Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(1,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, 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("572.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.79129 | 1.61155 | 0.805775 | − | 0.592221i | \(-0.201749\pi\) | ||||
0.805775 | + | 0.592221i | \(0.201749\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.208712 | 0.0788858 | 0.0394429 | − | 0.999222i | \(-0.487442\pi\) | ||||
0.0394429 | + | 0.999222i | \(0.487442\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.58258 | 1.44141 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.20871 | 0.277298 | 0.138649 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138649 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.582576 | 0.127128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.208712 | 0.0435195 | 0.0217597 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217597 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.58258 | −0.665268 | −0.332634 | − | 0.943056i | \(-0.607937\pi\) | ||||
−0.332634 | + | 0.943056i | \(0.607937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.79129 | −0.485901 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.417424 | 0.0705576 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.79129 | −0.446964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79129 | 0.279752 | 0.139876 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139876 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.16515 | −1.09268 | −0.546338 | − | 0.837565i | \(-0.683978\pi\) | ||||
−0.546338 | + | 0.837565i | \(0.683978\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.58258 | 1.42849 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.58258 | 0.522572 | 0.261286 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261286 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95644 | −0.993777 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.1652 | −1.56343 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37386 | 0.600796 | 0.300398 | − | 0.953814i | \(-0.402880\pi\) | ||||
0.300398 | + | 0.953814i | \(0.402880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.37386 | 0.446879 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.58258 | −0.726789 | −0.363395 | − | 0.931635i | \(-0.618382\pi\) | ||||
−0.363395 | + | 0.931635i | \(0.618382\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.41742 | 0.309519 | 0.154760 | − | 0.987952i | \(-0.450540\pi\) | ||||
0.154760 | + | 0.987952i | \(0.450540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1652 | 1.36404 | 0.682020 | − | 0.731333i | \(-0.261102\pi\) | ||||
0.682020 | + | 0.731333i | \(0.261102\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.582576 | 0.0701339 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7913 | −1.26302 | −0.631512 | − | 0.775366i | \(-0.717565\pi\) | ||||
−0.631512 | + | 0.775366i | \(0.717565\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.79129 | −0.322310 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.208712 | −0.0237850 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7477 | 1.43423 | 0.717116 | − | 0.696954i | \(-0.245462\pi\) | ||||
0.717116 | + | 0.696954i | \(0.245462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.626136 | 0.0687274 | 0.0343637 | − | 0.999409i | \(-0.489060\pi\) | ||||
0.0343637 | + | 0.999409i | \(0.489060\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.58258 | 1.01575 | 0.507875 | − | 0.861430i | \(-0.330431\pi\) | ||||
0.507875 | + | 0.861430i | \(0.330431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.208712 | −0.0218790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.41742 | 0.248023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.7477 | 1.90354 | 0.951772 | − | 0.306807i | \(-0.0992607\pi\) | ||||
0.951772 | + | 0.306807i | \(0.0992607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.79129 | −0.481543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.208712 | −0.0205650 | −0.0102825 | − | 0.999947i | \(-0.503273\pi\) | ||||
−0.0102825 | + | 0.999947i | \(0.503273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.16515 | 0.113707 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.58258 | 0.926383 | 0.463191 | − | 0.886258i | \(-0.346704\pi\) | ||||
0.463191 | + | 0.886258i | \(0.346704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.20871 | −0.115774 | −0.0578868 | − | 0.998323i | \(-0.518436\pi\) | ||||
−0.0578868 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1652 | 1.05975 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −21.1216 | −1.98695 | −0.993476 | − | 0.114041i | \(-0.963621\pi\) | ||||
−0.993476 | + | 0.114041i | \(0.963621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.417424 | 0.0389250 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.79129 | −0.442955 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.834849 | −0.0765304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.00000 | 0.450835 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5826 | 1.56020 | 0.780101 | − | 0.625654i | \(-0.215168\pi\) | ||||
0.780101 | + | 0.625654i | \(0.215168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.0000 | −1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.252273 | 0.0218748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0000 | 0.860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23.1652 | −1.97913 | −0.989566 | − | 0.144079i | \(-0.953978\pi\) | ||||
−0.989566 | + | 0.144079i | \(0.953978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.5826 | −1.66097 | −0.830486 | − | 0.557039i | \(-0.811937\pi\) | ||||
−0.830486 | + | 0.557039i | \(0.811937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0000 | 0.842152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.16515 | −0.595033 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.4174 | −1.60152 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.37386 | 0.112551 | 0.0562756 | − | 0.998415i | \(-0.482077\pi\) | ||||
0.0562756 | + | 0.998415i | \(0.482077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.16515 | 0.583092 | 0.291546 | − | 0.956557i | \(-0.405830\pi\) | ||||
0.291546 | + | 0.956557i | \(0.405830\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.1652 | −1.54941 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.5390 | −1.00072 | −0.500361 | − | 0.865817i | \(-0.666799\pi\) | ||||
−0.500361 | + | 0.865817i | \(0.666799\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2087 | 0.968214 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0435608 | 0.00343307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.16515 | −0.0912617 | −0.0456309 | − | 0.998958i | \(-0.514530\pi\) | ||||
−0.0456309 | + | 0.998958i | \(0.514530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.58258 | −0.434603 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.5390 | 1.20245 | 0.601223 | − | 0.799082i | \(-0.294681\pi\) | ||||
0.601223 | + | 0.799082i | \(0.294681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.79129 | 0.442871 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5826 | −1.18472 | −0.592361 | − | 0.805673i | \(-0.701804\pi\) | ||||
−0.592361 | + | 0.805673i | \(0.701804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.208712 | −0.0157772 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.5826 | −1.17126 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.16515 | 0.236575 | 0.118287 | − | 0.992979i | \(-0.462260\pi\) | ||||
0.118287 | + | 0.992979i | \(0.462260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3739 | 0.919742 | 0.459871 | − | 0.887986i | \(-0.347896\pi\) | ||||
0.459871 | + | 0.887986i | \(0.347896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.74773 | 0.498806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.04356 | 0.0759079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.04356 | −0.147867 | −0.0739334 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739334 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.37386 | 0.386819 | 0.193410 | − | 0.981118i | \(-0.438045\pi\) | ||||
0.193410 | + | 0.981118i | \(0.438045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.58258 | −0.399777 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.3739 | −1.73657 | −0.868283 | − | 0.496069i | \(-0.834776\pi\) | ||||
−0.868283 | + | 0.496069i | \(0.834776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.20871 | 0.0856833 | 0.0428417 | − | 0.999082i | \(-0.486359\pi\) | ||||
0.0428417 | + | 0.999082i | \(0.486359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.1652 | 2.19822 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.747727 | −0.0524802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.58258 | 0.250218 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.20871 | −0.0836084 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5826 | 0.935063 | 0.467532 | − | 0.883976i | \(-0.345143\pi\) | ||||
0.467532 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.3303 | −0.977319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.1216 | −2.03543 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.4174 | 1.23332 | 0.616661 | − | 0.787229i | \(-0.288485\pi\) | ||||
0.616661 | + | 0.787229i | \(0.288485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.79129 | −0.319419 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.62614 | −0.240675 | −0.120338 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120338 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.16515 | 0.605650 | 0.302825 | − | 0.953046i | \(-0.402070\pi\) | ||||
0.302825 | + | 0.953046i | \(0.402070\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.582576 | −0.0383307 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.74773 | 0.442058 | 0.221029 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221029 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.16515 | 0.467403 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35.5826 | 2.31134 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5390 | −0.746397 | −0.373198 | − | 0.927752i | \(-0.621739\pi\) | ||||
−0.373198 | + | 0.927752i | \(0.621739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7913 | −0.888375 | −0.444187 | − | 0.895934i | \(-0.646508\pi\) | ||||
−0.444187 | + | 0.895934i | \(0.646508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1652 | −1.03699 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9129 | −0.888861 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20871 | −0.0769085 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.74773 | 0.110758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7913 | −0.996737 | −0.498369 | − | 0.866965i | \(-0.666067\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.208712 | −0.0131216 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.3303 | −1.39838 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.79129 | −0.610764 | −0.305382 | − | 0.952230i | \(-0.598784\pi\) | ||||
−0.305382 | + | 0.952230i | \(0.598784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.834849 | 0.0518750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.1652 | −1.06250 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0000 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.74773 | 0.537369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.7477 | 1.63693 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.7042 | 1.44527 | 0.722634 | − | 0.691231i | \(-0.242931\pi\) | ||||
0.722634 | + | 0.691231i | \(0.242931\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.5390 | 1.67288 | 0.836438 | − | 0.548062i | \(-0.184634\pi\) | ||||
0.836438 | + | 0.548062i | \(0.184634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.582576 | −0.0352591 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000 | 1.20168 | 0.600842 | − | 0.799368i | \(-0.294832\pi\) | ||||
0.600842 | + | 0.799368i | \(0.294832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7042 | 1.59304 | 0.796519 | − | 0.604614i | \(-0.206673\pi\) | ||||
0.796519 | + | 0.604614i | \(0.206673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.4955 | 1.63444 | 0.817218 | − | 0.576329i | \(-0.195515\pi\) | ||||
0.817218 | + | 0.576329i | \(0.195515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.74773 | 0.399701 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.373864 | 0.0220685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.3303 | 3.06766 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1652 | 1.00280 | 0.501399 | − | 0.865216i | \(-0.332819\pi\) | ||||
0.501399 | + | 0.865216i | \(0.332819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1652 | −0.650060 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00000 | −0.290129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.208712 | −0.0120701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49545 | −0.0861965 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.4955 | −1.92426 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.83485 | 0.276843 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3303 | 1.04617 | 0.523083 | − | 0.852282i | \(-0.324782\pi\) | ||||
0.523083 | + | 0.852282i | \(0.324782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.582576 | −0.0331416 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5390 | 1.10796 | 0.553978 | − | 0.832531i | \(-0.313109\pi\) | ||||
0.553978 | + | 0.832531i | \(0.313109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.20871 | 0.124844 | 0.0624219 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624219 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.00000 | 0.449325 | 0.224662 | − | 0.974437i | \(-0.427872\pi\) | ||||
0.224662 | + | 0.974437i | \(0.427872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.58258 | 0.200586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.7477 | 1.49291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.83485 | −0.269018 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.37386 | −0.186575 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.747727 | 0.0412235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.1652 | 1.05024 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.3303 | 1.22003 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.3303 | −1.76114 | −0.880572 | − | 0.473913i | \(-0.842841\pi\) | ||||
−0.880572 | + | 0.473913i | \(0.842841\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −58.9564 | −3.20207 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.91288 | −0.157281 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16515 | 0.0627296 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.8348 | 0.796376 | 0.398188 | − | 0.917304i | \(-0.369639\pi\) | ||||
0.398188 | + | 0.917304i | \(0.369639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.1216 | 1.07708 | 0.538542 | − | 0.842599i | \(-0.318975\pi\) | ||||
0.538542 | + | 0.842599i | \(0.318975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.4174 | 0.554464 | 0.277232 | − | 0.960803i | \(-0.410583\pi\) | ||||
0.277232 | + | 0.960803i | \(0.410583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.33030 | −0.123333 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7042 | −1.35661 | −0.678307 | − | 0.734779i | \(-0.737286\pi\) | ||||
−0.678307 | + | 0.734779i | \(0.737286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5390 | −0.923106 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.79129 | 0.146505 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.5826 | −1.12968 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.04356 | 0.106673 | 0.0533365 | − | 0.998577i | \(-0.483014\pi\) | ||||
0.0533365 | + | 0.998577i | \(0.483014\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.58258 | 0.446791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.912878 | 0.0473943 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.58258 | 0.185499 | 0.0927494 | − | 0.995689i | \(-0.470434\pi\) | ||||
0.0927494 | + | 0.995689i | \(0.470434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.4955 | −1.72970 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.58258 | 0.184512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.74773 | −0.346607 | −0.173304 | − | 0.984868i | \(-0.555444\pi\) | ||||
−0.173304 | + | 0.984868i | \(0.555444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.0780 | 2.51434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.9129 | −1.52848 | −0.764238 | − | 0.644934i | \(-0.776885\pi\) | ||||
−0.764238 | + | 0.644934i | \(0.776885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.417424 | −0.0212739 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −34.3303 | −1.74511 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7042 | −1.35395 | −0.676977 | − | 0.736004i | \(-0.736711\pi\) | ||||
−0.676977 | + | 0.736004i | \(0.736711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.834849 | −0.0422201 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.7477 | −0.844811 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.4955 | 1.28282 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.1652 | 1.66451 | 0.832256 | − | 0.554392i | \(-0.187049\pi\) | ||||
0.832256 | + | 0.554392i | \(0.187049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.704166 | 0.0352524 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1652 | 0.757312 | 0.378656 | − | 0.925538i | \(-0.376386\pi\) | ||||
0.378656 | + | 0.925538i | \(0.376386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.834849 | −0.0414840 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8348 | 0.733536 | 0.366768 | − | 0.930312i | \(-0.380464\pi\) | ||||
0.366768 | + | 0.930312i | \(0.380464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −64.6606 | −3.18947 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.16515 | −0.0573334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.25227 | 0.0614717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −54.6606 | −2.67674 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.37386 | 0.360237 | 0.180118 | − | 0.983645i | \(-0.442352\pi\) | ||||
0.180118 | + | 0.983645i | \(0.442352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.1652 | 0.834598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.504546 | 0.0244167 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.79129 | 0.134765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6261 | −0.800853 | −0.400426 | − | 0.916329i | \(-0.631138\pi\) | ||||
−0.400426 | + | 0.916329i | \(0.631138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.6261 | −0.750944 | −0.375472 | − | 0.926834i | \(-0.622519\pi\) | ||||
−0.375472 | + | 0.926834i | \(0.622519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.0000 | −0.958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.252273 | 0.0120679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8348 | −0.708029 | −0.354014 | − | 0.935240i | \(-0.615184\pi\) | ||||
−0.354014 | + | 0.935240i | \(0.615184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.3303 | −1.58716 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.4519 | −1.73188 | −0.865941 | − | 0.500146i | \(-0.833280\pi\) | ||||
−0.865941 | + | 0.500146i | \(0.833280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.1652 | 0.908515 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.83485 | 0.181382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.16515 | −0.432530 | −0.216265 | − | 0.976335i | \(-0.569388\pi\) | ||||
−0.216265 | + | 0.976335i | \(0.569388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.79129 | −0.0843485 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.0000 | 0.939682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.417424 | −0.0195692 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.62614 | −0.356736 | −0.178368 | − | 0.983964i | \(-0.557082\pi\) | ||||
−0.178368 | + | 0.983964i | \(0.557082\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.0000 | −0.933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3739 | 0.576308 | 0.288154 | − | 0.957584i | \(-0.406958\pi\) | ||||
0.288154 | + | 0.957584i | \(0.406958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1652 | −1.82016 | −0.910079 | − | 0.414434i | \(-0.863980\pi\) | ||||
−0.910079 | + | 0.414434i | \(0.863980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.3303 | 1.03332 | 0.516662 | − | 0.856190i | \(-0.327175\pi\) | ||||
0.516662 | + | 0.856190i | \(0.327175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.33030 | 0.107603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.0000 | −1.61271 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.16515 | 0.329454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20871 | −0.0554595 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.9564 | 0.959529 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.1652 | −1.78950 | −0.894751 | − | 0.446566i | \(-0.852647\pi\) | ||||
−0.894751 | + | 0.446566i | \(0.852647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.121591 | 0.00553257 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.4955 | 1.70258 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5826 | 0.796743 | 0.398371 | − | 0.917224i | \(-0.369576\pi\) | ||||
0.398371 | + | 0.917224i | \(0.369576\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.25227 | −0.147073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.1652 | 0.955170 | 0.477585 | − | 0.878586i | \(-0.341512\pi\) | ||||
0.477585 | + | 0.878586i | \(0.341512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.3303 | 0.645404 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.58258 | −0.430705 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.3739 | 1.93780 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.4955 | 0.958435 | 0.479217 | − | 0.877696i | \(-0.340921\pi\) | ||||
0.479217 | + | 0.877696i | \(0.340921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.79129 | 0.123965 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.5826 | −0.867982 | −0.433991 | − | 0.900917i | \(-0.642895\pi\) | ||||
−0.433991 | + | 0.900917i | \(0.642895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.25227 | −0.0996347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.04356 | 0.266830 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.417424 | −0.0183939 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.58258 | −0.157561 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.4955 | −1.90924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.62614 | 0.115053 | 0.0575266 | − | 0.998344i | \(-0.481679\pi\) | ||||
0.0575266 | + | 0.998344i | \(0.481679\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.1652 | 1.10040 | 0.550198 | − | 0.835034i | \(-0.314552\pi\) | ||||
0.550198 | + | 0.835034i | \(0.314552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.582576 | −0.0254257 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9564 | −0.998106 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.7477 | −1.16075 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.79129 | −0.0775893 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.1652 | 0.828582 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.83485 | 0.381252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.95644 | 0.299635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.53901 | −0.367121 | −0.183560 | − | 0.983008i | \(-0.558762\pi\) | ||||
−0.183560 | + | 0.983008i | \(0.558762\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.5390 | 1.48221 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.41742 | −0.103551 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5826 | 0.494332 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.33030 | −0.184477 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.66061 | 0.113140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.3303 | 0.947869 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.8693 | 1.64695 | 0.823473 | − | 0.567356i | \(-0.192033\pi\) | ||||
0.823473 | + | 0.567356i | \(0.192033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.16515 | 0.303054 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.1652 | 0.471393 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5826 | −0.825307 | −0.412654 | − | 0.910888i | \(-0.635398\pi\) | ||||
−0.412654 | + | 0.910888i | \(0.635398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.2432 | −1.77718 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0871215 | −0.00365876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.7477 | 0.617173 | 0.308587 | − | 0.951196i | \(-0.400144\pi\) | ||||
0.308587 | + | 0.951196i | \(0.400144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.70417 | −0.238295 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.208712 | −0.00870390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5826 | −0.898494 | −0.449247 | − | 0.893408i | \(-0.648308\pi\) | ||||
−0.449247 | + | 0.893408i | \(0.648308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.0000 | 0.623379 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.130682 | 0.00542161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.37386 | −0.181147 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.58258 | −0.396191 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.4174 | −1.17291 | −0.586456 | − | 0.809981i | \(-0.699477\pi\) | ||||
−0.586456 | + | 0.809981i | \(0.699477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −68.0345 | −2.79856 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.3739 | 1.20624 | 0.603120 | − | 0.797650i | \(-0.293924\pi\) | ||||
0.603120 | + | 0.797650i | \(0.293924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.66970 | −0.0684509 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.37386 | 0.138083 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.79129 | 0.277484 | 0.138742 | − | 0.990329i | \(-0.455694\pi\) | ||||
0.138742 | + | 0.990329i | \(0.455694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.4174 | −0.832844 | −0.416422 | − | 0.909171i | \(-0.636716\pi\) | ||||
−0.416422 | + | 0.909171i | \(0.636716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 53.4955 | 2.17850 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.25227 | −0.213183 | −0.106592 | − | 0.994303i | \(-0.533994\pi\) | ||||
−0.106592 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.08712 | −0.0845744 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.58258 | −0.144935 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.12159 | −0.368418 | −0.184209 | − | 0.982887i | \(-0.558972\pi\) | ||||
−0.184209 | + | 0.982887i | \(0.558972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0000 | 0.403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7477 | −0.915789 | −0.457895 | − | 0.889007i | \(-0.651396\pi\) | ||||
−0.457895 | + | 0.889007i | \(0.651396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.834849 | −0.0335554 | −0.0167777 | − | 0.999859i | \(-0.505341\pi\) | ||||
−0.0167777 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.04356 | 0.0418767 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.37386 | −0.134739 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0000 | 0.477712 | 0.238856 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238856 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.9129 | 1.50690 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.1652 | 1.39549 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.95644 | 0.275624 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9564 | 0.511749 | 0.255874 | − | 0.966710i | \(-0.417637\pi\) | ||||
0.255874 | + | 0.966710i | \(0.417637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.91288 | −0.233181 | −0.116591 | − | 0.993180i | \(-0.537197\pi\) | ||||
−0.116591 | + | 0.993180i | \(0.537197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.0000 | −1.57500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.0436 | 0.552109 | 0.276055 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276055 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.58258 | 0.219135 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.0000 | 1.48705 | 0.743527 | − | 0.668705i | \(-0.233151\pi\) | ||||
0.743527 | + | 0.668705i | \(0.233151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −51.7042 | −2.01717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.4955 | −0.915253 | −0.457626 | − | 0.889145i | \(-0.651300\pi\) | ||||
−0.457626 | + | 0.889145i | \(0.651300\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0871215 | −0.00338863 | −0.00169432 | − | 0.999999i | \(-0.500539\pi\) | ||||
−0.00169432 | + | 0.999999i | \(0.500539\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.1652 | 0.433619 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.504546 | 0.0195654 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.747727 | −0.0289521 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51.4083 | 1.98756 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.41742 | −0.0933236 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.4955 | 1.44534 | 0.722672 | − | 0.691191i | \(-0.242914\pi\) | ||||
0.722672 | + | 0.691191i | \(0.242914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.33030 | −0.243293 | −0.121647 | − | 0.992573i | \(-0.538817\pi\) | ||||
−0.121647 | + | 0.992573i | \(0.538817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.91288 | 0.150162 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1216 | −0.387860 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.0000 | 1.45403 | 0.727015 | − | 0.686622i | \(-0.240907\pi\) | ||||
0.727015 | + | 0.686622i | \(0.240907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.3303 | −1.77019 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.5826 | 0.976036 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.37386 | −0.166631 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.9129 | −0.529271 | −0.264635 | − | 0.964349i | \(-0.585252\pi\) | ||||
−0.264635 | + | 0.964349i | \(0.585252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.1652 | −1.48562 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.16515 | −0.271399 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.8348 | 0.712399 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9129 | −1.12979 | −0.564897 | − | 0.825161i | \(-0.691084\pi\) | ||||
−0.564897 | + | 0.825161i | \(0.691084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.83485 | 0.182350 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.0000 | 0.753244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.50455 | −0.0941931 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0000 | −1.20179 | −0.600893 | − | 0.799330i | \(-0.705188\pi\) | ||||
−0.600893 | + | 0.799330i | \(0.705188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 61.0780 | 2.29061 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.2087 | −1.20286 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0435608 | −0.00162229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.4955 | −1.43166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58258 | 0.133054 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1216 | 1.41385 | 0.706926 | − | 0.707288i | \(-0.250081\pi\) | ||||
0.706926 | + | 0.707288i | \(0.250081\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.6606 | 1.06005 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0436 | −0.555647 | −0.277823 | − | 0.960632i | \(-0.589613\pi\) | ||||
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38.8348 | −1.43244 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.1652 | −0.411274 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.9564 | 1.28589 | 0.642947 | − | 0.765911i | \(-0.277712\pi\) | ||||
0.642947 | + | 0.765911i | \(0.277712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.37386 | −0.123942 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1652 | −0.556355 | −0.278178 | − | 0.960530i | \(-0.589730\pi\) | ||||
−0.278178 | + | 0.960530i | \(0.589730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.74773 | 0.100669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.00000 | 0.109764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.8693 | −1.52783 | −0.763917 | − | 0.645315i | \(-0.776726\pi\) | ||||
−0.763917 | + | 0.645315i | \(0.776726\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.0780 | −1.60629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3303 | 0.521533 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.956439 | −0.0347624 | −0.0173812 | − | 0.999849i | \(-0.505533\pi\) | ||||
−0.0173812 | + | 0.999849i | \(0.505533\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.582576 | −0.0211462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.37386 | 0.0498025 | 0.0249013 | − | 0.999690i | \(-0.492073\pi\) | ||||
0.0249013 | + | 0.999690i | \(0.492073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.252273 | −0.00913289 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.3303 | −1.38584 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.58258 | 0.201575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.4519 | −1.67510 | −0.837549 | − | 0.546362i | \(-0.816012\pi\) | ||||
−0.837549 | + | 0.546362i | \(0.816012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.3303 | −0.984277 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.49545 | −0.341528 | −0.170764 | − | 0.985312i | \(-0.554624\pi\) | ||||
−0.170764 | + | 0.985312i | \(0.554624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.33030 | 0.0835991 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.16515 | 0.0775746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.9129 | −0.640154 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.0780 | −0.895073 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7042 | −0.631085 | −0.315543 | − | 0.948911i | \(-0.602187\pi\) | ||||
−0.315543 | + | 0.948911i | \(0.602187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.2432 | 1.78870 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.40833 | −0.156742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.41742 | −0.0858453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.4174 | 0.865997 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1652 | −0.466334 | −0.233167 | − | 0.972437i | \(-0.574909\pi\) | ||||
−0.233167 | + | 0.972437i | \(0.574909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.3303 | −0.506970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.9129 | 1.62225 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7913 | 0.380816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0871215 | 0.00307063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 66.1652 | 2.32912 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.0000 | 1.26569 | 0.632846 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632846 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.95644 | 0.244274 | 0.122137 | − | 0.992513i | \(-0.461025\pi\) | ||||
0.122137 | + | 0.992513i | \(0.461025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 76.8693 | 2.69592 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.33030 | −0.0816269 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66061 | −0.302996 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.4955 | −1.79720 | −0.898602 | − | 0.438765i | \(-0.855416\pi\) | ||||
−0.898602 | + | 0.438765i | \(0.855416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.87841 | 0.204908 | 0.102454 | − | 0.994738i | \(-0.467330\pi\) | ||||
0.102454 | + | 0.994738i | \(0.467330\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.79129 | 0.0971802 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2867 | 0.427252 | 0.213626 | − | 0.976916i | \(-0.431473\pi\) | ||||
0.213626 | + | 0.976916i | \(0.431473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1216 | 0.421000 | 0.210500 | − | 0.977594i | \(-0.432491\pi\) | ||||
0.210500 | + | 0.977594i | \(0.432491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.8258 | 1.93657 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.8258 | 0.964105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.0780 | 1.07550 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.16515 | −0.0402255 | −0.0201127 | − | 0.999798i | \(-0.506403\pi\) | ||||
−0.0201127 | + | 0.999798i | \(0.506403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1652 | −0.557419 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 74.5390 | 2.56726 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.00000 | 0.0688021 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.208712 | 0.00717143 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 76.7477 | 2.63398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.834849 | 0.0286182 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.1216 | −1.13406 | −0.567031 | − | 0.823697i | \(-0.691908\pi\) | ||||
−0.567031 | + | 0.823697i | \(0.691908\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.5826 | 0.396116 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4955 | 0.870908 | 0.435454 | − | 0.900211i | \(-0.356588\pi\) | ||||
0.435454 | + | 0.900211i | \(0.356588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.6261 | 0.669635 | 0.334818 | − | 0.942283i | \(-0.391325\pi\) | ||||
0.334818 | + | 0.942283i | \(0.391325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.04356 | 0.0355645 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.6606 | −1.04370 | −0.521850 | − | 0.853038i | \(-0.674758\pi\) | ||||
−0.521850 | + | 0.853038i | \(0.674758\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.1652 | −1.05965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.79129 | −0.0947971 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.7477 | −0.432437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.1652 | −0.378317 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 89.8258 | 3.04014 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50455 | −0.0846691 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.9564 | 1.41677 | 0.708384 | − | 0.705827i | \(-0.249424\pi\) | ||||
0.708384 | + | 0.705827i | \(0.249424\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.9129 | 1.61606 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0436 | 0.473140 | 0.236570 | − | 0.971614i | \(-0.423977\pi\) | ||||
0.236570 | + | 0.971614i | \(0.423977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.2867 | 1.49037 | 0.745184 | − | 0.666859i | \(-0.232362\pi\) | ||||
0.745184 | + | 0.666859i | \(0.232362\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.1652 | −1.04761 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.0780 | −1.17780 | −0.588902 | − | 0.808204i | \(-0.700440\pi\) | ||||
−0.588902 | + | 0.808204i | \(0.700440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.66970 | 0.123078 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.417424 | 0.0139842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.33030 | 0.144908 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.33030 | 0.211599 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.582576 | −0.0194516 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.4955 | −0.582858 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.17424 | −0.138910 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.7477 | 0.822642 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8693 | 0.427319 | 0.213659 | − | 0.976908i | \(-0.431462\pi\) | ||||
0.213659 | + | 0.976908i | \(0.431462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −57.4955 | −1.90700 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6261 | −1.08095 | −0.540476 | − | 0.841359i | \(-0.681756\pi\) | ||||
−0.540476 | + | 0.841359i | \(0.681756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.626136 | −0.0207221 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.4955 | 0.446146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.25227 | −0.0413537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.4955 | −1.17089 | −0.585443 | − | 0.810713i | \(-0.699080\pi\) | ||||
−0.585443 | + | 0.810713i | \(0.699080\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.1652 | 1.68595 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.49545 | 0.311536 | 0.155768 | − | 0.987794i | \(-0.450215\pi\) | ||||
0.155768 | + | 0.987794i | \(0.450215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.40833 | −0.275572 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.5390 | 1.78553 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.8258 | 1.88909 | 0.944543 | − | 0.328389i | \(-0.106506\pi\) | ||||
0.944543 | + | 0.328389i | \(0.106506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.16515 | 0.201192 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.9564 | −1.10695 | −0.553474 | − | 0.832866i | \(-0.686698\pi\) | ||||
−0.553474 | + | 0.832866i | \(0.686698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.373864 | 0.0121747 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.08712 | 0.0678941 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0780 | 0.554961 | 0.277481 | − | 0.960731i | \(-0.410501\pi\) | ||||
0.277481 | + | 0.960731i | \(0.410501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.7913 | 0.350300 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.3303 | 0.724110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0780 | −0.747571 | −0.373785 | − | 0.927515i | \(-0.621940\pi\) | ||||
−0.373785 | + | 0.927515i | \(0.621940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.08712 | −0.132256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.0000 | 0.323254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.83485 | −0.156125 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.9129 | 1.47952 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.7477 | 0.345982 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.79129 | −0.0897618 | −0.0448809 | − | 0.998992i | \(-0.514291\pi\) | ||||
−0.0448809 | + | 0.998992i | \(0.514291\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.4955 | −0.433536 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.4519 | −1.13771 | −0.568853 | − | 0.822439i | \(-0.692613\pi\) | ||||
−0.568853 | + | 0.822439i | \(0.692613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.08712 | −0.131027 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.79129 | 0.0893928 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.66970 | 0.181390 | 0.0906948 | − | 0.995879i | \(-0.471091\pi\) | ||||
0.0906948 | + | 0.995879i | \(0.471091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.58258 | −0.306260 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.79129 | −0.184902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.16515 | −0.228533 | −0.114266 | − | 0.993450i | \(-0.536452\pi\) | ||||
−0.114266 | + | 0.993450i | \(0.536452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.7477 | −1.55323 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.08712 | 0.0664338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.49545 | −0.0475527 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.3739 | −1.15545 | −0.577727 | − | 0.816230i | \(-0.696060\pi\) | ||||
−0.577727 | + | 0.816230i | \(0.696060\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 78.1561 | 2.48021 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.41742 | 0.0766375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5826 | −0.430164 | −0.215082 | − | 0.976596i | \(-0.569002\pi\) | ||||
−0.215082 | + | 0.976596i | \(0.569002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.0000 | 0.632772 |
(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 | 572.2.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 5148.2.a.g.1.1 | 2 | |||
4.3 | odd | 2 | 2288.2.a.n.1.1 | 2 | |||
8.3 | odd | 2 | 9152.2.a.bn.1.2 | 2 | |||
8.5 | even | 2 | 9152.2.a.bl.1.1 | 2 | |||
11.10 | odd | 2 | 6292.2.a.o.1.2 | 2 | |||
13.12 | even | 2 | 7436.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2288.2.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
5148.2.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
6292.2.a.o.1.2 | 2 | 11.10 | odd | 2 | |||
7436.2.a.h.1.2 | 2 | 13.12 | even | 2 | |||
9152.2.a.bl.1.1 | 2 | 8.5 | even | 2 | |||
9152.2.a.bn.1.2 | 2 | 8.3 | odd | 2 |