Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.47 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | 0 | ||||||||
\(3\) | 3.04552 | 1.75833 | 0.879167 | − | 0.476513i | \(-0.158100\pi\) | ||||
0.879167 | + | 0.476513i | \(0.158100\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.431846 | 0.193127 | 0.0965637 | − | 0.995327i | \(-0.469215\pi\) | ||||
0.0965637 | + | 0.995327i | \(0.469215\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.556871 | −0.210477 | −0.105239 | − | 0.994447i | \(-0.533561\pi\) | ||||
−0.105239 | + | 0.994447i | \(0.533561\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.27522 | 2.09174 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64578 | 1.70227 | 0.851133 | − | 0.524950i | \(-0.175916\pi\) | ||||
0.851133 | + | 0.524950i | \(0.175916\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.81308 | −0.502858 | −0.251429 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251429 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.31520 | 0.339583 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52057 | −1.33894 | −0.669468 | − | 0.742841i | \(-0.733478\pi\) | ||||
−0.669468 | + | 0.742841i | \(0.733478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.92722 | −0.671549 | −0.335775 | − | 0.941942i | \(-0.608998\pi\) | ||||
−0.335775 | + | 0.941942i | \(0.608998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69596 | −0.370090 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.66295 | 0.763779 | 0.381889 | − | 0.924208i | \(-0.375274\pi\) | ||||
0.381889 | + | 0.924208i | \(0.375274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.81351 | −0.962702 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.97477 | 1.91965 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.96759 | 1.47954 | 0.739772 | − | 0.672857i | \(-0.234933\pi\) | ||||
0.739772 | + | 0.672857i | \(0.234933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0264 | 1.80079 | 0.900396 | − | 0.435072i | \(-0.143277\pi\) | ||||
0.900396 | + | 0.435072i | \(0.143277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.1944 | 2.99315 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.240483 | −0.0406490 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.39654 | −1.38038 | −0.690191 | − | 0.723627i | \(-0.742474\pi\) | ||||
−0.690191 | + | 0.723627i | \(0.742474\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.52178 | −0.884192 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.60870 | −0.407411 | −0.203706 | − | 0.979032i | \(-0.565299\pi\) | ||||
−0.203706 | + | 0.979032i | \(0.565299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.95510 | 1.21314 | 0.606571 | − | 0.795030i | \(-0.292545\pi\) | ||||
0.606571 | + | 0.795030i | \(0.292545\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.70993 | 0.403973 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.97252 | 1.01705 | 0.508523 | − | 0.861048i | \(-0.330192\pi\) | ||||
0.508523 | + | 0.861048i | \(0.330192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68989 | −0.955699 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8130 | −2.35430 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4233 | 1.84384 | 0.921919 | − | 0.387382i | \(-0.126620\pi\) | ||||
0.921919 | + | 0.387382i | \(0.126620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.43811 | 0.328754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.91491 | −1.18081 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.82100 | 0.757830 | 0.378915 | − | 0.925431i | \(-0.376297\pi\) | ||||
0.378915 | + | 0.925431i | \(0.376297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.35030 | −0.685036 | −0.342518 | − | 0.939511i | \(-0.611280\pi\) | ||||
−0.342518 | + | 0.939511i | \(0.611280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.49449 | −0.440264 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.782971 | −0.0971156 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.25200 | −0.152957 | −0.0764783 | − | 0.997071i | \(-0.524368\pi\) | ||||
−0.0764783 | + | 0.997071i | \(0.524368\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.1556 | 1.34298 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4685 | 1.83577 | 0.917884 | − | 0.396849i | \(-0.129896\pi\) | ||||
0.917884 | + | 0.396849i | \(0.129896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63973 | 0.777122 | 0.388561 | − | 0.921423i | \(-0.372972\pi\) | ||||
0.388561 | + | 0.921423i | \(0.372972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.6597 | −1.69275 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.14397 | −0.358289 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.96461 | −1.00860 | −0.504298 | − | 0.863529i | \(-0.668249\pi\) | ||||
−0.504298 | + | 0.863529i | \(0.668249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.5528 | 1.28364 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.14195 | 0.564402 | 0.282201 | − | 0.959355i | \(-0.408935\pi\) | ||||
0.282201 | + | 0.959355i | \(0.408935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38404 | −0.258585 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.2655 | 2.60154 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.35055 | −0.143158 | −0.0715788 | − | 0.997435i | \(-0.522804\pi\) | ||||
−0.0715788 | + | 0.997435i | \(0.522804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00965 | 0.105840 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30.5356 | 3.16639 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.26411 | −0.129695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.11507 | 0.925495 | 0.462748 | − | 0.886490i | \(-0.346864\pi\) | ||||
0.462748 | + | 0.886490i | \(0.346864\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 35.4285 | 3.56070 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5297 | 1.44576 | 0.722882 | − | 0.690972i | \(-0.242817\pi\) | ||||
0.722882 | + | 0.690972i | \(0.242817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.50046 | 0.837575 | 0.418788 | − | 0.908084i | \(-0.362455\pi\) | ||||
0.418788 | + | 0.908084i | \(0.362455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.732396 | −0.0714745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.98351 | 0.385100 | 0.192550 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192550 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1946 | −0.976470 | −0.488235 | − | 0.872712i | \(-0.662359\pi\) | ||||
−0.488235 | + | 0.872712i | \(0.662359\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −25.5719 | −2.42717 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.28835 | −0.779702 | −0.389851 | − | 0.920878i | \(-0.627474\pi\) | ||||
−0.389851 | + | 0.920878i | \(0.627474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.58183 | 0.147507 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.3775 | −1.05185 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.07425 | 0.281816 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8748 | 1.89771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.94487 | −0.716365 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.23793 | −0.379052 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1908 | −0.993020 | −0.496510 | − | 0.868031i | \(-0.665385\pi\) | ||||
−0.496510 | + | 0.868031i | \(0.665385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.2275 | 2.13311 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1151 | −1.32061 | −0.660307 | − | 0.750996i | \(-0.729574\pi\) | ||||
−0.660307 | + | 0.750996i | \(0.729574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.63008 | 0.141346 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.30757 | 0.370736 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23.0625 | −1.97036 | −0.985182 | − | 0.171510i | \(-0.945136\pi\) | ||||
−0.985182 | + | 0.171510i | \(0.945136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.94126 | −0.164656 | −0.0823278 | − | 0.996605i | \(-0.526235\pi\) | ||||
−0.0823278 | + | 0.996605i | \(0.526235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.2350 | 1.78831 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2362 | −0.855997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.44077 | 0.285741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.3742 | −1.68044 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1336 | −0.912096 | −0.456048 | − | 0.889955i | \(-0.650735\pi\) | ||||
−0.456048 | + | 0.889955i | \(0.650735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.42141 | −0.603946 | −0.301973 | − | 0.953317i | \(-0.597645\pi\) | ||||
−0.301973 | + | 0.953317i | \(0.597645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.6428 | −2.80071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.32985 | 0.347782 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.9820 | −1.59474 | −0.797370 | − | 0.603491i | \(-0.793776\pi\) | ||||
−0.797370 | + | 0.603491i | \(0.793776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 40.8811 | 3.24209 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.03979 | −0.160758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0483 | −1.10035 | −0.550176 | − | 0.835049i | \(-0.685439\pi\) | ||||
−0.550176 | + | 0.835049i | \(0.685439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.42531 | 0.578060 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4859 | 1.12095 | 0.560477 | − | 0.828170i | \(-0.310618\pi\) | ||||
0.560477 | + | 0.828170i | \(0.310618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.71274 | −0.747134 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.3689 | −1.40471 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1810 | 1.15419 | 0.577095 | − | 0.816677i | \(-0.304186\pi\) | ||||
0.577095 | + | 0.816677i | \(0.304186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.68050 | 0.202627 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.7280 | 1.33252 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.50270 | 0.486035 | 0.243017 | − | 0.970022i | \(-0.421863\pi\) | ||||
0.243017 | + | 0.970022i | \(0.421863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0604375 | 0.00449228 | 0.00224614 | − | 0.999997i | \(-0.499285\pi\) | ||||
0.00224614 | + | 0.999997i | \(0.499285\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.2945 | −1.20452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.62601 | −0.266590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.1679 | −2.27922 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.55466 | −0.404042 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.267998 | −0.0193917 | −0.00969583 | − | 0.999953i | \(-0.503086\pi\) | ||||
−0.00969583 | + | 0.999953i | \(0.503086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4597 | −0.752907 | −0.376453 | − | 0.926436i | \(-0.622857\pi\) | ||||
−0.376453 | + | 0.926436i | \(0.622857\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.38456 | −0.170762 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.97933 | 0.212269 | 0.106134 | − | 0.994352i | \(-0.466153\pi\) | ||||
0.106134 | + | 0.994352i | \(0.466153\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.134870 | −0.00956065 | −0.00478032 | − | 0.999989i | \(-0.501522\pi\) | ||||
−0.00478032 | + | 0.999989i | \(0.501522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.81301 | −0.268949 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.43692 | −0.311411 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.12656 | −0.0786822 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.9859 | 1.59763 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.5264 | −1.14316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0676 | 1.10614 | 0.553071 | − | 0.833134i | \(-0.313456\pi\) | ||||
0.553071 | + | 0.833134i | \(0.313456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47.1096 | 3.22789 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.43538 | 0.234291 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.58340 | −0.379026 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.2215 | 1.36644 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0092 | 0.673294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0357 | 0.805972 | 0.402986 | − | 0.915206i | \(-0.367972\pi\) | ||||
0.402986 | + | 0.915206i | \(0.367972\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30.2058 | −2.01372 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4378 | −0.958272 | −0.479136 | − | 0.877741i | \(-0.659050\pi\) | ||||
−0.479136 | + | 0.877741i | \(0.659050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.24016 | −0.346279 | −0.173140 | − | 0.984897i | \(-0.555391\pi\) | ||||
−0.173140 | + | 0.984897i | \(0.555391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.57504 | −0.629991 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.1314 | −1.05681 | −0.528403 | − | 0.848994i | \(-0.677209\pi\) | ||||
−0.528403 | + | 0.848994i | \(0.677209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.01105 | 0.196419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.3019 | −1.77345 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.75448 | 0.372227 | 0.186113 | − | 0.982528i | \(-0.440411\pi\) | ||||
0.186113 | + | 0.982528i | \(0.440411\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0221171 | −0.00142469 | −0.000712344 | − | 1.00000i | \(-0.500227\pi\) | ||||
−0.000712344 | 1.00000i | \(0.500227\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.25987 | 0.337421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.88900 | −0.184572 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.30727 | 0.337694 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.6599 | 0.992408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4453 | −1.47985 | −0.739926 | − | 0.672688i | \(-0.765139\pi\) | ||||
−0.739926 | + | 0.672688i | \(0.765139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.6802 | 1.30015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.26065 | −0.454679 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.90928 | 0.555746 | 0.277873 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277873 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.67579 | 0.290539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.9984 | 3.09482 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.7963 | 1.52901 | 0.764504 | − | 0.644619i | \(-0.222984\pi\) | ||||
0.764504 | + | 0.644619i | \(0.222984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.79682 | 0.356096 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.11312 | −0.251719 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7215 | −0.775646 | −0.387823 | − | 0.921734i | \(-0.626773\pi\) | ||||
−0.387823 | + | 0.921734i | \(0.626773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6495 | −0.889894 | −0.444947 | − | 0.895557i | \(-0.646777\pi\) | ||||
−0.444947 | + | 0.895557i | \(0.646777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.07492 | 0.186103 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.1760 | −1.63877 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27406 | 0.0765509 | 0.0382755 | − | 0.999267i | \(-0.487814\pi\) | ||||
0.0382755 | + | 0.999267i | \(0.487814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 62.9178 | 3.76679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.6217 | −1.11088 | −0.555440 | − | 0.831557i | \(-0.687450\pi\) | ||||
−0.555440 | + | 0.831557i | \(0.687450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.6087 | 1.70061 | 0.850305 | − | 0.526290i | \(-0.176417\pi\) | ||||
0.850305 | + | 0.526290i | \(0.176417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.84987 | −0.228047 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.45271 | 0.0857509 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.4767 | 0.792750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.7602 | 1.62733 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.2469 | −0.832315 | −0.416157 | − | 0.909293i | \(-0.636623\pi\) | ||||
−0.416157 | + | 0.909293i | \(0.636623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.51378 | 0.146358 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 56.3153 | 3.26775 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.64122 | −0.384072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.42996 | −0.255339 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 44.2507 | 2.54214 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.31051 | −0.132299 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9222 | −0.680437 | −0.340219 | − | 0.940346i | \(-0.610501\pi\) | ||||
−0.340219 | + | 0.940346i | \(0.610501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.8884 | 1.47274 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.926676 | 0.0525469 | 0.0262735 | − | 0.999655i | \(-0.491636\pi\) | ||||
0.0262735 | + | 0.999655i | \(0.491636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4996 | 0.649998 | 0.324999 | − | 0.945714i | \(-0.394636\pi\) | ||||
0.324999 | + | 0.945714i | \(0.394636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50908 | −0.0850271 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.84723 | 0.496910 | 0.248455 | − | 0.968643i | \(-0.420077\pi\) | ||||
0.248455 | + | 0.968643i | \(0.420077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44.9832 | 2.51858 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1319 | 0.677135 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.1599 | 0.899162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.72727 | 0.484102 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.0480 | −1.71696 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.88279 | −0.214065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.77317 | 0.262357 | 0.131179 | − | 0.991359i | \(-0.458124\pi\) | ||||
0.131179 | + | 0.991359i | \(0.458124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −52.6901 | −2.88740 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.540673 | −0.0295401 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.31159 | −0.507235 | −0.253617 | − | 0.967305i | \(-0.581620\pi\) | ||||
−0.253617 | + | 0.967305i | \(0.581620\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.2424 | −1.37098 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56.6067 | 3.06543 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.62351 | 0.411631 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.81751 | 0.259366 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.3545 | 0.877957 | 0.438978 | − | 0.898498i | \(-0.355340\pi\) | ||||
0.438978 | + | 0.898498i | \(0.355340\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.1583 | −1.56081 | −0.780405 | − | 0.625275i | \(-0.784987\pi\) | ||||
−0.780405 | + | 0.625275i | \(0.784987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0851 | −0.965309 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.7968 | 0.840778 | 0.420389 | − | 0.907344i | \(-0.361894\pi\) | ||||
0.420389 | + | 0.907344i | \(0.361894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.67999 | 0.354537 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.36270 | 0.495527 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.8941 | −0.838861 | −0.419430 | − | 0.907788i | \(-0.637770\pi\) | ||||
−0.419430 | + | 0.907788i | \(0.637770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.4314 | −0.549022 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 63.5747 | 3.33681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.86734 | 0.150084 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.5960 | 1.44050 | 0.720249 | − | 0.693716i | \(-0.244027\pi\) | ||||
0.720249 | + | 0.693716i | \(0.244027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.3702 | −0.852198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.47507 | −0.388087 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7126 | −1.43491 | −0.717453 | − | 0.696607i | \(-0.754692\pi\) | ||||
−0.717453 | + | 0.696607i | \(0.754692\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.9067 | −0.666500 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.4459 | −0.744000 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.5567 | −1.92916 | −0.964578 | − | 0.263797i | \(-0.915025\pi\) | ||||
−0.964578 | + | 0.263797i | \(0.915025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.0818 | −1.74606 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9850 | 0.867894 | 0.433947 | − | 0.900938i | \(-0.357121\pi\) | ||||
0.433947 | + | 0.900938i | \(0.357121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.35771 | −0.0691954 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 49.9200 | 2.53758 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6491 | 1.30046 | 0.650230 | − | 0.759737i | \(-0.274673\pi\) | ||||
0.650230 | + | 0.759737i | \(0.274673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2216 | −1.02265 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.0334 | −2.32208 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.87133 | −0.194788 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6198 | −0.884315 | −0.442157 | − | 0.896937i | \(-0.645787\pi\) | ||||
−0.442157 | + | 0.896937i | \(0.645787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.96445 | 0.248534 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0825765 | −0.00412368 | −0.00206184 | − | 0.999998i | \(-0.500656\pi\) | ||||
−0.00206184 | + | 0.999998i | \(0.500656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.1786 | −0.905542 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.98901 | 0.247906 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47.4050 | −2.34978 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1261 | 0.747937 | 0.373968 | − | 0.927441i | \(-0.377997\pi\) | ||||
0.373968 | + | 0.927441i | \(0.377997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −70.2375 | −3.46456 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.24155 | −0.159506 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.22053 | 0.109002 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.91216 | −0.289520 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6299 | −0.519303 | −0.259652 | − | 0.965702i | \(-0.583608\pi\) | ||||
−0.259652 | + | 0.965702i | \(0.583608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0443 | 0.635743 | 0.317871 | − | 0.948134i | \(-0.397032\pi\) | ||||
0.317871 | + | 0.948134i | \(0.397032\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 43.7541 | 2.12740 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.5733 | 1.28900 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.97943 | 0.144185 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.1747 | −1.50513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.98042 | −0.288067 | −0.144033 | − | 0.989573i | \(-0.546007\pi\) | ||||
−0.144033 | + | 0.989573i | \(0.546007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.4280 | −1.65450 | −0.827251 | − | 0.561832i | \(-0.810097\pi\) | ||||
−0.827251 | + | 0.561832i | \(0.810097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4790 | 0.502428 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.7223 | −0.512915 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6909 | −0.892067 | −0.446033 | − | 0.895016i | \(-0.647164\pi\) | ||||
−0.446033 | + | 0.895016i | \(0.647164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.9806 | −1.99908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2653 | 1.24790 | 0.623952 | − | 0.781463i | \(-0.285526\pi\) | ||||
0.623952 | + | 0.781463i | \(0.285526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.583228 | −0.0276477 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.9075 | −1.60377 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1457 | 1.46985 | 0.734927 | − | 0.678146i | \(-0.237216\pi\) | ||||
0.734927 | + | 0.678146i | \(0.237216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.7282 | −0.693522 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.6021 | −1.06194 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.436014 | 0.0204407 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.12951 | 0.146392 | 0.0731962 | − | 0.997318i | \(-0.476680\pi\) | ||||
0.0731962 | + | 0.997318i | \(0.476680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −55.0665 | −2.57028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0168 | 0.792551 | 0.396275 | − | 0.918132i | \(-0.370303\pi\) | ||||
0.396275 | + | 0.918132i | \(0.370303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4354 | −0.577922 | −0.288961 | − | 0.957341i | \(-0.593310\pi\) | ||||
−0.288961 | + | 0.957341i | \(0.593310\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.1867 | 0.611518 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.5862 | 0.906341 | 0.453170 | − | 0.891424i | \(-0.350293\pi\) | ||||
0.453170 | + | 0.891424i | \(0.350293\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.697205 | 0.0321939 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −60.8558 | −2.80409 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.9127 | 2.06509 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0902 | 0.646502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 84.2345 | 3.85683 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0728 | −0.780076 | −0.390038 | − | 0.920799i | \(-0.627538\pi\) | ||||
−0.390038 | + | 0.920799i | \(0.627538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2236 | 0.694136 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.21224 | −0.282667 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.93631 | 0.178739 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.75640 | 0.260848 | 0.130424 | − | 0.991458i | \(-0.458366\pi\) | ||||
0.130424 | + | 0.991458i | \(0.458366\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −42.7846 | −1.93479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.78761 | −0.351450 | −0.175725 | − | 0.984439i | \(-0.556227\pi\) | ||||
−0.175725 | + | 0.984439i | \(0.556227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.9857 | −1.98102 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.2997 | 0.687669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.61394 | −0.386388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.1058 | −1.16866 | −0.584328 | − | 0.811518i | \(-0.698642\pi\) | ||||
−0.584328 | + | 0.811518i | \(0.698642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.1172 | 1.97101 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.78309 | −0.391619 | −0.195809 | − | 0.980642i | \(-0.562733\pi\) | ||||
−0.195809 | + | 0.980642i | \(0.562733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.27461 | 0.279217 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.5804 | −1.31371 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.66671 | −0.384145 | −0.192073 | − | 0.981381i | \(-0.561521\pi\) | ||||
−0.192073 | + | 0.981381i | \(0.561521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.69748 | −0.163567 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.1983 | −1.28914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.67089 | 0.161759 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.3653 | 1.73128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.2341 | 2.02945 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.4799 | −0.721999 | −0.360999 | − | 0.932566i | \(-0.617564\pi\) | ||||
−0.360999 | + | 0.932566i | \(0.617564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.1570 | −1.62476 | −0.812381 | − | 0.583127i | \(-0.801829\pi\) | ||||
−0.812381 | + | 0.583127i | \(0.801829\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.16354 | 0.356286 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −55.3514 | −2.41114 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.58277 | −0.416642 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.5281 | 1.58518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.72979 | 0.204870 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.72026 | 0.0743734 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.8041 | 0.854612 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.7696 | −1.62685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5261 | −0.538541 | −0.269270 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269270 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.184064 | 0.00789893 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.40252 | −0.188583 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4441 | 1.51548 | 0.757740 | − | 0.652557i | \(-0.226304\pi\) | ||||
0.757740 | + | 0.652557i | \(0.226304\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.5743 | −1.43292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.3229 | −0.993587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.99213 | 0.212287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.0431 | −0.468754 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.0444 | −0.679824 | −0.339912 | − | 0.940457i | \(-0.610397\pi\) | ||||
−0.339912 | + | 0.940457i | \(0.610397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.4232 | −0.610037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −94.9227 | −4.00764 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.4497 | −1.66261 | −0.831303 | − | 0.555820i | \(-0.812404\pi\) | ||||
−0.831303 | + | 0.555820i | \(0.812404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.57929 | −0.150582 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.43339 | −0.270177 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.3829 | −1.65102 | −0.825509 | − | 0.564389i | \(-0.809112\pi\) | ||||
−0.825509 | + | 0.564389i | \(0.809112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0484 | 0.546058 | 0.273029 | − | 0.962006i | \(-0.411975\pi\) | ||||
0.273029 | + | 0.962006i | \(0.411975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.816195 | −0.0340970 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.6317 | −0.735291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.582063 | 0.0242316 | 0.0121158 | − | 0.999927i | \(-0.496143\pi\) | ||||
0.0121158 | + | 0.999927i | \(0.496143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.8553 | −1.32386 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.86340 | −0.118794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 75.7852 | 3.13870 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.91332 | −0.203141 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.6837 | 1.10135 | 0.550677 | − | 0.834718i | \(-0.314370\pi\) | ||||
0.550677 | + | 0.834718i | \(0.314370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.3494 | −1.20932 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.07363 | 0.373239 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.44506 | 0.0593417 | 0.0296708 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296708 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.32760 | 0.0544264 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.410749 | −0.0168108 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.0057 | 1.71631 | 0.858153 | − | 0.513394i | \(-0.171612\pi\) | ||||
0.858153 | + | 0.513394i | \(0.171612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7664 | 0.602333 | 0.301167 | − | 0.953572i | \(-0.402624\pi\) | ||||
0.301167 | + | 0.953572i | \(0.402624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.85660 | −0.319945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.01470 | 0.366500 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.99527 | −0.162163 | −0.0810816 | − | 0.996707i | \(-0.525837\pi\) | ||||
−0.0810816 | + | 0.996707i | \(0.525837\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.5128 | −0.547565 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6417 | −0.511429 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.68638 | 0.310450 | 0.155225 | − | 0.987879i | \(-0.450390\pi\) | ||||
0.155225 | + | 0.987879i | \(0.450390\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.43096 | −0.138350 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.1071 | 1.85620 | 0.928101 | − | 0.372330i | \(-0.121441\pi\) | ||||
0.928101 | + | 0.372330i | \(0.121441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.9780 | −1.36569 | −0.682845 | − | 0.730563i | \(-0.739258\pi\) | ||||
−0.682845 | + | 0.730563i | \(0.739258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.5371 | 1.46618 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.752080 | 0.0301315 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.2374 | 0.889497 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −50.3316 | −2.01005 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 46.3537 | 1.84824 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.3525 | 1.48698 | 0.743490 | − | 0.668747i | \(-0.233169\pi\) | ||||
0.743490 | + | 0.668747i | \(0.233169\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.9344 | 1.94497 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.83269 | −0.191779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.1293 | 0.480581 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 97.0680 | 3.83995 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.4926 | 1.24388 | 0.621941 | − | 0.783064i | \(-0.286344\pi\) | ||||
0.621941 | + | 0.783064i | \(0.286344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.8967 | 1.61281 | 0.806405 | − | 0.591364i | \(-0.201410\pi\) | ||||
0.806405 | + | 0.591364i | \(0.201410\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4625 | 0.411962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.4889 | −1.15933 | −0.579665 | − | 0.814855i | \(-0.696817\pi\) | ||||
−0.579665 | + | 0.814855i | \(0.696817\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.8641 | 1.29003 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.0044 | −0.666455 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.3354 | 1.85238 | 0.926188 | − | 0.377063i | \(-0.123066\pi\) | ||||
0.926188 | + | 0.377063i | \(0.123066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.52740 | −0.255047 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.6658 | 1.62554 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.3174 | −1.45368 | −0.726839 | − | 0.686808i | \(-0.759012\pi\) | ||||
−0.726839 | + | 0.686808i | \(0.759012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.6271 | 0.763404 | 0.381702 | − | 0.924285i | \(-0.375338\pi\) | ||||
0.381702 | + | 0.924285i | \(0.375338\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.4834 | 1.18388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.703944 | 0.0272978 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.1849 | 1.13004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.6551 | 1.41717 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.2066 | −1.16611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4867 | 0.442779 | 0.221390 | − | 0.975185i | \(-0.428941\pi\) | ||||
0.221390 | + | 0.975185i | \(0.428941\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −48.0137 | −1.84805 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.9150 | 0.457929 | 0.228964 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228964 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.07592 | −0.194796 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −43.9707 | −1.68496 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.7812 | −1.86656 | −0.933281 | − | 0.359148i | \(-0.883067\pi\) | ||||
−0.933281 | + | 0.359148i | \(0.883067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.95946 | −0.380532 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9590 | −0.608875 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.3376 | −0.927188 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8692 | −1.02215 | −0.511077 | − | 0.859535i | \(-0.670753\pi\) | ||||
−0.511077 | + | 0.859535i | \(0.670753\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.7291 | −0.749447 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.838326 | −0.0317995 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4015 | 0.545497 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.1287 | −1.85822 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.6147 | −1.30738 | −0.653689 | − | 0.756763i | \(-0.726780\pi\) | ||||
−0.653689 | + | 0.756763i | \(0.726780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.5785 | 0.926995 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.17024 | 0.345371 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.09119 | −0.304301 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.1391 | −1.46990 | −0.734950 | − | 0.678122i | \(-0.762794\pi\) | ||||
−0.734950 | + | 0.678122i | \(0.762794\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −56.2549 | −2.10972 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.7262 | 1.37541 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.42048 | −0.165317 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.5254 | 0.654499 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.9750 | −0.633059 | −0.316529 | − | 0.948583i | \(-0.602518\pi\) | ||||
−0.316529 | + | 0.948583i | \(0.602518\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.73366 | −0.176291 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0673582 | −0.00250508 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −38.3521 | −1.42436 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0663 | 1.18927 | 0.594637 | − | 0.803994i | \(-0.297296\pi\) | ||||
0.594637 | + | 0.803994i | \(0.297296\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6392 | −0.690340 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.9167 | −1.62432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1436 | 0.780955 | 0.390477 | − | 0.920613i | \(-0.372310\pi\) | ||||
0.390477 | + | 0.920613i | \(0.372310\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.79854 | −0.324539 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.06853 | −0.260373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.13147 | −0.151979 | −0.0759893 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759893 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.1634 | 0.593779 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.6327 | −1.52735 | −0.763677 | − | 0.645598i | \(-0.776608\pi\) | ||||
−0.763677 | + | 0.645598i | \(0.776608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.80798 | −0.176151 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.2669 | 1.18058 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.21830 | −0.0810549 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −71.4031 | −2.60207 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.20491 | −0.116638 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4031 | −0.523490 | −0.261745 | − | 0.965137i | \(-0.584298\pi\) | ||||
−0.261745 | + | 0.965137i | \(0.584298\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 62.9821 | 2.28611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.27444 | −0.0461984 | −0.0230992 | − | 0.999733i | \(-0.507353\pi\) | ||||
−0.0230992 | + | 0.999733i | \(0.507353\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.67710 | 0.205525 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.9604 | −0.540893 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.5539 | −0.381081 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.9962 | −1.08169 | −0.540845 | − | 0.841122i | \(-0.681895\pi\) | ||||
−0.540845 | + | 0.841122i | \(0.681895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.1334 | 0.977187 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.7228 | 0.961154 | 0.480577 | − | 0.876953i | \(-0.340427\pi\) | ||||
0.480577 | + | 0.876953i | \(0.340427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.2621 | −1.73363 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.2402 | 0.510866 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.63624 | 0.273597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 87.3314 | 3.12496 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 79.4749 | 2.84020 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.62916 | −0.307988 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.2183 | −1.75444 | −0.877222 | − | 0.480085i | \(-0.840606\pi\) | ||||
−0.877222 | + | 0.480085i | \(0.840606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 75.5178 | 2.68851 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.61554 | 0.164110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.70052 | 0.344475 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.6544 | 0.626136 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.02233 | −0.177900 | −0.0889500 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889500 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.4923 | −1.36176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.47498 | −0.299449 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.4864 | 1.32287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.880877 | −0.0310468 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.7438 | −1.36385 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.4195 | −1.13981 | −0.569905 | − | 0.821710i | \(-0.693020\pi\) | ||||
−0.569905 | + | 0.821710i | \(0.693020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0962 | 1.02171 | 0.510854 | − | 0.859668i | \(-0.329329\pi\) | ||||
0.510854 | + | 0.859668i | \(0.329329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.6154 | −1.56473 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.06672 | −0.212508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.2863 | −0.814684 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.33579 | 0.221390 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9253 | −0.695396 | −0.347698 | − | 0.937607i | \(-0.613037\pi\) | ||||
−0.347698 | + | 0.937607i | \(0.613037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.7933 | −1.70083 | −0.850414 | − | 0.526114i | \(-0.823649\pi\) | ||||
−0.850414 | + | 0.526114i | \(0.823649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −82.7652 | −2.88151 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4297 | −0.640862 | −0.320431 | − | 0.947272i | \(-0.603828\pi\) | ||||
−0.320431 | + | 0.947272i | \(0.603828\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.3126 | −0.636024 | −0.318012 | − | 0.948087i | \(-0.603015\pi\) | ||||
−0.318012 | + | 0.948087i | \(0.603015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.88019 | 0.134602 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.9321 | 1.27962 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.25568 | 0.216487 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 100.011 | 3.45688 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.3711 | 0.358049 | 0.179024 | − | 0.983845i | \(-0.442706\pi\) | ||||
0.179024 | + | 0.983845i | \(0.442706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.4825 | 1.18905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.7129 | −1.95330 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.19441 | −0.144292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.6246 | −0.399425 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 87.1285 | 2.99024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.7561 | −1.05431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.1874 | 0.691204 | 0.345602 | − | 0.938381i | \(-0.387675\pi\) | ||||
0.345602 | + | 0.938381i | \(0.387675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.93255 | −0.271288 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.0520 | 1.50479 | 0.752394 | − | 0.658713i | \(-0.228899\pi\) | ||||
0.752394 | + | 0.658713i | \(0.228899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6716 | 0.398229 | 0.199115 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199115 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.42427 | 0.150779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.93770 | 0.134041 | 0.0670204 | − | 0.997752i | \(-0.478651\pi\) | ||||
0.0670204 | + | 0.997752i | \(0.478651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.55585 | 0.222906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.0438 | 1.39392 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.6122 | −1.71690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.26998 | 0.0769154 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 57.1991 | 1.93590 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.35998 | 0.0797818 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.31165 | 0.246897 | 0.123448 | − | 0.992351i | \(-0.460605\pi\) | ||||
0.123448 | + | 0.992351i | \(0.460605\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.3894 | −1.46349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.0114 | 1.71862 | 0.859308 | − | 0.511458i | \(-0.170895\pi\) | ||||
0.859308 | + | 0.511458i | \(0.170895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.4691 | 1.63111 | 0.815557 | − | 0.578677i | \(-0.196431\pi\) | ||||
0.815557 | + | 0.578677i | \(0.196431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.65577 | 0.257346 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.5216 | 1.02482 | 0.512408 | − | 0.858742i | \(-0.328753\pi\) | ||||
0.512408 | + | 0.858742i | \(0.328753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.23181 | 0.209008 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 65.2242 | 2.18509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.4101 | −0.682997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.80817 | 0.0938667 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.2260 | −0.675327 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 79.8861 | 2.66435 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.1046 | −2.46878 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.4916 | −0.448971 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0260997 | 0.000867583 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5773 | −0.849279 | −0.424639 | − | 0.905363i | \(-0.639599\pi\) | ||||
−0.424639 | + | 0.905363i | \(0.639599\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 91.1773 | 3.02416 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.9596 | −0.860079 | −0.430040 | − | 0.902810i | \(-0.641500\pi\) | ||||
−0.430040 | + | 0.902810i | \(0.641500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.0303 | 0.960762 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.03670 | −0.232626 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.41717 | 0.277959 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.5924 | −1.40499 | −0.702497 | − | 0.711687i | \(-0.747932\pi\) | ||||
−0.702497 | + | 0.711687i | \(0.747932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.3094 | −1.19644 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.0455 | −0.923130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.4168 | 1.32890 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53.3423 | 1.75199 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5325 | −0.345561 | −0.172781 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172781 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5828 | 0.641799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.82221 | 0.0923951 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.4597 | −0.440181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.9576 | −1.40336 | −0.701681 | − | 0.712491i | \(-0.747567\pi\) | ||||
−0.701681 | + | 0.712491i | \(0.747567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.0224 | 1.14291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.3365 | 0.825947 | 0.412973 | − | 0.910743i | \(-0.364490\pi\) | ||||
0.412973 | + | 0.910743i | \(0.364490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.55556 | −0.311172 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.39876 | −0.0780316 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.0906 | −1.40026 | −0.700128 | − | 0.714017i | \(-0.746874\pi\) | ||||
−0.700128 | + | 0.714017i | \(0.746874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0384 | −0.390782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.9444 | 0.873734 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.2786 | 0.592104 | 0.296052 | − | 0.955172i | \(-0.404330\pi\) | ||||
0.296052 | + | 0.955172i | \(0.404330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.115734 | −0.00374506 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 136.998 | 4.42850 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8429 | 0.414717 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.5284 | 2.24285 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.9974 | 0.805529 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.51699 | −0.145407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.7804 | 1.53652 | 0.768258 | − | 0.640141i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640141i | \(0.221124\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.2154 | 1.58103 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.6508 | −1.62546 | −0.812731 | − | 0.582638i | \(-0.802020\pi\) | ||||
−0.812731 | + | 0.582638i | \(0.802020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.08103 | 0.0346563 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.5791 | 0.851213 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.6523 | 0.948660 | 0.474330 | − | 0.880347i | \(-0.342690\pi\) | ||||
0.474330 | + | 0.880347i | \(0.342690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.62488 | −0.243692 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −63.9736 | −2.04252 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.4889 | −0.525913 | −0.262956 | − | 0.964808i | \(-0.584698\pi\) | ||||
−0.262956 | + | 0.964808i | \(0.584698\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.28661 | 0.0409949 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.8251 | −0.376398 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.1392 | 0.926571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.4035 | −1.25169 | −0.625847 | − | 0.779946i | \(-0.715247\pi\) | ||||
−0.625847 | + | 0.779946i | \(0.715247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.5368 | 0.461311 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.0582429 | −0.00184642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.2256 | −0.703891 | −0.351945 | − | 0.936021i | \(-0.614480\pi\) | ||||
−0.351945 | + | 0.936021i | \(0.614480\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −83.7536 | −2.64985 |
(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 | 6008.2.a.e.1.47 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.47 | ✓ | 50 | 1.1 | even | 1 | trivial |