Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.60555 | −1.74073 | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.60555 | 1.23089 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.60555 | 1.05659 | 0.528293 | − | 0.849062i | \(-0.322832\pi\) | ||||
0.528293 | + | 0.849062i | \(0.322832\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.60555 | 1.00501 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39445 | 0.290763 | 0.145381 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145381 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.60555 | −0.870367 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60555 | 0.789846 | ||||||||
\(35\) | 4.60555 | 0.778480 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.21110 | −1.51430 | −0.757148 | − | 0.653243i | \(-0.773408\pi\) | ||||
−0.757148 | + | 0.653243i | \(0.773408\pi\) | |||||||
\(38\) | −4.60555 | −0.747119 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.21110 | −0.501490 | −0.250745 | − | 0.968053i | \(-0.580676\pi\) | ||||
−0.250745 | + | 0.968053i | \(0.580676\pi\) | |||||||
\(42\) | −4.60555 | −0.710652 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.39445 | −0.205600 | ||||||||
\(47\) | −9.21110 | −1.34358 | −0.671789 | − | 0.740743i | \(-0.734474\pi\) | ||||
−0.671789 | + | 0.740743i | \(0.734474\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 14.2111 | 2.03016 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 4.60555 | 0.644906 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.60555 | 0.615443 | ||||||||
\(57\) | −4.60555 | −0.610020 | ||||||||
\(58\) | −4.60555 | −0.604739 | ||||||||
\(59\) | −9.21110 | −1.19918 | −0.599592 | − | 0.800306i | \(-0.704670\pi\) | ||||
−0.599592 | + | 0.800306i | \(0.704670\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −11.2111 | −1.43543 | −0.717717 | − | 0.696335i | \(-0.754813\pi\) | ||||
−0.717717 | + | 0.696335i | \(0.754813\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −4.60555 | −0.580245 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.21110 | 0.392299 | 0.196149 | − | 0.980574i | \(-0.437156\pi\) | ||||
0.196149 | + | 0.980574i | \(0.437156\pi\) | |||||||
\(68\) | −4.60555 | −0.558505 | ||||||||
\(69\) | −1.39445 | −0.167872 | ||||||||
\(70\) | −4.60555 | −0.550469 | ||||||||
\(71\) | −9.21110 | −1.09316 | −0.546578 | − | 0.837408i | \(-0.684070\pi\) | ||||
−0.546578 | + | 0.837408i | \(0.684070\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.39445 | −0.163208 | −0.0816039 | − | 0.996665i | \(-0.526004\pi\) | ||||
−0.0816039 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(74\) | 9.21110 | 1.07077 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.60555 | 0.528293 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.21110 | 0.354607 | ||||||||
\(83\) | −2.78890 | −0.306121 | −0.153061 | − | 0.988217i | \(-0.548913\pi\) | ||||
−0.153061 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(84\) | 4.60555 | 0.502507 | ||||||||
\(85\) | 4.60555 | 0.499542 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | −4.60555 | −0.493767 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2111 | 1.61237 | 0.806187 | − | 0.591661i | \(-0.201528\pi\) | ||||
0.806187 | + | 0.591661i | \(0.201528\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.39445 | 0.145381 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 9.21110 | 0.950053 | ||||||||
\(95\) | −4.60555 | −0.472520 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.39445 | −0.141585 | −0.0707924 | − | 0.997491i | \(-0.522553\pi\) | ||||
−0.0707924 | + | 0.997491i | \(0.522553\pi\) | |||||||
\(98\) | −14.2111 | −1.43554 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.39445 | 0.735775 | 0.367888 | − | 0.929870i | \(-0.380081\pi\) | ||||
0.367888 | + | 0.929870i | \(0.380081\pi\) | |||||||
\(102\) | −4.60555 | −0.456018 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.60555 | −0.449456 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.39445 | −0.133564 | −0.0667820 | − | 0.997768i | \(-0.521273\pi\) | ||||
−0.0667820 | + | 0.997768i | \(0.521273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.21110 | 0.874279 | ||||||||
\(112\) | −4.60555 | −0.435184 | ||||||||
\(113\) | −13.8167 | −1.29976 | −0.649881 | − | 0.760036i | \(-0.725181\pi\) | ||||
−0.649881 | + | 0.760036i | \(0.725181\pi\) | |||||||
\(114\) | 4.60555 | 0.431349 | ||||||||
\(115\) | −1.39445 | −0.130033 | ||||||||
\(116\) | 4.60555 | 0.427615 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.21110 | 0.847951 | ||||||||
\(119\) | 21.2111 | 1.94442 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 11.2111 | 1.01501 | ||||||||
\(123\) | 3.21110 | 0.289535 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.60555 | 0.410295 | ||||||||
\(127\) | −1.21110 | −0.107468 | −0.0537340 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537340 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6056 | 1.97506 | 0.987528 | − | 0.157443i | \(-0.0503250\pi\) | ||||
0.987528 | + | 0.157443i | \(0.0503250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.2111 | −1.83924 | ||||||||
\(134\) | −3.21110 | −0.277397 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 4.60555 | 0.394923 | ||||||||
\(137\) | 3.21110 | 0.274343 | 0.137172 | − | 0.990547i | \(-0.456199\pi\) | ||||
0.137172 | + | 0.990547i | \(0.456199\pi\) | |||||||
\(138\) | 1.39445 | 0.118703 | ||||||||
\(139\) | 17.2111 | 1.45983 | 0.729913 | − | 0.683540i | \(-0.239560\pi\) | ||||
0.729913 | + | 0.683540i | \(0.239560\pi\) | |||||||
\(140\) | 4.60555 | 0.389240 | ||||||||
\(141\) | 9.21110 | 0.775715 | ||||||||
\(142\) | 9.21110 | 0.772979 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.60555 | −0.382470 | ||||||||
\(146\) | 1.39445 | 0.115405 | ||||||||
\(147\) | −14.2111 | −1.17211 | ||||||||
\(148\) | −9.21110 | −0.757148 | ||||||||
\(149\) | −15.2111 | −1.24614 | −0.623071 | − | 0.782165i | \(-0.714115\pi\) | ||||
−0.623071 | + | 0.782165i | \(0.714115\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 6.00000 | 0.488273 | 0.244137 | − | 0.969741i | \(-0.421495\pi\) | ||||
0.244137 | + | 0.969741i | \(0.421495\pi\) | |||||||
\(152\) | −4.60555 | −0.373560 | ||||||||
\(153\) | −4.60555 | −0.372337 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4222 | 1.62987 | 0.814935 | − | 0.579553i | \(-0.196773\pi\) | ||||
0.814935 | + | 0.579553i | \(0.196773\pi\) | |||||||
\(158\) | 14.4222 | 1.14737 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.42221 | −0.506141 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 24.4222 | 1.91289 | 0.956447 | − | 0.291905i | \(-0.0942891\pi\) | ||||
0.956447 | + | 0.291905i | \(0.0942891\pi\) | |||||||
\(164\) | −3.21110 | −0.250745 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.78890 | 0.216460 | ||||||||
\(167\) | 9.21110 | 0.712777 | 0.356388 | − | 0.934338i | \(-0.384008\pi\) | ||||
0.356388 | + | 0.934338i | \(0.384008\pi\) | |||||||
\(168\) | −4.60555 | −0.355326 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.60555 | −0.353230 | ||||||||
\(171\) | 4.60555 | 0.352195 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | 12.4222 | 0.944443 | 0.472221 | − | 0.881480i | \(-0.343452\pi\) | ||||
0.472221 | + | 0.881480i | \(0.343452\pi\) | |||||||
\(174\) | 4.60555 | 0.349146 | ||||||||
\(175\) | −4.60555 | −0.348147 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.21110 | 0.692349 | ||||||||
\(178\) | −15.2111 | −1.14012 | ||||||||
\(179\) | 19.8167 | 1.48117 | 0.740583 | − | 0.671965i | \(-0.234549\pi\) | ||||
0.740583 | + | 0.671965i | \(0.234549\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −8.42221 | −0.626018 | −0.313009 | − | 0.949750i | \(-0.601337\pi\) | ||||
−0.313009 | + | 0.949750i | \(0.601337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2111 | 0.828749 | ||||||||
\(184\) | −1.39445 | −0.102800 | ||||||||
\(185\) | 9.21110 | 0.677214 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.21110 | −0.671789 | ||||||||
\(189\) | 4.60555 | 0.335005 | ||||||||
\(190\) | 4.60555 | 0.334122 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.81665 | 0.562655 | 0.281328 | − | 0.959612i | \(-0.409225\pi\) | ||||
0.281328 | + | 0.959612i | \(0.409225\pi\) | |||||||
\(194\) | 1.39445 | 0.100116 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.2111 | 1.01508 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4222 | −1.58947 | −0.794734 | − | 0.606958i | \(-0.792390\pi\) | ||||
−0.794734 | + | 0.606958i | \(0.792390\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −3.21110 | −0.226494 | ||||||||
\(202\) | −7.39445 | −0.520272 | ||||||||
\(203\) | −21.2111 | −1.48873 | ||||||||
\(204\) | 4.60555 | 0.322453 | ||||||||
\(205\) | 3.21110 | 0.224273 | ||||||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 1.39445 | 0.0969209 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.60555 | 0.317813 | ||||||||
\(211\) | −17.2111 | −1.18486 | −0.592431 | − | 0.805622i | \(-0.701832\pi\) | ||||
−0.592431 | + | 0.805622i | \(0.701832\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 9.21110 | 0.631134 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 27.6333 | 1.87587 | ||||||||
\(218\) | 1.39445 | 0.0944440 | ||||||||
\(219\) | 1.39445 | 0.0942281 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.21110 | −0.618209 | ||||||||
\(223\) | −1.81665 | −0.121652 | −0.0608261 | − | 0.998148i | \(-0.519373\pi\) | ||||
−0.0608261 | + | 0.998148i | \(0.519373\pi\) | |||||||
\(224\) | 4.60555 | 0.307721 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.8167 | 0.919070 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | −4.60555 | −0.305010 | ||||||||
\(229\) | −19.8167 | −1.30952 | −0.654761 | − | 0.755836i | \(-0.727231\pi\) | ||||
−0.654761 | + | 0.755836i | \(0.727231\pi\) | |||||||
\(230\) | 1.39445 | 0.0919472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.60555 | −0.302369 | ||||||||
\(233\) | 1.81665 | 0.119013 | 0.0595065 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595065 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.21110 | 0.600866 | ||||||||
\(236\) | −9.21110 | −0.599592 | ||||||||
\(237\) | 14.4222 | 0.936823 | ||||||||
\(238\) | −21.2111 | −1.37491 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −6.42221 | −0.413691 | −0.206845 | − | 0.978374i | \(-0.566320\pi\) | ||||
−0.206845 | + | 0.978374i | \(0.566320\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.2111 | −0.717717 | ||||||||
\(245\) | −14.2111 | −0.907914 | ||||||||
\(246\) | −3.21110 | −0.204732 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 2.78890 | 0.176739 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 13.3944 | 0.845450 | 0.422725 | − | 0.906258i | \(-0.361074\pi\) | ||||
0.422725 | + | 0.906258i | \(0.361074\pi\) | |||||||
\(252\) | −4.60555 | −0.290122 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.21110 | 0.0759913 | ||||||||
\(255\) | −4.60555 | −0.288411 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.6056 | 1.78437 | 0.892183 | − | 0.451675i | \(-0.149173\pi\) | ||||
0.892183 | + | 0.451675i | \(0.149173\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 42.4222 | 2.63599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.60555 | 0.285076 | ||||||||
\(262\) | −22.6056 | −1.39658 | ||||||||
\(263\) | −7.81665 | −0.481996 | −0.240998 | − | 0.970526i | \(-0.577475\pi\) | ||||
−0.240998 | + | 0.970526i | \(0.577475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 21.2111 | 1.30054 | ||||||||
\(267\) | −15.2111 | −0.930904 | ||||||||
\(268\) | 3.21110 | 0.196149 | ||||||||
\(269\) | 25.8167 | 1.57407 | 0.787035 | − | 0.616909i | \(-0.211615\pi\) | ||||
0.787035 | + | 0.616909i | \(0.211615\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −0.422205 | −0.0256471 | −0.0128236 | − | 0.999918i | \(-0.504082\pi\) | ||||
−0.0128236 | + | 0.999918i | \(0.504082\pi\) | |||||||
\(272\) | −4.60555 | −0.279253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.21110 | −0.193990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.39445 | −0.0839359 | ||||||||
\(277\) | 16.4222 | 0.986715 | 0.493357 | − | 0.869827i | \(-0.335770\pi\) | ||||
0.493357 | + | 0.869827i | \(0.335770\pi\) | |||||||
\(278\) | −17.2111 | −1.03225 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | −4.60555 | −0.275234 | ||||||||
\(281\) | 27.2111 | 1.62328 | 0.811639 | − | 0.584159i | \(-0.198576\pi\) | ||||
0.811639 | + | 0.584159i | \(0.198576\pi\) | |||||||
\(282\) | −9.21110 | −0.548513 | ||||||||
\(283\) | −10.4222 | −0.619536 | −0.309768 | − | 0.950812i | \(-0.600251\pi\) | ||||
−0.309768 | + | 0.950812i | \(0.600251\pi\) | |||||||
\(284\) | −9.21110 | −0.546578 | ||||||||
\(285\) | 4.60555 | 0.272809 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7889 | 0.872961 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | 4.60555 | 0.270447 | ||||||||
\(291\) | 1.39445 | 0.0817440 | ||||||||
\(292\) | −1.39445 | −0.0816039 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 14.2111 | 0.828808 | ||||||||
\(295\) | 9.21110 | 0.536291 | ||||||||
\(296\) | 9.21110 | 0.535384 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2111 | 0.881156 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 36.8444 | 2.12368 | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | −7.39445 | −0.424800 | ||||||||
\(304\) | 4.60555 | 0.264146 | ||||||||
\(305\) | 11.2111 | 0.641946 | ||||||||
\(306\) | 4.60555 | 0.263282 | ||||||||
\(307\) | −8.78890 | −0.501609 | −0.250804 | − | 0.968038i | \(-0.580695\pi\) | ||||
−0.250804 | + | 0.968038i | \(0.580695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.57779 | 0.202229 | 0.101114 | − | 0.994875i | \(-0.467759\pi\) | ||||
0.101114 | + | 0.994875i | \(0.467759\pi\) | |||||||
\(314\) | −20.4222 | −1.15249 | ||||||||
\(315\) | 4.60555 | 0.259493 | ||||||||
\(316\) | −14.4222 | −0.811312 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.42221 | 0.357895 | ||||||||
\(323\) | −21.2111 | −1.18022 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.4222 | −1.35262 | ||||||||
\(327\) | 1.39445 | 0.0771132 | ||||||||
\(328\) | 3.21110 | 0.177303 | ||||||||
\(329\) | 42.4222 | 2.33881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.6056 | 0.912724 | 0.456362 | − | 0.889794i | \(-0.349152\pi\) | ||||
0.456362 | + | 0.889794i | \(0.349152\pi\) | |||||||
\(332\) | −2.78890 | −0.153061 | ||||||||
\(333\) | −9.21110 | −0.504765 | ||||||||
\(334\) | −9.21110 | −0.504009 | ||||||||
\(335\) | −3.21110 | −0.175441 | ||||||||
\(336\) | 4.60555 | 0.251253 | ||||||||
\(337\) | −13.6333 | −0.742654 | −0.371327 | − | 0.928502i | \(-0.621097\pi\) | ||||
−0.371327 | + | 0.928502i | \(0.621097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8167 | 0.750418 | ||||||||
\(340\) | 4.60555 | 0.249771 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.60555 | −0.249040 | ||||||||
\(343\) | −33.2111 | −1.79323 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 1.39445 | 0.0750746 | ||||||||
\(346\) | −12.4222 | −0.667822 | ||||||||
\(347\) | −27.6333 | −1.48343 | −0.741717 | − | 0.670713i | \(-0.765988\pi\) | ||||
−0.741717 | + | 0.670713i | \(0.765988\pi\) | |||||||
\(348\) | −4.60555 | −0.246883 | ||||||||
\(349\) | −7.81665 | −0.418416 | −0.209208 | − | 0.977871i | \(-0.567089\pi\) | ||||
−0.209208 | + | 0.977871i | \(0.567089\pi\) | |||||||
\(350\) | 4.60555 | 0.246177 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.78890 | 0.467786 | 0.233893 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233893 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(354\) | −9.21110 | −0.489565 | ||||||||
\(355\) | 9.21110 | 0.488875 | ||||||||
\(356\) | 15.2111 | 0.806187 | ||||||||
\(357\) | −21.2111 | −1.12261 | ||||||||
\(358\) | −19.8167 | −1.04734 | ||||||||
\(359\) | 15.6333 | 0.825094 | 0.412547 | − | 0.910936i | \(-0.364639\pi\) | ||||
0.412547 | + | 0.910936i | \(0.364639\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 2.21110 | 0.116374 | ||||||||
\(362\) | 8.42221 | 0.442661 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.39445 | 0.0729888 | ||||||||
\(366\) | −11.2111 | −0.586014 | ||||||||
\(367\) | −19.6333 | −1.02485 | −0.512425 | − | 0.858732i | \(-0.671253\pi\) | ||||
−0.512425 | + | 0.858732i | \(0.671253\pi\) | |||||||
\(368\) | 1.39445 | 0.0726907 | ||||||||
\(369\) | −3.21110 | −0.167163 | ||||||||
\(370\) | −9.21110 | −0.478862 | ||||||||
\(371\) | −27.6333 | −1.43465 | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −20.4222 | −1.05742 | −0.528711 | − | 0.848802i | \(-0.677324\pi\) | ||||
−0.528711 | + | 0.848802i | \(0.677324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 9.21110 | 0.475026 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.60555 | −0.236884 | ||||||||
\(379\) | −35.0278 | −1.79925 | −0.899627 | − | 0.436658i | \(-0.856162\pi\) | ||||
−0.899627 | + | 0.436658i | \(0.856162\pi\) | |||||||
\(380\) | −4.60555 | −0.236260 | ||||||||
\(381\) | 1.21110 | 0.0620467 | ||||||||
\(382\) | 12.0000 | 0.613973 | ||||||||
\(383\) | 27.6333 | 1.41200 | 0.705998 | − | 0.708214i | \(-0.250499\pi\) | ||||
0.705998 | + | 0.708214i | \(0.250499\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.81665 | −0.397857 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −1.39445 | −0.0707924 | ||||||||
\(389\) | −4.60555 | −0.233511 | −0.116755 | − | 0.993161i | \(-0.537249\pi\) | ||||
−0.116755 | + | 0.993161i | \(0.537249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.42221 | −0.324785 | ||||||||
\(392\) | −14.2111 | −0.717769 | ||||||||
\(393\) | −22.6056 | −1.14030 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 14.4222 | 0.725660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.63331 | −0.182350 | −0.0911752 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911752 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(398\) | 22.4222 | 1.12392 | ||||||||
\(399\) | 21.2111 | 1.06188 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 8.78890 | 0.438897 | 0.219448 | − | 0.975624i | \(-0.429574\pi\) | ||||
0.219448 | + | 0.975624i | \(0.429574\pi\) | |||||||
\(402\) | 3.21110 | 0.160155 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.39445 | 0.367888 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 21.2111 | 1.05269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.60555 | −0.228009 | ||||||||
\(409\) | 14.7889 | 0.731264 | 0.365632 | − | 0.930760i | \(-0.380853\pi\) | ||||
0.365632 | + | 0.930760i | \(0.380853\pi\) | |||||||
\(410\) | −3.21110 | −0.158585 | ||||||||
\(411\) | −3.21110 | −0.158392 | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | 42.4222 | 2.08746 | ||||||||
\(414\) | −1.39445 | −0.0685334 | ||||||||
\(415\) | 2.78890 | 0.136902 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.2111 | −0.842831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.18335 | 0.204370 | 0.102185 | − | 0.994765i | \(-0.467417\pi\) | ||||
0.102185 | + | 0.994765i | \(0.467417\pi\) | |||||||
\(420\) | −4.60555 | −0.224728 | ||||||||
\(421\) | 19.8167 | 0.965805 | 0.482902 | − | 0.875674i | \(-0.339583\pi\) | ||||
0.482902 | + | 0.875674i | \(0.339583\pi\) | |||||||
\(422\) | 17.2111 | 0.837823 | ||||||||
\(423\) | −9.21110 | −0.447859 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −4.60555 | −0.223402 | ||||||||
\(426\) | −9.21110 | −0.446279 | ||||||||
\(427\) | 51.6333 | 2.49871 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.2111 | −0.923227 | −0.461613 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(434\) | −27.6333 | −1.32644 | ||||||||
\(435\) | 4.60555 | 0.220819 | ||||||||
\(436\) | −1.39445 | −0.0667820 | ||||||||
\(437\) | 6.42221 | 0.307216 | ||||||||
\(438\) | −1.39445 | −0.0666293 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.2111 | 0.676719 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6333 | 0.742761 | 0.371380 | − | 0.928481i | \(-0.378885\pi\) | ||||
0.371380 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(444\) | 9.21110 | 0.437140 | ||||||||
\(445\) | −15.2111 | −0.721075 | ||||||||
\(446\) | 1.81665 | 0.0860211 | ||||||||
\(447\) | 15.2111 | 0.719460 | ||||||||
\(448\) | −4.60555 | −0.217592 | ||||||||
\(449\) | 33.6333 | 1.58725 | 0.793627 | − | 0.608405i | \(-0.208190\pi\) | ||||
0.793627 | + | 0.608405i | \(0.208190\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −13.8167 | −0.649881 | ||||||||
\(453\) | −6.00000 | −0.281905 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.60555 | 0.215675 | ||||||||
\(457\) | −38.2389 | −1.78874 | −0.894369 | − | 0.447330i | \(-0.852375\pi\) | ||||
−0.894369 | + | 0.447330i | \(0.852375\pi\) | |||||||
\(458\) | 19.8167 | 0.925971 | ||||||||
\(459\) | 4.60555 | 0.214969 | ||||||||
\(460\) | −1.39445 | −0.0650165 | ||||||||
\(461\) | 33.6333 | 1.56646 | 0.783230 | − | 0.621733i | \(-0.213571\pi\) | ||||
0.783230 | + | 0.621733i | \(0.213571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.3944 | −1.45902 | −0.729512 | − | 0.683968i | \(-0.760253\pi\) | ||||
−0.729512 | + | 0.683968i | \(0.760253\pi\) | |||||||
\(464\) | 4.60555 | 0.213807 | ||||||||
\(465\) | −6.00000 | −0.278243 | ||||||||
\(466\) | −1.81665 | −0.0841549 | ||||||||
\(467\) | 30.4222 | 1.40777 | 0.703886 | − | 0.710313i | \(-0.251447\pi\) | ||||
0.703886 | + | 0.710313i | \(0.251447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7889 | −0.682888 | ||||||||
\(470\) | −9.21110 | −0.424876 | ||||||||
\(471\) | −20.4222 | −0.941006 | ||||||||
\(472\) | 9.21110 | 0.423975 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −14.4222 | −0.662434 | ||||||||
\(475\) | 4.60555 | 0.211317 | ||||||||
\(476\) | 21.2111 | 0.972209 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.57779 | 0.254856 | 0.127428 | − | 0.991848i | \(-0.459328\pi\) | ||||
0.127428 | + | 0.991848i | \(0.459328\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.42221 | 0.292523 | ||||||||
\(483\) | 6.42221 | 0.292220 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 1.39445 | 0.0633187 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 0.972244 | 0.0440566 | 0.0220283 | − | 0.999757i | \(-0.492988\pi\) | ||||
0.0220283 | + | 0.999757i | \(0.492988\pi\) | |||||||
\(488\) | 11.2111 | 0.507503 | ||||||||
\(489\) | −24.4222 | −1.10441 | ||||||||
\(490\) | 14.2111 | 0.641992 | ||||||||
\(491\) | −7.81665 | −0.352761 | −0.176380 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176380 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(492\) | 3.21110 | 0.144768 | ||||||||
\(493\) | −21.2111 | −0.955300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 42.4222 | 1.90290 | ||||||||
\(498\) | −2.78890 | −0.124973 | ||||||||
\(499\) | −23.0278 | −1.03086 | −0.515432 | − | 0.856930i | \(-0.672369\pi\) | ||||
−0.515432 | + | 0.856930i | \(0.672369\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −9.21110 | −0.411522 | ||||||||
\(502\) | −13.3944 | −0.597824 | ||||||||
\(503\) | 23.4500 | 1.04558 | 0.522791 | − | 0.852461i | \(-0.324891\pi\) | ||||
0.522791 | + | 0.852461i | \(0.324891\pi\) | |||||||
\(504\) | 4.60555 | 0.205148 | ||||||||
\(505\) | −7.39445 | −0.329049 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.21110 | −0.0537340 | ||||||||
\(509\) | 33.6333 | 1.49077 | 0.745385 | − | 0.666634i | \(-0.232266\pi\) | ||||
0.745385 | + | 0.666634i | \(0.232266\pi\) | |||||||
\(510\) | 4.60555 | 0.203937 | ||||||||
\(511\) | 6.42221 | 0.284102 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.60555 | −0.203340 | ||||||||
\(514\) | −28.6056 | −1.26174 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −42.4222 | −1.86392 | ||||||||
\(519\) | −12.4222 | −0.545274 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6333 | 0.947772 | 0.473886 | − | 0.880586i | \(-0.342851\pi\) | ||||
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(522\) | −4.60555 | −0.201580 | ||||||||
\(523\) | 32.8444 | 1.43619 | 0.718093 | − | 0.695947i | \(-0.245015\pi\) | ||||
0.718093 | + | 0.695947i | \(0.245015\pi\) | |||||||
\(524\) | 22.6056 | 0.987528 | ||||||||
\(525\) | 4.60555 | 0.201003 | ||||||||
\(526\) | 7.81665 | 0.340822 | ||||||||
\(527\) | 27.6333 | 1.20373 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0555 | −0.915457 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | −9.21110 | −0.399728 | ||||||||
\(532\) | −21.2111 | −0.919618 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15.2111 | 0.658249 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.21110 | −0.138699 | ||||||||
\(537\) | −19.8167 | −0.855152 | ||||||||
\(538\) | −25.8167 | −1.11303 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 6.97224 | 0.299760 | 0.149880 | − | 0.988704i | \(-0.452111\pi\) | ||||
0.149880 | + | 0.988704i | \(0.452111\pi\) | |||||||
\(542\) | 0.422205 | 0.0181353 | ||||||||
\(543\) | 8.42221 | 0.361431 | ||||||||
\(544\) | 4.60555 | 0.197461 | ||||||||
\(545\) | 1.39445 | 0.0597316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4222 | 0.616649 | 0.308324 | − | 0.951281i | \(-0.400232\pi\) | ||||
0.308324 | + | 0.951281i | \(0.400232\pi\) | |||||||
\(548\) | 3.21110 | 0.137172 | ||||||||
\(549\) | −11.2111 | −0.478478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.2111 | 0.903623 | ||||||||
\(552\) | 1.39445 | 0.0593517 | ||||||||
\(553\) | 66.4222 | 2.82456 | ||||||||
\(554\) | −16.4222 | −0.697713 | ||||||||
\(555\) | −9.21110 | −0.390990 | ||||||||
\(556\) | 17.2111 | 0.729913 | ||||||||
\(557\) | 11.5778 | 0.490567 | 0.245283 | − | 0.969451i | \(-0.421119\pi\) | ||||
0.245283 | + | 0.969451i | \(0.421119\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.60555 | 0.194620 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.2111 | −1.14783 | ||||||||
\(563\) | −34.0555 | −1.43527 | −0.717634 | − | 0.696420i | \(-0.754775\pi\) | ||||
−0.717634 | + | 0.696420i | \(0.754775\pi\) | |||||||
\(564\) | 9.21110 | 0.387857 | ||||||||
\(565\) | 13.8167 | 0.581271 | ||||||||
\(566\) | 10.4222 | 0.438078 | ||||||||
\(567\) | −4.60555 | −0.193415 | ||||||||
\(568\) | 9.21110 | 0.386489 | ||||||||
\(569\) | −33.6333 | −1.40998 | −0.704991 | − | 0.709216i | \(-0.749049\pi\) | ||||
−0.704991 | + | 0.709216i | \(0.749049\pi\) | |||||||
\(570\) | −4.60555 | −0.192905 | ||||||||
\(571\) | 30.0555 | 1.25778 | 0.628892 | − | 0.777493i | \(-0.283509\pi\) | ||||
0.628892 | + | 0.777493i | \(0.283509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −14.7889 | −0.617277 | ||||||||
\(575\) | 1.39445 | 0.0581525 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 37.3944 | 1.55675 | 0.778376 | − | 0.627799i | \(-0.216044\pi\) | ||||
0.778376 | + | 0.627799i | \(0.216044\pi\) | |||||||
\(578\) | −4.21110 | −0.175159 | ||||||||
\(579\) | −7.81665 | −0.324849 | ||||||||
\(580\) | −4.60555 | −0.191235 | ||||||||
\(581\) | 12.8444 | 0.532876 | ||||||||
\(582\) | −1.39445 | −0.0578018 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.39445 | 0.0577027 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 6.42221 | 0.265073 | 0.132536 | − | 0.991178i | \(-0.457688\pi\) | ||||
0.132536 | + | 0.991178i | \(0.457688\pi\) | |||||||
\(588\) | −14.2111 | −0.586056 | ||||||||
\(589\) | −27.6333 | −1.13861 | ||||||||
\(590\) | −9.21110 | −0.379215 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −9.21110 | −0.378574 | ||||||||
\(593\) | −24.4222 | −1.00290 | −0.501450 | − | 0.865187i | \(-0.667200\pi\) | ||||
−0.501450 | + | 0.865187i | \(0.667200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.2111 | −0.869570 | ||||||||
\(596\) | −15.2111 | −0.623071 | ||||||||
\(597\) | 22.4222 | 0.917680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 1.63331 | 0.0666240 | 0.0333120 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333120 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(602\) | −36.8444 | −1.50167 | ||||||||
\(603\) | 3.21110 | 0.130766 | ||||||||
\(604\) | 6.00000 | 0.244137 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 7.39445 | 0.300379 | ||||||||
\(607\) | 17.2111 | 0.698577 | 0.349289 | − | 0.937015i | \(-0.386423\pi\) | ||||
0.349289 | + | 0.937015i | \(0.386423\pi\) | |||||||
\(608\) | −4.60555 | −0.186780 | ||||||||
\(609\) | 21.2111 | 0.859517 | ||||||||
\(610\) | −11.2111 | −0.453924 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.60555 | −0.186168 | ||||||||
\(613\) | 33.2111 | 1.34138 | 0.670692 | − | 0.741736i | \(-0.265997\pi\) | ||||
0.670692 | + | 0.741736i | \(0.265997\pi\) | |||||||
\(614\) | 8.78890 | 0.354691 | ||||||||
\(615\) | −3.21110 | −0.129484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.4222 | −0.500099 | −0.250050 | − | 0.968233i | \(-0.580447\pi\) | ||||
−0.250050 | + | 0.968233i | \(0.580447\pi\) | |||||||
\(618\) | 4.00000 | 0.160904 | ||||||||
\(619\) | 25.8167 | 1.03766 | 0.518829 | − | 0.854878i | \(-0.326368\pi\) | ||||
0.518829 | + | 0.854878i | \(0.326368\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | −1.39445 | −0.0559573 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | −70.0555 | −2.80671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.57779 | −0.142997 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.4222 | 0.814935 | ||||||||
\(629\) | 42.4222 | 1.69148 | ||||||||
\(630\) | −4.60555 | −0.183490 | ||||||||
\(631\) | 3.21110 | 0.127832 | 0.0639160 | − | 0.997955i | \(-0.479641\pi\) | ||||
0.0639160 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(632\) | 14.4222 | 0.573685 | ||||||||
\(633\) | 17.2111 | 0.684080 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 1.21110 | 0.0480611 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.21110 | −0.364386 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.422205 | −0.0166761 | −0.00833805 | − | 0.999965i | \(-0.502654\pi\) | ||||
−0.00833805 | + | 0.999965i | \(0.502654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.63331 | −0.379901 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(644\) | −6.42221 | −0.253070 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 21.2111 | 0.834540 | ||||||||
\(647\) | 34.6056 | 1.36048 | 0.680242 | − | 0.732987i | \(-0.261875\pi\) | ||||
0.680242 | + | 0.732987i | \(0.261875\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6333 | −1.08303 | ||||||||
\(652\) | 24.4222 | 0.956447 | ||||||||
\(653\) | 39.2111 | 1.53445 | 0.767225 | − | 0.641379i | \(-0.221637\pi\) | ||||
0.767225 | + | 0.641379i | \(0.221637\pi\) | |||||||
\(654\) | −1.39445 | −0.0545273 | ||||||||
\(655\) | −22.6056 | −0.883272 | ||||||||
\(656\) | −3.21110 | −0.125372 | ||||||||
\(657\) | −1.39445 | −0.0544026 | ||||||||
\(658\) | −42.4222 | −1.65379 | ||||||||
\(659\) | −26.2389 | −1.02212 | −0.511060 | − | 0.859545i | \(-0.670747\pi\) | ||||
−0.511060 | + | 0.859545i | \(0.670747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.2389 | 1.95407 | 0.977033 | − | 0.213090i | \(-0.0683528\pi\) | ||||
0.977033 | + | 0.213090i | \(0.0683528\pi\) | |||||||
\(662\) | −16.6056 | −0.645393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.78890 | 0.108230 | ||||||||
\(665\) | 21.2111 | 0.822531 | ||||||||
\(666\) | 9.21110 | 0.356923 | ||||||||
\(667\) | 6.42221 | 0.248669 | ||||||||
\(668\) | 9.21110 | 0.356388 | ||||||||
\(669\) | 1.81665 | 0.0702359 | ||||||||
\(670\) | 3.21110 | 0.124056 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.60555 | −0.177663 | ||||||||
\(673\) | 37.6333 | 1.45066 | 0.725329 | − | 0.688403i | \(-0.241688\pi\) | ||||
0.725329 | + | 0.688403i | \(0.241688\pi\) | |||||||
\(674\) | 13.6333 | 0.525135 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.0555 | −1.07826 | −0.539130 | − | 0.842222i | \(-0.681247\pi\) | ||||
−0.539130 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(678\) | −13.8167 | −0.530625 | ||||||||
\(679\) | 6.42221 | 0.246462 | ||||||||
\(680\) | −4.60555 | −0.176615 | ||||||||
\(681\) | 24.0000 | 0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.21110 | 0.352453 | 0.176227 | − | 0.984350i | \(-0.443611\pi\) | ||||
0.176227 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(684\) | 4.60555 | 0.176098 | ||||||||
\(685\) | −3.21110 | −0.122690 | ||||||||
\(686\) | 33.2111 | 1.26801 | ||||||||
\(687\) | 19.8167 | 0.756053 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.39445 | −0.0530858 | ||||||||
\(691\) | −20.2389 | −0.769922 | −0.384961 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384961 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(692\) | 12.4222 | 0.472221 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.6333 | 1.04895 | ||||||||
\(695\) | −17.2111 | −0.652854 | ||||||||
\(696\) | 4.60555 | 0.174573 | ||||||||
\(697\) | 14.7889 | 0.560169 | ||||||||
\(698\) | 7.81665 | 0.295865 | ||||||||
\(699\) | −1.81665 | −0.0687122 | ||||||||
\(700\) | −4.60555 | −0.174073 | ||||||||
\(701\) | −47.0278 | −1.77621 | −0.888107 | − | 0.459637i | \(-0.847980\pi\) | ||||
−0.888107 | + | 0.459637i | \(0.847980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.4222 | −1.59998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.21110 | −0.346910 | ||||||||
\(706\) | −8.78890 | −0.330775 | ||||||||
\(707\) | −34.0555 | −1.28079 | ||||||||
\(708\) | 9.21110 | 0.346174 | ||||||||
\(709\) | −1.39445 | −0.0523696 | −0.0261848 | − | 0.999657i | \(-0.508336\pi\) | ||||
−0.0261848 | + | 0.999657i | \(0.508336\pi\) | |||||||
\(710\) | −9.21110 | −0.345687 | ||||||||
\(711\) | −14.4222 | −0.540875 | ||||||||
\(712\) | −15.2111 | −0.570060 | ||||||||
\(713\) | −8.36669 | −0.313335 | ||||||||
\(714\) | 21.2111 | 0.793806 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.8167 | 0.740583 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.6333 | −0.583430 | ||||||||
\(719\) | 51.6333 | 1.92560 | 0.962799 | − | 0.270220i | \(-0.0870963\pi\) | ||||
0.962799 | + | 0.270220i | \(0.0870963\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −18.4222 | −0.686079 | ||||||||
\(722\) | −2.21110 | −0.0822887 | ||||||||
\(723\) | 6.42221 | 0.238844 | ||||||||
\(724\) | −8.42221 | −0.313009 | ||||||||
\(725\) | 4.60555 | 0.171046 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | 14.4222 | 0.534890 | 0.267445 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267445 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.39445 | −0.0516109 | ||||||||
\(731\) | 36.8444 | 1.36274 | ||||||||
\(732\) | 11.2111 | 0.414374 | ||||||||
\(733\) | 34.0555 | 1.25787 | 0.628935 | − | 0.777458i | \(-0.283491\pi\) | ||||
0.628935 | + | 0.777458i | \(0.283491\pi\) | |||||||
\(734\) | 19.6333 | 0.724679 | ||||||||
\(735\) | 14.2111 | 0.524184 | ||||||||
\(736\) | −1.39445 | −0.0514001 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.21110 | 0.118202 | ||||||||
\(739\) | 20.2389 | 0.744498 | 0.372249 | − | 0.928133i | \(-0.378587\pi\) | ||||
0.372249 | + | 0.928133i | \(0.378587\pi\) | |||||||
\(740\) | 9.21110 | 0.338607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.6333 | 1.01445 | ||||||||
\(743\) | −36.8444 | −1.35169 | −0.675845 | − | 0.737044i | \(-0.736221\pi\) | ||||
−0.675845 | + | 0.737044i | \(0.736221\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 15.2111 | 0.557292 | ||||||||
\(746\) | 20.4222 | 0.747710 | ||||||||
\(747\) | −2.78890 | −0.102040 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 10.4222 | 0.380312 | 0.190156 | − | 0.981754i | \(-0.439101\pi\) | ||||
0.190156 | + | 0.981754i | \(0.439101\pi\) | |||||||
\(752\) | −9.21110 | −0.335894 | ||||||||
\(753\) | −13.3944 | −0.488121 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | 4.60555 | 0.167502 | ||||||||
\(757\) | 12.7889 | 0.464820 | 0.232410 | − | 0.972618i | \(-0.425339\pi\) | ||||
0.232410 | + | 0.972618i | \(0.425339\pi\) | |||||||
\(758\) | 35.0278 | 1.27227 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.60555 | 0.167061 | ||||||||
\(761\) | 33.6333 | 1.21921 | 0.609603 | − | 0.792707i | \(-0.291329\pi\) | ||||
0.609603 | + | 0.792707i | \(0.291329\pi\) | |||||||
\(762\) | −1.21110 | −0.0438736 | ||||||||
\(763\) | 6.42221 | 0.232499 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 4.60555 | 0.166514 | ||||||||
\(766\) | −27.6333 | −0.998432 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.8444 | 0.463181 | 0.231591 | − | 0.972813i | \(-0.425607\pi\) | ||||
0.231591 | + | 0.972813i | \(0.425607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.6056 | −1.03020 | ||||||||
\(772\) | 7.81665 | 0.281328 | ||||||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 1.39445 | 0.0500578 | ||||||||
\(777\) | −42.4222 | −1.52189 | ||||||||
\(778\) | 4.60555 | 0.165117 | ||||||||
\(779\) | −14.7889 | −0.529867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.42221 | 0.229658 | ||||||||
\(783\) | −4.60555 | −0.164589 | ||||||||
\(784\) | 14.2111 | 0.507539 | ||||||||
\(785\) | −20.4222 | −0.728900 | ||||||||
\(786\) | 22.6056 | 0.806313 | ||||||||
\(787\) | 49.2666 | 1.75617 | 0.878083 | − | 0.478509i | \(-0.158823\pi\) | ||||
0.878083 | + | 0.478509i | \(0.158823\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 7.81665 | 0.278280 | ||||||||
\(790\) | −14.4222 | −0.513119 | ||||||||
\(791\) | 63.6333 | 2.26254 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.63331 | 0.128941 | ||||||||
\(795\) | 6.00000 | 0.212798 | ||||||||
\(796\) | −22.4222 | −0.794734 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | −21.2111 | −0.750865 | ||||||||
\(799\) | 42.4222 | 1.50079 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 15.2111 | 0.537458 | ||||||||
\(802\) | −8.78890 | −0.310347 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.21110 | −0.113247 | ||||||||
\(805\) | 6.42221 | 0.226353 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.8167 | −0.908789 | ||||||||
\(808\) | −7.39445 | −0.260136 | ||||||||
\(809\) | −6.84441 | −0.240637 | −0.120318 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −32.2389 | −1.13206 | −0.566030 | − | 0.824385i | \(-0.691521\pi\) | ||||
−0.566030 | + | 0.824385i | \(0.691521\pi\) | |||||||
\(812\) | −21.2111 | −0.744364 | ||||||||
\(813\) | 0.422205 | 0.0148074 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.4222 | −0.855473 | ||||||||
\(816\) | 4.60555 | 0.161227 | ||||||||
\(817\) | −36.8444 | −1.28902 | ||||||||
\(818\) | −14.7889 | −0.517082 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.21110 | 0.112137 | ||||||||
\(821\) | 3.21110 | 0.112068 | 0.0560341 | − | 0.998429i | \(-0.482154\pi\) | ||||
0.0560341 | + | 0.998429i | \(0.482154\pi\) | |||||||
\(822\) | 3.21110 | 0.112000 | ||||||||
\(823\) | 4.00000 | 0.139431 | 0.0697156 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697156 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(824\) | −4.00000 | −0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42.4222 | −1.47606 | ||||||||
\(827\) | −27.6333 | −0.960904 | −0.480452 | − | 0.877021i | \(-0.659527\pi\) | ||||
−0.480452 | + | 0.877021i | \(0.659527\pi\) | |||||||
\(828\) | 1.39445 | 0.0484604 | ||||||||
\(829\) | −46.8444 | −1.62697 | −0.813487 | − | 0.581583i | \(-0.802433\pi\) | ||||
−0.813487 | + | 0.581583i | \(0.802433\pi\) | |||||||
\(830\) | −2.78890 | −0.0968040 | ||||||||
\(831\) | −16.4222 | −0.569680 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −65.4500 | −2.26771 | ||||||||
\(834\) | 17.2111 | 0.595972 | ||||||||
\(835\) | −9.21110 | −0.318763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | −4.18335 | −0.144511 | ||||||||
\(839\) | −18.4222 | −0.636005 | −0.318003 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318003 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(840\) | 4.60555 | 0.158907 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | −19.8167 | −0.682927 | ||||||||
\(843\) | −27.2111 | −0.937200 | ||||||||
\(844\) | −17.2111 | −0.592431 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.21110 | 0.316684 | ||||||||
\(847\) | 50.6611 | 1.74073 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 10.4222 | 0.357689 | ||||||||
\(850\) | 4.60555 | 0.157969 | ||||||||
\(851\) | −12.8444 | −0.440301 | ||||||||
\(852\) | 9.21110 | 0.315567 | ||||||||
\(853\) | −14.7889 | −0.506362 | −0.253181 | − | 0.967419i | \(-0.581477\pi\) | ||||
−0.253181 | + | 0.967419i | \(0.581477\pi\) | |||||||
\(854\) | −51.6333 | −1.76686 | ||||||||
\(855\) | −4.60555 | −0.157507 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.0278 | 0.786613 | 0.393307 | − | 0.919407i | \(-0.371331\pi\) | ||||
0.393307 | + | 0.919407i | \(0.371331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2111 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | −14.7889 | −0.504004 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −51.6333 | −1.75762 | −0.878809 | − | 0.477173i | \(-0.841661\pi\) | ||||
−0.878809 | + | 0.477173i | \(0.841661\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −12.4222 | −0.422368 | ||||||||
\(866\) | 19.2111 | 0.652820 | ||||||||
\(867\) | −4.21110 | −0.143017 | ||||||||
\(868\) | 27.6333 | 0.937936 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.60555 | −0.156143 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.39445 | 0.0472220 | ||||||||
\(873\) | −1.39445 | −0.0471949 | ||||||||
\(874\) | −6.42221 | −0.217234 | ||||||||
\(875\) | 4.60555 | 0.155696 | ||||||||
\(876\) | 1.39445 | 0.0471141 | ||||||||
\(877\) | 24.8444 | 0.838936 | 0.419468 | − | 0.907770i | \(-0.362217\pi\) | ||||
0.419468 | + | 0.907770i | \(0.362217\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.2111 | −1.32106 | −0.660528 | − | 0.750802i | \(-0.729667\pi\) | ||||
−0.660528 | + | 0.750802i | \(0.729667\pi\) | |||||||
\(882\) | −14.2111 | −0.478513 | ||||||||
\(883\) | −9.57779 | −0.322318 | −0.161159 | − | 0.986928i | \(-0.551523\pi\) | ||||
−0.161159 | + | 0.986928i | \(0.551523\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.21110 | −0.309628 | ||||||||
\(886\) | −15.6333 | −0.525211 | ||||||||
\(887\) | 6.97224 | 0.234105 | 0.117053 | − | 0.993126i | \(-0.462655\pi\) | ||||
0.117053 | + | 0.993126i | \(0.462655\pi\) | |||||||
\(888\) | −9.21110 | −0.309104 | ||||||||
\(889\) | 5.57779 | 0.187073 | ||||||||
\(890\) | 15.2111 | 0.509877 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.81665 | −0.0608261 | ||||||||
\(893\) | −42.4222 | −1.41960 | ||||||||
\(894\) | −15.2111 | −0.508735 | ||||||||
\(895\) | −19.8167 | −0.662398 | ||||||||
\(896\) | 4.60555 | 0.153861 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.6333 | −1.12236 | ||||||||
\(899\) | −27.6333 | −0.921622 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −27.6333 | −0.920599 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.8444 | −1.22611 | ||||||||
\(904\) | 13.8167 | 0.459535 | ||||||||
\(905\) | 8.42221 | 0.279964 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | −21.5778 | −0.716479 | −0.358239 | − | 0.933630i | \(-0.616623\pi\) | ||||
−0.358239 | + | 0.933630i | \(0.616623\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 7.39445 | 0.245258 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6333 | −0.915532 | −0.457766 | − | 0.889073i | \(-0.651350\pi\) | ||||
−0.457766 | + | 0.889073i | \(0.651350\pi\) | |||||||
\(912\) | −4.60555 | −0.152505 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 38.2389 | 1.26483 | ||||||||
\(915\) | −11.2111 | −0.370628 | ||||||||
\(916\) | −19.8167 | −0.654761 | ||||||||
\(917\) | −104.111 | −3.43805 | ||||||||
\(918\) | −4.60555 | −0.152006 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 1.39445 | 0.0459736 | ||||||||
\(921\) | 8.78890 | 0.289604 | ||||||||
\(922\) | −33.6333 | −1.10765 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.21110 | −0.302859 | ||||||||
\(926\) | 31.3944 | 1.03169 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | −4.60555 | −0.151185 | ||||||||
\(929\) | −39.2111 | −1.28647 | −0.643237 | − | 0.765667i | \(-0.722409\pi\) | ||||
−0.643237 | + | 0.765667i | \(0.722409\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | 65.4500 | 2.14504 | ||||||||
\(932\) | 1.81665 | 0.0595065 | ||||||||
\(933\) | 12.0000 | 0.392862 | ||||||||
\(934\) | −30.4222 | −0.995445 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.3667 | −0.338665 | −0.169333 | − | 0.985559i | \(-0.554161\pi\) | ||||
−0.169333 | + | 0.985559i | \(0.554161\pi\) | |||||||
\(938\) | 14.7889 | 0.482875 | ||||||||
\(939\) | −3.57779 | −0.116757 | ||||||||
\(940\) | 9.21110 | 0.300433 | ||||||||
\(941\) | 54.0000 | 1.76035 | 0.880175 | − | 0.474650i | \(-0.157425\pi\) | ||||
0.880175 | + | 0.474650i | \(0.157425\pi\) | |||||||
\(942\) | 20.4222 | 0.665391 | ||||||||
\(943\) | −4.47772 | −0.145815 | ||||||||
\(944\) | −9.21110 | −0.299796 | ||||||||
\(945\) | −4.60555 | −0.149819 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6333 | −0.508014 | −0.254007 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254007 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(948\) | 14.4222 | 0.468411 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.60555 | −0.149424 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −21.2111 | −0.687456 | ||||||||
\(953\) | 20.2389 | 0.655601 | 0.327800 | − | 0.944747i | \(-0.393693\pi\) | ||||
0.327800 | + | 0.944747i | \(0.393693\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 12.0000 | 0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.57779 | −0.180210 | ||||||||
\(959\) | −14.7889 | −0.477558 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.42221 | −0.206845 | ||||||||
\(965\) | −7.81665 | −0.251627 | ||||||||
\(966\) | −6.42221 | −0.206631 | ||||||||
\(967\) | 8.23886 | 0.264944 | 0.132472 | − | 0.991187i | \(-0.457709\pi\) | ||||
0.132472 | + | 0.991187i | \(0.457709\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | 21.2111 | 0.681399 | ||||||||
\(970\) | −1.39445 | −0.0447731 | ||||||||
\(971\) | −53.0278 | −1.70174 | −0.850871 | − | 0.525375i | \(-0.823925\pi\) | ||||
−0.850871 | + | 0.525375i | \(0.823925\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −79.2666 | −2.54117 | ||||||||
\(974\) | −0.972244 | −0.0311527 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.2111 | −0.358859 | ||||||||
\(977\) | −18.8444 | −0.602886 | −0.301443 | − | 0.953484i | \(-0.597468\pi\) | ||||
−0.301443 | + | 0.953484i | \(0.597468\pi\) | |||||||
\(978\) | 24.4222 | 0.780936 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.2111 | −0.453957 | ||||||||
\(981\) | −1.39445 | −0.0445213 | ||||||||
\(982\) | 7.81665 | 0.249439 | ||||||||
\(983\) | −42.4222 | −1.35306 | −0.676529 | − | 0.736416i | \(-0.736517\pi\) | ||||
−0.676529 | + | 0.736416i | \(0.736517\pi\) | |||||||
\(984\) | −3.21110 | −0.102366 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 21.2111 | 0.675499 | ||||||||
\(987\) | −42.4222 | −1.35031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.1556 | −0.354727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.4222 | −0.712265 | −0.356132 | − | 0.934436i | \(-0.615905\pi\) | ||||
−0.356132 | + | 0.934436i | \(0.615905\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | −16.6056 | −0.526961 | ||||||||
\(994\) | −42.4222 | −1.34555 | ||||||||
\(995\) | 22.4222 | 0.710832 | ||||||||
\(996\) | 2.78890 | 0.0883696 | ||||||||
\(997\) | −16.4222 | −0.520096 | −0.260048 | − | 0.965596i | \(-0.583738\pi\) | ||||
−0.260048 | + | 0.965596i | \(0.583738\pi\) | |||||||
\(998\) | 23.0278 | 0.728931 | ||||||||
\(999\) | 9.21110 | 0.291426 |
(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 | 5070.2.a.z.1.1 | 2 | ||
13.5 | odd | 4 | 390.2.b.c.181.3 | yes | 4 | ||
13.8 | odd | 4 | 390.2.b.c.181.2 | ✓ | 4 | ||
13.12 | even | 2 | 5070.2.a.bf.1.2 | 2 | |||
39.5 | even | 4 | 1170.2.b.d.181.1 | 4 | |||
39.8 | even | 4 | 1170.2.b.d.181.4 | 4 | |||
52.31 | even | 4 | 3120.2.g.q.961.4 | 4 | |||
52.47 | even | 4 | 3120.2.g.q.961.1 | 4 | |||
65.8 | even | 4 | 1950.2.f.m.649.2 | 4 | |||
65.18 | even | 4 | 1950.2.f.n.649.1 | 4 | |||
65.34 | odd | 4 | 1950.2.b.k.1351.3 | 4 | |||
65.44 | odd | 4 | 1950.2.b.k.1351.2 | 4 | |||
65.47 | even | 4 | 1950.2.f.n.649.3 | 4 | |||
65.57 | even | 4 | 1950.2.f.m.649.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.2 | ✓ | 4 | 13.8 | odd | 4 | ||
390.2.b.c.181.3 | yes | 4 | 13.5 | odd | 4 | ||
1170.2.b.d.181.1 | 4 | 39.5 | even | 4 | |||
1170.2.b.d.181.4 | 4 | 39.8 | even | 4 | |||
1950.2.b.k.1351.2 | 4 | 65.44 | odd | 4 | |||
1950.2.b.k.1351.3 | 4 | 65.34 | odd | 4 | |||
1950.2.f.m.649.2 | 4 | 65.8 | even | 4 | |||
1950.2.f.m.649.4 | 4 | 65.57 | even | 4 | |||
1950.2.f.n.649.1 | 4 | 65.18 | even | 4 | |||
1950.2.f.n.649.3 | 4 | 65.47 | even | 4 | |||
3120.2.g.q.961.1 | 4 | 52.47 | even | 4 | |||
3120.2.g.q.961.4 | 4 | 52.31 | even | 4 | |||
5070.2.a.z.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.a.bf.1.2 | 2 | 13.12 | even | 2 |