Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2898,2,Mod(1,2898)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, 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("2898.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.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: | \(23.1406465058\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2898.1 |
$q$-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 | ||||||||
\(5\) | 3.70156 | 1.65539 | 0.827694 | − | 0.561179i | \(-0.189652\pi\) | ||||
0.827694 | + | 0.561179i | \(0.189652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.70156 | 1.17054 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.70156 | 1.58133 | 0.790664 | − | 0.612250i | \(-0.209735\pi\) | ||||
0.790664 | + | 0.612250i | \(0.209735\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.40312 | −1.23956 | −0.619781 | − | 0.784775i | \(-0.712779\pi\) | ||||
−0.619781 | + | 0.784775i | \(0.712779\pi\) | |||||||
\(20\) | 3.70156 | 0.827694 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70156 | 1.74031 | ||||||||
\(26\) | 5.70156 | 1.11817 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.298438 | −0.0554185 | −0.0277093 | − | 0.999616i | \(-0.508821\pi\) | ||||
−0.0277093 | + | 0.999616i | \(0.508821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.70156 | −0.625678 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70156 | 0.608533 | 0.304267 | − | 0.952587i | \(-0.401589\pi\) | ||||
0.304267 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(38\) | −5.40312 | −0.876502 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.70156 | 0.585268 | ||||||||
\(41\) | −7.70156 | −1.20278 | −0.601391 | − | 0.798955i | \(-0.705387\pi\) | ||||
−0.601391 | + | 0.798955i | \(0.705387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70156 | 0.869480 | 0.434740 | − | 0.900556i | \(-0.356840\pi\) | ||||
0.434740 | + | 0.900556i | \(0.356840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.70156 | −0.539928 | −0.269964 | − | 0.962870i | \(-0.587012\pi\) | ||||
−0.269964 | + | 0.962870i | \(0.587012\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.70156 | 1.23059 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.70156 | 0.790664 | ||||||||
\(53\) | −9.40312 | −1.29162 | −0.645809 | − | 0.763499i | \(-0.723480\pi\) | ||||
−0.645809 | + | 0.763499i | \(0.723480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.298438 | −0.0391868 | ||||||||
\(59\) | 0.596876 | 0.0777066 | 0.0388533 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388533 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 21.1047 | 2.61771 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.70156 | −0.442421 | ||||||||
\(71\) | −7.40312 | −0.878589 | −0.439295 | − | 0.898343i | \(-0.644772\pi\) | ||||
−0.439295 | + | 0.898343i | \(0.644772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.40312 | −0.632388 | −0.316194 | − | 0.948695i | \(-0.602405\pi\) | ||||
−0.316194 | + | 0.948695i | \(0.602405\pi\) | |||||||
\(74\) | 3.70156 | 0.430298 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.40312 | −0.619781 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 3.70156 | 0.413847 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.70156 | −0.850495 | ||||||||
\(83\) | 2.59688 | 0.285044 | 0.142522 | − | 0.989792i | \(-0.454479\pi\) | ||||
0.142522 | + | 0.989792i | \(0.454479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.70156 | 0.614815 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4031 | 1.63273 | 0.816364 | − | 0.577538i | \(-0.195986\pi\) | ||||
0.816364 | + | 0.577538i | \(0.195986\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.70156 | −0.597686 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.70156 | −0.381787 | ||||||||
\(95\) | −20.0000 | −2.05196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.10469 | −0.112164 | −0.0560820 | − | 0.998426i | \(-0.517861\pi\) | ||||
−0.0560820 | + | 0.998426i | \(0.517861\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.70156 | 0.870156 | ||||||||
\(101\) | −4.59688 | −0.457406 | −0.228703 | − | 0.973496i | \(-0.573449\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1047 | −1.68537 | −0.842687 | − | 0.538403i | \(-0.819028\pi\) | ||||
−0.842687 | + | 0.538403i | \(0.819028\pi\) | |||||||
\(104\) | 5.70156 | 0.559084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.40312 | −0.913312 | ||||||||
\(107\) | −14.8062 | −1.43137 | −0.715687 | − | 0.698421i | \(-0.753886\pi\) | ||||
−0.715687 | + | 0.698421i | \(0.753886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7016 | 1.50394 | 0.751968 | − | 0.659199i | \(-0.229105\pi\) | ||||
0.751968 | + | 0.659199i | \(0.229105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 4.29844 | 0.404363 | 0.202182 | − | 0.979348i | \(-0.435197\pi\) | ||||
0.202182 | + | 0.979348i | \(0.435197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.70156 | 0.345172 | ||||||||
\(116\) | −0.298438 | −0.0277093 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.596876 | 0.0549469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 13.7016 | 1.22550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1047 | 1.51780 | 0.758898 | − | 0.651210i | \(-0.225738\pi\) | ||||
0.758898 | + | 0.651210i | \(0.225738\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 21.1047 | 1.85100 | ||||||||
\(131\) | −15.4031 | −1.34578 | −0.672889 | − | 0.739744i | \(-0.734947\pi\) | ||||
−0.672889 | + | 0.739744i | \(0.734947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.40312 | 0.468510 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.895314 | −0.0764918 | −0.0382459 | − | 0.999268i | \(-0.512177\pi\) | ||||
−0.0382459 | + | 0.999268i | \(0.512177\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.1047 | −1.79008 | −0.895038 | − | 0.445990i | \(-0.852852\pi\) | ||||
−0.895038 | + | 0.445990i | \(0.852852\pi\) | |||||||
\(140\) | −3.70156 | −0.312839 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.40312 | −0.621256 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.10469 | −0.0917392 | ||||||||
\(146\) | −5.40312 | −0.447166 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.70156 | 0.304267 | ||||||||
\(149\) | 17.4031 | 1.42572 | 0.712860 | − | 0.701307i | \(-0.247400\pi\) | ||||
0.712860 | + | 0.701307i | \(0.247400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.10469 | 0.740929 | 0.370464 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370464 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(152\) | −5.40312 | −0.438251 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.2094 | 1.78390 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4031 | −1.06969 | −0.534843 | − | 0.844952i | \(-0.679629\pi\) | ||||
−0.534843 | + | 0.844952i | \(0.679629\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.70156 | 0.292634 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −7.70156 | −0.601391 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.59688 | 0.201557 | ||||||||
\(167\) | 21.4031 | 1.65622 | 0.828112 | − | 0.560563i | \(-0.189415\pi\) | ||||
0.828112 | + | 0.560563i | \(0.189415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.5078 | 1.50060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.70156 | 0.434740 | ||||||||
\(173\) | 3.40312 | 0.258735 | 0.129367 | − | 0.991597i | \(-0.458705\pi\) | ||||
0.129367 | + | 0.991597i | \(0.458705\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.70156 | −0.657776 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.4031 | 1.15451 | ||||||||
\(179\) | −5.70156 | −0.426155 | −0.213077 | − | 0.977035i | \(-0.568349\pi\) | ||||
−0.213077 | + | 0.977035i | \(0.568349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8062 | 1.24920 | 0.624599 | − | 0.780945i | \(-0.285262\pi\) | ||||
0.624599 | + | 0.780945i | \(0.285262\pi\) | |||||||
\(182\) | −5.70156 | −0.422628 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 13.7016 | 1.00736 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.70156 | −0.269964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.0000 | −1.45095 | ||||||||
\(191\) | −22.8062 | −1.65020 | −0.825101 | − | 0.564985i | \(-0.808882\pi\) | ||||
−0.825101 | + | 0.564985i | \(0.808882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.10469 | −0.511407 | −0.255703 | − | 0.966755i | \(-0.582307\pi\) | ||||
−0.255703 | + | 0.966755i | \(0.582307\pi\) | |||||||
\(194\) | −1.10469 | −0.0793119 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.50781 | −0.463662 | −0.231831 | − | 0.972756i | \(-0.574472\pi\) | ||||
−0.231831 | + | 0.972756i | \(0.574472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.10469 | 0.0783091 | 0.0391546 | − | 0.999233i | \(-0.487534\pi\) | ||||
0.0391546 | + | 0.999233i | \(0.487534\pi\) | |||||||
\(200\) | 8.70156 | 0.615293 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.59688 | −0.323435 | ||||||||
\(203\) | 0.298438 | 0.0209462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.5078 | −1.99107 | ||||||||
\(206\) | −17.1047 | −1.19174 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.70156 | 0.395332 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −9.40312 | −0.645809 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.8062 | −1.01213 | ||||||||
\(215\) | 21.1047 | 1.43933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 15.7016 | 1.06344 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.8062 | −1.39329 | −0.696645 | − | 0.717416i | \(-0.745325\pi\) | ||||
−0.696645 | + | 0.717416i | \(0.745325\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.29844 | 0.285928 | ||||||||
\(227\) | 26.5078 | 1.75939 | 0.879693 | − | 0.475543i | \(-0.157748\pi\) | ||||
0.879693 | + | 0.475543i | \(0.157748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.2094 | 1.86413 | 0.932064 | − | 0.362294i | \(-0.118006\pi\) | ||||
0.932064 | + | 0.362294i | \(0.118006\pi\) | |||||||
\(230\) | 3.70156 | 0.244074 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.298438 | −0.0195934 | ||||||||
\(233\) | −28.8062 | −1.88716 | −0.943580 | − | 0.331145i | \(-0.892565\pi\) | ||||
−0.943580 | + | 0.331145i | \(0.892565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.7016 | −0.893791 | ||||||||
\(236\) | 0.596876 | 0.0388533 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8062 | 1.21648 | 0.608238 | − | 0.793755i | \(-0.291877\pi\) | ||||
0.608238 | + | 0.793755i | \(0.291877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.10469 | 0.328822 | 0.164411 | − | 0.986392i | \(-0.447428\pi\) | ||||
0.164411 | + | 0.986392i | \(0.447428\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 3.70156 | 0.236484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.8062 | −1.96015 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.7016 | 0.866563 | ||||||||
\(251\) | −13.9109 | −0.878050 | −0.439025 | − | 0.898475i | \(-0.644676\pi\) | ||||
−0.439025 | + | 0.898475i | \(0.644676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 17.1047 | 1.07324 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.6125 | −1.47291 | −0.736454 | − | 0.676488i | \(-0.763501\pi\) | ||||
−0.736454 | + | 0.676488i | \(0.763501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.70156 | −0.230004 | ||||||||
\(260\) | 21.1047 | 1.30886 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.4031 | −0.951608 | ||||||||
\(263\) | 16.5078 | 1.01792 | 0.508958 | − | 0.860792i | \(-0.330031\pi\) | ||||
0.508958 | + | 0.860792i | \(0.330031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.8062 | −2.13813 | ||||||||
\(266\) | 5.40312 | 0.331287 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 3.40312 | 0.207492 | 0.103746 | − | 0.994604i | \(-0.466917\pi\) | ||||
0.103746 | + | 0.994604i | \(0.466917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4031 | 1.05716 | 0.528582 | − | 0.848882i | \(-0.322724\pi\) | ||||
0.528582 | + | 0.848882i | \(0.322724\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.895314 | −0.0540879 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4031 | −0.805316 | −0.402658 | − | 0.915351i | \(-0.631914\pi\) | ||||
−0.402658 | + | 0.915351i | \(0.631914\pi\) | |||||||
\(278\) | −21.1047 | −1.26577 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.70156 | −0.221211 | ||||||||
\(281\) | −4.29844 | −0.256423 | −0.128212 | − | 0.991747i | \(-0.540924\pi\) | ||||
−0.128212 | + | 0.991747i | \(0.540924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0000 | −0.594438 | −0.297219 | − | 0.954809i | \(-0.596059\pi\) | ||||
−0.297219 | + | 0.954809i | \(0.596059\pi\) | |||||||
\(284\) | −7.40312 | −0.439295 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.70156 | 0.454609 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −1.10469 | −0.0648694 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.40312 | −0.316194 | ||||||||
\(293\) | 3.19375 | 0.186581 | 0.0932905 | − | 0.995639i | \(-0.470261\pi\) | ||||
0.0932905 | + | 0.995639i | \(0.470261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20937 | 0.128635 | ||||||||
\(296\) | 3.70156 | 0.215149 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.4031 | 1.00814 | ||||||||
\(299\) | 5.70156 | 0.329730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.70156 | −0.328633 | ||||||||
\(302\) | 9.10469 | 0.523916 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.40312 | −0.309890 | ||||||||
\(305\) | 37.0156 | 2.11951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.10469 | 0.291340 | 0.145670 | − | 0.989333i | \(-0.453466\pi\) | ||||
0.145670 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.2094 | 1.26141 | ||||||||
\(311\) | 16.2094 | 0.919149 | 0.459575 | − | 0.888139i | \(-0.348002\pi\) | ||||
0.459575 | + | 0.888139i | \(0.348002\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.59688 | −0.259831 | −0.129915 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129915 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(314\) | −13.4031 | −0.756382 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.70156 | −0.432563 | −0.216281 | − | 0.976331i | \(-0.569393\pi\) | ||||
−0.216281 | + | 0.976331i | \(0.569393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.70156 | 0.206924 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49.6125 | 2.75201 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.70156 | −0.425248 | ||||||||
\(329\) | 3.70156 | 0.204074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6125 | −0.968070 | −0.484035 | − | 0.875049i | \(-0.660829\pi\) | ||||
−0.484035 | + | 0.875049i | \(0.660829\pi\) | |||||||
\(332\) | 2.59688 | 0.142522 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.4031 | 1.17113 | ||||||||
\(335\) | 14.8062 | 0.808952 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4031 | 0.948009 | 0.474004 | − | 0.880523i | \(-0.342808\pi\) | ||||
0.474004 | + | 0.880523i | \(0.342808\pi\) | |||||||
\(338\) | 19.5078 | 1.06109 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.70156 | 0.307408 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.40312 | 0.182953 | ||||||||
\(347\) | −20.5078 | −1.10092 | −0.550458 | − | 0.834863i | \(-0.685547\pi\) | ||||
−0.550458 | + | 0.834863i | \(0.685547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.2094 | 1.83119 | 0.915593 | − | 0.402107i | \(-0.131722\pi\) | ||||
0.915593 | + | 0.402107i | \(0.131722\pi\) | |||||||
\(350\) | −8.70156 | −0.465118 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.3141 | 1.77313 | 0.886564 | − | 0.462606i | \(-0.153085\pi\) | ||||
0.886564 | + | 0.462606i | \(0.153085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.4031 | −1.45441 | ||||||||
\(356\) | 15.4031 | 0.816364 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.70156 | −0.301337 | ||||||||
\(359\) | −9.70156 | −0.512029 | −0.256014 | − | 0.966673i | \(-0.582409\pi\) | ||||
−0.256014 | + | 0.966673i | \(0.582409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1938 | 0.536513 | ||||||||
\(362\) | 16.8062 | 0.883317 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.70156 | −0.298843 | ||||||||
\(365\) | −20.0000 | −1.04685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.9109 | 0.830544 | 0.415272 | − | 0.909697i | \(-0.363686\pi\) | ||||
0.415272 | + | 0.909697i | \(0.363686\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.7016 | 0.712310 | ||||||||
\(371\) | 9.40312 | 0.488186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.80625 | −0.248858 | −0.124429 | − | 0.992229i | \(-0.539710\pi\) | ||||
−0.124429 | + | 0.992229i | \(0.539710\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.70156 | −0.190893 | ||||||||
\(377\) | −1.70156 | −0.0876349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7016 | −0.909268 | −0.454634 | − | 0.890678i | \(-0.650230\pi\) | ||||
−0.454634 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(380\) | −20.0000 | −1.02598 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.8062 | −1.16687 | ||||||||
\(383\) | −6.80625 | −0.347783 | −0.173892 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173892 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.10469 | −0.361619 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.10469 | −0.0560820 | ||||||||
\(389\) | −36.8062 | −1.86615 | −0.933075 | − | 0.359681i | \(-0.882886\pi\) | ||||
−0.933075 | + | 0.359681i | \(0.882886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.50781 | −0.327859 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.20937 | 0.311639 | 0.155820 | − | 0.987786i | \(-0.450198\pi\) | ||||
0.155820 | + | 0.987786i | \(0.450198\pi\) | |||||||
\(398\) | 1.10469 | 0.0553729 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | −28.8062 | −1.43852 | −0.719258 | − | 0.694743i | \(-0.755518\pi\) | ||||
−0.719258 | + | 0.694743i | \(0.755518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.2094 | 1.70409 | ||||||||
\(404\) | −4.59688 | −0.228703 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.298438 | 0.0148112 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.2094 | −1.59265 | −0.796325 | − | 0.604868i | \(-0.793226\pi\) | ||||
−0.796325 | + | 0.604868i | \(0.793226\pi\) | |||||||
\(410\) | −28.5078 | −1.40790 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.1047 | −0.842687 | ||||||||
\(413\) | −0.596876 | −0.0293703 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.61250 | 0.471859 | ||||||||
\(416\) | 5.70156 | 0.279542 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.59688 | 0.126866 | 0.0634328 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634328 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7016 | 0.765247 | 0.382624 | − | 0.923904i | \(-0.375021\pi\) | ||||
0.382624 | + | 0.923904i | \(0.375021\pi\) | |||||||
\(422\) | −12.0000 | −0.584151 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.40312 | −0.456656 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | −14.8062 | −0.715687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.1047 | 1.01776 | ||||||||
\(431\) | −5.10469 | −0.245884 | −0.122942 | − | 0.992414i | \(-0.539233\pi\) | ||||
−0.122942 | + | 0.992414i | \(0.539233\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1047 | 0.821999 | 0.410999 | − | 0.911636i | \(-0.365180\pi\) | ||||
0.410999 | + | 0.911636i | \(0.365180\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.7016 | 0.751968 | ||||||||
\(437\) | −5.40312 | −0.258466 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.19375 | 0.152429 | 0.0762147 | − | 0.997091i | \(-0.475717\pi\) | ||||
0.0762147 | + | 0.997091i | \(0.475717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1047 | −0.812668 | −0.406334 | − | 0.913725i | \(-0.633193\pi\) | ||||
−0.406334 | + | 0.913725i | \(0.633193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57.0156 | 2.70280 | ||||||||
\(446\) | −20.8062 | −0.985204 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −27.6125 | −1.30311 | −0.651557 | − | 0.758600i | \(-0.725884\pi\) | ||||
−0.651557 | + | 0.758600i | \(0.725884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.29844 | 0.202182 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.5078 | 1.24407 | ||||||||
\(455\) | −21.1047 | −0.989403 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.2094 | −0.758242 | −0.379121 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379121 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(458\) | 28.2094 | 1.31814 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.70156 | 0.172586 | ||||||||
\(461\) | −27.4031 | −1.27629 | −0.638145 | − | 0.769916i | \(-0.720298\pi\) | ||||
−0.638145 | + | 0.769916i | \(0.720298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1047 | −0.609026 | −0.304513 | − | 0.952508i | \(-0.598494\pi\) | ||||
−0.304513 | + | 0.952508i | \(0.598494\pi\) | |||||||
\(464\) | −0.298438 | −0.0138546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.8062 | −1.33442 | ||||||||
\(467\) | 8.29844 | 0.384006 | 0.192003 | − | 0.981394i | \(-0.438502\pi\) | ||||
0.192003 | + | 0.981394i | \(0.438502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | −13.7016 | −0.632006 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.596876 | 0.0274734 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.0156 | −2.15722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8062 | 0.860178 | ||||||||
\(479\) | −7.40312 | −0.338257 | −0.169129 | − | 0.985594i | \(-0.554095\pi\) | ||||
−0.169129 | + | 0.985594i | \(0.554095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.1047 | 0.962291 | ||||||||
\(482\) | 5.10469 | 0.232512 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −4.08907 | −0.185675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.1047 | −0.593830 | −0.296915 | − | 0.954904i | \(-0.595958\pi\) | ||||
−0.296915 | + | 0.954904i | \(0.595958\pi\) | |||||||
\(488\) | 10.0000 | 0.452679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.70156 | 0.167220 | ||||||||
\(491\) | 17.6125 | 0.794841 | 0.397420 | − | 0.917637i | \(-0.369905\pi\) | ||||
0.397420 | + | 0.917637i | \(0.369905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −30.8062 | −1.38604 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 7.40312 | 0.332076 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0156 | 1.65705 | 0.828523 | − | 0.559954i | \(-0.189181\pi\) | ||||
0.828523 | + | 0.559954i | \(0.189181\pi\) | |||||||
\(500\) | 13.7016 | 0.612752 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.9109 | −0.620875 | ||||||||
\(503\) | 11.4031 | 0.508440 | 0.254220 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254220 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0156 | −0.757185 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.1047 | 0.758898 | ||||||||
\(509\) | 14.8062 | 0.656275 | 0.328138 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328138 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.40312 | 0.239020 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.6125 | −1.04150 | ||||||||
\(515\) | −63.3141 | −2.78995 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.70156 | −0.162637 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.1047 | 0.925502 | ||||||||
\(521\) | −15.4031 | −0.674823 | −0.337412 | − | 0.941357i | \(-0.609551\pi\) | ||||
−0.337412 | + | 0.941357i | \(0.609551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.4187 | −1.67993 | −0.839967 | − | 0.542637i | \(-0.817426\pi\) | ||||
−0.839967 | + | 0.542637i | \(0.817426\pi\) | |||||||
\(524\) | −15.4031 | −0.672889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.5078 | 0.719775 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −34.8062 | −1.51189 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.40312 | 0.234255 | ||||||||
\(533\) | −43.9109 | −1.90199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.8062 | −2.36948 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.40312 | 0.146719 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.2094 | −0.868869 | −0.434434 | − | 0.900703i | \(-0.643052\pi\) | ||||
−0.434434 | + | 0.900703i | \(0.643052\pi\) | |||||||
\(542\) | 17.4031 | 0.747528 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.1203 | 2.48960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2094 | −0.607549 | −0.303774 | − | 0.952744i | \(-0.598247\pi\) | ||||
−0.303774 | + | 0.952744i | \(0.598247\pi\) | |||||||
\(548\) | −0.895314 | −0.0382459 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61250 | 0.0686947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.4031 | −0.569444 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.1047 | −0.895038 | ||||||||
\(557\) | −21.4031 | −0.906879 | −0.453440 | − | 0.891287i | \(-0.649803\pi\) | ||||
−0.453440 | + | 0.891287i | \(0.649803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.5078 | 1.37493 | ||||||||
\(560\) | −3.70156 | −0.156420 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.29844 | −0.181319 | ||||||||
\(563\) | −44.7172 | −1.88460 | −0.942302 | − | 0.334763i | \(-0.891344\pi\) | ||||
−0.942302 | + | 0.334763i | \(0.891344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9109 | 0.669378 | ||||||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.40312 | −0.310628 | ||||||||
\(569\) | −11.1047 | −0.465533 | −0.232766 | − | 0.972533i | \(-0.574778\pi\) | ||||
−0.232766 | + | 0.972533i | \(0.574778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.70156 | 0.321457 | ||||||||
\(575\) | 8.70156 | 0.362880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6125 | −0.983001 | −0.491501 | − | 0.870877i | \(-0.663551\pi\) | ||||
−0.491501 | + | 0.870877i | \(0.663551\pi\) | |||||||
\(578\) | −17.0000 | −0.707107 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.10469 | −0.0458696 | ||||||||
\(581\) | −2.59688 | −0.107737 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.40312 | −0.223583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.19375 | 0.131933 | ||||||||
\(587\) | 1.19375 | 0.0492714 | 0.0246357 | − | 0.999696i | \(-0.492157\pi\) | ||||
0.0246357 | + | 0.999696i | \(0.492157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.4187 | −1.33579 | ||||||||
\(590\) | 2.20937 | 0.0909584 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.70156 | 0.152133 | ||||||||
\(593\) | 41.9109 | 1.72108 | 0.860538 | − | 0.509386i | \(-0.170128\pi\) | ||||
0.860538 | + | 0.509386i | \(0.170128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.4031 | 0.712860 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.70156 | 0.233154 | ||||||||
\(599\) | 29.6125 | 1.20993 | 0.604967 | − | 0.796251i | \(-0.293186\pi\) | ||||
0.604967 | + | 0.796251i | \(0.293186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4031 | 1.03622 | 0.518108 | − | 0.855315i | \(-0.326637\pi\) | ||||
0.518108 | + | 0.855315i | \(0.326637\pi\) | |||||||
\(602\) | −5.70156 | −0.232378 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.10469 | 0.370464 | ||||||||
\(605\) | −40.7172 | −1.65539 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.00000 | −0.0811775 | −0.0405887 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405887 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(608\) | −5.40312 | −0.219126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.0156 | 1.49872 | ||||||||
\(611\) | −21.1047 | −0.853804 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.3141 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(614\) | 5.10469 | 0.206008 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.0000 | −1.20580 | −0.602901 | − | 0.797816i | \(-0.705989\pi\) | ||||
−0.602901 | + | 0.797816i | \(0.705989\pi\) | |||||||
\(620\) | 22.2094 | 0.891950 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2094 | 0.649937 | ||||||||
\(623\) | −15.4031 | −0.617113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.20937 | 0.288375 | ||||||||
\(626\) | −4.59688 | −0.183728 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.4031 | −0.534843 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.19375 | 0.365997 | 0.182999 | − | 0.983113i | \(-0.441420\pi\) | ||||
0.182999 | + | 0.983113i | \(0.441420\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.70156 | −0.305868 | ||||||||
\(635\) | 63.3141 | 2.51254 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.70156 | 0.225904 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.70156 | 0.146317 | ||||||||
\(641\) | 11.7016 | 0.462184 | 0.231092 | − | 0.972932i | \(-0.425770\pi\) | ||||
0.231092 | + | 0.972932i | \(0.425770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.19375 | 0.125949 | 0.0629746 | − | 0.998015i | \(-0.479941\pi\) | ||||
0.0629746 | + | 0.998015i | \(0.479941\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.20937 | 0.165488 | 0.0827438 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827438 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 49.6125 | 1.94596 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −47.1047 | −1.84335 | −0.921674 | − | 0.387964i | \(-0.873178\pi\) | ||||
−0.921674 | + | 0.387964i | \(0.873178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.0156 | −2.22778 | ||||||||
\(656\) | −7.70156 | −0.300695 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.70156 | 0.144302 | ||||||||
\(659\) | −25.6125 | −0.997721 | −0.498861 | − | 0.866682i | \(-0.666248\pi\) | ||||
−0.498861 | + | 0.866682i | \(0.666248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.8062 | −0.809269 | −0.404635 | − | 0.914478i | \(-0.632601\pi\) | ||||
−0.404635 | + | 0.914478i | \(0.632601\pi\) | |||||||
\(662\) | −17.6125 | −0.684529 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.59688 | 0.100778 | ||||||||
\(665\) | 20.0000 | 0.775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.298438 | −0.0115556 | ||||||||
\(668\) | 21.4031 | 0.828112 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.8062 | 0.572015 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.29844 | −0.319881 | −0.159941 | − | 0.987127i | \(-0.551130\pi\) | ||||
−0.159941 | + | 0.987127i | \(0.551130\pi\) | |||||||
\(674\) | 17.4031 | 0.670343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.5078 | 0.750300 | ||||||||
\(677\) | 3.19375 | 0.122746 | 0.0613729 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613729 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10469 | 0.0423940 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.31406 | −0.126624 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.70156 | 0.217370 | ||||||||
\(689\) | −53.6125 | −2.04247 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.7016 | −1.58640 | −0.793201 | − | 0.608960i | \(-0.791587\pi\) | ||||
−0.793201 | + | 0.608960i | \(0.791587\pi\) | |||||||
\(692\) | 3.40312 | 0.129367 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.5078 | −0.778466 | ||||||||
\(695\) | −78.1203 | −2.96327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 34.2094 | 1.29484 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.70156 | −0.328888 | ||||||||
\(701\) | −14.5969 | −0.551316 | −0.275658 | − | 0.961256i | \(-0.588896\pi\) | ||||
−0.275658 | + | 0.961256i | \(0.588896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.3141 | 1.25379 | ||||||||
\(707\) | 4.59688 | 0.172883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.1938 | −0.570613 | −0.285307 | − | 0.958436i | \(-0.592095\pi\) | ||||
−0.285307 | + | 0.958436i | \(0.592095\pi\) | |||||||
\(710\) | −27.4031 | −1.02842 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.4031 | 0.577256 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.70156 | −0.213077 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.70156 | −0.362059 | ||||||||
\(719\) | −14.5078 | −0.541050 | −0.270525 | − | 0.962713i | \(-0.587197\pi\) | ||||
−0.270525 | + | 0.962713i | \(0.587197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1047 | 0.637012 | ||||||||
\(722\) | 10.1938 | 0.379372 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.8062 | 0.624599 | ||||||||
\(725\) | −2.59688 | −0.0964455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.0000 | −1.63187 | −0.815935 | − | 0.578144i | \(-0.803777\pi\) | ||||
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | −5.70156 | −0.211314 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.0000 | −0.740233 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.0156 | 1.14559 | 0.572794 | − | 0.819699i | \(-0.305859\pi\) | ||||
0.572794 | + | 0.819699i | \(0.305859\pi\) | |||||||
\(734\) | 15.9109 | 0.587283 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.2094 | 1.40555 | 0.702777 | − | 0.711410i | \(-0.251943\pi\) | ||||
0.702777 | + | 0.711410i | \(0.251943\pi\) | |||||||
\(740\) | 13.7016 | 0.503679 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.40312 | 0.345200 | ||||||||
\(743\) | 21.6125 | 0.792886 | 0.396443 | − | 0.918059i | \(-0.370245\pi\) | ||||
0.396443 | + | 0.918059i | \(0.370245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 64.4187 | 2.36012 | ||||||||
\(746\) | −4.80625 | −0.175969 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.8062 | 0.541009 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | −3.70156 | −0.134982 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.70156 | −0.0619672 | ||||||||
\(755\) | 33.7016 | 1.22653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.19375 | 0.261461 | 0.130731 | − | 0.991418i | \(-0.458268\pi\) | ||||
0.130731 | + | 0.991418i | \(0.458268\pi\) | |||||||
\(758\) | −17.7016 | −0.642950 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.0000 | −0.725476 | ||||||||
\(761\) | −15.6125 | −0.565953 | −0.282976 | − | 0.959127i | \(-0.591322\pi\) | ||||
−0.282976 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.7016 | −0.568435 | ||||||||
\(764\) | −22.8062 | −0.825101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.80625 | −0.245920 | ||||||||
\(767\) | 3.40312 | 0.122880 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.1047 | −1.04954 | −0.524771 | − | 0.851243i | \(-0.675849\pi\) | ||||
−0.524771 | + | 0.851243i | \(0.675849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.10469 | −0.255703 | ||||||||
\(773\) | −44.7172 | −1.60837 | −0.804183 | − | 0.594382i | \(-0.797397\pi\) | ||||
−0.804183 | + | 0.594382i | \(0.797397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 52.2094 | 1.87542 | ||||||||
\(776\) | −1.10469 | −0.0396559 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.8062 | −1.31957 | ||||||||
\(779\) | 41.6125 | 1.49092 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −49.6125 | −1.77075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.8219 | 1.77596 | 0.887979 | − | 0.459884i | \(-0.152109\pi\) | ||||
0.887979 | + | 0.459884i | \(0.152109\pi\) | |||||||
\(788\) | −6.50781 | −0.231831 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.29844 | −0.152835 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.0156 | 2.02468 | ||||||||
\(794\) | 6.20937 | 0.220362 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.10469 | 0.0391546 | ||||||||
\(797\) | 31.7016 | 1.12293 | 0.561463 | − | 0.827502i | \(-0.310239\pi\) | ||||
0.561463 | + | 0.827502i | \(0.310239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 8.70156 | 0.307647 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.8062 | −1.01718 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.70156 | −0.130463 | ||||||||
\(806\) | 34.2094 | 1.20497 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.59688 | −0.161718 | ||||||||
\(809\) | 21.4031 | 0.752494 | 0.376247 | − | 0.926519i | \(-0.377214\pi\) | ||||
0.376247 | + | 0.926519i | \(0.377214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3141 | 0.397290 | 0.198645 | − | 0.980071i | \(-0.436346\pi\) | ||||
0.198645 | + | 0.980071i | \(0.436346\pi\) | |||||||
\(812\) | 0.298438 | 0.0104731 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.4187 | −1.55592 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.8062 | −1.07777 | ||||||||
\(818\) | −32.2094 | −1.12617 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.5078 | −0.995536 | ||||||||
\(821\) | −6.00000 | −0.209401 | −0.104701 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104701 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.7172 | 1.62846 | 0.814229 | − | 0.580543i | \(-0.197160\pi\) | ||||
0.814229 | + | 0.580543i | \(0.197160\pi\) | |||||||
\(824\) | −17.1047 | −0.595870 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.596876 | −0.0207680 | ||||||||
\(827\) | 33.0156 | 1.14807 | 0.574033 | − | 0.818832i | \(-0.305378\pi\) | ||||
0.574033 | + | 0.818832i | \(0.305378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.2094 | −1.04921 | −0.524607 | − | 0.851344i | \(-0.675788\pi\) | ||||
−0.524607 | + | 0.851344i | \(0.675788\pi\) | |||||||
\(830\) | 9.61250 | 0.333655 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.70156 | 0.197666 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 79.2250 | 2.74169 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.59688 | 0.0897076 | ||||||||
\(839\) | 19.4031 | 0.669870 | 0.334935 | − | 0.942241i | \(-0.391286\pi\) | ||||
0.334935 | + | 0.942241i | \(0.391286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9109 | −0.996929 | ||||||||
\(842\) | 15.7016 | 0.541112 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 72.2094 | 2.48408 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | 0.377964 | ||||||||
\(848\) | −9.40312 | −0.322905 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.70156 | 0.126888 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.1047 | 1.40740 | 0.703699 | − | 0.710498i | \(-0.251530\pi\) | ||||
0.703699 | + | 0.710498i | \(0.251530\pi\) | |||||||
\(854\) | −10.0000 | −0.342193 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.8062 | −0.506067 | ||||||||
\(857\) | −2.08907 | −0.0713611 | −0.0356806 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356806 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.91093 | −0.133439 | −0.0667197 | − | 0.997772i | \(-0.521253\pi\) | ||||
−0.0667197 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(860\) | 21.1047 | 0.719664 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.10469 | −0.173866 | ||||||||
\(863\) | 10.8062 | 0.367849 | 0.183924 | − | 0.982940i | \(-0.441120\pi\) | ||||
0.183924 | + | 0.982940i | \(0.441120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.5969 | 0.428307 | ||||||||
\(866\) | 17.1047 | 0.581241 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.00000 | −0.203653 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.8062 | 0.772760 | ||||||||
\(872\) | 15.7016 | 0.531722 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.40312 | −0.182763 | ||||||||
\(875\) | −13.7016 | −0.463197 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.2094 | −1.62791 | −0.813957 | − | 0.580925i | \(-0.802691\pi\) | ||||
−0.813957 | + | 0.580925i | \(0.802691\pi\) | |||||||
\(878\) | 3.19375 | 0.107784 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2094 | 0.343963 | 0.171981 | − | 0.985100i | \(-0.444983\pi\) | ||||
0.171981 | + | 0.985100i | \(0.444983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5969 | 0.558529 | 0.279265 | − | 0.960214i | \(-0.409909\pi\) | ||||
0.279265 | + | 0.960214i | \(0.409909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.1047 | −0.574643 | ||||||||
\(887\) | 52.2094 | 1.75302 | 0.876510 | − | 0.481384i | \(-0.159866\pi\) | ||||
0.876510 | + | 0.481384i | \(0.159866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.1047 | −0.573673 | ||||||||
\(890\) | 57.0156 | 1.91117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.8062 | −0.696645 | ||||||||
\(893\) | 20.0000 | 0.669274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.1047 | −0.705452 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.6125 | −0.921441 | ||||||||
\(899\) | −1.79063 | −0.0597208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.29844 | 0.142964 | ||||||||
\(905\) | 62.2094 | 2.06791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.89531 | −0.0961373 | −0.0480687 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480687 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(908\) | 26.5078 | 0.879693 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21.1047 | −0.699614 | ||||||||
\(911\) | −1.70156 | −0.0563753 | −0.0281876 | − | 0.999603i | \(-0.508974\pi\) | ||||
−0.0281876 | + | 0.999603i | \(0.508974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.2094 | −0.536158 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.2094 | 0.932064 | ||||||||
\(917\) | 15.4031 | 0.508656 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.19375 | 0.0393782 | 0.0196891 | − | 0.999806i | \(-0.493732\pi\) | ||||
0.0196891 | + | 0.999806i | \(0.493732\pi\) | |||||||
\(920\) | 3.70156 | 0.122037 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.4031 | −0.902474 | ||||||||
\(923\) | −42.2094 | −1.38934 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.2094 | 1.05904 | ||||||||
\(926\) | −13.1047 | −0.430647 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.298438 | −0.00979670 | ||||||||
\(929\) | −23.7016 | −0.777623 | −0.388812 | − | 0.921317i | \(-0.627114\pi\) | ||||
−0.388812 | + | 0.921317i | \(0.627114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.40312 | −0.177080 | ||||||||
\(932\) | −28.8062 | −0.943580 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.29844 | 0.271533 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.3141 | 1.54568 | 0.772841 | − | 0.634599i | \(-0.218835\pi\) | ||||
0.772841 | + | 0.634599i | \(0.218835\pi\) | |||||||
\(938\) | −4.00000 | −0.130605 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.7016 | −0.446896 | ||||||||
\(941\) | 9.31406 | 0.303630 | 0.151815 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151815 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.70156 | −0.250797 | ||||||||
\(944\) | 0.596876 | 0.0194267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.49219 | −0.113481 | −0.0567405 | − | 0.998389i | \(-0.518071\pi\) | ||||
−0.0567405 | + | 0.998389i | \(0.518071\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8062 | −1.00001 | ||||||||
\(950\) | −47.0156 | −1.52539 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.8062 | 0.673980 | 0.336990 | − | 0.941508i | \(-0.390591\pi\) | ||||
0.336990 | + | 0.941508i | \(0.390591\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −84.4187 | −2.73173 | ||||||||
\(956\) | 18.8062 | 0.608238 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.40312 | −0.239184 | ||||||||
\(959\) | 0.895314 | 0.0289112 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 21.1047 | 0.680442 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.10469 | 0.164411 | ||||||||
\(965\) | −26.2984 | −0.846577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.4187 | 0.656623 | 0.328311 | − | 0.944570i | \(-0.393521\pi\) | ||||
0.328311 | + | 0.944570i | \(0.393521\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.08907 | −0.131292 | ||||||||
\(971\) | 33.4031 | 1.07196 | 0.535979 | − | 0.844232i | \(-0.319943\pi\) | ||||
0.535979 | + | 0.844232i | \(0.319943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.1047 | 0.676585 | ||||||||
\(974\) | −13.1047 | −0.419901 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 40.2984 | 1.28926 | 0.644631 | − | 0.764494i | \(-0.277011\pi\) | ||||
0.644631 | + | 0.764494i | \(0.277011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.70156 | 0.118242 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.6125 | 0.562037 | ||||||||
\(983\) | 55.8219 | 1.78044 | 0.890221 | − | 0.455530i | \(-0.150550\pi\) | ||||
0.890221 | + | 0.455530i | \(0.150550\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0891 | −0.767541 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.8062 | −0.980077 | ||||||||
\(989\) | 5.70156 | 0.181299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.40312 | 0.234813 | ||||||||
\(995\) | 4.08907 | 0.129632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.5969 | 1.53908 | 0.769539 | − | 0.638600i | \(-0.220486\pi\) | ||||
0.769539 | + | 0.638600i | \(0.220486\pi\) | |||||||
\(998\) | 37.0156 | 1.17171 | ||||||||
\(999\) | 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 | 2898.2.a.bc.1.2 | 2 | ||
3.2 | odd | 2 | 966.2.a.m.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 7728.2.a.z.1.1 | 2 | |||
21.20 | even | 2 | 6762.2.a.bq.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.a.m.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
2898.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6762.2.a.bq.1.2 | 2 | 21.20 | even | 2 | |||
7728.2.a.z.1.1 | 2 | 12.11 | even | 2 |