Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, 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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.10.52900342088704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 18x^{8} + 123x^{6} - 390x^{4} + 548x^{2} - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.878233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.83556 | 1.71531 | 0.857656 | − | 0.514223i | \(-0.171920\pi\) | ||||
0.857656 | + | 0.514223i | \(0.171920\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.08193 | −1.92079 | −0.960395 | − | 0.278641i | \(-0.910116\pi\) | ||||
−0.960395 | + | 0.278641i | \(0.910116\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.83556 | 1.21291 | ||||||||
\(11\) | 4.51702 | 1.36193 | 0.680966 | − | 0.732315i | \(-0.261560\pi\) | ||||
0.680966 | + | 0.732315i | \(0.261560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.32949 | −0.923433 | −0.461717 | − | 0.887028i | \(-0.652766\pi\) | ||||
−0.461717 | + | 0.887028i | \(0.652766\pi\) | |||||||
\(14\) | −5.08193 | −1.35820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.154095 | −0.0373735 | −0.0186868 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186868 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.25031 | −1.20450 | −0.602252 | − | 0.798306i | \(-0.705730\pi\) | ||||
−0.602252 | + | 0.798306i | \(0.705730\pi\) | |||||||
\(20\) | 3.83556 | 0.857656 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.51702 | 0.963031 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.71149 | 1.94230 | ||||||||
\(26\) | −3.32949 | −0.652966 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.08193 | −0.960395 | ||||||||
\(29\) | −5.23379 | −0.971891 | −0.485946 | − | 0.873989i | \(-0.661525\pi\) | ||||
−0.485946 | + | 0.873989i | \(0.661525\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26824 | 0.227782 | 0.113891 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113891 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.154095 | −0.0264271 | ||||||||
\(35\) | −19.4920 | −3.29476 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.45795 | 0.732883 | 0.366442 | − | 0.930441i | \(-0.380576\pi\) | ||||
0.366442 | + | 0.930441i | \(0.380576\pi\) | |||||||
\(38\) | −5.25031 | −0.851712 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.83556 | 0.606455 | ||||||||
\(41\) | 2.21152 | 0.345382 | 0.172691 | − | 0.984976i | \(-0.444754\pi\) | ||||
0.172691 | + | 0.984976i | \(0.444754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63867 | 0.402393 | 0.201196 | − | 0.979551i | \(-0.435517\pi\) | ||||
0.201196 | + | 0.979551i | \(0.435517\pi\) | |||||||
\(44\) | 4.51702 | 0.680966 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.10906 | 0.161773 | 0.0808865 | − | 0.996723i | \(-0.474225\pi\) | ||||
0.0808865 | + | 0.996723i | \(0.474225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.8261 | 2.68944 | ||||||||
\(50\) | 9.71149 | 1.37341 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.32949 | −0.461717 | ||||||||
\(53\) | 4.28457 | 0.588530 | 0.294265 | − | 0.955724i | \(-0.404925\pi\) | ||||
0.294265 | + | 0.955724i | \(0.404925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.3253 | 2.33614 | ||||||||
\(56\) | −5.08193 | −0.679102 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.23379 | −0.687231 | ||||||||
\(59\) | 3.22790 | 0.420236 | 0.210118 | − | 0.977676i | \(-0.432615\pi\) | ||||
0.210118 | + | 0.977676i | \(0.432615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1399 | 1.68239 | 0.841197 | − | 0.540729i | \(-0.181851\pi\) | ||||
0.841197 | + | 0.540729i | \(0.181851\pi\) | |||||||
\(62\) | 1.26824 | 0.161066 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.7704 | −1.58398 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4839 | 1.28082 | 0.640409 | − | 0.768034i | \(-0.278765\pi\) | ||||
0.640409 | + | 0.768034i | \(0.278765\pi\) | |||||||
\(68\) | −0.154095 | −0.0186868 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −19.4920 | −2.32975 | ||||||||
\(71\) | 14.2586 | 1.69219 | 0.846095 | − | 0.533032i | \(-0.178948\pi\) | ||||
0.846095 | + | 0.533032i | \(0.178948\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.20430 | 0.726158 | 0.363079 | − | 0.931758i | \(-0.381725\pi\) | ||||
0.363079 | + | 0.931758i | \(0.381725\pi\) | |||||||
\(74\) | 4.45795 | 0.518227 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.25031 | −0.602252 | ||||||||
\(77\) | −22.9552 | −2.61599 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.91689 | 0.328175 | 0.164088 | − | 0.986446i | \(-0.447532\pi\) | ||||
0.164088 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(80\) | 3.83556 | 0.428828 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.21152 | 0.244222 | ||||||||
\(83\) | 2.33395 | 0.256185 | 0.128092 | − | 0.991762i | \(-0.459115\pi\) | ||||
0.128092 | + | 0.991762i | \(0.459115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.591040 | −0.0641073 | ||||||||
\(86\) | 2.63867 | 0.284535 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.51702 | 0.481516 | ||||||||
\(89\) | 5.50801 | 0.583847 | 0.291924 | − | 0.956442i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956442i | \(0.405705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.9202 | 1.77372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.10906 | 0.114391 | ||||||||
\(95\) | −20.1378 | −2.06610 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1549 | 1.33567 | 0.667837 | − | 0.744307i | \(-0.267220\pi\) | ||||
0.667837 | + | 0.744307i | \(0.267220\pi\) | |||||||
\(98\) | 18.8261 | 1.90172 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.71149 | 0.971149 | ||||||||
\(101\) | −6.51687 | −0.648453 | −0.324227 | − | 0.945979i | \(-0.605104\pi\) | ||||
−0.324227 | + | 0.945979i | \(0.605104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.64524 | −0.556242 | −0.278121 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278121 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(104\) | −3.32949 | −0.326483 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.28457 | 0.416154 | ||||||||
\(107\) | 6.79406 | 0.656807 | 0.328404 | − | 0.944538i | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944538i | \(0.393489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.83285 | −0.558685 | −0.279343 | − | 0.960191i | \(-0.590117\pi\) | ||||
−0.279343 | + | 0.960191i | \(0.590117\pi\) | |||||||
\(110\) | 17.3253 | 1.65190 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.08193 | −0.480198 | ||||||||
\(113\) | 14.6584 | 1.37895 | 0.689473 | − | 0.724311i | \(-0.257842\pi\) | ||||
0.689473 | + | 0.724311i | \(0.257842\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.23379 | −0.485946 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.22790 | 0.297152 | ||||||||
\(119\) | 0.783101 | 0.0717868 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.40343 | 0.854858 | ||||||||
\(122\) | 13.1399 | 1.18963 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.26824 | 0.113891 | ||||||||
\(125\) | 18.0712 | 1.61634 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1093 | −0.985787 | −0.492893 | − | 0.870090i | \(-0.664061\pi\) | ||||
−0.492893 | + | 0.870090i | \(0.664061\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.7704 | −1.12004 | ||||||||
\(131\) | 2.08032 | 0.181759 | 0.0908793 | − | 0.995862i | \(-0.471032\pi\) | ||||
0.0908793 | + | 0.995862i | \(0.471032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.6817 | 2.31360 | ||||||||
\(134\) | 10.4839 | 0.905675 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.154095 | −0.0132135 | ||||||||
\(137\) | 16.5855 | 1.41699 | 0.708496 | − | 0.705714i | \(-0.249374\pi\) | ||||
0.708496 | + | 0.705714i | \(0.249374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.74700 | 0.402635 | 0.201318 | − | 0.979526i | \(-0.435478\pi\) | ||||
0.201318 | + | 0.979526i | \(0.435478\pi\) | |||||||
\(140\) | −19.4920 | −1.64738 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.2586 | 1.19656 | ||||||||
\(143\) | −15.0393 | −1.25765 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.0745 | −1.66710 | ||||||||
\(146\) | 6.20430 | 0.513471 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.45795 | 0.366442 | ||||||||
\(149\) | −17.0234 | −1.39461 | −0.697304 | − | 0.716775i | \(-0.745617\pi\) | ||||
−0.697304 | + | 0.716775i | \(0.745617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.05024 | −0.573741 | −0.286870 | − | 0.957969i | \(-0.592615\pi\) | ||||
−0.286870 | + | 0.957969i | \(0.592615\pi\) | |||||||
\(152\) | −5.25031 | −0.425856 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.9552 | −1.84978 | ||||||||
\(155\) | 4.86439 | 0.390717 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.11470 | 0.488006 | 0.244003 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244003 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(158\) | 2.91689 | 0.232055 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.83556 | 0.303227 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00203 | −0.470116 | −0.235058 | − | 0.971981i | \(-0.575528\pi\) | ||||
−0.235058 | + | 0.971981i | \(0.575528\pi\) | |||||||
\(164\) | 2.21152 | 0.172691 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.33395 | 0.181150 | ||||||||
\(167\) | −12.4878 | −0.966338 | −0.483169 | − | 0.875527i | \(-0.660514\pi\) | ||||
−0.483169 | + | 0.875527i | \(0.660514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.91453 | −0.147271 | ||||||||
\(170\) | −0.591040 | −0.0453307 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.63867 | 0.201196 | ||||||||
\(173\) | 3.79092 | 0.288218 | 0.144109 | − | 0.989562i | \(-0.453968\pi\) | ||||
0.144109 | + | 0.989562i | \(0.453968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −49.3532 | −3.73075 | ||||||||
\(176\) | 4.51702 | 0.340483 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.50801 | 0.412842 | ||||||||
\(179\) | −0.453414 | −0.0338898 | −0.0169449 | − | 0.999856i | \(-0.505394\pi\) | ||||
−0.0169449 | + | 0.999856i | \(0.505394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.83553 | −0.582410 | −0.291205 | − | 0.956661i | \(-0.594056\pi\) | ||||
−0.291205 | + | 0.956661i | \(0.594056\pi\) | |||||||
\(182\) | 16.9202 | 1.25421 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.0987 | 1.25712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.696050 | −0.0509002 | ||||||||
\(188\) | 1.10906 | 0.0808865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.1378 | −1.46095 | ||||||||
\(191\) | −15.3660 | −1.11184 | −0.555921 | − | 0.831235i | \(-0.687634\pi\) | ||||
−0.555921 | + | 0.831235i | \(0.687634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.77768 | 0.631831 | 0.315915 | − | 0.948787i | \(-0.397688\pi\) | ||||
0.315915 | + | 0.948787i | \(0.397688\pi\) | |||||||
\(194\) | 13.1549 | 0.944464 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.8261 | 1.34472 | ||||||||
\(197\) | −8.01971 | −0.571381 | −0.285690 | − | 0.958322i | \(-0.592223\pi\) | ||||
−0.285690 | + | 0.958322i | \(0.592223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.20296 | 0.439716 | 0.219858 | − | 0.975532i | \(-0.429441\pi\) | ||||
0.219858 | + | 0.975532i | \(0.429441\pi\) | |||||||
\(200\) | 9.71149 | 0.686706 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.51687 | −0.458526 | ||||||||
\(203\) | 26.5978 | 1.86680 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.48242 | 0.592438 | ||||||||
\(206\) | −5.64524 | −0.393322 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.32949 | −0.230858 | ||||||||
\(209\) | −23.7157 | −1.64045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1371 | −1.11092 | −0.555461 | − | 0.831542i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831542i | \(0.687458\pi\) | |||||||
\(212\) | 4.28457 | 0.294265 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.79406 | 0.464433 | ||||||||
\(215\) | 10.1208 | 0.690230 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.44510 | −0.437522 | ||||||||
\(218\) | −5.83285 | −0.395050 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.3253 | 1.16807 | ||||||||
\(221\) | 0.513057 | 0.0345120 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.15732 | −0.613219 | −0.306610 | − | 0.951835i | \(-0.599195\pi\) | ||||
−0.306610 | + | 0.951835i | \(0.599195\pi\) | |||||||
\(224\) | −5.08193 | −0.339551 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6584 | 0.975062 | ||||||||
\(227\) | 9.40435 | 0.624188 | 0.312094 | − | 0.950051i | \(-0.398970\pi\) | ||||
0.312094 | + | 0.950051i | \(0.398970\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.61058 | 0.238594 | 0.119297 | − | 0.992859i | \(-0.461936\pi\) | ||||
0.119297 | + | 0.992859i | \(0.461936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.23379 | −0.343615 | ||||||||
\(233\) | 0.558599 | 0.0365950 | 0.0182975 | − | 0.999833i | \(-0.494175\pi\) | ||||
0.0182975 | + | 0.999833i | \(0.494175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.25386 | 0.277491 | ||||||||
\(236\) | 3.22790 | 0.210118 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.783101 | 0.0507609 | ||||||||
\(239\) | −19.0720 | −1.23366 | −0.616832 | − | 0.787095i | \(-0.711584\pi\) | ||||
−0.616832 | + | 0.787095i | \(0.711584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6475 | 1.26561 | 0.632805 | − | 0.774311i | \(-0.281904\pi\) | ||||
0.632805 | + | 0.774311i | \(0.281904\pi\) | |||||||
\(242\) | 9.40343 | 0.604476 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.1399 | 0.841197 | ||||||||
\(245\) | 72.2084 | 4.61323 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.4808 | 1.11228 | ||||||||
\(248\) | 1.26824 | 0.0805331 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.0712 | 1.14292 | ||||||||
\(251\) | −19.1101 | −1.20622 | −0.603111 | − | 0.797657i | \(-0.706072\pi\) | ||||
−0.603111 | + | 0.797657i | \(0.706072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.1093 | −0.697056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.8927 | −1.61514 | −0.807572 | − | 0.589769i | \(-0.799219\pi\) | ||||
−0.807572 | + | 0.589769i | \(0.799219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.6550 | −1.40772 | ||||||||
\(260\) | −12.7704 | −0.791988 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.08032 | 0.128523 | ||||||||
\(263\) | 20.1945 | 1.24525 | 0.622623 | − | 0.782522i | \(-0.286067\pi\) | ||||
0.622623 | + | 0.782522i | \(0.286067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4337 | 1.00951 | ||||||||
\(266\) | 26.6817 | 1.63596 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.4839 | 0.640409 | ||||||||
\(269\) | 27.6781 | 1.68756 | 0.843780 | − | 0.536689i | \(-0.180325\pi\) | ||||
0.843780 | + | 0.536689i | \(0.180325\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.58260 | −0.582101 | −0.291051 | − | 0.956708i | \(-0.594005\pi\) | ||||
−0.291051 | + | 0.956708i | \(0.594005\pi\) | |||||||
\(272\) | −0.154095 | −0.00934338 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5855 | 1.00197 | ||||||||
\(275\) | 43.8670 | 2.64528 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.7038 | 1.24397 | 0.621986 | − | 0.783028i | \(-0.286326\pi\) | ||||
0.621986 | + | 0.783028i | \(0.286326\pi\) | |||||||
\(278\) | 4.74700 | 0.284706 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.4920 | −1.16487 | ||||||||
\(281\) | −27.0825 | −1.61561 | −0.807803 | − | 0.589452i | \(-0.799344\pi\) | ||||
−0.807803 | + | 0.589452i | \(0.799344\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1337 | 1.07794 | 0.538968 | − | 0.842326i | \(-0.318814\pi\) | ||||
0.538968 | + | 0.842326i | \(0.318814\pi\) | |||||||
\(284\) | 14.2586 | 0.846095 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.0393 | −0.889295 | ||||||||
\(287\) | −11.2388 | −0.663407 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9763 | −0.998603 | ||||||||
\(290\) | −20.0745 | −1.17882 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.20430 | 0.363079 | ||||||||
\(293\) | 22.2447 | 1.29955 | 0.649775 | − | 0.760126i | \(-0.274863\pi\) | ||||
0.649775 | + | 0.760126i | \(0.274863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.3808 | 0.720837 | ||||||||
\(296\) | 4.45795 | 0.259113 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.0234 | −0.986137 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4095 | −0.772912 | ||||||||
\(302\) | −7.05024 | −0.405696 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.25031 | −0.301126 | ||||||||
\(305\) | 50.3989 | 2.88583 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0626 | −0.631377 | −0.315689 | − | 0.948863i | \(-0.602236\pi\) | ||||
−0.315689 | + | 0.948863i | \(0.602236\pi\) | |||||||
\(308\) | −22.9552 | −1.30799 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.86439 | 0.276279 | ||||||||
\(311\) | −9.31522 | −0.528218 | −0.264109 | − | 0.964493i | \(-0.585078\pi\) | ||||
−0.264109 | + | 0.964493i | \(0.585078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9866 | 1.41233 | 0.706163 | − | 0.708049i | \(-0.250424\pi\) | ||||
0.706163 | + | 0.708049i | \(0.250424\pi\) | |||||||
\(314\) | 6.11470 | 0.345073 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.91689 | 0.164088 | ||||||||
\(317\) | 17.8811 | 1.00430 | 0.502152 | − | 0.864779i | \(-0.332542\pi\) | ||||
0.502152 | + | 0.864779i | \(0.332542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.6411 | −1.32365 | ||||||||
\(320\) | 3.83556 | 0.214414 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.809046 | 0.0450165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.3343 | −1.79358 | ||||||||
\(326\) | −6.00203 | −0.332422 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.21152 | 0.122111 | ||||||||
\(329\) | −5.63617 | −0.310732 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.40749 | −0.242258 | −0.121129 | − | 0.992637i | \(-0.538651\pi\) | ||||
−0.121129 | + | 0.992637i | \(0.538651\pi\) | |||||||
\(332\) | 2.33395 | 0.128092 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.4878 | −0.683304 | ||||||||
\(335\) | 40.2118 | 2.19700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.5323 | −0.737153 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(338\) | −1.91453 | −0.104136 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.591040 | −0.0320537 | ||||||||
\(341\) | 5.72865 | 0.310224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60.0993 | −3.24506 | ||||||||
\(344\) | 2.63867 | 0.142267 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.79092 | 0.203801 | ||||||||
\(347\) | −18.5971 | −0.998345 | −0.499173 | − | 0.866503i | \(-0.666363\pi\) | ||||
−0.499173 | + | 0.866503i | \(0.666363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.177691 | 0.00951160 | 0.00475580 | − | 0.999989i | \(-0.498486\pi\) | ||||
0.00475580 | + | 0.999989i | \(0.498486\pi\) | |||||||
\(350\) | −49.3532 | −2.63804 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.51702 | 0.240758 | ||||||||
\(353\) | 13.5394 | 0.720632 | 0.360316 | − | 0.932830i | \(-0.382669\pi\) | ||||
0.360316 | + | 0.932830i | \(0.382669\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.6898 | 2.90264 | ||||||||
\(356\) | 5.50801 | 0.291924 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.453414 | −0.0239637 | ||||||||
\(359\) | 16.6948 | 0.881117 | 0.440558 | − | 0.897724i | \(-0.354781\pi\) | ||||
0.440558 | + | 0.897724i | \(0.354781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.56572 | 0.450827 | ||||||||
\(362\) | −7.83553 | −0.411826 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.9202 | 0.886861 | ||||||||
\(365\) | 23.7969 | 1.24559 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.8815 | −1.50760 | −0.753800 | − | 0.657104i | \(-0.771781\pi\) | ||||
−0.753800 | + | 0.657104i | \(0.771781\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.0987 | 0.888921 | ||||||||
\(371\) | −21.7739 | −1.13044 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.5934 | 1.63585 | 0.817923 | − | 0.575327i | \(-0.195125\pi\) | ||||
0.817923 | + | 0.575327i | \(0.195125\pi\) | |||||||
\(374\) | −0.696050 | −0.0359919 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.10906 | 0.0571954 | ||||||||
\(377\) | 17.4258 | 0.897477 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6640 | 0.753237 | 0.376618 | − | 0.926369i | \(-0.377087\pi\) | ||||
0.376618 | + | 0.926369i | \(0.377087\pi\) | |||||||
\(380\) | −20.1378 | −1.03305 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.3660 | −0.786190 | ||||||||
\(383\) | −6.99286 | −0.357318 | −0.178659 | − | 0.983911i | \(-0.557176\pi\) | ||||
−0.178659 | + | 0.983911i | \(0.557176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −88.0459 | −4.48723 | ||||||||
\(386\) | 8.77768 | 0.446772 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.1549 | 0.667837 | ||||||||
\(389\) | −26.8167 | −1.35966 | −0.679830 | − | 0.733370i | \(-0.737946\pi\) | ||||
−0.679830 | + | 0.733370i | \(0.737946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.8261 | 0.950860 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.01971 | −0.404027 | ||||||||
\(395\) | 11.1879 | 0.562924 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.49361 | −0.376093 | −0.188047 | − | 0.982160i | \(-0.560216\pi\) | ||||
−0.188047 | + | 0.982160i | \(0.560216\pi\) | |||||||
\(398\) | 6.20296 | 0.310926 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.71149 | 0.485575 | ||||||||
\(401\) | −32.4616 | −1.62106 | −0.810528 | − | 0.585699i | \(-0.800820\pi\) | ||||
−0.810528 | + | 0.585699i | \(0.800820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.22258 | −0.210341 | ||||||||
\(404\) | −6.51687 | −0.324227 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.5978 | 1.32003 | ||||||||
\(407\) | 20.1367 | 0.998137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4518 | −0.615703 | −0.307852 | − | 0.951434i | \(-0.599610\pi\) | ||||
−0.307852 | + | 0.951434i | \(0.599610\pi\) | |||||||
\(410\) | 8.48242 | 0.418917 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.64524 | −0.278121 | ||||||||
\(413\) | −16.4040 | −0.807186 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.95201 | 0.439437 | ||||||||
\(416\) | −3.32949 | −0.163241 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.7157 | −1.15997 | ||||||||
\(419\) | −37.6239 | −1.83805 | −0.919025 | − | 0.394199i | \(-0.871022\pi\) | ||||
−0.919025 | + | 0.394199i | \(0.871022\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.4657 | −1.43607 | −0.718035 | − | 0.696007i | \(-0.754958\pi\) | ||||
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(422\) | −16.1371 | −0.785541 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.28457 | 0.208077 | ||||||||
\(425\) | −1.49649 | −0.0725906 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −66.7762 | −3.23153 | ||||||||
\(428\) | 6.79406 | 0.328404 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.1208 | 0.488066 | ||||||||
\(431\) | −26.4006 | −1.27167 | −0.635836 | − | 0.771824i | \(-0.719345\pi\) | ||||
−0.635836 | + | 0.771824i | \(0.719345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.67389 | 0.224613 | 0.112306 | − | 0.993674i | \(-0.464176\pi\) | ||||
0.112306 | + | 0.993674i | \(0.464176\pi\) | |||||||
\(434\) | −6.44510 | −0.309374 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.83285 | −0.279343 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9955 | −0.906605 | −0.453303 | − | 0.891357i | \(-0.649754\pi\) | ||||
−0.453303 | + | 0.891357i | \(0.649754\pi\) | |||||||
\(440\) | 17.3253 | 0.825950 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.513057 | 0.0244036 | ||||||||
\(443\) | −6.95701 | −0.330537 | −0.165269 | − | 0.986249i | \(-0.552849\pi\) | ||||
−0.165269 | + | 0.986249i | \(0.552849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.1263 | 1.00148 | ||||||||
\(446\) | −9.15732 | −0.433612 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.08193 | −0.240099 | ||||||||
\(449\) | −19.2356 | −0.907784 | −0.453892 | − | 0.891057i | \(-0.649965\pi\) | ||||
−0.453892 | + | 0.891057i | \(0.649965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.98949 | 0.470387 | ||||||||
\(452\) | 14.6584 | 0.689473 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.40435 | 0.441368 | ||||||||
\(455\) | 64.8985 | 3.04249 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.8469 | 0.694507 | 0.347253 | − | 0.937771i | \(-0.387114\pi\) | ||||
0.347253 | + | 0.937771i | \(0.387114\pi\) | |||||||
\(458\) | 3.61058 | 0.168711 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.15752 | 0.240209 | 0.120105 | − | 0.992761i | \(-0.461677\pi\) | ||||
0.120105 | + | 0.992761i | \(0.461677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4681 | −0.858284 | −0.429142 | − | 0.903237i | \(-0.641184\pi\) | ||||
−0.429142 | + | 0.903237i | \(0.641184\pi\) | |||||||
\(464\) | −5.23379 | −0.242973 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.558599 | 0.0258766 | ||||||||
\(467\) | 33.2249 | 1.53747 | 0.768733 | − | 0.639570i | \(-0.220888\pi\) | ||||
0.768733 | + | 0.639570i | \(0.220888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.2787 | −2.46018 | ||||||||
\(470\) | 4.25386 | 0.196216 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.22790 | 0.148576 | ||||||||
\(473\) | 11.9189 | 0.548031 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −50.9883 | −2.33950 | ||||||||
\(476\) | 0.783101 | 0.0358934 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.0720 | −0.872332 | ||||||||
\(479\) | 20.1872 | 0.922375 | 0.461187 | − | 0.887303i | \(-0.347424\pi\) | ||||
0.461187 | + | 0.887303i | \(0.347424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.8427 | −0.676769 | ||||||||
\(482\) | 19.6475 | 0.894921 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.40343 | 0.427429 | ||||||||
\(485\) | 50.4562 | 2.29110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.03341 | −0.0468284 | −0.0234142 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234142 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(488\) | 13.1399 | 0.594816 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 72.2084 | 3.26204 | ||||||||
\(491\) | −8.77567 | −0.396040 | −0.198020 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198020 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.806502 | 0.0363230 | ||||||||
\(494\) | 17.4808 | 0.786499 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.26824 | 0.0569455 | ||||||||
\(497\) | −72.4615 | −3.25034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.9855 | 1.47663 | 0.738316 | − | 0.674455i | \(-0.235621\pi\) | ||||
0.738316 | + | 0.674455i | \(0.235621\pi\) | |||||||
\(500\) | 18.0712 | 0.808168 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.1101 | −0.852927 | ||||||||
\(503\) | 43.2295 | 1.92751 | 0.963754 | − | 0.266794i | \(-0.0859642\pi\) | ||||
0.963754 | + | 0.266794i | \(0.0859642\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.9958 | −1.11230 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.1093 | −0.492893 | ||||||||
\(509\) | −23.1012 | −1.02394 | −0.511972 | − | 0.859002i | \(-0.671085\pi\) | ||||
−0.511972 | + | 0.859002i | \(0.671085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.5298 | −1.39480 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.8927 | −1.14208 | ||||||||
\(515\) | −21.6526 | −0.954129 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.00964 | 0.220324 | ||||||||
\(518\) | −22.6550 | −0.995405 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.7704 | −0.560020 | ||||||||
\(521\) | 15.6277 | 0.684660 | 0.342330 | − | 0.939580i | \(-0.388784\pi\) | ||||
0.342330 | + | 0.939580i | \(0.388784\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8417 | 0.955070 | 0.477535 | − | 0.878613i | \(-0.341530\pi\) | ||||
0.477535 | + | 0.878613i | \(0.341530\pi\) | |||||||
\(524\) | 2.08032 | 0.0908793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.1945 | 0.880521 | ||||||||
\(527\) | −0.195429 | −0.00851302 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 16.4337 | 0.713834 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.6817 | 1.15680 | ||||||||
\(533\) | −7.36324 | −0.318937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.0590 | 1.12663 | ||||||||
\(536\) | 10.4839 | 0.452837 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.6781 | 1.19329 | ||||||||
\(539\) | 85.0376 | 3.66283 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.2889 | 1.17324 | 0.586620 | − | 0.809862i | \(-0.300458\pi\) | ||||
0.586620 | + | 0.809862i | \(0.300458\pi\) | |||||||
\(542\) | −9.58260 | −0.411608 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.154095 | −0.00660677 | ||||||||
\(545\) | −22.3722 | −0.958320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.17954 | −0.178704 | −0.0893521 | − | 0.996000i | \(-0.528480\pi\) | ||||
−0.0893521 | + | 0.996000i | \(0.528480\pi\) | |||||||
\(548\) | 16.5855 | 0.708496 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 43.8670 | 1.87049 | ||||||||
\(551\) | 27.4790 | 1.17065 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8234 | −0.630356 | ||||||||
\(554\) | 20.7038 | 0.879621 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.74700 | 0.201318 | ||||||||
\(557\) | 24.6304 | 1.04362 | 0.521812 | − | 0.853060i | \(-0.325256\pi\) | ||||
0.521812 | + | 0.853060i | \(0.325256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.78540 | −0.371583 | ||||||||
\(560\) | −19.4920 | −0.823689 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.0825 | −1.14241 | ||||||||
\(563\) | 7.92169 | 0.333859 | 0.166930 | − | 0.985969i | \(-0.446615\pi\) | ||||
0.166930 | + | 0.985969i | \(0.446615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 56.2231 | 2.36532 | ||||||||
\(566\) | 18.1337 | 0.762216 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.2586 | 0.598280 | ||||||||
\(569\) | −28.0564 | −1.17618 | −0.588092 | − | 0.808794i | \(-0.700121\pi\) | ||||
−0.588092 | + | 0.808794i | \(0.700121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4816 | 1.40116 | 0.700582 | − | 0.713572i | \(-0.252924\pi\) | ||||
0.700582 | + | 0.713572i | \(0.252924\pi\) | |||||||
\(572\) | −15.0393 | −0.628826 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.2388 | −0.469099 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.8994 | 1.11984 | 0.559919 | − | 0.828548i | \(-0.310832\pi\) | ||||
0.559919 | + | 0.828548i | \(0.310832\pi\) | |||||||
\(578\) | −16.9763 | −0.706119 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.0745 | −0.833549 | ||||||||
\(581\) | −11.8610 | −0.492077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.3535 | 0.801538 | ||||||||
\(584\) | 6.20430 | 0.256736 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.2447 | 0.918921 | ||||||||
\(587\) | −27.8283 | −1.14860 | −0.574298 | − | 0.818647i | \(-0.694725\pi\) | ||||
−0.574298 | + | 0.818647i | \(0.694725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.65863 | −0.274364 | ||||||||
\(590\) | 12.3808 | 0.509709 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.45795 | 0.183221 | ||||||||
\(593\) | 25.8705 | 1.06237 | 0.531187 | − | 0.847255i | \(-0.321746\pi\) | ||||
0.531187 | + | 0.847255i | \(0.321746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00363 | 0.123137 | ||||||||
\(596\) | −17.0234 | −0.697304 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.3667 | −0.913878 | −0.456939 | − | 0.889498i | \(-0.651054\pi\) | ||||
−0.456939 | + | 0.889498i | \(0.651054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.9093 | −1.13844 | −0.569221 | − | 0.822184i | \(-0.692755\pi\) | ||||
−0.569221 | + | 0.822184i | \(0.692755\pi\) | |||||||
\(602\) | −13.4095 | −0.546532 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.05024 | −0.286870 | ||||||||
\(605\) | 36.0674 | 1.46635 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.1033 | −0.450670 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(608\) | −5.25031 | −0.212928 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 50.3989 | 2.04059 | ||||||||
\(611\) | −3.69260 | −0.149387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.48067 | −0.100193 | −0.0500966 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500966 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(614\) | −11.0626 | −0.446451 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.9552 | −0.924891 | ||||||||
\(617\) | −18.2825 | −0.736025 | −0.368012 | − | 0.929821i | \(-0.619962\pi\) | ||||
−0.368012 | + | 0.929821i | \(0.619962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.6082 | 1.31064 | 0.655318 | − | 0.755353i | \(-0.272535\pi\) | ||||
0.655318 | + | 0.755353i | \(0.272535\pi\) | |||||||
\(620\) | 4.86439 | 0.195359 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.31522 | −0.373506 | ||||||||
\(623\) | −27.9913 | −1.12145 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.7556 | 0.830225 | ||||||||
\(626\) | 24.9866 | 0.998666 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.11470 | 0.244003 | ||||||||
\(629\) | −0.686949 | −0.0273904 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.2094 | −0.446240 | −0.223120 | − | 0.974791i | \(-0.571624\pi\) | ||||
−0.223120 | + | 0.974791i | \(0.571624\pi\) | |||||||
\(632\) | 2.91689 | 0.116028 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.8811 | 0.710150 | ||||||||
\(635\) | −42.6102 | −1.69093 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.6811 | −2.48352 | ||||||||
\(638\) | −23.6411 | −0.935961 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.83556 | 0.151614 | ||||||||
\(641\) | 5.46480 | 0.215847 | 0.107923 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107923 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2191 | 0.521310 | 0.260655 | − | 0.965432i | \(-0.416061\pi\) | ||||
0.260655 | + | 0.965432i | \(0.416061\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.809046 | 0.0318315 | ||||||||
\(647\) | 18.6775 | 0.734289 | 0.367144 | − | 0.930164i | \(-0.380336\pi\) | ||||
0.367144 | + | 0.930164i | \(0.380336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.5805 | 0.572333 | ||||||||
\(650\) | −32.3343 | −1.26825 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00203 | −0.235058 | ||||||||
\(653\) | −7.33246 | −0.286941 | −0.143471 | − | 0.989655i | \(-0.545826\pi\) | ||||
−0.143471 | + | 0.989655i | \(0.545826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.97919 | 0.311773 | ||||||||
\(656\) | 2.21152 | 0.0863455 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.63617 | −0.219721 | ||||||||
\(659\) | −44.6806 | −1.74051 | −0.870255 | − | 0.492602i | \(-0.836046\pi\) | ||||
−0.870255 | + | 0.492602i | \(0.836046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.9982 | 0.816736 | 0.408368 | − | 0.912817i | \(-0.366098\pi\) | ||||
0.408368 | + | 0.912817i | \(0.366098\pi\) | |||||||
\(662\) | −4.40749 | −0.171302 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.33395 | 0.0905750 | ||||||||
\(665\) | 102.339 | 3.96854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −12.4878 | −0.483169 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 40.2118 | 1.55352 | ||||||||
\(671\) | 59.3532 | 2.29131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.0107 | 1.07973 | 0.539867 | − | 0.841750i | \(-0.318474\pi\) | ||||
0.539867 | + | 0.841750i | \(0.318474\pi\) | |||||||
\(674\) | −13.5323 | −0.521246 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.91453 | −0.0736356 | ||||||||
\(677\) | −43.2019 | −1.66038 | −0.830192 | − | 0.557477i | \(-0.811769\pi\) | ||||
−0.830192 | + | 0.557477i | \(0.811769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −66.8522 | −2.56555 | ||||||||
\(680\) | −0.591040 | −0.0226654 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.72865 | 0.219361 | ||||||||
\(683\) | −23.1421 | −0.885507 | −0.442754 | − | 0.896643i | \(-0.645998\pi\) | ||||
−0.442754 | + | 0.896643i | \(0.645998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.6145 | 2.43059 | ||||||||
\(686\) | −60.0993 | −2.29460 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.63867 | 0.100598 | ||||||||
\(689\) | −14.2654 | −0.543469 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0298 | 1.18043 | 0.590215 | − | 0.807246i | \(-0.299043\pi\) | ||||
0.590215 | + | 0.807246i | \(0.299043\pi\) | |||||||
\(692\) | 3.79092 | 0.144109 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5971 | −0.705937 | ||||||||
\(695\) | 18.2074 | 0.690646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.340785 | −0.0129081 | ||||||||
\(698\) | 0.177691 | 0.00672572 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −49.3532 | −1.86537 | ||||||||
\(701\) | −13.3405 | −0.503863 | −0.251931 | − | 0.967745i | \(-0.581066\pi\) | ||||
−0.251931 | + | 0.967745i | \(0.581066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.4056 | −0.882760 | ||||||||
\(704\) | 4.51702 | 0.170241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.5394 | 0.509564 | ||||||||
\(707\) | 33.1183 | 1.24554 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.0894 | −1.61826 | −0.809128 | − | 0.587632i | \(-0.800060\pi\) | ||||
−0.809128 | + | 0.587632i | \(0.800060\pi\) | |||||||
\(710\) | 54.6898 | 2.05247 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.50801 | 0.206421 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.6842 | −2.15727 | ||||||||
\(716\) | −0.453414 | −0.0169449 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.6948 | 0.623043 | ||||||||
\(719\) | 20.4222 | 0.761618 | 0.380809 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380809 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.6887 | 1.06842 | ||||||||
\(722\) | 8.56572 | 0.318783 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.83553 | −0.291205 | ||||||||
\(725\) | −50.8280 | −1.88770 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8691 | 0.551463 | 0.275732 | − | 0.961235i | \(-0.411080\pi\) | ||||
0.275732 | + | 0.961235i | \(0.411080\pi\) | |||||||
\(728\) | 16.9202 | 0.627105 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.7969 | 0.880764 | ||||||||
\(731\) | −0.406605 | −0.0150388 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.4036 | −0.975241 | −0.487620 | − | 0.873056i | \(-0.662135\pi\) | ||||
−0.487620 | + | 0.873056i | \(0.662135\pi\) | |||||||
\(734\) | −28.8815 | −1.06603 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.3561 | 1.74439 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.98205 | −0.330410 | −0.165205 | − | 0.986259i | \(-0.552829\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552829\pi\) | |||||||
\(740\) | 17.0987 | 0.628562 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.7739 | −0.799345 | ||||||||
\(743\) | −2.40734 | −0.0883169 | −0.0441584 | − | 0.999025i | \(-0.514061\pi\) | ||||
−0.0441584 | + | 0.999025i | \(0.514061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −65.2941 | −2.39219 | ||||||||
\(746\) | 31.5934 | 1.15672 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.696050 | −0.0254501 | ||||||||
\(749\) | −34.5270 | −1.26159 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.7899 | −1.05056 | −0.525279 | − | 0.850930i | \(-0.676039\pi\) | ||||
−0.525279 | + | 0.850930i | \(0.676039\pi\) | |||||||
\(752\) | 1.10906 | 0.0404433 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.4258 | 0.634612 | ||||||||
\(755\) | −27.0416 | −0.984145 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.9406 | −1.23359 | −0.616796 | − | 0.787123i | \(-0.711570\pi\) | ||||
−0.616796 | + | 0.787123i | \(0.711570\pi\) | |||||||
\(758\) | 14.6640 | 0.532619 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.1378 | −0.730476 | ||||||||
\(761\) | −33.7946 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.6421 | 1.07312 | ||||||||
\(764\) | −15.3660 | −0.555921 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.99286 | −0.252662 | ||||||||
\(767\) | −10.7472 | −0.388060 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.8036 | 1.90415 | 0.952073 | − | 0.305872i | \(-0.0989478\pi\) | ||||
0.952073 | + | 0.305872i | \(0.0989478\pi\) | |||||||
\(770\) | −88.0459 | −3.17295 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.77768 | 0.315915 | ||||||||
\(773\) | −1.46268 | −0.0526089 | −0.0263045 | − | 0.999654i | \(-0.508374\pi\) | ||||
−0.0263045 | + | 0.999654i | \(0.508374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3165 | 0.442421 | ||||||||
\(776\) | 13.1549 | 0.472232 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.8167 | −0.961425 | ||||||||
\(779\) | −11.6112 | −0.416014 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.4065 | 2.30465 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.8261 | 0.672359 | ||||||||
\(785\) | 23.4533 | 0.837084 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3652 | −0.619002 | −0.309501 | − | 0.950899i | \(-0.600162\pi\) | ||||
−0.309501 | + | 0.950899i | \(0.600162\pi\) | |||||||
\(788\) | −8.01971 | −0.285690 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.1879 | 0.398047 | ||||||||
\(791\) | −74.4930 | −2.64867 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43.7492 | −1.55358 | ||||||||
\(794\) | −7.49361 | −0.265938 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.20296 | 0.219858 | ||||||||
\(797\) | 52.5218 | 1.86042 | 0.930209 | − | 0.367029i | \(-0.119625\pi\) | ||||
0.930209 | + | 0.367029i | \(0.119625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.170901 | −0.00604603 | ||||||||
\(800\) | 9.71149 | 0.343353 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.4616 | −1.14626 | ||||||||
\(803\) | 28.0249 | 0.988978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.22258 | −0.148734 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.51687 | −0.229263 | ||||||||
\(809\) | 36.6261 | 1.28770 | 0.643852 | − | 0.765150i | \(-0.277335\pi\) | ||||
0.643852 | + | 0.765150i | \(0.277335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.6571 | 1.39255 | 0.696274 | − | 0.717776i | \(-0.254840\pi\) | ||||
0.696274 | + | 0.717776i | \(0.254840\pi\) | |||||||
\(812\) | 26.5978 | 0.933400 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.1367 | 0.705789 | ||||||||
\(815\) | −23.0211 | −0.806395 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8538 | −0.484683 | ||||||||
\(818\) | −12.4518 | −0.435368 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.48242 | 0.296219 | ||||||||
\(821\) | 30.7368 | 1.07272 | 0.536362 | − | 0.843988i | \(-0.319798\pi\) | ||||
0.536362 | + | 0.843988i | \(0.319798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1882 | 0.564286 | 0.282143 | − | 0.959372i | \(-0.408955\pi\) | ||||
0.282143 | + | 0.959372i | \(0.408955\pi\) | |||||||
\(824\) | −5.64524 | −0.196661 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.4040 | −0.570767 | ||||||||
\(827\) | −53.7834 | −1.87023 | −0.935115 | − | 0.354344i | \(-0.884704\pi\) | ||||
−0.935115 | + | 0.354344i | \(0.884704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.11983 | 0.212550 | 0.106275 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106275 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(830\) | 8.95201 | 0.310729 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.32949 | −0.115429 | ||||||||
\(833\) | −2.90100 | −0.100514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.8978 | −1.65757 | ||||||||
\(836\) | −23.7157 | −0.820225 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37.6239 | −1.29970 | ||||||||
\(839\) | 32.1106 | 1.10858 | 0.554290 | − | 0.832323i | \(-0.312990\pi\) | ||||
0.554290 | + | 0.832323i | \(0.312990\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.60740 | −0.0554274 | ||||||||
\(842\) | −29.4657 | −1.01545 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.1371 | −0.555461 | ||||||||
\(845\) | −7.34327 | −0.252616 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.7876 | −1.64200 | ||||||||
\(848\) | 4.28457 | 0.147133 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.49649 | −0.0513293 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.9558 | 0.854469 | 0.427234 | − | 0.904141i | \(-0.359488\pi\) | ||||
0.427234 | + | 0.904141i | \(0.359488\pi\) | |||||||
\(854\) | −66.7762 | −2.28503 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.79406 | 0.232216 | ||||||||
\(857\) | 45.2936 | 1.54720 | 0.773599 | − | 0.633675i | \(-0.218454\pi\) | ||||
0.773599 | + | 0.633675i | \(0.218454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.5676 | −1.93006 | −0.965031 | − | 0.262136i | \(-0.915573\pi\) | ||||
−0.965031 | + | 0.262136i | \(0.915573\pi\) | |||||||
\(860\) | 10.1208 | 0.345115 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.4006 | −0.899208 | ||||||||
\(863\) | −11.1251 | −0.378701 | −0.189351 | − | 0.981910i | \(-0.560638\pi\) | ||||
−0.189351 | + | 0.981910i | \(0.560638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.5403 | 0.494384 | ||||||||
\(866\) | 4.67389 | 0.158825 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.44510 | −0.218761 | ||||||||
\(869\) | 13.1756 | 0.446953 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.9061 | −1.18275 | ||||||||
\(872\) | −5.83285 | −0.197525 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −91.8366 | −3.10464 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0892 | −1.35372 | −0.676858 | − | 0.736114i | \(-0.736659\pi\) | ||||
−0.676858 | + | 0.736114i | \(0.736659\pi\) | |||||||
\(878\) | −18.9955 | −0.641067 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.3253 | 0.584035 | ||||||||
\(881\) | 44.2762 | 1.49170 | 0.745851 | − | 0.666113i | \(-0.232043\pi\) | ||||
0.745851 | + | 0.666113i | \(0.232043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.7486 | 1.53956 | 0.769781 | − | 0.638308i | \(-0.220365\pi\) | ||||
0.769781 | + | 0.638308i | \(0.220365\pi\) | |||||||
\(884\) | 0.513057 | 0.0172560 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.95701 | −0.233725 | ||||||||
\(887\) | 1.14721 | 0.0385195 | 0.0192597 | − | 0.999815i | \(-0.493869\pi\) | ||||
0.0192597 | + | 0.999815i | \(0.493869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.4565 | 1.89349 | ||||||||
\(890\) | 21.1263 | 0.708154 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.15732 | −0.306610 | ||||||||
\(893\) | −5.82291 | −0.194856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.73910 | −0.0581316 | ||||||||
\(896\) | −5.08193 | −0.169776 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.2356 | −0.641900 | ||||||||
\(899\) | −6.63769 | −0.221379 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.660231 | −0.0219955 | ||||||||
\(902\) | 9.98949 | 0.332614 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.6584 | 0.487531 | ||||||||
\(905\) | −30.0536 | −0.999016 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.31302 | −0.0435980 | −0.0217990 | − | 0.999762i | \(-0.506939\pi\) | ||||
−0.0217990 | + | 0.999762i | \(0.506939\pi\) | |||||||
\(908\) | 9.40435 | 0.312094 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 64.8985 | 2.15136 | ||||||||
\(911\) | 30.7937 | 1.02024 | 0.510120 | − | 0.860103i | \(-0.329601\pi\) | ||||
0.510120 | + | 0.860103i | \(0.329601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.5425 | 0.348906 | ||||||||
\(914\) | 14.8469 | 0.491090 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.61058 | 0.119297 | ||||||||
\(917\) | −10.5721 | −0.349120 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.9421 | 0.459906 | 0.229953 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229953 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.15752 | 0.169854 | ||||||||
\(923\) | −47.4740 | −1.56262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.2934 | 1.42348 | ||||||||
\(926\) | −18.4681 | −0.606898 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.23379 | −0.171808 | ||||||||
\(929\) | −21.2473 | −0.697100 | −0.348550 | − | 0.937290i | \(-0.613326\pi\) | ||||
−0.348550 | + | 0.937290i | \(0.613326\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −98.8426 | −3.23944 | ||||||||
\(932\) | 0.558599 | 0.0182975 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.2249 | 1.08715 | ||||||||
\(935\) | −2.66974 | −0.0873098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.87293 | −0.191860 | −0.0959302 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959302 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(938\) | −53.2787 | −1.73961 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.25386 | 0.138746 | ||||||||
\(941\) | 24.8884 | 0.811337 | 0.405669 | − | 0.914020i | \(-0.367039\pi\) | ||||
0.405669 | + | 0.914020i | \(0.367039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.22790 | 0.105059 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.9189 | 0.387517 | ||||||||
\(947\) | −49.0721 | −1.59463 | −0.797314 | − | 0.603564i | \(-0.793747\pi\) | ||||
−0.797314 | + | 0.603564i | \(0.793747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.6571 | −0.670558 | ||||||||
\(950\) | −50.9883 | −1.65428 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.783101 | 0.0253804 | ||||||||
\(953\) | 28.0932 | 0.910027 | 0.455014 | − | 0.890484i | \(-0.349634\pi\) | ||||
0.455014 | + | 0.890484i | \(0.349634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58.9370 | −1.90716 | ||||||||
\(956\) | −19.0720 | −0.616832 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.1872 | 0.652218 | ||||||||
\(959\) | −84.2863 | −2.72175 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3916 | −0.948115 | ||||||||
\(962\) | −14.8427 | −0.478548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.6475 | 0.632805 | ||||||||
\(965\) | 33.6673 | 1.08379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.6391 | −0.824498 | −0.412249 | − | 0.911071i | \(-0.635257\pi\) | ||||
−0.412249 | + | 0.911071i | \(0.635257\pi\) | |||||||
\(968\) | 9.40343 | 0.302238 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 50.4562 | 1.62005 | ||||||||
\(971\) | −8.44711 | −0.271081 | −0.135540 | − | 0.990772i | \(-0.543277\pi\) | ||||
−0.135540 | + | 0.990772i | \(0.543277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.1240 | −0.773378 | ||||||||
\(974\) | −1.03341 | −0.0331126 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.1399 | 0.420599 | ||||||||
\(977\) | 37.8257 | 1.21015 | 0.605076 | − | 0.796168i | \(-0.293143\pi\) | ||||
0.605076 | + | 0.796168i | \(0.293143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8798 | 0.795160 | ||||||||
\(980\) | 72.2084 | 2.30661 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.77567 | −0.280043 | ||||||||
\(983\) | 0.780538 | 0.0248953 | 0.0124477 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124477 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.7600 | −0.980096 | ||||||||
\(986\) | 0.806502 | 0.0256843 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.4808 | 0.556139 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.0952 | 1.24190 | 0.620950 | − | 0.783850i | \(-0.286747\pi\) | ||||
0.620950 | + | 0.783850i | \(0.286747\pi\) | |||||||
\(992\) | 1.26824 | 0.0402666 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −72.4615 | −2.29834 | ||||||||
\(995\) | 23.7918 | 0.754251 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9119 | −1.29569 | −0.647846 | − | 0.761771i | \(-0.724330\pi\) | ||||
−0.647846 | + | 0.761771i | \(0.724330\pi\) | |||||||
\(998\) | 32.9855 | 1.04414 | ||||||||
\(999\) | 0 | 0 |
(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 | 9522.2.a.cj.1.9 | 10 | ||
3.2 | odd | 2 | 9522.2.a.cg.1.2 | 10 | |||
23.9 | even | 11 | 414.2.i.g.127.1 | ✓ | 20 | ||
23.18 | even | 11 | 414.2.i.g.163.1 | yes | 20 | ||
23.22 | odd | 2 | 9522.2.a.ci.1.2 | 10 | |||
69.32 | odd | 22 | 414.2.i.h.127.2 | yes | 20 | ||
69.41 | odd | 22 | 414.2.i.h.163.2 | yes | 20 | ||
69.68 | even | 2 | 9522.2.a.ch.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.i.g.127.1 | ✓ | 20 | 23.9 | even | 11 | ||
414.2.i.g.163.1 | yes | 20 | 23.18 | even | 11 | ||
414.2.i.h.127.2 | yes | 20 | 69.32 | odd | 22 | ||
414.2.i.h.163.2 | yes | 20 | 69.41 | odd | 22 | ||
9522.2.a.cg.1.2 | 10 | 3.2 | odd | 2 | |||
9522.2.a.ch.1.9 | 10 | 69.68 | even | 2 | |||
9522.2.a.ci.1.2 | 10 | 23.22 | odd | 2 | |||
9522.2.a.cj.1.9 | 10 | 1.1 | even | 1 | trivial |