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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1710) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) 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 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.46410 | −1.51547 | −0.757735 | − | 0.652563i | \(-0.773694\pi\) | ||||
−0.757735 | + | 0.652563i | \(0.773694\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.46410 | 0.738549 | ||||||||
\(23\) | 6.92820 | 1.44463 | 0.722315 | − | 0.691564i | \(-0.243078\pi\) | ||||
0.722315 | + | 0.691564i | \(0.243078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | −3.46410 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.46410 | −0.262960 | −0.131480 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131480 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.46410 | 0.240697 | 0.120348 | − | 0.992732i | \(-0.461599\pi\) | ||||
0.120348 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.46410 | −0.833268 | −0.416634 | − | 0.909074i | \(-0.636790\pi\) | ||||
−0.416634 | + | 0.909074i | \(0.636790\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.92820 | 1.02151 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.46410 | −0.757735 | ||||||||
\(53\) | −12.9282 | −1.77583 | −0.887913 | − | 0.460012i | \(-0.847845\pi\) | ||||
−0.887913 | + | 0.460012i | \(0.847845\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.46410 | −0.454859 | ||||||||
\(59\) | 3.46410 | 0.450988 | 0.225494 | − | 0.974245i | \(-0.427600\pi\) | ||||
0.225494 | + | 0.974245i | \(0.427600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −1.46410 | −0.185941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9282 | −1.82377 | −0.911885 | − | 0.410445i | \(-0.865373\pi\) | ||||
−0.911885 | + | 0.410445i | \(0.865373\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.92820 | 0.576803 | 0.288401 | − | 0.957510i | \(-0.406876\pi\) | ||||
0.288401 | + | 0.957510i | \(0.406876\pi\) | |||||||
\(74\) | 1.46410 | 0.170198 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −6.92820 | −0.789542 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.46410 | −0.164724 | −0.0823622 | − | 0.996602i | \(-0.526246\pi\) | ||||
−0.0823622 | + | 0.996602i | \(0.526246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.53590 | −0.278351 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.46410 | −0.589209 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.46410 | 0.369274 | ||||||||
\(89\) | −6.92820 | −0.734388 | −0.367194 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367194 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9282 | 1.14559 | ||||||||
\(92\) | 6.92820 | 0.722315 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3923 | −1.86746 | −0.933728 | − | 0.357984i | \(-0.883464\pi\) | ||||
−0.933728 | + | 0.357984i | \(0.883464\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.92820 | 0.485590 | 0.242795 | − | 0.970078i | \(-0.421936\pi\) | ||||
0.242795 | + | 0.970078i | \(0.421936\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.9282 | −1.25570 | ||||||||
\(107\) | 6.92820 | 0.669775 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3923 | −1.37853 | −0.689266 | − | 0.724508i | \(-0.742067\pi\) | ||||
−0.689266 | + | 0.724508i | \(0.742067\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.46410 | −0.321634 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.46410 | 0.318896 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.46410 | −0.131480 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0000 | −1.24230 | −0.621150 | − | 0.783692i | \(-0.713334\pi\) | ||||
−0.621150 | + | 0.783692i | \(0.713334\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.46410 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | −0.173422 | ||||||||
\(134\) | −14.9282 | −1.28960 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | −0.297044 | ||||||||
\(137\) | −15.4641 | −1.32119 | −0.660594 | − | 0.750744i | \(-0.729695\pi\) | ||||
−0.660594 | + | 0.750744i | \(0.729695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.85641 | 0.836009 | 0.418005 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418005 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.92820 | 0.581402 | ||||||||
\(143\) | −18.9282 | −1.58286 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.92820 | 0.407861 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.46410 | 0.120348 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.39230 | −0.682956 | −0.341478 | − | 0.939890i | \(-0.610927\pi\) | ||||
−0.341478 | + | 0.939890i | \(0.610927\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.92820 | −0.558291 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3205 | 1.22271 | 0.611355 | − | 0.791357i | \(-0.290625\pi\) | ||||
0.611355 | + | 0.791357i | \(0.290625\pi\) | |||||||
\(158\) | −1.46410 | −0.116478 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.8564 | −1.09204 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53590 | 0.511931 | 0.255966 | − | 0.966686i | \(-0.417607\pi\) | ||||
0.255966 | + | 0.966686i | \(0.417607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.53590 | −0.196824 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.46410 | −0.416634 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.46410 | 0.261116 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.92820 | −0.519291 | ||||||||
\(179\) | −1.60770 | −0.120165 | −0.0600824 | − | 0.998193i | \(-0.519136\pi\) | ||||
−0.0600824 | + | 0.998193i | \(0.519136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3923 | 1.36709 | 0.683545 | − | 0.729909i | \(-0.260437\pi\) | ||||
0.683545 | + | 0.729909i | \(0.260437\pi\) | |||||||
\(182\) | 10.9282 | 0.810052 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.92820 | 0.510754 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3205 | −0.819123 | −0.409562 | − | 0.912282i | \(-0.634318\pi\) | ||||
−0.409562 | + | 0.912282i | \(0.634318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.39230 | −0.460128 | −0.230064 | − | 0.973175i | \(-0.573894\pi\) | ||||
−0.230064 | + | 0.973175i | \(0.573894\pi\) | |||||||
\(194\) | −18.3923 | −1.32049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 0.928203 | 0.0661317 | 0.0330659 | − | 0.999453i | \(-0.489473\pi\) | ||||
0.0330659 | + | 0.999453i | \(0.489473\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.92820 | 0.207575 | 0.103787 | − | 0.994600i | \(-0.466904\pi\) | ||||
0.103787 | + | 0.994600i | \(0.466904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 6.92820 | 0.486265 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.92820 | 0.343364 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.46410 | −0.378867 | ||||||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8564 | −1.22929 | −0.614643 | − | 0.788806i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788806i | \(0.710700\pi\) | |||||||
\(212\) | −12.9282 | −0.887913 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.92820 | 0.473602 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.92820 | 0.198779 | ||||||||
\(218\) | −14.3923 | −0.974770 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9282 | 1.27325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.8564 | 1.59754 | 0.798772 | − | 0.601634i | \(-0.205484\pi\) | ||||
0.798772 | + | 0.601634i | \(0.205484\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.9282 | −1.91163 | −0.955815 | − | 0.293970i | \(-0.905024\pi\) | ||||
−0.955815 | + | 0.293970i | \(0.905024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.46410 | −0.227429 | ||||||||
\(233\) | −8.53590 | −0.559205 | −0.279603 | − | 0.960116i | \(-0.590203\pi\) | ||||
−0.279603 | + | 0.960116i | \(0.590203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.46410 | 0.225494 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.92820 | 0.449089 | ||||||||
\(239\) | −2.53590 | −0.164034 | −0.0820168 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820168 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.143594 | 0.00924967 | 0.00462484 | − | 0.999989i | \(-0.498528\pi\) | ||||
0.00462484 | + | 0.999989i | \(0.498528\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.46410 | −0.347672 | ||||||||
\(248\) | −1.46410 | −0.0929705 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923 | 0.655956 | 0.327978 | − | 0.944685i | \(-0.393633\pi\) | ||||
0.327978 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | 1.50887 | ||||||||
\(254\) | −14.0000 | −0.878438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.9282 | −1.55498 | −0.777489 | − | 0.628896i | \(-0.783507\pi\) | ||||
−0.777489 | + | 0.628896i | \(0.783507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.92820 | −0.181950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.46410 | −0.214013 | ||||||||
\(263\) | −25.8564 | −1.59437 | −0.797187 | − | 0.603732i | \(-0.793680\pi\) | ||||
−0.797187 | + | 0.603732i | \(0.793680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.9282 | −0.911885 | ||||||||
\(269\) | −22.3923 | −1.36528 | −0.682641 | − | 0.730753i | \(-0.739169\pi\) | ||||
−0.682641 | + | 0.730753i | \(0.739169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7846 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4641 | −0.934221 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.392305 | −0.0235713 | −0.0117857 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117857 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(278\) | 9.85641 | 0.591148 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0718 | 1.01842 | 0.509209 | − | 0.860643i | \(-0.329938\pi\) | ||||
0.509209 | + | 0.860643i | \(0.329938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3923 | 1.21220 | 0.606098 | − | 0.795390i | \(-0.292734\pi\) | ||||
0.606098 | + | 0.795390i | \(0.292734\pi\) | |||||||
\(284\) | 6.92820 | 0.411113 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.9282 | −1.11925 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.92820 | 0.288401 | ||||||||
\(293\) | 12.9282 | 0.755274 | 0.377637 | − | 0.925954i | \(-0.376737\pi\) | ||||
0.377637 | + | 0.925954i | \(0.376737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.46410 | 0.0850992 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −37.8564 | −2.18929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9282 | 0.629891 | ||||||||
\(302\) | −8.39230 | −0.482923 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.7846 | 1.41453 | 0.707266 | − | 0.706947i | \(-0.249928\pi\) | ||||
0.707266 | + | 0.706947i | \(0.249928\pi\) | |||||||
\(308\) | −6.92820 | −0.394771 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3923 | 0.929522 | 0.464761 | − | 0.885436i | \(-0.346140\pi\) | ||||
0.464761 | + | 0.885436i | \(0.346140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.7846 | −1.28786 | −0.643931 | − | 0.765083i | \(-0.722698\pi\) | ||||
−0.643931 | + | 0.765083i | \(0.722698\pi\) | |||||||
\(314\) | 15.3205 | 0.864586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.46410 | −0.0823622 | ||||||||
\(317\) | −19.8564 | −1.11525 | −0.557623 | − | 0.830094i | \(-0.688287\pi\) | ||||
−0.557623 | + | 0.830094i | \(0.688287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.8564 | −0.772187 | ||||||||
\(323\) | −3.46410 | −0.192748 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.53590 | 0.361990 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.8564 | −0.763928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9282 | 0.820528 | 0.410264 | − | 0.911967i | \(-0.365437\pi\) | ||||
0.410264 | + | 0.911967i | \(0.365437\pi\) | |||||||
\(332\) | −2.53590 | −0.139176 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.9282 | −1.03571 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.32051 | −0.0719327 | −0.0359663 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359663 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(338\) | 16.8564 | 0.916868 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.07180 | −0.274653 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −5.46410 | −0.294605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | 37.1769 | 1.99576 | 0.997881 | − | 0.0650705i | \(-0.0207272\pi\) | ||||
0.997881 | + | 0.0650705i | \(0.0207272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8564 | −0.634659 | −0.317329 | − | 0.948315i | \(-0.602786\pi\) | ||||
−0.317329 | + | 0.948315i | \(0.602786\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.46410 | 0.184637 | ||||||||
\(353\) | −13.6077 | −0.724265 | −0.362132 | − | 0.932127i | \(-0.617951\pi\) | ||||
−0.362132 | + | 0.932127i | \(0.617951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.92820 | −0.367194 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.60770 | −0.0849693 | ||||||||
\(359\) | −33.4641 | −1.76617 | −0.883084 | − | 0.469215i | \(-0.844537\pi\) | ||||
−0.883084 | + | 0.469215i | \(0.844537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 18.3923 | 0.966678 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.9282 | 0.572793 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.7128 | 1.34220 | 0.671099 | − | 0.741368i | \(-0.265823\pi\) | ||||
0.671099 | + | 0.741368i | \(0.265823\pi\) | |||||||
\(368\) | 6.92820 | 0.361158 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.8564 | 1.34240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.392305 | −0.0203128 | −0.0101564 | − | 0.999948i | \(-0.503233\pi\) | ||||
−0.0101564 | + | 0.999948i | \(0.503233\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92820 | 0.357295 | ||||||||
\(377\) | 18.9282 | 0.974852 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.07180 | −0.465987 | −0.232993 | − | 0.972478i | \(-0.574852\pi\) | ||||
−0.232993 | + | 0.972478i | \(0.574852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3205 | −0.579208 | ||||||||
\(383\) | 18.9282 | 0.967186 | 0.483593 | − | 0.875293i | \(-0.339331\pi\) | ||||
0.483593 | + | 0.875293i | \(0.339331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.39230 | −0.325360 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.3923 | −0.933728 | ||||||||
\(389\) | 26.7846 | 1.35803 | 0.679017 | − | 0.734123i | \(-0.262406\pi\) | ||||
0.679017 | + | 0.734123i | \(0.262406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.928203 | 0.0467622 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3205 | −0.969669 | −0.484834 | − | 0.874606i | \(-0.661120\pi\) | ||||
−0.484834 | + | 0.874606i | \(0.661120\pi\) | |||||||
\(398\) | 2.92820 | 0.146778 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | 0.398508 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.92820 | 0.343841 | ||||||||
\(407\) | 5.07180 | 0.251400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.7846 | −1.52220 | −0.761100 | − | 0.648634i | \(-0.775341\pi\) | ||||
−0.761100 | + | 0.648634i | \(0.775341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.92820 | 0.242795 | ||||||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.46410 | 0.169435 | ||||||||
\(419\) | −13.6077 | −0.664779 | −0.332390 | − | 0.943142i | \(-0.607855\pi\) | ||||
−0.332390 | + | 0.943142i | \(0.607855\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.1769 | 1.90937 | 0.954683 | − | 0.297625i | \(-0.0961944\pi\) | ||||
0.954683 | + | 0.297625i | \(0.0961944\pi\) | |||||||
\(422\) | −17.8564 | −0.869236 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.9282 | −0.627849 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 6.92820 | 0.334887 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.9282 | −0.911739 | −0.455870 | − | 0.890047i | \(-0.650672\pi\) | ||||
−0.455870 | + | 0.890047i | \(0.650672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.3205 | 1.02460 | 0.512299 | − | 0.858807i | \(-0.328794\pi\) | ||||
0.512299 | + | 0.858807i | \(0.328794\pi\) | |||||||
\(434\) | 2.92820 | 0.140558 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.3923 | −0.689266 | ||||||||
\(437\) | 6.92820 | 0.331421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.32051 | −0.158479 | −0.0792396 | − | 0.996856i | \(-0.525249\pi\) | ||||
−0.0792396 | + | 0.996856i | \(0.525249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.9282 | 0.900323 | ||||||||
\(443\) | −4.39230 | −0.208685 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.8564 | 1.12963 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | 1.85641 | 0.0876092 | 0.0438046 | − | 0.999040i | \(-0.486052\pi\) | ||||
0.0438046 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | −28.9282 | −1.35173 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.9282 | 1.71992 | 0.859959 | − | 0.510363i | \(-0.170489\pi\) | ||||
0.859959 | + | 0.510363i | \(0.170489\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0718 | 0.700446 | 0.350223 | − | 0.936666i | \(-0.386106\pi\) | ||||
0.350223 | + | 0.936666i | \(0.386106\pi\) | |||||||
\(464\) | −3.46410 | −0.160817 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.53590 | −0.395418 | ||||||||
\(467\) | 21.4641 | 0.993240 | 0.496620 | − | 0.867968i | \(-0.334574\pi\) | ||||
0.496620 | + | 0.867968i | \(0.334574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.8564 | 1.37864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46410 | 0.159448 | ||||||||
\(473\) | −18.9282 | −0.870320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.92820 | 0.317554 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.53590 | −0.115989 | ||||||||
\(479\) | −7.60770 | −0.347604 | −0.173802 | − | 0.984781i | \(-0.555605\pi\) | ||||
−0.173802 | + | 0.984781i | \(0.555605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0.143594 | 0.00654051 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.7846 | −1.57624 | −0.788121 | − | 0.615521i | \(-0.788946\pi\) | ||||
−0.788121 | + | 0.615521i | \(0.788946\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.3205 | −1.86477 | −0.932384 | − | 0.361469i | \(-0.882275\pi\) | ||||
−0.932384 | + | 0.361469i | \(0.882275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | 0.540453 | ||||||||
\(494\) | −5.46410 | −0.245842 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.46410 | −0.0657401 | ||||||||
\(497\) | −13.8564 | −0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.9282 | −1.02641 | −0.513204 | − | 0.858267i | \(-0.671541\pi\) | ||||
−0.513204 | + | 0.858267i | \(0.671541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.3923 | 0.463831 | ||||||||
\(503\) | −6.92820 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.0000 | 1.06693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0000 | −0.621150 | ||||||||
\(509\) | −36.2487 | −1.60670 | −0.803348 | − | 0.595510i | \(-0.796950\pi\) | ||||
−0.803348 | + | 0.595510i | \(0.796950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.85641 | −0.436022 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.9282 | −1.09954 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | −2.92820 | −0.128658 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0000 | 1.22435 | 0.612177 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612177 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(524\) | −3.46410 | −0.151330 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.8564 | −1.12739 | ||||||||
\(527\) | 5.07180 | 0.220931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.9282 | −0.644800 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.3923 | −0.965401 | ||||||||
\(539\) | −10.3923 | −0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.5692 | −1.70121 | −0.850607 | − | 0.525802i | \(-0.823765\pi\) | ||||
−0.850607 | + | 0.525802i | \(0.823765\pi\) | |||||||
\(542\) | 16.7846 | 0.720961 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9282 | −1.15137 | −0.575683 | − | 0.817673i | \(-0.695264\pi\) | ||||
−0.575683 | + | 0.817673i | \(0.695264\pi\) | |||||||
\(548\) | −15.4641 | −0.660594 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46410 | −0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.92820 | 0.124520 | ||||||||
\(554\) | −0.392305 | −0.0166674 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.85641 | 0.418005 | ||||||||
\(557\) | 12.9282 | 0.547786 | 0.273893 | − | 0.961760i | \(-0.411689\pi\) | ||||
0.273893 | + | 0.961760i | \(0.411689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8564 | 1.26279 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.0718 | 0.720130 | ||||||||
\(563\) | −8.78461 | −0.370227 | −0.185114 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185114 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.3923 | 0.857153 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.92820 | 0.290701 | ||||||||
\(569\) | −25.8564 | −1.08396 | −0.541978 | − | 0.840392i | \(-0.682325\pi\) | ||||
−0.541978 | + | 0.840392i | \(0.682325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | −18.9282 | −0.791428 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.78461 | 0.282447 | 0.141223 | − | 0.989978i | \(-0.454896\pi\) | ||||
0.141223 | + | 0.989978i | \(0.454896\pi\) | |||||||
\(578\) | −5.00000 | −0.207973 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.07180 | 0.210414 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.7846 | −1.85479 | ||||||||
\(584\) | 4.92820 | 0.203931 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.9282 | 0.534059 | ||||||||
\(587\) | 40.3923 | 1.66717 | 0.833584 | − | 0.552392i | \(-0.186285\pi\) | ||||
0.833584 | + | 0.552392i | \(0.186285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.46410 | −0.0603273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.46410 | 0.0601742 | ||||||||
\(593\) | 12.2487 | 0.502994 | 0.251497 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251497 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −37.8564 | −1.54806 | ||||||||
\(599\) | −8.78461 | −0.358929 | −0.179465 | − | 0.983764i | \(-0.557437\pi\) | ||||
−0.179465 | + | 0.983764i | \(0.557437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0718 | 0.777955 | 0.388977 | − | 0.921247i | \(-0.372828\pi\) | ||||
0.388977 | + | 0.921247i | \(0.372828\pi\) | |||||||
\(602\) | 10.9282 | 0.445400 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.39230 | −0.341478 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6410 | −1.00015 | −0.500074 | − | 0.865983i | \(-0.666694\pi\) | ||||
−0.500074 | + | 0.865983i | \(0.666694\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.8564 | −1.53151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.39230 | 0.338962 | 0.169481 | − | 0.985533i | \(-0.445791\pi\) | ||||
0.169481 | + | 0.985533i | \(0.445791\pi\) | |||||||
\(614\) | 24.7846 | 1.00023 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.92820 | −0.279145 | ||||||||
\(617\) | −22.3923 | −0.901480 | −0.450740 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450740 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.7846 | 1.15695 | 0.578476 | − | 0.815700i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815700i | \(0.303648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.3923 | 0.657272 | ||||||||
\(623\) | 13.8564 | 0.555145 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.7846 | −0.910656 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3205 | 0.611355 | ||||||||
\(629\) | −5.07180 | −0.202226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.9282 | −0.912757 | −0.456379 | − | 0.889786i | \(-0.650854\pi\) | ||||
−0.456379 | + | 0.889786i | \(0.650854\pi\) | |||||||
\(632\) | −1.46410 | −0.0582388 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.8564 | −0.788599 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.3923 | 0.649487 | ||||||||
\(638\) | −12.0000 | −0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.1436 | 0.400648 | 0.200324 | − | 0.979730i | \(-0.435801\pi\) | ||||
0.200324 | + | 0.979730i | \(0.435801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.1769 | −1.78160 | −0.890802 | − | 0.454392i | \(-0.849857\pi\) | ||||
−0.890802 | + | 0.454392i | \(0.849857\pi\) | |||||||
\(644\) | −13.8564 | −0.546019 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.46410 | −0.136293 | ||||||||
\(647\) | 17.0718 | 0.671162 | 0.335581 | − | 0.942011i | \(-0.391067\pi\) | ||||
0.335581 | + | 0.942011i | \(0.391067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.53590 | 0.255966 | ||||||||
\(653\) | −45.7128 | −1.78888 | −0.894440 | − | 0.447187i | \(-0.852426\pi\) | ||||
−0.894440 | + | 0.447187i | \(0.852426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.8564 | −0.540179 | ||||||||
\(659\) | −22.3923 | −0.872280 | −0.436140 | − | 0.899879i | \(-0.643655\pi\) | ||||
−0.436140 | + | 0.899879i | \(0.643655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3923 | 1.64887 | 0.824435 | − | 0.565957i | \(-0.191493\pi\) | ||||
0.824435 | + | 0.565957i | \(0.191493\pi\) | |||||||
\(662\) | 14.9282 | 0.580201 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.53590 | −0.0984119 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | −18.9282 | −0.732354 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92820 | 0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.67949 | −0.103287 | −0.0516434 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516434 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(674\) | −1.32051 | −0.0508641 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.7846 | 1.41166 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.07180 | −0.194209 | ||||||||
\(683\) | −25.8564 | −0.989368 | −0.494684 | − | 0.869073i | \(-0.664716\pi\) | ||||
−0.494684 | + | 0.869073i | \(0.664716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.46410 | −0.208317 | ||||||||
\(689\) | 70.6410 | 2.69121 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.1769 | 1.41122 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −11.8564 | −0.448772 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.0718 | −0.871410 | −0.435705 | − | 0.900090i | \(-0.643501\pi\) | ||||
−0.435705 | + | 0.900090i | \(0.643501\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.46410 | 0.0552196 | ||||||||
\(704\) | 3.46410 | 0.130558 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.6077 | −0.512132 | ||||||||
\(707\) | −12.0000 | −0.451306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.7846 | 1.75703 | 0.878516 | − | 0.477712i | \(-0.158534\pi\) | ||||
0.878516 | + | 0.477712i | \(0.158534\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.92820 | −0.259645 | ||||||||
\(713\) | −10.1436 | −0.379881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.60770 | −0.0600824 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.4641 | −1.24887 | ||||||||
\(719\) | −14.5359 | −0.542098 | −0.271049 | − | 0.962566i | \(-0.587370\pi\) | ||||
−0.271049 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.85641 | −0.367072 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.3923 | 0.683545 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.143594 | −0.00532559 | −0.00266279 | − | 0.999996i | \(-0.500848\pi\) | ||||
−0.00266279 | + | 0.999996i | \(0.500848\pi\) | |||||||
\(728\) | 10.9282 | 0.405026 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9282 | 0.700085 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.1769 | 1.52090 | 0.760452 | − | 0.649394i | \(-0.224977\pi\) | ||||
0.760452 | + | 0.649394i | \(0.224977\pi\) | |||||||
\(734\) | 25.7128 | 0.949077 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.92820 | 0.255377 | ||||||||
\(737\) | −51.7128 | −1.90487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.7846 | −0.470289 | −0.235145 | − | 0.971960i | \(-0.575556\pi\) | ||||
−0.235145 | + | 0.971960i | \(0.575556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.8564 | 0.949219 | ||||||||
\(743\) | −10.1436 | −0.372132 | −0.186066 | − | 0.982537i | \(-0.559574\pi\) | ||||
−0.186066 | + | 0.982537i | \(0.559574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.392305 | −0.0143633 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.0000 | −0.438763 | ||||||||
\(749\) | −13.8564 | −0.506302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.46410 | −0.0534258 | −0.0267129 | − | 0.999643i | \(-0.508504\pi\) | ||||
−0.0267129 | + | 0.999643i | \(0.508504\pi\) | |||||||
\(752\) | 6.92820 | 0.252646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.9282 | 0.689325 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.1769 | 1.49660 | 0.748300 | − | 0.663360i | \(-0.230870\pi\) | ||||
0.748300 | + | 0.663360i | \(0.230870\pi\) | |||||||
\(758\) | −9.07180 | −0.329502 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.5692 | 1.94188 | 0.970941 | − | 0.239318i | \(-0.0769237\pi\) | ||||
0.970941 | + | 0.239318i | \(0.0769237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.7846 | 1.04207 | ||||||||
\(764\) | −11.3205 | −0.409562 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.9282 | 0.683904 | ||||||||
\(767\) | −18.9282 | −0.683458 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8564 | 1.00453 | 0.502264 | − | 0.864714i | \(-0.332501\pi\) | ||||
0.502264 | + | 0.864714i | \(0.332501\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.39230 | −0.230064 | ||||||||
\(773\) | 7.85641 | 0.282575 | 0.141288 | − | 0.989969i | \(-0.454876\pi\) | ||||
0.141288 | + | 0.989969i | \(0.454876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.3923 | −0.660245 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.7846 | 0.960275 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | −24.0000 | −0.858238 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | −0.712923 | −0.356462 | − | 0.934310i | \(-0.616017\pi\) | ||||
−0.356462 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(788\) | 0.928203 | 0.0330659 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9282 | −0.388072 | ||||||||
\(794\) | −19.3205 | −0.685659 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.92820 | 0.103787 | ||||||||
\(797\) | 33.7128 | 1.19417 | 0.597085 | − | 0.802178i | \(-0.296326\pi\) | ||||
0.597085 | + | 0.802178i | \(0.296326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000 | 0.423735 | ||||||||
\(803\) | 17.0718 | 0.602451 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | 46.6410 | 1.63981 | 0.819905 | − | 0.572499i | \(-0.194026\pi\) | ||||
0.819905 | + | 0.572499i | \(0.194026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(812\) | 6.92820 | 0.243132 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.07180 | 0.177766 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.46410 | −0.191165 | ||||||||
\(818\) | −30.7846 | −1.07636 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.85641 | −0.274190 | −0.137095 | − | 0.990558i | \(-0.543777\pi\) | ||||
−0.137095 | + | 0.990558i | \(0.543777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.7846 | 1.49138 | 0.745689 | − | 0.666294i | \(-0.232121\pi\) | ||||
0.745689 | + | 0.666294i | \(0.232121\pi\) | |||||||
\(824\) | 4.92820 | 0.171682 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.92820 | −0.241063 | ||||||||
\(827\) | −5.07180 | −0.176364 | −0.0881818 | − | 0.996104i | \(-0.528106\pi\) | ||||
−0.0881818 | + | 0.996104i | \(0.528106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.4641 | 1.64850 | 0.824248 | − | 0.566229i | \(-0.191598\pi\) | ||||
0.824248 | + | 0.566229i | \(0.191598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.46410 | −0.189434 | ||||||||
\(833\) | 10.3923 | 0.360072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.46410 | 0.119808 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.6077 | −0.470070 | ||||||||
\(839\) | 13.8564 | 0.478376 | 0.239188 | − | 0.970973i | \(-0.423119\pi\) | ||||
0.239188 | + | 0.970973i | \(0.423119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 39.1769 | 1.35013 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.8564 | −0.614643 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −12.9282 | −0.443956 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1436 | 0.347718 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.3205 | −0.661522 | −0.330761 | − | 0.943715i | \(-0.607305\pi\) | ||||
−0.330761 | + | 0.943715i | \(0.607305\pi\) | |||||||
\(854\) | −4.00000 | −0.136877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.92820 | 0.236801 | ||||||||
\(857\) | 14.7846 | 0.505033 | 0.252516 | − | 0.967593i | \(-0.418742\pi\) | ||||
0.252516 | + | 0.967593i | \(0.418742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8564 | −1.42812 | −0.714061 | − | 0.700083i | \(-0.753146\pi\) | ||||
−0.714061 | + | 0.700083i | \(0.753146\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.9282 | −0.644697 | ||||||||
\(863\) | 42.9282 | 1.46129 | 0.730647 | − | 0.682756i | \(-0.239219\pi\) | ||||
0.730647 | + | 0.682756i | \(0.239219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.3205 | 0.724500 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.92820 | 0.0993897 | ||||||||
\(869\) | −5.07180 | −0.172049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.5692 | 2.76387 | ||||||||
\(872\) | −14.3923 | −0.487385 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.92820 | 0.234350 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6077 | 0.797175 | 0.398588 | − | 0.917130i | \(-0.369500\pi\) | ||||
0.398588 | + | 0.917130i | \(0.369500\pi\) | |||||||
\(878\) | −3.32051 | −0.112062 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.92820 | −0.233417 | −0.116709 | − | 0.993166i | \(-0.537234\pi\) | ||||
−0.116709 | + | 0.993166i | \(0.537234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.60770 | −0.121409 | −0.0607043 | − | 0.998156i | \(-0.519335\pi\) | ||||
−0.0607043 | + | 0.998156i | \(0.519335\pi\) | |||||||
\(884\) | 18.9282 | 0.636624 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.39230 | −0.147562 | ||||||||
\(887\) | −41.5692 | −1.39576 | −0.697879 | − | 0.716216i | \(-0.745873\pi\) | ||||
−0.697879 | + | 0.716216i | \(0.745873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.0000 | 0.939090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.8564 | 0.798772 | ||||||||
\(893\) | 6.92820 | 0.231843 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.85641 | 0.0619491 | ||||||||
\(899\) | 5.07180 | 0.169154 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7846 | 1.49199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0000 | 0.531271 | 0.265636 | − | 0.964073i | \(-0.414418\pi\) | ||||
0.265636 | + | 0.964073i | \(0.414418\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1436 | −0.336072 | −0.168036 | − | 0.985781i | \(-0.553743\pi\) | ||||
−0.168036 | + | 0.985781i | \(0.553743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.78461 | −0.290728 | ||||||||
\(914\) | 22.0000 | 0.727695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.9282 | −0.955815 | ||||||||
\(917\) | 6.92820 | 0.228789 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.9282 | 1.28412 | 0.642061 | − | 0.766653i | \(-0.278079\pi\) | ||||
0.642061 | + | 0.766653i | \(0.278079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.9282 | 1.21617 | ||||||||
\(923\) | −37.8564 | −1.24606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0718 | 0.495290 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.46410 | −0.113715 | ||||||||
\(929\) | −12.0000 | −0.393707 | −0.196854 | − | 0.980433i | \(-0.563072\pi\) | ||||
−0.196854 | + | 0.980433i | \(0.563072\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | −8.53590 | −0.279603 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.4641 | 0.702327 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.5692 | −1.42334 | −0.711672 | − | 0.702512i | \(-0.752062\pi\) | ||||
−0.711672 | + | 0.702512i | \(0.752062\pi\) | |||||||
\(938\) | 29.8564 | 0.974846 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.2487 | −1.57286 | −0.786432 | − | 0.617677i | \(-0.788074\pi\) | ||||
−0.786432 | + | 0.617677i | \(0.788074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.46410 | 0.112747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.9282 | −0.615409 | ||||||||
\(947\) | 0.679492 | 0.0220805 | 0.0110403 | − | 0.999939i | \(-0.496486\pi\) | ||||
0.0110403 | + | 0.999939i | \(0.496486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.9282 | −0.874126 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.92820 | 0.224544 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.53590 | −0.0820168 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.60770 | −0.245793 | ||||||||
\(959\) | 30.9282 | 0.998724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | −8.00000 | −0.257930 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.143594 | 0.00462484 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.07180 | −0.227414 | −0.113707 | − | 0.993514i | \(-0.536272\pi\) | ||||
−0.113707 | + | 0.993514i | \(0.536272\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.6795 | −0.599453 | −0.299727 | − | 0.954025i | \(-0.596895\pi\) | ||||
−0.299727 | + | 0.954025i | \(0.596895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7128 | −0.631964 | ||||||||
\(974\) | −34.7846 | −1.11457 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 23.5692 | 0.754046 | 0.377023 | − | 0.926204i | \(-0.376948\pi\) | ||||
0.377023 | + | 0.926204i | \(0.376948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.3205 | −1.31859 | ||||||||
\(983\) | 60.4974 | 1.92957 | 0.964784 | − | 0.263043i | \(-0.0847262\pi\) | ||||
0.964784 | + | 0.263043i | \(0.0847262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.0000 | 0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.46410 | −0.173836 | ||||||||
\(989\) | −37.8564 | −1.20376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.39230 | −0.266590 | −0.133295 | − | 0.991076i | \(-0.542556\pi\) | ||||
−0.133295 | + | 0.991076i | \(0.542556\pi\) | |||||||
\(992\) | −1.46410 | −0.0464853 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.8564 | −0.439499 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.3923 | −0.392468 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(998\) | −22.9282 | −0.725780 | ||||||||
\(999\) | 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.bw.1.2 | 2 | ||
3.2 | odd | 2 | 8550.2.a.bo.1.1 | 2 | |||
5.4 | even | 2 | 1710.2.a.u.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 1710.2.a.y.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.a.u.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1710.2.a.y.1.1 | yes | 2 | 15.14 | odd | 2 | ||
8550.2.a.bo.1.1 | 2 | 3.2 | odd | 2 | |||
8550.2.a.bw.1.2 | 2 | 1.1 | even | 1 | trivial |