Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | 1.03782 | 0.599184 | 0.299592 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299592 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.03782 | −0.423687 | ||||||||
\(7\) | −3.65688 | −1.38217 | −0.691086 | − | 0.722773i | \(-0.742867\pi\) | ||||
−0.691086 | + | 0.722773i | \(0.742867\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.92294 | −0.640979 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.37688 | 1.01817 | 0.509083 | − | 0.860717i | \(-0.329984\pi\) | ||||
0.509083 | + | 0.860717i | \(0.329984\pi\) | |||||||
\(12\) | 1.03782 | 0.299592 | ||||||||
\(13\) | 3.74747 | 1.03936 | 0.519681 | − | 0.854361i | \(-0.326051\pi\) | ||||
0.519681 | + | 0.854361i | \(0.326051\pi\) | |||||||
\(14\) | 3.65688 | 0.977343 | ||||||||
\(15\) | 1.03782 | 0.267963 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.215513 | −0.0522697 | −0.0261348 | − | 0.999658i | \(-0.508320\pi\) | ||||
−0.0261348 | + | 0.999658i | \(0.508320\pi\) | |||||||
\(18\) | 1.92294 | 0.453240 | ||||||||
\(19\) | −3.16754 | −0.726685 | −0.363342 | − | 0.931656i | \(-0.618364\pi\) | ||||
−0.363342 | + | 0.931656i | \(0.618364\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.79517 | −0.828175 | ||||||||
\(22\) | −3.37688 | −0.719953 | ||||||||
\(23\) | 5.41020 | 1.12810 | 0.564052 | − | 0.825739i | \(-0.309242\pi\) | ||||
0.564052 | + | 0.825739i | \(0.309242\pi\) | |||||||
\(24\) | −1.03782 | −0.211843 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.74747 | −0.734939 | ||||||||
\(27\) | −5.10911 | −0.983248 | ||||||||
\(28\) | −3.65688 | −0.691086 | ||||||||
\(29\) | 0.812402 | 0.150859 | 0.0754297 | − | 0.997151i | \(-0.475967\pi\) | ||||
0.0754297 | + | 0.997151i | \(0.475967\pi\) | |||||||
\(30\) | −1.03782 | −0.189479 | ||||||||
\(31\) | 2.01579 | 0.362047 | 0.181024 | − | 0.983479i | \(-0.442059\pi\) | ||||
0.181024 | + | 0.983479i | \(0.442059\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.50458 | 0.610069 | ||||||||
\(34\) | 0.215513 | 0.0369602 | ||||||||
\(35\) | −3.65688 | −0.618126 | ||||||||
\(36\) | −1.92294 | −0.320489 | ||||||||
\(37\) | −1.23319 | −0.202736 | −0.101368 | − | 0.994849i | \(-0.532322\pi\) | ||||
−0.101368 | + | 0.994849i | \(0.532322\pi\) | |||||||
\(38\) | 3.16754 | 0.513844 | ||||||||
\(39\) | 3.88919 | 0.622768 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.22559 | −0.347578 | −0.173789 | − | 0.984783i | \(-0.555601\pi\) | ||||
−0.173789 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(42\) | 3.79517 | 0.585608 | ||||||||
\(43\) | 6.28835 | 0.958964 | 0.479482 | − | 0.877552i | \(-0.340825\pi\) | ||||
0.479482 | + | 0.877552i | \(0.340825\pi\) | |||||||
\(44\) | 3.37688 | 0.509083 | ||||||||
\(45\) | −1.92294 | −0.286654 | ||||||||
\(46\) | −5.41020 | −0.797690 | ||||||||
\(47\) | −2.31372 | −0.337491 | −0.168745 | − | 0.985660i | \(-0.553972\pi\) | ||||
−0.168745 | + | 0.985660i | \(0.553972\pi\) | |||||||
\(48\) | 1.03782 | 0.149796 | ||||||||
\(49\) | 6.37279 | 0.910398 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.223663 | −0.0313192 | ||||||||
\(52\) | 3.74747 | 0.519681 | ||||||||
\(53\) | 3.87618 | 0.532434 | 0.266217 | − | 0.963913i | \(-0.414226\pi\) | ||||
0.266217 | + | 0.963913i | \(0.414226\pi\) | |||||||
\(54\) | 5.10911 | 0.695261 | ||||||||
\(55\) | 3.37688 | 0.455338 | ||||||||
\(56\) | 3.65688 | 0.488671 | ||||||||
\(57\) | −3.28733 | −0.435418 | ||||||||
\(58\) | −0.812402 | −0.106674 | ||||||||
\(59\) | −13.5212 | −1.76031 | −0.880153 | − | 0.474690i | \(-0.842560\pi\) | ||||
−0.880153 | + | 0.474690i | \(0.842560\pi\) | |||||||
\(60\) | 1.03782 | 0.133982 | ||||||||
\(61\) | 10.9507 | 1.40209 | 0.701046 | − | 0.713116i | \(-0.252717\pi\) | ||||
0.701046 | + | 0.713116i | \(0.252717\pi\) | |||||||
\(62\) | −2.01579 | −0.256006 | ||||||||
\(63\) | 7.03195 | 0.885943 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.74747 | 0.464816 | ||||||||
\(66\) | −3.50458 | −0.431384 | ||||||||
\(67\) | 0.202415 | 0.0247289 | 0.0123645 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123645 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(68\) | −0.215513 | −0.0261348 | ||||||||
\(69\) | 5.61479 | 0.675942 | ||||||||
\(70\) | 3.65688 | 0.437081 | ||||||||
\(71\) | 4.07678 | 0.483825 | 0.241912 | − | 0.970298i | \(-0.422225\pi\) | ||||
0.241912 | + | 0.970298i | \(0.422225\pi\) | |||||||
\(72\) | 1.92294 | 0.226620 | ||||||||
\(73\) | −14.6244 | −1.71166 | −0.855831 | − | 0.517256i | \(-0.826954\pi\) | ||||
−0.855831 | + | 0.517256i | \(0.826954\pi\) | |||||||
\(74\) | 1.23319 | 0.143356 | ||||||||
\(75\) | 1.03782 | 0.119837 | ||||||||
\(76\) | −3.16754 | −0.363342 | ||||||||
\(77\) | −12.3488 | −1.40728 | ||||||||
\(78\) | −3.88919 | −0.440364 | ||||||||
\(79\) | 13.1650 | 1.48117 | 0.740587 | − | 0.671961i | \(-0.234548\pi\) | ||||
0.740587 | + | 0.671961i | \(0.234548\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0.466492 | 0.0518325 | ||||||||
\(82\) | 2.22559 | 0.245775 | ||||||||
\(83\) | 11.3538 | 1.24625 | 0.623123 | − | 0.782124i | \(-0.285864\pi\) | ||||
0.623123 | + | 0.782124i | \(0.285864\pi\) | |||||||
\(84\) | −3.79517 | −0.414087 | ||||||||
\(85\) | −0.215513 | −0.0233757 | ||||||||
\(86\) | −6.28835 | −0.678090 | ||||||||
\(87\) | 0.843125 | 0.0903925 | ||||||||
\(88\) | −3.37688 | −0.359976 | ||||||||
\(89\) | −10.8782 | −1.15309 | −0.576546 | − | 0.817065i | \(-0.695600\pi\) | ||||
−0.576546 | + | 0.817065i | \(0.695600\pi\) | |||||||
\(90\) | 1.92294 | 0.202695 | ||||||||
\(91\) | −13.7041 | −1.43658 | ||||||||
\(92\) | 5.41020 | 0.564052 | ||||||||
\(93\) | 2.09202 | 0.216933 | ||||||||
\(94\) | 2.31372 | 0.238642 | ||||||||
\(95\) | −3.16754 | −0.324983 | ||||||||
\(96\) | −1.03782 | −0.105922 | ||||||||
\(97\) | −11.0319 | −1.12012 | −0.560059 | − | 0.828453i | \(-0.689222\pi\) | ||||
−0.560059 | + | 0.828453i | \(0.689222\pi\) | |||||||
\(98\) | −6.37279 | −0.643749 | ||||||||
\(99\) | −6.49352 | −0.652623 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.63126 | 0.659835 | 0.329918 | − | 0.944010i | \(-0.392979\pi\) | ||||
0.329918 | + | 0.944010i | \(0.392979\pi\) | |||||||
\(102\) | 0.223663 | 0.0221460 | ||||||||
\(103\) | 3.21287 | 0.316573 | 0.158287 | − | 0.987393i | \(-0.449403\pi\) | ||||
0.158287 | + | 0.987393i | \(0.449403\pi\) | |||||||
\(104\) | −3.74747 | −0.367470 | ||||||||
\(105\) | −3.79517 | −0.370371 | ||||||||
\(106\) | −3.87618 | −0.376488 | ||||||||
\(107\) | −15.5948 | −1.50760 | −0.753801 | − | 0.657102i | \(-0.771782\pi\) | ||||
−0.753801 | + | 0.657102i | \(0.771782\pi\) | |||||||
\(108\) | −5.10911 | −0.491624 | ||||||||
\(109\) | 9.74833 | 0.933721 | 0.466860 | − | 0.884331i | \(-0.345385\pi\) | ||||
0.466860 | + | 0.884331i | \(0.345385\pi\) | |||||||
\(110\) | −3.37688 | −0.321973 | ||||||||
\(111\) | −1.27983 | −0.121476 | ||||||||
\(112\) | −3.65688 | −0.345543 | ||||||||
\(113\) | 4.69211 | 0.441397 | 0.220698 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220698 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(114\) | 3.28733 | 0.307887 | ||||||||
\(115\) | 5.41020 | 0.504503 | ||||||||
\(116\) | 0.812402 | 0.0754297 | ||||||||
\(117\) | −7.20615 | −0.666208 | ||||||||
\(118\) | 13.5212 | 1.24472 | ||||||||
\(119\) | 0.788107 | 0.0722457 | ||||||||
\(120\) | −1.03782 | −0.0947393 | ||||||||
\(121\) | 0.403297 | 0.0366634 | ||||||||
\(122\) | −10.9507 | −0.991428 | ||||||||
\(123\) | −2.30975 | −0.208263 | ||||||||
\(124\) | 2.01579 | 0.181024 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.03195 | −0.626456 | ||||||||
\(127\) | 13.3627 | 1.18575 | 0.592874 | − | 0.805296i | \(-0.297993\pi\) | ||||
0.592874 | + | 0.805296i | \(0.297993\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.52615 | 0.574596 | ||||||||
\(130\) | −3.74747 | −0.328675 | ||||||||
\(131\) | 11.5136 | 1.00595 | 0.502973 | − | 0.864302i | \(-0.332240\pi\) | ||||
0.502973 | + | 0.864302i | \(0.332240\pi\) | |||||||
\(132\) | 3.50458 | 0.305035 | ||||||||
\(133\) | 11.5833 | 1.00440 | ||||||||
\(134\) | −0.202415 | −0.0174860 | ||||||||
\(135\) | −5.10911 | −0.439722 | ||||||||
\(136\) | 0.215513 | 0.0184801 | ||||||||
\(137\) | 17.7664 | 1.51789 | 0.758945 | − | 0.651155i | \(-0.225715\pi\) | ||||
0.758945 | + | 0.651155i | \(0.225715\pi\) | |||||||
\(138\) | −5.61479 | −0.477963 | ||||||||
\(139\) | 5.17338 | 0.438800 | 0.219400 | − | 0.975635i | \(-0.429590\pi\) | ||||
0.219400 | + | 0.975635i | \(0.429590\pi\) | |||||||
\(140\) | −3.65688 | −0.309063 | ||||||||
\(141\) | −2.40122 | −0.202219 | ||||||||
\(142\) | −4.07678 | −0.342116 | ||||||||
\(143\) | 12.6547 | 1.05824 | ||||||||
\(144\) | −1.92294 | −0.160245 | ||||||||
\(145\) | 0.812402 | 0.0674663 | ||||||||
\(146\) | 14.6244 | 1.21033 | ||||||||
\(147\) | 6.61378 | 0.545496 | ||||||||
\(148\) | −1.23319 | −0.101368 | ||||||||
\(149\) | 8.93665 | 0.732119 | 0.366060 | − | 0.930591i | \(-0.380707\pi\) | ||||
0.366060 | + | 0.930591i | \(0.380707\pi\) | |||||||
\(150\) | −1.03782 | −0.0847374 | ||||||||
\(151\) | −3.91214 | −0.318365 | −0.159183 | − | 0.987249i | \(-0.550886\pi\) | ||||
−0.159183 | + | 0.987249i | \(0.550886\pi\) | |||||||
\(152\) | 3.16754 | 0.256922 | ||||||||
\(153\) | 0.414419 | 0.0335038 | ||||||||
\(154\) | 12.3488 | 0.995098 | ||||||||
\(155\) | 2.01579 | 0.161912 | ||||||||
\(156\) | 3.88919 | 0.311384 | ||||||||
\(157\) | 13.0752 | 1.04351 | 0.521756 | − | 0.853095i | \(-0.325277\pi\) | ||||
0.521756 | + | 0.853095i | \(0.325277\pi\) | |||||||
\(158\) | −13.1650 | −1.04735 | ||||||||
\(159\) | 4.02276 | 0.319026 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −19.7845 | −1.55923 | ||||||||
\(162\) | −0.466492 | −0.0366511 | ||||||||
\(163\) | −2.24469 | −0.175818 | −0.0879089 | − | 0.996129i | \(-0.528018\pi\) | ||||
−0.0879089 | + | 0.996129i | \(0.528018\pi\) | |||||||
\(164\) | −2.22559 | −0.173789 | ||||||||
\(165\) | 3.50458 | 0.272831 | ||||||||
\(166\) | −11.3538 | −0.881229 | ||||||||
\(167\) | −19.8554 | −1.53646 | −0.768228 | − | 0.640176i | \(-0.778861\pi\) | ||||
−0.768228 | + | 0.640176i | \(0.778861\pi\) | |||||||
\(168\) | 3.79517 | 0.292804 | ||||||||
\(169\) | 1.04353 | 0.0802717 | ||||||||
\(170\) | 0.215513 | 0.0165291 | ||||||||
\(171\) | 6.09099 | 0.465789 | ||||||||
\(172\) | 6.28835 | 0.479482 | ||||||||
\(173\) | −5.76255 | −0.438119 | −0.219059 | − | 0.975712i | \(-0.570299\pi\) | ||||
−0.219059 | + | 0.975712i | \(0.570299\pi\) | |||||||
\(174\) | −0.843125 | −0.0639171 | ||||||||
\(175\) | −3.65688 | −0.276434 | ||||||||
\(176\) | 3.37688 | 0.254542 | ||||||||
\(177\) | −14.0325 | −1.05475 | ||||||||
\(178\) | 10.8782 | 0.815359 | ||||||||
\(179\) | 15.8613 | 1.18553 | 0.592765 | − | 0.805376i | \(-0.298036\pi\) | ||||
0.592765 | + | 0.805376i | \(0.298036\pi\) | |||||||
\(180\) | −1.92294 | −0.143327 | ||||||||
\(181\) | 9.47492 | 0.704265 | 0.352132 | − | 0.935950i | \(-0.385457\pi\) | ||||
0.352132 | + | 0.935950i | \(0.385457\pi\) | |||||||
\(182\) | 13.7041 | 1.01581 | ||||||||
\(183\) | 11.3648 | 0.840110 | ||||||||
\(184\) | −5.41020 | −0.398845 | ||||||||
\(185\) | −1.23319 | −0.0906661 | ||||||||
\(186\) | −2.09202 | −0.153395 | ||||||||
\(187\) | −0.727762 | −0.0532193 | ||||||||
\(188\) | −2.31372 | −0.168745 | ||||||||
\(189\) | 18.6834 | 1.35902 | ||||||||
\(190\) | 3.16754 | 0.229798 | ||||||||
\(191\) | 14.6508 | 1.06010 | 0.530049 | − | 0.847967i | \(-0.322173\pi\) | ||||
0.530049 | + | 0.847967i | \(0.322173\pi\) | |||||||
\(192\) | 1.03782 | 0.0748980 | ||||||||
\(193\) | −17.4298 | −1.25463 | −0.627313 | − | 0.778767i | \(-0.715846\pi\) | ||||
−0.627313 | + | 0.778767i | \(0.715846\pi\) | |||||||
\(194\) | 11.0319 | 0.792043 | ||||||||
\(195\) | 3.88919 | 0.278511 | ||||||||
\(196\) | 6.37279 | 0.455199 | ||||||||
\(197\) | 5.43621 | 0.387314 | 0.193657 | − | 0.981069i | \(-0.437965\pi\) | ||||
0.193657 | + | 0.981069i | \(0.437965\pi\) | |||||||
\(198\) | 6.49352 | 0.461474 | ||||||||
\(199\) | 24.7689 | 1.75582 | 0.877911 | − | 0.478824i | \(-0.158937\pi\) | ||||
0.877911 | + | 0.478824i | \(0.158937\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0.210069 | 0.0148172 | ||||||||
\(202\) | −6.63126 | −0.466574 | ||||||||
\(203\) | −2.97086 | −0.208513 | ||||||||
\(204\) | −0.223663 | −0.0156596 | ||||||||
\(205\) | −2.22559 | −0.155442 | ||||||||
\(206\) | −3.21287 | −0.223851 | ||||||||
\(207\) | −10.4035 | −0.723091 | ||||||||
\(208\) | 3.74747 | 0.259840 | ||||||||
\(209\) | −10.6964 | −0.739886 | ||||||||
\(210\) | 3.79517 | 0.261892 | ||||||||
\(211\) | 27.0025 | 1.85893 | 0.929465 | − | 0.368911i | \(-0.120269\pi\) | ||||
0.929465 | + | 0.368911i | \(0.120269\pi\) | |||||||
\(212\) | 3.87618 | 0.266217 | ||||||||
\(213\) | 4.23095 | 0.289900 | ||||||||
\(214\) | 15.5948 | 1.06604 | ||||||||
\(215\) | 6.28835 | 0.428862 | ||||||||
\(216\) | 5.10911 | 0.347631 | ||||||||
\(217\) | −7.37152 | −0.500411 | ||||||||
\(218\) | −9.74833 | −0.660240 | ||||||||
\(219\) | −15.1775 | −1.02560 | ||||||||
\(220\) | 3.37688 | 0.227669 | ||||||||
\(221\) | −0.807630 | −0.0543271 | ||||||||
\(222\) | 1.27983 | 0.0858964 | ||||||||
\(223\) | 3.92520 | 0.262851 | 0.131425 | − | 0.991326i | \(-0.458045\pi\) | ||||
0.131425 | + | 0.991326i | \(0.458045\pi\) | |||||||
\(224\) | 3.65688 | 0.244336 | ||||||||
\(225\) | −1.92294 | −0.128196 | ||||||||
\(226\) | −4.69211 | −0.312115 | ||||||||
\(227\) | 22.6128 | 1.50087 | 0.750433 | − | 0.660946i | \(-0.229845\pi\) | ||||
0.750433 | + | 0.660946i | \(0.229845\pi\) | |||||||
\(228\) | −3.28733 | −0.217709 | ||||||||
\(229\) | 26.1728 | 1.72955 | 0.864774 | − | 0.502161i | \(-0.167462\pi\) | ||||
0.864774 | + | 0.502161i | \(0.167462\pi\) | |||||||
\(230\) | −5.41020 | −0.356738 | ||||||||
\(231\) | −12.8158 | −0.843220 | ||||||||
\(232\) | −0.812402 | −0.0533368 | ||||||||
\(233\) | 0.751493 | 0.0492319 | 0.0246160 | − | 0.999697i | \(-0.492164\pi\) | ||||
0.0246160 | + | 0.999697i | \(0.492164\pi\) | |||||||
\(234\) | 7.20615 | 0.471080 | ||||||||
\(235\) | −2.31372 | −0.150930 | ||||||||
\(236\) | −13.5212 | −0.880153 | ||||||||
\(237\) | 13.6628 | 0.887495 | ||||||||
\(238\) | −0.788107 | −0.0510854 | ||||||||
\(239\) | −7.58600 | −0.490698 | −0.245349 | − | 0.969435i | \(-0.578903\pi\) | ||||
−0.245349 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(240\) | 1.03782 | 0.0669908 | ||||||||
\(241\) | 26.0437 | 1.67762 | 0.838811 | − | 0.544423i | \(-0.183251\pi\) | ||||
0.838811 | + | 0.544423i | \(0.183251\pi\) | |||||||
\(242\) | −0.403297 | −0.0259249 | ||||||||
\(243\) | 15.8115 | 1.01431 | ||||||||
\(244\) | 10.9507 | 0.701046 | ||||||||
\(245\) | 6.37279 | 0.407142 | ||||||||
\(246\) | 2.30975 | 0.147264 | ||||||||
\(247\) | −11.8703 | −0.755288 | ||||||||
\(248\) | −2.01579 | −0.128003 | ||||||||
\(249\) | 11.7832 | 0.746730 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.7263 | 0.740158 | 0.370079 | − | 0.929000i | \(-0.379331\pi\) | ||||
0.370079 | + | 0.929000i | \(0.379331\pi\) | |||||||
\(252\) | 7.03195 | 0.442971 | ||||||||
\(253\) | 18.2696 | 1.14860 | ||||||||
\(254\) | −13.3627 | −0.838450 | ||||||||
\(255\) | −0.223663 | −0.0140064 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.6346 | 1.16240 | 0.581198 | − | 0.813763i | \(-0.302584\pi\) | ||||
0.581198 | + | 0.813763i | \(0.302584\pi\) | |||||||
\(258\) | −6.52615 | −0.406301 | ||||||||
\(259\) | 4.50964 | 0.280215 | ||||||||
\(260\) | 3.74747 | 0.232408 | ||||||||
\(261\) | −1.56220 | −0.0966976 | ||||||||
\(262\) | −11.5136 | −0.711311 | ||||||||
\(263\) | −12.6650 | −0.780959 | −0.390479 | − | 0.920612i | \(-0.627691\pi\) | ||||
−0.390479 | + | 0.920612i | \(0.627691\pi\) | |||||||
\(264\) | −3.50458 | −0.215692 | ||||||||
\(265\) | 3.87618 | 0.238112 | ||||||||
\(266\) | −11.5833 | −0.710220 | ||||||||
\(267\) | −11.2896 | −0.690914 | ||||||||
\(268\) | 0.202415 | 0.0123645 | ||||||||
\(269\) | 6.82885 | 0.416363 | 0.208181 | − | 0.978090i | \(-0.433246\pi\) | ||||
0.208181 | + | 0.978090i | \(0.433246\pi\) | |||||||
\(270\) | 5.10911 | 0.310930 | ||||||||
\(271\) | 19.4095 | 1.17905 | 0.589523 | − | 0.807752i | \(-0.299316\pi\) | ||||
0.589523 | + | 0.807752i | \(0.299316\pi\) | |||||||
\(272\) | −0.215513 | −0.0130674 | ||||||||
\(273\) | −14.2223 | −0.860773 | ||||||||
\(274\) | −17.7664 | −1.07331 | ||||||||
\(275\) | 3.37688 | 0.203633 | ||||||||
\(276\) | 5.61479 | 0.337971 | ||||||||
\(277\) | −29.0790 | −1.74719 | −0.873594 | − | 0.486655i | \(-0.838217\pi\) | ||||
−0.873594 | + | 0.486655i | \(0.838217\pi\) | |||||||
\(278\) | −5.17338 | −0.310279 | ||||||||
\(279\) | −3.87624 | −0.232064 | ||||||||
\(280\) | 3.65688 | 0.218541 | ||||||||
\(281\) | 28.2649 | 1.68614 | 0.843070 | − | 0.537803i | \(-0.180746\pi\) | ||||
0.843070 | + | 0.537803i | \(0.180746\pi\) | |||||||
\(282\) | 2.40122 | 0.142990 | ||||||||
\(283\) | 3.28111 | 0.195042 | 0.0975208 | − | 0.995233i | \(-0.468909\pi\) | ||||
0.0975208 | + | 0.995233i | \(0.468909\pi\) | |||||||
\(284\) | 4.07678 | 0.241912 | ||||||||
\(285\) | −3.28733 | −0.194725 | ||||||||
\(286\) | −12.6547 | −0.748291 | ||||||||
\(287\) | 8.13871 | 0.480413 | ||||||||
\(288\) | 1.92294 | 0.113310 | ||||||||
\(289\) | −16.9536 | −0.997268 | ||||||||
\(290\) | −0.812402 | −0.0477059 | ||||||||
\(291\) | −11.4491 | −0.671157 | ||||||||
\(292\) | −14.6244 | −0.855831 | ||||||||
\(293\) | −25.2458 | −1.47487 | −0.737437 | − | 0.675416i | \(-0.763964\pi\) | ||||
−0.737437 | + | 0.675416i | \(0.763964\pi\) | |||||||
\(294\) | −6.61378 | −0.385724 | ||||||||
\(295\) | −13.5212 | −0.787233 | ||||||||
\(296\) | 1.23319 | 0.0716779 | ||||||||
\(297\) | −17.2528 | −1.00111 | ||||||||
\(298\) | −8.93665 | −0.517686 | ||||||||
\(299\) | 20.2746 | 1.17251 | ||||||||
\(300\) | 1.03782 | 0.0599184 | ||||||||
\(301\) | −22.9957 | −1.32545 | ||||||||
\(302\) | 3.91214 | 0.225118 | ||||||||
\(303\) | 6.88203 | 0.395362 | ||||||||
\(304\) | −3.16754 | −0.181671 | ||||||||
\(305\) | 10.9507 | 0.627034 | ||||||||
\(306\) | −0.414419 | −0.0236907 | ||||||||
\(307\) | 21.3000 | 1.21565 | 0.607826 | − | 0.794070i | \(-0.292042\pi\) | ||||
0.607826 | + | 0.794070i | \(0.292042\pi\) | |||||||
\(308\) | −12.3488 | −0.703640 | ||||||||
\(309\) | 3.33437 | 0.189686 | ||||||||
\(310\) | −2.01579 | −0.114489 | ||||||||
\(311\) | −11.3248 | −0.642172 | −0.321086 | − | 0.947050i | \(-0.604048\pi\) | ||||
−0.321086 | + | 0.947050i | \(0.604048\pi\) | |||||||
\(312\) | −3.88919 | −0.220182 | ||||||||
\(313\) | 24.5480 | 1.38754 | 0.693768 | − | 0.720199i | \(-0.255950\pi\) | ||||
0.693768 | + | 0.720199i | \(0.255950\pi\) | |||||||
\(314\) | −13.0752 | −0.737874 | ||||||||
\(315\) | 7.03195 | 0.396206 | ||||||||
\(316\) | 13.1650 | 0.740587 | ||||||||
\(317\) | −6.12633 | −0.344089 | −0.172045 | − | 0.985089i | \(-0.555037\pi\) | ||||
−0.172045 | + | 0.985089i | \(0.555037\pi\) | |||||||
\(318\) | −4.02276 | −0.225585 | ||||||||
\(319\) | 2.74338 | 0.153600 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −16.1845 | −0.903331 | ||||||||
\(322\) | 19.7845 | 1.10254 | ||||||||
\(323\) | 0.682648 | 0.0379836 | ||||||||
\(324\) | 0.466492 | 0.0259162 | ||||||||
\(325\) | 3.74747 | 0.207872 | ||||||||
\(326\) | 2.24469 | 0.124322 | ||||||||
\(327\) | 10.1170 | 0.559470 | ||||||||
\(328\) | 2.22559 | 0.122887 | ||||||||
\(329\) | 8.46100 | 0.466470 | ||||||||
\(330\) | −3.50458 | −0.192921 | ||||||||
\(331\) | −0.250410 | −0.0137638 | −0.00688189 | − | 0.999976i | \(-0.502191\pi\) | ||||
−0.00688189 | + | 0.999976i | \(0.502191\pi\) | |||||||
\(332\) | 11.3538 | 0.623123 | ||||||||
\(333\) | 2.37135 | 0.129949 | ||||||||
\(334\) | 19.8554 | 1.08644 | ||||||||
\(335\) | 0.202415 | 0.0110591 | ||||||||
\(336\) | −3.79517 | −0.207044 | ||||||||
\(337\) | 10.7313 | 0.584569 | 0.292284 | − | 0.956331i | \(-0.405585\pi\) | ||||
0.292284 | + | 0.956331i | \(0.405585\pi\) | |||||||
\(338\) | −1.04353 | −0.0567607 | ||||||||
\(339\) | 4.86955 | 0.264478 | ||||||||
\(340\) | −0.215513 | −0.0116879 | ||||||||
\(341\) | 6.80708 | 0.368624 | ||||||||
\(342\) | −6.09099 | −0.329363 | ||||||||
\(343\) | 2.29365 | 0.123845 | ||||||||
\(344\) | −6.28835 | −0.339045 | ||||||||
\(345\) | 5.61479 | 0.302290 | ||||||||
\(346\) | 5.76255 | 0.309797 | ||||||||
\(347\) | −36.1651 | −1.94144 | −0.970722 | − | 0.240204i | \(-0.922786\pi\) | ||||
−0.970722 | + | 0.240204i | \(0.922786\pi\) | |||||||
\(348\) | 0.843125 | 0.0451962 | ||||||||
\(349\) | −34.5414 | −1.84896 | −0.924478 | − | 0.381235i | \(-0.875499\pi\) | ||||
−0.924478 | + | 0.381235i | \(0.875499\pi\) | |||||||
\(350\) | 3.65688 | 0.195469 | ||||||||
\(351\) | −19.1462 | −1.02195 | ||||||||
\(352\) | −3.37688 | −0.179988 | ||||||||
\(353\) | 9.77851 | 0.520458 | 0.260229 | − | 0.965547i | \(-0.416202\pi\) | ||||
0.260229 | + | 0.965547i | \(0.416202\pi\) | |||||||
\(354\) | 14.0325 | 0.745819 | ||||||||
\(355\) | 4.07678 | 0.216373 | ||||||||
\(356\) | −10.8782 | −0.576546 | ||||||||
\(357\) | 0.817911 | 0.0432884 | ||||||||
\(358\) | −15.8613 | −0.838296 | ||||||||
\(359\) | −2.30879 | −0.121854 | −0.0609268 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609268 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(360\) | 1.92294 | 0.101348 | ||||||||
\(361\) | −8.96666 | −0.471930 | ||||||||
\(362\) | −9.47492 | −0.497991 | ||||||||
\(363\) | 0.418549 | 0.0219681 | ||||||||
\(364\) | −13.7041 | −0.718288 | ||||||||
\(365\) | −14.6244 | −0.765478 | ||||||||
\(366\) | −11.3648 | −0.594048 | ||||||||
\(367\) | −32.3313 | −1.68768 | −0.843839 | − | 0.536596i | \(-0.819710\pi\) | ||||
−0.843839 | + | 0.536596i | \(0.819710\pi\) | |||||||
\(368\) | 5.41020 | 0.282026 | ||||||||
\(369\) | 4.27966 | 0.222790 | ||||||||
\(370\) | 1.23319 | 0.0641106 | ||||||||
\(371\) | −14.1747 | −0.735915 | ||||||||
\(372\) | 2.09202 | 0.108466 | ||||||||
\(373\) | −10.2869 | −0.532637 | −0.266319 | − | 0.963885i | \(-0.585807\pi\) | ||||
−0.266319 | + | 0.963885i | \(0.585807\pi\) | |||||||
\(374\) | 0.727762 | 0.0376317 | ||||||||
\(375\) | 1.03782 | 0.0535926 | ||||||||
\(376\) | 2.31372 | 0.119321 | ||||||||
\(377\) | 3.04445 | 0.156797 | ||||||||
\(378\) | −18.6834 | −0.960970 | ||||||||
\(379\) | −10.7646 | −0.552940 | −0.276470 | − | 0.961023i | \(-0.589165\pi\) | ||||
−0.276470 | + | 0.961023i | \(0.589165\pi\) | |||||||
\(380\) | −3.16754 | −0.162492 | ||||||||
\(381\) | 13.8680 | 0.710480 | ||||||||
\(382\) | −14.6508 | −0.749603 | ||||||||
\(383\) | −5.30417 | −0.271030 | −0.135515 | − | 0.990775i | \(-0.543269\pi\) | ||||
−0.135515 | + | 0.990775i | \(0.543269\pi\) | |||||||
\(384\) | −1.03782 | −0.0529609 | ||||||||
\(385\) | −12.3488 | −0.629355 | ||||||||
\(386\) | 17.4298 | 0.887155 | ||||||||
\(387\) | −12.0921 | −0.614676 | ||||||||
\(388\) | −11.0319 | −0.560059 | ||||||||
\(389\) | −9.53656 | −0.483523 | −0.241761 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241761 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(390\) | −3.88919 | −0.196937 | ||||||||
\(391\) | −1.16597 | −0.0589656 | ||||||||
\(392\) | −6.37279 | −0.321874 | ||||||||
\(393\) | 11.9490 | 0.602746 | ||||||||
\(394\) | −5.43621 | −0.273872 | ||||||||
\(395\) | 13.1650 | 0.662401 | ||||||||
\(396\) | −6.49352 | −0.326312 | ||||||||
\(397\) | −18.9346 | −0.950300 | −0.475150 | − | 0.879905i | \(-0.657606\pi\) | ||||
−0.475150 | + | 0.879905i | \(0.657606\pi\) | |||||||
\(398\) | −24.7689 | −1.24155 | ||||||||
\(399\) | 12.0214 | 0.601822 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −0.0627506 | −0.00313361 | −0.00156681 | − | 0.999999i | \(-0.500499\pi\) | ||||
−0.00156681 | + | 0.999999i | \(0.500499\pi\) | |||||||
\(402\) | −0.210069 | −0.0104773 | ||||||||
\(403\) | 7.55412 | 0.376298 | ||||||||
\(404\) | 6.63126 | 0.329918 | ||||||||
\(405\) | 0.466492 | 0.0231802 | ||||||||
\(406\) | 2.97086 | 0.147441 | ||||||||
\(407\) | −4.16434 | −0.206419 | ||||||||
\(408\) | 0.223663 | 0.0110730 | ||||||||
\(409\) | −4.26183 | −0.210734 | −0.105367 | − | 0.994433i | \(-0.533602\pi\) | ||||
−0.105367 | + | 0.994433i | \(0.533602\pi\) | |||||||
\(410\) | 2.22559 | 0.109914 | ||||||||
\(411\) | 18.4383 | 0.909495 | ||||||||
\(412\) | 3.21287 | 0.158287 | ||||||||
\(413\) | 49.4453 | 2.43304 | ||||||||
\(414\) | 10.4035 | 0.511302 | ||||||||
\(415\) | 11.3538 | 0.557338 | ||||||||
\(416\) | −3.74747 | −0.183735 | ||||||||
\(417\) | 5.36902 | 0.262922 | ||||||||
\(418\) | 10.6964 | 0.523178 | ||||||||
\(419\) | −2.69655 | −0.131735 | −0.0658674 | − | 0.997828i | \(-0.520981\pi\) | ||||
−0.0658674 | + | 0.997828i | \(0.520981\pi\) | |||||||
\(420\) | −3.79517 | −0.185186 | ||||||||
\(421\) | −20.7655 | −1.01205 | −0.506025 | − | 0.862519i | \(-0.668886\pi\) | ||||
−0.506025 | + | 0.862519i | \(0.668886\pi\) | |||||||
\(422\) | −27.0025 | −1.31446 | ||||||||
\(423\) | 4.44913 | 0.216324 | ||||||||
\(424\) | −3.87618 | −0.188244 | ||||||||
\(425\) | −0.215513 | −0.0104539 | ||||||||
\(426\) | −4.23095 | −0.204990 | ||||||||
\(427\) | −40.0454 | −1.93793 | ||||||||
\(428\) | −15.5948 | −0.753801 | ||||||||
\(429\) | 13.1333 | 0.634082 | ||||||||
\(430\) | −6.28835 | −0.303251 | ||||||||
\(431\) | −1.62083 | −0.0780728 | −0.0390364 | − | 0.999238i | \(-0.512429\pi\) | ||||
−0.0390364 | + | 0.999238i | \(0.512429\pi\) | |||||||
\(432\) | −5.10911 | −0.245812 | ||||||||
\(433\) | −5.50288 | −0.264451 | −0.132226 | − | 0.991220i | \(-0.542212\pi\) | ||||
−0.132226 | + | 0.991220i | \(0.542212\pi\) | |||||||
\(434\) | 7.37152 | 0.353844 | ||||||||
\(435\) | 0.843125 | 0.0404247 | ||||||||
\(436\) | 9.74833 | 0.466860 | ||||||||
\(437\) | −17.1370 | −0.819776 | ||||||||
\(438\) | 15.1775 | 0.725209 | ||||||||
\(439\) | 11.8038 | 0.563363 | 0.281682 | − | 0.959508i | \(-0.409108\pi\) | ||||
0.281682 | + | 0.959508i | \(0.409108\pi\) | |||||||
\(440\) | −3.37688 | −0.160986 | ||||||||
\(441\) | −12.2545 | −0.583546 | ||||||||
\(442\) | 0.807630 | 0.0384150 | ||||||||
\(443\) | 37.9919 | 1.80505 | 0.902525 | − | 0.430638i | \(-0.141711\pi\) | ||||
0.902525 | + | 0.430638i | \(0.141711\pi\) | |||||||
\(444\) | −1.27983 | −0.0607380 | ||||||||
\(445\) | −10.8782 | −0.515678 | ||||||||
\(446\) | −3.92520 | −0.185863 | ||||||||
\(447\) | 9.27461 | 0.438674 | ||||||||
\(448\) | −3.65688 | −0.172771 | ||||||||
\(449\) | −14.7413 | −0.695687 | −0.347843 | − | 0.937553i | \(-0.613086\pi\) | ||||
−0.347843 | + | 0.937553i | \(0.613086\pi\) | |||||||
\(450\) | 1.92294 | 0.0906481 | ||||||||
\(451\) | −7.51553 | −0.353893 | ||||||||
\(452\) | 4.69211 | 0.220698 | ||||||||
\(453\) | −4.06008 | −0.190759 | ||||||||
\(454\) | −22.6128 | −1.06127 | ||||||||
\(455\) | −13.7041 | −0.642456 | ||||||||
\(456\) | 3.28733 | 0.153943 | ||||||||
\(457\) | 20.5518 | 0.961370 | 0.480685 | − | 0.876893i | \(-0.340388\pi\) | ||||
0.480685 | + | 0.876893i | \(0.340388\pi\) | |||||||
\(458\) | −26.1728 | −1.22298 | ||||||||
\(459\) | 1.10108 | 0.0513941 | ||||||||
\(460\) | 5.41020 | 0.252252 | ||||||||
\(461\) | 26.0399 | 1.21280 | 0.606399 | − | 0.795160i | \(-0.292613\pi\) | ||||
0.606399 | + | 0.795160i | \(0.292613\pi\) | |||||||
\(462\) | 12.8158 | 0.596247 | ||||||||
\(463\) | −40.3534 | −1.87538 | −0.937692 | − | 0.347468i | \(-0.887042\pi\) | ||||
−0.937692 | + | 0.347468i | \(0.887042\pi\) | |||||||
\(464\) | 0.812402 | 0.0377148 | ||||||||
\(465\) | 2.09202 | 0.0970153 | ||||||||
\(466\) | −0.751493 | −0.0348122 | ||||||||
\(467\) | 19.0057 | 0.879479 | 0.439740 | − | 0.898125i | \(-0.355071\pi\) | ||||
0.439740 | + | 0.898125i | \(0.355071\pi\) | |||||||
\(468\) | −7.20615 | −0.333104 | ||||||||
\(469\) | −0.740207 | −0.0341796 | ||||||||
\(470\) | 2.31372 | 0.106724 | ||||||||
\(471\) | 13.5696 | 0.625255 | ||||||||
\(472\) | 13.5212 | 0.622362 | ||||||||
\(473\) | 21.2350 | 0.976385 | ||||||||
\(474\) | −13.6628 | −0.627554 | ||||||||
\(475\) | −3.16754 | −0.145337 | ||||||||
\(476\) | 0.788107 | 0.0361228 | ||||||||
\(477\) | −7.45364 | −0.341279 | ||||||||
\(478\) | 7.58600 | 0.346976 | ||||||||
\(479\) | −4.99765 | −0.228349 | −0.114174 | − | 0.993461i | \(-0.536422\pi\) | ||||
−0.114174 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(480\) | −1.03782 | −0.0473696 | ||||||||
\(481\) | −4.62135 | −0.210716 | ||||||||
\(482\) | −26.0437 | −1.18626 | ||||||||
\(483\) | −20.5326 | −0.934267 | ||||||||
\(484\) | 0.403297 | 0.0183317 | ||||||||
\(485\) | −11.0319 | −0.500932 | ||||||||
\(486\) | −15.8115 | −0.717222 | ||||||||
\(487\) | 33.5250 | 1.51916 | 0.759581 | − | 0.650413i | \(-0.225404\pi\) | ||||
0.759581 | + | 0.650413i | \(0.225404\pi\) | |||||||
\(488\) | −10.9507 | −0.495714 | ||||||||
\(489\) | −2.32958 | −0.105347 | ||||||||
\(490\) | −6.37279 | −0.287893 | ||||||||
\(491\) | −8.90643 | −0.401941 | −0.200971 | − | 0.979597i | \(-0.564410\pi\) | ||||
−0.200971 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(492\) | −2.30975 | −0.104132 | ||||||||
\(493\) | −0.175084 | −0.00788537 | ||||||||
\(494\) | 11.8703 | 0.534069 | ||||||||
\(495\) | −6.49352 | −0.291862 | ||||||||
\(496\) | 2.01579 | 0.0905118 | ||||||||
\(497\) | −14.9083 | −0.668729 | ||||||||
\(498\) | −11.7832 | −0.528018 | ||||||||
\(499\) | −13.3307 | −0.596764 | −0.298382 | − | 0.954447i | \(-0.596447\pi\) | ||||
−0.298382 | + | 0.954447i | \(0.596447\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −20.6063 | −0.920620 | ||||||||
\(502\) | −11.7263 | −0.523371 | ||||||||
\(503\) | 41.1360 | 1.83417 | 0.917083 | − | 0.398697i | \(-0.130538\pi\) | ||||
0.917083 | + | 0.398697i | \(0.130538\pi\) | |||||||
\(504\) | −7.03195 | −0.313228 | ||||||||
\(505\) | 6.63126 | 0.295087 | ||||||||
\(506\) | −18.2696 | −0.812181 | ||||||||
\(507\) | 1.08300 | 0.0480975 | ||||||||
\(508\) | 13.3627 | 0.592874 | ||||||||
\(509\) | 19.6597 | 0.871400 | 0.435700 | − | 0.900092i | \(-0.356501\pi\) | ||||
0.435700 | + | 0.900092i | \(0.356501\pi\) | |||||||
\(510\) | 0.223663 | 0.00990399 | ||||||||
\(511\) | 53.4799 | 2.36581 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.1833 | 0.714511 | ||||||||
\(514\) | −18.6346 | −0.821937 | ||||||||
\(515\) | 3.21287 | 0.141576 | ||||||||
\(516\) | 6.52615 | 0.287298 | ||||||||
\(517\) | −7.81314 | −0.343622 | ||||||||
\(518\) | −4.50964 | −0.198142 | ||||||||
\(519\) | −5.98048 | −0.262514 | ||||||||
\(520\) | −3.74747 | −0.164337 | ||||||||
\(521\) | −9.43214 | −0.413230 | −0.206615 | − | 0.978422i | \(-0.566245\pi\) | ||||
−0.206615 | + | 0.978422i | \(0.566245\pi\) | |||||||
\(522\) | 1.56220 | 0.0683755 | ||||||||
\(523\) | −2.68428 | −0.117376 | −0.0586878 | − | 0.998276i | \(-0.518692\pi\) | ||||
−0.0586878 | + | 0.998276i | \(0.518692\pi\) | |||||||
\(524\) | 11.5136 | 0.502973 | ||||||||
\(525\) | −3.79517 | −0.165635 | ||||||||
\(526\) | 12.6650 | 0.552221 | ||||||||
\(527\) | −0.434430 | −0.0189241 | ||||||||
\(528\) | 3.50458 | 0.152517 | ||||||||
\(529\) | 6.27023 | 0.272619 | ||||||||
\(530\) | −3.87618 | −0.168370 | ||||||||
\(531\) | 26.0003 | 1.12832 | ||||||||
\(532\) | 11.5833 | 0.502201 | ||||||||
\(533\) | −8.34032 | −0.361259 | ||||||||
\(534\) | 11.2896 | 0.488550 | ||||||||
\(535\) | −15.5948 | −0.674220 | ||||||||
\(536\) | −0.202415 | −0.00874299 | ||||||||
\(537\) | 16.4611 | 0.710350 | ||||||||
\(538\) | −6.82885 | −0.294413 | ||||||||
\(539\) | 21.5201 | 0.926937 | ||||||||
\(540\) | −5.10911 | −0.219861 | ||||||||
\(541\) | −10.0571 | −0.432389 | −0.216194 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216194 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(542\) | −19.4095 | −0.833711 | ||||||||
\(543\) | 9.83323 | 0.421984 | ||||||||
\(544\) | 0.215513 | 0.00924006 | ||||||||
\(545\) | 9.74833 | 0.417573 | ||||||||
\(546\) | 14.2223 | 0.608658 | ||||||||
\(547\) | −24.7023 | −1.05619 | −0.528097 | − | 0.849184i | \(-0.677094\pi\) | ||||
−0.528097 | + | 0.849184i | \(0.677094\pi\) | |||||||
\(548\) | 17.7664 | 0.758945 | ||||||||
\(549\) | −21.0575 | −0.898711 | ||||||||
\(550\) | −3.37688 | −0.143991 | ||||||||
\(551\) | −2.57332 | −0.109627 | ||||||||
\(552\) | −5.61479 | −0.238981 | ||||||||
\(553\) | −48.1427 | −2.04724 | ||||||||
\(554\) | 29.0790 | 1.23545 | ||||||||
\(555\) | −1.27983 | −0.0543257 | ||||||||
\(556\) | 5.17338 | 0.219400 | ||||||||
\(557\) | −27.0631 | −1.14670 | −0.573349 | − | 0.819311i | \(-0.694356\pi\) | ||||
−0.573349 | + | 0.819311i | \(0.694356\pi\) | |||||||
\(558\) | 3.87624 | 0.164094 | ||||||||
\(559\) | 23.5654 | 0.996710 | ||||||||
\(560\) | −3.65688 | −0.154531 | ||||||||
\(561\) | −0.755284 | −0.0318881 | ||||||||
\(562\) | −28.2649 | −1.19228 | ||||||||
\(563\) | 38.3795 | 1.61750 | 0.808751 | − | 0.588152i | \(-0.200144\pi\) | ||||
0.808751 | + | 0.588152i | \(0.200144\pi\) | |||||||
\(564\) | −2.40122 | −0.101109 | ||||||||
\(565\) | 4.69211 | 0.197399 | ||||||||
\(566\) | −3.28111 | −0.137915 | ||||||||
\(567\) | −1.70591 | −0.0716414 | ||||||||
\(568\) | −4.07678 | −0.171058 | ||||||||
\(569\) | 39.1862 | 1.64277 | 0.821386 | − | 0.570373i | \(-0.193201\pi\) | ||||
0.821386 | + | 0.570373i | \(0.193201\pi\) | |||||||
\(570\) | 3.28733 | 0.137691 | ||||||||
\(571\) | 30.6549 | 1.28287 | 0.641434 | − | 0.767178i | \(-0.278340\pi\) | ||||
0.641434 | + | 0.767178i | \(0.278340\pi\) | |||||||
\(572\) | 12.6547 | 0.529121 | ||||||||
\(573\) | 15.2049 | 0.635194 | ||||||||
\(574\) | −8.13871 | −0.339703 | ||||||||
\(575\) | 5.41020 | 0.225621 | ||||||||
\(576\) | −1.92294 | −0.0801223 | ||||||||
\(577\) | 24.5919 | 1.02377 | 0.511887 | − | 0.859053i | \(-0.328947\pi\) | ||||
0.511887 | + | 0.859053i | \(0.328947\pi\) | |||||||
\(578\) | 16.9536 | 0.705175 | ||||||||
\(579\) | −18.0890 | −0.751752 | ||||||||
\(580\) | 0.812402 | 0.0337332 | ||||||||
\(581\) | −41.5196 | −1.72252 | ||||||||
\(582\) | 11.4491 | 0.474579 | ||||||||
\(583\) | 13.0894 | 0.542106 | ||||||||
\(584\) | 14.6244 | 0.605164 | ||||||||
\(585\) | −7.20615 | −0.297937 | ||||||||
\(586\) | 25.2458 | 1.04289 | ||||||||
\(587\) | 22.9989 | 0.949265 | 0.474632 | − | 0.880184i | \(-0.342581\pi\) | ||||
0.474632 | + | 0.880184i | \(0.342581\pi\) | |||||||
\(588\) | 6.61378 | 0.272748 | ||||||||
\(589\) | −6.38511 | −0.263094 | ||||||||
\(590\) | 13.5212 | 0.556658 | ||||||||
\(591\) | 5.64179 | 0.232072 | ||||||||
\(592\) | −1.23319 | −0.0506839 | ||||||||
\(593\) | −31.7364 | −1.30326 | −0.651630 | − | 0.758537i | \(-0.725914\pi\) | ||||
−0.651630 | + | 0.758537i | \(0.725914\pi\) | |||||||
\(594\) | 17.2528 | 0.707892 | ||||||||
\(595\) | 0.788107 | 0.0323092 | ||||||||
\(596\) | 8.93665 | 0.366060 | ||||||||
\(597\) | 25.7056 | 1.05206 | ||||||||
\(598\) | −20.2746 | −0.829088 | ||||||||
\(599\) | 43.9098 | 1.79411 | 0.897053 | − | 0.441923i | \(-0.145704\pi\) | ||||
0.897053 | + | 0.441923i | \(0.145704\pi\) | |||||||
\(600\) | −1.03782 | −0.0423687 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 22.9957 | 0.937237 | ||||||||
\(603\) | −0.389231 | −0.0158507 | ||||||||
\(604\) | −3.91214 | −0.159183 | ||||||||
\(605\) | 0.403297 | 0.0163964 | ||||||||
\(606\) | −6.88203 | −0.279563 | ||||||||
\(607\) | −32.6908 | −1.32688 | −0.663440 | − | 0.748229i | \(-0.730904\pi\) | ||||
−0.663440 | + | 0.748229i | \(0.730904\pi\) | |||||||
\(608\) | 3.16754 | 0.128461 | ||||||||
\(609\) | −3.08321 | −0.124938 | ||||||||
\(610\) | −10.9507 | −0.443380 | ||||||||
\(611\) | −8.67059 | −0.350775 | ||||||||
\(612\) | 0.414419 | 0.0167519 | ||||||||
\(613\) | −30.8105 | −1.24442 | −0.622212 | − | 0.782848i | \(-0.713766\pi\) | ||||
−0.622212 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(614\) | −21.3000 | −0.859596 | ||||||||
\(615\) | −2.30975 | −0.0931382 | ||||||||
\(616\) | 12.3488 | 0.497549 | ||||||||
\(617\) | 34.6123 | 1.39344 | 0.696719 | − | 0.717344i | \(-0.254642\pi\) | ||||
0.696719 | + | 0.717344i | \(0.254642\pi\) | |||||||
\(618\) | −3.33437 | −0.134128 | ||||||||
\(619\) | 3.78119 | 0.151979 | 0.0759895 | − | 0.997109i | \(-0.475788\pi\) | ||||
0.0759895 | + | 0.997109i | \(0.475788\pi\) | |||||||
\(620\) | 2.01579 | 0.0809562 | ||||||||
\(621\) | −27.6413 | −1.10921 | ||||||||
\(622\) | 11.3248 | 0.454084 | ||||||||
\(623\) | 39.7805 | 1.59377 | ||||||||
\(624\) | 3.88919 | 0.155692 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.5480 | −0.981135 | ||||||||
\(627\) | −11.1009 | −0.443328 | ||||||||
\(628\) | 13.0752 | 0.521756 | ||||||||
\(629\) | 0.265770 | 0.0105969 | ||||||||
\(630\) | −7.03195 | −0.280160 | ||||||||
\(631\) | 19.0714 | 0.759221 | 0.379610 | − | 0.925146i | \(-0.376058\pi\) | ||||
0.379610 | + | 0.925146i | \(0.376058\pi\) | |||||||
\(632\) | −13.1650 | −0.523674 | ||||||||
\(633\) | 28.0237 | 1.11384 | ||||||||
\(634\) | 6.12633 | 0.243308 | ||||||||
\(635\) | 13.3627 | 0.530282 | ||||||||
\(636\) | 4.02276 | 0.159513 | ||||||||
\(637\) | 23.8818 | 0.946232 | ||||||||
\(638\) | −2.74338 | −0.108612 | ||||||||
\(639\) | −7.83939 | −0.310121 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 0.227937 | 0.00900295 | 0.00450148 | − | 0.999990i | \(-0.498567\pi\) | ||||
0.00450148 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(642\) | 16.1845 | 0.638752 | ||||||||
\(643\) | −1.27126 | −0.0501336 | −0.0250668 | − | 0.999686i | \(-0.507980\pi\) | ||||
−0.0250668 | + | 0.999686i | \(0.507980\pi\) | |||||||
\(644\) | −19.7845 | −0.779617 | ||||||||
\(645\) | 6.52615 | 0.256967 | ||||||||
\(646\) | −0.682648 | −0.0268584 | ||||||||
\(647\) | −34.8403 | −1.36972 | −0.684858 | − | 0.728677i | \(-0.740136\pi\) | ||||
−0.684858 | + | 0.728677i | \(0.740136\pi\) | |||||||
\(648\) | −0.466492 | −0.0183255 | ||||||||
\(649\) | −45.6593 | −1.79228 | ||||||||
\(650\) | −3.74747 | −0.146988 | ||||||||
\(651\) | −7.65028 | −0.299838 | ||||||||
\(652\) | −2.24469 | −0.0879089 | ||||||||
\(653\) | −27.4648 | −1.07478 | −0.537391 | − | 0.843333i | \(-0.680590\pi\) | ||||
−0.537391 | + | 0.843333i | \(0.680590\pi\) | |||||||
\(654\) | −10.1170 | −0.395605 | ||||||||
\(655\) | 11.5136 | 0.449873 | ||||||||
\(656\) | −2.22559 | −0.0868946 | ||||||||
\(657\) | 28.1219 | 1.09714 | ||||||||
\(658\) | −8.46100 | −0.329844 | ||||||||
\(659\) | 30.0151 | 1.16922 | 0.584611 | − | 0.811314i | \(-0.301247\pi\) | ||||
0.584611 | + | 0.811314i | \(0.301247\pi\) | |||||||
\(660\) | 3.50458 | 0.136416 | ||||||||
\(661\) | 10.0503 | 0.390911 | 0.195455 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195455 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(662\) | 0.250410 | 0.00973246 | ||||||||
\(663\) | −0.838172 | −0.0325519 | ||||||||
\(664\) | −11.3538 | −0.440614 | ||||||||
\(665\) | 11.5833 | 0.449182 | ||||||||
\(666\) | −2.37135 | −0.0918880 | ||||||||
\(667\) | 4.39526 | 0.170185 | ||||||||
\(668\) | −19.8554 | −0.768228 | ||||||||
\(669\) | 4.07364 | 0.157496 | ||||||||
\(670\) | −0.202415 | −0.00781996 | ||||||||
\(671\) | 36.9791 | 1.42756 | ||||||||
\(672\) | 3.79517 | 0.146402 | ||||||||
\(673\) | −10.4797 | −0.403964 | −0.201982 | − | 0.979389i | \(-0.564738\pi\) | ||||
−0.201982 | + | 0.979389i | \(0.564738\pi\) | |||||||
\(674\) | −10.7313 | −0.413353 | ||||||||
\(675\) | −5.10911 | −0.196650 | ||||||||
\(676\) | 1.04353 | 0.0401358 | ||||||||
\(677\) | 40.5800 | 1.55962 | 0.779809 | − | 0.626018i | \(-0.215316\pi\) | ||||
0.779809 | + | 0.626018i | \(0.215316\pi\) | |||||||
\(678\) | −4.86955 | −0.187014 | ||||||||
\(679\) | 40.3423 | 1.54820 | ||||||||
\(680\) | 0.215513 | 0.00826456 | ||||||||
\(681\) | 23.4680 | 0.899295 | ||||||||
\(682\) | −6.80708 | −0.260657 | ||||||||
\(683\) | −7.62692 | −0.291836 | −0.145918 | − | 0.989297i | \(-0.546614\pi\) | ||||
−0.145918 | + | 0.989297i | \(0.546614\pi\) | |||||||
\(684\) | 6.09099 | 0.232895 | ||||||||
\(685\) | 17.7664 | 0.678821 | ||||||||
\(686\) | −2.29365 | −0.0875718 | ||||||||
\(687\) | 27.1626 | 1.03632 | ||||||||
\(688\) | 6.28835 | 0.239741 | ||||||||
\(689\) | 14.5259 | 0.553391 | ||||||||
\(690\) | −5.61479 | −0.213752 | ||||||||
\(691\) | −5.46159 | −0.207769 | −0.103884 | − | 0.994589i | \(-0.533127\pi\) | ||||
−0.103884 | + | 0.994589i | \(0.533127\pi\) | |||||||
\(692\) | −5.76255 | −0.219059 | ||||||||
\(693\) | 23.7460 | 0.902037 | ||||||||
\(694\) | 36.1651 | 1.37281 | ||||||||
\(695\) | 5.17338 | 0.196237 | ||||||||
\(696\) | −0.843125 | −0.0319586 | ||||||||
\(697\) | 0.479644 | 0.0181678 | ||||||||
\(698\) | 34.5414 | 1.30741 | ||||||||
\(699\) | 0.779912 | 0.0294990 | ||||||||
\(700\) | −3.65688 | −0.138217 | ||||||||
\(701\) | −2.74812 | −0.103795 | −0.0518976 | − | 0.998652i | \(-0.516527\pi\) | ||||
−0.0518976 | + | 0.998652i | \(0.516527\pi\) | |||||||
\(702\) | 19.1462 | 0.722628 | ||||||||
\(703\) | 3.90619 | 0.147325 | ||||||||
\(704\) | 3.37688 | 0.127271 | ||||||||
\(705\) | −2.40122 | −0.0904350 | ||||||||
\(706\) | −9.77851 | −0.368019 | ||||||||
\(707\) | −24.2497 | −0.912005 | ||||||||
\(708\) | −14.0325 | −0.527373 | ||||||||
\(709\) | −21.5202 | −0.808209 | −0.404104 | − | 0.914713i | \(-0.632417\pi\) | ||||
−0.404104 | + | 0.914713i | \(0.632417\pi\) | |||||||
\(710\) | −4.07678 | −0.152999 | ||||||||
\(711\) | −25.3154 | −0.949400 | ||||||||
\(712\) | 10.8782 | 0.407680 | ||||||||
\(713\) | 10.9058 | 0.408427 | ||||||||
\(714\) | −0.817911 | −0.0306095 | ||||||||
\(715\) | 12.6547 | 0.473261 | ||||||||
\(716\) | 15.8613 | 0.592765 | ||||||||
\(717\) | −7.87288 | −0.294018 | ||||||||
\(718\) | 2.30879 | 0.0861635 | ||||||||
\(719\) | 30.9846 | 1.15553 | 0.577765 | − | 0.816203i | \(-0.303925\pi\) | ||||
0.577765 | + | 0.816203i | \(0.303925\pi\) | |||||||
\(720\) | −1.92294 | −0.0716636 | ||||||||
\(721\) | −11.7491 | −0.437559 | ||||||||
\(722\) | 8.96666 | 0.333705 | ||||||||
\(723\) | 27.0286 | 1.00520 | ||||||||
\(724\) | 9.47492 | 0.352132 | ||||||||
\(725\) | 0.812402 | 0.0301719 | ||||||||
\(726\) | −0.418549 | −0.0155338 | ||||||||
\(727\) | −23.4729 | −0.870561 | −0.435281 | − | 0.900295i | \(-0.643351\pi\) | ||||
−0.435281 | + | 0.900295i | \(0.643351\pi\) | |||||||
\(728\) | 13.7041 | 0.507906 | ||||||||
\(729\) | 15.0099 | 0.555923 | ||||||||
\(730\) | 14.6244 | 0.541275 | ||||||||
\(731\) | −1.35522 | −0.0501248 | ||||||||
\(732\) | 11.3648 | 0.420055 | ||||||||
\(733\) | −2.37074 | −0.0875654 | −0.0437827 | − | 0.999041i | \(-0.513941\pi\) | ||||
−0.0437827 | + | 0.999041i | \(0.513941\pi\) | |||||||
\(734\) | 32.3313 | 1.19337 | ||||||||
\(735\) | 6.61378 | 0.243953 | ||||||||
\(736\) | −5.41020 | −0.199423 | ||||||||
\(737\) | 0.683530 | 0.0251781 | ||||||||
\(738\) | −4.27966 | −0.157537 | ||||||||
\(739\) | −11.9266 | −0.438726 | −0.219363 | − | 0.975643i | \(-0.570398\pi\) | ||||
−0.219363 | + | 0.975643i | \(0.570398\pi\) | |||||||
\(740\) | −1.23319 | −0.0453331 | ||||||||
\(741\) | −12.3192 | −0.452556 | ||||||||
\(742\) | 14.1747 | 0.520370 | ||||||||
\(743\) | 15.2883 | 0.560872 | 0.280436 | − | 0.959873i | \(-0.409521\pi\) | ||||
0.280436 | + | 0.959873i | \(0.409521\pi\) | |||||||
\(744\) | −2.09202 | −0.0766973 | ||||||||
\(745\) | 8.93665 | 0.327414 | ||||||||
\(746\) | 10.2869 | 0.376632 | ||||||||
\(747\) | −21.8327 | −0.798817 | ||||||||
\(748\) | −0.727762 | −0.0266096 | ||||||||
\(749\) | 57.0282 | 2.08377 | ||||||||
\(750\) | −1.03782 | −0.0378957 | ||||||||
\(751\) | −23.6972 | −0.864724 | −0.432362 | − | 0.901700i | \(-0.642320\pi\) | ||||
−0.432362 | + | 0.901700i | \(0.642320\pi\) | |||||||
\(752\) | −2.31372 | −0.0843726 | ||||||||
\(753\) | 12.1698 | 0.443491 | ||||||||
\(754\) | −3.04445 | −0.110872 | ||||||||
\(755\) | −3.91214 | −0.142377 | ||||||||
\(756\) | 18.6834 | 0.679509 | ||||||||
\(757\) | −41.4932 | −1.50810 | −0.754048 | − | 0.656820i | \(-0.771901\pi\) | ||||
−0.754048 | + | 0.656820i | \(0.771901\pi\) | |||||||
\(758\) | 10.7646 | 0.390987 | ||||||||
\(759\) | 18.9605 | 0.688221 | ||||||||
\(760\) | 3.16754 | 0.114899 | ||||||||
\(761\) | 8.50542 | 0.308321 | 0.154161 | − | 0.988046i | \(-0.450733\pi\) | ||||
0.154161 | + | 0.988046i | \(0.450733\pi\) | |||||||
\(762\) | −13.8680 | −0.502386 | ||||||||
\(763\) | −35.6485 | −1.29056 | ||||||||
\(764\) | 14.6508 | 0.530049 | ||||||||
\(765\) | 0.414419 | 0.0149833 | ||||||||
\(766\) | 5.30417 | 0.191647 | ||||||||
\(767\) | −50.6702 | −1.82959 | ||||||||
\(768\) | 1.03782 | 0.0374490 | ||||||||
\(769\) | 6.47655 | 0.233551 | 0.116775 | − | 0.993158i | \(-0.462744\pi\) | ||||
0.116775 | + | 0.993158i | \(0.462744\pi\) | |||||||
\(770\) | 12.3488 | 0.445021 | ||||||||
\(771\) | 19.3393 | 0.696488 | ||||||||
\(772\) | −17.4298 | −0.627313 | ||||||||
\(773\) | −8.66929 | −0.311813 | −0.155906 | − | 0.987772i | \(-0.549830\pi\) | ||||
−0.155906 | + | 0.987772i | \(0.549830\pi\) | |||||||
\(774\) | 12.0921 | 0.434641 | ||||||||
\(775\) | 2.01579 | 0.0724094 | ||||||||
\(776\) | 11.0319 | 0.396021 | ||||||||
\(777\) | 4.68018 | 0.167901 | ||||||||
\(778\) | 9.53656 | 0.341902 | ||||||||
\(779\) | 7.04964 | 0.252580 | ||||||||
\(780\) | 3.88919 | 0.139255 | ||||||||
\(781\) | 13.7668 | 0.492614 | ||||||||
\(782\) | 1.16597 | 0.0416950 | ||||||||
\(783\) | −4.15065 | −0.148332 | ||||||||
\(784\) | 6.37279 | 0.227600 | ||||||||
\(785\) | 13.0752 | 0.466673 | ||||||||
\(786\) | −11.9490 | −0.426206 | ||||||||
\(787\) | −9.01728 | −0.321431 | −0.160716 | − | 0.987001i | \(-0.551380\pi\) | ||||
−0.160716 | + | 0.987001i | \(0.551380\pi\) | |||||||
\(788\) | 5.43621 | 0.193657 | ||||||||
\(789\) | −13.1440 | −0.467938 | ||||||||
\(790\) | −13.1650 | −0.468388 | ||||||||
\(791\) | −17.1585 | −0.610086 | ||||||||
\(792\) | 6.49352 | 0.230737 | ||||||||
\(793\) | 41.0374 | 1.45728 | ||||||||
\(794\) | 18.9346 | 0.671964 | ||||||||
\(795\) | 4.02276 | 0.142673 | ||||||||
\(796\) | 24.7689 | 0.877911 | ||||||||
\(797\) | 43.3680 | 1.53617 | 0.768086 | − | 0.640347i | \(-0.221209\pi\) | ||||
0.768086 | + | 0.640347i | \(0.221209\pi\) | |||||||
\(798\) | −12.0214 | −0.425552 | ||||||||
\(799\) | 0.498637 | 0.0176405 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 20.9182 | 0.739107 | ||||||||
\(802\) | 0.0627506 | 0.00221580 | ||||||||
\(803\) | −49.3849 | −1.74276 | ||||||||
\(804\) | 0.210069 | 0.00740858 | ||||||||
\(805\) | −19.7845 | −0.697310 | ||||||||
\(806\) | −7.55412 | −0.266083 | ||||||||
\(807\) | 7.08710 | 0.249478 | ||||||||
\(808\) | −6.63126 | −0.233287 | ||||||||
\(809\) | 9.04658 | 0.318061 | 0.159030 | − | 0.987274i | \(-0.449163\pi\) | ||||
0.159030 | + | 0.987274i | \(0.449163\pi\) | |||||||
\(810\) | −0.466492 | −0.0163909 | ||||||||
\(811\) | 20.6201 | 0.724070 | 0.362035 | − | 0.932164i | \(-0.382082\pi\) | ||||
0.362035 | + | 0.932164i | \(0.382082\pi\) | |||||||
\(812\) | −2.97086 | −0.104257 | ||||||||
\(813\) | 20.1435 | 0.706465 | ||||||||
\(814\) | 4.16434 | 0.145960 | ||||||||
\(815\) | −2.24469 | −0.0786281 | ||||||||
\(816\) | −0.223663 | −0.00782979 | ||||||||
\(817\) | −19.9186 | −0.696864 | ||||||||
\(818\) | 4.26183 | 0.149011 | ||||||||
\(819\) | 26.3520 | 0.920814 | ||||||||
\(820\) | −2.22559 | −0.0777209 | ||||||||
\(821\) | −29.1302 | −1.01665 | −0.508325 | − | 0.861165i | \(-0.669735\pi\) | ||||
−0.508325 | + | 0.861165i | \(0.669735\pi\) | |||||||
\(822\) | −18.4383 | −0.643110 | ||||||||
\(823\) | −8.47428 | −0.295395 | −0.147697 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147697 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(824\) | −3.21287 | −0.111926 | ||||||||
\(825\) | 3.50458 | 0.122014 | ||||||||
\(826\) | −49.4453 | −1.72042 | ||||||||
\(827\) | 38.8715 | 1.35169 | 0.675847 | − | 0.737042i | \(-0.263778\pi\) | ||||
0.675847 | + | 0.737042i | \(0.263778\pi\) | |||||||
\(828\) | −10.4035 | −0.361545 | ||||||||
\(829\) | −33.5907 | −1.16665 | −0.583327 | − | 0.812238i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812238i | \(0.698249\pi\) | |||||||
\(830\) | −11.3538 | −0.394097 | ||||||||
\(831\) | −30.1787 | −1.04689 | ||||||||
\(832\) | 3.74747 | 0.129920 | ||||||||
\(833\) | −1.37342 | −0.0475862 | ||||||||
\(834\) | −5.36902 | −0.185914 | ||||||||
\(835\) | −19.8554 | −0.687124 | ||||||||
\(836\) | −10.6964 | −0.369943 | ||||||||
\(837\) | −10.2989 | −0.355982 | ||||||||
\(838\) | 2.69655 | 0.0931506 | ||||||||
\(839\) | −26.5267 | −0.915802 | −0.457901 | − | 0.889003i | \(-0.651399\pi\) | ||||
−0.457901 | + | 0.889003i | \(0.651399\pi\) | |||||||
\(840\) | 3.79517 | 0.130946 | ||||||||
\(841\) | −28.3400 | −0.977241 | ||||||||
\(842\) | 20.7655 | 0.715627 | ||||||||
\(843\) | 29.3338 | 1.01031 | ||||||||
\(844\) | 27.0025 | 0.929465 | ||||||||
\(845\) | 1.04353 | 0.0358986 | ||||||||
\(846\) | −4.44913 | −0.152964 | ||||||||
\(847\) | −1.47481 | −0.0506751 | ||||||||
\(848\) | 3.87618 | 0.133108 | ||||||||
\(849\) | 3.40519 | 0.116866 | ||||||||
\(850\) | 0.215513 | 0.00739205 | ||||||||
\(851\) | −6.67182 | −0.228707 | ||||||||
\(852\) | 4.23095 | 0.144950 | ||||||||
\(853\) | 40.1425 | 1.37445 | 0.687226 | − | 0.726444i | \(-0.258828\pi\) | ||||
0.687226 | + | 0.726444i | \(0.258828\pi\) | |||||||
\(854\) | 40.0454 | 1.37032 | ||||||||
\(855\) | 6.09099 | 0.208307 | ||||||||
\(856\) | 15.5948 | 0.533018 | ||||||||
\(857\) | −1.04928 | −0.0358427 | −0.0179213 | − | 0.999839i | \(-0.505705\pi\) | ||||
−0.0179213 | + | 0.999839i | \(0.505705\pi\) | |||||||
\(858\) | −13.1333 | −0.448364 | ||||||||
\(859\) | 37.4295 | 1.27708 | 0.638540 | − | 0.769589i | \(-0.279539\pi\) | ||||
0.638540 | + | 0.769589i | \(0.279539\pi\) | |||||||
\(860\) | 6.28835 | 0.214431 | ||||||||
\(861\) | 8.44649 | 0.287856 | ||||||||
\(862\) | 1.62083 | 0.0552058 | ||||||||
\(863\) | −39.2898 | −1.33744 | −0.668721 | − | 0.743514i | \(-0.733158\pi\) | ||||
−0.668721 | + | 0.743514i | \(0.733158\pi\) | |||||||
\(864\) | 5.10911 | 0.173815 | ||||||||
\(865\) | −5.76255 | −0.195933 | ||||||||
\(866\) | 5.50288 | 0.186995 | ||||||||
\(867\) | −17.5947 | −0.597547 | ||||||||
\(868\) | −7.37152 | −0.250206 | ||||||||
\(869\) | 44.4564 | 1.50808 | ||||||||
\(870\) | −0.843125 | −0.0285846 | ||||||||
\(871\) | 0.758543 | 0.0257023 | ||||||||
\(872\) | −9.74833 | −0.330120 | ||||||||
\(873\) | 21.2136 | 0.717972 | ||||||||
\(874\) | 17.1370 | 0.579669 | ||||||||
\(875\) | −3.65688 | −0.123625 | ||||||||
\(876\) | −15.1775 | −0.512800 | ||||||||
\(877\) | 12.4506 | 0.420428 | 0.210214 | − | 0.977655i | \(-0.432584\pi\) | ||||
0.210214 | + | 0.977655i | \(0.432584\pi\) | |||||||
\(878\) | −11.8038 | −0.398358 | ||||||||
\(879\) | −26.2005 | −0.883720 | ||||||||
\(880\) | 3.37688 | 0.113834 | ||||||||
\(881\) | −27.7485 | −0.934871 | −0.467436 | − | 0.884027i | \(-0.654822\pi\) | ||||
−0.467436 | + | 0.884027i | \(0.654822\pi\) | |||||||
\(882\) | 12.2545 | 0.412629 | ||||||||
\(883\) | −32.3580 | −1.08893 | −0.544467 | − | 0.838782i | \(-0.683268\pi\) | ||||
−0.544467 | + | 0.838782i | \(0.683268\pi\) | |||||||
\(884\) | −0.807630 | −0.0271635 | ||||||||
\(885\) | −14.0325 | −0.471697 | ||||||||
\(886\) | −37.9919 | −1.27636 | ||||||||
\(887\) | 46.3314 | 1.55566 | 0.777829 | − | 0.628476i | \(-0.216321\pi\) | ||||
0.777829 | + | 0.628476i | \(0.216321\pi\) | |||||||
\(888\) | 1.27983 | 0.0429482 | ||||||||
\(889\) | −48.8658 | −1.63891 | ||||||||
\(890\) | 10.8782 | 0.364640 | ||||||||
\(891\) | 1.57529 | 0.0527741 | ||||||||
\(892\) | 3.92520 | 0.131425 | ||||||||
\(893\) | 7.32881 | 0.245249 | ||||||||
\(894\) | −9.27461 | −0.310189 | ||||||||
\(895\) | 15.8613 | 0.530185 | ||||||||
\(896\) | 3.65688 | 0.122168 | ||||||||
\(897\) | 21.0413 | 0.702548 | ||||||||
\(898\) | 14.7413 | 0.491925 | ||||||||
\(899\) | 1.63763 | 0.0546182 | ||||||||
\(900\) | −1.92294 | −0.0640979 | ||||||||
\(901\) | −0.835368 | −0.0278302 | ||||||||
\(902\) | 7.51553 | 0.250240 | ||||||||
\(903\) | −23.8654 | −0.794190 | ||||||||
\(904\) | −4.69211 | −0.156057 | ||||||||
\(905\) | 9.47492 | 0.314957 | ||||||||
\(906\) | 4.06008 | 0.134887 | ||||||||
\(907\) | −26.1113 | −0.867012 | −0.433506 | − | 0.901151i | \(-0.642724\pi\) | ||||
−0.433506 | + | 0.901151i | \(0.642724\pi\) | |||||||
\(908\) | 22.6128 | 0.750433 | ||||||||
\(909\) | −12.7515 | −0.422940 | ||||||||
\(910\) | 13.7041 | 0.454285 | ||||||||
\(911\) | 8.88789 | 0.294469 | 0.147234 | − | 0.989102i | \(-0.452963\pi\) | ||||
0.147234 | + | 0.989102i | \(0.452963\pi\) | |||||||
\(912\) | −3.28733 | −0.108854 | ||||||||
\(913\) | 38.3405 | 1.26889 | ||||||||
\(914\) | −20.5518 | −0.679792 | ||||||||
\(915\) | 11.3648 | 0.375709 | ||||||||
\(916\) | 26.1728 | 0.864774 | ||||||||
\(917\) | −42.1038 | −1.39039 | ||||||||
\(918\) | −1.10108 | −0.0363411 | ||||||||
\(919\) | 3.18645 | 0.105111 | 0.0525557 | − | 0.998618i | \(-0.483263\pi\) | ||||
0.0525557 | + | 0.998618i | \(0.483263\pi\) | |||||||
\(920\) | −5.41020 | −0.178369 | ||||||||
\(921\) | 22.1054 | 0.728399 | ||||||||
\(922\) | −26.0399 | −0.857578 | ||||||||
\(923\) | 15.2776 | 0.502869 | ||||||||
\(924\) | −12.8158 | −0.421610 | ||||||||
\(925\) | −1.23319 | −0.0405471 | ||||||||
\(926\) | 40.3534 | 1.32610 | ||||||||
\(927\) | −6.17814 | −0.202917 | ||||||||
\(928\) | −0.812402 | −0.0266684 | ||||||||
\(929\) | −60.2598 | −1.97706 | −0.988530 | − | 0.151024i | \(-0.951743\pi\) | ||||
−0.988530 | + | 0.151024i | \(0.951743\pi\) | |||||||
\(930\) | −2.09202 | −0.0686001 | ||||||||
\(931\) | −20.1861 | −0.661572 | ||||||||
\(932\) | 0.751493 | 0.0246160 | ||||||||
\(933\) | −11.7531 | −0.384779 | ||||||||
\(934\) | −19.0057 | −0.621886 | ||||||||
\(935\) | −0.727762 | −0.0238004 | ||||||||
\(936\) | 7.20615 | 0.235540 | ||||||||
\(937\) | 54.5953 | 1.78355 | 0.891775 | − | 0.452479i | \(-0.149460\pi\) | ||||
0.891775 | + | 0.452479i | \(0.149460\pi\) | |||||||
\(938\) | 0.740207 | 0.0241686 | ||||||||
\(939\) | 25.4763 | 0.831389 | ||||||||
\(940\) | −2.31372 | −0.0754652 | ||||||||
\(941\) | −17.8167 | −0.580807 | −0.290403 | − | 0.956904i | \(-0.593789\pi\) | ||||
−0.290403 | + | 0.956904i | \(0.593789\pi\) | |||||||
\(942\) | −13.5696 | −0.442122 | ||||||||
\(943\) | −12.0409 | −0.392104 | ||||||||
\(944\) | −13.5212 | −0.440076 | ||||||||
\(945\) | 18.6834 | 0.607771 | ||||||||
\(946\) | −21.2350 | −0.690409 | ||||||||
\(947\) | −57.0959 | −1.85537 | −0.927683 | − | 0.373368i | \(-0.878203\pi\) | ||||
−0.927683 | + | 0.373368i | \(0.878203\pi\) | |||||||
\(948\) | 13.6628 | 0.443747 | ||||||||
\(949\) | −54.8047 | −1.77903 | ||||||||
\(950\) | 3.16754 | 0.102769 | ||||||||
\(951\) | −6.35801 | −0.206173 | ||||||||
\(952\) | −0.788107 | −0.0255427 | ||||||||
\(953\) | −12.3794 | −0.401008 | −0.200504 | − | 0.979693i | \(-0.564258\pi\) | ||||
−0.200504 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(954\) | 7.45364 | 0.241321 | ||||||||
\(955\) | 14.6508 | 0.474090 | ||||||||
\(956\) | −7.58600 | −0.245349 | ||||||||
\(957\) | 2.84713 | 0.0920346 | ||||||||
\(958\) | 4.99765 | 0.161467 | ||||||||
\(959\) | −64.9698 | −2.09798 | ||||||||
\(960\) | 1.03782 | 0.0334954 | ||||||||
\(961\) | −26.9366 | −0.868922 | ||||||||
\(962\) | 4.62135 | 0.148998 | ||||||||
\(963\) | 29.9877 | 0.966341 | ||||||||
\(964\) | 26.0437 | 0.838811 | ||||||||
\(965\) | −17.4298 | −0.561086 | ||||||||
\(966\) | 20.5326 | 0.660627 | ||||||||
\(967\) | 57.8777 | 1.86122 | 0.930611 | − | 0.366009i | \(-0.119276\pi\) | ||||
0.930611 | + | 0.366009i | \(0.119276\pi\) | |||||||
\(968\) | −0.403297 | −0.0129625 | ||||||||
\(969\) | 0.708464 | 0.0227591 | ||||||||
\(970\) | 11.0319 | 0.354212 | ||||||||
\(971\) | 26.4547 | 0.848971 | 0.424485 | − | 0.905435i | \(-0.360455\pi\) | ||||
0.424485 | + | 0.905435i | \(0.360455\pi\) | |||||||
\(972\) | 15.8115 | 0.507153 | ||||||||
\(973\) | −18.9184 | −0.606497 | ||||||||
\(974\) | −33.5250 | −1.07421 | ||||||||
\(975\) | 3.88919 | 0.124554 | ||||||||
\(976\) | 10.9507 | 0.350523 | ||||||||
\(977\) | −9.41195 | −0.301115 | −0.150557 | − | 0.988601i | \(-0.548107\pi\) | ||||
−0.150557 | + | 0.988601i | \(0.548107\pi\) | |||||||
\(978\) | 2.32958 | 0.0744917 | ||||||||
\(979\) | −36.7345 | −1.17404 | ||||||||
\(980\) | 6.37279 | 0.203571 | ||||||||
\(981\) | −18.7454 | −0.598495 | ||||||||
\(982\) | 8.90643 | 0.284216 | ||||||||
\(983\) | −25.7156 | −0.820199 | −0.410100 | − | 0.912041i | \(-0.634506\pi\) | ||||
−0.410100 | + | 0.912041i | \(0.634506\pi\) | |||||||
\(984\) | 2.30975 | 0.0736322 | ||||||||
\(985\) | 5.43621 | 0.173212 | ||||||||
\(986\) | 0.175084 | 0.00557580 | ||||||||
\(987\) | 8.78096 | 0.279501 | ||||||||
\(988\) | −11.8703 | −0.377644 | ||||||||
\(989\) | 34.0212 | 1.08181 | ||||||||
\(990\) | 6.49352 | 0.206378 | ||||||||
\(991\) | 16.4151 | 0.521443 | 0.260722 | − | 0.965414i | \(-0.416040\pi\) | ||||
0.260722 | + | 0.965414i | \(0.416040\pi\) | |||||||
\(992\) | −2.01579 | −0.0640015 | ||||||||
\(993\) | −0.259880 | −0.00824703 | ||||||||
\(994\) | 14.9083 | 0.472863 | ||||||||
\(995\) | 24.7689 | 0.785227 | ||||||||
\(996\) | 11.7832 | 0.373365 | ||||||||
\(997\) | −30.2357 | −0.957574 | −0.478787 | − | 0.877931i | \(-0.658923\pi\) | ||||
−0.478787 | + | 0.877931i | \(0.658923\pi\) | |||||||
\(998\) | 13.3307 | 0.421976 | ||||||||
\(999\) | 6.30051 | 0.199339 |
(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 | 6010.2.a.g.1.15 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.g.1.15 | ✓ | 27 | 1.1 | even | 1 | trivial |