Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, 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("1710.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.12311 | 1.93635 | 0.968176 | − | 0.250270i | \(-0.0805195\pi\) | ||||
0.968176 | + | 0.250270i | \(0.0805195\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 5.12311 | 1.36921 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.12311 | −1.24254 | −0.621268 | − | 0.783598i | \(-0.713382\pi\) | ||||
−0.621268 | + | 0.783598i | \(0.713382\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.12311 | 0.968176 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.876894 | 0.157495 | 0.0787474 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787474 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.12311 | −0.878605 | ||||||||
\(35\) | −5.12311 | −0.865963 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.12311 | 0.487747 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24621 | −0.952538 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.24621 | −0.911104 | −0.455552 | − | 0.890209i | \(-0.650558\pi\) | ||||
−0.455552 | + | 0.890209i | \(0.650558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.2462 | 2.74946 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | 0.554700 | ||||||||
\(53\) | 12.2462 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 5.12311 | 0.684604 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | 5.12311 | 0.666972 | 0.333486 | − | 0.942755i | \(-0.391775\pi\) | ||||
0.333486 | + | 0.942755i | \(0.391775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.24621 | −0.543672 | −0.271836 | − | 0.962344i | \(-0.587631\pi\) | ||||
−0.271836 | + | 0.962344i | \(0.587631\pi\) | |||||||
\(62\) | 0.876894 | 0.111366 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2462 | −1.25177 | −0.625887 | − | 0.779914i | \(-0.715263\pi\) | ||||
−0.625887 | + | 0.779914i | \(0.715263\pi\) | |||||||
\(68\) | −5.12311 | −0.621268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.12311 | −0.612328 | ||||||||
\(71\) | −10.2462 | −1.21600 | −0.608001 | − | 0.793936i | \(-0.708028\pi\) | ||||
−0.608001 | + | 0.793936i | \(0.708028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 10.2462 | 1.16766 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.876894 | 0.0986583 | 0.0493292 | − | 0.998783i | \(-0.484292\pi\) | ||||
0.0493292 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.12311 | 0.344889 | ||||||||
\(83\) | 15.1231 | 1.65998 | 0.829988 | − | 0.557781i | \(-0.188347\pi\) | ||||
0.829988 | + | 0.557781i | \(0.188347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.12311 | 0.555679 | ||||||||
\(86\) | −6.24621 | −0.673546 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 13.3693 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.4924 | 2.14819 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.24621 | −0.644247 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 19.2462 | 1.94416 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.24621 | 0.812523 | 0.406262 | − | 0.913757i | \(-0.366832\pi\) | ||||
0.406262 | + | 0.913757i | \(0.366832\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2462 | 1.18946 | ||||||||
\(107\) | −2.24621 | −0.217149 | −0.108575 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108575 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.1231 | 1.25697 | 0.628483 | − | 0.777824i | \(-0.283676\pi\) | ||||
0.628483 | + | 0.777824i | \(0.283676\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.12311 | 0.484088 | ||||||||
\(113\) | −12.2462 | −1.15203 | −0.576013 | − | 0.817440i | \(-0.695392\pi\) | ||||
−0.576013 | + | 0.817440i | \(0.695392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.12311 | 0.471620 | ||||||||
\(119\) | −26.2462 | −2.40599 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −4.24621 | −0.384434 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.876894 | 0.0787474 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.2462 | −1.79656 | −0.898280 | − | 0.439423i | \(-0.855183\pi\) | ||||
−0.898280 | + | 0.439423i | \(0.855183\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.00000 | −0.350823 | ||||||||
\(131\) | 10.4924 | 0.916727 | 0.458364 | − | 0.888765i | \(-0.348436\pi\) | ||||
0.458364 | + | 0.888765i | \(0.348436\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.12311 | −0.444230 | ||||||||
\(134\) | −10.2462 | −0.885138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.12311 | −0.439303 | ||||||||
\(137\) | −10.8769 | −0.929276 | −0.464638 | − | 0.885501i | \(-0.653816\pi\) | ||||
−0.464638 | + | 0.885501i | \(0.653816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4924 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(140\) | −5.12311 | −0.432981 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.2462 | −0.859843 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0000 | −1.80231 | −0.901155 | − | 0.433497i | \(-0.857280\pi\) | ||||
−0.901155 | + | 0.433497i | \(0.857280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1231 | 0.905185 | 0.452593 | − | 0.891717i | \(-0.350499\pi\) | ||||
0.452593 | + | 0.891717i | \(0.350499\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.2462 | 0.825663 | ||||||||
\(155\) | −0.876894 | −0.0704339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.12311 | 0.568486 | 0.284243 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284243 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(158\) | 0.876894 | 0.0697620 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 3.12311 | 0.243874 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.1231 | 1.17378 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 5.12311 | 0.392924 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.24621 | −0.476269 | ||||||||
\(173\) | −8.24621 | −0.626948 | −0.313474 | − | 0.949597i | \(-0.601493\pi\) | ||||
−0.313474 | + | 0.949597i | \(0.601493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.12311 | 0.387270 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.3693 | 1.00207 | ||||||||
\(179\) | −17.1231 | −1.27984 | −0.639921 | − | 0.768441i | \(-0.721033\pi\) | ||||
−0.639921 | + | 0.768441i | \(0.721033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3693 | −1.14239 | −0.571196 | − | 0.820814i | \(-0.693520\pi\) | ||||
−0.571196 | + | 0.820814i | \(0.693520\pi\) | |||||||
\(182\) | 20.4924 | 1.51900 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.2462 | −0.749277 | ||||||||
\(188\) | −6.24621 | −0.455552 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.00000 | 0.0725476 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.4924 | −1.04319 | −0.521594 | − | 0.853194i | \(-0.674662\pi\) | ||||
−0.521594 | + | 0.853194i | \(0.674662\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.2462 | 1.37473 | ||||||||
\(197\) | 8.24621 | 0.587518 | 0.293759 | − | 0.955879i | \(-0.405094\pi\) | ||||
0.293759 | + | 0.955879i | \(0.405094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.24621 | −0.442782 | −0.221391 | − | 0.975185i | \(-0.571060\pi\) | ||||
−0.221391 | + | 0.975185i | \(0.571060\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.0000 | −0.703598 | ||||||||
\(203\) | −10.2462 | −0.719143 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.12311 | −0.218127 | ||||||||
\(206\) | 8.24621 | 0.574541 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 12.2462 | 0.841073 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.24621 | −0.153548 | ||||||||
\(215\) | 6.24621 | 0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.49242 | 0.304966 | ||||||||
\(218\) | 13.1231 | 0.888809 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −20.4924 | −1.37847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 5.12311 | 0.342302 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.2462 | −0.814606 | ||||||||
\(227\) | 12.4924 | 0.829151 | 0.414576 | − | 0.910015i | \(-0.363930\pi\) | ||||
0.414576 | + | 0.910015i | \(0.363930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.4924 | −0.957686 | −0.478843 | − | 0.877900i | \(-0.658944\pi\) | ||||
−0.478843 | + | 0.877900i | \(0.658944\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 23.3693 | 1.53097 | 0.765487 | − | 0.643451i | \(-0.222498\pi\) | ||||
0.765487 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.24621 | 0.407458 | ||||||||
\(236\) | 5.12311 | 0.333486 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.2462 | −1.70129 | ||||||||
\(239\) | −18.2462 | −1.18025 | −0.590125 | − | 0.807312i | \(-0.700921\pi\) | ||||
−0.590125 | + | 0.807312i | \(0.700921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.2462 | −1.04651 | −0.523255 | − | 0.852176i | \(-0.675283\pi\) | ||||
−0.523255 | + | 0.852176i | \(0.675283\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.24621 | −0.271836 | ||||||||
\(245\) | −19.2462 | −1.22960 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | −0.254514 | ||||||||
\(248\) | 0.876894 | 0.0556828 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −0.246211 | −0.0155407 | −0.00777036 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00777036 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −20.2462 | −1.27036 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0000 | 0.623783 | 0.311891 | − | 0.950118i | \(-0.399037\pi\) | ||||
0.311891 | + | 0.950118i | \(0.399037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.4924 | 0.648224 | ||||||||
\(263\) | −20.4924 | −1.26362 | −0.631808 | − | 0.775125i | \(-0.717687\pi\) | ||||
−0.631808 | + | 0.775125i | \(0.717687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2462 | −0.752279 | ||||||||
\(266\) | −5.12311 | −0.314118 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.2462 | −0.625887 | ||||||||
\(269\) | −28.7386 | −1.75223 | −0.876113 | − | 0.482106i | \(-0.839872\pi\) | ||||
−0.876113 | + | 0.482106i | \(0.839872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2462 | −0.865396 | −0.432698 | − | 0.901539i | \(-0.642438\pi\) | ||||
−0.432698 | + | 0.901539i | \(0.642438\pi\) | |||||||
\(272\) | −5.12311 | −0.310634 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8769 | −0.657097 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.6155 | 1.89959 | 0.949796 | − | 0.312868i | \(-0.101290\pi\) | ||||
0.949796 | + | 0.312868i | \(0.101290\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.12311 | −0.306164 | ||||||||
\(281\) | −5.36932 | −0.320307 | −0.160153 | − | 0.987092i | \(-0.551199\pi\) | ||||
−0.160153 | + | 0.987092i | \(0.551199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.4924 | −1.45592 | −0.727962 | − | 0.685618i | \(-0.759532\pi\) | ||||
−0.727962 | + | 0.685618i | \(0.759532\pi\) | |||||||
\(284\) | −10.2462 | −0.608001 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.00000 | 0.473050 | ||||||||
\(287\) | 16.0000 | 0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.24621 | 0.543895 | ||||||||
\(290\) | 2.00000 | 0.117444 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | 14.4924 | 0.846656 | 0.423328 | − | 0.905976i | \(-0.360862\pi\) | ||||
0.423328 | + | 0.905976i | \(0.360862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.12311 | −0.298279 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.0000 | −1.27443 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.0000 | −1.84445 | ||||||||
\(302\) | 11.1231 | 0.640063 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 4.24621 | 0.243137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2462 | −1.26966 | −0.634829 | − | 0.772653i | \(-0.718930\pi\) | ||||
−0.634829 | + | 0.772653i | \(0.718930\pi\) | |||||||
\(308\) | 10.2462 | 0.583832 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.876894 | −0.0498043 | ||||||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699155 | − | 0.714970i | \(-0.253560\pi\) | ||||
0.699155 | + | 0.714970i | \(0.253560\pi\) | |||||||
\(314\) | 7.12311 | 0.401980 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.876894 | 0.0493292 | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12311 | 0.285057 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.12311 | 0.172445 | ||||||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.49242 | 0.466786 | 0.233393 | − | 0.972383i | \(-0.425017\pi\) | ||||
0.233393 | + | 0.972383i | \(0.425017\pi\) | |||||||
\(332\) | 15.1231 | 0.829988 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 10.2462 | 0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.12311 | 0.277839 | ||||||||
\(341\) | 1.75379 | 0.0949730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 62.7386 | 3.38757 | ||||||||
\(344\) | −6.24621 | −0.336773 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.24621 | −0.443319 | ||||||||
\(347\) | 33.3693 | 1.79136 | 0.895679 | − | 0.444700i | \(-0.146690\pi\) | ||||
0.895679 | + | 0.444700i | \(0.146690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4924 | 1.20399 | 0.601996 | − | 0.798499i | \(-0.294372\pi\) | ||||
0.601996 | + | 0.798499i | \(0.294372\pi\) | |||||||
\(350\) | 5.12311 | 0.273842 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | −31.8617 | −1.69583 | −0.847915 | − | 0.530133i | \(-0.822142\pi\) | ||||
−0.847915 | + | 0.530133i | \(0.822142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2462 | 0.543812 | ||||||||
\(356\) | 13.3693 | 0.708572 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.1231 | −0.904984 | ||||||||
\(359\) | 6.24621 | 0.329662 | 0.164831 | − | 0.986322i | \(-0.447292\pi\) | ||||
0.164831 | + | 0.986322i | \(0.447292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −15.3693 | −0.807793 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.4924 | 1.07409 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.12311 | −0.476222 | −0.238111 | − | 0.971238i | \(-0.576528\pi\) | ||||
−0.238111 | + | 0.971238i | \(0.576528\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 62.7386 | 3.25723 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.24621 | 0.116304 | 0.0581522 | − | 0.998308i | \(-0.481479\pi\) | ||||
0.0581522 | + | 0.998308i | \(0.481479\pi\) | |||||||
\(374\) | −10.2462 | −0.529819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.24621 | −0.322124 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.4924 | −1.25809 | −0.629046 | − | 0.777368i | \(-0.716554\pi\) | ||||
−0.629046 | + | 0.777368i | \(0.716554\pi\) | |||||||
\(380\) | 1.00000 | 0.0512989 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | −0.204658 | ||||||||
\(383\) | 3.50758 | 0.179229 | 0.0896144 | − | 0.995977i | \(-0.471437\pi\) | ||||
0.0896144 | + | 0.995977i | \(0.471437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2462 | −0.522195 | ||||||||
\(386\) | −14.4924 | −0.737645 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | −1.50758 | −0.0764372 | −0.0382186 | − | 0.999269i | \(-0.512168\pi\) | ||||
−0.0382186 | + | 0.999269i | \(0.512168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 19.2462 | 0.972080 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.24621 | 0.415438 | ||||||||
\(395\) | −0.876894 | −0.0441213 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.87689 | 0.244764 | 0.122382 | − | 0.992483i | \(-0.460947\pi\) | ||||
0.122382 | + | 0.992483i | \(0.460947\pi\) | |||||||
\(398\) | −6.24621 | −0.313094 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 25.8617 | 1.29147 | 0.645737 | − | 0.763560i | \(-0.276550\pi\) | ||||
0.645737 | + | 0.763560i | \(0.276550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50758 | 0.174725 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.2462 | −0.508511 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | −3.12311 | −0.154239 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.24621 | 0.406262 | ||||||||
\(413\) | 26.2462 | 1.29149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1231 | −0.742364 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.00000 | −0.0978232 | ||||||||
\(419\) | 4.24621 | 0.207441 | 0.103720 | − | 0.994606i | \(-0.466925\pi\) | ||||
0.103720 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.87689 | −0.335159 | −0.167580 | − | 0.985859i | \(-0.553595\pi\) | ||||
−0.167580 | + | 0.985859i | \(0.553595\pi\) | |||||||
\(422\) | −20.0000 | −0.973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.2462 | 0.594729 | ||||||||
\(425\) | −5.12311 | −0.248507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7538 | −1.05274 | ||||||||
\(428\) | −2.24621 | −0.108575 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.24621 | 0.301219 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | 4.49242 | 0.215643 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.1231 | 0.628483 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.1231 | −0.912696 | −0.456348 | − | 0.889801i | \(-0.650843\pi\) | ||||
−0.456348 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.4924 | −0.974725 | ||||||||
\(443\) | 37.8617 | 1.79887 | 0.899433 | − | 0.437059i | \(-0.143980\pi\) | ||||
0.899433 | + | 0.437059i | \(0.143980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.3693 | −0.633766 | ||||||||
\(446\) | 10.0000 | 0.473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.12311 | 0.242044 | ||||||||
\(449\) | −29.3693 | −1.38602 | −0.693012 | − | 0.720926i | \(-0.743717\pi\) | ||||
−0.693012 | + | 0.720926i | \(0.743717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24621 | 0.294123 | ||||||||
\(452\) | −12.2462 | −0.576013 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.4924 | 0.586298 | ||||||||
\(455\) | −20.4924 | −0.960700 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.0000 | 1.21623 | 0.608114 | − | 0.793849i | \(-0.291926\pi\) | ||||
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | −14.4924 | −0.677186 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4924 | −0.488681 | −0.244340 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244340 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8769 | −0.691388 | −0.345694 | − | 0.938347i | \(-0.612356\pi\) | ||||
−0.345694 | + | 0.938347i | \(0.612356\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.3693 | 1.08256 | ||||||||
\(467\) | 39.1231 | 1.81040 | 0.905201 | − | 0.424984i | \(-0.139720\pi\) | ||||
0.905201 | + | 0.424984i | \(0.139720\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52.4924 | −2.42387 | ||||||||
\(470\) | 6.24621 | 0.288116 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.12311 | 0.235810 | ||||||||
\(473\) | −12.4924 | −0.574402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −26.2462 | −1.20299 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.2462 | −0.834562 | ||||||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2462 | −0.739995 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.2462 | −1.46122 | −0.730608 | − | 0.682798i | \(-0.760763\pi\) | ||||
−0.730608 | + | 0.682798i | \(0.760763\pi\) | |||||||
\(488\) | −4.24621 | −0.192217 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19.2462 | −0.869455 | ||||||||
\(491\) | 10.4924 | 0.473516 | 0.236758 | − | 0.971569i | \(-0.423915\pi\) | ||||
0.236758 | + | 0.971569i | \(0.423915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.2462 | 0.461466 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.876894 | 0.0393737 | ||||||||
\(497\) | −52.4924 | −2.35461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.246211 | −0.0109889 | ||||||||
\(503\) | 32.0000 | 1.42681 | 0.713405 | − | 0.700752i | \(-0.247152\pi\) | ||||
0.713405 | + | 0.700752i | \(0.247152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.2462 | −0.898280 | ||||||||
\(509\) | 9.50758 | 0.421416 | 0.210708 | − | 0.977549i | \(-0.432423\pi\) | ||||
0.210708 | + | 0.977549i | \(0.432423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.7386 | 1.35980 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.0000 | 0.441081 | ||||||||
\(515\) | −8.24621 | −0.363371 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4924 | −0.549416 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.00000 | −0.175412 | ||||||||
\(521\) | −27.6155 | −1.20986 | −0.604929 | − | 0.796279i | \(-0.706799\pi\) | ||||
−0.604929 | + | 0.796279i | \(0.706799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.73863 | −0.294660 | −0.147330 | − | 0.989087i | \(-0.547068\pi\) | ||||
−0.147330 | + | 0.989087i | \(0.547068\pi\) | |||||||
\(524\) | 10.4924 | 0.458364 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.4924 | −0.893512 | ||||||||
\(527\) | −4.49242 | −0.195693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −12.2462 | −0.531941 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.12311 | −0.222115 | ||||||||
\(533\) | 12.4924 | 0.541107 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.24621 | 0.0971122 | ||||||||
\(536\) | −10.2462 | −0.442569 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.7386 | −1.23901 | ||||||||
\(539\) | 38.4924 | 1.65799 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.4924 | −1.48295 | −0.741473 | − | 0.670983i | \(-0.765872\pi\) | ||||
−0.741473 | + | 0.670983i | \(0.765872\pi\) | |||||||
\(542\) | −14.2462 | −0.611927 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.12311 | −0.219651 | ||||||||
\(545\) | −13.1231 | −0.562132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2462 | −0.609124 | −0.304562 | − | 0.952493i | \(-0.598510\pi\) | ||||
−0.304562 | + | 0.952493i | \(0.598510\pi\) | |||||||
\(548\) | −10.8769 | −0.464638 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.49242 | 0.191037 | ||||||||
\(554\) | 31.6155 | 1.34322 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | −0.246211 | −0.0104323 | −0.00521615 | − | 0.999986i | \(-0.501660\pi\) | ||||
−0.00521615 | + | 0.999986i | \(0.501660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.9848 | −1.05675 | ||||||||
\(560\) | −5.12311 | −0.216491 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.36932 | −0.226491 | ||||||||
\(563\) | 39.2311 | 1.65339 | 0.826696 | − | 0.562649i | \(-0.190218\pi\) | ||||
0.826696 | + | 0.562649i | \(0.190218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2462 | 0.515202 | ||||||||
\(566\) | −24.4924 | −1.02949 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.2462 | −0.429921 | ||||||||
\(569\) | −32.8769 | −1.37827 | −0.689136 | − | 0.724632i | \(-0.742010\pi\) | ||||
−0.689136 | + | 0.724632i | \(0.742010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.492423 | −0.0206072 | −0.0103036 | − | 0.999947i | \(-0.503280\pi\) | ||||
−0.0103036 | + | 0.999947i | \(0.503280\pi\) | |||||||
\(572\) | 8.00000 | 0.334497 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.0000 | 0.667827 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7386 | −1.02988 | −0.514941 | − | 0.857225i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857225i | \(0.672186\pi\) | |||||||
\(578\) | 9.24621 | 0.384592 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | 77.4773 | 3.21430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.4924 | 1.01437 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.4924 | 0.598676 | ||||||||
\(587\) | −10.6307 | −0.438775 | −0.219388 | − | 0.975638i | \(-0.570406\pi\) | ||||
−0.219388 | + | 0.975638i | \(0.570406\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.876894 | −0.0361318 | ||||||||
\(590\) | −5.12311 | −0.210915 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.6155 | 1.05190 | 0.525952 | − | 0.850514i | \(-0.323709\pi\) | ||||
0.525952 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.2462 | 1.07599 | ||||||||
\(596\) | −22.0000 | −0.901155 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4924 | 0.837298 | 0.418649 | − | 0.908148i | \(-0.362504\pi\) | ||||
0.418649 | + | 0.908148i | \(0.362504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7386 | −0.519620 | −0.259810 | − | 0.965660i | \(-0.583660\pi\) | ||||
−0.259810 | + | 0.965660i | \(0.583660\pi\) | |||||||
\(602\) | −32.0000 | −1.30422 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1231 | 0.452593 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2462 | 0.497058 | 0.248529 | − | 0.968624i | \(-0.420053\pi\) | ||||
0.248529 | + | 0.968624i | \(0.420053\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.24621 | 0.171924 | ||||||||
\(611\) | −24.9848 | −1.01078 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.3693 | 1.67089 | 0.835445 | − | 0.549573i | \(-0.185210\pi\) | ||||
0.835445 | + | 0.549573i | \(0.185210\pi\) | |||||||
\(614\) | −22.2462 | −0.897784 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.2462 | 0.412832 | ||||||||
\(617\) | 9.12311 | 0.367282 | 0.183641 | − | 0.982993i | \(-0.441212\pi\) | ||||
0.183641 | + | 0.982993i | \(0.441212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0000 | 1.44696 | 0.723481 | − | 0.690344i | \(-0.242541\pi\) | ||||
0.723481 | + | 0.690344i | \(0.242541\pi\) | |||||||
\(620\) | −0.876894 | −0.0352169 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0000 | 0.801927 | ||||||||
\(623\) | 68.4924 | 2.74409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.7386 | 0.988755 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.12311 | 0.284243 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.9848 | 1.15387 | 0.576934 | − | 0.816791i | \(-0.304249\pi\) | ||||
0.576934 | + | 0.816791i | \(0.304249\pi\) | |||||||
\(632\) | 0.876894 | 0.0348810 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0000 | −0.556011 | ||||||||
\(635\) | 20.2462 | 0.803446 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 76.9848 | 3.05025 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −45.8617 | −1.81143 | −0.905715 | − | 0.423887i | \(-0.860665\pi\) | ||||
−0.905715 | + | 0.423887i | \(0.860665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.492423 | 0.0194192 | 0.00970962 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00970962 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.12311 | 0.201566 | ||||||||
\(647\) | −28.4924 | −1.12015 | −0.560076 | − | 0.828441i | \(-0.689228\pi\) | ||||
−0.560076 | + | 0.828441i | \(0.689228\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2462 | 0.402199 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000 | 0.469956 | ||||||||
\(653\) | −38.9848 | −1.52559 | −0.762797 | − | 0.646638i | \(-0.776175\pi\) | ||||
−0.762797 | + | 0.646638i | \(0.776175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4924 | −0.409973 | ||||||||
\(656\) | 3.12311 | 0.121937 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −32.0000 | −1.24749 | ||||||||
\(659\) | −41.6155 | −1.62111 | −0.810555 | − | 0.585662i | \(-0.800835\pi\) | ||||
−0.810555 | + | 0.585662i | \(0.800835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.61553 | 0.374001 | 0.187000 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187000 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(662\) | 8.49242 | 0.330067 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.1231 | 0.586890 | ||||||||
\(665\) | 5.12311 | 0.198666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.2462 | 0.395846 | ||||||||
\(671\) | −8.49242 | −0.327846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.00000 | 0.231283 | 0.115642 | − | 0.993291i | \(-0.463108\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463108\pi\) | |||||||
\(674\) | −26.0000 | −1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −30.9848 | −1.19084 | −0.595422 | − | 0.803413i | \(-0.703015\pi\) | ||||
−0.595422 | + | 0.803413i | \(0.703015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.7386 | −1.17964 | ||||||||
\(680\) | 5.12311 | 0.196462 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.75379 | 0.0671560 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8769 | 0.415585 | ||||||||
\(686\) | 62.7386 | 2.39537 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.24621 | −0.238135 | ||||||||
\(689\) | 48.9848 | 1.86617 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4924 | −1.23607 | −0.618035 | − | 0.786151i | \(-0.712071\pi\) | ||||
−0.618035 | + | 0.786151i | \(0.712071\pi\) | |||||||
\(692\) | −8.24621 | −0.313474 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.3693 | 1.26668 | ||||||||
\(695\) | −16.4924 | −0.625593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | 22.4924 | 0.851351 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.12311 | 0.193635 | ||||||||
\(701\) | 30.9848 | 1.17028 | 0.585141 | − | 0.810932i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810932i | \(0.301039\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.8617 | −1.19913 | ||||||||
\(707\) | −51.2311 | −1.92674 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 10.2462 | 0.384533 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.3693 | 0.501036 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | −17.1231 | −0.639921 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.24621 | 0.233107 | ||||||||
\(719\) | −6.24621 | −0.232944 | −0.116472 | − | 0.993194i | \(-0.537159\pi\) | ||||
−0.116472 | + | 0.993194i | \(0.537159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.2462 | 1.57333 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.3693 | −0.571196 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.3693 | 1.16342 | 0.581712 | − | 0.813395i | \(-0.302383\pi\) | ||||
0.581712 | + | 0.813395i | \(0.302383\pi\) | |||||||
\(728\) | 20.4924 | 0.759500 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.61553 | −0.281286 | −0.140643 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140643 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(734\) | −9.12311 | −0.336740 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.4924 | −0.754848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.4924 | 0.606684 | 0.303342 | − | 0.952882i | \(-0.401898\pi\) | ||||
0.303342 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 62.7386 | 2.30321 | ||||||||
\(743\) | −40.9848 | −1.50359 | −0.751794 | − | 0.659398i | \(-0.770811\pi\) | ||||
−0.751794 | + | 0.659398i | \(0.770811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.0000 | 0.806018 | ||||||||
\(746\) | 2.24621 | 0.0822396 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.2462 | −0.374639 | ||||||||
\(749\) | −11.5076 | −0.420478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.8617 | 1.81948 | 0.909740 | − | 0.415178i | \(-0.136281\pi\) | ||||
0.909740 | + | 0.415178i | \(0.136281\pi\) | |||||||
\(752\) | −6.24621 | −0.227776 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.00000 | −0.291343 | ||||||||
\(755\) | −11.1231 | −0.404811 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8617 | 0.794578 | 0.397289 | − | 0.917693i | \(-0.369951\pi\) | ||||
0.397289 | + | 0.917693i | \(0.369951\pi\) | |||||||
\(758\) | −24.4924 | −0.889605 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.00000 | 0.0362738 | ||||||||
\(761\) | −29.7538 | −1.07857 | −0.539287 | − | 0.842122i | \(-0.681306\pi\) | ||||
−0.539287 | + | 0.842122i | \(0.681306\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.2311 | 2.43393 | ||||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.50758 | 0.126734 | ||||||||
\(767\) | 20.4924 | 0.739938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.2462 | −1.45132 | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725658 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(770\) | −10.2462 | −0.369248 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.4924 | −0.521594 | ||||||||
\(773\) | 48.2462 | 1.73530 | 0.867648 | − | 0.497179i | \(-0.165631\pi\) | ||||
0.867648 | + | 0.497179i | \(0.165631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.876894 | 0.0314990 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.50758 | −0.0540493 | ||||||||
\(779\) | −3.12311 | −0.111897 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.4924 | −0.733277 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.2462 | 0.687365 | ||||||||
\(785\) | −7.12311 | −0.254235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.49242 | −0.302722 | −0.151361 | − | 0.988479i | \(-0.548366\pi\) | ||||
−0.151361 | + | 0.988479i | \(0.548366\pi\) | |||||||
\(788\) | 8.24621 | 0.293759 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.876894 | −0.0311985 | ||||||||
\(791\) | −62.7386 | −2.23073 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.9848 | −0.603150 | ||||||||
\(794\) | 4.87689 | 0.173075 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.24621 | −0.221391 | ||||||||
\(797\) | −30.4924 | −1.08010 | −0.540049 | − | 0.841634i | \(-0.681594\pi\) | ||||
−0.540049 | + | 0.841634i | \(0.681594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.8617 | 0.913210 | ||||||||
\(803\) | 12.0000 | 0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.50758 | 0.123549 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.0000 | −0.351799 | ||||||||
\(809\) | 14.2462 | 0.500870 | 0.250435 | − | 0.968133i | \(-0.419426\pi\) | ||||
0.250435 | + | 0.968133i | \(0.419426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9848 | 0.736878 | 0.368439 | − | 0.929652i | \(-0.379892\pi\) | ||||
0.368439 | + | 0.929652i | \(0.379892\pi\) | |||||||
\(812\) | −10.2462 | −0.359572 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.24621 | 0.218527 | ||||||||
\(818\) | −6.00000 | −0.209785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.12311 | −0.109064 | ||||||||
\(821\) | 14.0000 | 0.488603 | 0.244302 | − | 0.969699i | \(-0.421441\pi\) | ||||
0.244302 | + | 0.969699i | \(0.421441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.8617 | −1.94722 | −0.973609 | − | 0.228223i | \(-0.926709\pi\) | ||||
−0.973609 | + | 0.228223i | \(0.926709\pi\) | |||||||
\(824\) | 8.24621 | 0.287270 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.2462 | 0.913222 | ||||||||
\(827\) | 30.2462 | 1.05176 | 0.525882 | − | 0.850558i | \(-0.323735\pi\) | ||||
0.525882 | + | 0.850558i | \(0.323735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.1080 | 1.04569 | 0.522846 | − | 0.852427i | \(-0.324870\pi\) | ||||
0.522846 | + | 0.852427i | \(0.324870\pi\) | |||||||
\(830\) | −15.1231 | −0.524931 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | −98.6004 | −3.41630 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | −2.00000 | −0.0691714 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.24621 | 0.146683 | ||||||||
\(839\) | 40.9848 | 1.41495 | 0.707477 | − | 0.706736i | \(-0.249833\pi\) | ||||
0.707477 | + | 0.706736i | \(0.249833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −6.87689 | −0.236993 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.8617 | −1.23222 | ||||||||
\(848\) | 12.2462 | 0.420537 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.12311 | −0.175721 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.36932 | −0.320799 | −0.160400 | − | 0.987052i | \(-0.551278\pi\) | ||||
−0.160400 | + | 0.987052i | \(0.551278\pi\) | |||||||
\(854\) | −21.7538 | −0.744399 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.24621 | −0.0767739 | ||||||||
\(857\) | 43.4773 | 1.48516 | 0.742578 | − | 0.669760i | \(-0.233603\pi\) | ||||
0.742578 | + | 0.669760i | \(0.233603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.4924 | 1.10863 | 0.554314 | − | 0.832308i | \(-0.312981\pi\) | ||||
0.554314 | + | 0.832308i | \(0.312981\pi\) | |||||||
\(860\) | 6.24621 | 0.212994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0000 | 0.544962 | ||||||||
\(863\) | 4.49242 | 0.152924 | 0.0764619 | − | 0.997073i | \(-0.475638\pi\) | ||||
0.0764619 | + | 0.997073i | \(0.475638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.24621 | 0.280380 | ||||||||
\(866\) | −18.0000 | −0.611665 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.49242 | 0.152483 | ||||||||
\(869\) | 1.75379 | 0.0594932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.9848 | −1.38872 | ||||||||
\(872\) | 13.1231 | 0.444404 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.12311 | −0.173193 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.7538 | 0.734573 | 0.367287 | − | 0.930108i | \(-0.380287\pi\) | ||||
0.367287 | + | 0.930108i | \(0.380287\pi\) | |||||||
\(878\) | −19.1231 | −0.645374 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | 0.492423 | 0.0165901 | 0.00829507 | − | 0.999966i | \(-0.497360\pi\) | ||||
0.00829507 | + | 0.999966i | \(0.497360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.50758 | 0.252650 | 0.126325 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126325 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(884\) | −20.4924 | −0.689235 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37.8617 | 1.27199 | ||||||||
\(887\) | 56.9848 | 1.91336 | 0.956682 | − | 0.291135i | \(-0.0940330\pi\) | ||||
0.956682 | + | 0.291135i | \(0.0940330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −103.723 | −3.47877 | ||||||||
\(890\) | −13.3693 | −0.448141 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0000 | 0.334825 | ||||||||
\(893\) | 6.24621 | 0.209021 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.1231 | 0.572362 | ||||||||
\(896\) | 5.12311 | 0.171151 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.3693 | −0.980067 | ||||||||
\(899\) | −1.75379 | −0.0584921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −62.7386 | −2.09013 | ||||||||
\(902\) | 6.24621 | 0.207976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2462 | −0.407303 | ||||||||
\(905\) | 15.3693 | 0.510893 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.9848 | 1.62652 | 0.813258 | − | 0.581904i | \(-0.197692\pi\) | ||||
0.813258 | + | 0.581904i | \(0.197692\pi\) | |||||||
\(908\) | 12.4924 | 0.414576 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.4924 | −0.679317 | ||||||||
\(911\) | 56.9848 | 1.88799 | 0.943996 | − | 0.329957i | \(-0.107034\pi\) | ||||
0.943996 | + | 0.329957i | \(0.107034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.2462 | 1.00100 | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.4924 | −0.478843 | ||||||||
\(917\) | 53.7538 | 1.77511 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.4924 | −0.544035 | −0.272017 | − | 0.962292i | \(-0.587691\pi\) | ||||
−0.272017 | + | 0.962292i | \(0.587691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.4924 | −0.345550 | ||||||||
\(923\) | −40.9848 | −1.34903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.8769 | −0.488885 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.00000 | −0.0656532 | ||||||||
\(929\) | −16.4924 | −0.541099 | −0.270549 | − | 0.962706i | \(-0.587205\pi\) | ||||
−0.270549 | + | 0.962706i | \(0.587205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.2462 | −0.630769 | ||||||||
\(932\) | 23.3693 | 0.765487 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.1231 | 1.28015 | ||||||||
\(935\) | 10.2462 | 0.335087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2462 | 1.57614 | 0.788068 | − | 0.615589i | \(-0.211082\pi\) | ||||
0.788068 | + | 0.615589i | \(0.211082\pi\) | |||||||
\(938\) | −52.4924 | −1.71394 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.24621 | 0.203729 | ||||||||
\(941\) | −45.2311 | −1.47449 | −0.737245 | − | 0.675625i | \(-0.763874\pi\) | ||||
−0.737245 | + | 0.675625i | \(0.763874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 5.12311 | 0.166743 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4924 | −0.406164 | ||||||||
\(947\) | 31.6155 | 1.02737 | 0.513683 | − | 0.857980i | \(-0.328281\pi\) | ||||
0.513683 | + | 0.857980i | \(0.328281\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | −1.00000 | −0.0324443 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.2462 | −0.850645 | ||||||||
\(953\) | 39.4773 | 1.27879 | 0.639397 | − | 0.768877i | \(-0.279184\pi\) | ||||
0.639397 | + | 0.768877i | \(0.279184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00000 | 0.129437 | ||||||||
\(956\) | −18.2462 | −0.590125 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.00000 | 0.129234 | ||||||||
\(959\) | −55.7235 | −1.79940 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2311 | −0.975195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.2462 | −0.523255 | ||||||||
\(965\) | 14.4924 | 0.466528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.8769 | −1.37883 | −0.689414 | − | 0.724368i | \(-0.742132\pi\) | ||||
−0.689414 | + | 0.724368i | \(0.742132\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.00000 | 0.192648 | ||||||||
\(971\) | −1.61553 | −0.0518448 | −0.0259224 | − | 0.999664i | \(-0.508252\pi\) | ||||
−0.0259224 | + | 0.999664i | \(0.508252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 84.4924 | 2.70870 | ||||||||
\(974\) | −32.2462 | −1.03324 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.24621 | −0.135918 | ||||||||
\(977\) | −58.0000 | −1.85558 | −0.927792 | − | 0.373097i | \(-0.878296\pi\) | ||||
−0.927792 | + | 0.373097i | \(0.878296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.7386 | 0.854570 | ||||||||
\(980\) | −19.2462 | −0.614798 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.4924 | 0.334827 | ||||||||
\(983\) | −3.50758 | −0.111874 | −0.0559372 | − | 0.998434i | \(-0.517815\pi\) | ||||
−0.0559372 | + | 0.998434i | \(0.517815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.24621 | −0.262746 | ||||||||
\(986\) | 10.2462 | 0.326306 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.00000 | −0.127257 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.6155 | 1.25843 | 0.629214 | − | 0.777232i | \(-0.283377\pi\) | ||||
0.629214 | + | 0.777232i | \(0.283377\pi\) | |||||||
\(992\) | 0.876894 | 0.0278414 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −52.4924 | −1.66496 | ||||||||
\(995\) | 6.24621 | 0.198018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.6307 | 0.336677 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(998\) | −4.00000 | −0.126618 | ||||||||
\(999\) | 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 | 1710.2.a.x.1.2 | yes | 2 | |
3.2 | odd | 2 | 1710.2.a.v.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 8550.2.a.bp.1.1 | 2 | |||
15.14 | odd | 2 | 8550.2.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.a.v.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1710.2.a.x.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
8550.2.a.bp.1.1 | 2 | 5.4 | even | 2 | |||
8550.2.a.bx.1.1 | 2 | 15.14 | odd | 2 |