Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, 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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
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: | no (minimal twist has level 1890) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | \(-0.795397\pi\) | ||||
−0.800433 | + | 0.599423i | \(0.795397\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.77200 | −0.914845 | −0.457422 | − | 0.889250i | \(-0.651227\pi\) | ||||
−0.457422 | + | 0.889250i | \(0.651227\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.77200 | 0.804194 | ||||||||
\(23\) | 3.77200 | 0.786517 | 0.393258 | − | 0.919428i | \(-0.371348\pi\) | ||||
0.393258 | + | 0.919428i | \(0.371348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.77200 | −1.44211 | −0.721054 | − | 0.692879i | \(-0.756342\pi\) | ||||
−0.721054 | + | 0.692879i | \(0.756342\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.456860\pi\) | ||||
0.135114 | + | 0.990830i | \(0.456860\pi\) | |||||||
\(44\) | −3.77200 | −0.568651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.77200 | −0.556151 | ||||||||
\(47\) | −4.54400 | −0.662811 | −0.331406 | − | 0.943488i | \(-0.607523\pi\) | ||||
−0.331406 | + | 0.943488i | \(0.607523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.77200 | −0.800433 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.54400 | −1.16599 | −0.582993 | − | 0.812477i | \(-0.698118\pi\) | ||||
−0.582993 | + | 0.812477i | \(0.698118\pi\) | |||||||
\(68\) | −3.77200 | −0.457422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(-0.832343\pi\) | ||||
−0.864466 | + | 0.502691i | \(0.832343\pi\) | |||||||
\(74\) | 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 | \(0.531783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.77200 | −0.747843 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −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 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5440 | 1.78132 | 0.890662 | − | 0.454666i | \(-0.150241\pi\) | ||||
0.890662 | + | 0.454666i | \(0.150241\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −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 | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 5.77200 | 0.565991 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 18.7720 | 1.81476 | 0.907379 | − | 0.420313i | \(-0.138080\pi\) | ||||
0.907379 | + | 0.420313i | \(0.138080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.455996 | 0.0436765 | 0.0218383 | − | 0.999762i | \(-0.493048\pi\) | ||||
0.0218383 | + | 0.999762i | \(0.493048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −16.5440 | −1.55633 | −0.778164 | − | 0.628061i | \(-0.783849\pi\) | ||||
−0.778164 | + | 0.628061i | \(0.783849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.22800 | −0.641381 | −0.320691 | − | 0.947184i | \(-0.603915\pi\) | ||||
−0.320691 | + | 0.947184i | \(0.603915\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 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 | \(-0.316305\pi\) | ||||
0.545593 | + | 0.838050i | \(0.316305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.77200 | −0.568294 | ||||||||
\(143\) | 21.7720 | 1.82067 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3160 | 1.22235 | 0.611175 | − | 0.791495i | \(-0.290697\pi\) | ||||
0.611175 | + | 0.791495i | \(0.290697\pi\) | |||||||
\(158\) | 1.77200 | 0.140973 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.77200 | −0.297275 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2280 | −0.801119 | −0.400559 | − | 0.916271i | \(-0.631184\pi\) | ||||
−0.400559 | + | 0.916271i | \(0.631184\pi\) | |||||||
\(164\) | 6.77200 | 0.528805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.22800 | 0.404555 | 0.202277 | − | 0.979328i | \(-0.435166\pi\) | ||||
0.202277 | + | 0.979328i | \(0.435166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.3160 | 1.56277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.77200 | 0.135114 | ||||||||
\(173\) | −0.772002 | −0.0586942 | −0.0293471 | − | 0.999569i | \(-0.509343\pi\) | ||||
−0.0293471 | + | 0.999569i | \(0.509343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2280 | 1.04045 | ||||||||
\(188\) | −4.54400 | −0.331406 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(-0.574644\pi\) | ||||
−0.232356 | + | 0.972631i | \(0.574644\pi\) | |||||||
\(194\) | −17.5440 | −1.25959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3160 | 1.79460 | 0.897302 | − | 0.441417i | \(-0.145524\pi\) | ||||
0.897302 | + | 0.441417i | \(0.145524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.3160 | 1.21835 | ||||||||
\(203\) | −3.00000 | −0.210559 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.54400 | 0.580005 | ||||||||
\(218\) | −0.455996 | −0.0308840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.7720 | 1.46454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.45600 | 0.164466 | 0.0822328 | − | 0.996613i | \(-0.473795\pi\) | ||||
0.0822328 | + | 0.996613i | \(0.473795\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.5440 | 1.10049 | ||||||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.54400 | −0.366358 | −0.183179 | − | 0.983080i | \(-0.558639\pi\) | ||||
−0.183179 | + | 0.983080i | \(0.558639\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 24.7720 | 1.62287 | 0.811434 | − | 0.584444i | \(-0.198687\pi\) | ||||
0.811434 | + | 0.584444i | \(0.198687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5440 | −0.734527 | ||||||||
\(248\) | 8.54400 | 0.542545 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | \(-0.217567\pi\) | ||||
0.775362 | + | 0.631517i | \(0.217567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.77200 | 0.545066 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | −0.185341 | ||||||||
\(263\) | 24.0000 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 10.0000 | 0.599760 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.540946\pi\) | ||||
−0.128280 | + | 0.991738i | \(0.540946\pi\) | |||||||
\(284\) | 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 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7720 | −0.864466 | ||||||||
\(293\) | −3.68399 | −0.215221 | −0.107611 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107611 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.3160 | 1.90144 | 0.950722 | − | 0.310043i | \(-0.100344\pi\) | ||||
0.950722 | + | 0.310043i | \(0.100344\pi\) | |||||||
\(308\) | 3.77200 | 0.214930 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(-0.334867\pi\) | ||||
0.495823 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(314\) | −15.3160 | −0.864332 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.77200 | −0.0996829 | ||||||||
\(317\) | 25.5440 | 1.43469 | 0.717347 | − | 0.696716i | \(-0.245356\pi\) | ||||
0.717347 | + | 0.696716i | \(0.245356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3160 | −0.633575 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.77200 | 0.210205 | ||||||||
\(323\) | −7.54400 | −0.419760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | −20.3160 | −1.10505 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | \(-0.625544\pi\) | ||||
−0.384262 | + | 0.923224i | \(0.625544\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.77200 | 0.201048 | ||||||||
\(353\) | −11.3160 | −0.602290 | −0.301145 | − | 0.953578i | \(-0.597369\pi\) | ||||
−0.301145 | + | 0.953578i | \(0.597369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.08801 | −0.265592 | −0.132796 | − | 0.991143i | \(-0.542395\pi\) | ||||
−0.132796 | + | 0.991143i | \(0.542395\pi\) | |||||||
\(368\) | 3.77200 | 0.196629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.0000 | −1.19089 | −0.595447 | − | 0.803394i | \(-0.703025\pi\) | ||||
−0.595447 | + | 0.803394i | \(0.703025\pi\) | |||||||
\(374\) | −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 | \(0.320879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.0880 | −0.771970 | ||||||||
\(383\) | −17.3160 | −0.884807 | −0.442403 | − | 0.896816i | \(-0.645874\pi\) | ||||
−0.442403 | + | 0.896816i | \(0.645874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4040 | −1.12443 | −0.562213 | − | 0.826993i | \(-0.690050\pi\) | ||||
−0.562213 | + | 0.826993i | \(0.690050\pi\) | |||||||
\(398\) | −25.3160 | −1.26898 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −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 | \(0.597760\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.77200 | −0.134147 | ||||||||
\(428\) | 18.7720 | 0.907379 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.367966\pi\) | ||||
0.403005 | + | 0.915198i | \(0.367966\pi\) | |||||||
\(434\) | −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 | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.7720 | −1.03559 | ||||||||
\(443\) | 9.86001 | 0.468463 | 0.234232 | − | 0.972181i | \(-0.424743\pi\) | ||||
0.234232 | + | 0.972181i | \(0.424743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.5440 | 1.66268 | 0.831339 | − | 0.555765i | \(-0.187575\pi\) | ||||
0.831339 | + | 0.555765i | \(0.187575\pi\) | |||||||
\(458\) | 5.54400 | 0.259054 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 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 | \(-0.453114\pi\) | ||||
0.146765 | + | 0.989171i | \(0.453114\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.7720 | −1.14754 | ||||||||
\(467\) | −37.5440 | −1.73733 | −0.868665 | − | 0.495401i | \(-0.835021\pi\) | ||||
−0.868665 | + | 0.495401i | \(0.835021\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.54400 | 0.440701 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.77200 | 0.311707 | ||||||||
\(473\) | −6.68399 | −0.307330 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8600 | −0.537428 | −0.268714 | − | 0.963220i | \(-0.586599\pi\) | ||||
−0.268714 | + | 0.963220i | \(0.586599\pi\) | |||||||
\(488\) | −2.77200 | −0.125483 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | \(0.184181\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.22800 | −0.0994404 | ||||||||
\(503\) | 9.77200 | 0.435712 | 0.217856 | − | 0.975981i | \(-0.430094\pi\) | ||||
0.217856 | + | 0.975981i | \(0.430094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1400 | 0.753816 | ||||||||
\(518\) | −8.77200 | −0.385420 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.594033\pi\) | ||||
−0.291134 | + | 0.956682i | \(0.594033\pi\) | |||||||
\(524\) | 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 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | −39.0880 | −1.69309 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.86001 | 0.207799 | 0.103899 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103899 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(548\) | 12.7720 | 0.545593 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 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 | \(-0.682017\pi\) | ||||
−0.541167 | + | 0.840915i | \(0.682017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2280 | −0.432598 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.5440 | −1.07751 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.9480 | 1.70469 | 0.852344 | − | 0.522981i | \(-0.175180\pi\) | ||||
0.852344 | + | 0.522981i | \(0.175180\pi\) | |||||||
\(578\) | 2.77200 | 0.115300 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 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 | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0880 | −0.704099 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.77200 | −0.360527 | ||||||||
\(593\) | −17.3160 | −0.711083 | −0.355542 | − | 0.934660i | \(-0.615704\pi\) | ||||
−0.355542 | + | 0.934660i | \(0.615704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.7200 | 1.69336 | 0.846682 | − | 0.532100i | \(-0.178597\pi\) | ||||
0.846682 | + | 0.532100i | \(0.178597\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2280 | 1.06107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3160 | 1.58796 | 0.793979 | − | 0.607945i | \(-0.208006\pi\) | ||||
0.793979 | + | 0.607945i | \(0.208006\pi\) | |||||||
\(614\) | −33.3160 | −1.34452 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.77200 | −0.151978 | ||||||||
\(617\) | −39.1760 | −1.57717 | −0.788583 | − | 0.614928i | \(-0.789185\pi\) | ||||
−0.788583 | + | 0.614928i | \(0.789185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.455996 | 0.0183280 | 0.00916402 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916402 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.08801 | −0.364396 | ||||||||
\(623\) | 13.5440 | 0.542629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −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 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.77200 | −0.228695 | ||||||||
\(638\) | 11.3160 | 0.448005 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 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 | \(-0.175786\pi\) | ||||
0.851348 | + | 0.524602i | \(0.175786\pi\) | |||||||
\(644\) | −3.77200 | −0.148638 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.54400 | 0.296815 | ||||||||
\(647\) | 23.4040 | 0.920107 | 0.460053 | − | 0.887891i | \(-0.347830\pi\) | ||||
0.460053 | + | 0.887891i | \(0.347830\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.5440 | 1.00269 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.2280 | −0.400559 | ||||||||
\(653\) | −33.0880 | −1.29483 | −0.647417 | − | 0.762136i | \(-0.724151\pi\) | ||||
−0.647417 | + | 0.762136i | \(0.724151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3160 | 0.438157 | ||||||||
\(668\) | 5.22800 | 0.202277 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.4560 | −0.403649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.6320 | −1.87463 | −0.937313 | − | 0.348488i | \(-0.886695\pi\) | ||||
−0.937313 | + | 0.348488i | \(0.886695\pi\) | |||||||
\(674\) | −4.00000 | −0.154074 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.3160 | 0.781385 | ||||||||
\(677\) | −15.6840 | −0.602785 | −0.301392 | − | 0.953500i | \(-0.597451\pi\) | ||||
−0.301392 | + | 0.953500i | \(0.597451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5440 | −0.673277 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −32.2280 | −1.23407 | ||||||||
\(683\) | 23.2280 | 0.888795 | 0.444397 | − | 0.895830i | \(-0.353418\pi\) | ||||
0.444397 | + | 0.895830i | \(0.353418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.5440 | −0.967548 | ||||||||
\(698\) | 22.0000 | 0.832712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | \(0.387348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5440 | 0.507583 | ||||||||
\(713\) | −32.2280 | −1.20695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.54400 | −0.131440 | −0.0657199 | − | 0.997838i | \(-0.520934\pi\) | ||||
−0.0657199 | + | 0.997838i | \(0.520934\pi\) | |||||||
\(728\) | −5.77200 | −0.213925 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.68399 | −0.247216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.5440 | −1.46059 | −0.730296 | − | 0.683131i | \(-0.760618\pi\) | ||||
−0.730296 | + | 0.683131i | \(0.760618\pi\) | |||||||
\(734\) | 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 | \(0.457557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | 0.220267 | ||||||||
\(743\) | −12.6840 | −0.465331 | −0.232665 | − | 0.972557i | \(-0.574745\pi\) | ||||
−0.232665 | + | 0.972557i | \(0.574745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.6320 | −1.87660 | −0.938299 | − | 0.345826i | \(-0.887599\pi\) | ||||
−0.938299 | + | 0.345826i | \(0.887599\pi\) | |||||||
\(758\) | −20.7720 | −0.754473 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | \(0.726577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.45600 | −0.232356 | ||||||||
\(773\) | −15.8600 | −0.570445 | −0.285222 | − | 0.958461i | \(-0.592067\pi\) | ||||
−0.285222 | + | 0.958461i | \(0.592067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.6320 | −0.984975 | −0.492487 | − | 0.870320i | \(-0.663912\pi\) | ||||
−0.492487 | + | 0.870320i | \(0.663912\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 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 | \(-0.262582\pi\) | ||||
0.678611 | + | 0.734498i | \(0.262582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.1400 | 0.606369 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.6320 | 0.799164 | ||||||||
\(803\) | 55.7200 | 1.96632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.54400 | 0.123989 | ||||||||
\(818\) | 12.2280 | 0.427542 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −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 | \(-0.646002\pi\) | ||||
−0.442764 | + | 0.896638i | \(0.646002\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.77200 | −0.235628 | ||||||||
\(827\) | 14.3160 | 0.497816 | 0.248908 | − | 0.968527i | \(-0.419928\pi\) | ||||
0.248908 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(828\) | 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 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.22800 | −0.110915 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.0880 | −1.13424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8600 | 0.371840 | 0.185920 | − | 0.982565i | \(-0.440474\pi\) | ||||
0.185920 | + | 0.982565i | \(0.440474\pi\) | |||||||
\(854\) | 2.77200 | 0.0948560 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.7720 | −0.641614 | ||||||||
\(857\) | −49.7200 | −1.69840 | −0.849202 | − | 0.528069i | \(-0.822916\pi\) | ||||
−0.849202 | + | 0.528069i | \(0.822916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.0000 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.68399 | −0.329838 | ||||||||
\(863\) | 6.68399 | 0.227526 | 0.113763 | − | 0.993508i | \(-0.463710\pi\) | ||||
0.113763 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6320 | 0.595391 | 0.297695 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297695 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(878\) | −8.00000 | −0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.495115\pi\) | ||||
0.0153455 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(884\) | 21.7720 | 0.732272 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.86001 | −0.331253 | ||||||||
\(887\) | −16.5440 | −0.555493 | −0.277747 | − | 0.960654i | \(-0.589588\pi\) | ||||
−0.277747 | + | 0.960654i | \(0.589588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.22800 | 0.242419 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.45600 | 0.0822328 | ||||||||
\(893\) | −9.08801 | −0.304119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.7720 | 1.25420 | 0.627099 | − | 0.778939i | \(-0.284242\pi\) | ||||
0.627099 | + | 0.778939i | \(0.284242\pi\) | |||||||
\(908\) | 24.0000 | 0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | \(0.770101\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.4560 | −0.541949 | ||||||||
\(923\) | −39.0880 | −1.28660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −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 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.13999 | 0.200585 | 0.100292 | − | 0.994958i | \(-0.468022\pi\) | ||||
0.100292 | + | 0.994958i | \(0.468022\pi\) | |||||||
\(938\) | −9.54400 | −0.311623 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −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 | \(-0.880554\pi\) | ||||
−0.930415 | + | 0.366507i | \(0.880554\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 85.2640 | 2.76779 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.77200 | −0.122251 | ||||||||
\(953\) | 59.3160 | 1.92143 | 0.960717 | − | 0.277530i | \(-0.0895158\pi\) | ||||
0.960717 | + | 0.277530i | \(0.0895158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7720 | −0.667983 | −0.333991 | − | 0.942576i | \(-0.608396\pi\) | ||||
−0.333991 | + | 0.942576i | \(0.608396\pi\) | |||||||
\(968\) | −3.22800 | −0.103752 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | \(-0.691097\pi\) | ||||
−0.564930 | + | 0.825139i | \(0.691097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.0880 | 1.63278 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.0000 | −0.382935 | ||||||||
\(983\) | 36.8600 | 1.17565 | 0.587826 | − | 0.808987i | \(-0.299984\pi\) | ||||
0.587826 | + | 0.808987i | \(0.299984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.31601 | 0.105019 | 0.0525095 | − | 0.998620i | \(-0.483278\pi\) | ||||
0.0525095 | + | 0.998620i | \(0.483278\pi\) | |||||||
\(998\) | −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 | 9450.2.a.ed.1.1 | 2 | ||
3.2 | odd | 2 | 9450.2.a.eo.1.2 | 2 | |||
5.4 | even | 2 | 1890.2.a.bb.1.1 | yes | 2 | ||
15.14 | odd | 2 | 1890.2.a.z.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.a.z.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
1890.2.a.bb.1.1 | yes | 2 | 5.4 | even | 2 | ||
9450.2.a.ed.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9450.2.a.eo.1.2 | 2 | 3.2 | odd | 2 |