Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1710) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.86370 | 1.46034 | 0.730171 | − | 0.683264i | \(-0.239440\pi\) | ||||
0.730171 | + | 0.683264i | \(0.239440\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03528 | 0.312148 | 0.156074 | − | 0.987745i | \(-0.450116\pi\) | ||||
0.156074 | + | 0.987745i | \(0.450116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.86370 | −1.07160 | −0.535799 | − | 0.844345i | \(-0.679990\pi\) | ||||
−0.535799 | + | 0.844345i | \(0.679990\pi\) | |||||||
\(14\) | −3.86370 | −1.03262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.535898 | 0.129974 | 0.0649872 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649872 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.03528 | −0.220722 | ||||||||
\(23\) | 5.46410 | 1.13934 | 0.569672 | − | 0.821872i | \(-0.307070\pi\) | ||||
0.569672 | + | 0.821872i | \(0.307070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.86370 | 0.757735 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.86370 | 0.730171 | ||||||||
\(29\) | 4.62158 | 0.858206 | 0.429103 | − | 0.903256i | \(-0.358830\pi\) | ||||
0.429103 | + | 0.903256i | \(0.358830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.9282 | −1.96276 | −0.981382 | − | 0.192068i | \(-0.938481\pi\) | ||||
−0.981382 | + | 0.192068i | \(0.938481\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.535898 | −0.0919058 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.79315 | −0.294792 | −0.147396 | − | 0.989078i | \(-0.547089\pi\) | ||||
−0.147396 | + | 0.989078i | \(0.547089\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79315 | 0.280043 | 0.140022 | − | 0.990148i | \(-0.455283\pi\) | ||||
0.140022 | + | 0.990148i | \(0.455283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.69213 | −1.02054 | −0.510270 | − | 0.860014i | \(-0.670455\pi\) | ||||
−0.510270 | + | 0.860014i | \(0.670455\pi\) | |||||||
\(44\) | 1.03528 | 0.156074 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.46410 | −0.805638 | ||||||||
\(47\) | 2.53590 | 0.369899 | 0.184949 | − | 0.982748i | \(-0.440788\pi\) | ||||
0.184949 | + | 0.982748i | \(0.440788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.92820 | 1.13260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.86370 | −0.535799 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.86370 | −0.516309 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.62158 | −0.606843 | ||||||||
\(59\) | 6.96953 | 0.907356 | 0.453678 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453678 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 10.9282 | 1.38788 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3843 | 1.63515 | 0.817574 | − | 0.575824i | \(-0.195319\pi\) | ||||
0.817574 | + | 0.575824i | \(0.195319\pi\) | |||||||
\(68\) | 0.535898 | 0.0649872 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.14110 | 0.491459 | 0.245729 | − | 0.969338i | \(-0.420973\pi\) | ||||
0.245729 | + | 0.969338i | \(0.420973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.58630 | −0.419745 | −0.209872 | − | 0.977729i | \(-0.567305\pi\) | ||||
−0.209872 | + | 0.977729i | \(0.567305\pi\) | |||||||
\(74\) | 1.79315 | 0.208450 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.79315 | −0.198020 | ||||||||
\(83\) | 16.3923 | 1.79929 | 0.899645 | − | 0.436623i | \(-0.143826\pi\) | ||||
0.899645 | + | 0.436623i | \(0.143826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.69213 | 0.721631 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.03528 | −0.110361 | ||||||||
\(89\) | −3.86370 | −0.409552 | −0.204776 | − | 0.978809i | \(-0.565647\pi\) | ||||
−0.204776 | + | 0.978809i | \(0.565647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9282 | −1.56490 | ||||||||
\(92\) | 5.46410 | 0.569672 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.53590 | −0.261558 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.55103 | 0.259017 | 0.129509 | − | 0.991578i | \(-0.458660\pi\) | ||||
0.129509 | + | 0.991578i | \(0.458660\pi\) | |||||||
\(98\) | −7.92820 | −0.800869 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5558 | −1.05034 | −0.525172 | − | 0.850996i | \(-0.675999\pi\) | ||||
−0.525172 | + | 0.850996i | \(0.675999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898 | 0.482711 | 0.241355 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241355 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(104\) | 3.86370 | 0.378867 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −2.92820 | −0.283080 | −0.141540 | − | 0.989933i | \(-0.545205\pi\) | ||||
−0.141540 | + | 0.989933i | \(0.545205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.92820 | 0.855167 | 0.427583 | − | 0.903976i | \(-0.359365\pi\) | ||||
0.427583 | + | 0.903976i | \(0.359365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.86370 | 0.365086 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.62158 | 0.429103 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.96953 | −0.641597 | ||||||||
\(119\) | 2.07055 | 0.189807 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.92820 | −0.902564 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.9282 | −0.981382 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.48528 | 0.752947 | 0.376473 | − | 0.926427i | \(-0.377137\pi\) | ||||
0.376473 | + | 0.926427i | \(0.377137\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.10583 | 0.271357 | 0.135679 | − | 0.990753i | \(-0.456678\pi\) | ||||
0.135679 | + | 0.990753i | \(0.456678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.86370 | −0.335026 | ||||||||
\(134\) | −13.3843 | −1.15622 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.535898 | −0.0459529 | ||||||||
\(137\) | 0.535898 | 0.0457849 | 0.0228924 | − | 0.999738i | \(-0.492712\pi\) | ||||
0.0228924 | + | 0.999738i | \(0.492712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.14110 | −0.347514 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.58630 | 0.296804 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.79315 | −0.147396 | ||||||||
\(149\) | 20.3538 | 1.66745 | 0.833724 | − | 0.552182i | \(-0.186205\pi\) | ||||
0.833724 | + | 0.552182i | \(0.186205\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.85641 | 0.476588 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1421 | 1.12867 | 0.564333 | − | 0.825547i | \(-0.309134\pi\) | ||||
0.564333 | + | 0.825547i | \(0.309134\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.1117 | 1.66383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6627 | 1.85341 | 0.926703 | − | 0.375796i | \(-0.122631\pi\) | ||||
0.926703 | + | 0.375796i | \(0.122631\pi\) | |||||||
\(164\) | 1.79315 | 0.140022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.3923 | −1.27229 | ||||||||
\(167\) | 10.9282 | 0.845650 | 0.422825 | − | 0.906211i | \(-0.361039\pi\) | ||||
0.422825 | + | 0.906211i | \(0.361039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.92820 | 0.148323 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.69213 | −0.510270 | ||||||||
\(173\) | −22.7846 | −1.73228 | −0.866141 | − | 0.499800i | \(-0.833407\pi\) | ||||
−0.866141 | + | 0.499800i | \(0.833407\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.03528 | 0.0780369 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.86370 | 0.289597 | ||||||||
\(179\) | −16.7675 | −1.25326 | −0.626631 | − | 0.779316i | \(-0.715566\pi\) | ||||
−0.626631 | + | 0.779316i | \(0.715566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8564 | 1.47592 | 0.737958 | − | 0.674847i | \(-0.235790\pi\) | ||||
0.737958 | + | 0.674847i | \(0.235790\pi\) | |||||||
\(182\) | 14.9282 | 1.10655 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.46410 | −0.402819 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.554803 | 0.0405712 | ||||||||
\(188\) | 2.53590 | 0.184949 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2480 | −1.24802 | −0.624009 | − | 0.781417i | \(-0.714497\pi\) | ||||
−0.624009 | + | 0.781417i | \(0.714497\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76268 | 0.630752 | 0.315376 | − | 0.948967i | \(-0.397869\pi\) | ||||
0.315376 | + | 0.948967i | \(0.397869\pi\) | |||||||
\(194\) | −2.55103 | −0.183153 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.92820 | 0.566300 | ||||||||
\(197\) | 23.4641 | 1.67175 | 0.835874 | − | 0.548921i | \(-0.184961\pi\) | ||||
0.835874 | + | 0.548921i | \(0.184961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0718 | 0.926635 | 0.463318 | − | 0.886192i | \(-0.346659\pi\) | ||||
0.463318 | + | 0.886192i | \(0.346659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5558 | 0.742706 | ||||||||
\(203\) | 17.8564 | 1.25327 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.89898 | −0.341328 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.86370 | −0.267900 | ||||||||
\(209\) | −1.03528 | −0.0716116 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8564 | −1.22929 | −0.614643 | − | 0.788806i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788806i | \(0.710700\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.92820 | 0.200168 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −42.2233 | −2.86631 | ||||||||
\(218\) | −8.92820 | −0.604694 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.07055 | −0.139280 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5558 | −0.706871 | −0.353435 | − | 0.935459i | \(-0.614987\pi\) | ||||
−0.353435 | + | 0.935459i | \(0.614987\pi\) | |||||||
\(224\) | −3.86370 | −0.258155 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −1.85641 | −0.123214 | −0.0616070 | − | 0.998100i | \(-0.519623\pi\) | ||||
−0.0616070 | + | 0.998100i | \(0.519623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.85641 | −0.254839 | −0.127419 | − | 0.991849i | \(-0.540669\pi\) | ||||
−0.127419 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.62158 | −0.303421 | ||||||||
\(233\) | 12.5359 | 0.821254 | 0.410627 | − | 0.911803i | \(-0.365310\pi\) | ||||
0.410627 | + | 0.911803i | \(0.365310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.96953 | 0.453678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.07055 | −0.134214 | ||||||||
\(239\) | 13.1069 | 0.847812 | 0.423906 | − | 0.905706i | \(-0.360659\pi\) | ||||
0.423906 | + | 0.905706i | \(0.360659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 9.92820 | 0.638209 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.86370 | 0.245842 | ||||||||
\(248\) | 10.9282 | 0.693942 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.3586 | −1.78998 | −0.894990 | − | 0.446087i | \(-0.852817\pi\) | ||||
−0.894990 | + | 0.446087i | \(0.852817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65685 | 0.355643 | ||||||||
\(254\) | −8.48528 | −0.532414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.7846 | 1.42126 | 0.710632 | − | 0.703563i | \(-0.248409\pi\) | ||||
0.710632 | + | 0.703563i | \(0.248409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.92820 | −0.430498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.10583 | −0.191879 | ||||||||
\(263\) | 19.3205 | 1.19135 | 0.595677 | − | 0.803224i | \(-0.296884\pi\) | ||||
0.595677 | + | 0.803224i | \(0.296884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.86370 | 0.236899 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.3843 | 0.817574 | ||||||||
\(269\) | −31.9449 | −1.94772 | −0.973858 | − | 0.227160i | \(-0.927056\pi\) | ||||
−0.973858 | + | 0.227160i | \(0.927056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9282 | 0.663841 | 0.331921 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331921 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(272\) | 0.535898 | 0.0324936 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.535898 | −0.0323748 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2832 | −1.09853 | −0.549267 | − | 0.835647i | \(-0.685093\pi\) | ||||
−0.549267 | + | 0.835647i | \(0.685093\pi\) | |||||||
\(278\) | −6.92820 | −0.415526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1870 | −1.86046 | −0.930231 | − | 0.366974i | \(-0.880394\pi\) | ||||
−0.930231 | + | 0.366974i | \(0.880394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.17638 | 0.307704 | 0.153852 | − | 0.988094i | \(-0.450832\pi\) | ||||
0.153852 | + | 0.988094i | \(0.450832\pi\) | |||||||
\(284\) | 4.14110 | 0.245729 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 6.92820 | 0.408959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7128 | −0.983107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.58630 | −0.209872 | ||||||||
\(293\) | −19.8564 | −1.16002 | −0.580012 | − | 0.814608i | \(-0.696952\pi\) | ||||
−0.580012 | + | 0.814608i | \(0.696952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.79315 | 0.104225 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.3538 | −1.17906 | ||||||||
\(299\) | −21.1117 | −1.22092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.8564 | −1.49034 | ||||||||
\(302\) | −5.85641 | −0.336998 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5254 | 1.00023 | 0.500113 | − | 0.865960i | \(-0.333292\pi\) | ||||
0.500113 | + | 0.865960i | \(0.333292\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.79315 | −0.101680 | −0.0508401 | − | 0.998707i | \(-0.516190\pi\) | ||||
−0.0508401 | + | 0.998707i | \(0.516190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5959 | −1.10763 | −0.553813 | − | 0.832641i | \(-0.686828\pi\) | ||||
−0.553813 | + | 0.832641i | \(0.686828\pi\) | |||||||
\(314\) | −14.1421 | −0.798087 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.78461 | 0.267887 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.1117 | −1.17651 | ||||||||
\(323\) | −0.535898 | −0.0298182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.6627 | −1.31056 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.79315 | −0.0990102 | ||||||||
\(329\) | 9.79796 | 0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8564 | 0.761617 | 0.380808 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380808 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(332\) | 16.3923 | 0.899645 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.9282 | −0.597965 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.03528 | 0.0563951 | 0.0281975 | − | 0.999602i | \(-0.491023\pi\) | ||||
0.0281975 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(338\) | −1.92820 | −0.104880 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3137 | −0.612672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.58630 | 0.193642 | ||||||||
\(344\) | 6.69213 | 0.360815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.7846 | 1.22491 | ||||||||
\(347\) | 18.5359 | 0.995059 | 0.497530 | − | 0.867447i | \(-0.334241\pi\) | ||||
0.497530 | + | 0.867447i | \(0.334241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.14359 | 0.221801 | 0.110901 | − | 0.993831i | \(-0.464626\pi\) | ||||
0.110901 | + | 0.993831i | \(0.464626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.03528 | −0.0551804 | ||||||||
\(353\) | 21.3205 | 1.13478 | 0.567388 | − | 0.823451i | \(-0.307954\pi\) | ||||
0.567388 | + | 0.823451i | \(0.307954\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.86370 | −0.204776 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.7675 | 0.886189 | ||||||||
\(359\) | 34.7733 | 1.83527 | 0.917633 | − | 0.397429i | \(-0.130097\pi\) | ||||
0.917633 | + | 0.397429i | \(0.130097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.8564 | −1.04363 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.9282 | −0.782450 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.37945 | −0.280805 | −0.140403 | − | 0.990094i | \(-0.544840\pi\) | ||||
−0.140403 | + | 0.990094i | \(0.544840\pi\) | |||||||
\(368\) | 5.46410 | 0.284836 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.1822 | 1.20356 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.9754 | −1.29318 | −0.646588 | − | 0.762840i | \(-0.723805\pi\) | ||||
−0.646588 | + | 0.762840i | \(0.723805\pi\) | |||||||
\(374\) | −0.554803 | −0.0286882 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.53590 | −0.130779 | ||||||||
\(377\) | −17.8564 | −0.919652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.7128 | −1.83444 | −0.917222 | − | 0.398376i | \(-0.869574\pi\) | ||||
−0.917222 | + | 0.398376i | \(0.869574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.2480 | 0.882483 | ||||||||
\(383\) | −22.9282 | −1.17158 | −0.585788 | − | 0.810464i | \(-0.699215\pi\) | ||||
−0.585788 | + | 0.810464i | \(0.699215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.76268 | −0.446009 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.55103 | 0.129509 | ||||||||
\(389\) | −19.7990 | −1.00385 | −0.501924 | − | 0.864912i | \(-0.667374\pi\) | ||||
−0.501924 | + | 0.864912i | \(0.667374\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92820 | 0.148086 | ||||||||
\(392\) | −7.92820 | −0.400435 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.4641 | −1.18210 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2832 | 0.917610 | 0.458805 | − | 0.888537i | \(-0.348278\pi\) | ||||
0.458805 | + | 0.888537i | \(0.348278\pi\) | |||||||
\(398\) | −13.0718 | −0.655230 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.52056 | 0.475434 | 0.237717 | − | 0.971334i | \(-0.423601\pi\) | ||||
0.237717 | + | 0.971334i | \(0.423601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.2233 | 2.10329 | ||||||||
\(404\) | −10.5558 | −0.525172 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.8564 | −0.886199 | ||||||||
\(407\) | −1.85641 | −0.0920187 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9282 | −1.03483 | −0.517417 | − | 0.855734i | \(-0.673106\pi\) | ||||
−0.517417 | + | 0.855734i | \(0.673106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.89898 | 0.241355 | ||||||||
\(413\) | 26.9282 | 1.32505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.86370 | 0.189434 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.03528 | 0.0506370 | ||||||||
\(419\) | 29.3195 | 1.43235 | 0.716177 | − | 0.697919i | \(-0.245890\pi\) | ||||
0.716177 | + | 0.697919i | \(0.245890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7128 | 1.44811 | 0.724057 | − | 0.689740i | \(-0.242275\pi\) | ||||
0.724057 | + | 0.689740i | \(0.242275\pi\) | |||||||
\(422\) | 17.8564 | 0.869236 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.72741 | −0.373955 | ||||||||
\(428\) | −2.92820 | −0.141540 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.2137 | −1.26267 | −0.631335 | − | 0.775510i | \(-0.717493\pi\) | ||||
−0.631335 | + | 0.775510i | \(0.717493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.8332 | −0.520612 | −0.260306 | − | 0.965526i | \(-0.583823\pi\) | ||||
−0.260306 | + | 0.965526i | \(0.583823\pi\) | |||||||
\(434\) | 42.2233 | 2.02678 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.92820 | 0.427583 | ||||||||
\(437\) | −5.46410 | −0.261383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0000 | 0.954548 | 0.477274 | − | 0.878755i | \(-0.341625\pi\) | ||||
0.477274 | + | 0.878755i | \(0.341625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.07055 | 0.0984861 | ||||||||
\(443\) | 16.3923 | 0.778822 | 0.389411 | − | 0.921064i | \(-0.372679\pi\) | ||||
0.389411 | + | 0.921064i | \(0.372679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.5558 | 0.499833 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.86370 | 0.182543 | ||||||||
\(449\) | −40.4302 | −1.90802 | −0.954009 | − | 0.299777i | \(-0.903088\pi\) | ||||
−0.954009 | + | 0.299777i | \(0.903088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85641 | 0.0874148 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.85641 | 0.0871255 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.9411 | −1.58770 | −0.793849 | − | 0.608114i | \(-0.791926\pi\) | ||||
−0.793849 | + | 0.608114i | \(0.791926\pi\) | |||||||
\(458\) | 3.85641 | 0.180198 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5264 | 1.28203 | 0.641016 | − | 0.767527i | \(-0.278513\pi\) | ||||
0.641016 | + | 0.767527i | \(0.278513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8733 | 0.923591 | 0.461796 | − | 0.886986i | \(-0.347205\pi\) | ||||
0.461796 | + | 0.886986i | \(0.347205\pi\) | |||||||
\(464\) | 4.62158 | 0.214551 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.5359 | −0.580714 | ||||||||
\(467\) | 2.53590 | 0.117347 | 0.0586737 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586737 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.7128 | 2.38788 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.96953 | −0.320799 | ||||||||
\(473\) | −6.92820 | −0.318559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.07055 | 0.0949036 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.1069 | −0.599494 | ||||||||
\(479\) | 16.6932 | 0.762730 | 0.381365 | − | 0.924425i | \(-0.375454\pi\) | ||||
0.381365 | + | 0.924425i | \(0.375454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820 | 0.315899 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.92820 | −0.451282 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.38323 | −0.153309 | −0.0766544 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766544 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5606 | 0.837630 | 0.418815 | − | 0.908072i | \(-0.362446\pi\) | ||||
0.418815 | + | 0.908072i | \(0.362446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47670 | 0.111545 | ||||||||
\(494\) | −3.86370 | −0.173836 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.9282 | −0.490691 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8564 | 1.15749 | 0.578746 | − | 0.815508i | \(-0.303542\pi\) | ||||
0.578746 | + | 0.815508i | \(0.303542\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.3586 | 1.26571 | ||||||||
\(503\) | −11.3205 | −0.504757 | −0.252378 | − | 0.967629i | \(-0.581213\pi\) | ||||
−0.252378 | + | 0.967629i | \(0.581213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.65685 | −0.251478 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.48528 | 0.376473 | ||||||||
\(509\) | −37.0470 | −1.64208 | −0.821039 | − | 0.570873i | \(-0.806605\pi\) | ||||
−0.821039 | + | 0.570873i | \(0.806605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8564 | −0.612971 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.7846 | −1.00499 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.62536 | 0.115463 | ||||||||
\(518\) | 6.92820 | 0.304408 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.52056 | 0.417103 | 0.208552 | − | 0.978011i | \(-0.433125\pi\) | ||||
0.208552 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.7685 | 1.17051 | 0.585253 | − | 0.810851i | \(-0.300995\pi\) | ||||
0.585253 | + | 0.810851i | \(0.300995\pi\) | |||||||
\(524\) | 3.10583 | 0.135679 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.3205 | −0.842414 | ||||||||
\(527\) | −5.85641 | −0.255109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.86370 | −0.167513 | ||||||||
\(533\) | −6.92820 | −0.300094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.3843 | −0.578112 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.9449 | 1.37724 | ||||||||
\(539\) | 8.20788 | 0.353538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | −10.9282 | −0.469407 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.535898 | −0.0229765 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3528 | −0.442652 | −0.221326 | − | 0.975200i | \(-0.571039\pi\) | ||||
−0.221326 | + | 0.975200i | \(0.571039\pi\) | |||||||
\(548\) | 0.535898 | 0.0228924 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.62158 | −0.196886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.4548 | −0.657206 | ||||||||
\(554\) | 18.2832 | 0.776780 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.92820 | 0.293821 | ||||||||
\(557\) | 31.4641 | 1.33318 | 0.666588 | − | 0.745426i | \(-0.267754\pi\) | ||||
0.666588 | + | 0.745426i | \(0.267754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8564 | 1.09361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.1870 | 1.31555 | ||||||||
\(563\) | 25.8564 | 1.08972 | 0.544859 | − | 0.838528i | \(-0.316583\pi\) | ||||
0.544859 | + | 0.838528i | \(0.316583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.17638 | −0.217580 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.14110 | −0.173757 | ||||||||
\(569\) | 44.0165 | 1.84527 | 0.922634 | − | 0.385678i | \(-0.126032\pi\) | ||||
0.922634 | + | 0.385678i | \(0.126032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9282 | 0.624726 | 0.312363 | − | 0.949963i | \(-0.398880\pi\) | ||||
0.312363 | + | 0.949963i | \(0.398880\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.92820 | −0.289178 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65685 | 0.235498 | 0.117749 | − | 0.993043i | \(-0.462432\pi\) | ||||
0.117749 | + | 0.993043i | \(0.462432\pi\) | |||||||
\(578\) | 16.7128 | 0.695161 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.3350 | 2.62758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.21166 | 0.257261 | ||||||||
\(584\) | 3.58630 | 0.148402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.8564 | 0.820261 | ||||||||
\(587\) | 24.3923 | 1.00678 | 0.503389 | − | 0.864060i | \(-0.332086\pi\) | ||||
0.503389 | + | 0.864060i | \(0.332086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9282 | 0.450289 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.79315 | −0.0736980 | ||||||||
\(593\) | −4.53590 | −0.186267 | −0.0931335 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931335 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.3538 | 0.833724 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.1117 | 0.863320 | ||||||||
\(599\) | −20.5569 | −0.839931 | −0.419965 | − | 0.907540i | \(-0.637958\pi\) | ||||
−0.419965 | + | 0.907540i | \(0.637958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7846 | −0.766240 | −0.383120 | − | 0.923699i | \(-0.625150\pi\) | ||||
−0.383120 | + | 0.923699i | \(0.625150\pi\) | |||||||
\(602\) | 25.8564 | 1.05383 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.85641 | 0.238294 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.6066 | −1.85111 | −0.925557 | − | 0.378609i | \(-0.876402\pi\) | ||||
−0.925557 | + | 0.378609i | \(0.876402\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.79796 | −0.396383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.85993 | −0.236680 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(614\) | −17.5254 | −0.707266 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 28.2487 | 1.13725 | 0.568625 | − | 0.822597i | \(-0.307476\pi\) | ||||
0.568625 | + | 0.822597i | \(0.307476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.6410 | −1.39234 | −0.696170 | − | 0.717877i | \(-0.745114\pi\) | ||||
−0.696170 | + | 0.717877i | \(0.745114\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.79315 | 0.0718988 | ||||||||
\(623\) | −14.9282 | −0.598086 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.5959 | 0.783210 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.1421 | 0.564333 | ||||||||
\(629\) | −0.960947 | −0.0383155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8564 | 0.870090 | 0.435045 | − | 0.900409i | \(-0.356732\pi\) | ||||
0.435045 | + | 0.900409i | \(0.356732\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0000 | −0.556011 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.6322 | −1.21369 | ||||||||
\(638\) | −4.78461 | −0.189425 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2480 | 0.681254 | 0.340627 | − | 0.940199i | \(-0.389361\pi\) | ||||
0.340627 | + | 0.940199i | \(0.389361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.0470 | −1.46099 | −0.730495 | − | 0.682918i | \(-0.760710\pi\) | ||||
−0.730495 | + | 0.682918i | \(0.760710\pi\) | |||||||
\(644\) | 21.1117 | 0.831916 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.535898 | 0.0210846 | ||||||||
\(647\) | 13.4641 | 0.529328 | 0.264664 | − | 0.964341i | \(-0.414739\pi\) | ||||
0.264664 | + | 0.964341i | \(0.414739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.21539 | 0.283229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.6627 | 0.926703 | ||||||||
\(653\) | −24.2487 | −0.948925 | −0.474463 | − | 0.880276i | \(-0.657358\pi\) | ||||
−0.474463 | + | 0.880276i | \(0.657358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.79315 | 0.0700108 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.79796 | −0.381964 | ||||||||
\(659\) | 20.3538 | 0.792871 | 0.396436 | − | 0.918063i | \(-0.370247\pi\) | ||||
0.396436 | + | 0.918063i | \(0.370247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7846 | −0.419473 | −0.209736 | − | 0.977758i | \(-0.567261\pi\) | ||||
−0.209736 | + | 0.977758i | \(0.567261\pi\) | |||||||
\(662\) | −13.8564 | −0.538545 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.3923 | −0.636145 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.2528 | 0.977791 | ||||||||
\(668\) | 10.9282 | 0.422825 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.07055 | −0.0799328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.2490 | −1.05037 | −0.525186 | − | 0.850988i | \(-0.676004\pi\) | ||||
−0.525186 | + | 0.850988i | \(0.676004\pi\) | |||||||
\(674\) | −1.03528 | −0.0398773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.92820 | 0.0741617 | ||||||||
\(677\) | 36.6410 | 1.40823 | 0.704114 | − | 0.710087i | \(-0.251344\pi\) | ||||
0.704114 | + | 0.710087i | \(0.251344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.85641 | 0.378254 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.3137 | 0.433224 | ||||||||
\(683\) | 18.9282 | 0.724268 | 0.362134 | − | 0.932126i | \(-0.382048\pi\) | ||||
0.362134 | + | 0.932126i | \(0.382048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.58630 | −0.136926 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.69213 | −0.255135 | ||||||||
\(689\) | −23.1822 | −0.883172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9282 | 1.48090 | 0.740449 | − | 0.672112i | \(-0.234613\pi\) | ||||
0.740449 | + | 0.672112i | \(0.234613\pi\) | |||||||
\(692\) | −22.7846 | −0.866141 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5359 | −0.703613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.960947 | 0.0363985 | ||||||||
\(698\) | −4.14359 | −0.156837 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.52433 | −0.284190 | −0.142095 | − | 0.989853i | \(-0.545384\pi\) | ||||
−0.142095 | + | 0.989853i | \(0.545384\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.79315 | 0.0676300 | ||||||||
\(704\) | 1.03528 | 0.0390184 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.3205 | −0.802408 | ||||||||
\(707\) | −40.7846 | −1.53386 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8564 | −0.445277 | −0.222638 | − | 0.974901i | \(-0.571467\pi\) | ||||
−0.222638 | + | 0.974901i | \(0.571467\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.86370 | 0.144798 | ||||||||
\(713\) | −59.7128 | −2.23626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.7675 | −0.626631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.7733 | −1.29773 | ||||||||
\(719\) | 46.6418 | 1.73945 | 0.869724 | − | 0.493539i | \(-0.164297\pi\) | ||||
0.869724 | + | 0.493539i | \(0.164297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9282 | 0.704923 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.8564 | 0.737958 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.1774 | −0.562899 | −0.281450 | − | 0.959576i | \(-0.590815\pi\) | ||||
−0.281450 | + | 0.959576i | \(0.590815\pi\) | |||||||
\(728\) | 14.9282 | 0.553276 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.58630 | −0.132644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.8695 | −0.807770 | −0.403885 | − | 0.914810i | \(-0.632340\pi\) | ||||
−0.403885 | + | 0.914810i | \(0.632340\pi\) | |||||||
\(734\) | 5.37945 | 0.198559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.46410 | −0.201409 | ||||||||
\(737\) | 13.8564 | 0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7128 | 0.872290 | 0.436145 | − | 0.899876i | \(-0.356343\pi\) | ||||
0.436145 | + | 0.899876i | \(0.356343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.1822 | −0.851046 | ||||||||
\(743\) | −34.6410 | −1.27086 | −0.635428 | − | 0.772160i | \(-0.719176\pi\) | ||||
−0.635428 | + | 0.772160i | \(0.719176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.9754 | 0.914413 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.554803 | 0.0202856 | ||||||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.85641 | 0.213703 | 0.106852 | − | 0.994275i | \(-0.465923\pi\) | ||||
0.106852 | + | 0.994275i | \(0.465923\pi\) | |||||||
\(752\) | 2.53590 | 0.0924747 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.8564 | 0.650292 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.3559 | 1.46676 | 0.733379 | − | 0.679820i | \(-0.237942\pi\) | ||||
0.733379 | + | 0.679820i | \(0.237942\pi\) | |||||||
\(758\) | 35.7128 | 1.29715 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1822 | 0.840355 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.4959 | 1.24884 | ||||||||
\(764\) | −17.2480 | −0.624009 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9282 | 0.828430 | ||||||||
\(767\) | −26.9282 | −0.972321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.8564 | 1.29302 | 0.646508 | − | 0.762908i | \(-0.276229\pi\) | ||||
0.646508 | + | 0.762908i | \(0.276229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.76268 | 0.315376 | ||||||||
\(773\) | −7.85641 | −0.282575 | −0.141288 | − | 0.989969i | \(-0.545124\pi\) | ||||
−0.141288 | + | 0.989969i | \(0.545124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.55103 | −0.0915765 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.7990 | 0.709828 | ||||||||
\(779\) | −1.79315 | −0.0642463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.28719 | 0.153408 | ||||||||
\(782\) | −2.92820 | −0.104712 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.92820 | 0.283150 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.17260 | 0.255676 | 0.127838 | − | 0.991795i | \(-0.459196\pi\) | ||||
0.127838 | + | 0.991795i | \(0.459196\pi\) | |||||||
\(788\) | 23.4641 | 0.835874 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1822 | 0.824265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.72741 | 0.274408 | ||||||||
\(794\) | −18.2832 | −0.648848 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0718 | 0.463318 | ||||||||
\(797\) | 40.6410 | 1.43958 | 0.719789 | − | 0.694193i | \(-0.244238\pi\) | ||||
0.719789 | + | 0.694193i | \(0.244238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.35898 | 0.0480774 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.52056 | −0.336183 | ||||||||
\(803\) | −3.71281 | −0.131022 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.2233 | −1.48725 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.5558 | 0.371353 | ||||||||
\(809\) | 44.8487 | 1.57680 | 0.788398 | − | 0.615166i | \(-0.210911\pi\) | ||||
0.788398 | + | 0.615166i | \(0.210911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4974 | −1.42206 | −0.711028 | − | 0.703163i | \(-0.751770\pi\) | ||||
−0.711028 | + | 0.703163i | \(0.751770\pi\) | |||||||
\(812\) | 17.8564 | 0.626637 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.85641 | 0.0650670 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.69213 | 0.234128 | ||||||||
\(818\) | 20.9282 | 0.731737 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.93048 | −0.276776 | −0.138388 | − | 0.990378i | \(-0.544192\pi\) | ||||
−0.138388 | + | 0.990378i | \(0.544192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.1966 | −1.64517 | −0.822586 | − | 0.568641i | \(-0.807469\pi\) | ||||
−0.822586 | + | 0.568641i | \(0.807469\pi\) | |||||||
\(824\) | −4.89898 | −0.170664 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.9282 | −0.936952 | ||||||||
\(827\) | 6.92820 | 0.240917 | 0.120459 | − | 0.992718i | \(-0.461563\pi\) | ||||
0.120459 | + | 0.992718i | \(0.461563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.7846 | 0.513491 | 0.256745 | − | 0.966479i | \(-0.417350\pi\) | ||||
0.256745 | + | 0.966479i | \(0.417350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.86370 | −0.133950 | ||||||||
\(833\) | 4.24871 | 0.147209 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.03528 | −0.0358058 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.3195 | −1.01283 | ||||||||
\(839\) | −28.2843 | −0.976481 | −0.488241 | − | 0.872709i | \(-0.662361\pi\) | ||||
−0.488241 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.64102 | −0.263483 | ||||||||
\(842\) | −29.7128 | −1.02397 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.8564 | −0.614643 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.3596 | −1.31805 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79796 | −0.335870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.6969 | −0.503214 | −0.251607 | − | 0.967830i | \(-0.580959\pi\) | ||||
−0.251607 | + | 0.967830i | \(0.580959\pi\) | |||||||
\(854\) | 7.72741 | 0.264426 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.92820 | 0.100084 | ||||||||
\(857\) | 16.6410 | 0.568446 | 0.284223 | − | 0.958758i | \(-0.408264\pi\) | ||||
0.284223 | + | 0.958758i | \(0.408264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.78461 | −0.163249 | −0.0816244 | − | 0.996663i | \(-0.526011\pi\) | ||||
−0.0816244 | + | 0.996663i | \(0.526011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.2137 | 0.892843 | ||||||||
\(863\) | 20.7846 | 0.707516 | 0.353758 | − | 0.935337i | \(-0.384904\pi\) | ||||
0.353758 | + | 0.935337i | \(0.384904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.8332 | 0.368128 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −42.2233 | −1.43315 | ||||||||
\(869\) | −4.14110 | −0.140477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.7128 | −1.75222 | ||||||||
\(872\) | −8.92820 | −0.302347 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.46410 | 0.184826 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.6713 | 1.00193 | 0.500964 | − | 0.865468i | \(-0.332979\pi\) | ||||
0.500964 | + | 0.865468i | \(0.332979\pi\) | |||||||
\(878\) | −20.0000 | −0.674967 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6370 | −1.30171 | −0.650857 | − | 0.759200i | \(-0.725590\pi\) | ||||
−0.650857 | + | 0.759200i | \(0.725590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.4703 | −1.66481 | −0.832404 | − | 0.554170i | \(-0.813036\pi\) | ||||
−0.832404 | + | 0.554170i | \(0.813036\pi\) | |||||||
\(884\) | −2.07055 | −0.0696402 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.3923 | −0.550710 | ||||||||
\(887\) | −15.7128 | −0.527585 | −0.263792 | − | 0.964580i | \(-0.584973\pi\) | ||||
−0.263792 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.7846 | 1.09956 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.5558 | −0.353435 | ||||||||
\(893\) | −2.53590 | −0.0848606 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.86370 | −0.129077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.4302 | 1.34917 | ||||||||
\(899\) | −50.5055 | −1.68445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21539 | 0.107120 | ||||||||
\(902\) | −1.85641 | −0.0618116 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.5665 | 1.21417 | 0.607085 | − | 0.794637i | \(-0.292339\pi\) | ||||
0.607085 | + | 0.794637i | \(0.292339\pi\) | |||||||
\(908\) | −1.85641 | −0.0616070 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.2548 | 1.49936 | 0.749680 | − | 0.661801i | \(-0.230208\pi\) | ||||
0.749680 | + | 0.661801i | \(0.230208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9706 | 0.561644 | ||||||||
\(914\) | 33.9411 | 1.12267 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.85641 | −0.127419 | ||||||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7128 | 0.914161 | 0.457081 | − | 0.889425i | \(-0.348895\pi\) | ||||
0.457081 | + | 0.889425i | \(0.348895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.5264 | −0.906534 | ||||||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.8733 | −0.653078 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.62158 | −0.151711 | ||||||||
\(929\) | 11.3137 | 0.371191 | 0.185595 | − | 0.982626i | \(-0.440579\pi\) | ||||
0.185595 | + | 0.982626i | \(0.440579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.92820 | −0.259836 | ||||||||
\(932\) | 12.5359 | 0.410627 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.53590 | −0.0829771 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5569 | 0.671563 | 0.335782 | − | 0.941940i | \(-0.391000\pi\) | ||||
0.335782 | + | 0.941940i | \(0.391000\pi\) | |||||||
\(938\) | −51.7128 | −1.68848 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9353 | 0.519475 | 0.259738 | − | 0.965679i | \(-0.416364\pi\) | ||||
0.259738 | + | 0.965679i | \(0.416364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.79796 | 0.319065 | ||||||||
\(944\) | 6.96953 | 0.226839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.92820 | 0.225255 | ||||||||
\(947\) | −25.1769 | −0.818140 | −0.409070 | − | 0.912503i | \(-0.634147\pi\) | ||||
−0.409070 | + | 0.912503i | \(0.634147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.8564 | 0.449798 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.07055 | −0.0671070 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.1069 | 0.423906 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.6932 | −0.539332 | ||||||||
\(959\) | 2.07055 | 0.0668616 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | −6.92820 | −0.223374 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.2480 | 0.554657 | 0.277329 | − | 0.960775i | \(-0.410551\pi\) | ||||
0.277329 | + | 0.960775i | \(0.410551\pi\) | |||||||
\(968\) | 9.92820 | 0.319105 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.2949 | 1.74241 | 0.871203 | − | 0.490922i | \(-0.163340\pi\) | ||||
0.871203 | + | 0.490922i | \(0.163340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7685 | 0.858159 | ||||||||
\(974\) | 3.38323 | 0.108406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 5.71281 | 0.182769 | 0.0913845 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913845 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.5606 | −0.592294 | ||||||||
\(983\) | 7.21539 | 0.230135 | 0.115068 | − | 0.993358i | \(-0.463292\pi\) | ||||
0.115068 | + | 0.993358i | \(0.463292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.47670 | −0.0788741 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.86370 | 0.122921 | ||||||||
\(989\) | −36.5665 | −1.16275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.7846 | −0.660245 | −0.330122 | − | 0.943938i | \(-0.607090\pi\) | ||||
−0.330122 | + | 0.943938i | \(0.607090\pi\) | |||||||
\(992\) | 10.9282 | 0.346971 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.2832 | 0.579036 | 0.289518 | − | 0.957173i | \(-0.406505\pi\) | ||||
0.289518 | + | 0.957173i | \(0.406505\pi\) | |||||||
\(998\) | −25.8564 | −0.818470 | ||||||||
\(999\) | 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 | 8550.2.a.cu.1.4 | 4 | ||
3.2 | odd | 2 | 8550.2.a.cv.1.4 | 4 | |||
5.2 | odd | 4 | 1710.2.d.g.1369.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1710.2.d.g.1369.5 | yes | 8 | ||
5.4 | even | 2 | 8550.2.a.cv.1.1 | 4 | |||
15.2 | even | 4 | 1710.2.d.g.1369.7 | yes | 8 | ||
15.8 | even | 4 | 1710.2.d.g.1369.4 | yes | 8 | ||
15.14 | odd | 2 | inner | 8550.2.a.cu.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.d.g.1369.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1710.2.d.g.1369.4 | yes | 8 | 15.8 | even | 4 | ||
1710.2.d.g.1369.5 | yes | 8 | 5.3 | odd | 4 | ||
1710.2.d.g.1369.7 | yes | 8 | 15.2 | even | 4 | ||
8550.2.a.cu.1.1 | 4 | 15.14 | odd | 2 | inner | ||
8550.2.a.cu.1.4 | 4 | 1.1 | even | 1 | trivial | ||
8550.2.a.cv.1.1 | 4 | 5.4 | even | 2 | |||
8550.2.a.cv.1.4 | 4 | 3.2 | odd | 2 |