Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8400,2,Mod(1,8400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8400.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: | \(67.0743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 840) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8400.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.26180 | 0.983468 | 0.491734 | − | 0.870745i | \(-0.336363\pi\) | ||||
0.491734 | + | 0.870745i | \(0.336363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.340173 | −0.0943470 | −0.0471735 | − | 0.998887i | \(-0.515021\pi\) | ||||
−0.0471735 | + | 0.998887i | \(0.515021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.75872 | −1.39670 | −0.698348 | − | 0.715759i | \(-0.746081\pi\) | ||||
−0.698348 | + | 0.715759i | \(0.746081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.49693 | 1.49050 | 0.745249 | − | 0.666786i | \(-0.232331\pi\) | ||||
0.745249 | + | 0.666786i | \(0.232331\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.49693 | −1.77173 | −0.885866 | − | 0.463941i | \(-0.846435\pi\) | ||||
−0.885866 | + | 0.463941i | \(0.846435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34017 | 1.49794 | 0.748970 | − | 0.662604i | \(-0.230549\pi\) | ||||
0.748970 | + | 0.662604i | \(0.230549\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.26180 | 0.567806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.15676 | 1.01216 | 0.506082 | − | 0.862485i | \(-0.331093\pi\) | ||||
0.506082 | + | 0.862485i | \(0.331093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.340173 | −0.0544713 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.340173 | 0.0531261 | 0.0265630 | − | 0.999647i | \(-0.491544\pi\) | ||||
0.0265630 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.68035 | −1.32374 | −0.661870 | − | 0.749618i | \(-0.730237\pi\) | ||||
−0.661870 | + | 0.749618i | \(0.730237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.75872 | −0.806383 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.34017 | 1.14561 | 0.572805 | − | 0.819691i | \(-0.305855\pi\) | ||||
0.572805 | + | 0.819691i | \(0.305855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.49693 | 0.860539 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.83710 | −0.890115 | −0.445057 | − | 0.895502i | \(-0.646817\pi\) | ||||
−0.445057 | + | 0.895502i | \(0.646817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.3607 | 1.96674 | 0.983368 | − | 0.181627i | \(-0.0581363\pi\) | ||||
0.983368 | + | 0.181627i | \(0.0581363\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.8371 | 1.81264 | 0.906320 | − | 0.422592i | \(-0.138880\pi\) | ||||
0.906320 | + | 0.422592i | \(0.138880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.49693 | −1.02291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9421 | 1.89198 | 0.945992 | − | 0.324190i | \(-0.105092\pi\) | ||||
0.945992 | + | 0.324190i | \(0.105092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50307 | 0.175921 | 0.0879606 | − | 0.996124i | \(-0.471965\pi\) | ||||
0.0879606 | + | 0.996124i | \(0.471965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.26180 | 0.371716 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.68035 | −0.976615 | −0.488308 | − | 0.872672i | \(-0.662386\pi\) | ||||
−0.488308 | + | 0.872672i | \(0.662386\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.83710 | 0.750469 | 0.375235 | − | 0.926930i | \(-0.377562\pi\) | ||||
0.375235 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1773 | −1.60879 | −0.804394 | − | 0.594096i | \(-0.797510\pi\) | ||||
−0.804394 | + | 0.594096i | \(0.797510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.340173 | −0.0356598 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.34017 | 0.864836 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.49693 | 0.659663 | 0.329832 | − | 0.944040i | \(-0.393008\pi\) | ||||
0.329832 | + | 0.944040i | \(0.393008\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.26180 | 0.327823 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.18342 | −0.217258 | −0.108629 | − | 0.994082i | \(-0.534646\pi\) | ||||
−0.108629 | + | 0.994082i | \(0.534646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.84324 | −0.575752 | −0.287876 | − | 0.957668i | \(-0.592949\pi\) | ||||
−0.287876 | + | 0.957668i | \(0.592949\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.18342 | −0.791121 | −0.395560 | − | 0.918440i | \(-0.629450\pi\) | ||||
−0.395560 | + | 0.918440i | \(0.629450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8371 | 1.61270 | 0.806351 | − | 0.591437i | \(-0.201439\pi\) | ||||
0.806351 | + | 0.591437i | \(0.201439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.15676 | 0.584373 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0205 | 1.22487 | 0.612434 | − | 0.790522i | \(-0.290191\pi\) | ||||
0.612434 | + | 0.790522i | \(0.290191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.340173 | −0.0314490 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.75872 | −0.527901 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.360692 | −0.0327902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.340173 | 0.0306724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.84324 | −0.163562 | −0.0817808 | − | 0.996650i | \(-0.526061\pi\) | ||||
−0.0817808 | + | 0.996650i | \(0.526061\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.68035 | −0.764262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.313511 | 0.0273916 | 0.0136958 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136958 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.49693 | 0.563355 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.18342 | 0.186542 | 0.0932710 | − | 0.995641i | \(-0.470268\pi\) | ||||
0.0932710 | + | 0.995641i | \(0.470268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.02052 | 0.0865593 | 0.0432796 | − | 0.999063i | \(-0.486219\pi\) | ||||
0.0432796 | + | 0.999063i | \(0.486219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.10957 | −0.0927873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6803 | 1.20266 | 0.601330 | − | 0.799000i | \(-0.294638\pi\) | ||||
0.601330 | + | 0.799000i | \(0.294638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.15676 | −0.175514 | −0.0877571 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877571 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.75872 | −0.465565 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.18342 | 0.493490 | 0.246745 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246745 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.34017 | 0.661419 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.49693 | −0.669652 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.47641 | 0.114248 | 0.0571240 | − | 0.998367i | \(-0.481807\pi\) | ||||
0.0571240 | + | 0.998367i | \(0.481807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8843 | −0.991099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.49693 | 0.496833 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.75872 | −0.133713 | −0.0668566 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668566 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.83710 | −0.513908 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.424694 | −0.0317431 | −0.0158716 | − | 0.999874i | \(-0.505052\pi\) | ||||
−0.0158716 | + | 0.999874i | \(0.505052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3668 | 0.770561 | 0.385280 | − | 0.922800i | \(-0.374105\pi\) | ||||
0.385280 | + | 0.922800i | \(0.374105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3607 | 1.13550 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.7838 | −1.37361 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7321 | 1.57248 | 0.786238 | − | 0.617923i | \(-0.212026\pi\) | ||||
0.786238 | + | 0.617923i | \(0.212026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.36683 | −0.602258 | −0.301129 | − | 0.953583i | \(-0.597363\pi\) | ||||
−0.301129 | + | 0.953583i | \(0.597363\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3340 | 0.950010 | 0.475005 | − | 0.879983i | \(-0.342446\pi\) | ||||
0.475005 | + | 0.879983i | \(0.342446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.49693 | −0.460555 | −0.230278 | − | 0.973125i | \(-0.573963\pi\) | ||||
−0.230278 | + | 0.973125i | \(0.573963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8371 | 1.04653 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.49693 | −0.590577 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.1917 | 1.46586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.83710 | −0.470685 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.9421 | 1.09234 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.34017 | 0.566168 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50307 | 0.101568 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.95896 | 0.131774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3607 | −1.16256 | −0.581279 | − | 0.813704i | \(-0.697447\pi\) | ||||
−0.581279 | + | 0.813704i | \(0.697447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1568 | −0.674128 | −0.337064 | − | 0.941482i | \(-0.609434\pi\) | ||||
−0.337064 | + | 0.941482i | \(0.609434\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9939 | 0.990822 | 0.495411 | − | 0.868659i | \(-0.335017\pi\) | ||||
0.495411 | + | 0.868659i | \(0.335017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.26180 | 0.214610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5441 | −0.756280 | −0.378140 | − | 0.925748i | \(-0.623436\pi\) | ||||
−0.378140 | + | 0.925748i | \(0.623436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.68035 | −0.563849 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8950 | 0.704736 | 0.352368 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352368 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.68035 | −0.430319 | −0.215159 | − | 0.976579i | \(-0.569027\pi\) | ||||
−0.215159 | + | 0.976579i | \(0.569027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21008 | −0.140624 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.83710 | 0.433284 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1978 | −1.52735 | −0.763676 | − | 0.645600i | \(-0.776607\pi\) | ||||
−0.763676 | + | 0.645600i | \(0.776607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.7152 | −1.74244 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2351 | 0.950342 | 0.475171 | − | 0.879894i | \(-0.342386\pi\) | ||||
0.475171 | + | 0.879894i | \(0.342386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.15676 | 0.382562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.1773 | −1.79915 | −0.899574 | − | 0.436769i | \(-0.856123\pi\) | ||||
−0.899574 | + | 0.436769i | \(0.856123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.1773 | −0.928834 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.13009 | −0.373758 | −0.186879 | − | 0.982383i | \(-0.559837\pi\) | ||||
−0.186879 | + | 0.982383i | \(0.559837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7009 | −1.56122 | −0.780608 | − | 0.625021i | \(-0.785091\pi\) | ||||
−0.780608 | + | 0.625021i | \(0.785091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.340173 | −0.0205882 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2039 | 0.673179 | 0.336590 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336590 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.34017 | 0.499313 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.3545 | 1.45287 | 0.726435 | − | 0.687235i | \(-0.241176\pi\) | ||||
0.726435 | + | 0.687235i | \(0.241176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.15676 | 0.365981 | 0.182991 | − | 0.983115i | \(-0.441422\pi\) | ||||
0.182991 | + | 0.983115i | \(0.441422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.340173 | 0.0200798 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1629 | 0.950759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.49693 | 0.380857 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.75872 | 0.102746 | 0.0513729 | − | 0.998680i | \(-0.483640\pi\) | ||||
0.0513729 | + | 0.998680i | \(0.483640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.26180 | 0.189269 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.89043 | 0.167158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.68035 | −0.500327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.18342 | −0.125434 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.2039 | 1.55261 | 0.776305 | − | 0.630357i | \(-0.217092\pi\) | ||||
0.776305 | + | 0.630357i | \(0.217092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.84324 | −0.332411 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8432 | 1.23862 | 0.619308 | − | 0.785148i | \(-0.287413\pi\) | ||||
0.619308 | + | 0.785148i | \(0.287413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.3874 | 1.43498 | 0.717489 | − | 0.696570i | \(-0.245291\pi\) | ||||
0.717489 | + | 0.696570i | \(0.245291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.6947 | −1.27466 | −0.637331 | − | 0.770590i | \(-0.719962\pi\) | ||||
−0.637331 | + | 0.770590i | \(0.719962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.52359 | −0.365251 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.18342 | −0.456754 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −37.4140 | −2.08177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.8371 | 0.931094 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47641 | −0.301011 | −0.150505 | − | 0.988609i | \(-0.548090\pi\) | ||||
−0.150505 | + | 0.988609i | \(0.548090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.15676 | 0.337388 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.6742 | −0.744881 | −0.372441 | − | 0.928056i | \(-0.621479\pi\) | ||||
−0.372441 | + | 0.928056i | \(0.621479\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.0205 | 0.707178 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.2039 | 1.47318 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.183417 | −0.00984637 | −0.00492318 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492318 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.67420 | −0.410791 | −0.205395 | − | 0.978679i | \(-0.565848\pi\) | ||||
−0.205395 | + | 0.978679i | \(0.565848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.340173 | −0.0181571 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4329 | 1.03431 | 0.517155 | − | 0.855892i | \(-0.326991\pi\) | ||||
0.517155 | + | 0.855892i | \(0.326991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.75872 | −0.304784 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.4186 | 1.34154 | 0.670770 | − | 0.741666i | \(-0.265964\pi\) | ||||
0.670770 | + | 0.741666i | \(0.265964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2101 | 1.22158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.360692 | −0.0189314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.36069 | −0.488624 | −0.244312 | − | 0.969697i | \(-0.578562\pi\) | ||||
−0.244312 | + | 0.969697i | \(0.578562\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.340173 | 0.0177087 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.34017 | 0.433000 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5174 | 1.42480 | 0.712400 | − | 0.701774i | \(-0.247608\pi\) | ||||
0.712400 | + | 0.701774i | \(0.247608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.680346 | 0.0350396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.84324 | −0.505614 | −0.252807 | − | 0.967517i | \(-0.581354\pi\) | ||||
−0.252807 | + | 0.967517i | \(0.581354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84324 | −0.0944323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8310 | 1.42210 | 0.711048 | − | 0.703144i | \(-0.248221\pi\) | ||||
0.711048 | + | 0.703144i | \(0.248221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.68035 | −0.441247 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.67420 | −0.186289 | −0.0931447 | − | 0.995653i | \(-0.529692\pi\) | ||||
−0.0931447 | + | 0.995653i | \(0.529692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.9315 | 2.47457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.313511 | 0.0158145 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8638 | 1.14750 | 0.573750 | − | 0.819031i | \(-0.305488\pi\) | ||||
0.573750 | + | 0.819031i | \(0.305488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.49693 | 0.325253 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31965 | 0.265651 | 0.132825 | − | 0.991139i | \(-0.457595\pi\) | ||||
0.132825 | + | 0.991139i | \(0.457595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.83710 | −0.141326 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0821 | 0.995432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7275 | 1.37104 | 0.685519 | − | 0.728055i | \(-0.259575\pi\) | ||||
0.685519 | + | 0.728055i | \(0.259575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.18342 | 0.107700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.83710 | −0.336432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.02052 | 0.0499750 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.5174 | 1.14890 | 0.574451 | − | 0.818539i | \(-0.305215\pi\) | ||||
0.574451 | + | 0.818539i | \(0.305215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.15061 | −0.0560774 | −0.0280387 | − | 0.999607i | \(-0.508926\pi\) | ||||
−0.0280387 | + | 0.999607i | \(0.508926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.3607 | 0.743356 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.10957 | −0.0535708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4186 | −0.839022 | −0.419511 | − | 0.907750i | \(-0.637798\pi\) | ||||
−0.419511 | + | 0.907750i | \(0.637798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0144 | 1.25017 | 0.625086 | − | 0.780556i | \(-0.285064\pi\) | ||||
0.625086 | + | 0.780556i | \(0.285064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −55.2039 | −2.64076 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.13624 | −0.245139 | −0.122570 | − | 0.992460i | \(-0.539113\pi\) | ||||
−0.122570 | + | 0.992460i | \(0.539113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5380 | 0.880765 | 0.440383 | − | 0.897810i | \(-0.354843\pi\) | ||||
0.440383 | + | 0.897810i | \(0.354843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.6803 | 0.694357 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3135 | −0.486725 | −0.243362 | − | 0.969935i | \(-0.578250\pi\) | ||||
−0.243362 | + | 0.969935i | \(0.578250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.10957 | 0.0522478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.15676 | −0.101333 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.36683 | −0.204272 | −0.102136 | − | 0.994770i | \(-0.532568\pi\) | ||||
−0.102136 | + | 0.994770i | \(0.532568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.75872 | −0.268794 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.7009 | −1.56961 | −0.784803 | − | 0.619745i | \(-0.787236\pi\) | ||||
−0.784803 | + | 0.619745i | \(0.787236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.4703 | −0.486595 | −0.243297 | − | 0.969952i | \(-0.578229\pi\) | ||||
−0.243297 | + | 0.969952i | \(0.578229\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.51745 | −0.162768 | −0.0813840 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813840 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8371 | 0.685114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18342 | 0.284917 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.3135 | −1.30186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.34017 | 0.381870 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.8432 | 0.998043 | 0.499022 | − | 0.866590i | \(-0.333693\pi\) | ||||
0.499022 | + | 0.866590i | \(0.333693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09436 | −0.0954947 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.49693 | −0.386624 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.88428 | 0.357271 | 0.178635 | − | 0.983915i | \(-0.442832\pi\) | ||||
0.178635 | + | 0.983915i | \(0.442832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7731 | −0.892347 | −0.446174 | − | 0.894946i | \(-0.647214\pi\) | ||||
−0.446174 | + | 0.894946i | \(0.647214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5174 | 0.518720 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.9421 | 0.715103 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5174 | −1.76904 | −0.884522 | − | 0.466499i | \(-0.845515\pi\) | ||||
−0.884522 | + | 0.466499i | \(0.845515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.47641 | 0.0659611 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.2039 | −0.499559 | −0.249779 | − | 0.968303i | \(-0.580358\pi\) | ||||
−0.249779 | + | 0.968303i | \(0.580358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8843 | −0.572211 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.5441 | −1.04357 | −0.521787 | − | 0.853076i | \(-0.674734\pi\) | ||||
−0.521787 | + | 0.853076i | \(0.674734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50307 | 0.0664920 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.49693 | 0.286846 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.75872 | −0.0771994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.6537 | 1.08010 | 0.540049 | − | 0.841634i | \(-0.318406\pi\) | ||||
0.540049 | + | 0.841634i | \(0.318406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.63931 | −0.115409 | −0.0577044 | − | 0.998334i | \(-0.518378\pi\) | ||||
−0.0577044 | + | 0.998334i | \(0.518378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −48.0288 | −2.09217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.1978 | 2.13903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83710 | −0.296705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.115718 | −0.00501229 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.424694 | −0.0183269 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.26180 | 0.140495 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.1506 | 1.08131 | 0.540655 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540655 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3668 | 0.444883 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.1506 | −1.50293 | −0.751466 | − | 0.659772i | \(-0.770653\pi\) | ||||
−0.751466 | + | 0.659772i | \(0.770653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3607 | 0.655578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9939 | −0.553557 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.68035 | −0.369126 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.3812 | −1.11781 | −0.558904 | − | 0.829232i | \(-0.688778\pi\) | ||||
−0.558904 | + | 0.829232i | \(0.688778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.95282 | 0.124891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.7838 | −0.793052 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9939 | 0.547626 | 0.273813 | − | 0.961783i | \(-0.411715\pi\) | ||||
0.273813 | + | 0.961783i | \(0.411715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.36683 | −0.266912 | −0.133456 | − | 0.991055i | \(-0.542607\pi\) | ||||
−0.133456 | + | 0.991055i | \(0.542607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.63931 | −0.110452 | −0.0552258 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552258 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.7321 | 0.907870 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.3340 | −1.38771 | −0.693857 | − | 0.720113i | \(-0.744090\pi\) | ||||
−0.693857 | + | 0.720113i | \(0.744090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.36683 | −0.347714 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.83710 | 0.283651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.2039 | 1.12667 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.3074 | −0.714352 | −0.357176 | − | 0.934037i | \(-0.616260\pi\) | ||||
−0.357176 | + | 0.934037i | \(0.616260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.1855 | 2.23267 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3340 | 0.548489 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.1194 | −1.93496 | −0.967481 | − | 0.252943i | \(-0.918602\pi\) | ||||
−0.967481 | + | 0.252943i | \(0.918602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.49693 | −0.265902 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1050 | 0.535457 | 0.267729 | − | 0.963494i | \(-0.413727\pi\) | ||||
0.267729 | + | 0.963494i | \(0.413727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0349 | 1.18436 | 0.592179 | − | 0.805806i | \(-0.298268\pi\) | ||||
0.592179 | + | 0.805806i | \(0.298268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8371 | 0.604213 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9877 | 1.05481 | 0.527404 | − | 0.849614i | \(-0.323165\pi\) | ||||
0.527404 | + | 0.849614i | \(0.323165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.1978 | −0.815781 | −0.407891 | − | 0.913031i | \(-0.633736\pi\) | ||||
−0.407891 | + | 0.913031i | \(0.633736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.8576 | −1.92668 | −0.963338 | − | 0.268292i | \(-0.913541\pi\) | ||||
−0.963338 | + | 0.268292i | \(0.913541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.3812 | 0.738803 | 0.369402 | − | 0.929270i | \(-0.379563\pi\) | ||||
0.369402 | + | 0.929270i | \(0.379563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.49693 | −0.340970 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.1773 | −0.608065 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.1917 | 0.846313 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.4551 | −1.41369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.94668 | 0.316352 | 0.158176 | − | 0.987411i | \(-0.449439\pi\) | ||||
0.158176 | + | 0.987411i | \(0.449439\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.83710 | −0.271750 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.340173 | −0.0134781 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.9421 | 0.630661 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.7275 | 0.621200 | 0.310600 | − | 0.950541i | \(-0.399470\pi\) | ||||
0.310600 | + | 0.950541i | \(0.399470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.5646 | 1.75746 | 0.878729 | − | 0.477322i | \(-0.158392\pi\) | ||||
0.878729 | + | 0.477322i | \(0.158392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.16290 | −0.202974 | −0.101487 | − | 0.994837i | \(-0.532360\pi\) | ||||
−0.101487 | + | 0.994837i | \(0.532360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.3012 | −0.875400 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.34017 | 0.326877 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.49079 | 0.293137 | 0.146569 | − | 0.989201i | \(-0.453177\pi\) | ||||
0.146569 | + | 0.989201i | \(0.453177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.50307 | 0.0586404 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.7259 | 0.885276 | 0.442638 | − | 0.896700i | \(-0.354043\pi\) | ||||
0.442638 | + | 0.896700i | \(0.354043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3258 | −0.479418 | −0.239709 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239709 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.95896 | 0.0760798 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9939 | 0.658005 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.3607 | −0.671203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.1034 | 1.93422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6742 | −0.989668 | −0.494834 | − | 0.868988i | \(-0.664771\pi\) | ||||
−0.494834 | + | 0.868988i | \(0.664771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.2762 | 1.12517 | 0.562587 | − | 0.826738i | \(-0.309806\pi\) | ||||
0.562587 | + | 0.826738i | \(0.309806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.49693 | 0.249329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1568 | −0.389208 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.5441 | −0.977418 | −0.488709 | − | 0.872447i | \(-0.662532\pi\) | ||||
−0.488709 | + | 0.872447i | \(0.662532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.9939 | 0.572051 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.83710 | −0.108085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3812 | −1.00359 | −0.501794 | − | 0.864987i | \(-0.667327\pi\) | ||||
−0.501794 | + | 0.864987i | \(0.667327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.26180 | 0.123905 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.95896 | −0.0742010 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5441 | −0.436638 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.6742 | −0.894162 | −0.447081 | − | 0.894493i | \(-0.647536\pi\) | ||||
−0.447081 | + | 0.894493i | \(0.647536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.0000 | 1.50863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.18342 | −0.0821159 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.7214 | −1.52932 | −0.764662 | − | 0.644432i | \(-0.777094\pi\) | ||||
−0.764662 | + | 0.644432i | \(0.777094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.68035 | −0.325538 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −70.8659 | −2.65395 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.8950 | 0.406880 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.3545 | −0.833684 | −0.416842 | − | 0.908979i | \(-0.636863\pi\) | ||||
−0.416842 | + | 0.908979i | \(0.636863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.84324 | −0.217614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.68035 | −0.248445 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.10957 | 0.189504 | 0.0947518 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947518 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.9877 | 1.84886 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.6475 | 1.53829 | 0.769144 | − | 0.639076i | \(-0.220683\pi\) | ||||
0.769144 | + | 0.639076i | \(0.220683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.3956 | 1.78267 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3135 | −1.18867 | −0.594336 | − | 0.804217i | \(-0.702585\pi\) | ||||
−0.594336 | + | 0.804217i | \(0.702585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.21008 | −0.0811893 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.1711 | −1.10687 | −0.553436 | − | 0.832892i | \(-0.686684\pi\) | ||||
−0.553436 | + | 0.832892i | \(0.686684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.83710 | 0.250156 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.18342 | −0.299016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.1855 | 1.68533 | 0.842667 | − | 0.538436i | \(-0.180985\pi\) | ||||
0.842667 | + | 0.538436i | \(0.180985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.1978 | −0.881817 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.5523 | 1.83736 | 0.918678 | − | 0.395007i | \(-0.129258\pi\) | ||||
0.918678 | + | 0.395007i | \(0.129258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.7152 | −1.00600 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1711 | −0.441203 | −0.220602 | − | 0.975364i | \(-0.570802\pi\) | ||||
−0.220602 | + | 0.975364i | \(0.570802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.8371 | 0.609544 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.32580 | 0.0839797 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.36069 | 0.265433 | 0.132717 | − | 0.991154i | \(-0.457630\pi\) | ||||
0.132717 | + | 0.991154i | \(0.457630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2351 | 0.548680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.5548 | −0.379629 | −0.189815 | − | 0.981820i | \(-0.560789\pi\) | ||||
−0.189815 | + | 0.981820i | \(0.560789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.15676 | 0.220872 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.21008 | 0.0791843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0000 | 1.86071 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.04718 | −0.322497 | −0.161249 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161249 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.1773 | −1.03874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.0205 | 0.462956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.22529 | −0.185556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.9627 | 0.600848 | 0.300424 | − | 0.953806i | \(-0.402872\pi\) | ||||
0.300424 | + | 0.953806i | \(0.402872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1773 | −0.536263 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.90271 | 0.173013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.13009 | −0.215790 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.9877 | 0.562098 | 0.281049 | − | 0.959693i | \(-0.409318\pi\) | ||||
0.281049 | + | 0.959693i | \(0.409318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.39350 | 0.294736 | 0.147368 | − | 0.989082i | \(-0.452920\pi\) | ||||
0.147368 | + | 0.989082i | \(0.452920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.7009 | −0.901369 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.3956 | −1.97303 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.340173 | −0.0118866 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.0288 | 1.32721 | 0.663606 | − | 0.748082i | \(-0.269025\pi\) | ||||
0.663606 | + | 0.748082i | \(0.269025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1568 | 0.772336 | 0.386168 | − | 0.922428i | \(-0.373799\pi\) | ||||
0.386168 | + | 0.922428i | \(0.373799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8227 | −0.515437 | −0.257718 | − | 0.966220i | \(-0.582971\pi\) | ||||
−0.257718 | + | 0.966220i | \(0.582971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.9467 | 0.484388 | 0.242194 | − | 0.970228i | \(-0.422133\pi\) | ||||
0.242194 | + | 0.970228i | \(0.422133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2039 | 0.388660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.75872 | −0.199528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.34017 | 0.288279 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4764 | 0.879543 | 0.439772 | − | 0.898110i | \(-0.355059\pi\) | ||||
0.439772 | + | 0.898110i | \(0.355059\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.3545 | 0.838815 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.360692 | −0.0123935 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.15676 | 0.211299 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52.3135 | −1.79328 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −58.1588 | −1.99132 | −0.995660 | − | 0.0930604i | \(-0.970335\pi\) | ||||
−0.995660 | + | 0.0930604i | \(0.970335\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.9093 | 0.987524 | 0.493762 | − | 0.869597i | \(-0.335621\pi\) | ||||
0.493762 | + | 0.869597i | \(0.335621\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.1834 | −1.71224 | −0.856118 | − | 0.516780i | \(-0.827130\pi\) | ||||
−0.856118 | + | 0.516780i | \(0.827130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.340173 | 0.0115931 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.13009 | 0.276752 | 0.138376 | − | 0.990380i | \(-0.455812\pi\) | ||||
0.138376 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.1629 | 0.548921 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.3135 | −0.960470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.04718 | −0.171017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.49693 | 0.219888 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8371 | 0.906225 | 0.453112 | − | 0.891453i | \(-0.350314\pi\) | ||||
0.453112 | + | 0.891453i | \(0.350314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.75872 | 0.0593203 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.4846 | −1.49873 | −0.749363 | − | 0.662160i | \(-0.769640\pi\) | ||||
−0.749363 | + | 0.662160i | \(0.769640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.8781 | −0.702605 | −0.351303 | − | 0.936262i | \(-0.614261\pi\) | ||||
−0.351303 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.4079 | −0.752383 | −0.376191 | − | 0.926542i | \(-0.622766\pi\) | ||||
−0.376191 | + | 0.926542i | \(0.622766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.84324 | −0.0618204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.26180 | 0.109274 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.89043 | 0.0965085 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.6803 | −0.556321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0288 | −1.60007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.68035 | −0.288864 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8781 | −0.693247 | −0.346624 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346624 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.18342 | −0.0724194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.52198 | −0.116688 | −0.0583442 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583442 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3012 | 0.738063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.313511 | 0.0103530 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1978 | −0.402368 | −0.201184 | − | 0.979553i | \(-0.564479\pi\) | ||||
−0.201184 | + | 0.979553i | \(0.564479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.2039 | 0.896400 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.42309 | −0.178503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.84324 | −0.191917 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.86376 | 0.0939570 | 0.0469785 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469785 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.49693 | 0.212928 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.8432 | 0.715116 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.7480 | −0.873821 | −0.436910 | − | 0.899505i | \(-0.643927\pi\) | ||||
−0.436910 | + | 0.899505i | \(0.643927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.3874 | 0.828485 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0144 | 0.326459 | 0.163230 | − | 0.986588i | \(-0.447809\pi\) | ||||
0.163230 | + | 0.986588i | \(0.447809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.89043 | −0.0941252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.2183 | 1.53439 | 0.767194 | − | 0.641415i | \(-0.221652\pi\) | ||||
0.767194 | + | 0.641415i | \(0.221652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.511304 | −0.0165976 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.6947 | −0.735927 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.6660 | −0.475077 | −0.237539 | − | 0.971378i | \(-0.576341\pi\) | ||||
−0.237539 | + | 0.971378i | \(0.576341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.52359 | −0.210878 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.18342 | 0.0705062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.5585 | 1.24382 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.18342 | −0.263707 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.3894 | −1.84552 | −0.922760 | − | 0.385375i | \(-0.874072\pi\) | ||||
−0.922760 | + | 0.385375i | \(0.874072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.4140 | −1.20191 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4017 | 0.750997 | 0.375499 | − | 0.926823i | \(-0.377471\pi\) | ||||
0.375499 | + | 0.926823i | \(0.377471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.02052 | 0.0327163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.54411 | −0.113386 | −0.0566931 | − | 0.998392i | \(-0.518056\pi\) | ||||
−0.0566931 | + | 0.998392i | \(0.518056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.5052 | −1.58219 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8371 | 0.537567 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7152 | 0.373658 | 0.186829 | − | 0.982392i | \(-0.440179\pi\) | ||||
0.186829 | + | 0.982392i | \(0.440179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 73.7563 | 2.34531 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.5113 | −1.79514 | −0.897570 | − | 0.440871i | \(-0.854670\pi\) | ||||
−0.897570 | + | 0.440871i | \(0.854670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.47641 | −0.173789 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9048 | −1.29547 | −0.647734 | − | 0.761867i | \(-0.724283\pi\) | ||||
−0.647734 | + | 0.761867i | \(0.724283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.15676 | 0.194791 |
(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 | 8400.2.a.dl.1.2 | 3 | ||
4.3 | odd | 2 | 4200.2.a.bn.1.2 | 3 | |||
5.2 | odd | 4 | 1680.2.t.j.1009.1 | 6 | |||
5.3 | odd | 4 | 1680.2.t.j.1009.4 | 6 | |||
5.4 | even | 2 | 8400.2.a.di.1.2 | 3 | |||
15.2 | even | 4 | 5040.2.t.z.1009.5 | 6 | |||
15.8 | even | 4 | 5040.2.t.z.1009.6 | 6 | |||
20.3 | even | 4 | 840.2.t.d.169.1 | ✓ | 6 | ||
20.7 | even | 4 | 840.2.t.d.169.4 | yes | 6 | ||
20.19 | odd | 2 | 4200.2.a.bp.1.2 | 3 | |||
60.23 | odd | 4 | 2520.2.t.k.1009.6 | 6 | |||
60.47 | odd | 4 | 2520.2.t.k.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.d.169.1 | ✓ | 6 | 20.3 | even | 4 | ||
840.2.t.d.169.4 | yes | 6 | 20.7 | even | 4 | ||
1680.2.t.j.1009.1 | 6 | 5.2 | odd | 4 | |||
1680.2.t.j.1009.4 | 6 | 5.3 | odd | 4 | |||
2520.2.t.k.1009.5 | 6 | 60.47 | odd | 4 | |||
2520.2.t.k.1009.6 | 6 | 60.23 | odd | 4 | |||
4200.2.a.bn.1.2 | 3 | 4.3 | odd | 2 | |||
4200.2.a.bp.1.2 | 3 | 20.19 | odd | 2 | |||
5040.2.t.z.1009.5 | 6 | 15.2 | even | 4 | |||
5040.2.t.z.1009.6 | 6 | 15.8 | even | 4 | |||
8400.2.a.di.1.2 | 3 | 5.4 | even | 2 | |||
8400.2.a.dl.1.2 | 3 | 1.1 | even | 1 | trivial |