Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.894762 | −0.516591 | −0.258296 | − | 0.966066i | \(-0.583161\pi\) | ||||
−0.258296 | + | 0.966066i | \(0.583161\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0669598 | −0.0299453 | −0.0149727 | − | 0.999888i | \(-0.504766\pi\) | ||||
−0.0149727 | + | 0.999888i | \(0.504766\pi\) | |||||||
\(6\) | −0.894762 | −0.365285 | ||||||||
\(7\) | 1.42997 | 0.540479 | 0.270239 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270239 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.19940 | −0.733134 | ||||||||
\(10\) | −0.0669598 | −0.0211745 | ||||||||
\(11\) | −3.23328 | −0.974872 | −0.487436 | − | 0.873159i | \(-0.662068\pi\) | ||||
−0.487436 | + | 0.873159i | \(0.662068\pi\) | |||||||
\(12\) | −0.894762 | −0.258296 | ||||||||
\(13\) | 4.17646 | 1.15834 | 0.579171 | − | 0.815206i | \(-0.303376\pi\) | ||||
0.579171 | + | 0.815206i | \(0.303376\pi\) | |||||||
\(14\) | 1.42997 | 0.382176 | ||||||||
\(15\) | 0.0599131 | 0.0154695 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.463825 | −0.112494 | −0.0562471 | − | 0.998417i | \(-0.517913\pi\) | ||||
−0.0562471 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(18\) | −2.19940 | −0.518404 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.0669598 | −0.0149727 | ||||||||
\(21\) | −1.27948 | −0.279206 | ||||||||
\(22\) | −3.23328 | −0.689338 | ||||||||
\(23\) | −2.96000 | −0.617203 | −0.308602 | − | 0.951191i | \(-0.599861\pi\) | ||||
−0.308602 | + | 0.951191i | \(0.599861\pi\) | |||||||
\(24\) | −0.894762 | −0.182643 | ||||||||
\(25\) | −4.99552 | −0.999103 | ||||||||
\(26\) | 4.17646 | 0.819071 | ||||||||
\(27\) | 4.65223 | 0.895321 | ||||||||
\(28\) | 1.42997 | 0.270239 | ||||||||
\(29\) | 5.89722 | 1.09509 | 0.547543 | − | 0.836778i | \(-0.315563\pi\) | ||||
0.547543 | + | 0.836778i | \(0.315563\pi\) | |||||||
\(30\) | 0.0599131 | 0.0109386 | ||||||||
\(31\) | −5.02580 | −0.902660 | −0.451330 | − | 0.892357i | \(-0.649050\pi\) | ||||
−0.451330 | + | 0.892357i | \(0.649050\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.89302 | 0.503610 | ||||||||
\(34\) | −0.463825 | −0.0795454 | ||||||||
\(35\) | −0.0957506 | −0.0161848 | ||||||||
\(36\) | −2.19940 | −0.366567 | ||||||||
\(37\) | −5.53876 | −0.910566 | −0.455283 | − | 0.890347i | \(-0.650462\pi\) | ||||
−0.455283 | + | 0.890347i | \(0.650462\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −3.73694 | −0.598389 | ||||||||
\(40\) | −0.0669598 | −0.0105873 | ||||||||
\(41\) | 3.26660 | 0.510157 | 0.255079 | − | 0.966920i | \(-0.417899\pi\) | ||||
0.255079 | + | 0.966920i | \(0.417899\pi\) | |||||||
\(42\) | −1.27948 | −0.197429 | ||||||||
\(43\) | 0.640662 | 0.0977000 | 0.0488500 | − | 0.998806i | \(-0.484444\pi\) | ||||
0.0488500 | + | 0.998806i | \(0.484444\pi\) | |||||||
\(44\) | −3.23328 | −0.487436 | ||||||||
\(45\) | 0.147271 | 0.0219539 | ||||||||
\(46\) | −2.96000 | −0.436428 | ||||||||
\(47\) | 0.940223 | 0.137146 | 0.0685728 | − | 0.997646i | \(-0.478155\pi\) | ||||
0.0685728 | + | 0.997646i | \(0.478155\pi\) | |||||||
\(48\) | −0.894762 | −0.129148 | ||||||||
\(49\) | −4.95518 | −0.707883 | ||||||||
\(50\) | −4.99552 | −0.706473 | ||||||||
\(51\) | 0.415013 | 0.0581135 | ||||||||
\(52\) | 4.17646 | 0.579171 | ||||||||
\(53\) | −11.0185 | −1.51351 | −0.756756 | − | 0.653698i | \(-0.773217\pi\) | ||||
−0.756756 | + | 0.653698i | \(0.773217\pi\) | |||||||
\(54\) | 4.65223 | 0.633088 | ||||||||
\(55\) | 0.216500 | 0.0291928 | ||||||||
\(56\) | 1.42997 | 0.191088 | ||||||||
\(57\) | −0.894762 | −0.118514 | ||||||||
\(58\) | 5.89722 | 0.774343 | ||||||||
\(59\) | 3.02758 | 0.394157 | 0.197079 | − | 0.980388i | \(-0.436855\pi\) | ||||
0.197079 | + | 0.980388i | \(0.436855\pi\) | |||||||
\(60\) | 0.0599131 | 0.00773474 | ||||||||
\(61\) | 11.8105 | 1.51218 | 0.756092 | − | 0.654465i | \(-0.227106\pi\) | ||||
0.756092 | + | 0.654465i | \(0.227106\pi\) | |||||||
\(62\) | −5.02580 | −0.638277 | ||||||||
\(63\) | −3.14508 | −0.396243 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.279655 | −0.0346869 | ||||||||
\(66\) | 2.89302 | 0.356106 | ||||||||
\(67\) | −7.46996 | −0.912601 | −0.456301 | − | 0.889826i | \(-0.650826\pi\) | ||||
−0.456301 | + | 0.889826i | \(0.650826\pi\) | |||||||
\(68\) | −0.463825 | −0.0562471 | ||||||||
\(69\) | 2.64850 | 0.318842 | ||||||||
\(70\) | −0.0957506 | −0.0114444 | ||||||||
\(71\) | −2.88742 | −0.342674 | −0.171337 | − | 0.985212i | \(-0.554809\pi\) | ||||
−0.171337 | + | 0.985212i | \(0.554809\pi\) | |||||||
\(72\) | −2.19940 | −0.259202 | ||||||||
\(73\) | −11.7213 | −1.37188 | −0.685938 | − | 0.727660i | \(-0.740608\pi\) | ||||
−0.685938 | + | 0.727660i | \(0.740608\pi\) | |||||||
\(74\) | −5.53876 | −0.643867 | ||||||||
\(75\) | 4.46980 | 0.516128 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −4.62350 | −0.526897 | ||||||||
\(78\) | −3.73694 | −0.423125 | ||||||||
\(79\) | 13.6699 | 1.53798 | 0.768990 | − | 0.639261i | \(-0.220760\pi\) | ||||
0.768990 | + | 0.639261i | \(0.220760\pi\) | |||||||
\(80\) | −0.0669598 | −0.00748633 | ||||||||
\(81\) | 2.43557 | 0.270618 | ||||||||
\(82\) | 3.26660 | 0.360736 | ||||||||
\(83\) | 1.25135 | 0.137354 | 0.0686768 | − | 0.997639i | \(-0.478122\pi\) | ||||
0.0686768 | + | 0.997639i | \(0.478122\pi\) | |||||||
\(84\) | −1.27948 | −0.139603 | ||||||||
\(85\) | 0.0310576 | 0.00336867 | ||||||||
\(86\) | 0.640662 | 0.0690844 | ||||||||
\(87\) | −5.27661 | −0.565712 | ||||||||
\(88\) | −3.23328 | −0.344669 | ||||||||
\(89\) | −3.46503 | −0.367292 | −0.183646 | − | 0.982992i | \(-0.558790\pi\) | ||||
−0.183646 | + | 0.982992i | \(0.558790\pi\) | |||||||
\(90\) | 0.147271 | 0.0155238 | ||||||||
\(91\) | 5.97222 | 0.626059 | ||||||||
\(92\) | −2.96000 | −0.308602 | ||||||||
\(93\) | 4.49690 | 0.466306 | ||||||||
\(94\) | 0.940223 | 0.0969766 | ||||||||
\(95\) | −0.0669598 | −0.00686993 | ||||||||
\(96\) | −0.894762 | −0.0913213 | ||||||||
\(97\) | −16.2444 | −1.64937 | −0.824684 | − | 0.565593i | \(-0.808647\pi\) | ||||
−0.824684 | + | 0.565593i | \(0.808647\pi\) | |||||||
\(98\) | −4.95518 | −0.500549 | ||||||||
\(99\) | 7.11129 | 0.714711 | ||||||||
\(100\) | −4.99552 | −0.499552 | ||||||||
\(101\) | 0.143986 | 0.0143271 | 0.00716355 | − | 0.999974i | \(-0.497720\pi\) | ||||
0.00716355 | + | 0.999974i | \(0.497720\pi\) | |||||||
\(102\) | 0.415013 | 0.0410924 | ||||||||
\(103\) | −17.1246 | −1.68734 | −0.843669 | − | 0.536864i | \(-0.819609\pi\) | ||||
−0.843669 | + | 0.536864i | \(0.819609\pi\) | |||||||
\(104\) | 4.17646 | 0.409536 | ||||||||
\(105\) | 0.0856740 | 0.00836092 | ||||||||
\(106\) | −11.0185 | −1.07021 | ||||||||
\(107\) | 3.36857 | 0.325652 | 0.162826 | − | 0.986655i | \(-0.447939\pi\) | ||||
0.162826 | + | 0.986655i | \(0.447939\pi\) | |||||||
\(108\) | 4.65223 | 0.447661 | ||||||||
\(109\) | 2.29513 | 0.219834 | 0.109917 | − | 0.993941i | \(-0.464941\pi\) | ||||
0.109917 | + | 0.993941i | \(0.464941\pi\) | |||||||
\(110\) | 0.216500 | 0.0206425 | ||||||||
\(111\) | 4.95587 | 0.470390 | ||||||||
\(112\) | 1.42997 | 0.135120 | ||||||||
\(113\) | 4.15323 | 0.390703 | 0.195352 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195352 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(114\) | −0.894762 | −0.0838021 | ||||||||
\(115\) | 0.198201 | 0.0184823 | ||||||||
\(116\) | 5.89722 | 0.547543 | ||||||||
\(117\) | −9.18571 | −0.849219 | ||||||||
\(118\) | 3.02758 | 0.278711 | ||||||||
\(119\) | −0.663257 | −0.0608007 | ||||||||
\(120\) | 0.0599131 | 0.00546929 | ||||||||
\(121\) | −0.545879 | −0.0496254 | ||||||||
\(122\) | 11.8105 | 1.06928 | ||||||||
\(123\) | −2.92283 | −0.263543 | ||||||||
\(124\) | −5.02580 | −0.451330 | ||||||||
\(125\) | 0.669297 | 0.0598638 | ||||||||
\(126\) | −3.14508 | −0.280186 | ||||||||
\(127\) | 5.73201 | 0.508634 | 0.254317 | − | 0.967121i | \(-0.418149\pi\) | ||||
0.254317 | + | 0.967121i | \(0.418149\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.573240 | −0.0504710 | ||||||||
\(130\) | −0.279655 | −0.0245274 | ||||||||
\(131\) | −21.0961 | −1.84318 | −0.921589 | − | 0.388167i | \(-0.873108\pi\) | ||||
−0.921589 | + | 0.388167i | \(0.873108\pi\) | |||||||
\(132\) | 2.89302 | 0.251805 | ||||||||
\(133\) | 1.42997 | 0.123994 | ||||||||
\(134\) | −7.46996 | −0.645306 | ||||||||
\(135\) | −0.311512 | −0.0268107 | ||||||||
\(136\) | −0.463825 | −0.0397727 | ||||||||
\(137\) | 10.7451 | 0.918019 | 0.459009 | − | 0.888431i | \(-0.348204\pi\) | ||||
0.459009 | + | 0.888431i | \(0.348204\pi\) | |||||||
\(138\) | 2.64850 | 0.225455 | ||||||||
\(139\) | −2.46250 | −0.208867 | −0.104433 | − | 0.994532i | \(-0.533303\pi\) | ||||
−0.104433 | + | 0.994532i | \(0.533303\pi\) | |||||||
\(140\) | −0.0957506 | −0.00809240 | ||||||||
\(141\) | −0.841276 | −0.0708482 | ||||||||
\(142\) | −2.88742 | −0.242307 | ||||||||
\(143\) | −13.5037 | −1.12923 | ||||||||
\(144\) | −2.19940 | −0.183283 | ||||||||
\(145\) | −0.394876 | −0.0327927 | ||||||||
\(146\) | −11.7213 | −0.970063 | ||||||||
\(147\) | 4.43371 | 0.365686 | ||||||||
\(148\) | −5.53876 | −0.455283 | ||||||||
\(149\) | 9.41318 | 0.771157 | 0.385579 | − | 0.922675i | \(-0.374002\pi\) | ||||
0.385579 | + | 0.922675i | \(0.374002\pi\) | |||||||
\(150\) | 4.46980 | 0.364958 | ||||||||
\(151\) | 10.1727 | 0.827839 | 0.413920 | − | 0.910313i | \(-0.364159\pi\) | ||||
0.413920 | + | 0.910313i | \(0.364159\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 1.02014 | 0.0824732 | ||||||||
\(154\) | −4.62350 | −0.372573 | ||||||||
\(155\) | 0.336526 | 0.0270304 | ||||||||
\(156\) | −3.73694 | −0.299195 | ||||||||
\(157\) | −17.5166 | −1.39797 | −0.698987 | − | 0.715135i | \(-0.746365\pi\) | ||||
−0.698987 | + | 0.715135i | \(0.746365\pi\) | |||||||
\(158\) | 13.6699 | 1.08752 | ||||||||
\(159\) | 9.85896 | 0.781867 | ||||||||
\(160\) | −0.0669598 | −0.00529363 | ||||||||
\(161\) | −4.23272 | −0.333585 | ||||||||
\(162\) | 2.43557 | 0.191356 | ||||||||
\(163\) | 4.95308 | 0.387955 | 0.193977 | − | 0.981006i | \(-0.437861\pi\) | ||||
0.193977 | + | 0.981006i | \(0.437861\pi\) | |||||||
\(164\) | 3.26660 | 0.255079 | ||||||||
\(165\) | −0.193716 | −0.0150808 | ||||||||
\(166\) | 1.25135 | 0.0971236 | ||||||||
\(167\) | −19.9309 | −1.54230 | −0.771151 | − | 0.636652i | \(-0.780319\pi\) | ||||
−0.771151 | + | 0.636652i | \(0.780319\pi\) | |||||||
\(168\) | −1.27948 | −0.0987144 | ||||||||
\(169\) | 4.44283 | 0.341756 | ||||||||
\(170\) | 0.0310576 | 0.00238201 | ||||||||
\(171\) | −2.19940 | −0.168192 | ||||||||
\(172\) | 0.640662 | 0.0488500 | ||||||||
\(173\) | −12.1777 | −0.925851 | −0.462926 | − | 0.886397i | \(-0.653200\pi\) | ||||
−0.462926 | + | 0.886397i | \(0.653200\pi\) | |||||||
\(174\) | −5.27661 | −0.400019 | ||||||||
\(175\) | −7.14345 | −0.539994 | ||||||||
\(176\) | −3.23328 | −0.243718 | ||||||||
\(177\) | −2.70896 | −0.203618 | ||||||||
\(178\) | −3.46503 | −0.259715 | ||||||||
\(179\) | −18.0969 | −1.35263 | −0.676314 | − | 0.736614i | \(-0.736424\pi\) | ||||
−0.676314 | + | 0.736614i | \(0.736424\pi\) | |||||||
\(180\) | 0.147271 | 0.0109770 | ||||||||
\(181\) | −8.35520 | −0.621037 | −0.310518 | − | 0.950567i | \(-0.600503\pi\) | ||||
−0.310518 | + | 0.950567i | \(0.600503\pi\) | |||||||
\(182\) | 5.97222 | 0.442691 | ||||||||
\(183\) | −10.5676 | −0.781181 | ||||||||
\(184\) | −2.96000 | −0.218214 | ||||||||
\(185\) | 0.370874 | 0.0272672 | ||||||||
\(186\) | 4.49690 | 0.329728 | ||||||||
\(187\) | 1.49968 | 0.109667 | ||||||||
\(188\) | 0.940223 | 0.0685728 | ||||||||
\(189\) | 6.65255 | 0.483902 | ||||||||
\(190\) | −0.0669598 | −0.00485777 | ||||||||
\(191\) | 3.42398 | 0.247750 | 0.123875 | − | 0.992298i | \(-0.460468\pi\) | ||||
0.123875 | + | 0.992298i | \(0.460468\pi\) | |||||||
\(192\) | −0.894762 | −0.0645739 | ||||||||
\(193\) | −23.2628 | −1.67449 | −0.837247 | − | 0.546824i | \(-0.815837\pi\) | ||||
−0.837247 | + | 0.546824i | \(0.815837\pi\) | |||||||
\(194\) | −16.2444 | −1.16628 | ||||||||
\(195\) | 0.250225 | 0.0179190 | ||||||||
\(196\) | −4.95518 | −0.353941 | ||||||||
\(197\) | 8.23004 | 0.586366 | 0.293183 | − | 0.956056i | \(-0.405285\pi\) | ||||
0.293183 | + | 0.956056i | \(0.405285\pi\) | |||||||
\(198\) | 7.11129 | 0.505377 | ||||||||
\(199\) | 13.7781 | 0.976704 | 0.488352 | − | 0.872647i | \(-0.337598\pi\) | ||||
0.488352 | + | 0.872647i | \(0.337598\pi\) | |||||||
\(200\) | −4.99552 | −0.353236 | ||||||||
\(201\) | 6.68384 | 0.471442 | ||||||||
\(202\) | 0.143986 | 0.0101308 | ||||||||
\(203\) | 8.43286 | 0.591871 | ||||||||
\(204\) | 0.415013 | 0.0290567 | ||||||||
\(205\) | −0.218731 | −0.0152768 | ||||||||
\(206\) | −17.1246 | −1.19313 | ||||||||
\(207\) | 6.51023 | 0.452492 | ||||||||
\(208\) | 4.17646 | 0.289585 | ||||||||
\(209\) | −3.23328 | −0.223651 | ||||||||
\(210\) | 0.0856740 | 0.00591207 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −11.0185 | −0.756756 | ||||||||
\(213\) | 2.58355 | 0.177022 | ||||||||
\(214\) | 3.36857 | 0.230271 | ||||||||
\(215\) | −0.0428986 | −0.00292566 | ||||||||
\(216\) | 4.65223 | 0.316544 | ||||||||
\(217\) | −7.18675 | −0.487869 | ||||||||
\(218\) | 2.29513 | 0.155446 | ||||||||
\(219\) | 10.4878 | 0.708699 | ||||||||
\(220\) | 0.216500 | 0.0145964 | ||||||||
\(221\) | −1.93715 | −0.130307 | ||||||||
\(222\) | 4.95587 | 0.332616 | ||||||||
\(223\) | 0.0330141 | 0.00221079 | 0.00110539 | − | 0.999999i | \(-0.499648\pi\) | ||||
0.00110539 | + | 0.999999i | \(0.499648\pi\) | |||||||
\(224\) | 1.42997 | 0.0955440 | ||||||||
\(225\) | 10.9871 | 0.732476 | ||||||||
\(226\) | 4.15323 | 0.276269 | ||||||||
\(227\) | 9.85789 | 0.654291 | 0.327146 | − | 0.944974i | \(-0.393913\pi\) | ||||
0.327146 | + | 0.944974i | \(0.393913\pi\) | |||||||
\(228\) | −0.894762 | −0.0592571 | ||||||||
\(229\) | −26.1817 | −1.73013 | −0.865066 | − | 0.501657i | \(-0.832724\pi\) | ||||
−0.865066 | + | 0.501657i | \(0.832724\pi\) | |||||||
\(230\) | 0.198201 | 0.0130690 | ||||||||
\(231\) | 4.13694 | 0.272190 | ||||||||
\(232\) | 5.89722 | 0.387171 | ||||||||
\(233\) | −18.5618 | −1.21602 | −0.608011 | − | 0.793929i | \(-0.708032\pi\) | ||||
−0.608011 | + | 0.793929i | \(0.708032\pi\) | |||||||
\(234\) | −9.18571 | −0.600489 | ||||||||
\(235\) | −0.0629571 | −0.00410687 | ||||||||
\(236\) | 3.02758 | 0.197079 | ||||||||
\(237\) | −12.2313 | −0.794507 | ||||||||
\(238\) | −0.663257 | −0.0429926 | ||||||||
\(239\) | 10.0354 | 0.649137 | 0.324568 | − | 0.945862i | \(-0.394781\pi\) | ||||
0.324568 | + | 0.945862i | \(0.394781\pi\) | |||||||
\(240\) | 0.0599131 | 0.00386737 | ||||||||
\(241\) | 9.53632 | 0.614289 | 0.307144 | − | 0.951663i | \(-0.400627\pi\) | ||||
0.307144 | + | 0.951663i | \(0.400627\pi\) | |||||||
\(242\) | −0.545879 | −0.0350904 | ||||||||
\(243\) | −16.1359 | −1.03512 | ||||||||
\(244\) | 11.8105 | 0.756092 | ||||||||
\(245\) | 0.331798 | 0.0211978 | ||||||||
\(246\) | −2.92283 | −0.186353 | ||||||||
\(247\) | 4.17646 | 0.265742 | ||||||||
\(248\) | −5.02580 | −0.319139 | ||||||||
\(249\) | −1.11966 | −0.0709556 | ||||||||
\(250\) | 0.669297 | 0.0423301 | ||||||||
\(251\) | 24.8990 | 1.57161 | 0.785807 | − | 0.618472i | \(-0.212248\pi\) | ||||
0.785807 | + | 0.618472i | \(0.212248\pi\) | |||||||
\(252\) | −3.14508 | −0.198121 | ||||||||
\(253\) | 9.57053 | 0.601694 | ||||||||
\(254\) | 5.73201 | 0.359658 | ||||||||
\(255\) | −0.0277892 | −0.00174023 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.12662 | 0.0702763 | 0.0351382 | − | 0.999382i | \(-0.488813\pi\) | ||||
0.0351382 | + | 0.999382i | \(0.488813\pi\) | |||||||
\(258\) | −0.573240 | −0.0356884 | ||||||||
\(259\) | −7.92027 | −0.492141 | ||||||||
\(260\) | −0.279655 | −0.0173435 | ||||||||
\(261\) | −12.9703 | −0.802844 | ||||||||
\(262\) | −21.0961 | −1.30332 | ||||||||
\(263\) | −1.34463 | −0.0829133 | −0.0414567 | − | 0.999140i | \(-0.513200\pi\) | ||||
−0.0414567 | + | 0.999140i | \(0.513200\pi\) | |||||||
\(264\) | 2.89302 | 0.178053 | ||||||||
\(265\) | 0.737798 | 0.0453226 | ||||||||
\(266\) | 1.42997 | 0.0876772 | ||||||||
\(267\) | 3.10037 | 0.189740 | ||||||||
\(268\) | −7.46996 | −0.456301 | ||||||||
\(269\) | −16.7280 | −1.01992 | −0.509961 | − | 0.860197i | \(-0.670340\pi\) | ||||
−0.509961 | + | 0.860197i | \(0.670340\pi\) | |||||||
\(270\) | −0.311512 | −0.0189580 | ||||||||
\(271\) | −17.8311 | −1.08316 | −0.541582 | − | 0.840648i | \(-0.682174\pi\) | ||||
−0.541582 | + | 0.840648i | \(0.682174\pi\) | |||||||
\(272\) | −0.463825 | −0.0281235 | ||||||||
\(273\) | −5.34372 | −0.323417 | ||||||||
\(274\) | 10.7451 | 0.649137 | ||||||||
\(275\) | 16.1519 | 0.973997 | ||||||||
\(276\) | 2.64850 | 0.159421 | ||||||||
\(277\) | −2.04524 | −0.122887 | −0.0614434 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614434 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(278\) | −2.46250 | −0.147691 | ||||||||
\(279\) | 11.0537 | 0.661771 | ||||||||
\(280\) | −0.0957506 | −0.00572219 | ||||||||
\(281\) | −9.57838 | −0.571398 | −0.285699 | − | 0.958319i | \(-0.592226\pi\) | ||||
−0.285699 | + | 0.958319i | \(0.592226\pi\) | |||||||
\(282\) | −0.841276 | −0.0500972 | ||||||||
\(283\) | 13.8347 | 0.822386 | 0.411193 | − | 0.911548i | \(-0.365112\pi\) | ||||
0.411193 | + | 0.911548i | \(0.365112\pi\) | |||||||
\(284\) | −2.88742 | −0.171337 | ||||||||
\(285\) | 0.0599131 | 0.00354894 | ||||||||
\(286\) | −13.5037 | −0.798490 | ||||||||
\(287\) | 4.67115 | 0.275729 | ||||||||
\(288\) | −2.19940 | −0.129601 | ||||||||
\(289\) | −16.7849 | −0.987345 | ||||||||
\(290\) | −0.394876 | −0.0231879 | ||||||||
\(291\) | 14.5349 | 0.852049 | ||||||||
\(292\) | −11.7213 | −0.685938 | ||||||||
\(293\) | 28.0241 | 1.63718 | 0.818592 | − | 0.574376i | \(-0.194755\pi\) | ||||
0.818592 | + | 0.574376i | \(0.194755\pi\) | |||||||
\(294\) | 4.43371 | 0.258579 | ||||||||
\(295\) | −0.202726 | −0.0118032 | ||||||||
\(296\) | −5.53876 | −0.321934 | ||||||||
\(297\) | −15.0420 | −0.872823 | ||||||||
\(298\) | 9.41318 | 0.545291 | ||||||||
\(299\) | −12.3623 | −0.714932 | ||||||||
\(300\) | 4.46980 | 0.258064 | ||||||||
\(301\) | 0.916129 | 0.0528048 | ||||||||
\(302\) | 10.1727 | 0.585371 | ||||||||
\(303\) | −0.128833 | −0.00740126 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −0.790831 | −0.0452828 | ||||||||
\(306\) | 1.02014 | 0.0583174 | ||||||||
\(307\) | −0.669660 | −0.0382195 | −0.0191098 | − | 0.999817i | \(-0.506083\pi\) | ||||
−0.0191098 | + | 0.999817i | \(0.506083\pi\) | |||||||
\(308\) | −4.62350 | −0.263449 | ||||||||
\(309\) | 15.3224 | 0.871664 | ||||||||
\(310\) | 0.336526 | 0.0191134 | ||||||||
\(311\) | −26.6499 | −1.51118 | −0.755589 | − | 0.655046i | \(-0.772649\pi\) | ||||
−0.755589 | + | 0.655046i | \(0.772649\pi\) | |||||||
\(312\) | −3.73694 | −0.211563 | ||||||||
\(313\) | 13.8057 | 0.780347 | 0.390173 | − | 0.920741i | \(-0.372415\pi\) | ||||
0.390173 | + | 0.920741i | \(0.372415\pi\) | |||||||
\(314\) | −17.5166 | −0.988517 | ||||||||
\(315\) | 0.210594 | 0.0118656 | ||||||||
\(316\) | 13.6699 | 0.768990 | ||||||||
\(317\) | −7.28445 | −0.409135 | −0.204568 | − | 0.978852i | \(-0.565579\pi\) | ||||
−0.204568 | + | 0.978852i | \(0.565579\pi\) | |||||||
\(318\) | 9.85896 | 0.552863 | ||||||||
\(319\) | −19.0674 | −1.06757 | ||||||||
\(320\) | −0.0669598 | −0.00374316 | ||||||||
\(321\) | −3.01407 | −0.168229 | ||||||||
\(322\) | −4.23272 | −0.235880 | ||||||||
\(323\) | −0.463825 | −0.0258079 | ||||||||
\(324\) | 2.43557 | 0.135309 | ||||||||
\(325\) | −20.8636 | −1.15730 | ||||||||
\(326\) | 4.95308 | 0.274325 | ||||||||
\(327\) | −2.05360 | −0.113564 | ||||||||
\(328\) | 3.26660 | 0.180368 | ||||||||
\(329\) | 1.34449 | 0.0741243 | ||||||||
\(330\) | −0.193716 | −0.0106637 | ||||||||
\(331\) | 20.6018 | 1.13238 | 0.566188 | − | 0.824276i | \(-0.308417\pi\) | ||||
0.566188 | + | 0.824276i | \(0.308417\pi\) | |||||||
\(332\) | 1.25135 | 0.0686768 | ||||||||
\(333\) | 12.1819 | 0.667566 | ||||||||
\(334\) | −19.9309 | −1.09057 | ||||||||
\(335\) | 0.500187 | 0.0273281 | ||||||||
\(336\) | −1.27948 | −0.0698016 | ||||||||
\(337\) | −2.81924 | −0.153574 | −0.0767869 | − | 0.997048i | \(-0.524466\pi\) | ||||
−0.0767869 | + | 0.997048i | \(0.524466\pi\) | |||||||
\(338\) | 4.44283 | 0.241658 | ||||||||
\(339\) | −3.71615 | −0.201834 | ||||||||
\(340\) | 0.0310576 | 0.00168434 | ||||||||
\(341\) | 16.2498 | 0.879978 | ||||||||
\(342\) | −2.19940 | −0.118930 | ||||||||
\(343\) | −17.0956 | −0.923074 | ||||||||
\(344\) | 0.640662 | 0.0345422 | ||||||||
\(345\) | −0.177343 | −0.00954781 | ||||||||
\(346\) | −12.1777 | −0.654676 | ||||||||
\(347\) | 27.5593 | 1.47946 | 0.739730 | − | 0.672904i | \(-0.234953\pi\) | ||||
0.739730 | + | 0.672904i | \(0.234953\pi\) | |||||||
\(348\) | −5.27661 | −0.282856 | ||||||||
\(349\) | 15.7773 | 0.844537 | 0.422269 | − | 0.906471i | \(-0.361234\pi\) | ||||
0.422269 | + | 0.906471i | \(0.361234\pi\) | |||||||
\(350\) | −7.14345 | −0.381833 | ||||||||
\(351\) | 19.4298 | 1.03709 | ||||||||
\(352\) | −3.23328 | −0.172335 | ||||||||
\(353\) | −21.9369 | −1.16758 | −0.583790 | − | 0.811904i | \(-0.698431\pi\) | ||||
−0.583790 | + | 0.811904i | \(0.698431\pi\) | |||||||
\(354\) | −2.70896 | −0.143980 | ||||||||
\(355\) | 0.193341 | 0.0102615 | ||||||||
\(356\) | −3.46503 | −0.183646 | ||||||||
\(357\) | 0.593457 | 0.0314091 | ||||||||
\(358\) | −18.0969 | −0.956452 | ||||||||
\(359\) | −22.8882 | −1.20799 | −0.603996 | − | 0.796987i | \(-0.706426\pi\) | ||||
−0.603996 | + | 0.796987i | \(0.706426\pi\) | |||||||
\(360\) | 0.147271 | 0.00776188 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −8.35520 | −0.439139 | ||||||||
\(363\) | 0.488432 | 0.0256360 | ||||||||
\(364\) | 5.97222 | 0.313030 | ||||||||
\(365\) | 0.784856 | 0.0410812 | ||||||||
\(366\) | −10.5676 | −0.552378 | ||||||||
\(367\) | −27.0452 | −1.41175 | −0.705874 | − | 0.708337i | \(-0.749446\pi\) | ||||
−0.705874 | + | 0.708337i | \(0.749446\pi\) | |||||||
\(368\) | −2.96000 | −0.154301 | ||||||||
\(369\) | −7.18456 | −0.374013 | ||||||||
\(370\) | 0.370874 | 0.0192808 | ||||||||
\(371\) | −15.7562 | −0.818020 | ||||||||
\(372\) | 4.49690 | 0.233153 | ||||||||
\(373\) | 14.7445 | 0.763443 | 0.381722 | − | 0.924277i | \(-0.375331\pi\) | ||||
0.381722 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(374\) | 1.49968 | 0.0775465 | ||||||||
\(375\) | −0.598862 | −0.0309251 | ||||||||
\(376\) | 0.940223 | 0.0484883 | ||||||||
\(377\) | 24.6295 | 1.26848 | ||||||||
\(378\) | 6.65255 | 0.342170 | ||||||||
\(379\) | −17.3322 | −0.890298 | −0.445149 | − | 0.895457i | \(-0.646849\pi\) | ||||
−0.445149 | + | 0.895457i | \(0.646849\pi\) | |||||||
\(380\) | −0.0669598 | −0.00343496 | ||||||||
\(381\) | −5.12878 | −0.262756 | ||||||||
\(382\) | 3.42398 | 0.175186 | ||||||||
\(383\) | −31.3055 | −1.59964 | −0.799818 | − | 0.600243i | \(-0.795071\pi\) | ||||
−0.799818 | + | 0.600243i | \(0.795071\pi\) | |||||||
\(384\) | −0.894762 | −0.0456606 | ||||||||
\(385\) | 0.309589 | 0.0157781 | ||||||||
\(386\) | −23.2628 | −1.18405 | ||||||||
\(387\) | −1.40907 | −0.0716272 | ||||||||
\(388\) | −16.2444 | −0.824684 | ||||||||
\(389\) | −19.1839 | −0.972663 | −0.486332 | − | 0.873774i | \(-0.661665\pi\) | ||||
−0.486332 | + | 0.873774i | \(0.661665\pi\) | |||||||
\(390\) | 0.250225 | 0.0126706 | ||||||||
\(391\) | 1.37292 | 0.0694317 | ||||||||
\(392\) | −4.95518 | −0.250274 | ||||||||
\(393\) | 18.8760 | 0.952169 | ||||||||
\(394\) | 8.23004 | 0.414624 | ||||||||
\(395\) | −0.915331 | −0.0460553 | ||||||||
\(396\) | 7.11129 | 0.357356 | ||||||||
\(397\) | 24.9671 | 1.25306 | 0.626531 | − | 0.779396i | \(-0.284474\pi\) | ||||
0.626531 | + | 0.779396i | \(0.284474\pi\) | |||||||
\(398\) | 13.7781 | 0.690634 | ||||||||
\(399\) | −1.27948 | −0.0640543 | ||||||||
\(400\) | −4.99552 | −0.249776 | ||||||||
\(401\) | 16.2670 | 0.812336 | 0.406168 | − | 0.913798i | \(-0.366865\pi\) | ||||
0.406168 | + | 0.913798i | \(0.366865\pi\) | |||||||
\(402\) | 6.68384 | 0.333360 | ||||||||
\(403\) | −20.9901 | −1.04559 | ||||||||
\(404\) | 0.143986 | 0.00716355 | ||||||||
\(405\) | −0.163085 | −0.00810376 | ||||||||
\(406\) | 8.43286 | 0.418516 | ||||||||
\(407\) | 17.9084 | 0.887685 | ||||||||
\(408\) | 0.415013 | 0.0205462 | ||||||||
\(409\) | −16.4952 | −0.815635 | −0.407817 | − | 0.913064i | \(-0.633710\pi\) | ||||
−0.407817 | + | 0.913064i | \(0.633710\pi\) | |||||||
\(410\) | −0.218731 | −0.0108023 | ||||||||
\(411\) | −9.61434 | −0.474240 | ||||||||
\(412\) | −17.1246 | −0.843669 | ||||||||
\(413\) | 4.32936 | 0.213034 | ||||||||
\(414\) | 6.51023 | 0.319960 | ||||||||
\(415\) | −0.0837901 | −0.00411310 | ||||||||
\(416\) | 4.17646 | 0.204768 | ||||||||
\(417\) | 2.20335 | 0.107899 | ||||||||
\(418\) | −3.23328 | −0.158145 | ||||||||
\(419\) | −18.5736 | −0.907380 | −0.453690 | − | 0.891159i | \(-0.649893\pi\) | ||||
−0.453690 | + | 0.891159i | \(0.649893\pi\) | |||||||
\(420\) | 0.0856740 | 0.00418046 | ||||||||
\(421\) | −27.7847 | −1.35414 | −0.677072 | − | 0.735917i | \(-0.736751\pi\) | ||||
−0.677072 | + | 0.735917i | \(0.736751\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −2.06793 | −0.100546 | ||||||||
\(424\) | −11.0185 | −0.535107 | ||||||||
\(425\) | 2.31705 | 0.112393 | ||||||||
\(426\) | 2.58355 | 0.125174 | ||||||||
\(427\) | 16.8887 | 0.817303 | ||||||||
\(428\) | 3.36857 | 0.162826 | ||||||||
\(429\) | 12.0826 | 0.583353 | ||||||||
\(430\) | −0.0428986 | −0.00206875 | ||||||||
\(431\) | −34.7106 | −1.67195 | −0.835977 | − | 0.548765i | \(-0.815098\pi\) | ||||
−0.835977 | + | 0.548765i | \(0.815098\pi\) | |||||||
\(432\) | 4.65223 | 0.223830 | ||||||||
\(433\) | −23.7888 | −1.14322 | −0.571609 | − | 0.820526i | \(-0.693681\pi\) | ||||
−0.571609 | + | 0.820526i | \(0.693681\pi\) | |||||||
\(434\) | −7.18675 | −0.344975 | ||||||||
\(435\) | 0.353320 | 0.0169404 | ||||||||
\(436\) | 2.29513 | 0.109917 | ||||||||
\(437\) | −2.96000 | −0.141596 | ||||||||
\(438\) | 10.4878 | 0.501126 | ||||||||
\(439\) | 36.8791 | 1.76014 | 0.880072 | − | 0.474840i | \(-0.157494\pi\) | ||||
0.880072 | + | 0.474840i | \(0.157494\pi\) | |||||||
\(440\) | 0.216500 | 0.0103212 | ||||||||
\(441\) | 10.8984 | 0.518973 | ||||||||
\(442\) | −1.93715 | −0.0921408 | ||||||||
\(443\) | 18.7710 | 0.891837 | 0.445918 | − | 0.895074i | \(-0.352877\pi\) | ||||
0.445918 | + | 0.895074i | \(0.352877\pi\) | |||||||
\(444\) | 4.95587 | 0.235195 | ||||||||
\(445\) | 0.232017 | 0.0109987 | ||||||||
\(446\) | 0.0330141 | 0.00156326 | ||||||||
\(447\) | −8.42255 | −0.398373 | ||||||||
\(448\) | 1.42997 | 0.0675598 | ||||||||
\(449\) | 7.66794 | 0.361873 | 0.180936 | − | 0.983495i | \(-0.442087\pi\) | ||||
0.180936 | + | 0.983495i | \(0.442087\pi\) | |||||||
\(450\) | 10.9871 | 0.517939 | ||||||||
\(451\) | −10.5618 | −0.497338 | ||||||||
\(452\) | 4.15323 | 0.195352 | ||||||||
\(453\) | −9.10211 | −0.427654 | ||||||||
\(454\) | 9.85789 | 0.462654 | ||||||||
\(455\) | −0.399899 | −0.0187475 | ||||||||
\(456\) | −0.894762 | −0.0419011 | ||||||||
\(457\) | −13.5028 | −0.631636 | −0.315818 | − | 0.948820i | \(-0.602279\pi\) | ||||
−0.315818 | + | 0.948820i | \(0.602279\pi\) | |||||||
\(458\) | −26.1817 | −1.22339 | ||||||||
\(459\) | −2.15782 | −0.100718 | ||||||||
\(460\) | 0.198201 | 0.00924117 | ||||||||
\(461\) | 11.3288 | 0.527634 | 0.263817 | − | 0.964573i | \(-0.415018\pi\) | ||||
0.263817 | + | 0.964573i | \(0.415018\pi\) | |||||||
\(462\) | 4.13694 | 0.192468 | ||||||||
\(463\) | −2.50054 | −0.116210 | −0.0581049 | − | 0.998310i | \(-0.518506\pi\) | ||||
−0.0581049 | + | 0.998310i | \(0.518506\pi\) | |||||||
\(464\) | 5.89722 | 0.273772 | ||||||||
\(465\) | −0.301111 | −0.0139637 | ||||||||
\(466\) | −18.5618 | −0.859857 | ||||||||
\(467\) | −9.47731 | −0.438557 | −0.219279 | − | 0.975662i | \(-0.570370\pi\) | ||||
−0.219279 | + | 0.975662i | \(0.570370\pi\) | |||||||
\(468\) | −9.18571 | −0.424610 | ||||||||
\(469\) | −10.6818 | −0.493241 | ||||||||
\(470\) | −0.0629571 | −0.00290399 | ||||||||
\(471\) | 15.6732 | 0.722181 | ||||||||
\(472\) | 3.02758 | 0.139356 | ||||||||
\(473\) | −2.07144 | −0.0952450 | ||||||||
\(474\) | −12.2313 | −0.561801 | ||||||||
\(475\) | −4.99552 | −0.229210 | ||||||||
\(476\) | −0.663257 | −0.0304003 | ||||||||
\(477\) | 24.2342 | 1.10961 | ||||||||
\(478\) | 10.0354 | 0.459009 | ||||||||
\(479\) | 25.1951 | 1.15119 | 0.575597 | − | 0.817734i | \(-0.304770\pi\) | ||||
0.575597 | + | 0.817734i | \(0.304770\pi\) | |||||||
\(480\) | 0.0599131 | 0.00273464 | ||||||||
\(481\) | −23.1324 | −1.05475 | ||||||||
\(482\) | 9.53632 | 0.434368 | ||||||||
\(483\) | 3.78728 | 0.172327 | ||||||||
\(484\) | −0.545879 | −0.0248127 | ||||||||
\(485\) | 1.08772 | 0.0493909 | ||||||||
\(486\) | −16.1359 | −0.731941 | ||||||||
\(487\) | −10.4758 | −0.474706 | −0.237353 | − | 0.971423i | \(-0.576280\pi\) | ||||
−0.237353 | + | 0.971423i | \(0.576280\pi\) | |||||||
\(488\) | 11.8105 | 0.534638 | ||||||||
\(489\) | −4.43182 | −0.200414 | ||||||||
\(490\) | 0.331798 | 0.0149891 | ||||||||
\(491\) | 39.2210 | 1.77002 | 0.885010 | − | 0.465572i | \(-0.154151\pi\) | ||||
0.885010 | + | 0.465572i | \(0.154151\pi\) | |||||||
\(492\) | −2.92283 | −0.131771 | ||||||||
\(493\) | −2.73528 | −0.123191 | ||||||||
\(494\) | 4.17646 | 0.187908 | ||||||||
\(495\) | −0.476170 | −0.0214022 | ||||||||
\(496\) | −5.02580 | −0.225665 | ||||||||
\(497\) | −4.12893 | −0.185208 | ||||||||
\(498\) | −1.11966 | −0.0501732 | ||||||||
\(499\) | −7.95532 | −0.356129 | −0.178065 | − | 0.984019i | \(-0.556984\pi\) | ||||
−0.178065 | + | 0.984019i | \(0.556984\pi\) | |||||||
\(500\) | 0.669297 | 0.0299319 | ||||||||
\(501\) | 17.8335 | 0.796740 | ||||||||
\(502\) | 24.8990 | 1.11130 | ||||||||
\(503\) | 34.2518 | 1.52721 | 0.763605 | − | 0.645683i | \(-0.223427\pi\) | ||||
0.763605 | + | 0.645683i | \(0.223427\pi\) | |||||||
\(504\) | −3.14508 | −0.140093 | ||||||||
\(505\) | −0.00964125 | −0.000429030 0 | ||||||||
\(506\) | 9.57053 | 0.425462 | ||||||||
\(507\) | −3.97528 | −0.176548 | ||||||||
\(508\) | 5.73201 | 0.254317 | ||||||||
\(509\) | 5.15090 | 0.228310 | 0.114155 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114155 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(510\) | −0.0277892 | −0.00123053 | ||||||||
\(511\) | −16.7611 | −0.741469 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.65223 | 0.205401 | ||||||||
\(514\) | 1.12662 | 0.0496929 | ||||||||
\(515\) | 1.14666 | 0.0505279 | ||||||||
\(516\) | −0.573240 | −0.0252355 | ||||||||
\(517\) | −3.04001 | −0.133699 | ||||||||
\(518\) | −7.92027 | −0.347996 | ||||||||
\(519\) | 10.8961 | 0.478287 | ||||||||
\(520\) | −0.279655 | −0.0122637 | ||||||||
\(521\) | −16.5531 | −0.725202 | −0.362601 | − | 0.931944i | \(-0.618111\pi\) | ||||
−0.362601 | + | 0.931944i | \(0.618111\pi\) | |||||||
\(522\) | −12.9703 | −0.567697 | ||||||||
\(523\) | −32.7917 | −1.43388 | −0.716939 | − | 0.697135i | \(-0.754458\pi\) | ||||
−0.716939 | + | 0.697135i | \(0.754458\pi\) | |||||||
\(524\) | −21.0961 | −0.921589 | ||||||||
\(525\) | 6.39169 | 0.278956 | ||||||||
\(526\) | −1.34463 | −0.0586286 | ||||||||
\(527\) | 2.33109 | 0.101544 | ||||||||
\(528\) | 2.89302 | 0.125903 | ||||||||
\(529\) | −14.2384 | −0.619060 | ||||||||
\(530\) | 0.737798 | 0.0320479 | ||||||||
\(531\) | −6.65886 | −0.288970 | ||||||||
\(532\) | 1.42997 | 0.0619971 | ||||||||
\(533\) | 13.6428 | 0.590937 | ||||||||
\(534\) | 3.10037 | 0.134166 | ||||||||
\(535\) | −0.225558 | −0.00975174 | ||||||||
\(536\) | −7.46996 | −0.322653 | ||||||||
\(537\) | 16.1924 | 0.698755 | ||||||||
\(538\) | −16.7280 | −0.721194 | ||||||||
\(539\) | 16.0215 | 0.690095 | ||||||||
\(540\) | −0.311512 | −0.0134053 | ||||||||
\(541\) | −30.1889 | −1.29792 | −0.648961 | − | 0.760822i | \(-0.724796\pi\) | ||||
−0.648961 | + | 0.760822i | \(0.724796\pi\) | |||||||
\(542\) | −17.8311 | −0.765912 | ||||||||
\(543\) | 7.47591 | 0.320822 | ||||||||
\(544\) | −0.463825 | −0.0198863 | ||||||||
\(545\) | −0.153682 | −0.00658300 | ||||||||
\(546\) | −5.34372 | −0.228690 | ||||||||
\(547\) | 10.2456 | 0.438068 | 0.219034 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219034 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(548\) | 10.7451 | 0.459009 | ||||||||
\(549\) | −25.9761 | −1.10863 | ||||||||
\(550\) | 16.1519 | 0.688720 | ||||||||
\(551\) | 5.89722 | 0.251230 | ||||||||
\(552\) | 2.64850 | 0.112728 | ||||||||
\(553\) | 19.5475 | 0.831245 | ||||||||
\(554\) | −2.04524 | −0.0868940 | ||||||||
\(555\) | −0.331844 | −0.0140860 | ||||||||
\(556\) | −2.46250 | −0.104433 | ||||||||
\(557\) | 34.9497 | 1.48087 | 0.740433 | − | 0.672130i | \(-0.234620\pi\) | ||||
0.740433 | + | 0.672130i | \(0.234620\pi\) | |||||||
\(558\) | 11.0537 | 0.467943 | ||||||||
\(559\) | 2.67570 | 0.113170 | ||||||||
\(560\) | −0.0957506 | −0.00404620 | ||||||||
\(561\) | −1.34186 | −0.0566532 | ||||||||
\(562\) | −9.57838 | −0.404039 | ||||||||
\(563\) | 34.9170 | 1.47157 | 0.735787 | − | 0.677213i | \(-0.236812\pi\) | ||||
0.735787 | + | 0.677213i | \(0.236812\pi\) | |||||||
\(564\) | −0.841276 | −0.0354241 | ||||||||
\(565\) | −0.278099 | −0.0116997 | ||||||||
\(566\) | 13.8347 | 0.581515 | ||||||||
\(567\) | 3.48279 | 0.146263 | ||||||||
\(568\) | −2.88742 | −0.121153 | ||||||||
\(569\) | 33.2616 | 1.39440 | 0.697199 | − | 0.716878i | \(-0.254429\pi\) | ||||
0.697199 | + | 0.716878i | \(0.254429\pi\) | |||||||
\(570\) | 0.0599131 | 0.00250948 | ||||||||
\(571\) | −32.2694 | −1.35043 | −0.675217 | − | 0.737619i | \(-0.735950\pi\) | ||||
−0.675217 | + | 0.737619i | \(0.735950\pi\) | |||||||
\(572\) | −13.5037 | −0.564617 | ||||||||
\(573\) | −3.06365 | −0.127986 | ||||||||
\(574\) | 4.67115 | 0.194970 | ||||||||
\(575\) | 14.7867 | 0.616650 | ||||||||
\(576\) | −2.19940 | −0.0916417 | ||||||||
\(577\) | −24.6167 | −1.02481 | −0.512403 | − | 0.858745i | \(-0.671245\pi\) | ||||
−0.512403 | + | 0.858745i | \(0.671245\pi\) | |||||||
\(578\) | −16.7849 | −0.698158 | ||||||||
\(579\) | 20.8147 | 0.865029 | ||||||||
\(580\) | −0.394876 | −0.0163963 | ||||||||
\(581\) | 1.78940 | 0.0742367 | ||||||||
\(582\) | 14.5349 | 0.602490 | ||||||||
\(583\) | 35.6260 | 1.47548 | ||||||||
\(584\) | −11.7213 | −0.485031 | ||||||||
\(585\) | 0.615073 | 0.0254301 | ||||||||
\(586\) | 28.0241 | 1.15766 | ||||||||
\(587\) | 32.2113 | 1.32950 | 0.664752 | − | 0.747064i | \(-0.268537\pi\) | ||||
0.664752 | + | 0.747064i | \(0.268537\pi\) | |||||||
\(588\) | 4.43371 | 0.182843 | ||||||||
\(589\) | −5.02580 | −0.207085 | ||||||||
\(590\) | −0.202726 | −0.00834610 | ||||||||
\(591\) | −7.36393 | −0.302912 | ||||||||
\(592\) | −5.53876 | −0.227641 | ||||||||
\(593\) | 32.0403 | 1.31574 | 0.657869 | − | 0.753132i | \(-0.271458\pi\) | ||||
0.657869 | + | 0.753132i | \(0.271458\pi\) | |||||||
\(594\) | −15.0420 | −0.617179 | ||||||||
\(595\) | 0.0444115 | 0.00182070 | ||||||||
\(596\) | 9.41318 | 0.385579 | ||||||||
\(597\) | −12.3281 | −0.504557 | ||||||||
\(598\) | −12.3623 | −0.505533 | ||||||||
\(599\) | 19.9390 | 0.814687 | 0.407343 | − | 0.913275i | \(-0.366455\pi\) | ||||
0.407343 | + | 0.913275i | \(0.366455\pi\) | |||||||
\(600\) | 4.46980 | 0.182479 | ||||||||
\(601\) | −8.82658 | −0.360044 | −0.180022 | − | 0.983663i | \(-0.557617\pi\) | ||||
−0.180022 | + | 0.983663i | \(0.557617\pi\) | |||||||
\(602\) | 0.916129 | 0.0373386 | ||||||||
\(603\) | 16.4294 | 0.669059 | ||||||||
\(604\) | 10.1727 | 0.413920 | ||||||||
\(605\) | 0.0365519 | 0.00148605 | ||||||||
\(606\) | −0.128833 | −0.00523348 | ||||||||
\(607\) | −6.03639 | −0.245009 | −0.122505 | − | 0.992468i | \(-0.539093\pi\) | ||||
−0.122505 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −7.54540 | −0.305755 | ||||||||
\(610\) | −0.790831 | −0.0320198 | ||||||||
\(611\) | 3.92680 | 0.158862 | ||||||||
\(612\) | 1.02014 | 0.0412366 | ||||||||
\(613\) | 15.5906 | 0.629699 | 0.314850 | − | 0.949142i | \(-0.398046\pi\) | ||||
0.314850 | + | 0.949142i | \(0.398046\pi\) | |||||||
\(614\) | −0.669660 | −0.0270253 | ||||||||
\(615\) | 0.195712 | 0.00789187 | ||||||||
\(616\) | −4.62350 | −0.186286 | ||||||||
\(617\) | −9.28165 | −0.373665 | −0.186833 | − | 0.982392i | \(-0.559822\pi\) | ||||
−0.186833 | + | 0.982392i | \(0.559822\pi\) | |||||||
\(618\) | 15.3224 | 0.616359 | ||||||||
\(619\) | 5.34460 | 0.214817 | 0.107409 | − | 0.994215i | \(-0.465745\pi\) | ||||
0.107409 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(620\) | 0.336526 | 0.0135152 | ||||||||
\(621\) | −13.7706 | −0.552595 | ||||||||
\(622\) | −26.6499 | −1.06856 | ||||||||
\(623\) | −4.95489 | −0.198514 | ||||||||
\(624\) | −3.73694 | −0.149597 | ||||||||
\(625\) | 24.9328 | 0.997311 | ||||||||
\(626\) | 13.8057 | 0.551788 | ||||||||
\(627\) | 2.89302 | 0.115536 | ||||||||
\(628\) | −17.5166 | −0.698987 | ||||||||
\(629\) | 2.56902 | 0.102433 | ||||||||
\(630\) | 0.210594 | 0.00839026 | ||||||||
\(631\) | −21.5798 | −0.859079 | −0.429540 | − | 0.903048i | \(-0.641324\pi\) | ||||
−0.429540 | + | 0.903048i | \(0.641324\pi\) | |||||||
\(632\) | 13.6699 | 0.543758 | ||||||||
\(633\) | 0.894762 | 0.0355636 | ||||||||
\(634\) | −7.28445 | −0.289302 | ||||||||
\(635\) | −0.383814 | −0.0152312 | ||||||||
\(636\) | 9.85896 | 0.390933 | ||||||||
\(637\) | −20.6951 | −0.819971 | ||||||||
\(638\) | −19.0674 | −0.754885 | ||||||||
\(639\) | 6.35060 | 0.251226 | ||||||||
\(640\) | −0.0669598 | −0.00264682 | ||||||||
\(641\) | 24.7578 | 0.977874 | 0.488937 | − | 0.872319i | \(-0.337385\pi\) | ||||
0.488937 | + | 0.872319i | \(0.337385\pi\) | |||||||
\(642\) | −3.01407 | −0.118956 | ||||||||
\(643\) | 1.69702 | 0.0669241 | 0.0334621 | − | 0.999440i | \(-0.489347\pi\) | ||||
0.0334621 | + | 0.999440i | \(0.489347\pi\) | |||||||
\(644\) | −4.23272 | −0.166793 | ||||||||
\(645\) | 0.0383840 | 0.00151137 | ||||||||
\(646\) | −0.463825 | −0.0182490 | ||||||||
\(647\) | 15.4827 | 0.608686 | 0.304343 | − | 0.952562i | \(-0.401563\pi\) | ||||
0.304343 | + | 0.952562i | \(0.401563\pi\) | |||||||
\(648\) | 2.43557 | 0.0956781 | ||||||||
\(649\) | −9.78903 | −0.384253 | ||||||||
\(650\) | −20.8636 | −0.818337 | ||||||||
\(651\) | 6.43043 | 0.252029 | ||||||||
\(652\) | 4.95308 | 0.193977 | ||||||||
\(653\) | 3.27690 | 0.128235 | 0.0641175 | − | 0.997942i | \(-0.479577\pi\) | ||||
0.0641175 | + | 0.997942i | \(0.479577\pi\) | |||||||
\(654\) | −2.05360 | −0.0803021 | ||||||||
\(655\) | 1.41259 | 0.0551945 | ||||||||
\(656\) | 3.26660 | 0.127539 | ||||||||
\(657\) | 25.7799 | 1.00577 | ||||||||
\(658\) | 1.34449 | 0.0524138 | ||||||||
\(659\) | −10.5496 | −0.410954 | −0.205477 | − | 0.978662i | \(-0.565875\pi\) | ||||
−0.205477 | + | 0.978662i | \(0.565875\pi\) | |||||||
\(660\) | −0.193716 | −0.00754038 | ||||||||
\(661\) | −26.4876 | −1.03025 | −0.515125 | − | 0.857115i | \(-0.672255\pi\) | ||||
−0.515125 | + | 0.857115i | \(0.672255\pi\) | |||||||
\(662\) | 20.6018 | 0.800711 | ||||||||
\(663\) | 1.73329 | 0.0673153 | ||||||||
\(664\) | 1.25135 | 0.0485618 | ||||||||
\(665\) | −0.0957506 | −0.00371305 | ||||||||
\(666\) | 12.1819 | 0.472041 | ||||||||
\(667\) | −17.4558 | −0.675890 | ||||||||
\(668\) | −19.9309 | −0.771151 | ||||||||
\(669\) | −0.0295398 | −0.00114207 | ||||||||
\(670\) | 0.500187 | 0.0193239 | ||||||||
\(671\) | −38.1868 | −1.47419 | ||||||||
\(672\) | −1.27948 | −0.0493572 | ||||||||
\(673\) | −4.62534 | −0.178294 | −0.0891468 | − | 0.996018i | \(-0.528414\pi\) | ||||
−0.0891468 | + | 0.996018i | \(0.528414\pi\) | |||||||
\(674\) | −2.81924 | −0.108593 | ||||||||
\(675\) | −23.2403 | −0.894519 | ||||||||
\(676\) | 4.44283 | 0.170878 | ||||||||
\(677\) | 26.1516 | 1.00509 | 0.502543 | − | 0.864552i | \(-0.332398\pi\) | ||||
0.502543 | + | 0.864552i | \(0.332398\pi\) | |||||||
\(678\) | −3.71615 | −0.142718 | ||||||||
\(679\) | −23.2290 | −0.891448 | ||||||||
\(680\) | 0.0310576 | 0.00119101 | ||||||||
\(681\) | −8.82047 | −0.338001 | ||||||||
\(682\) | 16.2498 | 0.622238 | ||||||||
\(683\) | −30.8227 | −1.17940 | −0.589699 | − | 0.807623i | \(-0.700754\pi\) | ||||
−0.589699 | + | 0.807623i | \(0.700754\pi\) | |||||||
\(684\) | −2.19940 | −0.0840962 | ||||||||
\(685\) | −0.719492 | −0.0274904 | ||||||||
\(686\) | −17.0956 | −0.652712 | ||||||||
\(687\) | 23.4264 | 0.893771 | ||||||||
\(688\) | 0.640662 | 0.0244250 | ||||||||
\(689\) | −46.0185 | −1.75316 | ||||||||
\(690\) | −0.177343 | −0.00675132 | ||||||||
\(691\) | 11.0033 | 0.418586 | 0.209293 | − | 0.977853i | \(-0.432884\pi\) | ||||
0.209293 | + | 0.977853i | \(0.432884\pi\) | |||||||
\(692\) | −12.1777 | −0.462926 | ||||||||
\(693\) | 10.1689 | 0.386286 | ||||||||
\(694\) | 27.5593 | 1.04614 | ||||||||
\(695\) | 0.164888 | 0.00625458 | ||||||||
\(696\) | −5.27661 | −0.200009 | ||||||||
\(697\) | −1.51513 | −0.0573897 | ||||||||
\(698\) | 15.7773 | 0.597178 | ||||||||
\(699\) | 16.6084 | 0.628186 | ||||||||
\(700\) | −7.14345 | −0.269997 | ||||||||
\(701\) | −32.5727 | −1.23025 | −0.615126 | − | 0.788429i | \(-0.710895\pi\) | ||||
−0.615126 | + | 0.788429i | \(0.710895\pi\) | |||||||
\(702\) | 19.4298 | 0.733332 | ||||||||
\(703\) | −5.53876 | −0.208898 | ||||||||
\(704\) | −3.23328 | −0.121859 | ||||||||
\(705\) | 0.0563316 | 0.00212157 | ||||||||
\(706\) | −21.9369 | −0.825604 | ||||||||
\(707\) | 0.205895 | 0.00774350 | ||||||||
\(708\) | −2.70896 | −0.101809 | ||||||||
\(709\) | −10.8216 | −0.406415 | −0.203208 | − | 0.979136i | \(-0.565137\pi\) | ||||
−0.203208 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(710\) | 0.193341 | 0.00725596 | ||||||||
\(711\) | −30.0655 | −1.12754 | ||||||||
\(712\) | −3.46503 | −0.129857 | ||||||||
\(713\) | 14.8764 | 0.557125 | ||||||||
\(714\) | 0.593457 | 0.0222096 | ||||||||
\(715\) | 0.904203 | 0.0338153 | ||||||||
\(716\) | −18.0969 | −0.676314 | ||||||||
\(717\) | −8.97931 | −0.335338 | ||||||||
\(718\) | −22.8882 | −0.854180 | ||||||||
\(719\) | 12.0564 | 0.449626 | 0.224813 | − | 0.974402i | \(-0.427823\pi\) | ||||
0.224813 | + | 0.974402i | \(0.427823\pi\) | |||||||
\(720\) | 0.147271 | 0.00548848 | ||||||||
\(721\) | −24.4877 | −0.911970 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −8.53274 | −0.317336 | ||||||||
\(724\) | −8.35520 | −0.310518 | ||||||||
\(725\) | −29.4597 | −1.09410 | ||||||||
\(726\) | 0.488432 | 0.0181274 | ||||||||
\(727\) | 6.97553 | 0.258708 | 0.129354 | − | 0.991598i | \(-0.458710\pi\) | ||||
0.129354 | + | 0.991598i | \(0.458710\pi\) | |||||||
\(728\) | 5.97222 | 0.221345 | ||||||||
\(729\) | 7.13112 | 0.264116 | ||||||||
\(730\) | 0.784856 | 0.0290488 | ||||||||
\(731\) | −0.297155 | −0.0109907 | ||||||||
\(732\) | −10.5676 | −0.390591 | ||||||||
\(733\) | −23.8008 | −0.879102 | −0.439551 | − | 0.898218i | \(-0.644862\pi\) | ||||
−0.439551 | + | 0.898218i | \(0.644862\pi\) | |||||||
\(734\) | −27.0452 | −0.998256 | ||||||||
\(735\) | −0.296880 | −0.0109506 | ||||||||
\(736\) | −2.96000 | −0.109107 | ||||||||
\(737\) | 24.1525 | 0.889669 | ||||||||
\(738\) | −7.18456 | −0.264467 | ||||||||
\(739\) | 14.6454 | 0.538741 | 0.269371 | − | 0.963037i | \(-0.413184\pi\) | ||||
0.269371 | + | 0.963037i | \(0.413184\pi\) | |||||||
\(740\) | 0.370874 | 0.0136336 | ||||||||
\(741\) | −3.73694 | −0.137280 | ||||||||
\(742\) | −15.7562 | −0.578428 | ||||||||
\(743\) | −12.5843 | −0.461672 | −0.230836 | − | 0.972993i | \(-0.574146\pi\) | ||||
−0.230836 | + | 0.972993i | \(0.574146\pi\) | |||||||
\(744\) | 4.49690 | 0.164864 | ||||||||
\(745\) | −0.630304 | −0.0230925 | ||||||||
\(746\) | 14.7445 | 0.539836 | ||||||||
\(747\) | −2.75222 | −0.100699 | ||||||||
\(748\) | 1.49968 | 0.0548337 | ||||||||
\(749\) | 4.81696 | 0.176008 | ||||||||
\(750\) | −0.598862 | −0.0218673 | ||||||||
\(751\) | −8.54675 | −0.311875 | −0.155938 | − | 0.987767i | \(-0.549840\pi\) | ||||
−0.155938 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(752\) | 0.940223 | 0.0342864 | ||||||||
\(753\) | −22.2787 | −0.811882 | ||||||||
\(754\) | 24.6295 | 0.896954 | ||||||||
\(755\) | −0.681159 | −0.0247899 | ||||||||
\(756\) | 6.65255 | 0.241951 | ||||||||
\(757\) | 1.53898 | 0.0559351 | 0.0279675 | − | 0.999609i | \(-0.491096\pi\) | ||||
0.0279675 | + | 0.999609i | \(0.491096\pi\) | |||||||
\(758\) | −17.3322 | −0.629535 | ||||||||
\(759\) | −8.56334 | −0.310830 | ||||||||
\(760\) | −0.0669598 | −0.00242889 | ||||||||
\(761\) | 5.68064 | 0.205923 | 0.102961 | − | 0.994685i | \(-0.467168\pi\) | ||||
0.102961 | + | 0.994685i | \(0.467168\pi\) | |||||||
\(762\) | −5.12878 | −0.185796 | ||||||||
\(763\) | 3.28198 | 0.118816 | ||||||||
\(764\) | 3.42398 | 0.123875 | ||||||||
\(765\) | −0.0683082 | −0.00246969 | ||||||||
\(766\) | −31.3055 | −1.13111 | ||||||||
\(767\) | 12.6446 | 0.456569 | ||||||||
\(768\) | −0.894762 | −0.0322869 | ||||||||
\(769\) | −25.4526 | −0.917843 | −0.458922 | − | 0.888477i | \(-0.651764\pi\) | ||||
−0.458922 | + | 0.888477i | \(0.651764\pi\) | |||||||
\(770\) | 0.309589 | 0.0111568 | ||||||||
\(771\) | −1.00805 | −0.0363041 | ||||||||
\(772\) | −23.2628 | −0.837247 | ||||||||
\(773\) | −1.87884 | −0.0675772 | −0.0337886 | − | 0.999429i | \(-0.510757\pi\) | ||||
−0.0337886 | + | 0.999429i | \(0.510757\pi\) | |||||||
\(774\) | −1.40907 | −0.0506481 | ||||||||
\(775\) | 25.1065 | 0.901851 | ||||||||
\(776\) | −16.2444 | −0.583140 | ||||||||
\(777\) | 7.08675 | 0.254236 | ||||||||
\(778\) | −19.1839 | −0.687777 | ||||||||
\(779\) | 3.26660 | 0.117038 | ||||||||
\(780\) | 0.250225 | 0.00895948 | ||||||||
\(781\) | 9.33585 | 0.334063 | ||||||||
\(782\) | 1.37292 | 0.0490957 | ||||||||
\(783\) | 27.4352 | 0.980454 | ||||||||
\(784\) | −4.95518 | −0.176971 | ||||||||
\(785\) | 1.17290 | 0.0418628 | ||||||||
\(786\) | 18.8760 | 0.673285 | ||||||||
\(787\) | −22.6411 | −0.807068 | −0.403534 | − | 0.914965i | \(-0.632218\pi\) | ||||
−0.403534 | + | 0.914965i | \(0.632218\pi\) | |||||||
\(788\) | 8.23004 | 0.293183 | ||||||||
\(789\) | 1.20312 | 0.0428323 | ||||||||
\(790\) | −0.915331 | −0.0325660 | ||||||||
\(791\) | 5.93900 | 0.211167 | ||||||||
\(792\) | 7.11129 | 0.252689 | ||||||||
\(793\) | 49.3263 | 1.75163 | ||||||||
\(794\) | 24.9671 | 0.886049 | ||||||||
\(795\) | −0.660154 | −0.0234132 | ||||||||
\(796\) | 13.7781 | 0.488352 | ||||||||
\(797\) | −49.2885 | −1.74589 | −0.872945 | − | 0.487819i | \(-0.837793\pi\) | ||||
−0.872945 | + | 0.487819i | \(0.837793\pi\) | |||||||
\(798\) | −1.27948 | −0.0452933 | ||||||||
\(799\) | −0.436099 | −0.0154281 | ||||||||
\(800\) | −4.99552 | −0.176618 | ||||||||
\(801\) | 7.62098 | 0.269274 | ||||||||
\(802\) | 16.2670 | 0.574408 | ||||||||
\(803\) | 37.8983 | 1.33740 | ||||||||
\(804\) | 6.68384 | 0.235721 | ||||||||
\(805\) | 0.283422 | 0.00998931 | ||||||||
\(806\) | −20.9901 | −0.739343 | ||||||||
\(807\) | 14.9676 | 0.526883 | ||||||||
\(808\) | 0.143986 | 0.00506540 | ||||||||
\(809\) | 46.0017 | 1.61733 | 0.808667 | − | 0.588267i | \(-0.200189\pi\) | ||||
0.808667 | + | 0.588267i | \(0.200189\pi\) | |||||||
\(810\) | −0.163085 | −0.00573022 | ||||||||
\(811\) | −10.0420 | −0.352624 | −0.176312 | − | 0.984334i | \(-0.556417\pi\) | ||||
−0.176312 | + | 0.984334i | \(0.556417\pi\) | |||||||
\(812\) | 8.43286 | 0.295935 | ||||||||
\(813\) | 15.9546 | 0.559552 | ||||||||
\(814\) | 17.9084 | 0.627688 | ||||||||
\(815\) | −0.331657 | −0.0116174 | ||||||||
\(816\) | 0.415013 | 0.0145284 | ||||||||
\(817\) | 0.640662 | 0.0224139 | ||||||||
\(818\) | −16.4952 | −0.576741 | ||||||||
\(819\) | −13.1353 | −0.458985 | ||||||||
\(820\) | −0.218731 | −0.00763841 | ||||||||
\(821\) | −18.0128 | −0.628650 | −0.314325 | − | 0.949315i | \(-0.601778\pi\) | ||||
−0.314325 | + | 0.949315i | \(0.601778\pi\) | |||||||
\(822\) | −9.61434 | −0.335339 | ||||||||
\(823\) | 9.25191 | 0.322501 | 0.161251 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161251 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(824\) | −17.1246 | −0.596564 | ||||||||
\(825\) | −14.4521 | −0.503158 | ||||||||
\(826\) | 4.32936 | 0.150638 | ||||||||
\(827\) | 29.7423 | 1.03424 | 0.517121 | − | 0.855913i | \(-0.327004\pi\) | ||||
0.517121 | + | 0.855913i | \(0.327004\pi\) | |||||||
\(828\) | 6.51023 | 0.226246 | ||||||||
\(829\) | −7.63241 | −0.265085 | −0.132542 | − | 0.991177i | \(-0.542314\pi\) | ||||
−0.132542 | + | 0.991177i | \(0.542314\pi\) | |||||||
\(830\) | −0.0837901 | −0.00290840 | ||||||||
\(831\) | 1.83001 | 0.0634822 | ||||||||
\(832\) | 4.17646 | 0.144793 | ||||||||
\(833\) | 2.29834 | 0.0796327 | ||||||||
\(834\) | 2.20335 | 0.0762959 | ||||||||
\(835\) | 1.33457 | 0.0461847 | ||||||||
\(836\) | −3.23328 | −0.111825 | ||||||||
\(837\) | −23.3812 | −0.808171 | ||||||||
\(838\) | −18.5736 | −0.641615 | ||||||||
\(839\) | 21.6760 | 0.748337 | 0.374169 | − | 0.927361i | \(-0.377928\pi\) | ||||
0.374169 | + | 0.927361i | \(0.377928\pi\) | |||||||
\(840\) | 0.0856740 | 0.00295603 | ||||||||
\(841\) | 5.77719 | 0.199213 | ||||||||
\(842\) | −27.7847 | −0.957524 | ||||||||
\(843\) | 8.57037 | 0.295179 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −0.297491 | −0.0102340 | ||||||||
\(846\) | −2.06793 | −0.0710968 | ||||||||
\(847\) | −0.780591 | −0.0268214 | ||||||||
\(848\) | −11.0185 | −0.378378 | ||||||||
\(849\) | −12.3787 | −0.424837 | ||||||||
\(850\) | 2.31705 | 0.0794740 | ||||||||
\(851\) | 16.3947 | 0.562004 | ||||||||
\(852\) | 2.58355 | 0.0885111 | ||||||||
\(853\) | 44.7515 | 1.53226 | 0.766132 | − | 0.642683i | \(-0.222179\pi\) | ||||
0.766132 | + | 0.642683i | \(0.222179\pi\) | |||||||
\(854\) | 16.8887 | 0.577921 | ||||||||
\(855\) | 0.147271 | 0.00503657 | ||||||||
\(856\) | 3.36857 | 0.115135 | ||||||||
\(857\) | −10.1111 | −0.345390 | −0.172695 | − | 0.984975i | \(-0.555247\pi\) | ||||
−0.172695 | + | 0.984975i | \(0.555247\pi\) | |||||||
\(858\) | 12.0826 | 0.412493 | ||||||||
\(859\) | 49.2301 | 1.67971 | 0.839854 | − | 0.542812i | \(-0.182640\pi\) | ||||
0.839854 | + | 0.542812i | \(0.182640\pi\) | |||||||
\(860\) | −0.0428986 | −0.00146283 | ||||||||
\(861\) | −4.17956 | −0.142439 | ||||||||
\(862\) | −34.7106 | −1.18225 | ||||||||
\(863\) | −14.1606 | −0.482033 | −0.241016 | − | 0.970521i | \(-0.577481\pi\) | ||||
−0.241016 | + | 0.970521i | \(0.577481\pi\) | |||||||
\(864\) | 4.65223 | 0.158272 | ||||||||
\(865\) | 0.815414 | 0.0277249 | ||||||||
\(866\) | −23.7888 | −0.808377 | ||||||||
\(867\) | 15.0185 | 0.510054 | ||||||||
\(868\) | −7.18675 | −0.243934 | ||||||||
\(869\) | −44.1985 | −1.49933 | ||||||||
\(870\) | 0.353320 | 0.0119787 | ||||||||
\(871\) | −31.1980 | −1.05710 | ||||||||
\(872\) | 2.29513 | 0.0777231 | ||||||||
\(873\) | 35.7279 | 1.20921 | ||||||||
\(874\) | −2.96000 | −0.100124 | ||||||||
\(875\) | 0.957076 | 0.0323551 | ||||||||
\(876\) | 10.4878 | 0.354349 | ||||||||
\(877\) | 8.88043 | 0.299871 | 0.149935 | − | 0.988696i | \(-0.452093\pi\) | ||||
0.149935 | + | 0.988696i | \(0.452093\pi\) | |||||||
\(878\) | 36.8791 | 1.24461 | ||||||||
\(879\) | −25.0749 | −0.845755 | ||||||||
\(880\) | 0.216500 | 0.00729821 | ||||||||
\(881\) | 20.7540 | 0.699219 | 0.349609 | − | 0.936896i | \(-0.386314\pi\) | ||||
0.349609 | + | 0.936896i | \(0.386314\pi\) | |||||||
\(882\) | 10.8984 | 0.366969 | ||||||||
\(883\) | −45.9956 | −1.54788 | −0.773938 | − | 0.633262i | \(-0.781716\pi\) | ||||
−0.773938 | + | 0.633262i | \(0.781716\pi\) | |||||||
\(884\) | −1.93715 | −0.0651534 | ||||||||
\(885\) | 0.181392 | 0.00609741 | ||||||||
\(886\) | 18.7710 | 0.630624 | ||||||||
\(887\) | −22.3918 | −0.751844 | −0.375922 | − | 0.926651i | \(-0.622674\pi\) | ||||
−0.375922 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(888\) | 4.95587 | 0.166308 | ||||||||
\(889\) | 8.19661 | 0.274906 | ||||||||
\(890\) | 0.232017 | 0.00777724 | ||||||||
\(891\) | −7.87488 | −0.263818 | ||||||||
\(892\) | 0.0330141 | 0.00110539 | ||||||||
\(893\) | 0.940223 | 0.0314634 | ||||||||
\(894\) | −8.42255 | −0.281692 | ||||||||
\(895\) | 1.21177 | 0.0405048 | ||||||||
\(896\) | 1.42997 | 0.0477720 | ||||||||
\(897\) | 11.0613 | 0.369328 | ||||||||
\(898\) | 7.66794 | 0.255883 | ||||||||
\(899\) | −29.6382 | −0.988491 | ||||||||
\(900\) | 10.9871 | 0.366238 | ||||||||
\(901\) | 5.11067 | 0.170261 | ||||||||
\(902\) | −10.5618 | −0.351671 | ||||||||
\(903\) | −0.819717 | −0.0272785 | ||||||||
\(904\) | 4.15323 | 0.138134 | ||||||||
\(905\) | 0.559462 | 0.0185971 | ||||||||
\(906\) | −9.10211 | −0.302397 | ||||||||
\(907\) | −11.2584 | −0.373830 | −0.186915 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186915 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(908\) | 9.85789 | 0.327146 | ||||||||
\(909\) | −0.316682 | −0.0105037 | ||||||||
\(910\) | −0.399899 | −0.0132565 | ||||||||
\(911\) | 15.0265 | 0.497849 | 0.248925 | − | 0.968523i | \(-0.419923\pi\) | ||||
0.248925 | + | 0.968523i | \(0.419923\pi\) | |||||||
\(912\) | −0.894762 | −0.0296285 | ||||||||
\(913\) | −4.04597 | −0.133902 | ||||||||
\(914\) | −13.5028 | −0.446634 | ||||||||
\(915\) | 0.707605 | 0.0233927 | ||||||||
\(916\) | −26.1817 | −0.865066 | ||||||||
\(917\) | −30.1669 | −0.996198 | ||||||||
\(918\) | −2.15782 | −0.0712187 | ||||||||
\(919\) | −31.0414 | −1.02396 | −0.511981 | − | 0.858997i | \(-0.671088\pi\) | ||||
−0.511981 | + | 0.858997i | \(0.671088\pi\) | |||||||
\(920\) | 0.198201 | 0.00653449 | ||||||||
\(921\) | 0.599186 | 0.0197439 | ||||||||
\(922\) | 11.3288 | 0.373094 | ||||||||
\(923\) | −12.0592 | −0.396933 | ||||||||
\(924\) | 4.13694 | 0.136095 | ||||||||
\(925\) | 27.6689 | 0.909749 | ||||||||
\(926\) | −2.50054 | −0.0821727 | ||||||||
\(927\) | 37.6639 | 1.23704 | ||||||||
\(928\) | 5.89722 | 0.193586 | ||||||||
\(929\) | −31.9212 | −1.04730 | −0.523650 | − | 0.851934i | \(-0.675430\pi\) | ||||
−0.523650 | + | 0.851934i | \(0.675430\pi\) | |||||||
\(930\) | −0.301111 | −0.00987382 | ||||||||
\(931\) | −4.95518 | −0.162399 | ||||||||
\(932\) | −18.5618 | −0.608011 | ||||||||
\(933\) | 23.8453 | 0.780661 | ||||||||
\(934\) | −9.47731 | −0.310107 | ||||||||
\(935\) | −0.100418 | −0.00328402 | ||||||||
\(936\) | −9.18571 | −0.300244 | ||||||||
\(937\) | 35.5515 | 1.16142 | 0.580709 | − | 0.814111i | \(-0.302775\pi\) | ||||
0.580709 | + | 0.814111i | \(0.302775\pi\) | |||||||
\(938\) | −10.6818 | −0.348774 | ||||||||
\(939\) | −12.3529 | −0.403120 | ||||||||
\(940\) | −0.0629571 | −0.00205343 | ||||||||
\(941\) | −51.0565 | −1.66439 | −0.832196 | − | 0.554481i | \(-0.812917\pi\) | ||||
−0.832196 | + | 0.554481i | \(0.812917\pi\) | |||||||
\(942\) | 15.6732 | 0.510659 | ||||||||
\(943\) | −9.66914 | −0.314871 | ||||||||
\(944\) | 3.02758 | 0.0985394 | ||||||||
\(945\) | −0.445453 | −0.0144906 | ||||||||
\(946\) | −2.07144 | −0.0673484 | ||||||||
\(947\) | −22.4032 | −0.728006 | −0.364003 | − | 0.931398i | \(-0.618590\pi\) | ||||
−0.364003 | + | 0.931398i | \(0.618590\pi\) | |||||||
\(948\) | −12.2313 | −0.397253 | ||||||||
\(949\) | −48.9536 | −1.58910 | ||||||||
\(950\) | −4.99552 | −0.162076 | ||||||||
\(951\) | 6.51785 | 0.211356 | ||||||||
\(952\) | −0.663257 | −0.0214963 | ||||||||
\(953\) | −16.4898 | −0.534157 | −0.267079 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267079 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(954\) | 24.2342 | 0.784610 | ||||||||
\(955\) | −0.229269 | −0.00741897 | ||||||||
\(956\) | 10.0354 | 0.324568 | ||||||||
\(957\) | 17.0608 | 0.551496 | ||||||||
\(958\) | 25.1951 | 0.814017 | ||||||||
\(959\) | 15.3652 | 0.496169 | ||||||||
\(960\) | 0.0599131 | 0.00193369 | ||||||||
\(961\) | −5.74133 | −0.185204 | ||||||||
\(962\) | −23.1324 | −0.745819 | ||||||||
\(963\) | −7.40883 | −0.238746 | ||||||||
\(964\) | 9.53632 | 0.307144 | ||||||||
\(965\) | 1.55767 | 0.0501433 | ||||||||
\(966\) | 3.78728 | 0.121854 | ||||||||
\(967\) | 44.2347 | 1.42249 | 0.711246 | − | 0.702943i | \(-0.248131\pi\) | ||||
0.711246 | + | 0.702943i | \(0.248131\pi\) | |||||||
\(968\) | −0.545879 | −0.0175452 | ||||||||
\(969\) | 0.415013 | 0.0133321 | ||||||||
\(970\) | 1.08772 | 0.0349246 | ||||||||
\(971\) | −8.90513 | −0.285779 | −0.142890 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142890 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(972\) | −16.1359 | −0.517560 | ||||||||
\(973\) | −3.52131 | −0.112888 | ||||||||
\(974\) | −10.4758 | −0.335668 | ||||||||
\(975\) | 18.6679 | 0.597853 | ||||||||
\(976\) | 11.8105 | 0.378046 | ||||||||
\(977\) | 5.69080 | 0.182065 | 0.0910325 | − | 0.995848i | \(-0.470983\pi\) | ||||
0.0910325 | + | 0.995848i | \(0.470983\pi\) | |||||||
\(978\) | −4.43182 | −0.141714 | ||||||||
\(979\) | 11.2034 | 0.358063 | ||||||||
\(980\) | 0.331798 | 0.0105989 | ||||||||
\(981\) | −5.04792 | −0.161168 | ||||||||
\(982\) | 39.2210 | 1.25159 | ||||||||
\(983\) | 1.30631 | 0.0416648 | 0.0208324 | − | 0.999783i | \(-0.493368\pi\) | ||||
0.0208324 | + | 0.999783i | \(0.493368\pi\) | |||||||
\(984\) | −2.92283 | −0.0931764 | ||||||||
\(985\) | −0.551082 | −0.0175589 | ||||||||
\(986\) | −2.73528 | −0.0871090 | ||||||||
\(987\) | −1.20300 | −0.0382919 | ||||||||
\(988\) | 4.17646 | 0.132871 | ||||||||
\(989\) | −1.89636 | −0.0603008 | ||||||||
\(990\) | −0.476170 | −0.0151337 | ||||||||
\(991\) | 47.8763 | 1.52084 | 0.760421 | − | 0.649430i | \(-0.224993\pi\) | ||||
0.760421 | + | 0.649430i | \(0.224993\pi\) | |||||||
\(992\) | −5.02580 | −0.159569 | ||||||||
\(993\) | −18.4337 | −0.584976 | ||||||||
\(994\) | −4.12893 | −0.130962 | ||||||||
\(995\) | −0.922579 | −0.0292477 | ||||||||
\(996\) | −1.11966 | −0.0354778 | ||||||||
\(997\) | −16.9545 | −0.536953 | −0.268477 | − | 0.963286i | \(-0.586520\pi\) | ||||
−0.268477 | + | 0.963286i | \(0.586520\pi\) | |||||||
\(998\) | −7.95532 | −0.251821 | ||||||||
\(999\) | −25.7675 | −0.815249 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.d.1.13 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.13 | ✓ | 30 | 1.1 | even | 1 | trivial |