Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 14x^{5} + 29x^{4} + 48x^{3} - 14x^{2} - 35x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.05485\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.05485 | −1.36617 | −0.683086 | − | 0.730338i | \(-0.739363\pi\) | ||||
−0.683086 | + | 0.730338i | \(0.739363\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.36098 | −0.892368 | −0.446184 | − | 0.894941i | \(-0.647217\pi\) | ||||
−0.446184 | + | 0.894941i | \(0.647217\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.05485 | 0.966030 | ||||||||
\(11\) | 2.94877 | 0.889086 | 0.444543 | − | 0.895757i | \(-0.353366\pi\) | ||||
0.444543 | + | 0.895757i | \(0.353366\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.467072 | 0.129543 | 0.0647713 | − | 0.997900i | \(-0.479368\pi\) | ||||
0.0647713 | + | 0.997900i | \(0.479368\pi\) | |||||||
\(14\) | 2.36098 | 0.630999 | ||||||||
\(15\) | −3.05485 | −0.788760 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.03227 | −0.250362 | −0.125181 | − | 0.992134i | \(-0.539951\pi\) | ||||
−0.125181 | + | 0.992134i | \(0.539951\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −3.05485 | −0.683086 | ||||||||
\(21\) | −2.36098 | −0.515209 | ||||||||
\(22\) | −2.94877 | −0.628679 | ||||||||
\(23\) | 5.42335 | 1.13085 | 0.565424 | − | 0.824801i | \(-0.308713\pi\) | ||||
0.565424 | + | 0.824801i | \(0.308713\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.33214 | 0.866428 | ||||||||
\(26\) | −0.467072 | −0.0916004 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.36098 | −0.446184 | ||||||||
\(29\) | −3.45694 | −0.641938 | −0.320969 | − | 0.947090i | \(-0.604008\pi\) | ||||
−0.320969 | + | 0.947090i | \(0.604008\pi\) | |||||||
\(30\) | 3.05485 | 0.557738 | ||||||||
\(31\) | −3.18333 | −0.571744 | −0.285872 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285872 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.94877 | 0.513314 | ||||||||
\(34\) | 1.03227 | 0.177033 | ||||||||
\(35\) | 7.21246 | 1.21913 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.86635 | 0.800023 | 0.400012 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400012 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0.467072 | 0.0747914 | ||||||||
\(40\) | 3.05485 | 0.483015 | ||||||||
\(41\) | −6.40596 | −1.00044 | −0.500221 | − | 0.865898i | \(-0.666748\pi\) | ||||
−0.500221 | + | 0.865898i | \(0.666748\pi\) | |||||||
\(42\) | 2.36098 | 0.364308 | ||||||||
\(43\) | −9.23651 | −1.40855 | −0.704277 | − | 0.709925i | \(-0.748729\pi\) | ||||
−0.704277 | + | 0.709925i | \(0.748729\pi\) | |||||||
\(44\) | 2.94877 | 0.444543 | ||||||||
\(45\) | −3.05485 | −0.455391 | ||||||||
\(46\) | −5.42335 | −0.799630 | ||||||||
\(47\) | 9.30607 | 1.35743 | 0.678715 | − | 0.734402i | \(-0.262537\pi\) | ||||
0.678715 | + | 0.734402i | \(0.262537\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.42576 | −0.203680 | ||||||||
\(50\) | −4.33214 | −0.612657 | ||||||||
\(51\) | −1.03227 | −0.144546 | ||||||||
\(52\) | 0.467072 | 0.0647713 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −9.00805 | −1.21465 | ||||||||
\(56\) | 2.36098 | 0.315500 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 3.45694 | 0.453918 | ||||||||
\(59\) | 9.29102 | 1.20959 | 0.604794 | − | 0.796382i | \(-0.293255\pi\) | ||||
0.604794 | + | 0.796382i | \(0.293255\pi\) | |||||||
\(60\) | −3.05485 | −0.394380 | ||||||||
\(61\) | 11.0740 | 1.41788 | 0.708941 | − | 0.705268i | \(-0.249173\pi\) | ||||
0.708941 | + | 0.705268i | \(0.249173\pi\) | |||||||
\(62\) | 3.18333 | 0.404284 | ||||||||
\(63\) | −2.36098 | −0.297456 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.42684 | −0.176977 | ||||||||
\(66\) | −2.94877 | −0.362968 | ||||||||
\(67\) | 10.9860 | 1.34215 | 0.671075 | − | 0.741390i | \(-0.265833\pi\) | ||||
0.671075 | + | 0.741390i | \(0.265833\pi\) | |||||||
\(68\) | −1.03227 | −0.125181 | ||||||||
\(69\) | 5.42335 | 0.652895 | ||||||||
\(70\) | −7.21246 | −0.862054 | ||||||||
\(71\) | −2.33797 | −0.277466 | −0.138733 | − | 0.990330i | \(-0.544303\pi\) | ||||
−0.138733 | + | 0.990330i | \(0.544303\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.6910 | −1.36833 | −0.684166 | − | 0.729326i | \(-0.739834\pi\) | ||||
−0.684166 | + | 0.729326i | \(0.739834\pi\) | |||||||
\(74\) | −4.86635 | −0.565702 | ||||||||
\(75\) | 4.33214 | 0.500232 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −6.96198 | −0.793392 | ||||||||
\(78\) | −0.467072 | −0.0528855 | ||||||||
\(79\) | −14.0517 | −1.58094 | −0.790470 | − | 0.612500i | \(-0.790164\pi\) | ||||
−0.790470 | + | 0.612500i | \(0.790164\pi\) | |||||||
\(80\) | −3.05485 | −0.341543 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.40596 | 0.707420 | ||||||||
\(83\) | 4.08187 | 0.448044 | 0.224022 | − | 0.974584i | \(-0.428081\pi\) | ||||
0.224022 | + | 0.974584i | \(0.428081\pi\) | |||||||
\(84\) | −2.36098 | −0.257604 | ||||||||
\(85\) | 3.15343 | 0.342037 | ||||||||
\(86\) | 9.23651 | 0.995998 | ||||||||
\(87\) | −3.45694 | −0.370623 | ||||||||
\(88\) | −2.94877 | −0.314339 | ||||||||
\(89\) | −0.763691 | −0.0809511 | −0.0404755 | − | 0.999181i | \(-0.512887\pi\) | ||||
−0.0404755 | + | 0.999181i | \(0.512887\pi\) | |||||||
\(90\) | 3.05485 | 0.322010 | ||||||||
\(91\) | −1.10275 | −0.115600 | ||||||||
\(92\) | 5.42335 | 0.565424 | ||||||||
\(93\) | −3.18333 | −0.330096 | ||||||||
\(94\) | −9.30607 | −0.959847 | ||||||||
\(95\) | 3.05485 | 0.313421 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.6888 | −1.28835 | −0.644176 | − | 0.764878i | \(-0.722799\pi\) | ||||
−0.644176 | + | 0.764878i | \(0.722799\pi\) | |||||||
\(98\) | 1.42576 | 0.144024 | ||||||||
\(99\) | 2.94877 | 0.296362 | ||||||||
\(100\) | 4.33214 | 0.433214 | ||||||||
\(101\) | 1.34084 | 0.133419 | 0.0667094 | − | 0.997772i | \(-0.478750\pi\) | ||||
0.0667094 | + | 0.997772i | \(0.478750\pi\) | |||||||
\(102\) | 1.03227 | 0.102210 | ||||||||
\(103\) | 15.2194 | 1.49961 | 0.749806 | − | 0.661658i | \(-0.230147\pi\) | ||||
0.749806 | + | 0.661658i | \(0.230147\pi\) | |||||||
\(104\) | −0.467072 | −0.0458002 | ||||||||
\(105\) | 7.21246 | 0.703864 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 9.49726 | 0.918135 | 0.459067 | − | 0.888402i | \(-0.348184\pi\) | ||||
0.459067 | + | 0.888402i | \(0.348184\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 6.91309 | 0.662154 | 0.331077 | − | 0.943604i | \(-0.392588\pi\) | ||||
0.331077 | + | 0.943604i | \(0.392588\pi\) | |||||||
\(110\) | 9.00805 | 0.858884 | ||||||||
\(111\) | 4.86635 | 0.461894 | ||||||||
\(112\) | −2.36098 | −0.223092 | ||||||||
\(113\) | −2.88232 | −0.271145 | −0.135573 | − | 0.990767i | \(-0.543287\pi\) | ||||
−0.135573 | + | 0.990767i | \(0.543287\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −16.5676 | −1.54493 | ||||||||
\(116\) | −3.45694 | −0.320969 | ||||||||
\(117\) | 0.467072 | 0.0431808 | ||||||||
\(118\) | −9.29102 | −0.855308 | ||||||||
\(119\) | 2.43717 | 0.223415 | ||||||||
\(120\) | 3.05485 | 0.278869 | ||||||||
\(121\) | −2.30478 | −0.209526 | ||||||||
\(122\) | −11.0740 | −1.00259 | ||||||||
\(123\) | −6.40596 | −0.577606 | ||||||||
\(124\) | −3.18333 | −0.285872 | ||||||||
\(125\) | 2.04022 | 0.182483 | ||||||||
\(126\) | 2.36098 | 0.210333 | ||||||||
\(127\) | 2.53418 | 0.224873 | 0.112436 | − | 0.993659i | \(-0.464135\pi\) | ||||
0.112436 | + | 0.993659i | \(0.464135\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.23651 | −0.813229 | ||||||||
\(130\) | 1.42684 | 0.125142 | ||||||||
\(131\) | −10.4202 | −0.910413 | −0.455207 | − | 0.890386i | \(-0.650435\pi\) | ||||
−0.455207 | + | 0.890386i | \(0.650435\pi\) | |||||||
\(132\) | 2.94877 | 0.256657 | ||||||||
\(133\) | 2.36098 | 0.204723 | ||||||||
\(134\) | −10.9860 | −0.949043 | ||||||||
\(135\) | −3.05485 | −0.262920 | ||||||||
\(136\) | 1.03227 | 0.0885163 | ||||||||
\(137\) | 10.7967 | 0.922427 | 0.461213 | − | 0.887289i | \(-0.347414\pi\) | ||||
0.461213 | + | 0.887289i | \(0.347414\pi\) | |||||||
\(138\) | −5.42335 | −0.461666 | ||||||||
\(139\) | −12.9504 | −1.09844 | −0.549220 | − | 0.835678i | \(-0.685075\pi\) | ||||
−0.549220 | + | 0.835678i | \(0.685075\pi\) | |||||||
\(140\) | 7.21246 | 0.609564 | ||||||||
\(141\) | 9.30607 | 0.783712 | ||||||||
\(142\) | 2.33797 | 0.196198 | ||||||||
\(143\) | 1.37729 | 0.115174 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.5604 | 0.876998 | ||||||||
\(146\) | 11.6910 | 0.967557 | ||||||||
\(147\) | −1.42576 | −0.117595 | ||||||||
\(148\) | 4.86635 | 0.400012 | ||||||||
\(149\) | 18.5105 | 1.51644 | 0.758219 | − | 0.652000i | \(-0.226070\pi\) | ||||
0.758219 | + | 0.652000i | \(0.226070\pi\) | |||||||
\(150\) | −4.33214 | −0.353718 | ||||||||
\(151\) | 1.03687 | 0.0843789 | 0.0421894 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421894 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −1.03227 | −0.0834539 | ||||||||
\(154\) | 6.96198 | 0.561013 | ||||||||
\(155\) | 9.72462 | 0.781101 | ||||||||
\(156\) | 0.467072 | 0.0373957 | ||||||||
\(157\) | −7.59160 | −0.605876 | −0.302938 | − | 0.953010i | \(-0.597967\pi\) | ||||
−0.302938 | + | 0.953010i | \(0.597967\pi\) | |||||||
\(158\) | 14.0517 | 1.11789 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 3.05485 | 0.241507 | ||||||||
\(161\) | −12.8044 | −1.00913 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −9.85353 | −0.771788 | −0.385894 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385894 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(164\) | −6.40596 | −0.500221 | ||||||||
\(165\) | −9.00805 | −0.701276 | ||||||||
\(166\) | −4.08187 | −0.316815 | ||||||||
\(167\) | −13.7419 | −1.06338 | −0.531689 | − | 0.846940i | \(-0.678442\pi\) | ||||
−0.531689 | + | 0.846940i | \(0.678442\pi\) | |||||||
\(168\) | 2.36098 | 0.182154 | ||||||||
\(169\) | −12.7818 | −0.983219 | ||||||||
\(170\) | −3.15343 | −0.241857 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −9.23651 | −0.704277 | ||||||||
\(173\) | −11.6103 | −0.882718 | −0.441359 | − | 0.897331i | \(-0.645503\pi\) | ||||
−0.441359 | + | 0.897331i | \(0.645503\pi\) | |||||||
\(174\) | 3.45694 | 0.262070 | ||||||||
\(175\) | −10.2281 | −0.773172 | ||||||||
\(176\) | 2.94877 | 0.222272 | ||||||||
\(177\) | 9.29102 | 0.698356 | ||||||||
\(178\) | 0.763691 | 0.0572410 | ||||||||
\(179\) | 12.6980 | 0.949090 | 0.474545 | − | 0.880231i | \(-0.342613\pi\) | ||||
0.474545 | + | 0.880231i | \(0.342613\pi\) | |||||||
\(180\) | −3.05485 | −0.227695 | ||||||||
\(181\) | 4.92417 | 0.366010 | 0.183005 | − | 0.983112i | \(-0.441417\pi\) | ||||
0.183005 | + | 0.983112i | \(0.441417\pi\) | |||||||
\(182\) | 1.10275 | 0.0817412 | ||||||||
\(183\) | 11.0740 | 0.818615 | ||||||||
\(184\) | −5.42335 | −0.399815 | ||||||||
\(185\) | −14.8660 | −1.09297 | ||||||||
\(186\) | 3.18333 | 0.233413 | ||||||||
\(187\) | −3.04392 | −0.222593 | ||||||||
\(188\) | 9.30607 | 0.678715 | ||||||||
\(189\) | −2.36098 | −0.171736 | ||||||||
\(190\) | −3.05485 | −0.221622 | ||||||||
\(191\) | −4.57585 | −0.331097 | −0.165548 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165548 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −18.2444 | −1.31326 | −0.656632 | − | 0.754211i | \(-0.728019\pi\) | ||||
−0.656632 | + | 0.754211i | \(0.728019\pi\) | |||||||
\(194\) | 12.6888 | 0.911002 | ||||||||
\(195\) | −1.42684 | −0.102178 | ||||||||
\(196\) | −1.42576 | −0.101840 | ||||||||
\(197\) | −23.0005 | −1.63872 | −0.819360 | − | 0.573279i | \(-0.805671\pi\) | ||||
−0.819360 | + | 0.573279i | \(0.805671\pi\) | |||||||
\(198\) | −2.94877 | −0.209560 | ||||||||
\(199\) | −22.1077 | −1.56717 | −0.783585 | − | 0.621285i | \(-0.786611\pi\) | ||||
−0.783585 | + | 0.621285i | \(0.786611\pi\) | |||||||
\(200\) | −4.33214 | −0.306328 | ||||||||
\(201\) | 10.9860 | 0.774890 | ||||||||
\(202\) | −1.34084 | −0.0943414 | ||||||||
\(203\) | 8.16177 | 0.572844 | ||||||||
\(204\) | −1.03227 | −0.0722732 | ||||||||
\(205\) | 19.5693 | 1.36678 | ||||||||
\(206\) | −15.2194 | −1.06039 | ||||||||
\(207\) | 5.42335 | 0.376949 | ||||||||
\(208\) | 0.467072 | 0.0323856 | ||||||||
\(209\) | −2.94877 | −0.203970 | ||||||||
\(210\) | −7.21246 | −0.497707 | ||||||||
\(211\) | 7.45899 | 0.513498 | 0.256749 | − | 0.966478i | \(-0.417349\pi\) | ||||
0.256749 | + | 0.966478i | \(0.417349\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −2.33797 | −0.160195 | ||||||||
\(214\) | −9.49726 | −0.649219 | ||||||||
\(215\) | 28.2162 | 1.92433 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 7.51580 | 0.510206 | ||||||||
\(218\) | −6.91309 | −0.468214 | ||||||||
\(219\) | −11.6910 | −0.790007 | ||||||||
\(220\) | −9.00805 | −0.607323 | ||||||||
\(221\) | −0.482144 | −0.0324325 | ||||||||
\(222\) | −4.86635 | −0.326608 | ||||||||
\(223\) | −2.93783 | −0.196732 | −0.0983658 | − | 0.995150i | \(-0.531362\pi\) | ||||
−0.0983658 | + | 0.995150i | \(0.531362\pi\) | |||||||
\(224\) | 2.36098 | 0.157750 | ||||||||
\(225\) | 4.33214 | 0.288809 | ||||||||
\(226\) | 2.88232 | 0.191729 | ||||||||
\(227\) | −0.660602 | −0.0438457 | −0.0219228 | − | 0.999760i | \(-0.506979\pi\) | ||||
−0.0219228 | + | 0.999760i | \(0.506979\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | 0.217202 | 0.0143531 | 0.00717654 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717654 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(230\) | 16.5676 | 1.09243 | ||||||||
\(231\) | −6.96198 | −0.458065 | ||||||||
\(232\) | 3.45694 | 0.226959 | ||||||||
\(233\) | −5.80594 | −0.380360 | −0.190180 | − | 0.981749i | \(-0.560907\pi\) | ||||
−0.190180 | + | 0.981749i | \(0.560907\pi\) | |||||||
\(234\) | −0.467072 | −0.0305335 | ||||||||
\(235\) | −28.4287 | −1.85448 | ||||||||
\(236\) | 9.29102 | 0.604794 | ||||||||
\(237\) | −14.0517 | −0.912756 | ||||||||
\(238\) | −2.43717 | −0.157978 | ||||||||
\(239\) | −2.07250 | −0.134059 | −0.0670295 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670295 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(240\) | −3.05485 | −0.197190 | ||||||||
\(241\) | −15.0145 | −0.967167 | −0.483584 | − | 0.875298i | \(-0.660665\pi\) | ||||
−0.483584 | + | 0.875298i | \(0.660665\pi\) | |||||||
\(242\) | 2.30478 | 0.148157 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.0740 | 0.708941 | ||||||||
\(245\) | 4.35549 | 0.278262 | ||||||||
\(246\) | 6.40596 | 0.408429 | ||||||||
\(247\) | −0.467072 | −0.0297191 | ||||||||
\(248\) | 3.18333 | 0.202142 | ||||||||
\(249\) | 4.08187 | 0.258678 | ||||||||
\(250\) | −2.04022 | −0.129035 | ||||||||
\(251\) | −18.3751 | −1.15983 | −0.579913 | − | 0.814678i | \(-0.696914\pi\) | ||||
−0.579913 | + | 0.814678i | \(0.696914\pi\) | |||||||
\(252\) | −2.36098 | −0.148728 | ||||||||
\(253\) | 15.9922 | 1.00542 | ||||||||
\(254\) | −2.53418 | −0.159009 | ||||||||
\(255\) | 3.15343 | 0.197475 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.0606 | −1.00183 | −0.500917 | − | 0.865495i | \(-0.667004\pi\) | ||||
−0.500917 | + | 0.865495i | \(0.667004\pi\) | |||||||
\(258\) | 9.23651 | 0.575040 | ||||||||
\(259\) | −11.4894 | −0.713915 | ||||||||
\(260\) | −1.42684 | −0.0884887 | ||||||||
\(261\) | −3.45694 | −0.213979 | ||||||||
\(262\) | 10.4202 | 0.643759 | ||||||||
\(263\) | −13.3943 | −0.825925 | −0.412962 | − | 0.910748i | \(-0.635506\pi\) | ||||
−0.412962 | + | 0.910748i | \(0.635506\pi\) | |||||||
\(264\) | −2.94877 | −0.181484 | ||||||||
\(265\) | −3.05485 | −0.187658 | ||||||||
\(266\) | −2.36098 | −0.144761 | ||||||||
\(267\) | −0.763691 | −0.0467371 | ||||||||
\(268\) | 10.9860 | 0.671075 | ||||||||
\(269\) | −20.7591 | −1.26571 | −0.632854 | − | 0.774271i | \(-0.718117\pi\) | ||||
−0.632854 | + | 0.774271i | \(0.718117\pi\) | |||||||
\(270\) | 3.05485 | 0.185913 | ||||||||
\(271\) | −25.0383 | −1.52097 | −0.760484 | − | 0.649357i | \(-0.775038\pi\) | ||||
−0.760484 | + | 0.649357i | \(0.775038\pi\) | |||||||
\(272\) | −1.03227 | −0.0625905 | ||||||||
\(273\) | −1.10275 | −0.0667414 | ||||||||
\(274\) | −10.7967 | −0.652254 | ||||||||
\(275\) | 12.7745 | 0.770329 | ||||||||
\(276\) | 5.42335 | 0.326447 | ||||||||
\(277\) | −18.6210 | −1.11882 | −0.559412 | − | 0.828889i | \(-0.688973\pi\) | ||||
−0.559412 | + | 0.828889i | \(0.688973\pi\) | |||||||
\(278\) | 12.9504 | 0.776715 | ||||||||
\(279\) | −3.18333 | −0.190581 | ||||||||
\(280\) | −7.21246 | −0.431027 | ||||||||
\(281\) | −4.89194 | −0.291829 | −0.145914 | − | 0.989297i | \(-0.546612\pi\) | ||||
−0.145914 | + | 0.989297i | \(0.546612\pi\) | |||||||
\(282\) | −9.30607 | −0.554168 | ||||||||
\(283\) | −25.4088 | −1.51040 | −0.755199 | − | 0.655495i | \(-0.772460\pi\) | ||||
−0.755199 | + | 0.655495i | \(0.772460\pi\) | |||||||
\(284\) | −2.33797 | −0.138733 | ||||||||
\(285\) | 3.05485 | 0.180954 | ||||||||
\(286\) | −1.37729 | −0.0814407 | ||||||||
\(287\) | 15.1244 | 0.892763 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.9344 | −0.937319 | ||||||||
\(290\) | −10.5604 | −0.620131 | ||||||||
\(291\) | −12.6888 | −0.743830 | ||||||||
\(292\) | −11.6910 | −0.684166 | ||||||||
\(293\) | −29.1944 | −1.70556 | −0.852778 | − | 0.522273i | \(-0.825084\pi\) | ||||
−0.852778 | + | 0.522273i | \(0.825084\pi\) | |||||||
\(294\) | 1.42576 | 0.0831521 | ||||||||
\(295\) | −28.3827 | −1.65251 | ||||||||
\(296\) | −4.86635 | −0.282851 | ||||||||
\(297\) | 2.94877 | 0.171105 | ||||||||
\(298\) | −18.5105 | −1.07228 | ||||||||
\(299\) | 2.53310 | 0.146493 | ||||||||
\(300\) | 4.33214 | 0.250116 | ||||||||
\(301\) | 21.8072 | 1.25695 | ||||||||
\(302\) | −1.03687 | −0.0596649 | ||||||||
\(303\) | 1.34084 | 0.0770294 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −33.8295 | −1.93707 | ||||||||
\(306\) | 1.03227 | 0.0590108 | ||||||||
\(307\) | −27.4232 | −1.56512 | −0.782562 | − | 0.622573i | \(-0.786088\pi\) | ||||
−0.782562 | + | 0.622573i | \(0.786088\pi\) | |||||||
\(308\) | −6.96198 | −0.396696 | ||||||||
\(309\) | 15.2194 | 0.865801 | ||||||||
\(310\) | −9.72462 | −0.552322 | ||||||||
\(311\) | 24.0999 | 1.36658 | 0.683289 | − | 0.730148i | \(-0.260549\pi\) | ||||
0.683289 | + | 0.730148i | \(0.260549\pi\) | |||||||
\(312\) | −0.467072 | −0.0264428 | ||||||||
\(313\) | −10.0949 | −0.570599 | −0.285299 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285299 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(314\) | 7.59160 | 0.428419 | ||||||||
\(315\) | 7.21246 | 0.406376 | ||||||||
\(316\) | −14.0517 | −0.790470 | ||||||||
\(317\) | −26.4727 | −1.48685 | −0.743427 | − | 0.668817i | \(-0.766801\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −10.1937 | −0.570738 | ||||||||
\(320\) | −3.05485 | −0.170772 | ||||||||
\(321\) | 9.49726 | 0.530085 | ||||||||
\(322\) | 12.8044 | 0.713564 | ||||||||
\(323\) | 1.03227 | 0.0574369 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.02342 | 0.112239 | ||||||||
\(326\) | 9.85353 | 0.545737 | ||||||||
\(327\) | 6.91309 | 0.382295 | ||||||||
\(328\) | 6.40596 | 0.353710 | ||||||||
\(329\) | −21.9715 | −1.21133 | ||||||||
\(330\) | 9.00805 | 0.495877 | ||||||||
\(331\) | 0.606122 | 0.0333155 | 0.0166577 | − | 0.999861i | \(-0.494697\pi\) | ||||
0.0166577 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(332\) | 4.08187 | 0.224022 | ||||||||
\(333\) | 4.86635 | 0.266674 | ||||||||
\(334\) | 13.7419 | 0.751922 | ||||||||
\(335\) | −33.5605 | −1.83361 | ||||||||
\(336\) | −2.36098 | −0.128802 | ||||||||
\(337\) | −28.4705 | −1.55088 | −0.775442 | − | 0.631418i | \(-0.782473\pi\) | ||||
−0.775442 | + | 0.631418i | \(0.782473\pi\) | |||||||
\(338\) | 12.7818 | 0.695241 | ||||||||
\(339\) | −2.88232 | −0.156546 | ||||||||
\(340\) | 3.15343 | 0.171019 | ||||||||
\(341\) | −9.38691 | −0.508329 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 19.8931 | 1.07413 | ||||||||
\(344\) | 9.23651 | 0.497999 | ||||||||
\(345\) | −16.5676 | −0.891967 | ||||||||
\(346\) | 11.6103 | 0.624176 | ||||||||
\(347\) | 16.3619 | 0.878353 | 0.439176 | − | 0.898401i | \(-0.355270\pi\) | ||||
0.439176 | + | 0.898401i | \(0.355270\pi\) | |||||||
\(348\) | −3.45694 | −0.185311 | ||||||||
\(349\) | 28.2919 | 1.51443 | 0.757217 | − | 0.653164i | \(-0.226559\pi\) | ||||
0.757217 | + | 0.653164i | \(0.226559\pi\) | |||||||
\(350\) | 10.2281 | 0.546715 | ||||||||
\(351\) | 0.467072 | 0.0249305 | ||||||||
\(352\) | −2.94877 | −0.157170 | ||||||||
\(353\) | 36.6087 | 1.94849 | 0.974243 | − | 0.225500i | \(-0.0724017\pi\) | ||||
0.974243 | + | 0.225500i | \(0.0724017\pi\) | |||||||
\(354\) | −9.29102 | −0.493812 | ||||||||
\(355\) | 7.14216 | 0.379066 | ||||||||
\(356\) | −0.763691 | −0.0404755 | ||||||||
\(357\) | 2.43717 | 0.128989 | ||||||||
\(358\) | −12.6980 | −0.671108 | ||||||||
\(359\) | 24.8100 | 1.30942 | 0.654710 | − | 0.755880i | \(-0.272791\pi\) | ||||
0.654710 | + | 0.755880i | \(0.272791\pi\) | |||||||
\(360\) | 3.05485 | 0.161005 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −4.92417 | −0.258808 | ||||||||
\(363\) | −2.30478 | −0.120970 | ||||||||
\(364\) | −1.10275 | −0.0577998 | ||||||||
\(365\) | 35.7144 | 1.86938 | ||||||||
\(366\) | −11.0740 | −0.578848 | ||||||||
\(367\) | 4.68071 | 0.244331 | 0.122165 | − | 0.992510i | \(-0.461016\pi\) | ||||
0.122165 | + | 0.992510i | \(0.461016\pi\) | |||||||
\(368\) | 5.42335 | 0.282712 | ||||||||
\(369\) | −6.40596 | −0.333481 | ||||||||
\(370\) | 14.8660 | 0.772846 | ||||||||
\(371\) | −2.36098 | −0.122576 | ||||||||
\(372\) | −3.18333 | −0.165048 | ||||||||
\(373\) | −6.67864 | −0.345807 | −0.172904 | − | 0.984939i | \(-0.555315\pi\) | ||||
−0.172904 | + | 0.984939i | \(0.555315\pi\) | |||||||
\(374\) | 3.04392 | 0.157397 | ||||||||
\(375\) | 2.04022 | 0.105357 | ||||||||
\(376\) | −9.30607 | −0.479924 | ||||||||
\(377\) | −1.61464 | −0.0831582 | ||||||||
\(378\) | 2.36098 | 0.121436 | ||||||||
\(379\) | 4.81313 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(380\) | 3.05485 | 0.156711 | ||||||||
\(381\) | 2.53418 | 0.129830 | ||||||||
\(382\) | 4.57585 | 0.234121 | ||||||||
\(383\) | 30.1449 | 1.54033 | 0.770165 | − | 0.637845i | \(-0.220174\pi\) | ||||
0.770165 | + | 0.637845i | \(0.220174\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 21.2678 | 1.08391 | ||||||||
\(386\) | 18.2444 | 0.928617 | ||||||||
\(387\) | −9.23651 | −0.469518 | ||||||||
\(388\) | −12.6888 | −0.644176 | ||||||||
\(389\) | 15.8885 | 0.805577 | 0.402788 | − | 0.915293i | \(-0.368041\pi\) | ||||
0.402788 | + | 0.915293i | \(0.368041\pi\) | |||||||
\(390\) | 1.42684 | 0.0722508 | ||||||||
\(391\) | −5.59835 | −0.283121 | ||||||||
\(392\) | 1.42576 | 0.0720118 | ||||||||
\(393\) | −10.4202 | −0.525627 | ||||||||
\(394\) | 23.0005 | 1.15875 | ||||||||
\(395\) | 42.9259 | 2.15984 | ||||||||
\(396\) | 2.94877 | 0.148181 | ||||||||
\(397\) | −29.2482 | −1.46793 | −0.733963 | − | 0.679190i | \(-0.762331\pi\) | ||||
−0.733963 | + | 0.679190i | \(0.762331\pi\) | |||||||
\(398\) | 22.1077 | 1.10816 | ||||||||
\(399\) | 2.36098 | 0.118197 | ||||||||
\(400\) | 4.33214 | 0.216607 | ||||||||
\(401\) | 13.0332 | 0.650849 | 0.325425 | − | 0.945568i | \(-0.394493\pi\) | ||||
0.325425 | + | 0.945568i | \(0.394493\pi\) | |||||||
\(402\) | −10.9860 | −0.547930 | ||||||||
\(403\) | −1.48685 | −0.0740651 | ||||||||
\(404\) | 1.34084 | 0.0667094 | ||||||||
\(405\) | −3.05485 | −0.151797 | ||||||||
\(406\) | −8.16177 | −0.405062 | ||||||||
\(407\) | 14.3497 | 0.711290 | ||||||||
\(408\) | 1.03227 | 0.0511049 | ||||||||
\(409\) | −14.6172 | −0.722772 | −0.361386 | − | 0.932416i | \(-0.617696\pi\) | ||||
−0.361386 | + | 0.932416i | \(0.617696\pi\) | |||||||
\(410\) | −19.5693 | −0.966458 | ||||||||
\(411\) | 10.7967 | 0.532563 | ||||||||
\(412\) | 15.2194 | 0.749806 | ||||||||
\(413\) | −21.9359 | −1.07940 | ||||||||
\(414\) | −5.42335 | −0.266543 | ||||||||
\(415\) | −12.4695 | −0.612105 | ||||||||
\(416\) | −0.467072 | −0.0229001 | ||||||||
\(417\) | −12.9504 | −0.634185 | ||||||||
\(418\) | 2.94877 | 0.144229 | ||||||||
\(419\) | −28.6303 | −1.39868 | −0.699342 | − | 0.714787i | \(-0.746523\pi\) | ||||
−0.699342 | + | 0.714787i | \(0.746523\pi\) | |||||||
\(420\) | 7.21246 | 0.351932 | ||||||||
\(421\) | −3.12631 | −0.152367 | −0.0761836 | − | 0.997094i | \(-0.524274\pi\) | ||||
−0.0761836 | + | 0.997094i | \(0.524274\pi\) | |||||||
\(422\) | −7.45899 | −0.363098 | ||||||||
\(423\) | 9.30607 | 0.452476 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −4.47193 | −0.216920 | ||||||||
\(426\) | 2.33797 | 0.113275 | ||||||||
\(427\) | −26.1456 | −1.26527 | ||||||||
\(428\) | 9.49726 | 0.459067 | ||||||||
\(429\) | 1.37729 | 0.0664960 | ||||||||
\(430\) | −28.2162 | −1.36071 | ||||||||
\(431\) | −26.0258 | −1.25362 | −0.626808 | − | 0.779173i | \(-0.715639\pi\) | ||||
−0.626808 | + | 0.779173i | \(0.715639\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 26.2500 | 1.26150 | 0.630748 | − | 0.775988i | \(-0.282748\pi\) | ||||
0.630748 | + | 0.775988i | \(0.282748\pi\) | |||||||
\(434\) | −7.51580 | −0.360770 | ||||||||
\(435\) | 10.5604 | 0.506335 | ||||||||
\(436\) | 6.91309 | 0.331077 | ||||||||
\(437\) | −5.42335 | −0.259434 | ||||||||
\(438\) | 11.6910 | 0.558619 | ||||||||
\(439\) | 13.1102 | 0.625718 | 0.312859 | − | 0.949800i | \(-0.398713\pi\) | ||||
0.312859 | + | 0.949800i | \(0.398713\pi\) | |||||||
\(440\) | 9.00805 | 0.429442 | ||||||||
\(441\) | −1.42576 | −0.0678934 | ||||||||
\(442\) | 0.482144 | 0.0229332 | ||||||||
\(443\) | −34.5171 | −1.63996 | −0.819978 | − | 0.572395i | \(-0.806014\pi\) | ||||
−0.819978 | + | 0.572395i | \(0.806014\pi\) | |||||||
\(444\) | 4.86635 | 0.230947 | ||||||||
\(445\) | 2.33296 | 0.110593 | ||||||||
\(446\) | 2.93783 | 0.139110 | ||||||||
\(447\) | 18.5105 | 0.875515 | ||||||||
\(448\) | −2.36098 | −0.111546 | ||||||||
\(449\) | 26.9889 | 1.27368 | 0.636842 | − | 0.770995i | \(-0.280240\pi\) | ||||
0.636842 | + | 0.770995i | \(0.280240\pi\) | |||||||
\(450\) | −4.33214 | −0.204219 | ||||||||
\(451\) | −18.8897 | −0.889480 | ||||||||
\(452\) | −2.88232 | −0.135573 | ||||||||
\(453\) | 1.03687 | 0.0487162 | ||||||||
\(454\) | 0.660602 | 0.0310036 | ||||||||
\(455\) | 3.36874 | 0.157929 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 5.84877 | 0.273594 | 0.136797 | − | 0.990599i | \(-0.456319\pi\) | ||||
0.136797 | + | 0.990599i | \(0.456319\pi\) | |||||||
\(458\) | −0.217202 | −0.0101492 | ||||||||
\(459\) | −1.03227 | −0.0481822 | ||||||||
\(460\) | −16.5676 | −0.772466 | ||||||||
\(461\) | 31.2790 | 1.45681 | 0.728405 | − | 0.685147i | \(-0.240262\pi\) | ||||
0.728405 | + | 0.685147i | \(0.240262\pi\) | |||||||
\(462\) | 6.96198 | 0.323901 | ||||||||
\(463\) | 30.7051 | 1.42699 | 0.713494 | − | 0.700661i | \(-0.247111\pi\) | ||||
0.713494 | + | 0.700661i | \(0.247111\pi\) | |||||||
\(464\) | −3.45694 | −0.160484 | ||||||||
\(465\) | 9.72462 | 0.450969 | ||||||||
\(466\) | 5.80594 | 0.268955 | ||||||||
\(467\) | −7.78851 | −0.360409 | −0.180205 | − | 0.983629i | \(-0.557676\pi\) | ||||
−0.180205 | + | 0.983629i | \(0.557676\pi\) | |||||||
\(468\) | 0.467072 | 0.0215904 | ||||||||
\(469\) | −25.9377 | −1.19769 | ||||||||
\(470\) | 28.4287 | 1.31132 | ||||||||
\(471\) | −7.59160 | −0.349803 | ||||||||
\(472\) | −9.29102 | −0.427654 | ||||||||
\(473\) | −27.2363 | −1.25233 | ||||||||
\(474\) | 14.0517 | 0.645416 | ||||||||
\(475\) | −4.33214 | −0.198772 | ||||||||
\(476\) | 2.43717 | 0.111707 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 2.07250 | 0.0947941 | ||||||||
\(479\) | 20.9794 | 0.958572 | 0.479286 | − | 0.877659i | \(-0.340896\pi\) | ||||
0.479286 | + | 0.877659i | \(0.340896\pi\) | |||||||
\(480\) | 3.05485 | 0.139434 | ||||||||
\(481\) | 2.27294 | 0.103637 | ||||||||
\(482\) | 15.0145 | 0.683891 | ||||||||
\(483\) | −12.8044 | −0.582622 | ||||||||
\(484\) | −2.30478 | −0.104763 | ||||||||
\(485\) | 38.7624 | 1.76011 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 3.78612 | 0.171566 | 0.0857828 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857828 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(488\) | −11.0740 | −0.501297 | ||||||||
\(489\) | −9.85353 | −0.445592 | ||||||||
\(490\) | −4.35549 | −0.196761 | ||||||||
\(491\) | 0.315595 | 0.0142426 | 0.00712130 | − | 0.999975i | \(-0.497733\pi\) | ||||
0.00712130 | + | 0.999975i | \(0.497733\pi\) | |||||||
\(492\) | −6.40596 | −0.288803 | ||||||||
\(493\) | 3.56849 | 0.160717 | ||||||||
\(494\) | 0.467072 | 0.0210146 | ||||||||
\(495\) | −9.00805 | −0.404882 | ||||||||
\(496\) | −3.18333 | −0.142936 | ||||||||
\(497\) | 5.51991 | 0.247602 | ||||||||
\(498\) | −4.08187 | −0.182913 | ||||||||
\(499\) | 26.9669 | 1.20720 | 0.603602 | − | 0.797286i | \(-0.293732\pi\) | ||||
0.603602 | + | 0.797286i | \(0.293732\pi\) | |||||||
\(500\) | 2.04022 | 0.0912415 | ||||||||
\(501\) | −13.7419 | −0.613942 | ||||||||
\(502\) | 18.3751 | 0.820121 | ||||||||
\(503\) | 16.7529 | 0.746974 | 0.373487 | − | 0.927635i | \(-0.378162\pi\) | ||||
0.373487 | + | 0.927635i | \(0.378162\pi\) | |||||||
\(504\) | 2.36098 | 0.105167 | ||||||||
\(505\) | −4.09608 | −0.182273 | ||||||||
\(506\) | −15.9922 | −0.710940 | ||||||||
\(507\) | −12.7818 | −0.567662 | ||||||||
\(508\) | 2.53418 | 0.112436 | ||||||||
\(509\) | 37.5630 | 1.66495 | 0.832475 | − | 0.554062i | \(-0.186923\pi\) | ||||
0.832475 | + | 0.554062i | \(0.186923\pi\) | |||||||
\(510\) | −3.15343 | −0.139636 | ||||||||
\(511\) | 27.6023 | 1.22106 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 16.0606 | 0.708404 | ||||||||
\(515\) | −46.4930 | −2.04873 | ||||||||
\(516\) | −9.23651 | −0.406614 | ||||||||
\(517\) | 27.4414 | 1.20687 | ||||||||
\(518\) | 11.4894 | 0.504814 | ||||||||
\(519\) | −11.6103 | −0.509637 | ||||||||
\(520\) | 1.42684 | 0.0625710 | ||||||||
\(521\) | −1.07233 | −0.0469795 | −0.0234898 | − | 0.999724i | \(-0.507478\pi\) | ||||
−0.0234898 | + | 0.999724i | \(0.507478\pi\) | |||||||
\(522\) | 3.45694 | 0.151306 | ||||||||
\(523\) | 15.0092 | 0.656306 | 0.328153 | − | 0.944625i | \(-0.393574\pi\) | ||||
0.328153 | + | 0.944625i | \(0.393574\pi\) | |||||||
\(524\) | −10.4202 | −0.455207 | ||||||||
\(525\) | −10.2281 | −0.446391 | ||||||||
\(526\) | 13.3943 | 0.584017 | ||||||||
\(527\) | 3.28605 | 0.143143 | ||||||||
\(528\) | 2.94877 | 0.128329 | ||||||||
\(529\) | 6.41275 | 0.278815 | ||||||||
\(530\) | 3.05485 | 0.132694 | ||||||||
\(531\) | 9.29102 | 0.403196 | ||||||||
\(532\) | 2.36098 | 0.102362 | ||||||||
\(533\) | −2.99205 | −0.129600 | ||||||||
\(534\) | 0.763691 | 0.0330481 | ||||||||
\(535\) | −29.0127 | −1.25433 | ||||||||
\(536\) | −10.9860 | −0.474522 | ||||||||
\(537\) | 12.6980 | 0.547957 | ||||||||
\(538\) | 20.7591 | 0.894990 | ||||||||
\(539\) | −4.20423 | −0.181089 | ||||||||
\(540\) | −3.05485 | −0.131460 | ||||||||
\(541\) | −15.7786 | −0.678375 | −0.339187 | − | 0.940719i | \(-0.610152\pi\) | ||||
−0.339187 | + | 0.940719i | \(0.610152\pi\) | |||||||
\(542\) | 25.0383 | 1.07549 | ||||||||
\(543\) | 4.92417 | 0.211316 | ||||||||
\(544\) | 1.03227 | 0.0442581 | ||||||||
\(545\) | −21.1185 | −0.904617 | ||||||||
\(546\) | 1.10275 | 0.0471933 | ||||||||
\(547\) | −5.71240 | −0.244245 | −0.122122 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122122 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(548\) | 10.7967 | 0.461213 | ||||||||
\(549\) | 11.0740 | 0.472627 | ||||||||
\(550\) | −12.7745 | −0.544705 | ||||||||
\(551\) | 3.45694 | 0.147271 | ||||||||
\(552\) | −5.42335 | −0.230833 | ||||||||
\(553\) | 33.1758 | 1.41078 | ||||||||
\(554\) | 18.6210 | 0.791129 | ||||||||
\(555\) | −14.8660 | −0.631026 | ||||||||
\(556\) | −12.9504 | −0.549220 | ||||||||
\(557\) | −40.2201 | −1.70418 | −0.852090 | − | 0.523395i | \(-0.824665\pi\) | ||||
−0.852090 | + | 0.523395i | \(0.824665\pi\) | |||||||
\(558\) | 3.18333 | 0.134761 | ||||||||
\(559\) | −4.31412 | −0.182468 | ||||||||
\(560\) | 7.21246 | 0.304782 | ||||||||
\(561\) | −3.04392 | −0.128514 | ||||||||
\(562\) | 4.89194 | 0.206354 | ||||||||
\(563\) | −12.5826 | −0.530292 | −0.265146 | − | 0.964208i | \(-0.585420\pi\) | ||||
−0.265146 | + | 0.964208i | \(0.585420\pi\) | |||||||
\(564\) | 9.30607 | 0.391856 | ||||||||
\(565\) | 8.80506 | 0.370431 | ||||||||
\(566\) | 25.4088 | 1.06801 | ||||||||
\(567\) | −2.36098 | −0.0991520 | ||||||||
\(568\) | 2.33797 | 0.0980990 | ||||||||
\(569\) | 14.9175 | 0.625375 | 0.312687 | − | 0.949856i | \(-0.398771\pi\) | ||||
0.312687 | + | 0.949856i | \(0.398771\pi\) | |||||||
\(570\) | −3.05485 | −0.127954 | ||||||||
\(571\) | −0.661022 | −0.0276629 | −0.0138315 | − | 0.999904i | \(-0.504403\pi\) | ||||
−0.0138315 | + | 0.999904i | \(0.504403\pi\) | |||||||
\(572\) | 1.37729 | 0.0575872 | ||||||||
\(573\) | −4.57585 | −0.191159 | ||||||||
\(574\) | −15.1244 | −0.631279 | ||||||||
\(575\) | 23.4947 | 0.979797 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −10.0325 | −0.417660 | −0.208830 | − | 0.977952i | \(-0.566965\pi\) | ||||
−0.208830 | + | 0.977952i | \(0.566965\pi\) | |||||||
\(578\) | 15.9344 | 0.662785 | ||||||||
\(579\) | −18.2444 | −0.758213 | ||||||||
\(580\) | 10.5604 | 0.438499 | ||||||||
\(581\) | −9.63723 | −0.399820 | ||||||||
\(582\) | 12.6888 | 0.525967 | ||||||||
\(583\) | 2.94877 | 0.122125 | ||||||||
\(584\) | 11.6910 | 0.483779 | ||||||||
\(585\) | −1.42684 | −0.0589925 | ||||||||
\(586\) | 29.1944 | 1.20601 | ||||||||
\(587\) | −28.2821 | −1.16733 | −0.583664 | − | 0.811995i | \(-0.698382\pi\) | ||||
−0.583664 | + | 0.811995i | \(0.698382\pi\) | |||||||
\(588\) | −1.42576 | −0.0587974 | ||||||||
\(589\) | 3.18333 | 0.131167 | ||||||||
\(590\) | 28.3827 | 1.16850 | ||||||||
\(591\) | −23.0005 | −0.946115 | ||||||||
\(592\) | 4.86635 | 0.200006 | ||||||||
\(593\) | −5.11628 | −0.210100 | −0.105050 | − | 0.994467i | \(-0.533500\pi\) | ||||
−0.105050 | + | 0.994467i | \(0.533500\pi\) | |||||||
\(594\) | −2.94877 | −0.120989 | ||||||||
\(595\) | −7.44519 | −0.305223 | ||||||||
\(596\) | 18.5105 | 0.758219 | ||||||||
\(597\) | −22.1077 | −0.904806 | ||||||||
\(598\) | −2.53310 | −0.103586 | ||||||||
\(599\) | −39.0728 | −1.59647 | −0.798236 | − | 0.602344i | \(-0.794233\pi\) | ||||
−0.798236 | + | 0.602344i | \(0.794233\pi\) | |||||||
\(600\) | −4.33214 | −0.176859 | ||||||||
\(601\) | 8.78731 | 0.358442 | 0.179221 | − | 0.983809i | \(-0.442642\pi\) | ||||
0.179221 | + | 0.983809i | \(0.442642\pi\) | |||||||
\(602\) | −21.8072 | −0.888796 | ||||||||
\(603\) | 10.9860 | 0.447383 | ||||||||
\(604\) | 1.03687 | 0.0421894 | ||||||||
\(605\) | 7.04078 | 0.286248 | ||||||||
\(606\) | −1.34084 | −0.0544680 | ||||||||
\(607\) | −26.8347 | −1.08919 | −0.544593 | − | 0.838701i | \(-0.683316\pi\) | ||||
−0.544593 | + | 0.838701i | \(0.683316\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 8.16177 | 0.330732 | ||||||||
\(610\) | 33.8295 | 1.36972 | ||||||||
\(611\) | 4.34661 | 0.175845 | ||||||||
\(612\) | −1.03227 | −0.0417270 | ||||||||
\(613\) | −21.9900 | −0.888167 | −0.444084 | − | 0.895985i | \(-0.646471\pi\) | ||||
−0.444084 | + | 0.895985i | \(0.646471\pi\) | |||||||
\(614\) | 27.4232 | 1.10671 | ||||||||
\(615\) | 19.5693 | 0.789109 | ||||||||
\(616\) | 6.96198 | 0.280506 | ||||||||
\(617\) | 7.04273 | 0.283530 | 0.141765 | − | 0.989900i | \(-0.454722\pi\) | ||||
0.141765 | + | 0.989900i | \(0.454722\pi\) | |||||||
\(618\) | −15.2194 | −0.612214 | ||||||||
\(619\) | 9.92872 | 0.399069 | 0.199534 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199534 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(620\) | 9.72462 | 0.390550 | ||||||||
\(621\) | 5.42335 | 0.217632 | ||||||||
\(622\) | −24.0999 | −0.966317 | ||||||||
\(623\) | 1.80306 | 0.0722381 | ||||||||
\(624\) | 0.467072 | 0.0186979 | ||||||||
\(625\) | −27.8933 | −1.11573 | ||||||||
\(626\) | 10.0949 | 0.403474 | ||||||||
\(627\) | −2.94877 | −0.117762 | ||||||||
\(628\) | −7.59160 | −0.302938 | ||||||||
\(629\) | −5.02338 | −0.200295 | ||||||||
\(630\) | −7.21246 | −0.287351 | ||||||||
\(631\) | 40.6271 | 1.61734 | 0.808670 | − | 0.588262i | \(-0.200188\pi\) | ||||
0.808670 | + | 0.588262i | \(0.200188\pi\) | |||||||
\(632\) | 14.0517 | 0.558947 | ||||||||
\(633\) | 7.45899 | 0.296468 | ||||||||
\(634\) | 26.4727 | 1.05136 | ||||||||
\(635\) | −7.74157 | −0.307215 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | −0.665933 | −0.0263852 | ||||||||
\(638\) | 10.1937 | 0.403573 | ||||||||
\(639\) | −2.33797 | −0.0924886 | ||||||||
\(640\) | 3.05485 | 0.120754 | ||||||||
\(641\) | −6.30739 | −0.249127 | −0.124564 | − | 0.992212i | \(-0.539753\pi\) | ||||
−0.124564 | + | 0.992212i | \(0.539753\pi\) | |||||||
\(642\) | −9.49726 | −0.374827 | ||||||||
\(643\) | 2.46952 | 0.0973882 | 0.0486941 | − | 0.998814i | \(-0.484494\pi\) | ||||
0.0486941 | + | 0.998814i | \(0.484494\pi\) | |||||||
\(644\) | −12.8044 | −0.504566 | ||||||||
\(645\) | 28.2162 | 1.11101 | ||||||||
\(646\) | −1.03227 | −0.0406140 | ||||||||
\(647\) | −41.1171 | −1.61648 | −0.808241 | − | 0.588852i | \(-0.799580\pi\) | ||||
−0.808241 | + | 0.588852i | \(0.799580\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 27.3970 | 1.07543 | ||||||||
\(650\) | −2.02342 | −0.0793651 | ||||||||
\(651\) | 7.51580 | 0.294567 | ||||||||
\(652\) | −9.85353 | −0.385894 | ||||||||
\(653\) | 18.2208 | 0.713034 | 0.356517 | − | 0.934289i | \(-0.383964\pi\) | ||||
0.356517 | + | 0.934289i | \(0.383964\pi\) | |||||||
\(654\) | −6.91309 | −0.270323 | ||||||||
\(655\) | 31.8321 | 1.24378 | ||||||||
\(656\) | −6.40596 | −0.250111 | ||||||||
\(657\) | −11.6910 | −0.456111 | ||||||||
\(658\) | 21.9715 | 0.856537 | ||||||||
\(659\) | 28.4830 | 1.10954 | 0.554770 | − | 0.832004i | \(-0.312806\pi\) | ||||
0.554770 | + | 0.832004i | \(0.312806\pi\) | |||||||
\(660\) | −9.00805 | −0.350638 | ||||||||
\(661\) | 46.5649 | 1.81117 | 0.905583 | − | 0.424170i | \(-0.139434\pi\) | ||||
0.905583 | + | 0.424170i | \(0.139434\pi\) | |||||||
\(662\) | −0.606122 | −0.0235576 | ||||||||
\(663\) | −0.482144 | −0.0187249 | ||||||||
\(664\) | −4.08187 | −0.158407 | ||||||||
\(665\) | −7.21246 | −0.279687 | ||||||||
\(666\) | −4.86635 | −0.188567 | ||||||||
\(667\) | −18.7482 | −0.725933 | ||||||||
\(668\) | −13.7419 | −0.531689 | ||||||||
\(669\) | −2.93783 | −0.113583 | ||||||||
\(670\) | 33.5605 | 1.29656 | ||||||||
\(671\) | 32.6547 | 1.26062 | ||||||||
\(672\) | 2.36098 | 0.0910769 | ||||||||
\(673\) | 5.30383 | 0.204448 | 0.102224 | − | 0.994761i | \(-0.467404\pi\) | ||||
0.102224 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(674\) | 28.4705 | 1.09664 | ||||||||
\(675\) | 4.33214 | 0.166744 | ||||||||
\(676\) | −12.7818 | −0.491609 | ||||||||
\(677\) | −21.3073 | −0.818906 | −0.409453 | − | 0.912331i | \(-0.634280\pi\) | ||||
−0.409453 | + | 0.912331i | \(0.634280\pi\) | |||||||
\(678\) | 2.88232 | 0.110695 | ||||||||
\(679\) | 29.9580 | 1.14968 | ||||||||
\(680\) | −3.15343 | −0.120928 | ||||||||
\(681\) | −0.660602 | −0.0253143 | ||||||||
\(682\) | 9.38691 | 0.359443 | ||||||||
\(683\) | −17.7596 | −0.679553 | −0.339777 | − | 0.940506i | \(-0.610351\pi\) | ||||
−0.339777 | + | 0.940506i | \(0.610351\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −32.9824 | −1.26019 | ||||||||
\(686\) | −19.8931 | −0.759521 | ||||||||
\(687\) | 0.217202 | 0.00828676 | ||||||||
\(688\) | −9.23651 | −0.352138 | ||||||||
\(689\) | 0.467072 | 0.0177940 | ||||||||
\(690\) | 16.5676 | 0.630716 | ||||||||
\(691\) | −32.2263 | −1.22595 | −0.612973 | − | 0.790104i | \(-0.710027\pi\) | ||||
−0.612973 | + | 0.790104i | \(0.710027\pi\) | |||||||
\(692\) | −11.6103 | −0.441359 | ||||||||
\(693\) | −6.96198 | −0.264464 | ||||||||
\(694\) | −16.3619 | −0.621089 | ||||||||
\(695\) | 39.5617 | 1.50066 | ||||||||
\(696\) | 3.45694 | 0.131035 | ||||||||
\(697\) | 6.61267 | 0.250473 | ||||||||
\(698\) | −28.2919 | −1.07087 | ||||||||
\(699\) | −5.80594 | −0.219601 | ||||||||
\(700\) | −10.2281 | −0.386586 | ||||||||
\(701\) | −19.4199 | −0.733481 | −0.366740 | − | 0.930323i | \(-0.619526\pi\) | ||||
−0.366740 | + | 0.930323i | \(0.619526\pi\) | |||||||
\(702\) | −0.467072 | −0.0176285 | ||||||||
\(703\) | −4.86635 | −0.183538 | ||||||||
\(704\) | 2.94877 | 0.111136 | ||||||||
\(705\) | −28.4287 | −1.07069 | ||||||||
\(706\) | −36.6087 | −1.37779 | ||||||||
\(707\) | −3.16571 | −0.119059 | ||||||||
\(708\) | 9.29102 | 0.349178 | ||||||||
\(709\) | −25.6695 | −0.964039 | −0.482020 | − | 0.876160i | \(-0.660097\pi\) | ||||
−0.482020 | + | 0.876160i | \(0.660097\pi\) | |||||||
\(710\) | −7.14216 | −0.268040 | ||||||||
\(711\) | −14.0517 | −0.526980 | ||||||||
\(712\) | 0.763691 | 0.0286205 | ||||||||
\(713\) | −17.2643 | −0.646555 | ||||||||
\(714\) | −2.43717 | −0.0912087 | ||||||||
\(715\) | −4.20741 | −0.157348 | ||||||||
\(716\) | 12.6980 | 0.474545 | ||||||||
\(717\) | −2.07250 | −0.0773990 | ||||||||
\(718\) | −24.8100 | −0.925899 | ||||||||
\(719\) | 41.7103 | 1.55553 | 0.777765 | − | 0.628555i | \(-0.216353\pi\) | ||||
0.777765 | + | 0.628555i | \(0.216353\pi\) | |||||||
\(720\) | −3.05485 | −0.113848 | ||||||||
\(721\) | −35.9327 | −1.33820 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −15.0145 | −0.558394 | ||||||||
\(724\) | 4.92417 | 0.183005 | ||||||||
\(725\) | −14.9759 | −0.556192 | ||||||||
\(726\) | 2.30478 | 0.0855386 | ||||||||
\(727\) | −8.55694 | −0.317359 | −0.158680 | − | 0.987330i | \(-0.550724\pi\) | ||||
−0.158680 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(728\) | 1.10275 | 0.0408706 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.7144 | −1.32185 | ||||||||
\(731\) | 9.53455 | 0.352648 | ||||||||
\(732\) | 11.0740 | 0.409307 | ||||||||
\(733\) | 21.8653 | 0.807612 | 0.403806 | − | 0.914845i | \(-0.367687\pi\) | ||||
0.403806 | + | 0.914845i | \(0.367687\pi\) | |||||||
\(734\) | −4.68071 | −0.172768 | ||||||||
\(735\) | 4.35549 | 0.160655 | ||||||||
\(736\) | −5.42335 | −0.199907 | ||||||||
\(737\) | 32.3950 | 1.19329 | ||||||||
\(738\) | 6.40596 | 0.235807 | ||||||||
\(739\) | 9.87845 | 0.363385 | 0.181692 | − | 0.983355i | \(-0.441842\pi\) | ||||
0.181692 | + | 0.983355i | \(0.441842\pi\) | |||||||
\(740\) | −14.8660 | −0.546485 | ||||||||
\(741\) | −0.467072 | −0.0171583 | ||||||||
\(742\) | 2.36098 | 0.0866744 | ||||||||
\(743\) | −21.4800 | −0.788024 | −0.394012 | − | 0.919105i | \(-0.628913\pi\) | ||||
−0.394012 | + | 0.919105i | \(0.628913\pi\) | |||||||
\(744\) | 3.18333 | 0.116707 | ||||||||
\(745\) | −56.5468 | −2.07171 | ||||||||
\(746\) | 6.67864 | 0.244522 | ||||||||
\(747\) | 4.08187 | 0.149348 | ||||||||
\(748\) | −3.04392 | −0.111297 | ||||||||
\(749\) | −22.4229 | −0.819313 | ||||||||
\(750\) | −2.04022 | −0.0744984 | ||||||||
\(751\) | −31.0878 | −1.13441 | −0.567205 | − | 0.823577i | \(-0.691975\pi\) | ||||
−0.567205 | + | 0.823577i | \(0.691975\pi\) | |||||||
\(752\) | 9.30607 | 0.339357 | ||||||||
\(753\) | −18.3751 | −0.669626 | ||||||||
\(754\) | 1.61464 | 0.0588017 | ||||||||
\(755\) | −3.16747 | −0.115276 | ||||||||
\(756\) | −2.36098 | −0.0858681 | ||||||||
\(757\) | −39.0199 | −1.41820 | −0.709101 | − | 0.705107i | \(-0.750899\pi\) | ||||
−0.709101 | + | 0.705107i | \(0.750899\pi\) | |||||||
\(758\) | −4.81313 | −0.174821 | ||||||||
\(759\) | 15.9922 | 0.580480 | ||||||||
\(760\) | −3.05485 | −0.110811 | ||||||||
\(761\) | −46.0662 | −1.66990 | −0.834949 | − | 0.550328i | \(-0.814503\pi\) | ||||
−0.834949 | + | 0.550328i | \(0.814503\pi\) | |||||||
\(762\) | −2.53418 | −0.0918038 | ||||||||
\(763\) | −16.3217 | −0.590885 | ||||||||
\(764\) | −4.57585 | −0.165548 | ||||||||
\(765\) | 3.15343 | 0.114012 | ||||||||
\(766\) | −30.1449 | −1.08918 | ||||||||
\(767\) | 4.33958 | 0.156693 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 29.1435 | 1.05094 | 0.525471 | − | 0.850812i | \(-0.323889\pi\) | ||||
0.525471 | + | 0.850812i | \(0.323889\pi\) | |||||||
\(770\) | −21.2678 | −0.766440 | ||||||||
\(771\) | −16.0606 | −0.578410 | ||||||||
\(772\) | −18.2444 | −0.656632 | ||||||||
\(773\) | −8.32980 | −0.299602 | −0.149801 | − | 0.988716i | \(-0.547863\pi\) | ||||
−0.149801 | + | 0.988716i | \(0.547863\pi\) | |||||||
\(774\) | 9.23651 | 0.331999 | ||||||||
\(775\) | −13.7906 | −0.495375 | ||||||||
\(776\) | 12.6888 | 0.455501 | ||||||||
\(777\) | −11.4894 | −0.412179 | ||||||||
\(778\) | −15.8885 | −0.569629 | ||||||||
\(779\) | 6.40596 | 0.229517 | ||||||||
\(780\) | −1.42684 | −0.0510890 | ||||||||
\(781\) | −6.89412 | −0.246691 | ||||||||
\(782\) | 5.59835 | 0.200197 | ||||||||
\(783\) | −3.45694 | −0.123541 | ||||||||
\(784\) | −1.42576 | −0.0509200 | ||||||||
\(785\) | 23.1912 | 0.827731 | ||||||||
\(786\) | 10.4202 | 0.371675 | ||||||||
\(787\) | 8.62351 | 0.307395 | 0.153698 | − | 0.988118i | \(-0.450882\pi\) | ||||
0.153698 | + | 0.988118i | \(0.450882\pi\) | |||||||
\(788\) | −23.0005 | −0.819360 | ||||||||
\(789\) | −13.3943 | −0.476848 | ||||||||
\(790\) | −42.9259 | −1.52724 | ||||||||
\(791\) | 6.80510 | 0.241961 | ||||||||
\(792\) | −2.94877 | −0.104780 | ||||||||
\(793\) | 5.17236 | 0.183676 | ||||||||
\(794\) | 29.2482 | 1.03798 | ||||||||
\(795\) | −3.05485 | −0.108345 | ||||||||
\(796\) | −22.1077 | −0.783585 | ||||||||
\(797\) | −16.8222 | −0.595872 | −0.297936 | − | 0.954586i | \(-0.596298\pi\) | ||||
−0.297936 | + | 0.954586i | \(0.596298\pi\) | |||||||
\(798\) | −2.36098 | −0.0835779 | ||||||||
\(799\) | −9.60636 | −0.339848 | ||||||||
\(800\) | −4.33214 | −0.153164 | ||||||||
\(801\) | −0.763691 | −0.0269837 | ||||||||
\(802\) | −13.0332 | −0.460220 | ||||||||
\(803\) | −34.4741 | −1.21657 | ||||||||
\(804\) | 10.9860 | 0.387445 | ||||||||
\(805\) | 39.1157 | 1.37865 | ||||||||
\(806\) | 1.48685 | 0.0523720 | ||||||||
\(807\) | −20.7591 | −0.730757 | ||||||||
\(808\) | −1.34084 | −0.0471707 | ||||||||
\(809\) | 26.5709 | 0.934185 | 0.467092 | − | 0.884208i | \(-0.345302\pi\) | ||||
0.467092 | + | 0.884208i | \(0.345302\pi\) | |||||||
\(810\) | 3.05485 | 0.107337 | ||||||||
\(811\) | 1.96526 | 0.0690095 | 0.0345048 | − | 0.999405i | \(-0.489015\pi\) | ||||
0.0345048 | + | 0.999405i | \(0.489015\pi\) | |||||||
\(812\) | 8.16177 | 0.286422 | ||||||||
\(813\) | −25.0383 | −0.878131 | ||||||||
\(814\) | −14.3497 | −0.502958 | ||||||||
\(815\) | 30.1011 | 1.05440 | ||||||||
\(816\) | −1.03227 | −0.0361366 | ||||||||
\(817\) | 9.23651 | 0.323144 | ||||||||
\(818\) | 14.6172 | 0.511077 | ||||||||
\(819\) | −1.10275 | −0.0385332 | ||||||||
\(820\) | 19.5693 | 0.683389 | ||||||||
\(821\) | 13.7481 | 0.479811 | 0.239905 | − | 0.970796i | \(-0.422884\pi\) | ||||
0.239905 | + | 0.970796i | \(0.422884\pi\) | |||||||
\(822\) | −10.7967 | −0.376579 | ||||||||
\(823\) | 42.4458 | 1.47957 | 0.739784 | − | 0.672845i | \(-0.234928\pi\) | ||||
0.739784 | + | 0.672845i | \(0.234928\pi\) | |||||||
\(824\) | −15.2194 | −0.530193 | ||||||||
\(825\) | 12.7745 | 0.444750 | ||||||||
\(826\) | 21.9359 | 0.763249 | ||||||||
\(827\) | −46.1469 | −1.60469 | −0.802343 | − | 0.596863i | \(-0.796413\pi\) | ||||
−0.802343 | + | 0.596863i | \(0.796413\pi\) | |||||||
\(828\) | 5.42335 | 0.188475 | ||||||||
\(829\) | −22.6353 | −0.786156 | −0.393078 | − | 0.919505i | \(-0.628590\pi\) | ||||
−0.393078 | + | 0.919505i | \(0.628590\pi\) | |||||||
\(830\) | 12.4695 | 0.432823 | ||||||||
\(831\) | −18.6210 | −0.645954 | ||||||||
\(832\) | 0.467072 | 0.0161928 | ||||||||
\(833\) | 1.47177 | 0.0509937 | ||||||||
\(834\) | 12.9504 | 0.448436 | ||||||||
\(835\) | 41.9794 | 1.45276 | ||||||||
\(836\) | −2.94877 | −0.101985 | ||||||||
\(837\) | −3.18333 | −0.110032 | ||||||||
\(838\) | 28.6303 | 0.989019 | ||||||||
\(839\) | −42.3525 | −1.46217 | −0.731086 | − | 0.682286i | \(-0.760986\pi\) | ||||
−0.731086 | + | 0.682286i | \(0.760986\pi\) | |||||||
\(840\) | −7.21246 | −0.248853 | ||||||||
\(841\) | −17.0496 | −0.587916 | ||||||||
\(842\) | 3.12631 | 0.107740 | ||||||||
\(843\) | −4.89194 | −0.168487 | ||||||||
\(844\) | 7.45899 | 0.256749 | ||||||||
\(845\) | 39.0467 | 1.34325 | ||||||||
\(846\) | −9.30607 | −0.319949 | ||||||||
\(847\) | 5.44156 | 0.186974 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −25.4088 | −0.872029 | ||||||||
\(850\) | 4.47193 | 0.153386 | ||||||||
\(851\) | 26.3919 | 0.904704 | ||||||||
\(852\) | −2.33797 | −0.0800975 | ||||||||
\(853\) | −15.4607 | −0.529363 | −0.264681 | − | 0.964336i | \(-0.585267\pi\) | ||||
−0.264681 | + | 0.964336i | \(0.585267\pi\) | |||||||
\(854\) | 26.1456 | 0.894682 | ||||||||
\(855\) | 3.05485 | 0.104474 | ||||||||
\(856\) | −9.49726 | −0.324610 | ||||||||
\(857\) | −30.5061 | −1.04207 | −0.521034 | − | 0.853536i | \(-0.674454\pi\) | ||||
−0.521034 | + | 0.853536i | \(0.674454\pi\) | |||||||
\(858\) | −1.37729 | −0.0470198 | ||||||||
\(859\) | 47.8285 | 1.63189 | 0.815944 | − | 0.578131i | \(-0.196218\pi\) | ||||
0.815944 | + | 0.578131i | \(0.196218\pi\) | |||||||
\(860\) | 28.2162 | 0.962164 | ||||||||
\(861\) | 15.1244 | 0.515437 | ||||||||
\(862\) | 26.0258 | 0.886441 | ||||||||
\(863\) | 19.5319 | 0.664874 | 0.332437 | − | 0.943125i | \(-0.392129\pi\) | ||||
0.332437 | + | 0.943125i | \(0.392129\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 35.4679 | 1.20594 | ||||||||
\(866\) | −26.2500 | −0.892012 | ||||||||
\(867\) | −15.9344 | −0.541161 | ||||||||
\(868\) | 7.51580 | 0.255103 | ||||||||
\(869\) | −41.4352 | −1.40559 | ||||||||
\(870\) | −10.5604 | −0.358033 | ||||||||
\(871\) | 5.13124 | 0.173865 | ||||||||
\(872\) | −6.91309 | −0.234107 | ||||||||
\(873\) | −12.6888 | −0.429450 | ||||||||
\(874\) | 5.42335 | 0.183448 | ||||||||
\(875\) | −4.81693 | −0.162842 | ||||||||
\(876\) | −11.6910 | −0.395004 | ||||||||
\(877\) | 36.8538 | 1.24446 | 0.622231 | − | 0.782833i | \(-0.286226\pi\) | ||||
0.622231 | + | 0.782833i | \(0.286226\pi\) | |||||||
\(878\) | −13.1102 | −0.442449 | ||||||||
\(879\) | −29.1944 | −0.984704 | ||||||||
\(880\) | −9.00805 | −0.303661 | ||||||||
\(881\) | −36.4867 | −1.22927 | −0.614634 | − | 0.788812i | \(-0.710696\pi\) | ||||
−0.614634 | + | 0.788812i | \(0.710696\pi\) | |||||||
\(882\) | 1.42576 | 0.0480079 | ||||||||
\(883\) | 10.4386 | 0.351287 | 0.175643 | − | 0.984454i | \(-0.443799\pi\) | ||||
0.175643 | + | 0.984454i | \(0.443799\pi\) | |||||||
\(884\) | −0.482144 | −0.0162163 | ||||||||
\(885\) | −28.3827 | −0.954075 | ||||||||
\(886\) | 34.5171 | 1.15962 | ||||||||
\(887\) | 17.5511 | 0.589308 | 0.294654 | − | 0.955604i | \(-0.404796\pi\) | ||||
0.294654 | + | 0.955604i | \(0.404796\pi\) | |||||||
\(888\) | −4.86635 | −0.163304 | ||||||||
\(889\) | −5.98317 | −0.200669 | ||||||||
\(890\) | −2.33296 | −0.0782011 | ||||||||
\(891\) | 2.94877 | 0.0987873 | ||||||||
\(892\) | −2.93783 | −0.0983658 | ||||||||
\(893\) | −9.30607 | −0.311416 | ||||||||
\(894\) | −18.5105 | −0.619083 | ||||||||
\(895\) | −38.7904 | −1.29662 | ||||||||
\(896\) | 2.36098 | 0.0788749 | ||||||||
\(897\) | 2.53310 | 0.0845777 | ||||||||
\(898\) | −26.9889 | −0.900630 | ||||||||
\(899\) | 11.0046 | 0.367024 | ||||||||
\(900\) | 4.33214 | 0.144405 | ||||||||
\(901\) | −1.03227 | −0.0343898 | ||||||||
\(902\) | 18.8897 | 0.628957 | ||||||||
\(903\) | 21.8072 | 0.725699 | ||||||||
\(904\) | 2.88232 | 0.0958644 | ||||||||
\(905\) | −15.0426 | −0.500033 | ||||||||
\(906\) | −1.03687 | −0.0344475 | ||||||||
\(907\) | −39.5437 | −1.31303 | −0.656514 | − | 0.754314i | \(-0.727970\pi\) | ||||
−0.656514 | + | 0.754314i | \(0.727970\pi\) | |||||||
\(908\) | −0.660602 | −0.0219228 | ||||||||
\(909\) | 1.34084 | 0.0444730 | ||||||||
\(910\) | −3.36874 | −0.111673 | ||||||||
\(911\) | 9.24415 | 0.306272 | 0.153136 | − | 0.988205i | \(-0.451063\pi\) | ||||
0.153136 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | 12.0365 | 0.398349 | ||||||||
\(914\) | −5.84877 | −0.193460 | ||||||||
\(915\) | −33.8295 | −1.11837 | ||||||||
\(916\) | 0.217202 | 0.00717654 | ||||||||
\(917\) | 24.6018 | 0.812423 | ||||||||
\(918\) | 1.03227 | 0.0340699 | ||||||||
\(919\) | −9.24029 | −0.304809 | −0.152405 | − | 0.988318i | \(-0.548702\pi\) | ||||
−0.152405 | + | 0.988318i | \(0.548702\pi\) | |||||||
\(920\) | 16.5676 | 0.546216 | ||||||||
\(921\) | −27.4232 | −0.903625 | ||||||||
\(922\) | −31.2790 | −1.03012 | ||||||||
\(923\) | −1.09200 | −0.0359436 | ||||||||
\(924\) | −6.96198 | −0.229032 | ||||||||
\(925\) | 21.0817 | 0.693162 | ||||||||
\(926\) | −30.7051 | −1.00903 | ||||||||
\(927\) | 15.2194 | 0.499870 | ||||||||
\(928\) | 3.45694 | 0.113480 | ||||||||
\(929\) | 39.1491 | 1.28444 | 0.642221 | − | 0.766520i | \(-0.278013\pi\) | ||||
0.642221 | + | 0.766520i | \(0.278013\pi\) | |||||||
\(930\) | −9.72462 | −0.318883 | ||||||||
\(931\) | 1.42576 | 0.0467274 | ||||||||
\(932\) | −5.80594 | −0.190180 | ||||||||
\(933\) | 24.0999 | 0.788995 | ||||||||
\(934\) | 7.78851 | 0.254848 | ||||||||
\(935\) | 9.29872 | 0.304101 | ||||||||
\(936\) | −0.467072 | −0.0152667 | ||||||||
\(937\) | −52.8355 | −1.72606 | −0.863031 | − | 0.505151i | \(-0.831437\pi\) | ||||
−0.863031 | + | 0.505151i | \(0.831437\pi\) | |||||||
\(938\) | 25.9377 | 0.846895 | ||||||||
\(939\) | −10.0949 | −0.329435 | ||||||||
\(940\) | −28.4287 | −0.927241 | ||||||||
\(941\) | 21.9569 | 0.715775 | 0.357888 | − | 0.933765i | \(-0.383497\pi\) | ||||
0.357888 | + | 0.933765i | \(0.383497\pi\) | |||||||
\(942\) | 7.59160 | 0.247348 | ||||||||
\(943\) | −34.7418 | −1.13135 | ||||||||
\(944\) | 9.29102 | 0.302397 | ||||||||
\(945\) | 7.21246 | 0.234621 | ||||||||
\(946\) | 27.2363 | 0.885528 | ||||||||
\(947\) | −17.3109 | −0.562530 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(948\) | −14.0517 | −0.456378 | ||||||||
\(949\) | −5.46056 | −0.177257 | ||||||||
\(950\) | 4.33214 | 0.140553 | ||||||||
\(951\) | −26.4727 | −0.858436 | ||||||||
\(952\) | −2.43717 | −0.0789890 | ||||||||
\(953\) | 6.84215 | 0.221639 | 0.110820 | − | 0.993841i | \(-0.464652\pi\) | ||||
0.110820 | + | 0.993841i | \(0.464652\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | 13.9786 | 0.452336 | ||||||||
\(956\) | −2.07250 | −0.0670295 | ||||||||
\(957\) | −10.1937 | −0.329516 | ||||||||
\(958\) | −20.9794 | −0.677813 | ||||||||
\(959\) | −25.4909 | −0.823144 | ||||||||
\(960\) | −3.05485 | −0.0985950 | ||||||||
\(961\) | −20.8664 | −0.673109 | ||||||||
\(962\) | −2.27294 | −0.0732825 | ||||||||
\(963\) | 9.49726 | 0.306045 | ||||||||
\(964\) | −15.0145 | −0.483584 | ||||||||
\(965\) | 55.7341 | 1.79414 | ||||||||
\(966\) | 12.8044 | 0.411976 | ||||||||
\(967\) | 46.6132 | 1.49898 | 0.749490 | − | 0.662016i | \(-0.230299\pi\) | ||||
0.749490 | + | 0.662016i | \(0.230299\pi\) | |||||||
\(968\) | 2.30478 | 0.0740786 | ||||||||
\(969\) | 1.03227 | 0.0331612 | ||||||||
\(970\) | −38.7624 | −1.24459 | ||||||||
\(971\) | −4.26613 | −0.136907 | −0.0684533 | − | 0.997654i | \(-0.521806\pi\) | ||||
−0.0684533 | + | 0.997654i | \(0.521806\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 30.5757 | 0.980212 | ||||||||
\(974\) | −3.78612 | −0.121315 | ||||||||
\(975\) | 2.02342 | 0.0648014 | ||||||||
\(976\) | 11.0740 | 0.354471 | ||||||||
\(977\) | 40.4957 | 1.29557 | 0.647786 | − | 0.761822i | \(-0.275695\pi\) | ||||
0.647786 | + | 0.761822i | \(0.275695\pi\) | |||||||
\(978\) | 9.85353 | 0.315081 | ||||||||
\(979\) | −2.25194 | −0.0719725 | ||||||||
\(980\) | 4.35549 | 0.139131 | ||||||||
\(981\) | 6.91309 | 0.220718 | ||||||||
\(982\) | −0.315595 | −0.0100710 | ||||||||
\(983\) | −26.8211 | −0.855460 | −0.427730 | − | 0.903907i | \(-0.640687\pi\) | ||||
−0.427730 | + | 0.903907i | \(0.640687\pi\) | |||||||
\(984\) | 6.40596 | 0.204215 | ||||||||
\(985\) | 70.2633 | 2.23877 | ||||||||
\(986\) | −3.56849 | −0.113644 | ||||||||
\(987\) | −21.9715 | −0.699359 | ||||||||
\(988\) | −0.467072 | −0.0148595 | ||||||||
\(989\) | −50.0928 | −1.59286 | ||||||||
\(990\) | 9.00805 | 0.286295 | ||||||||
\(991\) | 51.5895 | 1.63879 | 0.819397 | − | 0.573226i | \(-0.194308\pi\) | ||||
0.819397 | + | 0.573226i | \(0.194308\pi\) | |||||||
\(992\) | 3.18333 | 0.101071 | ||||||||
\(993\) | 0.606122 | 0.0192347 | ||||||||
\(994\) | −5.51991 | −0.175081 | ||||||||
\(995\) | 67.5357 | 2.14102 | ||||||||
\(996\) | 4.08187 | 0.129339 | ||||||||
\(997\) | −6.03196 | −0.191034 | −0.0955170 | − | 0.995428i | \(-0.530450\pi\) | ||||
−0.0955170 | + | 0.995428i | \(0.530450\pi\) | |||||||
\(998\) | −26.9669 | −0.853622 | ||||||||
\(999\) | 4.86635 | 0.153965 |
(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 | 6042.2.a.y.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.y.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial |