||
\(612\) | 14.9154 | 0.602921 | ||||||||
\(613\) | −20.4924 | −0.827679 | −0.413839 | − | 0.910350i | \(-0.635812\pi\) | ||||
−0.413839 | + | 0.910350i | \(0.635812\pi\) | |||||||
\(614\) | −1.49101 | −0.0601722 | ||||||||
\(615\) | 10.4513 | 0.421435 | ||||||||
\(616\) | 7.13508 | 0.287481 | ||||||||
\(617\) | 16.7332 | 0.673654 | 0.336827 | − | 0.941567i | \(-0.390646\pi\) | ||||
0.336827 | + | 0.941567i | \(0.390646\pi\) | |||||||
\(618\) | −6.84666 | −0.275413 | ||||||||
\(619\) | 28.4818 | 1.14478 | 0.572390 | − | 0.819982i | \(-0.306016\pi\) | ||||
0.572390 | + | 0.819982i | \(0.306016\pi\) | |||||||
\(620\) | −12.7992 | −0.514027 | ||||||||
\(621\) | −14.4541 | −0.580021 | ||||||||
\(622\) | 11.4657 | 0.459731 | ||||||||
\(623\) | 15.8821 | 0.636302 | ||||||||
\(624\) | −8.70846 | −0.348617 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.3341 | 0.572905 | ||||||||
\(627\) | −5.17140 | −0.206526 | ||||||||
\(628\) | 15.6133 | 0.623037 | ||||||||
\(629\) | −23.0293 | −0.918237 | ||||||||
\(630\) | 3.42276 | 0.136366 | ||||||||
\(631\) | −33.8003 | −1.34557 | −0.672784 | − | 0.739839i | \(-0.734902\pi\) | ||||
−0.672784 | + | 0.739839i | \(0.734902\pi\) | |||||||
\(632\) | −6.58565 | −0.261963 | ||||||||
\(633\) | 16.2520 | 0.645960 | ||||||||
\(634\) | −8.19541 | −0.325481 | ||||||||
\(635\) | 6.65081 | 0.263929 | ||||||||
\(636\) | −25.3869 | −1.00666 | ||||||||
\(637\) | −30.1322 | −1.19388 | ||||||||
\(638\) | 0.922700 | 0.0365300 | ||||||||
\(639\) | 28.0869 | 1.11110 | ||||||||
\(640\) | 10.9377 | 0.432352 | ||||||||
\(641\) | −24.2574 | −0.958109 | −0.479054 | − | 0.877785i | \(-0.659020\pi\) | ||||
−0.479054 | + | 0.877785i | \(0.659020\pi\) | |||||||
\(642\) | −3.38597 | −0.133634 | ||||||||
\(643\) | −20.4656 | −0.807086 | −0.403543 | − | 0.914961i | \(-0.632221\pi\) | ||||
−0.403543 | + | 0.914961i | \(0.632221\pi\) | |||||||
\(644\) | −20.9097 | −0.823959 | ||||||||
\(645\) | 11.9956 | 0.472328 | ||||||||
\(646\) | 9.67306 | 0.380581 | ||||||||
\(647\) | −26.6310 | −1.04697 | −0.523486 | − | 0.852034i | \(-0.675369\pi\) | ||||
−0.523486 | + | 0.852034i | \(0.675369\pi\) | |||||||
\(648\) | −0.350703 | −0.0137769 | ||||||||
\(649\) | −14.0926 | −0.553184 | ||||||||
\(650\) | 1.26095 | 0.0494584 | ||||||||
\(651\) | 32.4173 | 1.27053 | ||||||||
\(652\) | −31.9558 | −1.25149 | ||||||||
\(653\) | 4.56814 | 0.178765 | 0.0893825 | − | 0.995997i | \(-0.471511\pi\) | ||||
0.0893825 | + | 0.995997i | \(0.471511\pi\) | |||||||
\(654\) | 3.29811 | 0.128966 | ||||||||
\(655\) | −15.2775 | −0.596942 | ||||||||
\(656\) | 27.3908 | 1.06943 | ||||||||
\(657\) | −1.82316 | −0.0711281 | ||||||||
\(658\) | 1.26390 | 0.0492718 | ||||||||
\(659\) | 1.77338 | 0.0690811 | 0.0345405 | − | 0.999403i | \(-0.489003\pi\) | ||||
0.0345405 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(660\) | −1.95329 | −0.0760316 | ||||||||
\(661\) | −25.9729 | −1.01023 | −0.505114 | − | 0.863053i | \(-0.668550\pi\) | ||||
−0.505114 | + | 0.863053i | \(0.668550\pi\) | |||||||
\(662\) | 0.423514 | 0.0164603 | ||||||||
\(663\) | −13.9172 | −0.540499 | ||||||||
\(664\) | 6.38811 | 0.247907 | ||||||||
\(665\) | −20.0397 | −0.777107 | ||||||||
\(666\) | −4.12675 | −0.159908 | ||||||||
\(667\) | −5.70756 | −0.220998 | ||||||||
\(668\) | −36.8394 | −1.42536 | ||||||||
\(669\) | −12.7994 | −0.494854 | ||||||||
\(670\) | −3.45408 | −0.133443 | ||||||||
\(671\) | 1.12602 | 0.0434693 | ||||||||
\(672\) | −21.2710 | −0.820546 | ||||||||
\(673\) | −19.3947 | −0.747610 | −0.373805 | − | 0.927507i | \(-0.621947\pi\) | ||||
−0.373805 | + | 0.927507i | \(0.621947\pi\) | |||||||
\(674\) | −0.223238 | −0.00859879 | ||||||||
\(675\) | −5.23228 | −0.201390 | ||||||||
\(676\) | 9.05297 | 0.348191 | ||||||||
\(677\) | −38.8712 | −1.49394 | −0.746970 | − | 0.664858i | \(-0.768492\pi\) | ||||
−0.746970 | + | 0.664858i | \(0.768492\pi\) | |||||||
\(678\) | −8.72235 | −0.334980 | ||||||||
\(679\) | 60.4446 | 2.31965 | ||||||||
\(680\) | 7.71191 | 0.295738 | ||||||||
\(681\) | 24.9565 | 0.956335 | ||||||||
\(682\) | −3.17457 | −0.121560 | ||||||||
\(683\) | −35.1512 | −1.34502 | −0.672512 | − | 0.740086i | \(-0.734785\pi\) | ||||
−0.672512 | + | 0.740086i | \(0.734785\pi\) | |||||||
\(684\) | −15.6488 | −0.598346 | ||||||||
\(685\) | −12.9074 | −0.493165 | ||||||||
\(686\) | −6.89366 | −0.263201 | ||||||||
\(687\) | 19.6168 | 0.748426 | ||||||||
\(688\) | 31.4383 | 1.19858 | ||||||||
\(689\) | −36.6970 | −1.39805 | ||||||||
\(690\) | −1.33834 | −0.0509499 | ||||||||
\(691\) | −32.5538 | −1.23841 | −0.619203 | − | 0.785231i | \(-0.712544\pi\) | ||||
−0.619203 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(692\) | 40.0004 | 1.52059 | ||||||||
\(693\) | −7.66420 | −0.291139 | ||||||||
\(694\) | 8.21450 | 0.311818 | ||||||||
\(695\) | −1.39769 | −0.0530175 | ||||||||
\(696\) | −3.80423 | −0.144199 | ||||||||
\(697\) | 43.7738 | 1.65805 | ||||||||
\(698\) | −11.5525 | −0.437270 | ||||||||
\(699\) | 21.7896 | 0.824160 | ||||||||
\(700\) | −7.56919 | −0.286088 | ||||||||
\(701\) | 19.3571 | 0.731109 | 0.365554 | − | 0.930790i | \(-0.380879\pi\) | ||||
0.365554 | + | 0.930790i | \(0.380879\pi\) | |||||||
\(702\) | −6.59762 | −0.249011 | ||||||||
\(703\) | 24.1615 | 0.911268 | ||||||||
\(704\) | −3.60321 | −0.135801 | ||||||||
\(705\) | −0.730330 | −0.0275058 | ||||||||
\(706\) | −5.14870 | −0.193774 | ||||||||
\(707\) | −56.2079 | −2.11392 | ||||||||
\(708\) | 27.5270 | 1.03453 | ||||||||
\(709\) | −28.2575 | −1.06123 | −0.530616 | − | 0.847612i | \(-0.678039\pi\) | ||||
−0.530616 | + | 0.847612i | \(0.678039\pi\) | |||||||
\(710\) | 6.88000 | 0.258202 | ||||||||
\(711\) | 7.07401 | 0.265296 | ||||||||
\(712\) | 6.41242 | 0.240316 | ||||||||
\(713\) | 19.6370 | 0.735410 | ||||||||
\(714\) | −9.25372 | −0.346312 | ||||||||
\(715\) | −2.82350 | −0.105593 | ||||||||
\(716\) | −10.7065 | −0.400120 | ||||||||
\(717\) | 17.8599 | 0.666989 | ||||||||
\(718\) | 5.96022 | 0.222433 | ||||||||
\(719\) | 13.7927 | 0.514382 | 0.257191 | − | 0.966361i | \(-0.417203\pi\) | ||||
0.257191 | + | 0.966361i | \(0.417203\pi\) | |||||||
\(720\) | −5.18345 | −0.193176 | ||||||||
\(721\) | 59.4090 | 2.21251 | ||||||||
\(722\) | −1.66342 | −0.0619062 | ||||||||
\(723\) | 12.6659 | 0.471048 | ||||||||
\(724\) | −7.47450 | −0.277788 | ||||||||
\(725\) | −2.06610 | −0.0767330 | ||||||||
\(726\) | −0.484472 | −0.0179804 | ||||||||
\(727\) | 2.82936 | 0.104935 | 0.0524676 | − | 0.998623i | \(-0.483291\pi\) | ||||
0.0524676 | + | 0.998623i | \(0.483291\pi\) | |||||||
\(728\) | −20.1459 | −0.746656 | ||||||||
\(729\) | 17.4050 | 0.644630 | ||||||||
\(730\) | −0.446590 | −0.0165291 | ||||||||
\(731\) | 50.2423 | 1.85828 | ||||||||
\(732\) | −2.19943 | −0.0812933 | ||||||||
\(733\) | −47.5696 | −1.75702 | −0.878511 | − | 0.477722i | \(-0.841463\pi\) | ||||
−0.878511 | + | 0.477722i | \(0.841463\pi\) | |||||||
\(734\) | 2.21041 | 0.0815879 | ||||||||
\(735\) | 11.5772 | 0.427031 | ||||||||
\(736\) | −12.8850 | −0.474948 | ||||||||
\(737\) | 7.73434 | 0.284898 | ||||||||
\(738\) | 7.84410 | 0.288745 | ||||||||
\(739\) | 17.2405 | 0.634203 | 0.317101 | − | 0.948392i | \(-0.397290\pi\) | ||||
0.317101 | + | 0.948392i | \(0.397290\pi\) | |||||||
\(740\) | 9.12602 | 0.335479 | ||||||||
\(741\) | 14.6014 | 0.536397 | ||||||||
\(742\) | −24.4003 | −0.895764 | ||||||||
\(743\) | −31.7628 | −1.16527 | −0.582633 | − | 0.812736i | \(-0.697977\pi\) | ||||
−0.582633 | + | 0.812736i | \(0.697977\pi\) | |||||||
\(744\) | 13.0885 | 0.479849 | ||||||||
\(745\) | −3.27780 | −0.120089 | ||||||||
\(746\) | −16.0325 | −0.586992 | ||||||||
\(747\) | −6.86183 | −0.251061 | ||||||||
\(748\) | −8.18111 | −0.299131 | ||||||||
\(749\) | 29.3803 | 1.07353 | ||||||||
\(750\) | −0.484472 | −0.0176904 | ||||||||
\(751\) | −40.7925 | −1.48854 | −0.744271 | − | 0.667878i | \(-0.767203\pi\) | ||||
−0.744271 | + | 0.667878i | \(0.767203\pi\) | |||||||
\(752\) | −1.91406 | −0.0697985 | ||||||||
\(753\) | 32.5952 | 1.18783 | ||||||||
\(754\) | −2.60524 | −0.0948772 | ||||||||
\(755\) | −6.18263 | −0.225009 | ||||||||
\(756\) | 39.6041 | 1.44039 | ||||||||
\(757\) | −39.6054 | −1.43948 | −0.719742 | − | 0.694242i | \(-0.755740\pi\) | ||||
−0.719742 | + | 0.694242i | \(0.755740\pi\) | |||||||
\(758\) | 11.0271 | 0.400523 | ||||||||
\(759\) | 2.99680 | 0.108777 | ||||||||
\(760\) | −8.09107 | −0.293494 | ||||||||
\(761\) | 1.53536 | 0.0556566 | 0.0278283 | − | 0.999613i | \(-0.491141\pi\) | ||||
0.0278283 | + | 0.999613i | \(0.491141\pi\) | |||||||
\(762\) | −3.22213 | −0.116726 | ||||||||
\(763\) | −28.6180 | −1.03604 | ||||||||
\(764\) | −15.8037 | −0.571758 | ||||||||
\(765\) | −8.28380 | −0.299501 | ||||||||
\(766\) | −7.61012 | −0.274965 | ||||||||
\(767\) | 39.7905 | 1.43675 | ||||||||
\(768\) | 2.51866 | 0.0908845 | ||||||||
\(769\) | 26.4808 | 0.954923 | 0.477461 | − | 0.878653i | \(-0.341557\pi\) | ||||
0.477461 | + | 0.878653i | \(0.341557\pi\) | |||||||
\(770\) | −1.87738 | −0.0676560 | ||||||||
\(771\) | 13.7392 | 0.494804 | ||||||||
\(772\) | 22.6280 | 0.814399 | ||||||||
\(773\) | 14.5416 | 0.523024 | 0.261512 | − | 0.965200i | \(-0.415779\pi\) | ||||
0.261512 | + | 0.965200i | \(0.415779\pi\) | |||||||
\(774\) | 9.00322 | 0.323614 | ||||||||
\(775\) | 7.10845 | 0.255343 | ||||||||
\(776\) | 24.4046 | 0.876074 | ||||||||
\(777\) | −23.1141 | −0.829212 | ||||||||
\(778\) | 5.66500 | 0.203100 | ||||||||
\(779\) | −45.9260 | −1.64547 | ||||||||
\(780\) | 5.51510 | 0.197472 | ||||||||
\(781\) | −15.4056 | −0.551256 | ||||||||
\(782\) | −5.60549 | −0.200452 | ||||||||
\(783\) | 10.8104 | 0.386332 | ||||||||
\(784\) | 30.3417 | 1.08363 | ||||||||
\(785\) | −8.67135 | −0.309494 | ||||||||
\(786\) | 7.40153 | 0.264004 | ||||||||
\(787\) | 24.9365 | 0.888889 | 0.444444 | − | 0.895806i | \(-0.353401\pi\) | ||||
0.444444 | + | 0.895806i | \(0.353401\pi\) | |||||||
\(788\) | 8.31079 | 0.296060 | ||||||||
\(789\) | 25.5027 | 0.907919 | ||||||||
\(790\) | 1.73281 | 0.0616506 | ||||||||
\(791\) | 75.6846 | 2.69103 | ||||||||
\(792\) | −3.09443 | −0.109956 | ||||||||
\(793\) | −3.17930 | −0.112900 | ||||||||
\(794\) | −1.05135 | −0.0373110 | ||||||||
\(795\) | 14.0995 | 0.500057 | ||||||||
\(796\) | −16.2393 | −0.575585 | ||||||||
\(797\) | −18.9986 | −0.672964 | −0.336482 | − | 0.941690i | \(-0.609237\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(798\) | 9.70868 | 0.343684 | ||||||||
\(799\) | −3.05890 | −0.108216 | ||||||||
\(800\) | −4.66429 | −0.164908 | ||||||||
\(801\) | −6.88794 | −0.243373 | ||||||||
\(802\) | 11.6687 | 0.412037 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −15.1074 | −0.532796 | ||||||||
\(805\) | 11.6129 | 0.409302 | ||||||||
\(806\) | 8.96337 | 0.315721 | ||||||||
\(807\) | −8.73818 | −0.307598 | ||||||||
\(808\) | −22.6940 | −0.798373 | ||||||||
\(809\) | −14.7798 | −0.519629 | −0.259815 | − | 0.965659i | \(-0.583661\pi\) | ||||
−0.259815 | + | 0.965659i | \(0.583661\pi\) | |||||||
\(810\) | 0.0922767 | 0.00324227 | ||||||||
\(811\) | 31.0921 | 1.09179 | 0.545896 | − | 0.837853i | \(-0.316189\pi\) | ||||
0.545896 | + | 0.837853i | \(0.316189\pi\) | |||||||
\(812\) | 15.6387 | 0.548810 | ||||||||
\(813\) | −3.69811 | −0.129698 | ||||||||
\(814\) | 2.26352 | 0.0793363 | ||||||||
\(815\) | 17.7477 | 0.621676 | ||||||||
\(816\) | 14.0139 | 0.490585 | ||||||||
\(817\) | −52.7125 | −1.84418 | ||||||||
\(818\) | 2.75703 | 0.0963974 | ||||||||
\(819\) | 21.6398 | 0.756157 | ||||||||
\(820\) | −17.3467 | −0.605772 | ||||||||
\(821\) | −11.3198 | −0.395064 | −0.197532 | − | 0.980296i | \(-0.563293\pi\) | ||||
−0.197532 | + | 0.980296i | \(0.563293\pi\) | |||||||
\(822\) | 6.25325 | 0.218107 | ||||||||
\(823\) | −40.2698 | −1.40372 | −0.701859 | − | 0.712316i | \(-0.747646\pi\) | ||||
−0.701859 | + | 0.712316i | \(0.747646\pi\) | |||||||
\(824\) | 23.9865 | 0.835609 | ||||||||
\(825\) | 1.08482 | 0.0377687 | ||||||||
\(826\) | 26.4572 | 0.920564 | ||||||||
\(827\) | −7.73425 | −0.268946 | −0.134473 | − | 0.990917i | \(-0.542934\pi\) | ||||
−0.134473 | + | 0.990917i | \(0.542934\pi\) | |||||||
\(828\) | 9.06839 | 0.315148 | ||||||||
\(829\) | −3.54130 | −0.122994 | −0.0614972 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0614972 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(830\) | −1.68084 | −0.0583427 | ||||||||
\(831\) | −14.1800 | −0.491898 | ||||||||
\(832\) | 10.1736 | 0.352708 | ||||||||
\(833\) | 48.4897 | 1.68007 | ||||||||
\(834\) | 0.677142 | 0.0234475 | ||||||||
\(835\) | 20.4600 | 0.708047 | ||||||||
\(836\) | 8.58334 | 0.296861 | ||||||||
\(837\) | −37.1934 | −1.28559 | ||||||||
\(838\) | 5.66257 | 0.195610 | ||||||||
\(839\) | 31.3132 | 1.08105 | 0.540526 | − | 0.841327i | \(-0.318225\pi\) | ||||
0.540526 | + | 0.841327i | \(0.318225\pi\) | |||||||
\(840\) | 7.74031 | 0.267066 | ||||||||
\(841\) | −24.7312 | −0.852801 | ||||||||
\(842\) | 4.38693 | 0.151184 | ||||||||
\(843\) | −27.1054 | −0.933560 | ||||||||
\(844\) | −26.9746 | −0.928505 | ||||||||
\(845\) | −5.02787 | −0.172964 | ||||||||
\(846\) | −0.548143 | −0.0188455 | ||||||||
\(847\) | 4.20380 | 0.144444 | ||||||||
\(848\) | 36.9521 | 1.26894 | ||||||||
\(849\) | −30.9085 | −1.06078 | ||||||||
\(850\) | −2.02915 | −0.0695994 | ||||||||
\(851\) | −14.0015 | −0.479965 | ||||||||
\(852\) | 30.0916 | 1.03092 | ||||||||
\(853\) | 17.8102 | 0.609809 | 0.304905 | − | 0.952383i | \(-0.401375\pi\) | ||||
0.304905 | + | 0.952383i | \(0.401375\pi\) | |||||||
\(854\) | −2.11396 | −0.0723381 | ||||||||
\(855\) | 8.69107 | 0.297228 | ||||||||
\(856\) | 11.8624 | 0.405447 | ||||||||
\(857\) | −4.76167 | −0.162656 | −0.0813278 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813278 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(858\) | 1.36790 | 0.0466995 | ||||||||
\(859\) | −54.5172 | −1.86010 | −0.930051 | − | 0.367431i | \(-0.880237\pi\) | ||||
−0.930051 | + | 0.367431i | \(0.880237\pi\) | |||||||
\(860\) | −19.9100 | −0.678925 | ||||||||
\(861\) | 43.9350 | 1.49730 | ||||||||
\(862\) | −12.4260 | −0.423232 | ||||||||
\(863\) | −50.5845 | −1.72192 | −0.860959 | − | 0.508675i | \(-0.830136\pi\) | ||||
−0.860959 | + | 0.508675i | \(0.830136\pi\) | |||||||
\(864\) | 24.4049 | 0.830271 | ||||||||
\(865\) | −22.2156 | −0.755353 | ||||||||
\(866\) | −0.844797 | −0.0287074 | ||||||||
\(867\) | 3.95396 | 0.134284 | ||||||||
\(868\) | −53.8052 | −1.82627 | ||||||||
\(869\) | −3.88009 | −0.131623 | ||||||||
\(870\) | 1.00097 | 0.0339360 | ||||||||
\(871\) | −21.8379 | −0.739948 | ||||||||
\(872\) | −11.5546 | −0.391287 | ||||||||
\(873\) | −26.2144 | −0.887222 | ||||||||
\(874\) | 5.88109 | 0.198931 | ||||||||
\(875\) | 4.20380 | 0.142114 | ||||||||
\(876\) | −1.95329 | −0.0659955 | ||||||||
\(877\) | −0.191186 | −0.00645590 | −0.00322795 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322795 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(878\) | 5.71296 | 0.192803 | ||||||||
\(879\) | 21.2390 | 0.716375 | ||||||||
\(880\) | 2.84312 | 0.0958415 | ||||||||
\(881\) | 32.7952 | 1.10490 | 0.552450 | − | 0.833546i | \(-0.313693\pi\) | ||||
0.552450 | + | 0.833546i | \(0.313693\pi\) | |||||||
\(882\) | 8.68916 | 0.292579 | ||||||||
\(883\) | 0.495202 | 0.0166649 | 0.00833244 | − | 0.999965i | \(-0.497348\pi\) | ||||
0.00833244 | + | 0.999965i | \(0.497348\pi\) | |||||||
\(884\) | 23.0993 | 0.776914 | ||||||||
\(885\) | −15.2880 | −0.513901 | ||||||||
\(886\) | −9.67958 | −0.325192 | ||||||||
\(887\) | −30.3178 | −1.01797 | −0.508986 | − | 0.860775i | \(-0.669979\pi\) | ||||
−0.508986 | + | 0.860775i | \(0.669979\pi\) | |||||||
\(888\) | −9.33234 | −0.313173 | ||||||||
\(889\) | 27.9587 | 0.937705 | ||||||||
\(890\) | −1.68723 | −0.0565561 | ||||||||
\(891\) | −0.206625 | −0.00692219 | ||||||||
\(892\) | 21.2441 | 0.711305 | ||||||||
\(893\) | 3.20929 | 0.107395 | ||||||||
\(894\) | 1.58800 | 0.0531108 | ||||||||
\(895\) | 5.94621 | 0.198760 | ||||||||
\(896\) | 45.9801 | 1.53609 | ||||||||
\(897\) | −8.46146 | −0.282520 | ||||||||
\(898\) | −9.41340 | −0.314129 | ||||||||
\(899\) | −14.6868 | −0.489831 | ||||||||
\(900\) | 3.28270 | 0.109423 | ||||||||
\(901\) | 59.0540 | 1.96737 | ||||||||
\(902\) | −4.30248 | −0.143257 | ||||||||
\(903\) | 50.4273 | 1.67812 | ||||||||
\(904\) | 30.5578 | 1.01634 | ||||||||
\(905\) | 4.15122 | 0.137991 | ||||||||
\(906\) | 2.99531 | 0.0995125 | ||||||||
\(907\) | −29.1269 | −0.967142 | −0.483571 | − | 0.875305i | \(-0.660661\pi\) | ||||
−0.483571 | + | 0.875305i | \(0.660661\pi\) | |||||||
\(908\) | −41.4220 | −1.37464 | ||||||||
\(909\) | 24.3769 | 0.808532 | ||||||||
\(910\) | 5.30077 | 0.175719 | ||||||||
\(911\) | −25.3571 | −0.840119 | −0.420060 | − | 0.907497i | \(-0.637991\pi\) | ||||
−0.420060 | + | 0.907497i | \(0.637991\pi\) | |||||||
\(912\) | −14.7029 | −0.486862 | ||||||||
\(913\) | 3.76371 | 0.124561 | ||||||||
\(914\) | −11.0592 | −0.365806 | ||||||||
\(915\) | 1.22153 | 0.0403825 | ||||||||
\(916\) | −32.5593 | −1.07579 | ||||||||
\(917\) | −64.2237 | −2.12085 | ||||||||
\(918\) | 10.6171 | 0.350416 | ||||||||
\(919\) | −14.1662 | −0.467299 | −0.233649 | − | 0.972321i | \(-0.575067\pi\) | ||||
−0.233649 | + | 0.972321i | \(0.575067\pi\) | |||||||
\(920\) | 4.68874 | 0.154583 | ||||||||
\(921\) | 3.62184 | 0.119344 | ||||||||
\(922\) | 4.57298 | 0.150603 | ||||||||
\(923\) | 43.4977 | 1.43174 | ||||||||
\(924\) | −8.21123 | −0.270130 | ||||||||
\(925\) | −5.06844 | −0.166649 | ||||||||
\(926\) | 1.43711 | 0.0472263 | ||||||||
\(927\) | −25.7652 | −0.846241 | ||||||||
\(928\) | 9.63689 | 0.316347 | ||||||||
\(929\) | 47.3845 | 1.55464 | 0.777318 | − | 0.629108i | \(-0.216580\pi\) | ||||
0.777318 | + | 0.629108i | \(0.216580\pi\) | |||||||
\(930\) | −3.44385 | −0.112928 | ||||||||
\(931\) | −50.8737 | −1.66732 | ||||||||
\(932\) | −36.1658 | −1.18465 | ||||||||
\(933\) | −27.8515 | −0.911818 | ||||||||
\(934\) | −8.44773 | −0.276418 | ||||||||
\(935\) | 4.54365 | 0.148593 | ||||||||
\(936\) | 8.73711 | 0.285581 | ||||||||
\(937\) | 28.4129 | 0.928209 | 0.464104 | − | 0.885781i | \(-0.346376\pi\) | ||||
0.464104 | + | 0.885781i | \(0.346376\pi\) | |||||||
\(938\) | −14.5203 | −0.474104 | ||||||||
\(939\) | −34.8193 | −1.13628 | ||||||||
\(940\) | 1.21218 | 0.0395369 | ||||||||
\(941\) | −2.83238 | −0.0923328 | −0.0461664 | − | 0.998934i | \(-0.514700\pi\) | ||||
−0.0461664 | + | 0.998934i | \(0.514700\pi\) | |||||||
\(942\) | 4.20102 | 0.136877 | ||||||||
\(943\) | 26.6139 | 0.866668 | ||||||||
\(944\) | −40.0671 | −1.30407 | ||||||||
\(945\) | −21.9955 | −0.715512 | ||||||||
\(946\) | −4.93826 | −0.160557 | ||||||||
\(947\) | 38.7106 | 1.25792 | 0.628962 | − | 0.777436i | \(-0.283480\pi\) | ||||
0.628962 | + | 0.777436i | \(0.283480\pi\) | |||||||
\(948\) | 7.57893 | 0.246152 | ||||||||
\(949\) | −2.82350 | −0.0916545 | ||||||||
\(950\) | 2.12892 | 0.0690712 | ||||||||
\(951\) | 19.9077 | 0.645550 | ||||||||
\(952\) | 32.4194 | 1.05072 | ||||||||
\(953\) | 30.4692 | 0.986994 | 0.493497 | − | 0.869747i | \(-0.335718\pi\) | ||||
0.493497 | + | 0.869747i | \(0.335718\pi\) | |||||||
\(954\) | 10.5822 | 0.342612 | ||||||||
\(955\) | 8.77712 | 0.284021 | ||||||||
\(956\) | −29.6432 | −0.958731 | ||||||||
\(957\) | −2.24135 | −0.0724527 | ||||||||
\(958\) | −1.00774 | −0.0325586 | ||||||||
\(959\) | −54.2600 | −1.75215 | ||||||||
\(960\) | −3.90885 | −0.126158 | ||||||||
\(961\) | 19.5301 | 0.630003 | ||||||||
\(962\) | −6.39104 | −0.206055 | ||||||||
\(963\) | −12.7420 | −0.410606 | ||||||||
\(964\) | −21.0224 | −0.677086 | ||||||||
\(965\) | −12.5672 | −0.404553 | ||||||||
\(966\) | −5.62614 | −0.181018 | ||||||||
\(967\) | 21.5064 | 0.691600 | 0.345800 | − | 0.938308i | \(-0.387608\pi\) | ||||
0.345800 | + | 0.938308i | \(0.387608\pi\) | |||||||
\(968\) | 1.69729 | 0.0545530 | ||||||||
\(969\) | −23.4971 | −0.754835 | ||||||||
\(970\) | −6.42132 | −0.206176 | ||||||||
\(971\) | −1.68790 | −0.0541673 | −0.0270837 | − | 0.999633i | \(-0.508622\pi\) | ||||
−0.0270837 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(972\) | −27.8594 | −0.893592 | ||||||||
\(973\) | −5.87562 | −0.188364 | ||||||||
\(974\) | −4.79334 | −0.153588 | ||||||||
\(975\) | −3.06299 | −0.0980943 | ||||||||
\(976\) | 3.20140 | 0.102474 | ||||||||
\(977\) | 8.68726 | 0.277930 | 0.138965 | − | 0.990297i | \(-0.455622\pi\) | ||||
0.138965 | + | 0.990297i | \(0.455622\pi\) | |||||||
\(978\) | −8.59828 | −0.274943 | ||||||||
\(979\) | 3.77803 | 0.120746 | ||||||||
\(980\) | −19.2155 | −0.613816 | ||||||||
\(981\) | 12.4114 | 0.396266 | ||||||||
\(982\) | 4.35890 | 0.139098 | ||||||||
\(983\) | 47.5368 | 1.51619 | 0.758095 | − | 0.652144i | \(-0.226130\pi\) | ||||
0.758095 | + | 0.652144i | \(0.226130\pi\) | |||||||
\(984\) | 17.7388 | 0.565494 | ||||||||
\(985\) | −4.61568 | −0.147068 | ||||||||
\(986\) | 4.19243 | 0.133514 | ||||||||
\(987\) | −3.07016 | −0.0977244 | ||||||||
\(988\) | −24.2350 | −0.771018 | ||||||||
\(989\) | 30.5466 | 0.971327 | ||||||||
\(990\) | 0.814205 | 0.0258771 | ||||||||
\(991\) | −19.6531 | −0.624301 | −0.312150 | − | 0.950033i | \(-0.601049\pi\) | ||||
−0.312150 | + | 0.950033i | \(0.601049\pi\) | |||||||
\(992\) | −33.1559 | −1.05270 | ||||||||
\(993\) | −1.02877 | −0.0326470 | ||||||||
\(994\) | 28.9222 | 0.917356 | ||||||||
\(995\) | 9.01902 | 0.285922 | ||||||||
\(996\) | −7.35160 | −0.232944 | ||||||||
\(997\) | −6.91185 | −0.218900 | −0.109450 | − | 0.993992i | \(-0.534909\pi\) | ||||
−0.109450 | + | 0.993992i | \(0.534909\pi\) | |||||||
\(998\) | 3.66132 | 0.115897 | ||||||||
\(999\) | 26.5195 | 0.839040 |
(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 | 4015.2.a.h.1.15 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.15 | ✓ | 37 | 1.1 | even | 1 | trivial |