Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, 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("1890.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.1 |
$q$-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 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.77200 | −1.13730 | −0.568651 | − | 0.822579i | \(-0.692534\pi\) | ||||
−0.568651 | + | 0.822579i | \(0.692534\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.77200 | 1.60087 | 0.800433 | − | 0.599423i | \(-0.204603\pi\) | ||||
0.800433 | + | 0.599423i | \(0.204603\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.77200 | 0.914845 | 0.457422 | − | 0.889250i | \(-0.348773\pi\) | ||||
0.457422 | + | 0.889250i | \(0.348773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.77200 | −0.804194 | ||||||||
\(23\) | −3.77200 | −0.786517 | −0.393258 | − | 0.919428i | \(-0.628652\pi\) | ||||
−0.393258 | + | 0.919428i | \(0.628652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.77200 | 1.13198 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.54400 | −1.53455 | −0.767274 | − | 0.641319i | \(-0.778387\pi\) | ||||
−0.767274 | + | 0.641319i | \(0.778387\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.77200 | 0.646893 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.77200 | 1.44211 | 0.721054 | − | 0.692879i | \(-0.243658\pi\) | ||||
0.721054 | + | 0.692879i | \(0.243658\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.77200 | 1.05761 | 0.528805 | − | 0.848744i | \(-0.322640\pi\) | ||||
0.528805 | + | 0.848744i | \(0.322640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77200 | −0.270228 | −0.135114 | − | 0.990830i | \(-0.543140\pi\) | ||||
−0.135114 | + | 0.990830i | \(0.543140\pi\) | |||||||
\(44\) | −3.77200 | −0.568651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.77200 | −0.556151 | ||||||||
\(47\) | 4.54400 | 0.662811 | 0.331406 | − | 0.943488i | \(-0.392477\pi\) | ||||
0.331406 | + | 0.943488i | \(0.392477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.77200 | 0.800433 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.77200 | −0.508617 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | −6.77200 | −0.881640 | −0.440820 | − | 0.897596i | \(-0.645312\pi\) | ||||
−0.440820 | + | 0.897596i | \(0.645312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.77200 | 0.354918 | 0.177459 | − | 0.984128i | \(-0.443212\pi\) | ||||
0.177459 | + | 0.984128i | \(0.443212\pi\) | |||||||
\(62\) | −8.54400 | −1.08509 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.77200 | 0.715929 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.54400 | 1.16599 | 0.582993 | − | 0.812477i | \(-0.301882\pi\) | ||||
0.582993 | + | 0.812477i | \(0.301882\pi\) | |||||||
\(68\) | 3.77200 | 0.457422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 6.77200 | 0.803689 | 0.401844 | − | 0.915708i | \(-0.368369\pi\) | ||||
0.401844 | + | 0.915708i | \(0.368369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7720 | 1.72893 | 0.864466 | − | 0.502691i | \(-0.167657\pi\) | ||||
0.864466 | + | 0.502691i | \(0.167657\pi\) | |||||||
\(74\) | 8.77200 | 1.01972 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −3.77200 | −0.429860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.77200 | −0.199366 | −0.0996829 | − | 0.995019i | \(-0.531783\pi\) | ||||
−0.0996829 | + | 0.995019i | \(0.531783\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.77200 | 0.747843 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.77200 | 0.409131 | ||||||||
\(86\) | −1.77200 | −0.191080 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.77200 | −0.402097 | ||||||||
\(89\) | −13.5440 | −1.43566 | −0.717831 | − | 0.696218i | \(-0.754865\pi\) | ||||
−0.717831 | + | 0.696218i | \(0.754865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.77200 | 0.605070 | ||||||||
\(92\) | −3.77200 | −0.393258 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.54400 | 0.468678 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.5440 | −1.78132 | −0.890662 | − | 0.454666i | \(-0.849759\pi\) | ||||
−0.890662 | + | 0.454666i | \(0.849759\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.3160 | −1.72301 | −0.861503 | − | 0.507752i | \(-0.830477\pi\) | ||||
−0.861503 | + | 0.507752i | \(0.830477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 5.77200 | 0.565991 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −18.7720 | −1.81476 | −0.907379 | − | 0.420313i | \(-0.861920\pi\) | ||||
−0.907379 | + | 0.420313i | \(0.861920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.455996 | 0.0436765 | 0.0218383 | − | 0.999762i | \(-0.493048\pi\) | ||||
0.0218383 | + | 0.999762i | \(0.493048\pi\) | |||||||
\(110\) | −3.77200 | −0.359646 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 16.5440 | 1.55633 | 0.778164 | − | 0.628061i | \(-0.216151\pi\) | ||||
0.778164 | + | 0.628061i | \(0.216151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.77200 | −0.351741 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.77200 | −0.623413 | ||||||||
\(119\) | 3.77200 | 0.345779 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.22800 | 0.293454 | ||||||||
\(122\) | 2.77200 | 0.250965 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.54400 | −0.767274 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.22800 | 0.641381 | 0.320691 | − | 0.947184i | \(-0.396085\pi\) | ||||
0.320691 | + | 0.947184i | \(0.396085\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.77200 | 0.506238 | ||||||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | 0.173422 | ||||||||
\(134\) | 9.54400 | 0.824476 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.77200 | 0.323446 | ||||||||
\(137\) | −12.7720 | −1.09119 | −0.545593 | − | 0.838050i | \(-0.683695\pi\) | ||||
−0.545593 | + | 0.838050i | \(0.683695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.77200 | 0.568294 | ||||||||
\(143\) | −21.7720 | −1.82067 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | 0.249136 | ||||||||
\(146\) | 14.7720 | 1.22254 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.77200 | 0.721054 | ||||||||
\(149\) | 11.3160 | 0.927043 | 0.463522 | − | 0.886086i | \(-0.346586\pi\) | ||||
0.463522 | + | 0.886086i | \(0.346586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.31601 | 0.107095 | 0.0535475 | − | 0.998565i | \(-0.482947\pi\) | ||||
0.0535475 | + | 0.998565i | \(0.482947\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.77200 | −0.303957 | ||||||||
\(155\) | −8.54400 | −0.686271 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3160 | −1.22235 | −0.611175 | − | 0.791495i | \(-0.709303\pi\) | ||||
−0.611175 | + | 0.791495i | \(0.709303\pi\) | |||||||
\(158\) | −1.77200 | −0.140973 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.77200 | −0.297275 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2280 | 0.801119 | 0.400559 | − | 0.916271i | \(-0.368816\pi\) | ||||
0.400559 | + | 0.916271i | \(0.368816\pi\) | |||||||
\(164\) | 6.77200 | 0.528805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.22800 | −0.404555 | −0.202277 | − | 0.979328i | \(-0.564834\pi\) | ||||
−0.202277 | + | 0.979328i | \(0.564834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.3160 | 1.56277 | ||||||||
\(170\) | 3.77200 | 0.289299 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.77200 | −0.135114 | ||||||||
\(173\) | 0.772002 | 0.0586942 | 0.0293471 | − | 0.999569i | \(-0.490657\pi\) | ||||
0.0293471 | + | 0.999569i | \(0.490657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −3.77200 | −0.284325 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.5440 | −1.01517 | ||||||||
\(179\) | 1.54400 | 0.115404 | 0.0577021 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0577021 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.31601 | 0.320806 | 0.160403 | − | 0.987052i | \(-0.448721\pi\) | ||||
0.160403 | + | 0.987052i | \(0.448721\pi\) | |||||||
\(182\) | 5.77200 | 0.427849 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.77200 | −0.278076 | ||||||||
\(185\) | 8.77200 | 0.644930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.2280 | −1.04045 | ||||||||
\(188\) | 4.54400 | 0.331406 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | 0.145095 | ||||||||
\(191\) | 15.0880 | 1.09173 | 0.545865 | − | 0.837873i | \(-0.316201\pi\) | ||||
0.545865 | + | 0.837873i | \(0.316201\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.45600 | 0.464713 | 0.232356 | − | 0.972631i | \(-0.425356\pi\) | ||||
0.232356 | + | 0.972631i | \(0.425356\pi\) | |||||||
\(194\) | −17.5440 | −1.25959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3160 | 1.79460 | 0.897302 | − | 0.441417i | \(-0.145524\pi\) | ||||
0.897302 | + | 0.441417i | \(0.145524\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.3160 | −1.21835 | ||||||||
\(203\) | 3.00000 | 0.210559 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.77200 | 0.472977 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.77200 | 0.400216 | ||||||||
\(209\) | −7.54400 | −0.521830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3160 | 0.710183 | 0.355092 | − | 0.934832i | \(-0.384450\pi\) | ||||
0.355092 | + | 0.934832i | \(0.384450\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.7720 | −1.28323 | ||||||||
\(215\) | −1.77200 | −0.120850 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.54400 | −0.580005 | ||||||||
\(218\) | 0.455996 | 0.0308840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.77200 | −0.254308 | ||||||||
\(221\) | 21.7720 | 1.46454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.45600 | −0.164466 | −0.0822328 | − | 0.996613i | \(-0.526205\pi\) | ||||
−0.0822328 | + | 0.996613i | \(0.526205\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.5440 | 1.10049 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.54400 | −0.366358 | −0.183179 | − | 0.983080i | \(-0.558639\pi\) | ||||
−0.183179 | + | 0.983080i | \(0.558639\pi\) | |||||||
\(230\) | −3.77200 | −0.248718 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −24.7720 | −1.62287 | −0.811434 | − | 0.584444i | \(-0.801313\pi\) | ||||
−0.811434 | + | 0.584444i | \(0.801313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.54400 | 0.296418 | ||||||||
\(236\) | −6.77200 | −0.440820 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.77200 | 0.244503 | ||||||||
\(239\) | −21.8600 | −1.41401 | −0.707003 | − | 0.707210i | \(-0.749953\pi\) | ||||
−0.707003 | + | 0.707210i | \(0.749953\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7720 | −1.27363 | −0.636813 | − | 0.771018i | \(-0.719748\pi\) | ||||
−0.636813 | + | 0.771018i | \(0.719748\pi\) | |||||||
\(242\) | 3.22800 | 0.207504 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.77200 | 0.177459 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5440 | 0.734527 | ||||||||
\(248\) | −8.54400 | −0.542545 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 2.22800 | 0.140630 | 0.0703150 | − | 0.997525i | \(-0.477600\pi\) | ||||
0.0703150 | + | 0.997525i | \(0.477600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2280 | 0.894507 | ||||||||
\(254\) | 7.22800 | 0.453525 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.8600 | −1.55072 | −0.775362 | − | 0.631517i | \(-0.782433\pi\) | ||||
−0.775362 | + | 0.631517i | \(0.782433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.77200 | 0.545066 | ||||||||
\(260\) | 5.77200 | 0.357964 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.00000 | 0.185341 | ||||||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 2.00000 | 0.122628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.54400 | 0.582993 | ||||||||
\(269\) | −0.683994 | −0.0417039 | −0.0208519 | − | 0.999783i | \(-0.506638\pi\) | ||||
−0.0208519 | + | 0.999783i | \(0.506638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4040 | −1.66468 | −0.832338 | − | 0.554269i | \(-0.812998\pi\) | ||||
−0.832338 | + | 0.554269i | \(0.812998\pi\) | |||||||
\(272\) | 3.77200 | 0.228711 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.7720 | −0.771585 | ||||||||
\(275\) | −3.77200 | −0.227460 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | −10.0000 | −0.599760 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 25.5440 | 1.52383 | 0.761914 | − | 0.647678i | \(-0.224260\pi\) | ||||
0.761914 | + | 0.647678i | \(0.224260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.31601 | 0.256560 | 0.128280 | − | 0.991738i | \(-0.459054\pi\) | ||||
0.128280 | + | 0.991738i | \(0.459054\pi\) | |||||||
\(284\) | 6.77200 | 0.401844 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.7720 | −1.28741 | ||||||||
\(287\) | 6.77200 | 0.399739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.77200 | −0.163059 | ||||||||
\(290\) | 3.00000 | 0.176166 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.7720 | 0.864466 | ||||||||
\(293\) | 3.68399 | 0.215221 | 0.107611 | − | 0.994193i | \(-0.465680\pi\) | ||||
0.107611 | + | 0.994193i | \(0.465680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.77200 | −0.394281 | ||||||||
\(296\) | 8.77200 | 0.509862 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3160 | 0.655519 | ||||||||
\(299\) | −21.7720 | −1.25911 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77200 | −0.102136 | ||||||||
\(302\) | 1.31601 | 0.0757276 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 2.77200 | 0.158724 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.3160 | −1.90144 | −0.950722 | − | 0.310043i | \(-0.899656\pi\) | ||||
−0.950722 | + | 0.310043i | \(0.899656\pi\) | |||||||
\(308\) | −3.77200 | −0.214930 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.54400 | −0.485267 | ||||||||
\(311\) | 9.08801 | 0.515334 | 0.257667 | − | 0.966234i | \(-0.417046\pi\) | ||||
0.257667 | + | 0.966234i | \(0.417046\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5440 | −0.991646 | −0.495823 | − | 0.868424i | \(-0.665133\pi\) | ||||
−0.495823 | + | 0.868424i | \(0.665133\pi\) | |||||||
\(314\) | −15.3160 | −0.864332 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.77200 | −0.0996829 | ||||||||
\(317\) | −25.5440 | −1.43469 | −0.717347 | − | 0.696716i | \(-0.754644\pi\) | ||||
−0.717347 | + | 0.696716i | \(0.754644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3160 | −0.633575 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.77200 | −0.210205 | ||||||||
\(323\) | 7.54400 | 0.419760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.77200 | 0.320173 | ||||||||
\(326\) | 10.2280 | 0.566476 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.77200 | 0.373921 | ||||||||
\(329\) | 4.54400 | 0.250519 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8600 | −1.09160 | −0.545802 | − | 0.837914i | \(-0.683775\pi\) | ||||
−0.545802 | + | 0.837914i | \(0.683775\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.22800 | −0.286063 | ||||||||
\(335\) | 9.54400 | 0.521445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.00000 | −0.217894 | −0.108947 | − | 0.994048i | \(-0.534748\pi\) | ||||
−0.108947 | + | 0.994048i | \(0.534748\pi\) | |||||||
\(338\) | 20.3160 | 1.10505 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.77200 | 0.204566 | ||||||||
\(341\) | 32.2280 | 1.74524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.77200 | −0.0955399 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.772002 | 0.0415031 | ||||||||
\(347\) | 14.3160 | 0.768523 | 0.384262 | − | 0.923224i | \(-0.374456\pi\) | ||||
0.384262 | + | 0.923224i | \(0.374456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.77200 | −0.201048 | ||||||||
\(353\) | 11.3160 | 0.602290 | 0.301145 | − | 0.953578i | \(-0.402631\pi\) | ||||
0.301145 | + | 0.953578i | \(0.402631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.77200 | 0.359421 | ||||||||
\(356\) | −13.5440 | −0.717831 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.54400 | 0.0816031 | ||||||||
\(359\) | −4.45600 | −0.235178 | −0.117589 | − | 0.993062i | \(-0.537517\pi\) | ||||
−0.117589 | + | 0.993062i | \(0.537517\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 4.31601 | 0.226844 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.77200 | 0.302535 | ||||||||
\(365\) | 14.7720 | 0.773202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.08801 | 0.265592 | 0.132796 | − | 0.991143i | \(-0.457605\pi\) | ||||
0.132796 | + | 0.991143i | \(0.457605\pi\) | |||||||
\(368\) | −3.77200 | −0.196629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.77200 | 0.456035 | ||||||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.0000 | 1.19089 | 0.595447 | − | 0.803394i | \(-0.296975\pi\) | ||||
0.595447 | + | 0.803394i | \(0.296975\pi\) | |||||||
\(374\) | −14.2280 | −0.735712 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.54400 | 0.234339 | ||||||||
\(377\) | 17.3160 | 0.891820 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7720 | 1.06699 | 0.533493 | − | 0.845804i | \(-0.320879\pi\) | ||||
0.533493 | + | 0.845804i | \(0.320879\pi\) | |||||||
\(380\) | 2.00000 | 0.102598 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0880 | 0.771970 | ||||||||
\(383\) | 17.3160 | 0.884807 | 0.442403 | − | 0.896816i | \(-0.354126\pi\) | ||||
0.442403 | + | 0.896816i | \(0.354126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.77200 | −0.192239 | ||||||||
\(386\) | 6.45600 | 0.328602 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.5440 | −0.890662 | ||||||||
\(389\) | 3.00000 | 0.152106 | 0.0760530 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760530 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.2280 | −0.719541 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −1.77200 | −0.0891591 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.4040 | 1.12443 | 0.562213 | − | 0.826993i | \(-0.309950\pi\) | ||||
0.562213 | + | 0.826993i | \(0.309950\pi\) | |||||||
\(398\) | 25.3160 | 1.26898 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −22.6320 | −1.13019 | −0.565094 | − | 0.825026i | \(-0.691160\pi\) | ||||
−0.565094 | + | 0.825026i | \(0.691160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.3160 | −2.45661 | ||||||||
\(404\) | −17.3160 | −0.861503 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | 0.148888 | ||||||||
\(407\) | −33.0880 | −1.64011 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.2280 | −0.604636 | −0.302318 | − | 0.953207i | \(-0.597760\pi\) | ||||
−0.302318 | + | 0.953207i | \(0.597760\pi\) | |||||||
\(410\) | 6.77200 | 0.334445 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | −6.77200 | −0.333228 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.77200 | 0.282996 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.54400 | −0.368989 | ||||||||
\(419\) | 3.00000 | 0.146560 | 0.0732798 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732798 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5440 | −0.855042 | −0.427521 | − | 0.904005i | \(-0.640613\pi\) | ||||
−0.427521 | + | 0.904005i | \(0.640613\pi\) | |||||||
\(422\) | 10.3160 | 0.502175 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 3.77200 | 0.182969 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.77200 | 0.134147 | ||||||||
\(428\) | −18.7720 | −0.907379 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.77200 | −0.0854535 | ||||||||
\(431\) | 9.68399 | 0.466462 | 0.233231 | − | 0.972421i | \(-0.425070\pi\) | ||||
0.233231 | + | 0.972421i | \(0.425070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7720 | −0.806011 | −0.403005 | − | 0.915198i | \(-0.632034\pi\) | ||||
−0.403005 | + | 0.915198i | \(0.632034\pi\) | |||||||
\(434\) | −8.54400 | −0.410125 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.455996 | 0.0218383 | ||||||||
\(437\) | −7.54400 | −0.360879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −3.77200 | −0.179823 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.7720 | 1.03559 | ||||||||
\(443\) | −9.86001 | −0.468463 | −0.234232 | − | 0.972181i | \(-0.575257\pi\) | ||||
−0.234232 | + | 0.972181i | \(0.575257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5440 | −0.642047 | ||||||||
\(446\) | −2.45600 | −0.116295 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −15.0880 | −0.712047 | −0.356024 | − | 0.934477i | \(-0.615868\pi\) | ||||
−0.356024 | + | 0.934477i | \(0.615868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.5440 | −1.20282 | ||||||||
\(452\) | 16.5440 | 0.778164 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 5.77200 | 0.270596 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.5440 | −1.66268 | −0.831339 | − | 0.555765i | \(-0.812425\pi\) | ||||
−0.831339 | + | 0.555765i | \(0.812425\pi\) | |||||||
\(458\) | −5.54400 | −0.259054 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.77200 | −0.175870 | ||||||||
\(461\) | 16.4560 | 0.766432 | 0.383216 | − | 0.923659i | \(-0.374816\pi\) | ||||
0.383216 | + | 0.923659i | \(0.374816\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.31601 | −0.293530 | −0.146765 | − | 0.989171i | \(-0.546886\pi\) | ||||
−0.146765 | + | 0.989171i | \(0.546886\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.7720 | −1.14754 | ||||||||
\(467\) | 37.5440 | 1.73733 | 0.868665 | − | 0.495401i | \(-0.164979\pi\) | ||||
0.868665 | + | 0.495401i | \(0.164979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.54400 | 0.440701 | ||||||||
\(470\) | 4.54400 | 0.209599 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.77200 | −0.311707 | ||||||||
\(473\) | 6.68399 | 0.307330 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 3.77200 | 0.172889 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.8600 | −0.999854 | ||||||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.6320 | 2.30862 | ||||||||
\(482\) | −19.7720 | −0.900590 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.22800 | 0.146727 | ||||||||
\(485\) | −17.5440 | −0.796632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8600 | 0.537428 | 0.268714 | − | 0.963220i | \(-0.413401\pi\) | ||||
0.268714 | + | 0.963220i | \(0.413401\pi\) | |||||||
\(488\) | 2.77200 | 0.125483 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3160 | 0.509647 | ||||||||
\(494\) | 11.5440 | 0.519389 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.54400 | −0.383637 | ||||||||
\(497\) | 6.77200 | 0.303766 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.4040 | 1.67443 | 0.837217 | − | 0.546871i | \(-0.184181\pi\) | ||||
0.837217 | + | 0.546871i | \(0.184181\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.22800 | 0.0994404 | ||||||||
\(503\) | −9.77200 | −0.435712 | −0.217856 | − | 0.975981i | \(-0.569906\pi\) | ||||
−0.217856 | + | 0.975981i | \(0.569906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3160 | −0.770552 | ||||||||
\(506\) | 14.2280 | 0.632512 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.22800 | 0.320691 | ||||||||
\(509\) | 32.4040 | 1.43628 | 0.718141 | − | 0.695897i | \(-0.244993\pi\) | ||||
0.718141 | + | 0.695897i | \(0.244993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.7720 | 0.653475 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.8600 | −1.09653 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.1400 | −0.753816 | ||||||||
\(518\) | 8.77200 | 0.385420 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.77200 | 0.253119 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3160 | 0.582268 | 0.291134 | − | 0.956682i | \(-0.405967\pi\) | ||||
0.291134 | + | 0.956682i | \(0.405967\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −32.2280 | −1.40387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.77200 | −0.381391 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | 0.0867110 | ||||||||
\(533\) | 39.0880 | 1.69309 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.7720 | −0.811584 | ||||||||
\(536\) | 9.54400 | 0.412238 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.683994 | −0.0294891 | ||||||||
\(539\) | −3.77200 | −0.162472 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.6320 | 1.05901 | 0.529506 | − | 0.848306i | \(-0.322377\pi\) | ||||
0.529506 | + | 0.848306i | \(0.322377\pi\) | |||||||
\(542\) | −27.4040 | −1.17710 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.77200 | 0.161723 | ||||||||
\(545\) | 0.455996 | 0.0195327 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.86001 | −0.207799 | −0.103899 | − | 0.994588i | \(-0.533132\pi\) | ||||
−0.103899 | + | 0.994588i | \(0.533132\pi\) | |||||||
\(548\) | −12.7720 | −0.545593 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.77200 | −0.160839 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.77200 | −0.0753532 | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0000 | −0.424094 | ||||||||
\(557\) | 25.5440 | 1.08233 | 0.541167 | − | 0.840915i | \(-0.317983\pi\) | ||||
0.541167 | + | 0.840915i | \(0.317983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2280 | −0.432598 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.5440 | 1.07751 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5440 | 0.696011 | ||||||||
\(566\) | 4.31601 | 0.181415 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.77200 | 0.284147 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8600 | −0.580023 | −0.290012 | − | 0.957023i | \(-0.593659\pi\) | ||||
−0.290012 | + | 0.957023i | \(0.593659\pi\) | |||||||
\(572\) | −21.7720 | −0.910333 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.77200 | 0.282658 | ||||||||
\(575\) | −3.77200 | −0.157303 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.9480 | −1.70469 | −0.852344 | − | 0.522981i | \(-0.824820\pi\) | ||||
−0.852344 | + | 0.522981i | \(0.824820\pi\) | |||||||
\(578\) | −2.77200 | −0.115300 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6320 | 0.937322 | ||||||||
\(584\) | 14.7720 | 0.611270 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.68399 | 0.152184 | ||||||||
\(587\) | −36.0000 | −1.48588 | −0.742940 | − | 0.669359i | \(-0.766569\pi\) | ||||
−0.742940 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0880 | −0.704099 | ||||||||
\(590\) | −6.77200 | −0.278799 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.77200 | 0.360527 | ||||||||
\(593\) | 17.3160 | 0.711083 | 0.355542 | − | 0.934660i | \(-0.384296\pi\) | ||||
0.355542 | + | 0.934660i | \(0.384296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.77200 | 0.154637 | ||||||||
\(596\) | 11.3160 | 0.463522 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.7720 | −0.890323 | ||||||||
\(599\) | −39.8600 | −1.62864 | −0.814318 | − | 0.580419i | \(-0.802889\pi\) | ||||
−0.814318 | + | 0.580419i | \(0.802889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.68399 | 0.109482 | 0.0547412 | − | 0.998501i | \(-0.482567\pi\) | ||||
0.0547412 | + | 0.998501i | \(0.482567\pi\) | |||||||
\(602\) | −1.77200 | −0.0722214 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.31601 | 0.0535475 | ||||||||
\(605\) | 3.22800 | 0.131237 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.7200 | −1.69336 | −0.846682 | − | 0.532100i | \(-0.821403\pi\) | ||||
−0.846682 | + | 0.532100i | \(0.821403\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.77200 | 0.112235 | ||||||||
\(611\) | 26.2280 | 1.06107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.3160 | −1.58796 | −0.793979 | − | 0.607945i | \(-0.791994\pi\) | ||||
−0.793979 | + | 0.607945i | \(0.791994\pi\) | |||||||
\(614\) | −33.3160 | −1.34452 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.77200 | −0.151978 | ||||||||
\(617\) | 39.1760 | 1.57717 | 0.788583 | − | 0.614928i | \(-0.210815\pi\) | ||||
0.788583 | + | 0.614928i | \(0.210815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.455996 | 0.0183280 | 0.00916402 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916402 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(620\) | −8.54400 | −0.343135 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.08801 | 0.364396 | ||||||||
\(623\) | −13.5440 | −0.542629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.5440 | −0.701199 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.3160 | −0.611175 | ||||||||
\(629\) | 33.0880 | 1.31931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5440 | 0.857653 | 0.428827 | − | 0.903387i | \(-0.358927\pi\) | ||||
0.428827 | + | 0.903387i | \(0.358927\pi\) | |||||||
\(632\) | −1.77200 | −0.0704864 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.5440 | −1.01448 | ||||||||
\(635\) | 7.22800 | 0.286834 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.77200 | 0.228695 | ||||||||
\(638\) | −11.3160 | −0.448005 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 34.6320 | 1.36788 | 0.683941 | − | 0.729537i | \(-0.260265\pi\) | ||||
0.683941 | + | 0.729537i | \(0.260265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.1760 | −1.70270 | −0.851348 | − | 0.524602i | \(-0.824214\pi\) | ||||
−0.851348 | + | 0.524602i | \(0.824214\pi\) | |||||||
\(644\) | −3.77200 | −0.148638 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.54400 | 0.296815 | ||||||||
\(647\) | −23.4040 | −0.920107 | −0.460053 | − | 0.887891i | \(-0.652170\pi\) | ||||
−0.460053 | + | 0.887891i | \(0.652170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.5440 | 1.00269 | ||||||||
\(650\) | 5.77200 | 0.226397 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.2280 | 0.400559 | ||||||||
\(653\) | 33.0880 | 1.29483 | 0.647417 | − | 0.762136i | \(-0.275849\pi\) | ||||
0.647417 | + | 0.762136i | \(0.275849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00000 | 0.117220 | ||||||||
\(656\) | 6.77200 | 0.264402 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.54400 | 0.177144 | ||||||||
\(659\) | 42.1760 | 1.64294 | 0.821472 | − | 0.570249i | \(-0.193153\pi\) | ||||
0.821472 | + | 0.570249i | \(0.193153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.68399 | −0.0654998 | −0.0327499 | − | 0.999464i | \(-0.510426\pi\) | ||||
−0.0327499 | + | 0.999464i | \(0.510426\pi\) | |||||||
\(662\) | −19.8600 | −0.771881 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.3160 | −0.438157 | ||||||||
\(668\) | −5.22800 | −0.202277 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.54400 | 0.368717 | ||||||||
\(671\) | −10.4560 | −0.403649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.6320 | 1.87463 | 0.937313 | − | 0.348488i | \(-0.113305\pi\) | ||||
0.937313 | + | 0.348488i | \(0.113305\pi\) | |||||||
\(674\) | −4.00000 | −0.154074 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.3160 | 0.781385 | ||||||||
\(677\) | 15.6840 | 0.602785 | 0.301392 | − | 0.953500i | \(-0.402549\pi\) | ||||
0.301392 | + | 0.953500i | \(0.402549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5440 | −0.673277 | ||||||||
\(680\) | 3.77200 | 0.144650 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 32.2280 | 1.23407 | ||||||||
\(683\) | −23.2280 | −0.888795 | −0.444397 | − | 0.895830i | \(-0.646582\pi\) | ||||
−0.444397 | + | 0.895830i | \(0.646582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.7720 | −0.487993 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.77200 | −0.0675569 | ||||||||
\(689\) | −34.6320 | −1.31937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.0880 | 1.56306 | 0.781531 | − | 0.623867i | \(-0.214439\pi\) | ||||
0.781531 | + | 0.623867i | \(0.214439\pi\) | |||||||
\(692\) | 0.772002 | 0.0293471 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.3160 | 0.543428 | ||||||||
\(695\) | −10.0000 | −0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.5440 | 0.967548 | ||||||||
\(698\) | −22.0000 | −0.832712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5440 | 0.661685 | ||||||||
\(704\) | −3.77200 | −0.142163 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.3160 | 0.425883 | ||||||||
\(707\) | −17.3160 | −0.651235 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4560 | 0.693129 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(710\) | 6.77200 | 0.254149 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.5440 | −0.507583 | ||||||||
\(713\) | 32.2280 | 1.20695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.7720 | −0.814227 | ||||||||
\(716\) | 1.54400 | 0.0577021 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.45600 | −0.166296 | ||||||||
\(719\) | 40.6320 | 1.51532 | 0.757659 | − | 0.652650i | \(-0.226343\pi\) | ||||
0.757659 | + | 0.652650i | \(0.226343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.31601 | 0.160403 | ||||||||
\(725\) | 3.00000 | 0.111417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.54400 | 0.131440 | 0.0657199 | − | 0.997838i | \(-0.479066\pi\) | ||||
0.0657199 | + | 0.997838i | \(0.479066\pi\) | |||||||
\(728\) | 5.77200 | 0.213925 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.7720 | 0.546736 | ||||||||
\(731\) | −6.68399 | −0.247216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5440 | 1.46059 | 0.730296 | − | 0.683131i | \(-0.239382\pi\) | ||||
0.730296 | + | 0.683131i | \(0.239382\pi\) | |||||||
\(734\) | 5.08801 | 0.187802 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.77200 | −0.139038 | ||||||||
\(737\) | −36.0000 | −1.32608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.22800 | 0.265886 | 0.132943 | − | 0.991124i | \(-0.457557\pi\) | ||||
0.132943 | + | 0.991124i | \(0.457557\pi\) | |||||||
\(740\) | 8.77200 | 0.322465 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 12.6840 | 0.465331 | 0.232665 | − | 0.972557i | \(-0.425255\pi\) | ||||
0.232665 | + | 0.972557i | \(0.425255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.3160 | 0.414586 | ||||||||
\(746\) | 23.0000 | 0.842090 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.2280 | −0.520227 | ||||||||
\(749\) | −18.7720 | −0.685914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7720 | 1.30534 | 0.652669 | − | 0.757643i | \(-0.273649\pi\) | ||||
0.652669 | + | 0.757643i | \(0.273649\pi\) | |||||||
\(752\) | 4.54400 | 0.165703 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.3160 | 0.630612 | ||||||||
\(755\) | 1.31601 | 0.0478943 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.6320 | 1.87660 | 0.938299 | − | 0.345826i | \(-0.112401\pi\) | ||||
0.938299 | + | 0.345826i | \(0.112401\pi\) | |||||||
\(758\) | 20.7720 | 0.754473 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | 0.0725476 | ||||||||
\(761\) | 12.7720 | 0.462985 | 0.231492 | − | 0.972837i | \(-0.425639\pi\) | ||||
0.231492 | + | 0.972837i | \(0.425639\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.455996 | 0.0165082 | ||||||||
\(764\) | 15.0880 | 0.545865 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.3160 | 0.625653 | ||||||||
\(767\) | −39.0880 | −1.41139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2280 | −1.30642 | −0.653208 | − | 0.757179i | \(-0.726577\pi\) | ||||
−0.653208 | + | 0.757179i | \(0.726577\pi\) | |||||||
\(770\) | −3.77200 | −0.135934 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.45600 | 0.232356 | ||||||||
\(773\) | 15.8600 | 0.570445 | 0.285222 | − | 0.958461i | \(-0.407933\pi\) | ||||
0.285222 | + | 0.958461i | \(0.407933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.54400 | −0.306910 | ||||||||
\(776\) | −17.5440 | −0.629793 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.00000 | 0.107555 | ||||||||
\(779\) | 13.5440 | 0.485264 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.5440 | −0.914036 | ||||||||
\(782\) | −14.2280 | −0.508792 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −15.3160 | −0.546652 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6320 | 0.984975 | 0.492487 | − | 0.870320i | \(-0.336088\pi\) | ||||
0.492487 | + | 0.870320i | \(0.336088\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.77200 | −0.0630450 | ||||||||
\(791\) | 16.5440 | 0.588237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 22.4040 | 0.795089 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.3160 | 0.897302 | ||||||||
\(797\) | −38.3160 | −1.35722 | −0.678611 | − | 0.734498i | \(-0.737418\pi\) | ||||
−0.678611 | + | 0.734498i | \(0.737418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.1400 | 0.606369 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.6320 | −0.799164 | ||||||||
\(803\) | −55.7200 | −1.96632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.77200 | −0.132946 | ||||||||
\(806\) | −49.3160 | −1.73708 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −17.3160 | −0.609175 | ||||||||
\(809\) | −43.7200 | −1.53711 | −0.768557 | − | 0.639781i | \(-0.779025\pi\) | ||||
−0.768557 | + | 0.639781i | \(0.779025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.91199 | 0.172483 | 0.0862417 | − | 0.996274i | \(-0.472514\pi\) | ||||
0.0862417 | + | 0.996274i | \(0.472514\pi\) | |||||||
\(812\) | 3.00000 | 0.105279 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33.0880 | −1.15973 | ||||||||
\(815\) | 10.2280 | 0.358271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.54400 | −0.123989 | ||||||||
\(818\) | −12.2280 | −0.427542 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.77200 | 0.236489 | ||||||||
\(821\) | −9.08801 | −0.317174 | −0.158587 | − | 0.987345i | \(-0.550694\pi\) | ||||
−0.158587 | + | 0.987345i | \(0.550694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4040 | 0.885528 | 0.442764 | − | 0.896638i | \(-0.353998\pi\) | ||||
0.442764 | + | 0.896638i | \(0.353998\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.77200 | −0.235628 | ||||||||
\(827\) | −14.3160 | −0.497816 | −0.248908 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248908 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.6320 | −0.716579 | −0.358290 | − | 0.933610i | \(-0.616640\pi\) | ||||
−0.358290 | + | 0.933610i | \(0.616640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.77200 | 0.200108 | ||||||||
\(833\) | 3.77200 | 0.130692 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.22800 | −0.180922 | ||||||||
\(836\) | −7.54400 | −0.260915 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.00000 | 0.103633 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −17.5440 | −0.604606 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3160 | 0.355092 | ||||||||
\(845\) | 20.3160 | 0.698892 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.22800 | 0.110915 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.77200 | 0.129379 | ||||||||
\(851\) | −33.0880 | −1.13424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.8600 | −0.371840 | −0.185920 | − | 0.982565i | \(-0.559526\pi\) | ||||
−0.185920 | + | 0.982565i | \(0.559526\pi\) | |||||||
\(854\) | 2.77200 | 0.0948560 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.7720 | −0.641614 | ||||||||
\(857\) | 49.7200 | 1.69840 | 0.849202 | − | 0.528069i | \(-0.177084\pi\) | ||||
0.849202 | + | 0.528069i | \(0.177084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.0000 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(860\) | −1.77200 | −0.0604248 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.68399 | 0.329838 | ||||||||
\(863\) | −6.68399 | −0.227526 | −0.113763 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113763 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.772002 | 0.0262489 | ||||||||
\(866\) | −16.7720 | −0.569936 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.54400 | −0.290002 | ||||||||
\(869\) | 6.68399 | 0.226739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.0880 | 1.86659 | ||||||||
\(872\) | 0.455996 | 0.0154420 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.54400 | −0.255180 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6320 | −0.595391 | −0.297695 | − | 0.954661i | \(-0.596218\pi\) | ||||
−0.297695 | + | 0.954661i | \(0.596218\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.77200 | −0.127154 | ||||||||
\(881\) | −8.31601 | −0.280173 | −0.140087 | − | 0.990139i | \(-0.544738\pi\) | ||||
−0.140087 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.911993 | −0.0306910 | −0.0153455 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153455 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(884\) | 21.7720 | 0.732272 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.86001 | −0.331253 | ||||||||
\(887\) | 16.5440 | 0.555493 | 0.277747 | − | 0.960654i | \(-0.410412\pi\) | ||||
0.277747 | + | 0.960654i | \(0.410412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.22800 | 0.242419 | ||||||||
\(890\) | −13.5440 | −0.453996 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.45600 | −0.0822328 | ||||||||
\(893\) | 9.08801 | 0.304119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54400 | 0.0516104 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0880 | −0.503493 | ||||||||
\(899\) | −25.6320 | −0.854875 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.6320 | −0.753982 | ||||||||
\(902\) | −25.5440 | −0.850522 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.5440 | 0.550245 | ||||||||
\(905\) | 4.31601 | 0.143469 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.7720 | −1.25420 | −0.627099 | − | 0.778939i | \(-0.715758\pi\) | ||||
−0.627099 | + | 0.778939i | \(0.715758\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.77200 | 0.191340 | ||||||||
\(911\) | −32.3160 | −1.07068 | −0.535339 | − | 0.844638i | \(-0.679816\pi\) | ||||
−0.535339 | + | 0.844638i | \(0.679816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −35.5440 | −1.17569 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.54400 | −0.183179 | ||||||||
\(917\) | 3.00000 | 0.0990687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.4920 | −1.50064 | −0.750322 | − | 0.661073i | \(-0.770101\pi\) | ||||
−0.750322 | + | 0.661073i | \(0.770101\pi\) | |||||||
\(920\) | −3.77200 | −0.124359 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.4560 | 0.541949 | ||||||||
\(923\) | 39.0880 | 1.28660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.77200 | 0.288422 | ||||||||
\(926\) | −6.31601 | −0.207557 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | −21.0880 | −0.691875 | −0.345938 | − | 0.938258i | \(-0.612439\pi\) | ||||
−0.345938 | + | 0.938258i | \(0.612439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | −24.7720 | −0.811434 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.5440 | 1.22848 | ||||||||
\(935\) | −14.2280 | −0.465305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.13999 | −0.200585 | −0.100292 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100292 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(938\) | 9.54400 | 0.311623 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.54400 | 0.148209 | ||||||||
\(941\) | −23.3160 | −0.760080 | −0.380040 | − | 0.924970i | \(-0.624090\pi\) | ||||
−0.380040 | + | 0.924970i | \(0.624090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.5440 | −0.831827 | ||||||||
\(944\) | −6.77200 | −0.220410 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.68399 | 0.217315 | ||||||||
\(947\) | 57.2640 | 1.86083 | 0.930415 | − | 0.366507i | \(-0.119446\pi\) | ||||
0.930415 | + | 0.366507i | \(0.119446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.2640 | 2.76779 | ||||||||
\(950\) | 2.00000 | 0.0648886 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.77200 | 0.122251 | ||||||||
\(953\) | −59.3160 | −1.92143 | −0.960717 | − | 0.277530i | \(-0.910484\pi\) | ||||
−0.960717 | + | 0.277530i | \(0.910484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0880 | 0.488236 | ||||||||
\(956\) | −21.8600 | −0.707003 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.0000 | −1.16311 | ||||||||
\(959\) | −12.7720 | −0.412429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.0000 | 1.35484 | ||||||||
\(962\) | 50.6320 | 1.63244 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.7720 | −0.636813 | ||||||||
\(965\) | 6.45600 | 0.207826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7720 | 0.667983 | 0.333991 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333991 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(968\) | 3.22800 | 0.103752 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.5440 | −0.563304 | ||||||||
\(971\) | 45.0000 | 1.44412 | 0.722059 | − | 0.691831i | \(-0.243196\pi\) | ||||
0.722059 | + | 0.691831i | \(0.243196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | −0.320585 | ||||||||
\(974\) | 11.8600 | 0.380019 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.77200 | 0.0887296 | ||||||||
\(977\) | 35.3160 | 1.12986 | 0.564930 | − | 0.825139i | \(-0.308903\pi\) | ||||
0.564930 | + | 0.825139i | \(0.308903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.0880 | 1.63278 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.0000 | 0.382935 | ||||||||
\(983\) | −36.8600 | −1.17565 | −0.587826 | − | 0.808987i | \(-0.700016\pi\) | ||||
−0.587826 | + | 0.808987i | \(0.700016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 11.3160 | 0.360375 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.5440 | 0.367264 | ||||||||
\(989\) | 6.68399 | 0.212539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4040 | 0.330494 | 0.165247 | − | 0.986252i | \(-0.447158\pi\) | ||||
0.165247 | + | 0.986252i | \(0.447158\pi\) | |||||||
\(992\) | −8.54400 | −0.271272 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.77200 | 0.214795 | ||||||||
\(995\) | 25.3160 | 0.802571 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.31601 | −0.105019 | −0.0525095 | − | 0.998620i | \(-0.516722\pi\) | ||||
−0.0525095 | + | 0.998620i | \(0.516722\pi\) | |||||||
\(998\) | 37.4040 | 1.18400 | ||||||||
\(999\) | 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 | 1890.2.a.bb.1.1 | yes | 2 | |
3.2 | odd | 2 | 1890.2.a.z.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 9450.2.a.ed.1.1 | 2 | |||
15.14 | odd | 2 | 9450.2.a.eo.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.a.z.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1890.2.a.bb.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
9450.2.a.ed.1.1 | 2 | 5.4 | even | 2 | |||
9450.2.a.eo.1.2 | 2 | 15.14 | odd | 2 |