Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(575,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.h (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.5473632256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 49x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.4 | ||
Root | \(1.81129 - 1.81129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.g.575.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.20837i | − 0.987613i | −0.869572 | − | 0.493806i | \(-0.835605\pi\) | ||||
0.869572 | − | 0.493806i | \(-0.164395\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.794156 | −0.239447 | −0.119723 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119723 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.12311 | 1.42089 | 0.710447 | − | 0.703751i | \(-0.248493\pi\) | ||||
0.710447 | + | 0.703751i | \(0.248493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 0.620058i | − 0.150386i | −0.997169 | − | 0.0751931i | \(-0.976043\pi\) | ||||
0.997169 | − | 0.0751931i | \(-0.0239573\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.00000i | − 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.794156 | 0.165593 | 0.0827964 | − | 0.996566i | \(-0.473615\pi\) | ||||
0.0827964 | + | 0.996566i | \(0.473615\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.123106 | 0.0246211 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00252i | 0.557555i | 0.960356 | + | 0.278777i | \(0.0899292\pi\) | ||||
−0.960356 | + | 0.278777i | \(0.910071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24621i | 1.12185i | 0.827866 | + | 0.560926i | \(0.189555\pi\) | ||||
−0.827866 | + | 0.560926i | \(0.810445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.20837 | 0.373283 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1231 | 1.82863 | 0.914314 | − | 0.405007i | \(-0.132731\pi\) | ||||
0.914314 | + | 0.405007i | \(0.132731\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 3.44849i | − 0.538563i | −0.963062 | − | 0.269281i | \(-0.913214\pi\) | ||||
0.963062 | − | 0.269281i | \(-0.0867862\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9020 | −1.88195 | −0.940976 | − | 0.338472i | \(-0.890090\pi\) | ||||
−0.940976 | + | 0.338472i | \(0.890090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00252i | 0.412428i | 0.978507 | + | 0.206214i | \(0.0661144\pi\) | ||||
−0.978507 | + | 0.206214i | \(0.933886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.75379i | 0.236481i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.58831 | −0.206781 | −0.103390 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103390 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 11.3137i | − 1.40329i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.12311i | − 0.625887i | −0.949772 | − | 0.312943i | \(-0.898685\pi\) | ||||
0.949772 | − | 0.312943i | \(-0.101315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.03932 | 0.954092 | 0.477046 | − | 0.878878i | \(-0.341708\pi\) | ||||
0.477046 | + | 0.878878i | \(0.341708\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.12311 | 0.131450 | 0.0657248 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657248 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.794156i | − 0.0905024i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.3693i | − 1.27915i | −0.768729 | − | 0.639574i | \(-0.779111\pi\) | ||||
0.768729 | − | 0.639574i | \(-0.220889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4903 | 1.59052 | 0.795260 | − | 0.606268i | \(-0.207334\pi\) | ||||
0.795260 | + | 0.606268i | \(0.207334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.36932 | −0.148523 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.20837i | 0.234087i | 0.993127 | + | 0.117043i | \(0.0373416\pi\) | ||||
−0.993127 | + | 0.117043i | \(0.962658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.12311i | 0.537047i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.83348 | −0.906296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.12311 | 0.114034 | 0.0570170 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570170 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.03680i | 0.501180i | 0.968093 | + | 0.250590i | \(0.0806246\pi\) | ||||
−0.968093 | + | 0.250590i | \(0.919375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000i | 1.18240i | 0.806527 | + | 0.591198i | \(0.201345\pi\) | ||||
−0.806527 | + | 0.591198i | \(0.798655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.38247 | 0.230322 | 0.115161 | − | 0.993347i | \(-0.463262\pi\) | ||||
0.115161 | + | 0.993347i | \(0.463262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0000 | 1.14939 | 0.574696 | − | 0.818367i | \(-0.305120\pi\) | ||||
0.574696 | + | 0.818367i | \(0.305120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 20.3213i | − 1.91167i | −0.293911 | − | 0.955833i | \(-0.594957\pi\) | ||||
0.293911 | − | 0.955833i | \(-0.405043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.75379i | − 0.163542i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.620058 | 0.0568406 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3693 | −0.942665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.3137i | − 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3693i | 1.71875i | 0.511347 | + | 0.859374i | \(0.329147\pi\) | ||||
−0.511347 | + | 0.859374i | \(0.670853\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 18.3848i | − 1.57072i | −0.619041 | − | 0.785359i | \(-0.712479\pi\) | ||||
0.619041 | − | 0.785359i | \(-0.287521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.06854 | −0.340229 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.63068 | 0.550648 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 13.0761i | − 1.07124i | −0.844460 | − | 0.535619i | \(-0.820078\pi\) | ||||
0.844460 | − | 0.535619i | \(-0.179922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.7939 | 1.10796 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.794156i | 0.0625882i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.6155i | − 1.37975i | −0.723926 | − | 0.689877i | \(-0.757664\pi\) | ||||
0.723926 | − | 0.689877i | \(-0.242336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.24517 | 0.560648 | 0.280324 | − | 0.959905i | \(-0.409558\pi\) | ||||
0.280324 | + | 0.959905i | \(0.409558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2462 | 1.01894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 20.7672i | − 1.57890i | −0.613812 | − | 0.789452i | \(-0.710365\pi\) | ||||
0.613812 | − | 0.789452i | \(-0.289635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.123106i | 0.00930591i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9413 | −1.56523 | −0.782615 | − | 0.622506i | \(-0.786114\pi\) | ||||
−0.782615 | + | 0.622506i | \(0.786114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.12311 | 0.380797 | 0.190399 | − | 0.981707i | \(-0.439022\pi\) | ||||
0.190399 | + | 0.981707i | \(0.439022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 24.5639i | − 1.80598i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.492423i | 0.0360095i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.86270 | −0.351853 | −0.175926 | − | 0.984403i | \(-0.556292\pi\) | ||||
−0.175926 | + | 0.984403i | \(0.556292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.12311 | −0.512732 | −0.256366 | − | 0.966580i | \(-0.582525\pi\) | ||||
−0.256366 | + | 0.966580i | \(0.582525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.3162i | − 1.01999i | −0.860178 | − | 0.509995i | \(-0.829647\pi\) | ||||
0.860178 | − | 0.509995i | \(-0.170353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5.75379i | − 0.407875i | −0.978984 | − | 0.203938i | \(-0.934626\pi\) | ||||
0.978984 | − | 0.203938i | \(-0.0653740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00252 | −0.210736 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.61553 | −0.531892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.17662i | 0.219732i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.4924i | − 1.13539i | −0.823241 | − | 0.567693i | \(-0.807836\pi\) | ||||
0.823241 | − | 0.567693i | \(-0.192164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.83348 | −0.602438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.24621 | −0.424020 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.17662i | − 0.213683i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.24621i | 0.150417i | 0.997168 | + | 0.0752087i | \(0.0239623\pi\) | ||||
−0.997168 | + | 0.0752087i | \(0.976038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.8726 | −1.98271 | −0.991356 | − | 0.131196i | \(-0.958118\pi\) | ||||
−0.991356 | + | 0.131196i | \(0.958118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.8769 | −0.718765 | −0.359383 | − | 0.933190i | \(-0.617013\pi\) | ||||
−0.359383 | + | 0.933190i | \(0.617013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.83095i | 0.381998i | 0.981590 | + | 0.190999i | \(0.0611728\pi\) | ||||
−0.981590 | + | 0.190999i | \(0.938827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.4924i | 1.85864i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.03932 | 0.520020 | 0.260010 | − | 0.965606i | \(-0.416274\pi\) | ||||
0.260010 | + | 0.965606i | \(0.416274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.12311 | −0.587671 | −0.293835 | − | 0.955856i | \(-0.594932\pi\) | ||||
−0.293835 | + | 0.955856i | \(0.594932\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.20837i | 0.141088i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 20.4924i | − 1.30390i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9020 | 0.814368 | 0.407184 | − | 0.913346i | \(-0.366511\pi\) | ||||
0.407184 | + | 0.913346i | \(0.366511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.630683 | −0.0396507 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.62511i | 0.413263i | 0.978419 | + | 0.206631i | \(0.0662501\pi\) | ||||
−0.978419 | + | 0.206631i | \(0.933750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1231i | 0.691156i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.5982 | 1.64011 | 0.820057 | − | 0.572281i | \(-0.193941\pi\) | ||||
0.820057 | + | 0.572281i | \(0.193941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.63068 | 0.407320 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 10.3455i | − 0.630774i | −0.948963 | − | 0.315387i | \(-0.897866\pi\) | ||||
0.948963 | − | 0.315387i | \(-0.102134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000i | 0.242983i | 0.992592 | + | 0.121491i | \(0.0387677\pi\) | ||||
−0.992592 | + | 0.121491i | \(0.961232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0977650 | −0.00589545 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.12311 | 0.548154 | 0.274077 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274077 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9045i | 0.948786i | 0.880313 | + | 0.474393i | \(0.157332\pi\) | ||||
−0.880313 | + | 0.474393i | \(0.842668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000i | 0.713326i | 0.934233 | + | 0.356663i | \(0.116086\pi\) | ||||
−0.934233 | + | 0.356663i | \(0.883914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.44849 | 0.203558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6155 | 0.977384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.03680i | − 0.294253i | −0.989118 | − | 0.147126i | \(-0.952998\pi\) | ||||
0.989118 | − | 0.147126i | \(-0.0470024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.50758i | 0.204219i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.06854 | 0.235290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 4.41674i | − 0.252902i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 14.2462i | − 0.813074i | −0.913634 | − | 0.406537i | \(-0.866736\pi\) | ||||
0.913634 | − | 0.406537i | \(-0.133264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0786 | −0.911736 | −0.455868 | − | 0.890047i | \(-0.650671\pi\) | ||||
−0.455868 | + | 0.890047i | \(0.650671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2462 | 1.14438 | 0.572192 | − | 0.820120i | \(-0.306093\pi\) | ||||
0.572192 | + | 0.820120i | \(0.306093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.3898i | 1.36987i | 0.728605 | + | 0.684935i | \(0.240169\pi\) | ||||
−0.728605 | + | 0.684935i | \(0.759831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.38447i | − 0.133505i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.48023 | −0.138004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.630683 | 0.0349840 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 12.9020i | − 0.711311i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 0.492423i | − 0.0270660i | −0.999908 | − | 0.0135330i | \(-0.995692\pi\) | ||||
0.999908 | − | 0.0135330i | \(-0.00430782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7538 | 0.749217 | 0.374608 | − | 0.927183i | \(-0.377777\pi\) | ||||
0.374608 | + | 0.927183i | \(0.377777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.96046i | − 0.268624i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.0099 | 1.34260 | 0.671300 | − | 0.741185i | \(-0.265736\pi\) | ||||
0.671300 | + | 0.741185i | \(0.265736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2462 | −1.29787 | −0.648935 | − | 0.760844i | \(-0.724785\pi\) | ||||
−0.648935 | + | 0.760844i | \(0.724785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.86017i | − 0.0990071i | −0.998774 | − | 0.0495035i | \(-0.984236\pi\) | ||||
0.998774 | − | 0.0495035i | \(-0.0157639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 17.7538i | − 0.942273i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.0784 | 1.53470 | 0.767350 | − | 0.641228i | \(-0.221575\pi\) | ||||
0.767350 | + | 0.641228i | \(0.221575\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.48023i | − 0.129821i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 36.4924i | − 1.90489i | −0.304712 | − | 0.952444i | \(-0.598560\pi\) | ||||
0.304712 | − | 0.952444i | \(-0.401440\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00252 | −0.155883 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7386 | 1.28092 | 0.640459 | − | 0.767992i | \(-0.278744\pi\) | ||||
0.640459 | + | 0.767992i | \(0.278744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.3823i | 0.792226i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000i | 1.43826i | 0.694874 | + | 0.719132i | \(0.255460\pi\) | ||||
−0.694874 | + | 0.719132i | \(0.744540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.75379 | −0.0893814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.06602i | − 0.0540493i | −0.999635 | − | 0.0270246i | \(-0.991397\pi\) | ||||
0.999635 | − | 0.0270246i | \(-0.00860326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.492423i | − 0.0249029i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.1076 | −1.26330 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 4.59084i | − 0.229255i | −0.993409 | − | 0.114628i | \(-0.963432\pi\) | ||||
0.993409 | − | 0.114628i | \(-0.0365675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.0000i | 1.59403i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.83348 | −0.437859 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.3693 | 1.35333 | 0.676663 | − | 0.736293i | \(-0.263425\pi\) | ||||
0.676663 | + | 0.736293i | \(0.263425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.58831i | − 0.0781557i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 32.0000i | − 1.57082i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.7355 | −1.06185 | −0.530924 | − | 0.847419i | \(-0.678155\pi\) | ||||
−0.530924 | + | 0.847419i | \(0.678155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1231 | −1.61432 | −0.807161 | − | 0.590332i | \(-0.798997\pi\) | ||||
−0.807161 | + | 0.590332i | \(0.798997\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 0.0763326i | − 0.00370268i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.7353 | 1.67314 | 0.836570 | − | 0.547860i | \(-0.184557\pi\) | ||||
0.836570 | + | 0.547860i | \(0.184557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7386 | 1.38109 | 0.690545 | − | 0.723289i | \(-0.257371\pi\) | ||||
0.690545 | + | 0.723289i | \(0.257371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.17662i | − 0.151958i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9848i | 1.57428i | 0.616774 | + | 0.787140i | \(0.288439\pi\) | ||||
−0.616774 | + | 0.787140i | \(0.711561\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.45101 | −0.306497 | −0.153248 | − | 0.988188i | \(-0.548973\pi\) | ||||
−0.153248 | + | 0.988188i | \(0.548973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.87689 | 0.231187 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.8066i | 1.35947i | 0.733460 | + | 0.679733i | \(0.237904\pi\) | ||||
−0.733460 | + | 0.679733i | \(0.762096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.73863i | 0.128957i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3137 | 0.530395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0000 | −1.12267 | −0.561336 | − | 0.827588i | \(-0.689713\pi\) | ||||
−0.561336 | + | 0.827588i | \(0.689713\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.27691i | 0.292345i | 0.989259 | + | 0.146172i | \(0.0466954\pi\) | ||||
−0.989259 | + | 0.146172i | \(0.953305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.8617i | − 1.10895i | −0.832201 | − | 0.554475i | \(-0.812919\pi\) | ||||
0.832201 | − | 0.554475i | \(-0.187081\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.0786 | −0.744031 | −0.372015 | − | 0.928227i | \(-0.621333\pi\) | ||||
−0.372015 | + | 0.928227i | \(0.621333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.12311 | 0.236563 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.17662i | 0.146061i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.492423i | − 0.0225939i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.0492 | −1.51006 | −0.755028 | − | 0.655692i | \(-0.772377\pi\) | ||||
−0.755028 | + | 0.655692i | \(0.772377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.9848 | 2.59829 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.48023i | − 0.112622i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5982 | 1.20036 | 0.600180 | − | 0.799865i | \(-0.295096\pi\) | ||||
0.600180 | + | 0.799865i | \(0.295096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.86174 | 0.0838485 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.03932i | 0.360613i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9848i | 1.29754i | 0.760985 | + | 0.648770i | \(0.224716\pi\) | ||||
−0.760985 | + | 0.648770i | \(0.775284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.9411 | 1.51336 | 0.756680 | − | 0.653785i | \(-0.226820\pi\) | ||||
0.756680 | + | 0.653785i | \(0.226820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1231 | 0.494972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 34.9094i | − 1.54733i | −0.633594 | − | 0.773666i | \(-0.718421\pi\) | ||||
0.633594 | − | 0.773666i | \(-0.281579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.12311i | 0.0496833i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.5004 | 1.16775 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2462 | 0.450628 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.0175i | 1.49033i | 0.666879 | + | 0.745166i | \(0.267630\pi\) | ||||
−0.666879 | + | 0.745166i | \(0.732370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.4924i | − 1.24589i | −0.782267 | − | 0.622943i | \(-0.785937\pi\) | ||||
0.782267 | − | 0.622943i | \(-0.214063\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.87301 | 0.168711 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3693 | −0.972579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17.6670i | − 0.765241i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 5.26137i | − 0.227469i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.794156 | 0.0342067 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.87689 | −0.295661 | −0.147830 | − | 0.989013i | \(-0.547229\pi\) | ||||
−0.147830 | + | 0.989013i | \(0.547229\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 26.5004i | − 1.13515i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10.8769i | − 0.465062i | −0.972589 | − | 0.232531i | \(-0.925299\pi\) | ||||
0.972589 | − | 0.232531i | \(-0.0747008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0101 | 0.511647 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3693 | 0.483473 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3848i | 0.778988i | 0.921029 | + | 0.389494i | \(0.127350\pi\) | ||||
−0.921029 | + | 0.389494i | \(0.872650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 20.4924i | − 0.866737i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.8827 | −1.76514 | −0.882572 | − | 0.470177i | \(-0.844190\pi\) | ||||
−0.882572 | + | 0.470177i | \(0.844190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −44.8769 | −1.88799 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 22.4533i | − 0.941292i | −0.882322 | − | 0.470646i | \(-0.844021\pi\) | ||||
0.882322 | − | 0.470646i | \(-0.155979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8769i | 1.45955i | 0.683686 | + | 0.729776i | \(0.260376\pi\) | ||||
−0.683686 | + | 0.729776i | \(0.739624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0977650 | 0.00407708 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.9848 | −1.62296 | −0.811480 | − | 0.584380i | \(-0.801338\pi\) | ||||
−0.811480 | + | 0.584380i | \(0.801338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4903i | 0.601160i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.38447i | − 0.0987547i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2056 | 0.503780 | 0.251890 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251890 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9848 | 1.02948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.1545i | 1.73108i | 0.500840 | + | 0.865540i | \(0.333024\pi\) | ||||
−0.500840 | + | 0.865540i | \(0.666976\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.36932i | − 0.0561365i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9018 | 1.05832 | 0.529160 | − | 0.848522i | \(-0.322507\pi\) | ||||
0.529160 | + | 0.848522i | \(0.322507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.9848 | −1.42706 | −0.713531 | − | 0.700624i | \(-0.752905\pi\) | ||||
−0.713531 | + | 0.700624i | \(0.752905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.8993i | 0.930988i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4924i | 1.15647i | 0.815870 | + | 0.578236i | \(0.196259\pi\) | ||||
−0.815870 | + | 0.578236i | \(0.803741\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −66.0984 | −2.67406 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.50758 | 0.222449 | 0.111224 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111224 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.5715i | 1.35154i | 0.737114 | + | 0.675769i | \(0.236188\pi\) | ||||
−0.737114 | + | 0.675769i | \(0.763812\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 22.7386i | − 0.913943i | −0.889481 | − | 0.456971i | \(-0.848934\pi\) | ||||
0.889481 | − | 0.456971i | \(-0.151066\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.20837 | −0.0884764 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3693 | −0.974773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 6.89697i | − 0.275000i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.3693i | 1.72651i | 0.504772 | + | 0.863253i | \(0.331577\pi\) | ||||
−0.504772 | + | 0.863253i | \(0.668423\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.7746 | 1.69746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.12311 | −0.202985 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.1447i | 0.677173i | 0.940935 | + | 0.338587i | \(0.109949\pi\) | ||||
−0.940935 | + | 0.338587i | \(0.890051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.5589 | −0.729625 | −0.364812 | − | 0.931081i | \(-0.618867\pi\) | ||||
−0.364812 | + | 0.931081i | \(0.618867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26137 | 0.0495130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.2132i | 0.830137i | 0.909790 | + | 0.415068i | \(0.136242\pi\) | ||||
−0.909790 | + | 0.415068i | \(0.863758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 12.4924i | − 0.488119i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9119 | 1.47684 | 0.738419 | − | 0.674342i | \(-0.235573\pi\) | ||||
0.738419 | + | 0.674342i | \(0.235573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.73863 | −0.339893 | −0.169947 | − | 0.985453i | \(-0.554360\pi\) | ||||
−0.169947 | + | 0.985453i | \(0.554360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 8.83348i | − 0.342548i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.38447i | 0.0923271i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.58831 | −0.0613161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1080 | −1.70024 | −0.850118 | − | 0.526592i | \(-0.823470\pi\) | ||||
−0.850118 | + | 0.526592i | \(0.823470\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.6348i | 1.71545i | 0.514106 | + | 0.857727i | \(0.328124\pi\) | ||||
−0.514106 | + | 0.857727i | \(0.671876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12311i | 0.0431008i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5297 | −0.862073 | −0.431037 | − | 0.902334i | \(-0.641852\pi\) | ||||
−0.431037 | + | 0.902334i | \(0.641852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.6004 | −1.55126 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3823i | 0.586017i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13.7538i | − 0.523219i | −0.965174 | − | 0.261609i | \(-0.915747\pi\) | ||||
0.965174 | − | 0.261609i | \(-0.0842532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.13826 | −0.0809924 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 8.31118i | − 0.313909i | −0.987606 | − | 0.156955i | \(-0.949832\pi\) | ||||
0.987606 | − | 0.156955i | \(-0.0501676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 44.4924i | − 1.67806i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.03680 | −0.189428 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | 0.150223 | 0.0751116 | − | 0.997175i | \(-0.476069\pi\) | ||||
0.0751116 | + | 0.997175i | \(0.476069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.96046i | 0.185771i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.98485i | 0.336014i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.696391 | 0.0259710 | 0.0129855 | − | 0.999916i | \(-0.495866\pi\) | ||||
0.0129855 | + | 0.999916i | \(0.495866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | −0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.369628i | 0.0137276i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.9848i | 1.66840i | 0.551465 | + | 0.834198i | \(0.314069\pi\) | ||||
−0.551465 | + | 0.834198i | \(0.685931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.48023 | −0.0917347 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.3542 | −1.78600 | −0.893001 | − | 0.450055i | \(-0.851404\pi\) | ||||
−0.893001 | + | 0.450055i | \(0.851404\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.06854i | 0.149867i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.61553i | 0.353713i | 0.984237 | + | 0.176856i | \(0.0565928\pi\) | ||||
−0.984237 | + | 0.176856i | \(0.943407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5881 | 0.535185 | 0.267593 | − | 0.963532i | \(-0.413772\pi\) | ||||
0.267593 | + | 0.963532i | \(0.413772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.8769 | −1.05797 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.38247i | 0.0870534i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 36.4924i | − 1.33163i | −0.746118 | − | 0.665814i | \(-0.768085\pi\) | ||||
0.746118 | − | 0.665814i | \(-0.231915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4924 | −0.599427 | −0.299714 | − | 0.954029i | \(-0.596891\pi\) | ||||
−0.299714 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3160i | 0.990205i | 0.868835 | + | 0.495102i | \(0.164869\pi\) | ||||
−0.868835 | + | 0.495102i | \(0.835131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000i | 0.434429i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.13709 | −0.293813 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7538 | 0.856584 | 0.428292 | − | 0.903641i | \(-0.359116\pi\) | ||||
0.428292 | + | 0.903641i | \(0.359116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.21342i | − 0.295416i | −0.989031 | − | 0.147708i | \(-0.952810\pi\) | ||||
0.989031 | − | 0.147708i | \(-0.0471896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.768944i | 0.0276213i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.7939 | −0.494219 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.38447 | −0.228454 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 30.9172i | − 1.10348i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 46.7386i | − 1.66605i | −0.553234 | − | 0.833026i | \(-0.686606\pi\) | ||||
0.553234 | − | 0.833026i | \(-0.313394\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.3213 | 0.722542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2462 | 0.363854 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.5271i | 0.691686i | 0.938292 | + | 0.345843i | \(0.112407\pi\) | ||||
−0.938292 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.891921 | −0.0314752 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75379 | 0.0618129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 16.2527i | − 0.571416i | −0.958317 | − | 0.285708i | \(-0.907771\pi\) | ||||
0.958317 | − | 0.285708i | \(-0.0922287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 5.75379i | − 0.202043i | −0.994884 | − | 0.101021i | \(-0.967789\pi\) | ||||
0.994884 | − | 0.101021i | \(-0.0322111\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.9016 | −1.36266 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.8015i | 0.795778i | 0.917433 | + | 0.397889i | \(0.130257\pi\) | ||||
−0.917433 | + | 0.397889i | \(0.869743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.63068i | 0.161415i | 0.996738 | + | 0.0807077i | \(0.0257180\pi\) | ||||
−0.996738 | + | 0.0807077i | \(0.974282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.8825 | 1.90845 | 0.954225 | − | 0.299089i | \(-0.0966828\pi\) | ||||
0.954225 | + | 0.299089i | \(0.0966828\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6155 | 0.611813 | 0.305906 | − | 0.952062i | \(-0.401041\pi\) | ||||
0.305906 | + | 0.952062i | \(0.401041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.620058i | 0.0214837i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 16.0000i | − 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.72540 | −0.335758 | −0.167879 | − | 0.985808i | \(-0.553692\pi\) | ||||
−0.167879 | + | 0.985808i | \(0.553692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.9848 | 0.689133 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 29.2525i | − 1.00632i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.3693i | − 0.356294i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.83348 | 0.302808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7538 | −0.539399 | −0.269700 | − | 0.962944i | \(-0.586924\pi\) | ||||
−0.269700 | + | 0.962944i | \(0.586924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 37.3896i | − 1.27720i | −0.769537 | − | 0.638602i | \(-0.779513\pi\) | ||||
0.769537 | − | 0.638602i | \(-0.220487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 31.2311i | − 1.06559i | −0.846244 | − | 0.532795i | \(-0.821142\pi\) | ||||
0.846244 | − | 0.532795i | \(-0.178858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.0200 | −1.26017 | −0.630087 | − | 0.776524i | \(-0.716981\pi\) | ||||
−0.630087 | + | 0.776524i | \(0.716981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.8617 | −1.55935 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.02901i | 0.306288i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 26.2462i | − 0.889319i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | 0.382473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7538 | 0.802108 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.1941i | 1.25310i | 0.779381 | + | 0.626550i | \(0.215534\pi\) | ||||
−0.779381 | + | 0.626550i | \(0.784466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9848i | 0.975418i | 0.873006 | + | 0.487709i | \(0.162167\pi\) | ||||
−0.873006 | + | 0.487709i | \(0.837833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.0492 | −1.10968 | −0.554842 | − | 0.831956i | \(-0.687221\pi\) | ||||
−0.554842 | + | 0.831956i | \(0.687221\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.3693 | −0.649626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.6081i | 1.72700i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.2462i | 1.54584i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.7544 | −0.625494 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86174 | 0.0620235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 11.3137i | − 0.376080i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24.4924i | − 0.813258i | −0.913593 | − | 0.406629i | \(-0.866704\pi\) | ||||
0.913593 | − | 0.406629i | \(-0.133296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.0885 | −1.36132 | −0.680662 | − | 0.732598i | \(-0.738308\pi\) | ||||
−0.680662 | + | 0.732598i | \(0.738308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5076 | −0.380845 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.65685i | 0.186806i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.9848i | 1.08807i | 0.839063 | + | 0.544035i | \(0.183104\pi\) | ||||
−0.839063 | + | 0.544035i | \(0.816896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.1863 | 1.35566 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.36932 | 0.0450229 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 24.8358i | − 0.814836i | −0.913242 | − | 0.407418i | \(-0.866429\pi\) | ||||
0.913242 | − | 0.407418i | \(-0.133571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000i | 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.08745 | 0.0355634 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2614 | −0.367893 | −0.183946 | − | 0.982936i | \(-0.558887\pi\) | ||||
−0.183946 | + | 0.982936i | \(0.558887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.4926i | 0.994032i | 0.867741 | + | 0.497016i | \(0.165571\pi\) | ||||
−0.867741 | + | 0.497016i | \(0.834429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.73863i | − 0.0891822i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.45101 | −0.209630 | −0.104815 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104815 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.75379 | 0.186776 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.1051i | 0.716055i | 0.933711 | + | 0.358028i | \(0.116551\pi\) | ||||
−0.933711 | + | 0.358028i | \(0.883449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7386i | 0.347494i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.3848 | 0.593675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.01515 | −0.258553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.7304i | 0.506381i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1231i | 1.06517i | 0.846377 | + | 0.532584i | \(0.178779\pi\) | ||||
−0.846377 | + | 0.532584i | \(0.821221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.1472 | −0.646554 | −0.323277 | − | 0.946304i | \(-0.604785\pi\) | ||||
−0.323277 | + | 0.946304i | \(0.604785\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.3898i | − 0.780300i | −0.920751 | − | 0.390150i | \(-0.872423\pi\) | ||||
0.920751 | − | 0.390150i | \(-0.127577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.75379i | − 0.0560513i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.3238 | 0.743914 | 0.371957 | − | 0.928250i | \(-0.378687\pi\) | ||||
0.371957 | + | 0.928250i | \(0.378687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.6155 | −1.00735 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.17662i | − 0.101011i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 24.0000i | − 0.762385i | −0.924496 | − | 0.381193i | \(-0.875513\pi\) | ||||
0.924496 | − | 0.381193i | \(-0.124487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.7065 | −0.402823 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.246211 | −0.00779759 | −0.00389879 | − | 0.999992i | \(-0.501241\pi\) | ||||
−0.00389879 | + | 0.999992i | \(0.501241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4032.2.h.g.575.4 | 8 | ||
3.2 | odd | 2 | inner | 4032.2.h.g.575.6 | 8 | ||
4.3 | odd | 2 | inner | 4032.2.h.g.575.3 | 8 | ||
8.3 | odd | 2 | 2016.2.h.e.575.5 | yes | 8 | ||
8.5 | even | 2 | 2016.2.h.e.575.6 | yes | 8 | ||
12.11 | even | 2 | inner | 4032.2.h.g.575.5 | 8 | ||
24.5 | odd | 2 | 2016.2.h.e.575.4 | yes | 8 | ||
24.11 | even | 2 | 2016.2.h.e.575.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.h.e.575.3 | ✓ | 8 | 24.11 | even | 2 | ||
2016.2.h.e.575.4 | yes | 8 | 24.5 | odd | 2 | ||
2016.2.h.e.575.5 | yes | 8 | 8.3 | odd | 2 | ||
2016.2.h.e.575.6 | yes | 8 | 8.5 | even | 2 | ||
4032.2.h.g.575.3 | 8 | 4.3 | odd | 2 | inner | ||
4032.2.h.g.575.4 | 8 | 1.1 | even | 1 | trivial | ||
4032.2.h.g.575.5 | 8 | 12.11 | even | 2 | inner | ||
4032.2.h.g.575.6 | 8 | 3.2 | odd | 2 | inner |