Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −1.74363 | −1.00668 | −0.503342 | − | 0.864087i | \(-0.667896\pi\) | ||||
−0.503342 | + | 0.864087i | \(0.667896\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36417 | 0.610074 | 0.305037 | − | 0.952341i | \(-0.401331\pi\) | ||||
0.305037 | + | 0.952341i | \(0.401331\pi\) | |||||||
\(6\) | −1.74363 | −0.711833 | ||||||||
\(7\) | 0.246249 | 0.0930733 | 0.0465367 | − | 0.998917i | \(-0.485182\pi\) | ||||
0.0465367 | + | 0.998917i | \(0.485182\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0402388 | 0.0134129 | ||||||||
\(10\) | 1.36417 | 0.431387 | ||||||||
\(11\) | 0.997185 | 0.300663 | 0.150331 | − | 0.988636i | \(-0.451966\pi\) | ||||
0.150331 | + | 0.988636i | \(0.451966\pi\) | |||||||
\(12\) | −1.74363 | −0.503342 | ||||||||
\(13\) | 1.44270 | 0.400132 | 0.200066 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200066 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(14\) | 0.246249 | 0.0658128 | ||||||||
\(15\) | −2.37860 | −0.614152 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.37189 | 1.78795 | 0.893973 | − | 0.448120i | \(-0.147906\pi\) | ||||
0.893973 | + | 0.448120i | \(0.147906\pi\) | |||||||
\(18\) | 0.0402388 | 0.00948437 | ||||||||
\(19\) | 0.127079 | 0.0291539 | 0.0145770 | − | 0.999894i | \(-0.495360\pi\) | ||||
0.0145770 | + | 0.999894i | \(0.495360\pi\) | |||||||
\(20\) | 1.36417 | 0.305037 | ||||||||
\(21\) | −0.429367 | −0.0936955 | ||||||||
\(22\) | 0.997185 | 0.212601 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.74363 | −0.355917 | ||||||||
\(25\) | −3.13905 | −0.627810 | ||||||||
\(26\) | 1.44270 | 0.282936 | ||||||||
\(27\) | 5.16072 | 0.993182 | ||||||||
\(28\) | 0.246249 | 0.0465367 | ||||||||
\(29\) | 3.04044 | 0.564595 | 0.282298 | − | 0.959327i | \(-0.408903\pi\) | ||||
0.282298 | + | 0.959327i | \(0.408903\pi\) | |||||||
\(30\) | −2.37860 | −0.434271 | ||||||||
\(31\) | −7.07979 | −1.27157 | −0.635784 | − | 0.771867i | \(-0.719323\pi\) | ||||
−0.635784 | + | 0.771867i | \(0.719323\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.73872 | −0.302672 | ||||||||
\(34\) | 7.37189 | 1.26427 | ||||||||
\(35\) | 0.335924 | 0.0567816 | ||||||||
\(36\) | 0.0402388 | 0.00670646 | ||||||||
\(37\) | 2.76502 | 0.454566 | 0.227283 | − | 0.973829i | \(-0.427016\pi\) | ||||
0.227283 | + | 0.973829i | \(0.427016\pi\) | |||||||
\(38\) | 0.127079 | 0.0206149 | ||||||||
\(39\) | −2.51553 | −0.402807 | ||||||||
\(40\) | 1.36417 | 0.215694 | ||||||||
\(41\) | 9.95597 | 1.55486 | 0.777430 | − | 0.628969i | \(-0.216523\pi\) | ||||
0.777430 | + | 0.628969i | \(0.216523\pi\) | |||||||
\(42\) | −0.429367 | −0.0662527 | ||||||||
\(43\) | 8.18686 | 1.24849 | 0.624243 | − | 0.781231i | \(-0.285408\pi\) | ||||
0.624243 | + | 0.781231i | \(0.285408\pi\) | |||||||
\(44\) | 0.997185 | 0.150331 | ||||||||
\(45\) | 0.0548924 | 0.00818288 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −11.5529 | −1.68516 | −0.842580 | − | 0.538572i | \(-0.818964\pi\) | ||||
−0.842580 | + | 0.538572i | \(0.818964\pi\) | |||||||
\(48\) | −1.74363 | −0.251671 | ||||||||
\(49\) | −6.93936 | −0.991337 | ||||||||
\(50\) | −3.13905 | −0.443929 | ||||||||
\(51\) | −12.8538 | −1.79990 | ||||||||
\(52\) | 1.44270 | 0.200066 | ||||||||
\(53\) | 3.11372 | 0.427703 | 0.213851 | − | 0.976866i | \(-0.431399\pi\) | ||||
0.213851 | + | 0.976866i | \(0.431399\pi\) | |||||||
\(54\) | 5.16072 | 0.702285 | ||||||||
\(55\) | 1.36033 | 0.183426 | ||||||||
\(56\) | 0.246249 | 0.0329064 | ||||||||
\(57\) | −0.221579 | −0.0293488 | ||||||||
\(58\) | 3.04044 | 0.399229 | ||||||||
\(59\) | 10.4811 | 1.36452 | 0.682262 | − | 0.731108i | \(-0.260996\pi\) | ||||
0.682262 | + | 0.731108i | \(0.260996\pi\) | |||||||
\(60\) | −2.37860 | −0.307076 | ||||||||
\(61\) | −2.02027 | −0.258668 | −0.129334 | − | 0.991601i | \(-0.541284\pi\) | ||||
−0.129334 | + | 0.991601i | \(0.541284\pi\) | |||||||
\(62\) | −7.07979 | −0.899135 | ||||||||
\(63\) | 0.00990876 | 0.00124839 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.96808 | 0.244110 | ||||||||
\(66\) | −1.73872 | −0.214022 | ||||||||
\(67\) | −14.1574 | −1.72960 | −0.864800 | − | 0.502117i | \(-0.832555\pi\) | ||||
−0.864800 | + | 0.502117i | \(0.832555\pi\) | |||||||
\(68\) | 7.37189 | 0.893973 | ||||||||
\(69\) | 1.74363 | 0.209908 | ||||||||
\(70\) | 0.335924 | 0.0401507 | ||||||||
\(71\) | 9.72966 | 1.15470 | 0.577349 | − | 0.816497i | \(-0.304087\pi\) | ||||
0.577349 | + | 0.816497i | \(0.304087\pi\) | |||||||
\(72\) | 0.0402388 | 0.00474219 | ||||||||
\(73\) | −2.07341 | −0.242674 | −0.121337 | − | 0.992611i | \(-0.538718\pi\) | ||||
−0.121337 | + | 0.992611i | \(0.538718\pi\) | |||||||
\(74\) | 2.76502 | 0.321427 | ||||||||
\(75\) | 5.47334 | 0.632006 | ||||||||
\(76\) | 0.127079 | 0.0145770 | ||||||||
\(77\) | 0.245556 | 0.0279837 | ||||||||
\(78\) | −2.51553 | −0.284827 | ||||||||
\(79\) | −10.9624 | −1.23336 | −0.616681 | − | 0.787213i | \(-0.711523\pi\) | ||||
−0.616681 | + | 0.787213i | \(0.711523\pi\) | |||||||
\(80\) | 1.36417 | 0.152518 | ||||||||
\(81\) | −9.11910 | −1.01323 | ||||||||
\(82\) | 9.95597 | 1.09945 | ||||||||
\(83\) | −0.120817 | −0.0132614 | −0.00663068 | − | 0.999978i | \(-0.502111\pi\) | ||||
−0.00663068 | + | 0.999978i | \(0.502111\pi\) | |||||||
\(84\) | −0.429367 | −0.0468477 | ||||||||
\(85\) | 10.0565 | 1.09078 | ||||||||
\(86\) | 8.18686 | 0.882812 | ||||||||
\(87\) | −5.30140 | −0.568369 | ||||||||
\(88\) | 0.997185 | 0.106300 | ||||||||
\(89\) | 0.217175 | 0.0230205 | 0.0115103 | − | 0.999934i | \(-0.496336\pi\) | ||||
0.0115103 | + | 0.999934i | \(0.496336\pi\) | |||||||
\(90\) | 0.0548924 | 0.00578617 | ||||||||
\(91\) | 0.355262 | 0.0372416 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 12.3445 | 1.28007 | ||||||||
\(94\) | −11.5529 | −1.19159 | ||||||||
\(95\) | 0.173357 | 0.0177860 | ||||||||
\(96\) | −1.74363 | −0.177958 | ||||||||
\(97\) | 11.2033 | 1.13752 | 0.568762 | − | 0.822502i | \(-0.307423\pi\) | ||||
0.568762 | + | 0.822502i | \(0.307423\pi\) | |||||||
\(98\) | −6.93936 | −0.700981 | ||||||||
\(99\) | 0.0401255 | 0.00403277 | ||||||||
\(100\) | −3.13905 | −0.313905 | ||||||||
\(101\) | 8.93549 | 0.889115 | 0.444557 | − | 0.895750i | \(-0.353361\pi\) | ||||
0.444557 | + | 0.895750i | \(0.353361\pi\) | |||||||
\(102\) | −12.8538 | −1.27272 | ||||||||
\(103\) | −9.02603 | −0.889361 | −0.444680 | − | 0.895689i | \(-0.646683\pi\) | ||||
−0.444680 | + | 0.895689i | \(0.646683\pi\) | |||||||
\(104\) | 1.44270 | 0.141468 | ||||||||
\(105\) | −0.585727 | −0.0571611 | ||||||||
\(106\) | 3.11372 | 0.302432 | ||||||||
\(107\) | 13.9188 | 1.34559 | 0.672793 | − | 0.739831i | \(-0.265095\pi\) | ||||
0.672793 | + | 0.739831i | \(0.265095\pi\) | |||||||
\(108\) | 5.16072 | 0.496591 | ||||||||
\(109\) | 10.4582 | 1.00172 | 0.500859 | − | 0.865529i | \(-0.333018\pi\) | ||||
0.500859 | + | 0.865529i | \(0.333018\pi\) | |||||||
\(110\) | 1.36033 | 0.129702 | ||||||||
\(111\) | −4.82116 | −0.457605 | ||||||||
\(112\) | 0.246249 | 0.0232683 | ||||||||
\(113\) | 19.5060 | 1.83497 | 0.917484 | − | 0.397773i | \(-0.130217\pi\) | ||||
0.917484 | + | 0.397773i | \(0.130217\pi\) | |||||||
\(114\) | −0.221579 | −0.0207527 | ||||||||
\(115\) | −1.36417 | −0.127209 | ||||||||
\(116\) | 3.04044 | 0.282298 | ||||||||
\(117\) | 0.0580524 | 0.00536694 | ||||||||
\(118\) | 10.4811 | 0.964864 | ||||||||
\(119\) | 1.81532 | 0.166410 | ||||||||
\(120\) | −2.37860 | −0.217135 | ||||||||
\(121\) | −10.0056 | −0.909602 | ||||||||
\(122\) | −2.02027 | −0.182906 | ||||||||
\(123\) | −17.3595 | −1.56525 | ||||||||
\(124\) | −7.07979 | −0.635784 | ||||||||
\(125\) | −11.1030 | −0.993084 | ||||||||
\(126\) | 0.00990876 | 0.000882742 0 | ||||||||
\(127\) | 15.2538 | 1.35355 | 0.676776 | − | 0.736189i | \(-0.263376\pi\) | ||||
0.676776 | + | 0.736189i | \(0.263376\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −14.2748 | −1.25683 | ||||||||
\(130\) | 1.96808 | 0.172612 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −1.73872 | −0.151336 | ||||||||
\(133\) | 0.0312931 | 0.00271345 | ||||||||
\(134\) | −14.1574 | −1.22301 | ||||||||
\(135\) | 7.04008 | 0.605914 | ||||||||
\(136\) | 7.37189 | 0.632135 | ||||||||
\(137\) | −6.20057 | −0.529751 | −0.264875 | − | 0.964283i | \(-0.585331\pi\) | ||||
−0.264875 | + | 0.964283i | \(0.585331\pi\) | |||||||
\(138\) | 1.74363 | 0.148427 | ||||||||
\(139\) | 10.1560 | 0.861419 | 0.430709 | − | 0.902491i | \(-0.358263\pi\) | ||||
0.430709 | + | 0.902491i | \(0.358263\pi\) | |||||||
\(140\) | 0.335924 | 0.0283908 | ||||||||
\(141\) | 20.1439 | 1.69642 | ||||||||
\(142\) | 9.72966 | 0.816495 | ||||||||
\(143\) | 1.43864 | 0.120305 | ||||||||
\(144\) | 0.0402388 | 0.00335323 | ||||||||
\(145\) | 4.14766 | 0.344445 | ||||||||
\(146\) | −2.07341 | −0.171597 | ||||||||
\(147\) | 12.0997 | 0.997964 | ||||||||
\(148\) | 2.76502 | 0.227283 | ||||||||
\(149\) | −9.75595 | −0.799239 | −0.399619 | − | 0.916681i | \(-0.630858\pi\) | ||||
−0.399619 | + | 0.916681i | \(0.630858\pi\) | |||||||
\(150\) | 5.47334 | 0.446896 | ||||||||
\(151\) | −3.15127 | −0.256447 | −0.128224 | − | 0.991745i | \(-0.540927\pi\) | ||||
−0.128224 | + | 0.991745i | \(0.540927\pi\) | |||||||
\(152\) | 0.127079 | 0.0103075 | ||||||||
\(153\) | 0.296636 | 0.0239816 | ||||||||
\(154\) | 0.245556 | 0.0197875 | ||||||||
\(155\) | −9.65802 | −0.775751 | ||||||||
\(156\) | −2.51553 | −0.201403 | ||||||||
\(157\) | 10.0010 | 0.798169 | 0.399084 | − | 0.916914i | \(-0.369328\pi\) | ||||
0.399084 | + | 0.916914i | \(0.369328\pi\) | |||||||
\(158\) | −10.9624 | −0.872119 | ||||||||
\(159\) | −5.42918 | −0.430562 | ||||||||
\(160\) | 1.36417 | 0.107847 | ||||||||
\(161\) | −0.246249 | −0.0194071 | ||||||||
\(162\) | −9.11910 | −0.716464 | ||||||||
\(163\) | −2.38311 | −0.186660 | −0.0933299 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933299 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(164\) | 9.95597 | 0.777430 | ||||||||
\(165\) | −2.37190 | −0.184652 | ||||||||
\(166\) | −0.120817 | −0.00937719 | ||||||||
\(167\) | 19.8944 | 1.53947 | 0.769736 | − | 0.638362i | \(-0.220388\pi\) | ||||
0.769736 | + | 0.638362i | \(0.220388\pi\) | |||||||
\(168\) | −0.429367 | −0.0331263 | ||||||||
\(169\) | −10.9186 | −0.839894 | ||||||||
\(170\) | 10.0565 | 0.771297 | ||||||||
\(171\) | 0.00511351 | 0.000391040 0 | ||||||||
\(172\) | 8.18686 | 0.624243 | ||||||||
\(173\) | −11.9110 | −0.905577 | −0.452788 | − | 0.891618i | \(-0.649571\pi\) | ||||
−0.452788 | + | 0.891618i | \(0.649571\pi\) | |||||||
\(174\) | −5.30140 | −0.401898 | ||||||||
\(175\) | −0.772988 | −0.0584324 | ||||||||
\(176\) | 0.997185 | 0.0751657 | ||||||||
\(177\) | −18.2752 | −1.37364 | ||||||||
\(178\) | 0.217175 | 0.0162780 | ||||||||
\(179\) | 2.85347 | 0.213278 | 0.106639 | − | 0.994298i | \(-0.465991\pi\) | ||||
0.106639 | + | 0.994298i | \(0.465991\pi\) | |||||||
\(180\) | 0.0548924 | 0.00409144 | ||||||||
\(181\) | 6.40380 | 0.475990 | 0.237995 | − | 0.971266i | \(-0.423510\pi\) | ||||
0.237995 | + | 0.971266i | \(0.423510\pi\) | |||||||
\(182\) | 0.355262 | 0.0263338 | ||||||||
\(183\) | 3.52259 | 0.260397 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 3.77194 | 0.277319 | ||||||||
\(186\) | 12.3445 | 0.905145 | ||||||||
\(187\) | 7.35114 | 0.537569 | ||||||||
\(188\) | −11.5529 | −0.842580 | ||||||||
\(189\) | 1.27082 | 0.0924387 | ||||||||
\(190\) | 0.173357 | 0.0125766 | ||||||||
\(191\) | −1.54073 | −0.111483 | −0.0557416 | − | 0.998445i | \(-0.517752\pi\) | ||||
−0.0557416 | + | 0.998445i | \(0.517752\pi\) | |||||||
\(192\) | −1.74363 | −0.125836 | ||||||||
\(193\) | −10.3850 | −0.747529 | −0.373764 | − | 0.927524i | \(-0.621933\pi\) | ||||
−0.373764 | + | 0.927524i | \(0.621933\pi\) | |||||||
\(194\) | 11.2033 | 0.804351 | ||||||||
\(195\) | −3.43160 | −0.245742 | ||||||||
\(196\) | −6.93936 | −0.495669 | ||||||||
\(197\) | 23.0211 | 1.64019 | 0.820094 | − | 0.572229i | \(-0.193921\pi\) | ||||
0.820094 | + | 0.572229i | \(0.193921\pi\) | |||||||
\(198\) | 0.0401255 | 0.00285160 | ||||||||
\(199\) | −13.8274 | −0.980196 | −0.490098 | − | 0.871667i | \(-0.663039\pi\) | ||||
−0.490098 | + | 0.871667i | \(0.663039\pi\) | |||||||
\(200\) | −3.13905 | −0.221964 | ||||||||
\(201\) | 24.6852 | 1.74116 | ||||||||
\(202\) | 8.93549 | 0.628699 | ||||||||
\(203\) | 0.748705 | 0.0525488 | ||||||||
\(204\) | −12.8538 | −0.899949 | ||||||||
\(205\) | 13.5816 | 0.948580 | ||||||||
\(206\) | −9.02603 | −0.628873 | ||||||||
\(207\) | −0.0402388 | −0.00279679 | ||||||||
\(208\) | 1.44270 | 0.100033 | ||||||||
\(209\) | 0.126721 | 0.00876550 | ||||||||
\(210\) | −0.585727 | −0.0404190 | ||||||||
\(211\) | 0.717238 | 0.0493767 | 0.0246883 | − | 0.999695i | \(-0.492141\pi\) | ||||
0.0246883 | + | 0.999695i | \(0.492141\pi\) | |||||||
\(212\) | 3.11372 | 0.213851 | ||||||||
\(213\) | −16.9649 | −1.16242 | ||||||||
\(214\) | 13.9188 | 0.951473 | ||||||||
\(215\) | 11.1682 | 0.761668 | ||||||||
\(216\) | 5.16072 | 0.351143 | ||||||||
\(217\) | −1.74339 | −0.118349 | ||||||||
\(218\) | 10.4582 | 0.708321 | ||||||||
\(219\) | 3.61526 | 0.244296 | ||||||||
\(220\) | 1.36033 | 0.0917132 | ||||||||
\(221\) | 10.6354 | 0.715415 | ||||||||
\(222\) | −4.82116 | −0.323575 | ||||||||
\(223\) | 28.0974 | 1.88154 | 0.940771 | − | 0.339041i | \(-0.110103\pi\) | ||||
0.940771 | + | 0.339041i | \(0.110103\pi\) | |||||||
\(224\) | 0.246249 | 0.0164532 | ||||||||
\(225\) | −0.126312 | −0.00842077 | ||||||||
\(226\) | 19.5060 | 1.29752 | ||||||||
\(227\) | −10.8000 | −0.716820 | −0.358410 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358410 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(228\) | −0.221579 | −0.0146744 | ||||||||
\(229\) | −3.86486 | −0.255397 | −0.127698 | − | 0.991813i | \(-0.540759\pi\) | ||||
−0.127698 | + | 0.991813i | \(0.540759\pi\) | |||||||
\(230\) | −1.36417 | −0.0899505 | ||||||||
\(231\) | −0.428158 | −0.0281707 | ||||||||
\(232\) | 3.04044 | 0.199615 | ||||||||
\(233\) | 9.20161 | 0.602817 | 0.301409 | − | 0.953495i | \(-0.402543\pi\) | ||||
0.301409 | + | 0.953495i | \(0.402543\pi\) | |||||||
\(234\) | 0.0580524 | 0.00379500 | ||||||||
\(235\) | −15.7600 | −1.02807 | ||||||||
\(236\) | 10.4811 | 0.682262 | ||||||||
\(237\) | 19.1143 | 1.24161 | ||||||||
\(238\) | 1.81532 | 0.117670 | ||||||||
\(239\) | −7.41788 | −0.479823 | −0.239912 | − | 0.970795i | \(-0.577118\pi\) | ||||
−0.239912 | + | 0.970795i | \(0.577118\pi\) | |||||||
\(240\) | −2.37860 | −0.153538 | ||||||||
\(241\) | 14.9370 | 0.962177 | 0.481089 | − | 0.876672i | \(-0.340242\pi\) | ||||
0.481089 | + | 0.876672i | \(0.340242\pi\) | |||||||
\(242\) | −10.0056 | −0.643186 | ||||||||
\(243\) | 0.418146 | 0.0268241 | ||||||||
\(244\) | −2.02027 | −0.129334 | ||||||||
\(245\) | −9.46644 | −0.604789 | ||||||||
\(246\) | −17.3595 | −1.10680 | ||||||||
\(247\) | 0.183337 | 0.0116654 | ||||||||
\(248\) | −7.07979 | −0.449567 | ||||||||
\(249\) | 0.210659 | 0.0133500 | ||||||||
\(250\) | −11.1030 | −0.702217 | ||||||||
\(251\) | 9.89554 | 0.624601 | 0.312300 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312300 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(252\) | 0.00990876 | 0.000624193 0 | ||||||||
\(253\) | −0.997185 | −0.0626925 | ||||||||
\(254\) | 15.2538 | 0.957106 | ||||||||
\(255\) | −17.5348 | −1.09807 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.73200 | 0.607066 | 0.303533 | − | 0.952821i | \(-0.401834\pi\) | ||||
0.303533 | + | 0.952821i | \(0.401834\pi\) | |||||||
\(258\) | −14.2748 | −0.888713 | ||||||||
\(259\) | 0.680883 | 0.0423080 | ||||||||
\(260\) | 1.96808 | 0.122055 | ||||||||
\(261\) | 0.122344 | 0.00757288 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | −27.9012 | −1.72046 | −0.860231 | − | 0.509904i | \(-0.829681\pi\) | ||||
−0.860231 | + | 0.509904i | \(0.829681\pi\) | |||||||
\(264\) | −1.73872 | −0.107011 | ||||||||
\(265\) | 4.24764 | 0.260930 | ||||||||
\(266\) | 0.0312931 | 0.00191870 | ||||||||
\(267\) | −0.378672 | −0.0231744 | ||||||||
\(268\) | −14.1574 | −0.864800 | ||||||||
\(269\) | 29.5144 | 1.79953 | 0.899763 | − | 0.436380i | \(-0.143739\pi\) | ||||
0.899763 | + | 0.436380i | \(0.143739\pi\) | |||||||
\(270\) | 7.04008 | 0.428446 | ||||||||
\(271\) | 5.94548 | 0.361162 | 0.180581 | − | 0.983560i | \(-0.442202\pi\) | ||||
0.180581 | + | 0.983560i | \(0.442202\pi\) | |||||||
\(272\) | 7.37189 | 0.446987 | ||||||||
\(273\) | −0.619446 | −0.0374906 | ||||||||
\(274\) | −6.20057 | −0.374590 | ||||||||
\(275\) | −3.13022 | −0.188759 | ||||||||
\(276\) | 1.74363 | 0.104954 | ||||||||
\(277\) | 4.76161 | 0.286097 | 0.143049 | − | 0.989716i | \(-0.454309\pi\) | ||||
0.143049 | + | 0.989716i | \(0.454309\pi\) | |||||||
\(278\) | 10.1560 | 0.609115 | ||||||||
\(279\) | −0.284882 | −0.0170555 | ||||||||
\(280\) | 0.335924 | 0.0200753 | ||||||||
\(281\) | −2.55357 | −0.152333 | −0.0761666 | − | 0.997095i | \(-0.524268\pi\) | ||||
−0.0761666 | + | 0.997095i | \(0.524268\pi\) | |||||||
\(282\) | 20.1439 | 1.19955 | ||||||||
\(283\) | 19.0982 | 1.13527 | 0.567636 | − | 0.823279i | \(-0.307858\pi\) | ||||
0.567636 | + | 0.823279i | \(0.307858\pi\) | |||||||
\(284\) | 9.72966 | 0.577349 | ||||||||
\(285\) | −0.302270 | −0.0179049 | ||||||||
\(286\) | 1.43864 | 0.0850683 | ||||||||
\(287\) | 2.45165 | 0.144716 | ||||||||
\(288\) | 0.0402388 | 0.00237109 | ||||||||
\(289\) | 37.3448 | 2.19675 | ||||||||
\(290\) | 4.14766 | 0.243559 | ||||||||
\(291\) | −19.5344 | −1.14513 | ||||||||
\(292\) | −2.07341 | −0.121337 | ||||||||
\(293\) | 25.3806 | 1.48275 | 0.741376 | − | 0.671089i | \(-0.234173\pi\) | ||||
0.741376 | + | 0.671089i | \(0.234173\pi\) | |||||||
\(294\) | 12.0997 | 0.705667 | ||||||||
\(295\) | 14.2980 | 0.832460 | ||||||||
\(296\) | 2.76502 | 0.160713 | ||||||||
\(297\) | 5.14620 | 0.298613 | ||||||||
\(298\) | −9.75595 | −0.565147 | ||||||||
\(299\) | −1.44270 | −0.0834333 | ||||||||
\(300\) | 5.47334 | 0.316003 | ||||||||
\(301\) | 2.01601 | 0.116201 | ||||||||
\(302\) | −3.15127 | −0.181335 | ||||||||
\(303\) | −15.5802 | −0.895058 | ||||||||
\(304\) | 0.127079 | 0.00728848 | ||||||||
\(305\) | −2.75598 | −0.157807 | ||||||||
\(306\) | 0.296636 | 0.0169576 | ||||||||
\(307\) | −28.7690 | −1.64193 | −0.820967 | − | 0.570975i | \(-0.806565\pi\) | ||||
−0.820967 | + | 0.570975i | \(0.806565\pi\) | |||||||
\(308\) | 0.245556 | 0.0139918 | ||||||||
\(309\) | 15.7380 | 0.895305 | ||||||||
\(310\) | −9.65802 | −0.548539 | ||||||||
\(311\) | 7.33784 | 0.416091 | 0.208046 | − | 0.978119i | \(-0.433290\pi\) | ||||
0.208046 | + | 0.978119i | \(0.433290\pi\) | |||||||
\(312\) | −2.51553 | −0.142414 | ||||||||
\(313\) | −23.4443 | −1.32515 | −0.662576 | − | 0.748995i | \(-0.730537\pi\) | ||||
−0.662576 | + | 0.748995i | \(0.730537\pi\) | |||||||
\(314\) | 10.0010 | 0.564391 | ||||||||
\(315\) | 0.0135172 | 0.000761608 0 | ||||||||
\(316\) | −10.9624 | −0.616681 | ||||||||
\(317\) | 7.85505 | 0.441183 | 0.220592 | − | 0.975366i | \(-0.429201\pi\) | ||||
0.220592 | + | 0.975366i | \(0.429201\pi\) | |||||||
\(318\) | −5.42918 | −0.304453 | ||||||||
\(319\) | 3.03188 | 0.169753 | ||||||||
\(320\) | 1.36417 | 0.0762592 | ||||||||
\(321\) | −24.2693 | −1.35458 | ||||||||
\(322\) | −0.246249 | −0.0137229 | ||||||||
\(323\) | 0.936813 | 0.0521257 | ||||||||
\(324\) | −9.11910 | −0.506617 | ||||||||
\(325\) | −4.52870 | −0.251207 | ||||||||
\(326\) | −2.38311 | −0.131988 | ||||||||
\(327\) | −18.2353 | −1.00841 | ||||||||
\(328\) | 9.95597 | 0.549726 | ||||||||
\(329\) | −2.84488 | −0.156843 | ||||||||
\(330\) | −2.37190 | −0.130569 | ||||||||
\(331\) | 5.10693 | 0.280702 | 0.140351 | − | 0.990102i | \(-0.455177\pi\) | ||||
0.140351 | + | 0.990102i | \(0.455177\pi\) | |||||||
\(332\) | −0.120817 | −0.00663068 | ||||||||
\(333\) | 0.111261 | 0.00609706 | ||||||||
\(334\) | 19.8944 | 1.08857 | ||||||||
\(335\) | −19.3130 | −1.05518 | ||||||||
\(336\) | −0.429367 | −0.0234239 | ||||||||
\(337\) | −5.56800 | −0.303308 | −0.151654 | − | 0.988434i | \(-0.548460\pi\) | ||||
−0.151654 | + | 0.988434i | \(0.548460\pi\) | |||||||
\(338\) | −10.9186 | −0.593895 | ||||||||
\(339\) | −34.0112 | −1.84723 | ||||||||
\(340\) | 10.0565 | 0.545390 | ||||||||
\(341\) | −7.05987 | −0.382313 | ||||||||
\(342\) | 0.00511351 | 0.000276507 0 | ||||||||
\(343\) | −3.43255 | −0.185340 | ||||||||
\(344\) | 8.18686 | 0.441406 | ||||||||
\(345\) | 2.37860 | 0.128059 | ||||||||
\(346\) | −11.9110 | −0.640339 | ||||||||
\(347\) | 23.3865 | 1.25545 | 0.627727 | − | 0.778434i | \(-0.283986\pi\) | ||||
0.627727 | + | 0.778434i | \(0.283986\pi\) | |||||||
\(348\) | −5.30140 | −0.284185 | ||||||||
\(349\) | −11.2297 | −0.601113 | −0.300557 | − | 0.953764i | \(-0.597172\pi\) | ||||
−0.300557 | + | 0.953764i | \(0.597172\pi\) | |||||||
\(350\) | −0.772988 | −0.0413179 | ||||||||
\(351\) | 7.44536 | 0.397404 | ||||||||
\(352\) | 0.997185 | 0.0531502 | ||||||||
\(353\) | −18.4868 | −0.983952 | −0.491976 | − | 0.870609i | \(-0.663725\pi\) | ||||
−0.491976 | + | 0.870609i | \(0.663725\pi\) | |||||||
\(354\) | −18.2752 | −0.971314 | ||||||||
\(355\) | 13.2729 | 0.704451 | ||||||||
\(356\) | 0.217175 | 0.0115103 | ||||||||
\(357\) | −3.16524 | −0.167522 | ||||||||
\(358\) | 2.85347 | 0.150810 | ||||||||
\(359\) | 15.5631 | 0.821390 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(360\) | 0.0548924 | 0.00289308 | ||||||||
\(361\) | −18.9839 | −0.999150 | ||||||||
\(362\) | 6.40380 | 0.336576 | ||||||||
\(363\) | 17.4461 | 0.915682 | ||||||||
\(364\) | 0.355262 | 0.0186208 | ||||||||
\(365\) | −2.82848 | −0.148049 | ||||||||
\(366\) | 3.52259 | 0.184129 | ||||||||
\(367\) | −6.14723 | −0.320883 | −0.160441 | − | 0.987045i | \(-0.551292\pi\) | ||||
−0.160441 | + | 0.987045i | \(0.551292\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0.400616 | 0.0208552 | ||||||||
\(370\) | 3.77194 | 0.196094 | ||||||||
\(371\) | 0.766751 | 0.0398077 | ||||||||
\(372\) | 12.3445 | 0.640034 | ||||||||
\(373\) | 11.8605 | 0.614115 | 0.307057 | − | 0.951691i | \(-0.400656\pi\) | ||||
0.307057 | + | 0.951691i | \(0.400656\pi\) | |||||||
\(374\) | 7.35114 | 0.380119 | ||||||||
\(375\) | 19.3595 | 0.999722 | ||||||||
\(376\) | −11.5529 | −0.595794 | ||||||||
\(377\) | 4.38643 | 0.225913 | ||||||||
\(378\) | 1.27082 | 0.0653640 | ||||||||
\(379\) | −34.6762 | −1.78120 | −0.890600 | − | 0.454788i | \(-0.849715\pi\) | ||||
−0.890600 | + | 0.454788i | \(0.849715\pi\) | |||||||
\(380\) | 0.173357 | 0.00889302 | ||||||||
\(381\) | −26.5969 | −1.36260 | ||||||||
\(382\) | −1.54073 | −0.0788306 | ||||||||
\(383\) | 34.3641 | 1.75592 | 0.877962 | − | 0.478730i | \(-0.158903\pi\) | ||||
0.877962 | + | 0.478730i | \(0.158903\pi\) | |||||||
\(384\) | −1.74363 | −0.0889791 | ||||||||
\(385\) | 0.334979 | 0.0170721 | ||||||||
\(386\) | −10.3850 | −0.528583 | ||||||||
\(387\) | 0.329429 | 0.0167458 | ||||||||
\(388\) | 11.2033 | 0.568762 | ||||||||
\(389\) | 16.8196 | 0.852790 | 0.426395 | − | 0.904537i | \(-0.359783\pi\) | ||||
0.426395 | + | 0.904537i | \(0.359783\pi\) | |||||||
\(390\) | −3.43160 | −0.173766 | ||||||||
\(391\) | −7.37189 | −0.372813 | ||||||||
\(392\) | −6.93936 | −0.350491 | ||||||||
\(393\) | 1.74363 | 0.0879544 | ||||||||
\(394\) | 23.0211 | 1.15979 | ||||||||
\(395\) | −14.9545 | −0.752442 | ||||||||
\(396\) | 0.0401255 | 0.00201638 | ||||||||
\(397\) | 14.1294 | 0.709134 | 0.354567 | − | 0.935031i | \(-0.384628\pi\) | ||||
0.354567 | + | 0.935031i | \(0.384628\pi\) | |||||||
\(398\) | −13.8274 | −0.693103 | ||||||||
\(399\) | −0.0545635 | −0.00273159 | ||||||||
\(400\) | −3.13905 | −0.156953 | ||||||||
\(401\) | −5.45756 | −0.272538 | −0.136269 | − | 0.990672i | \(-0.543511\pi\) | ||||
−0.136269 | + | 0.990672i | \(0.543511\pi\) | |||||||
\(402\) | 24.6852 | 1.23119 | ||||||||
\(403\) | −10.2140 | −0.508795 | ||||||||
\(404\) | 8.93549 | 0.444557 | ||||||||
\(405\) | −12.4400 | −0.618147 | ||||||||
\(406\) | 0.748705 | 0.0371576 | ||||||||
\(407\) | 2.75724 | 0.136671 | ||||||||
\(408\) | −12.8538 | −0.636360 | ||||||||
\(409\) | 39.2662 | 1.94159 | 0.970794 | − | 0.239914i | \(-0.0771192\pi\) | ||||
0.970794 | + | 0.239914i | \(0.0771192\pi\) | |||||||
\(410\) | 13.5816 | 0.670747 | ||||||||
\(411\) | 10.8115 | 0.533291 | ||||||||
\(412\) | −9.02603 | −0.444680 | ||||||||
\(413\) | 2.58096 | 0.127001 | ||||||||
\(414\) | −0.0402388 | −0.00197763 | ||||||||
\(415\) | −0.164814 | −0.00809040 | ||||||||
\(416\) | 1.44270 | 0.0707340 | ||||||||
\(417\) | −17.7082 | −0.867176 | ||||||||
\(418\) | 0.126721 | 0.00619814 | ||||||||
\(419\) | 1.83398 | 0.0895958 | 0.0447979 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447979 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(420\) | −0.585727 | −0.0285806 | ||||||||
\(421\) | −1.43510 | −0.0699424 | −0.0349712 | − | 0.999388i | \(-0.511134\pi\) | ||||
−0.0349712 | + | 0.999388i | \(0.511134\pi\) | |||||||
\(422\) | 0.717238 | 0.0349146 | ||||||||
\(423\) | −0.464874 | −0.0226029 | ||||||||
\(424\) | 3.11372 | 0.151216 | ||||||||
\(425\) | −23.1407 | −1.12249 | ||||||||
\(426\) | −16.9649 | −0.821953 | ||||||||
\(427\) | −0.497488 | −0.0240751 | ||||||||
\(428\) | 13.9188 | 0.672793 | ||||||||
\(429\) | −2.50845 | −0.121109 | ||||||||
\(430\) | 11.1682 | 0.538581 | ||||||||
\(431\) | −8.27409 | −0.398549 | −0.199275 | − | 0.979944i | \(-0.563859\pi\) | ||||
−0.199275 | + | 0.979944i | \(0.563859\pi\) | |||||||
\(432\) | 5.16072 | 0.248295 | ||||||||
\(433\) | 18.7308 | 0.900146 | 0.450073 | − | 0.892992i | \(-0.351398\pi\) | ||||
0.450073 | + | 0.892992i | \(0.351398\pi\) | |||||||
\(434\) | −1.74339 | −0.0836855 | ||||||||
\(435\) | −7.23198 | −0.346747 | ||||||||
\(436\) | 10.4582 | 0.500859 | ||||||||
\(437\) | −0.127079 | −0.00607901 | ||||||||
\(438\) | 3.61526 | 0.172744 | ||||||||
\(439\) | 7.31923 | 0.349328 | 0.174664 | − | 0.984628i | \(-0.444116\pi\) | ||||
0.174664 | + | 0.984628i | \(0.444116\pi\) | |||||||
\(440\) | 1.36033 | 0.0648510 | ||||||||
\(441\) | −0.279231 | −0.0132967 | ||||||||
\(442\) | 10.6354 | 0.505875 | ||||||||
\(443\) | −9.31350 | −0.442498 | −0.221249 | − | 0.975217i | \(-0.571013\pi\) | ||||
−0.221249 | + | 0.975217i | \(0.571013\pi\) | |||||||
\(444\) | −4.82116 | −0.228802 | ||||||||
\(445\) | 0.296263 | 0.0140442 | ||||||||
\(446\) | 28.0974 | 1.33045 | ||||||||
\(447\) | 17.0108 | 0.804581 | ||||||||
\(448\) | 0.246249 | 0.0116342 | ||||||||
\(449\) | 11.8291 | 0.558252 | 0.279126 | − | 0.960254i | \(-0.409955\pi\) | ||||
0.279126 | + | 0.960254i | \(0.409955\pi\) | |||||||
\(450\) | −0.126312 | −0.00595439 | ||||||||
\(451\) | 9.92794 | 0.467489 | ||||||||
\(452\) | 19.5060 | 0.917484 | ||||||||
\(453\) | 5.49465 | 0.258161 | ||||||||
\(454\) | −10.8000 | −0.506868 | ||||||||
\(455\) | 0.484637 | 0.0227201 | ||||||||
\(456\) | −0.221579 | −0.0103764 | ||||||||
\(457\) | −7.75579 | −0.362801 | −0.181400 | − | 0.983409i | \(-0.558063\pi\) | ||||
−0.181400 | + | 0.983409i | \(0.558063\pi\) | |||||||
\(458\) | −3.86486 | −0.180593 | ||||||||
\(459\) | 38.0443 | 1.77576 | ||||||||
\(460\) | −1.36417 | −0.0636046 | ||||||||
\(461\) | −14.4336 | −0.672242 | −0.336121 | − | 0.941819i | \(-0.609115\pi\) | ||||
−0.336121 | + | 0.941819i | \(0.609115\pi\) | |||||||
\(462\) | −0.428158 | −0.0199197 | ||||||||
\(463\) | −3.16041 | −0.146877 | −0.0734383 | − | 0.997300i | \(-0.523397\pi\) | ||||
−0.0734383 | + | 0.997300i | \(0.523397\pi\) | |||||||
\(464\) | 3.04044 | 0.141149 | ||||||||
\(465\) | 16.8400 | 0.780936 | ||||||||
\(466\) | 9.20161 | 0.426256 | ||||||||
\(467\) | −24.0200 | −1.11151 | −0.555757 | − | 0.831345i | \(-0.687572\pi\) | ||||
−0.555757 | + | 0.831345i | \(0.687572\pi\) | |||||||
\(468\) | 0.0580524 | 0.00268347 | ||||||||
\(469\) | −3.48624 | −0.160980 | ||||||||
\(470\) | −15.7600 | −0.726956 | ||||||||
\(471\) | −17.4381 | −0.803504 | ||||||||
\(472\) | 10.4811 | 0.482432 | ||||||||
\(473\) | 8.16382 | 0.375373 | ||||||||
\(474\) | 19.1143 | 0.877949 | ||||||||
\(475\) | −0.398908 | −0.0183031 | ||||||||
\(476\) | 1.81532 | 0.0832051 | ||||||||
\(477\) | 0.125293 | 0.00573675 | ||||||||
\(478\) | −7.41788 | −0.339286 | ||||||||
\(479\) | 9.17663 | 0.419291 | 0.209646 | − | 0.977777i | \(-0.432769\pi\) | ||||
0.209646 | + | 0.977777i | \(0.432769\pi\) | |||||||
\(480\) | −2.37860 | −0.108568 | ||||||||
\(481\) | 3.98908 | 0.181887 | ||||||||
\(482\) | 14.9370 | 0.680362 | ||||||||
\(483\) | 0.429367 | 0.0195369 | ||||||||
\(484\) | −10.0056 | −0.454801 | ||||||||
\(485\) | 15.2832 | 0.693973 | ||||||||
\(486\) | 0.418146 | 0.0189675 | ||||||||
\(487\) | 20.1543 | 0.913279 | 0.456640 | − | 0.889652i | \(-0.349053\pi\) | ||||
0.456640 | + | 0.889652i | \(0.349053\pi\) | |||||||
\(488\) | −2.02027 | −0.0914531 | ||||||||
\(489\) | 4.15526 | 0.187907 | ||||||||
\(490\) | −9.46644 | −0.427650 | ||||||||
\(491\) | 35.6510 | 1.60891 | 0.804454 | − | 0.594015i | \(-0.202458\pi\) | ||||
0.804454 | + | 0.594015i | \(0.202458\pi\) | |||||||
\(492\) | −17.3595 | −0.782627 | ||||||||
\(493\) | 22.4138 | 1.00947 | ||||||||
\(494\) | 0.183337 | 0.00824870 | ||||||||
\(495\) | 0.0547379 | 0.00246029 | ||||||||
\(496\) | −7.07979 | −0.317892 | ||||||||
\(497\) | 2.39592 | 0.107472 | ||||||||
\(498\) | 0.210659 | 0.00943987 | ||||||||
\(499\) | −28.9004 | −1.29376 | −0.646879 | − | 0.762593i | \(-0.723926\pi\) | ||||
−0.646879 | + | 0.762593i | \(0.723926\pi\) | |||||||
\(500\) | −11.1030 | −0.496542 | ||||||||
\(501\) | −34.6884 | −1.54976 | ||||||||
\(502\) | 9.89554 | 0.441659 | ||||||||
\(503\) | 19.1967 | 0.855941 | 0.427970 | − | 0.903793i | \(-0.359229\pi\) | ||||
0.427970 | + | 0.903793i | \(0.359229\pi\) | |||||||
\(504\) | 0.00990876 | 0.000441371 0 | ||||||||
\(505\) | 12.1895 | 0.542426 | ||||||||
\(506\) | −0.997185 | −0.0443303 | ||||||||
\(507\) | 19.0380 | 0.845508 | ||||||||
\(508\) | 15.2538 | 0.676776 | ||||||||
\(509\) | 4.21290 | 0.186733 | 0.0933667 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933667 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(510\) | −17.5348 | −0.776453 | ||||||||
\(511\) | −0.510575 | −0.0225865 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.655820 | 0.0289551 | ||||||||
\(514\) | 9.73200 | 0.429260 | ||||||||
\(515\) | −12.3130 | −0.542576 | ||||||||
\(516\) | −14.2748 | −0.628415 | ||||||||
\(517\) | −11.5204 | −0.506665 | ||||||||
\(518\) | 0.680883 | 0.0299163 | ||||||||
\(519\) | 20.7684 | 0.911630 | ||||||||
\(520\) | 1.96808 | 0.0863059 | ||||||||
\(521\) | −33.7554 | −1.47885 | −0.739426 | − | 0.673238i | \(-0.764903\pi\) | ||||
−0.739426 | + | 0.673238i | \(0.764903\pi\) | |||||||
\(522\) | 0.122344 | 0.00535483 | ||||||||
\(523\) | −32.4611 | −1.41943 | −0.709713 | − | 0.704491i | \(-0.751175\pi\) | ||||
−0.709713 | + | 0.704491i | \(0.751175\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 1.34780 | 0.0588229 | ||||||||
\(526\) | −27.9012 | −1.21655 | ||||||||
\(527\) | −52.1915 | −2.27350 | ||||||||
\(528\) | −1.73872 | −0.0756681 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 4.24764 | 0.184506 | ||||||||
\(531\) | 0.421747 | 0.0183023 | ||||||||
\(532\) | 0.0312931 | 0.00135673 | ||||||||
\(533\) | 14.3634 | 0.622150 | ||||||||
\(534\) | −0.378672 | −0.0163868 | ||||||||
\(535\) | 18.9876 | 0.820906 | ||||||||
\(536\) | −14.1574 | −0.611506 | ||||||||
\(537\) | −4.97539 | −0.214704 | ||||||||
\(538\) | 29.5144 | 1.27246 | ||||||||
\(539\) | −6.91983 | −0.298058 | ||||||||
\(540\) | 7.04008 | 0.302957 | ||||||||
\(541\) | 12.8940 | 0.554356 | 0.277178 | − | 0.960819i | \(-0.410601\pi\) | ||||
0.277178 | + | 0.960819i | \(0.410601\pi\) | |||||||
\(542\) | 5.94548 | 0.255380 | ||||||||
\(543\) | −11.1658 | −0.479172 | ||||||||
\(544\) | 7.37189 | 0.316067 | ||||||||
\(545\) | 14.2668 | 0.611121 | ||||||||
\(546\) | −0.619446 | −0.0265098 | ||||||||
\(547\) | 3.71031 | 0.158641 | 0.0793206 | − | 0.996849i | \(-0.474725\pi\) | ||||
0.0793206 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(548\) | −6.20057 | −0.264875 | ||||||||
\(549\) | −0.0812930 | −0.00346950 | ||||||||
\(550\) | −3.13022 | −0.133473 | ||||||||
\(551\) | 0.386376 | 0.0164602 | ||||||||
\(552\) | 1.74363 | 0.0742137 | ||||||||
\(553\) | −2.69947 | −0.114793 | ||||||||
\(554\) | 4.76161 | 0.202301 | ||||||||
\(555\) | −6.57687 | −0.279173 | ||||||||
\(556\) | 10.1560 | 0.430709 | ||||||||
\(557\) | 6.88278 | 0.291633 | 0.145816 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145816 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(558\) | −0.284882 | −0.0120600 | ||||||||
\(559\) | 11.8112 | 0.499559 | ||||||||
\(560\) | 0.335924 | 0.0141954 | ||||||||
\(561\) | −12.8177 | −0.541162 | ||||||||
\(562\) | −2.55357 | −0.107716 | ||||||||
\(563\) | −31.3575 | −1.32156 | −0.660780 | − | 0.750579i | \(-0.729775\pi\) | ||||
−0.660780 | + | 0.750579i | \(0.729775\pi\) | |||||||
\(564\) | 20.1439 | 0.848212 | ||||||||
\(565\) | 26.6094 | 1.11947 | ||||||||
\(566\) | 19.0982 | 0.802759 | ||||||||
\(567\) | −2.24557 | −0.0943050 | ||||||||
\(568\) | 9.72966 | 0.408248 | ||||||||
\(569\) | 0.412572 | 0.0172959 | 0.00864796 | − | 0.999963i | \(-0.497247\pi\) | ||||
0.00864796 | + | 0.999963i | \(0.497247\pi\) | |||||||
\(570\) | −0.302270 | −0.0126607 | ||||||||
\(571\) | −16.4158 | −0.686981 | −0.343491 | − | 0.939156i | \(-0.611609\pi\) | ||||
−0.343491 | + | 0.939156i | \(0.611609\pi\) | |||||||
\(572\) | 1.43864 | 0.0601524 | ||||||||
\(573\) | 2.68646 | 0.112228 | ||||||||
\(574\) | 2.45165 | 0.102330 | ||||||||
\(575\) | 3.13905 | 0.130907 | ||||||||
\(576\) | 0.0402388 | 0.00167662 | ||||||||
\(577\) | 31.4910 | 1.31099 | 0.655493 | − | 0.755201i | \(-0.272461\pi\) | ||||
0.655493 | + | 0.755201i | \(0.272461\pi\) | |||||||
\(578\) | 37.3448 | 1.55334 | ||||||||
\(579\) | 18.1076 | 0.752525 | ||||||||
\(580\) | 4.14766 | 0.172222 | ||||||||
\(581\) | −0.0297510 | −0.00123428 | ||||||||
\(582\) | −19.5344 | −0.809727 | ||||||||
\(583\) | 3.10496 | 0.128594 | ||||||||
\(584\) | −2.07341 | −0.0857983 | ||||||||
\(585\) | 0.0791931 | 0.00327423 | ||||||||
\(586\) | 25.3806 | 1.04846 | ||||||||
\(587\) | −12.8077 | −0.528630 | −0.264315 | − | 0.964436i | \(-0.585146\pi\) | ||||
−0.264315 | + | 0.964436i | \(0.585146\pi\) | |||||||
\(588\) | 12.0997 | 0.498982 | ||||||||
\(589\) | −0.899694 | −0.0370712 | ||||||||
\(590\) | 14.2980 | 0.588638 | ||||||||
\(591\) | −40.1403 | −1.65115 | ||||||||
\(592\) | 2.76502 | 0.113642 | ||||||||
\(593\) | −45.6946 | −1.87645 | −0.938226 | − | 0.346024i | \(-0.887531\pi\) | ||||
−0.938226 | + | 0.346024i | \(0.887531\pi\) | |||||||
\(594\) | 5.14620 | 0.211151 | ||||||||
\(595\) | 2.47640 | 0.101522 | ||||||||
\(596\) | −9.75595 | −0.399619 | ||||||||
\(597\) | 24.1098 | 0.986748 | ||||||||
\(598\) | −1.44270 | −0.0589963 | ||||||||
\(599\) | −44.7825 | −1.82976 | −0.914882 | − | 0.403722i | \(-0.867716\pi\) | ||||
−0.914882 | + | 0.403722i | \(0.867716\pi\) | |||||||
\(600\) | 5.47334 | 0.223448 | ||||||||
\(601\) | −24.2363 | −0.988619 | −0.494309 | − | 0.869286i | \(-0.664579\pi\) | ||||
−0.494309 | + | 0.869286i | \(0.664579\pi\) | |||||||
\(602\) | 2.01601 | 0.0821663 | ||||||||
\(603\) | −0.569676 | −0.0231990 | ||||||||
\(604\) | −3.15127 | −0.128224 | ||||||||
\(605\) | −13.6493 | −0.554924 | ||||||||
\(606\) | −15.5802 | −0.632901 | ||||||||
\(607\) | 6.32673 | 0.256794 | 0.128397 | − | 0.991723i | \(-0.459017\pi\) | ||||
0.128397 | + | 0.991723i | \(0.459017\pi\) | |||||||
\(608\) | 0.127079 | 0.00515374 | ||||||||
\(609\) | −1.30546 | −0.0529000 | ||||||||
\(610\) | −2.75598 | −0.111586 | ||||||||
\(611\) | −16.6673 | −0.674286 | ||||||||
\(612\) | 0.296636 | 0.0119908 | ||||||||
\(613\) | 4.42348 | 0.178663 | 0.0893314 | − | 0.996002i | \(-0.471527\pi\) | ||||
0.0893314 | + | 0.996002i | \(0.471527\pi\) | |||||||
\(614\) | −28.7690 | −1.16102 | ||||||||
\(615\) | −23.6812 | −0.954920 | ||||||||
\(616\) | 0.245556 | 0.00989373 | ||||||||
\(617\) | 28.2911 | 1.13896 | 0.569478 | − | 0.822007i | \(-0.307145\pi\) | ||||
0.569478 | + | 0.822007i | \(0.307145\pi\) | |||||||
\(618\) | 15.7380 | 0.633076 | ||||||||
\(619\) | −5.85911 | −0.235497 | −0.117749 | − | 0.993043i | \(-0.537568\pi\) | ||||
−0.117749 | + | 0.993043i | \(0.537568\pi\) | |||||||
\(620\) | −9.65802 | −0.387875 | ||||||||
\(621\) | −5.16072 | −0.207093 | ||||||||
\(622\) | 7.33784 | 0.294221 | ||||||||
\(623\) | 0.0534791 | 0.00214260 | ||||||||
\(624\) | −2.51553 | −0.100702 | ||||||||
\(625\) | 0.548889 | 0.0219556 | ||||||||
\(626\) | −23.4443 | −0.937024 | ||||||||
\(627\) | −0.220955 | −0.00882409 | ||||||||
\(628\) | 10.0010 | 0.399084 | ||||||||
\(629\) | 20.3834 | 0.812740 | ||||||||
\(630\) | 0.0135172 | 0.000538538 0 | ||||||||
\(631\) | 7.60584 | 0.302784 | 0.151392 | − | 0.988474i | \(-0.451624\pi\) | ||||
0.151392 | + | 0.988474i | \(0.451624\pi\) | |||||||
\(632\) | −10.9624 | −0.436060 | ||||||||
\(633\) | −1.25060 | −0.0497067 | ||||||||
\(634\) | 7.85505 | 0.311964 | ||||||||
\(635\) | 20.8087 | 0.825767 | ||||||||
\(636\) | −5.42918 | −0.215281 | ||||||||
\(637\) | −10.0114 | −0.396666 | ||||||||
\(638\) | 3.03188 | 0.120033 | ||||||||
\(639\) | 0.391510 | 0.0154879 | ||||||||
\(640\) | 1.36417 | 0.0539234 | ||||||||
\(641\) | −11.8032 | −0.466199 | −0.233099 | − | 0.972453i | \(-0.574887\pi\) | ||||
−0.233099 | + | 0.972453i | \(0.574887\pi\) | |||||||
\(642\) | −24.2693 | −0.957833 | ||||||||
\(643\) | −8.95080 | −0.352985 | −0.176492 | − | 0.984302i | \(-0.556475\pi\) | ||||
−0.176492 | + | 0.984302i | \(0.556475\pi\) | |||||||
\(644\) | −0.246249 | −0.00970357 | ||||||||
\(645\) | −19.4733 | −0.766759 | ||||||||
\(646\) | 0.936813 | 0.0368584 | ||||||||
\(647\) | −35.2340 | −1.38519 | −0.692596 | − | 0.721325i | \(-0.743533\pi\) | ||||
−0.692596 | + | 0.721325i | \(0.743533\pi\) | |||||||
\(648\) | −9.11910 | −0.358232 | ||||||||
\(649\) | 10.4516 | 0.410262 | ||||||||
\(650\) | −4.52870 | −0.177630 | ||||||||
\(651\) | 3.03983 | 0.119140 | ||||||||
\(652\) | −2.38311 | −0.0933299 | ||||||||
\(653\) | −33.1240 | −1.29624 | −0.648120 | − | 0.761538i | \(-0.724445\pi\) | ||||
−0.648120 | + | 0.761538i | \(0.724445\pi\) | |||||||
\(654\) | −18.2353 | −0.713055 | ||||||||
\(655\) | −1.36417 | −0.0533024 | ||||||||
\(656\) | 9.95597 | 0.388715 | ||||||||
\(657\) | −0.0834315 | −0.00325497 | ||||||||
\(658\) | −2.84488 | −0.110905 | ||||||||
\(659\) | −0.0712961 | −0.00277730 | −0.00138865 | − | 0.999999i | \(-0.500442\pi\) | ||||
−0.00138865 | + | 0.999999i | \(0.500442\pi\) | |||||||
\(660\) | −2.37190 | −0.0923262 | ||||||||
\(661\) | −32.6138 | −1.26853 | −0.634265 | − | 0.773116i | \(-0.718697\pi\) | ||||
−0.634265 | + | 0.773116i | \(0.718697\pi\) | |||||||
\(662\) | 5.10693 | 0.198486 | ||||||||
\(663\) | −18.5442 | −0.720197 | ||||||||
\(664\) | −0.120817 | −0.00468860 | ||||||||
\(665\) | 0.0426890 | 0.00165541 | ||||||||
\(666\) | 0.111261 | 0.00431128 | ||||||||
\(667\) | −3.04044 | −0.117726 | ||||||||
\(668\) | 19.8944 | 0.769736 | ||||||||
\(669\) | −48.9915 | −1.89412 | ||||||||
\(670\) | −19.3130 | −0.746127 | ||||||||
\(671\) | −2.01458 | −0.0777720 | ||||||||
\(672\) | −0.429367 | −0.0165632 | ||||||||
\(673\) | 18.4365 | 0.710675 | 0.355338 | − | 0.934738i | \(-0.384366\pi\) | ||||
0.355338 | + | 0.934738i | \(0.384366\pi\) | |||||||
\(674\) | −5.56800 | −0.214471 | ||||||||
\(675\) | −16.1998 | −0.623529 | ||||||||
\(676\) | −10.9186 | −0.419947 | ||||||||
\(677\) | 17.2492 | 0.662939 | 0.331470 | − | 0.943466i | \(-0.392456\pi\) | ||||
0.331470 | + | 0.943466i | \(0.392456\pi\) | |||||||
\(678\) | −34.0112 | −1.30619 | ||||||||
\(679\) | 2.75880 | 0.105873 | ||||||||
\(680\) | 10.0565 | 0.385649 | ||||||||
\(681\) | 18.8311 | 0.721611 | ||||||||
\(682\) | −7.05987 | −0.270336 | ||||||||
\(683\) | 21.8802 | 0.837224 | 0.418612 | − | 0.908165i | \(-0.362517\pi\) | ||||
0.418612 | + | 0.908165i | \(0.362517\pi\) | |||||||
\(684\) | 0.00511351 | 0.000195520 0 | ||||||||
\(685\) | −8.45861 | −0.323187 | ||||||||
\(686\) | −3.43255 | −0.131055 | ||||||||
\(687\) | 6.73887 | 0.257104 | ||||||||
\(688\) | 8.18686 | 0.312121 | ||||||||
\(689\) | 4.49216 | 0.171138 | ||||||||
\(690\) | 2.37860 | 0.0905517 | ||||||||
\(691\) | −21.4768 | −0.817017 | −0.408509 | − | 0.912754i | \(-0.633951\pi\) | ||||
−0.408509 | + | 0.912754i | \(0.633951\pi\) | |||||||
\(692\) | −11.9110 | −0.452788 | ||||||||
\(693\) | 0.00988087 | 0.000375343 0 | ||||||||
\(694\) | 23.3865 | 0.887740 | ||||||||
\(695\) | 13.8544 | 0.525529 | ||||||||
\(696\) | −5.30140 | −0.200949 | ||||||||
\(697\) | 73.3943 | 2.78001 | ||||||||
\(698\) | −11.2297 | −0.425051 | ||||||||
\(699\) | −16.0442 | −0.606847 | ||||||||
\(700\) | −0.772988 | −0.0292162 | ||||||||
\(701\) | −36.7402 | −1.38766 | −0.693830 | − | 0.720139i | \(-0.744078\pi\) | ||||
−0.693830 | + | 0.720139i | \(0.744078\pi\) | |||||||
\(702\) | 7.44536 | 0.281007 | ||||||||
\(703\) | 0.351376 | 0.0132524 | ||||||||
\(704\) | 0.997185 | 0.0375828 | ||||||||
\(705\) | 27.4796 | 1.03494 | ||||||||
\(706\) | −18.4868 | −0.695759 | ||||||||
\(707\) | 2.20036 | 0.0827529 | ||||||||
\(708\) | −18.2752 | −0.686822 | ||||||||
\(709\) | 13.3657 | 0.501961 | 0.250980 | − | 0.967992i | \(-0.419247\pi\) | ||||
0.250980 | + | 0.967992i | \(0.419247\pi\) | |||||||
\(710\) | 13.2729 | 0.498122 | ||||||||
\(711\) | −0.441112 | −0.0165430 | ||||||||
\(712\) | 0.217175 | 0.00813898 | ||||||||
\(713\) | 7.07979 | 0.265140 | ||||||||
\(714\) | −3.16524 | −0.118456 | ||||||||
\(715\) | 1.96254 | 0.0733948 | ||||||||
\(716\) | 2.85347 | 0.106639 | ||||||||
\(717\) | 12.9340 | 0.483030 | ||||||||
\(718\) | 15.5631 | 0.580810 | ||||||||
\(719\) | 0.603503 | 0.0225069 | 0.0112534 | − | 0.999937i | \(-0.496418\pi\) | ||||
0.0112534 | + | 0.999937i | \(0.496418\pi\) | |||||||
\(720\) | 0.0548924 | 0.00204572 | ||||||||
\(721\) | −2.22265 | −0.0827758 | ||||||||
\(722\) | −18.9839 | −0.706506 | ||||||||
\(723\) | −26.0446 | −0.968609 | ||||||||
\(724\) | 6.40380 | 0.237995 | ||||||||
\(725\) | −9.54409 | −0.354459 | ||||||||
\(726\) | 17.4461 | 0.647485 | ||||||||
\(727\) | 28.8113 | 1.06855 | 0.534276 | − | 0.845310i | \(-0.320584\pi\) | ||||
0.534276 | + | 0.845310i | \(0.320584\pi\) | |||||||
\(728\) | 0.355262 | 0.0131669 | ||||||||
\(729\) | 26.6282 | 0.986230 | ||||||||
\(730\) | −2.82848 | −0.104687 | ||||||||
\(731\) | 60.3527 | 2.23222 | ||||||||
\(732\) | 3.52259 | 0.130199 | ||||||||
\(733\) | 45.3067 | 1.67344 | 0.836720 | − | 0.547631i | \(-0.184470\pi\) | ||||
0.836720 | + | 0.547631i | \(0.184470\pi\) | |||||||
\(734\) | −6.14723 | −0.226898 | ||||||||
\(735\) | 16.5060 | 0.608831 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −14.1175 | −0.520026 | ||||||||
\(738\) | 0.400616 | 0.0147469 | ||||||||
\(739\) | −44.2885 | −1.62918 | −0.814589 | − | 0.580039i | \(-0.803037\pi\) | ||||
−0.814589 | + | 0.580039i | \(0.803037\pi\) | |||||||
\(740\) | 3.77194 | 0.138659 | ||||||||
\(741\) | −0.319671 | −0.0117434 | ||||||||
\(742\) | 0.766751 | 0.0281483 | ||||||||
\(743\) | −19.8217 | −0.727189 | −0.363594 | − | 0.931557i | \(-0.618451\pi\) | ||||
−0.363594 | + | 0.931557i | \(0.618451\pi\) | |||||||
\(744\) | 12.3445 | 0.452572 | ||||||||
\(745\) | −13.3087 | −0.487595 | ||||||||
\(746\) | 11.8605 | 0.434245 | ||||||||
\(747\) | −0.00486152 | −0.000177874 0 | ||||||||
\(748\) | 7.35114 | 0.268784 | ||||||||
\(749\) | 3.42750 | 0.125238 | ||||||||
\(750\) | 19.3595 | 0.706910 | ||||||||
\(751\) | 21.3947 | 0.780703 | 0.390352 | − | 0.920666i | \(-0.372353\pi\) | ||||
0.390352 | + | 0.920666i | \(0.372353\pi\) | |||||||
\(752\) | −11.5529 | −0.421290 | ||||||||
\(753\) | −17.2541 | −0.628776 | ||||||||
\(754\) | 4.38643 | 0.159744 | ||||||||
\(755\) | −4.29886 | −0.156452 | ||||||||
\(756\) | 1.27082 | 0.0462194 | ||||||||
\(757\) | 37.7286 | 1.37127 | 0.685635 | − | 0.727945i | \(-0.259524\pi\) | ||||
0.685635 | + | 0.727945i | \(0.259524\pi\) | |||||||
\(758\) | −34.6762 | −1.25950 | ||||||||
\(759\) | 1.73872 | 0.0631116 | ||||||||
\(760\) | 0.173357 | 0.00628832 | ||||||||
\(761\) | 10.0487 | 0.364266 | 0.182133 | − | 0.983274i | \(-0.441700\pi\) | ||||
0.182133 | + | 0.983274i | \(0.441700\pi\) | |||||||
\(762\) | −26.5969 | −0.963504 | ||||||||
\(763\) | 2.57533 | 0.0932331 | ||||||||
\(764\) | −1.54073 | −0.0557416 | ||||||||
\(765\) | 0.404661 | 0.0146305 | ||||||||
\(766\) | 34.3641 | 1.24163 | ||||||||
\(767\) | 15.1211 | 0.545990 | ||||||||
\(768\) | −1.74363 | −0.0629178 | ||||||||
\(769\) | −11.8606 | −0.427705 | −0.213852 | − | 0.976866i | \(-0.568601\pi\) | ||||
−0.213852 | + | 0.976866i | \(0.568601\pi\) | |||||||
\(770\) | 0.334979 | 0.0120718 | ||||||||
\(771\) | −16.9690 | −0.611123 | ||||||||
\(772\) | −10.3850 | −0.373764 | ||||||||
\(773\) | −38.6458 | −1.38999 | −0.694996 | − | 0.719013i | \(-0.744594\pi\) | ||||
−0.694996 | + | 0.719013i | \(0.744594\pi\) | |||||||
\(774\) | 0.329429 | 0.0118411 | ||||||||
\(775\) | 22.2238 | 0.798304 | ||||||||
\(776\) | 11.2033 | 0.402175 | ||||||||
\(777\) | −1.18721 | −0.0425908 | ||||||||
\(778\) | 16.8196 | 0.603013 | ||||||||
\(779\) | 1.26519 | 0.0453303 | ||||||||
\(780\) | −3.43160 | −0.122871 | ||||||||
\(781\) | 9.70228 | 0.347175 | ||||||||
\(782\) | −7.37189 | −0.263618 | ||||||||
\(783\) | 15.6909 | 0.560746 | ||||||||
\(784\) | −6.93936 | −0.247834 | ||||||||
\(785\) | 13.6431 | 0.486942 | ||||||||
\(786\) | 1.74363 | 0.0621932 | ||||||||
\(787\) | −27.7596 | −0.989524 | −0.494762 | − | 0.869028i | \(-0.664745\pi\) | ||||
−0.494762 | + | 0.869028i | \(0.664745\pi\) | |||||||
\(788\) | 23.0211 | 0.820094 | ||||||||
\(789\) | 48.6493 | 1.73196 | ||||||||
\(790\) | −14.9545 | −0.532057 | ||||||||
\(791\) | 4.80332 | 0.170787 | ||||||||
\(792\) | 0.0401255 | 0.00142580 | ||||||||
\(793\) | −2.91463 | −0.103502 | ||||||||
\(794\) | 14.1294 | 0.501433 | ||||||||
\(795\) | −7.40630 | −0.262674 | ||||||||
\(796\) | −13.8274 | −0.490098 | ||||||||
\(797\) | 0.721464 | 0.0255556 | 0.0127778 | − | 0.999918i | \(-0.495933\pi\) | ||||
0.0127778 | + | 0.999918i | \(0.495933\pi\) | |||||||
\(798\) | −0.0545635 | −0.00193153 | ||||||||
\(799\) | −85.1665 | −3.01298 | ||||||||
\(800\) | −3.13905 | −0.110982 | ||||||||
\(801\) | 0.00873886 | 0.000308772 0 | ||||||||
\(802\) | −5.45756 | −0.192713 | ||||||||
\(803\) | −2.06757 | −0.0729631 | ||||||||
\(804\) | 24.6852 | 0.870580 | ||||||||
\(805\) | −0.335924 | −0.0118398 | ||||||||
\(806\) | −10.2140 | −0.359773 | ||||||||
\(807\) | −51.4622 | −1.81155 | ||||||||
\(808\) | 8.93549 | 0.314350 | ||||||||
\(809\) | 38.2714 | 1.34555 | 0.672775 | − | 0.739847i | \(-0.265102\pi\) | ||||
0.672775 | + | 0.739847i | \(0.265102\pi\) | |||||||
\(810\) | −12.4400 | −0.437096 | ||||||||
\(811\) | −35.8424 | −1.25860 | −0.629298 | − | 0.777164i | \(-0.716658\pi\) | ||||
−0.629298 | + | 0.777164i | \(0.716658\pi\) | |||||||
\(812\) | 0.748705 | 0.0262744 | ||||||||
\(813\) | −10.3667 | −0.363576 | ||||||||
\(814\) | 2.75724 | 0.0966411 | ||||||||
\(815\) | −3.25096 | −0.113876 | ||||||||
\(816\) | −12.8538 | −0.449974 | ||||||||
\(817\) | 1.04038 | 0.0363982 | ||||||||
\(818\) | 39.2662 | 1.37291 | ||||||||
\(819\) | 0.0142953 | 0.000499519 0 | ||||||||
\(820\) | 13.5816 | 0.474290 | ||||||||
\(821\) | 13.1870 | 0.460230 | 0.230115 | − | 0.973163i | \(-0.426090\pi\) | ||||
0.230115 | + | 0.973163i | \(0.426090\pi\) | |||||||
\(822\) | 10.8115 | 0.377094 | ||||||||
\(823\) | 11.6916 | 0.407542 | 0.203771 | − | 0.979019i | \(-0.434680\pi\) | ||||
0.203771 | + | 0.979019i | \(0.434680\pi\) | |||||||
\(824\) | −9.02603 | −0.314437 | ||||||||
\(825\) | 5.45793 | 0.190021 | ||||||||
\(826\) | 2.58096 | 0.0898031 | ||||||||
\(827\) | 35.0321 | 1.21819 | 0.609093 | − | 0.793099i | \(-0.291533\pi\) | ||||
0.609093 | + | 0.793099i | \(0.291533\pi\) | |||||||
\(828\) | −0.0402388 | −0.00139839 | ||||||||
\(829\) | 35.4622 | 1.23165 | 0.615827 | − | 0.787882i | \(-0.288822\pi\) | ||||
0.615827 | + | 0.787882i | \(0.288822\pi\) | |||||||
\(830\) | −0.164814 | −0.00572078 | ||||||||
\(831\) | −8.30247 | −0.288010 | ||||||||
\(832\) | 1.44270 | 0.0500165 | ||||||||
\(833\) | −51.1562 | −1.77246 | ||||||||
\(834\) | −17.7082 | −0.613186 | ||||||||
\(835\) | 27.1392 | 0.939191 | ||||||||
\(836\) | 0.126721 | 0.00438275 | ||||||||
\(837\) | −36.5369 | −1.26290 | ||||||||
\(838\) | 1.83398 | 0.0633538 | ||||||||
\(839\) | 12.1039 | 0.417872 | 0.208936 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208936 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(840\) | −0.585727 | −0.0202095 | ||||||||
\(841\) | −19.7557 | −0.681232 | ||||||||
\(842\) | −1.43510 | −0.0494568 | ||||||||
\(843\) | 4.45248 | 0.153351 | ||||||||
\(844\) | 0.717238 | 0.0246883 | ||||||||
\(845\) | −14.8948 | −0.512397 | ||||||||
\(846\) | −0.464874 | −0.0159827 | ||||||||
\(847\) | −2.46387 | −0.0846597 | ||||||||
\(848\) | 3.11372 | 0.106926 | ||||||||
\(849\) | −33.3002 | −1.14286 | ||||||||
\(850\) | −23.1407 | −0.793721 | ||||||||
\(851\) | −2.76502 | −0.0947836 | ||||||||
\(852\) | −16.9649 | −0.581208 | ||||||||
\(853\) | −58.0382 | −1.98719 | −0.993595 | − | 0.112998i | \(-0.963955\pi\) | ||||
−0.993595 | + | 0.112998i | \(0.963955\pi\) | |||||||
\(854\) | −0.497488 | −0.0170237 | ||||||||
\(855\) | 0.00697567 | 0.000238563 0 | ||||||||
\(856\) | 13.9188 | 0.475736 | ||||||||
\(857\) | −16.2303 | −0.554415 | −0.277207 | − | 0.960810i | \(-0.589409\pi\) | ||||
−0.277207 | + | 0.960810i | \(0.589409\pi\) | |||||||
\(858\) | −2.50845 | −0.0856369 | ||||||||
\(859\) | −22.6080 | −0.771375 | −0.385688 | − | 0.922629i | \(-0.626036\pi\) | ||||
−0.385688 | + | 0.922629i | \(0.626036\pi\) | |||||||
\(860\) | 11.1682 | 0.380834 | ||||||||
\(861\) | −4.27476 | −0.145683 | ||||||||
\(862\) | −8.27409 | −0.281817 | ||||||||
\(863\) | −21.6136 | −0.735735 | −0.367868 | − | 0.929878i | \(-0.619912\pi\) | ||||
−0.367868 | + | 0.929878i | \(0.619912\pi\) | |||||||
\(864\) | 5.16072 | 0.175571 | ||||||||
\(865\) | −16.2486 | −0.552468 | ||||||||
\(866\) | 18.7308 | 0.636499 | ||||||||
\(867\) | −65.1154 | −2.21144 | ||||||||
\(868\) | −1.74339 | −0.0591746 | ||||||||
\(869\) | −10.9315 | −0.370826 | ||||||||
\(870\) | −7.23198 | −0.245187 | ||||||||
\(871\) | −20.4248 | −0.692068 | ||||||||
\(872\) | 10.4582 | 0.354160 | ||||||||
\(873\) | 0.450808 | 0.0152575 | ||||||||
\(874\) | −0.127079 | −0.00429851 | ||||||||
\(875\) | −2.73411 | −0.0924297 | ||||||||
\(876\) | 3.61526 | 0.122148 | ||||||||
\(877\) | −33.5071 | −1.13145 | −0.565727 | − | 0.824592i | \(-0.691404\pi\) | ||||
−0.565727 | + | 0.824592i | \(0.691404\pi\) | |||||||
\(878\) | 7.31923 | 0.247012 | ||||||||
\(879\) | −44.2544 | −1.49266 | ||||||||
\(880\) | 1.36033 | 0.0458566 | ||||||||
\(881\) | 23.2254 | 0.782483 | 0.391242 | − | 0.920288i | \(-0.372046\pi\) | ||||
0.391242 | + | 0.920288i | \(0.372046\pi\) | |||||||
\(882\) | −0.279231 | −0.00940221 | ||||||||
\(883\) | −21.6898 | −0.729918 | −0.364959 | − | 0.931024i | \(-0.618917\pi\) | ||||
−0.364959 | + | 0.931024i | \(0.618917\pi\) | |||||||
\(884\) | 10.6354 | 0.357707 | ||||||||
\(885\) | −24.9304 | −0.838025 | ||||||||
\(886\) | −9.31350 | −0.312893 | ||||||||
\(887\) | 22.9021 | 0.768976 | 0.384488 | − | 0.923130i | \(-0.374378\pi\) | ||||
0.384488 | + | 0.923130i | \(0.374378\pi\) | |||||||
\(888\) | −4.82116 | −0.161788 | ||||||||
\(889\) | 3.75622 | 0.125980 | ||||||||
\(890\) | 0.296263 | 0.00993075 | ||||||||
\(891\) | −9.09343 | −0.304641 | ||||||||
\(892\) | 28.0974 | 0.940771 | ||||||||
\(893\) | −1.46813 | −0.0491290 | ||||||||
\(894\) | 17.0108 | 0.568925 | ||||||||
\(895\) | 3.89260 | 0.130115 | ||||||||
\(896\) | 0.246249 | 0.00822660 | ||||||||
\(897\) | 2.51553 | 0.0839910 | ||||||||
\(898\) | 11.8291 | 0.394744 | ||||||||
\(899\) | −21.5257 | −0.717922 | ||||||||
\(900\) | −0.126312 | −0.00421039 | ||||||||
\(901\) | 22.9540 | 0.764710 | ||||||||
\(902\) | 9.92794 | 0.330564 | ||||||||
\(903\) | −3.51517 | −0.116977 | ||||||||
\(904\) | 19.5060 | 0.648759 | ||||||||
\(905\) | 8.73584 | 0.290389 | ||||||||
\(906\) | 5.49465 | 0.182548 | ||||||||
\(907\) | −23.5007 | −0.780329 | −0.390165 | − | 0.920745i | \(-0.627582\pi\) | ||||
−0.390165 | + | 0.920745i | \(0.627582\pi\) | |||||||
\(908\) | −10.8000 | −0.358410 | ||||||||
\(909\) | 0.359553 | 0.0119256 | ||||||||
\(910\) | 0.484637 | 0.0160656 | ||||||||
\(911\) | −33.9597 | −1.12514 | −0.562568 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562568 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(912\) | −0.221579 | −0.00733720 | ||||||||
\(913\) | −0.120477 | −0.00398719 | ||||||||
\(914\) | −7.75579 | −0.256539 | ||||||||
\(915\) | 4.80540 | 0.158862 | ||||||||
\(916\) | −3.86486 | −0.127698 | ||||||||
\(917\) | −0.246249 | −0.00813186 | ||||||||
\(918\) | 38.0443 | 1.25565 | ||||||||
\(919\) | −40.0329 | −1.32056 | −0.660282 | − | 0.751018i | \(-0.729563\pi\) | ||||
−0.660282 | + | 0.751018i | \(0.729563\pi\) | |||||||
\(920\) | −1.36417 | −0.0449752 | ||||||||
\(921\) | 50.1625 | 1.65291 | ||||||||
\(922\) | −14.4336 | −0.475347 | ||||||||
\(923\) | 14.0369 | 0.462032 | ||||||||
\(924\) | −0.428158 | −0.0140854 | ||||||||
\(925\) | −8.67953 | −0.285381 | ||||||||
\(926\) | −3.16041 | −0.103857 | ||||||||
\(927\) | −0.363196 | −0.0119289 | ||||||||
\(928\) | 3.04044 | 0.0998073 | ||||||||
\(929\) | −0.704161 | −0.0231028 | −0.0115514 | − | 0.999933i | \(-0.503677\pi\) | ||||
−0.0115514 | + | 0.999933i | \(0.503677\pi\) | |||||||
\(930\) | 16.8400 | 0.552205 | ||||||||
\(931\) | −0.881847 | −0.0289014 | ||||||||
\(932\) | 9.20161 | 0.301409 | ||||||||
\(933\) | −12.7945 | −0.418872 | ||||||||
\(934\) | −24.0200 | −0.785960 | ||||||||
\(935\) | 10.0282 | 0.327957 | ||||||||
\(936\) | 0.0580524 | 0.00189750 | ||||||||
\(937\) | −30.7695 | −1.00520 | −0.502598 | − | 0.864520i | \(-0.667622\pi\) | ||||
−0.502598 | + | 0.864520i | \(0.667622\pi\) | |||||||
\(938\) | −3.48624 | −0.113830 | ||||||||
\(939\) | 40.8782 | 1.33401 | ||||||||
\(940\) | −15.7600 | −0.514036 | ||||||||
\(941\) | 13.7610 | 0.448596 | 0.224298 | − | 0.974521i | \(-0.427991\pi\) | ||||
0.224298 | + | 0.974521i | \(0.427991\pi\) | |||||||
\(942\) | −17.4381 | −0.568163 | ||||||||
\(943\) | −9.95597 | −0.324211 | ||||||||
\(944\) | 10.4811 | 0.341131 | ||||||||
\(945\) | 1.73361 | 0.0563944 | ||||||||
\(946\) | 8.16382 | 0.265429 | ||||||||
\(947\) | 18.9787 | 0.616725 | 0.308363 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308363 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(948\) | 19.1143 | 0.620803 | ||||||||
\(949\) | −2.99130 | −0.0971018 | ||||||||
\(950\) | −0.398908 | −0.0129423 | ||||||||
\(951\) | −13.6963 | −0.444132 | ||||||||
\(952\) | 1.81532 | 0.0588349 | ||||||||
\(953\) | −42.3132 | −1.37066 | −0.685329 | − | 0.728233i | \(-0.740342\pi\) | ||||
−0.685329 | + | 0.728233i | \(0.740342\pi\) | |||||||
\(954\) | 0.125293 | 0.00405649 | ||||||||
\(955\) | −2.10181 | −0.0680130 | ||||||||
\(956\) | −7.41788 | −0.239912 | ||||||||
\(957\) | −5.28647 | −0.170887 | ||||||||
\(958\) | 9.17663 | 0.296484 | ||||||||
\(959\) | −1.52688 | −0.0493057 | ||||||||
\(960\) | −2.37860 | −0.0767689 | ||||||||
\(961\) | 19.1235 | 0.616887 | ||||||||
\(962\) | 3.98908 | 0.128613 | ||||||||
\(963\) | 0.560078 | 0.0180482 | ||||||||
\(964\) | 14.9370 | 0.481089 | ||||||||
\(965\) | −14.1669 | −0.456048 | ||||||||
\(966\) | 0.429367 | 0.0138146 | ||||||||
\(967\) | 17.6001 | 0.565980 | 0.282990 | − | 0.959123i | \(-0.408674\pi\) | ||||
0.282990 | + | 0.959123i | \(0.408674\pi\) | |||||||
\(968\) | −10.0056 | −0.321593 | ||||||||
\(969\) | −1.63345 | −0.0524741 | ||||||||
\(970\) | 15.2832 | 0.490713 | ||||||||
\(971\) | −24.1878 | −0.776225 | −0.388112 | − | 0.921612i | \(-0.626873\pi\) | ||||
−0.388112 | + | 0.921612i | \(0.626873\pi\) | |||||||
\(972\) | 0.418146 | 0.0134120 | ||||||||
\(973\) | 2.50090 | 0.0801751 | ||||||||
\(974\) | 20.1543 | 0.645786 | ||||||||
\(975\) | 7.89636 | 0.252886 | ||||||||
\(976\) | −2.02027 | −0.0646671 | ||||||||
\(977\) | −9.61496 | −0.307610 | −0.153805 | − | 0.988101i | \(-0.549153\pi\) | ||||
−0.153805 | + | 0.988101i | \(0.549153\pi\) | |||||||
\(978\) | 4.15526 | 0.132871 | ||||||||
\(979\) | 0.216564 | 0.00692141 | ||||||||
\(980\) | −9.46644 | −0.302394 | ||||||||
\(981\) | 0.420827 | 0.0134360 | ||||||||
\(982\) | 35.6510 | 1.13767 | ||||||||
\(983\) | −51.4645 | −1.64146 | −0.820731 | − | 0.571314i | \(-0.806434\pi\) | ||||
−0.820731 | + | 0.571314i | \(0.806434\pi\) | |||||||
\(984\) | −17.3595 | −0.553401 | ||||||||
\(985\) | 31.4047 | 1.00064 | ||||||||
\(986\) | 22.4138 | 0.713801 | ||||||||
\(987\) | 4.96042 | 0.157892 | ||||||||
\(988\) | 0.183337 | 0.00583271 | ||||||||
\(989\) | −8.18686 | −0.260327 | ||||||||
\(990\) | 0.0547379 | 0.00173968 | ||||||||
\(991\) | 29.0849 | 0.923912 | 0.461956 | − | 0.886903i | \(-0.347148\pi\) | ||||
0.461956 | + | 0.886903i | \(0.347148\pi\) | |||||||
\(992\) | −7.07979 | −0.224784 | ||||||||
\(993\) | −8.90458 | −0.282578 | ||||||||
\(994\) | 2.39592 | 0.0759939 | ||||||||
\(995\) | −18.8628 | −0.597992 | ||||||||
\(996\) | 0.210659 | 0.00667500 | ||||||||
\(997\) | −39.4162 | −1.24832 | −0.624162 | − | 0.781295i | \(-0.714560\pi\) | ||||
−0.624162 | + | 0.781295i | \(0.714560\pi\) | |||||||
\(998\) | −28.9004 | −0.914825 | ||||||||
\(999\) | 14.2695 | 0.451467 |
(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 | 6026.2.a.k.1.10 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.k.1.10 | ✓ | 35 | 1.1 | even | 1 | trivial |