Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, 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("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.116160\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-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 | ||||||||
\(3\) | −0.116160 | −0.0670651 | −0.0335325 | − | 0.999438i | \(-0.510676\pi\) | ||||
−0.0335325 | + | 0.999438i | \(0.510676\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.498551 | −0.222959 | −0.111479 | − | 0.993767i | \(-0.535559\pi\) | ||||
−0.111479 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(6\) | 0.116160 | 0.0474222 | ||||||||
\(7\) | −2.29128 | −0.866022 | −0.433011 | − | 0.901389i | \(-0.642549\pi\) | ||||
−0.433011 | + | 0.901389i | \(0.642549\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.98651 | −0.995502 | ||||||||
\(10\) | 0.498551 | 0.157656 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.116160 | −0.0335325 | ||||||||
\(13\) | 0.281152 | 0.0779777 | 0.0389888 | − | 0.999240i | \(-0.487586\pi\) | ||||
0.0389888 | + | 0.999240i | \(0.487586\pi\) | |||||||
\(14\) | 2.29128 | 0.612370 | ||||||||
\(15\) | 0.0579118 | 0.0149528 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.65358 | 0.401051 | 0.200526 | − | 0.979688i | \(-0.435735\pi\) | ||||
0.200526 | + | 0.979688i | \(0.435735\pi\) | |||||||
\(18\) | 2.98651 | 0.703926 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.498551 | −0.111479 | ||||||||
\(21\) | 0.266155 | 0.0580798 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 8.04296 | 1.67707 | 0.838537 | − | 0.544845i | \(-0.183412\pi\) | ||||
0.838537 | + | 0.544845i | \(0.183412\pi\) | |||||||
\(24\) | 0.116160 | 0.0237111 | ||||||||
\(25\) | −4.75145 | −0.950289 | ||||||||
\(26\) | −0.281152 | −0.0551385 | ||||||||
\(27\) | 0.695394 | 0.133829 | ||||||||
\(28\) | −2.29128 | −0.433011 | ||||||||
\(29\) | −2.32572 | −0.431875 | −0.215937 | − | 0.976407i | \(-0.569281\pi\) | ||||
−0.215937 | + | 0.976407i | \(0.569281\pi\) | |||||||
\(30\) | −0.0579118 | −0.0105732 | ||||||||
\(31\) | −3.69373 | −0.663413 | −0.331707 | − | 0.943383i | \(-0.607624\pi\) | ||||
−0.331707 | + | 0.943383i | \(0.607624\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.116160 | −0.0202209 | ||||||||
\(34\) | −1.65358 | −0.283586 | ||||||||
\(35\) | 1.14232 | 0.193087 | ||||||||
\(36\) | −2.98651 | −0.497751 | ||||||||
\(37\) | 5.88414 | 0.967346 | 0.483673 | − | 0.875249i | \(-0.339302\pi\) | ||||
0.483673 | + | 0.875249i | \(0.339302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0326587 | −0.00522958 | ||||||||
\(40\) | 0.498551 | 0.0788279 | ||||||||
\(41\) | 0.535174 | 0.0835802 | 0.0417901 | − | 0.999126i | \(-0.486694\pi\) | ||||
0.0417901 | + | 0.999126i | \(0.486694\pi\) | |||||||
\(42\) | −0.266155 | −0.0410686 | ||||||||
\(43\) | −5.13015 | −0.782340 | −0.391170 | − | 0.920318i | \(-0.627930\pi\) | ||||
−0.391170 | + | 0.920318i | \(0.627930\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.48893 | 0.221956 | ||||||||
\(46\) | −8.04296 | −1.18587 | ||||||||
\(47\) | 10.6311 | 1.55070 | 0.775352 | − | 0.631529i | \(-0.217572\pi\) | ||||
0.775352 | + | 0.631529i | \(0.217572\pi\) | |||||||
\(48\) | −0.116160 | −0.0167663 | ||||||||
\(49\) | −1.75004 | −0.250006 | ||||||||
\(50\) | 4.75145 | 0.671956 | ||||||||
\(51\) | −0.192080 | −0.0268965 | ||||||||
\(52\) | 0.281152 | 0.0389888 | ||||||||
\(53\) | 8.71898 | 1.19764 | 0.598822 | − | 0.800882i | \(-0.295636\pi\) | ||||
0.598822 | + | 0.800882i | \(0.295636\pi\) | |||||||
\(54\) | −0.695394 | −0.0946311 | ||||||||
\(55\) | −0.498551 | −0.0672246 | ||||||||
\(56\) | 2.29128 | 0.306185 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.32572 | 0.305382 | ||||||||
\(59\) | −2.84215 | −0.370016 | −0.185008 | − | 0.982737i | \(-0.559231\pi\) | ||||
−0.185008 | + | 0.982737i | \(0.559231\pi\) | |||||||
\(60\) | 0.0579118 | 0.00747638 | ||||||||
\(61\) | −12.4970 | −1.60008 | −0.800039 | − | 0.599948i | \(-0.795188\pi\) | ||||
−0.800039 | + | 0.599948i | \(0.795188\pi\) | |||||||
\(62\) | 3.69373 | 0.469104 | ||||||||
\(63\) | 6.84292 | 0.862127 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.140169 | −0.0173858 | ||||||||
\(66\) | 0.116160 | 0.0142983 | ||||||||
\(67\) | −11.7338 | −1.43351 | −0.716756 | − | 0.697324i | \(-0.754374\pi\) | ||||
−0.716756 | + | 0.697324i | \(0.754374\pi\) | |||||||
\(68\) | 1.65358 | 0.200526 | ||||||||
\(69\) | −0.934272 | −0.112473 | ||||||||
\(70\) | −1.14232 | −0.136533 | ||||||||
\(71\) | 5.50926 | 0.653829 | 0.326914 | − | 0.945054i | \(-0.393991\pi\) | ||||
0.326914 | + | 0.945054i | \(0.393991\pi\) | |||||||
\(72\) | 2.98651 | 0.351963 | ||||||||
\(73\) | 2.38179 | 0.278768 | 0.139384 | − | 0.990238i | \(-0.455488\pi\) | ||||
0.139384 | + | 0.990238i | \(0.455488\pi\) | |||||||
\(74\) | −5.88414 | −0.684017 | ||||||||
\(75\) | 0.551929 | 0.0637312 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.29128 | −0.261115 | ||||||||
\(78\) | 0.0326587 | 0.00369787 | ||||||||
\(79\) | 14.1034 | 1.58676 | 0.793379 | − | 0.608727i | \(-0.208320\pi\) | ||||
0.793379 | + | 0.608727i | \(0.208320\pi\) | |||||||
\(80\) | −0.498551 | −0.0557397 | ||||||||
\(81\) | 8.87874 | 0.986527 | ||||||||
\(82\) | −0.535174 | −0.0591001 | ||||||||
\(83\) | −15.6876 | −1.72194 | −0.860971 | − | 0.508653i | \(-0.830144\pi\) | ||||
−0.860971 | + | 0.508653i | \(0.830144\pi\) | |||||||
\(84\) | 0.266155 | 0.0290399 | ||||||||
\(85\) | −0.824392 | −0.0894179 | ||||||||
\(86\) | 5.13015 | 0.553198 | ||||||||
\(87\) | 0.270156 | 0.0289637 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 6.41709 | 0.680210 | 0.340105 | − | 0.940387i | \(-0.389537\pi\) | ||||
0.340105 | + | 0.940387i | \(0.389537\pi\) | |||||||
\(90\) | −1.48893 | −0.156947 | ||||||||
\(91\) | −0.644199 | −0.0675304 | ||||||||
\(92\) | 8.04296 | 0.838537 | ||||||||
\(93\) | 0.429064 | 0.0444919 | ||||||||
\(94\) | −10.6311 | −1.09651 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.116160 | 0.0118555 | ||||||||
\(97\) | 15.4833 | 1.57209 | 0.786044 | − | 0.618170i | \(-0.212126\pi\) | ||||
0.786044 | + | 0.618170i | \(0.212126\pi\) | |||||||
\(98\) | 1.75004 | 0.176781 | ||||||||
\(99\) | −2.98651 | −0.300155 | ||||||||
\(100\) | −4.75145 | −0.475145 | ||||||||
\(101\) | −0.380477 | −0.0378588 | −0.0189294 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189294 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(102\) | 0.192080 | 0.0190187 | ||||||||
\(103\) | −6.42485 | −0.633060 | −0.316530 | − | 0.948583i | \(-0.602518\pi\) | ||||
−0.316530 | + | 0.948583i | \(0.602518\pi\) | |||||||
\(104\) | −0.281152 | −0.0275693 | ||||||||
\(105\) | −0.132692 | −0.0129494 | ||||||||
\(106\) | −8.71898 | −0.846862 | ||||||||
\(107\) | −10.6754 | −1.03203 | −0.516014 | − | 0.856580i | \(-0.672585\pi\) | ||||
−0.516014 | + | 0.856580i | \(0.672585\pi\) | |||||||
\(108\) | 0.695394 | 0.0669143 | ||||||||
\(109\) | 6.06721 | 0.581133 | 0.290567 | − | 0.956855i | \(-0.406156\pi\) | ||||
0.290567 | + | 0.956855i | \(0.406156\pi\) | |||||||
\(110\) | 0.498551 | 0.0475350 | ||||||||
\(111\) | −0.683502 | −0.0648752 | ||||||||
\(112\) | −2.29128 | −0.216505 | ||||||||
\(113\) | 12.9988 | 1.22282 | 0.611411 | − | 0.791313i | \(-0.290602\pi\) | ||||
0.611411 | + | 0.791313i | \(0.290602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00983 | −0.373918 | ||||||||
\(116\) | −2.32572 | −0.215937 | ||||||||
\(117\) | −0.839664 | −0.0776269 | ||||||||
\(118\) | 2.84215 | 0.261641 | ||||||||
\(119\) | −3.78880 | −0.347319 | ||||||||
\(120\) | −0.0579118 | −0.00528660 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 12.4970 | 1.13143 | ||||||||
\(123\) | −0.0621659 | −0.00560531 | ||||||||
\(124\) | −3.69373 | −0.331707 | ||||||||
\(125\) | 4.86159 | 0.434834 | ||||||||
\(126\) | −6.84292 | −0.609616 | ||||||||
\(127\) | 17.5813 | 1.56009 | 0.780043 | − | 0.625726i | \(-0.215197\pi\) | ||||
0.780043 | + | 0.625726i | \(0.215197\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.595919 | 0.0524677 | ||||||||
\(130\) | 0.140169 | 0.0122936 | ||||||||
\(131\) | 5.13325 | 0.448494 | 0.224247 | − | 0.974532i | \(-0.428008\pi\) | ||||
0.224247 | + | 0.974532i | \(0.428008\pi\) | |||||||
\(132\) | −0.116160 | −0.0101104 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.7338 | 1.01365 | ||||||||
\(135\) | −0.346689 | −0.0298383 | ||||||||
\(136\) | −1.65358 | −0.141793 | ||||||||
\(137\) | 3.01949 | 0.257972 | 0.128986 | − | 0.991646i | \(-0.458828\pi\) | ||||
0.128986 | + | 0.991646i | \(0.458828\pi\) | |||||||
\(138\) | 0.934272 | 0.0795305 | ||||||||
\(139\) | −2.94278 | −0.249604 | −0.124802 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124802 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(140\) | 1.14232 | 0.0965436 | ||||||||
\(141\) | −1.23491 | −0.103998 | ||||||||
\(142\) | −5.50926 | −0.462327 | ||||||||
\(143\) | 0.281152 | 0.0235112 | ||||||||
\(144\) | −2.98651 | −0.248876 | ||||||||
\(145\) | 1.15949 | 0.0962903 | ||||||||
\(146\) | −2.38179 | −0.197119 | ||||||||
\(147\) | 0.203285 | 0.0167667 | ||||||||
\(148\) | 5.88414 | 0.483673 | ||||||||
\(149\) | 2.60187 | 0.213153 | 0.106577 | − | 0.994304i | \(-0.466011\pi\) | ||||
0.106577 | + | 0.994304i | \(0.466011\pi\) | |||||||
\(150\) | −0.551929 | −0.0450648 | ||||||||
\(151\) | 15.7549 | 1.28212 | 0.641059 | − | 0.767492i | \(-0.278495\pi\) | ||||
0.641059 | + | 0.767492i | \(0.278495\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.93842 | −0.399247 | ||||||||
\(154\) | 2.29128 | 0.184636 | ||||||||
\(155\) | 1.84151 | 0.147914 | ||||||||
\(156\) | −0.0326587 | −0.00261479 | ||||||||
\(157\) | 1.39782 | 0.111558 | 0.0557791 | − | 0.998443i | \(-0.482236\pi\) | ||||
0.0557791 | + | 0.998443i | \(0.482236\pi\) | |||||||
\(158\) | −14.1034 | −1.12201 | ||||||||
\(159\) | −1.01280 | −0.0803201 | ||||||||
\(160\) | 0.498551 | 0.0394139 | ||||||||
\(161\) | −18.4287 | −1.45238 | ||||||||
\(162\) | −8.87874 | −0.697580 | ||||||||
\(163\) | −16.7244 | −1.30995 | −0.654977 | − | 0.755649i | \(-0.727322\pi\) | ||||
−0.654977 | + | 0.755649i | \(0.727322\pi\) | |||||||
\(164\) | 0.535174 | 0.0417901 | ||||||||
\(165\) | 0.0579118 | 0.00450843 | ||||||||
\(166\) | 15.6876 | 1.21760 | ||||||||
\(167\) | −9.79562 | −0.758008 | −0.379004 | − | 0.925395i | \(-0.623733\pi\) | ||||
−0.379004 | + | 0.925395i | \(0.623733\pi\) | |||||||
\(168\) | −0.266155 | −0.0205343 | ||||||||
\(169\) | −12.9210 | −0.993919 | ||||||||
\(170\) | 0.824392 | 0.0632280 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.13015 | −0.391170 | ||||||||
\(173\) | 13.5070 | 1.02692 | 0.513460 | − | 0.858113i | \(-0.328363\pi\) | ||||
0.513460 | + | 0.858113i | \(0.328363\pi\) | |||||||
\(174\) | −0.270156 | −0.0204805 | ||||||||
\(175\) | 10.8869 | 0.822971 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0.330144 | 0.0248151 | ||||||||
\(178\) | −6.41709 | −0.480981 | ||||||||
\(179\) | −17.7695 | −1.32816 | −0.664079 | − | 0.747662i | \(-0.731176\pi\) | ||||
−0.664079 | + | 0.747662i | \(0.731176\pi\) | |||||||
\(180\) | 1.48893 | 0.110978 | ||||||||
\(181\) | −11.3679 | −0.844970 | −0.422485 | − | 0.906370i | \(-0.638842\pi\) | ||||
−0.422485 | + | 0.906370i | \(0.638842\pi\) | |||||||
\(182\) | 0.644199 | 0.0477512 | ||||||||
\(183\) | 1.45165 | 0.107309 | ||||||||
\(184\) | −8.04296 | −0.592935 | ||||||||
\(185\) | −2.93354 | −0.215678 | ||||||||
\(186\) | −0.429064 | −0.0314605 | ||||||||
\(187\) | 1.65358 | 0.120921 | ||||||||
\(188\) | 10.6311 | 0.775352 | ||||||||
\(189\) | −1.59334 | −0.115898 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.81314 | −0.637697 | −0.318848 | − | 0.947806i | \(-0.603296\pi\) | ||||
−0.318848 | + | 0.947806i | \(0.603296\pi\) | |||||||
\(192\) | −0.116160 | −0.00838314 | ||||||||
\(193\) | 1.62372 | 0.116878 | 0.0584388 | − | 0.998291i | \(-0.481388\pi\) | ||||
0.0584388 | + | 0.998291i | \(0.481388\pi\) | |||||||
\(194\) | −15.4833 | −1.11163 | ||||||||
\(195\) | 0.0162820 | 0.00116598 | ||||||||
\(196\) | −1.75004 | −0.125003 | ||||||||
\(197\) | −20.2131 | −1.44012 | −0.720062 | − | 0.693910i | \(-0.755887\pi\) | ||||
−0.720062 | + | 0.693910i | \(0.755887\pi\) | |||||||
\(198\) | 2.98651 | 0.212242 | ||||||||
\(199\) | −17.2777 | −1.22478 | −0.612392 | − | 0.790554i | \(-0.709793\pi\) | ||||
−0.612392 | + | 0.790554i | \(0.709793\pi\) | |||||||
\(200\) | 4.75145 | 0.335978 | ||||||||
\(201\) | 1.36300 | 0.0961387 | ||||||||
\(202\) | 0.380477 | 0.0267702 | ||||||||
\(203\) | 5.32887 | 0.374013 | ||||||||
\(204\) | −0.192080 | −0.0134483 | ||||||||
\(205\) | −0.266812 | −0.0186349 | ||||||||
\(206\) | 6.42485 | 0.447641 | ||||||||
\(207\) | −24.0204 | −1.66953 | ||||||||
\(208\) | 0.281152 | 0.0194944 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.132692 | 0.00915662 | ||||||||
\(211\) | 7.33059 | 0.504659 | 0.252329 | − | 0.967641i | \(-0.418803\pi\) | ||||
0.252329 | + | 0.967641i | \(0.418803\pi\) | |||||||
\(212\) | 8.71898 | 0.598822 | ||||||||
\(213\) | −0.639956 | −0.0438491 | ||||||||
\(214\) | 10.6754 | 0.729755 | ||||||||
\(215\) | 2.55764 | 0.174430 | ||||||||
\(216\) | −0.695394 | −0.0473155 | ||||||||
\(217\) | 8.46336 | 0.574530 | ||||||||
\(218\) | −6.06721 | −0.410923 | ||||||||
\(219\) | −0.276670 | −0.0186956 | ||||||||
\(220\) | −0.498551 | −0.0336123 | ||||||||
\(221\) | 0.464907 | 0.0312730 | ||||||||
\(222\) | 0.683502 | 0.0458737 | ||||||||
\(223\) | 4.52822 | 0.303232 | 0.151616 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151616 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(224\) | 2.29128 | 0.153092 | ||||||||
\(225\) | 14.1902 | 0.946015 | ||||||||
\(226\) | −12.9988 | −0.864666 | ||||||||
\(227\) | −23.3452 | −1.54947 | −0.774737 | − | 0.632283i | \(-0.782118\pi\) | ||||
−0.774737 | + | 0.632283i | \(0.782118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.7244 | −1.17126 | −0.585630 | − | 0.810579i | \(-0.699153\pi\) | ||||
−0.585630 | + | 0.810579i | \(0.699153\pi\) | |||||||
\(230\) | 4.00983 | 0.264400 | ||||||||
\(231\) | 0.266155 | 0.0175117 | ||||||||
\(232\) | 2.32572 | 0.152691 | ||||||||
\(233\) | −16.4045 | −1.07469 | −0.537347 | − | 0.843361i | \(-0.680573\pi\) | ||||
−0.537347 | + | 0.843361i | \(0.680573\pi\) | |||||||
\(234\) | 0.839664 | 0.0548905 | ||||||||
\(235\) | −5.30015 | −0.345743 | ||||||||
\(236\) | −2.84215 | −0.185008 | ||||||||
\(237\) | −1.63826 | −0.106416 | ||||||||
\(238\) | 3.78880 | 0.245592 | ||||||||
\(239\) | 18.2990 | 1.18367 | 0.591833 | − | 0.806060i | \(-0.298404\pi\) | ||||
0.591833 | + | 0.806060i | \(0.298404\pi\) | |||||||
\(240\) | 0.0579118 | 0.00373819 | ||||||||
\(241\) | 6.06680 | 0.390797 | 0.195399 | − | 0.980724i | \(-0.437400\pi\) | ||||
0.195399 | + | 0.980724i | \(0.437400\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −3.11754 | −0.199990 | ||||||||
\(244\) | −12.4970 | −0.800039 | ||||||||
\(245\) | 0.872486 | 0.0557411 | ||||||||
\(246\) | 0.0621659 | 0.00396355 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.69373 | 0.234552 | ||||||||
\(249\) | 1.82228 | 0.115482 | ||||||||
\(250\) | −4.86159 | −0.307474 | ||||||||
\(251\) | −17.0918 | −1.07882 | −0.539411 | − | 0.842043i | \(-0.681353\pi\) | ||||
−0.539411 | + | 0.842043i | \(0.681353\pi\) | |||||||
\(252\) | 6.84292 | 0.431063 | ||||||||
\(253\) | 8.04296 | 0.505657 | ||||||||
\(254\) | −17.5813 | −1.10315 | ||||||||
\(255\) | 0.0957615 | 0.00599682 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.9996 | −1.55943 | −0.779716 | − | 0.626133i | \(-0.784637\pi\) | ||||
−0.779716 | + | 0.626133i | \(0.784637\pi\) | |||||||
\(258\) | −0.595919 | −0.0371003 | ||||||||
\(259\) | −13.4822 | −0.837743 | ||||||||
\(260\) | −0.140169 | −0.00869291 | ||||||||
\(261\) | 6.94577 | 0.429932 | ||||||||
\(262\) | −5.13325 | −0.317133 | ||||||||
\(263\) | 4.06122 | 0.250425 | 0.125213 | − | 0.992130i | \(-0.460039\pi\) | ||||
0.125213 | + | 0.992130i | \(0.460039\pi\) | |||||||
\(264\) | 0.116160 | 0.00714916 | ||||||||
\(265\) | −4.34686 | −0.267025 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.745410 | −0.0456183 | ||||||||
\(268\) | −11.7338 | −0.716756 | ||||||||
\(269\) | 0.576207 | 0.0351320 | 0.0175660 | − | 0.999846i | \(-0.494408\pi\) | ||||
0.0175660 | + | 0.999846i | \(0.494408\pi\) | |||||||
\(270\) | 0.346689 | 0.0210988 | ||||||||
\(271\) | −26.7182 | −1.62301 | −0.811507 | − | 0.584343i | \(-0.801352\pi\) | ||||
−0.811507 | + | 0.584343i | \(0.801352\pi\) | |||||||
\(272\) | 1.65358 | 0.100263 | ||||||||
\(273\) | 0.0748302 | 0.00452893 | ||||||||
\(274\) | −3.01949 | −0.182414 | ||||||||
\(275\) | −4.75145 | −0.286523 | ||||||||
\(276\) | −0.934272 | −0.0562365 | ||||||||
\(277\) | −3.12741 | −0.187908 | −0.0939538 | − | 0.995577i | \(-0.529951\pi\) | ||||
−0.0939538 | + | 0.995577i | \(0.529951\pi\) | |||||||
\(278\) | 2.94278 | 0.176496 | ||||||||
\(279\) | 11.0313 | 0.660429 | ||||||||
\(280\) | −1.14232 | −0.0682666 | ||||||||
\(281\) | −24.8620 | −1.48314 | −0.741572 | − | 0.670874i | \(-0.765919\pi\) | ||||
−0.741572 | + | 0.670874i | \(0.765919\pi\) | |||||||
\(282\) | 1.23491 | 0.0735378 | ||||||||
\(283\) | −1.16115 | −0.0690235 | −0.0345117 | − | 0.999404i | \(-0.510988\pi\) | ||||
−0.0345117 | + | 0.999404i | \(0.510988\pi\) | |||||||
\(284\) | 5.50926 | 0.326914 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.281152 | −0.0166249 | ||||||||
\(287\) | −1.22623 | −0.0723822 | ||||||||
\(288\) | 2.98651 | 0.175982 | ||||||||
\(289\) | −14.2657 | −0.839158 | ||||||||
\(290\) | −1.15949 | −0.0680875 | ||||||||
\(291\) | −1.79854 | −0.105432 | ||||||||
\(292\) | 2.38179 | 0.139384 | ||||||||
\(293\) | −26.8022 | −1.56580 | −0.782901 | − | 0.622146i | \(-0.786261\pi\) | ||||
−0.782901 | + | 0.622146i | \(0.786261\pi\) | |||||||
\(294\) | −0.203285 | −0.0118558 | ||||||||
\(295\) | 1.41695 | 0.0824983 | ||||||||
\(296\) | −5.88414 | −0.342009 | ||||||||
\(297\) | 0.695394 | 0.0403508 | ||||||||
\(298\) | −2.60187 | −0.150722 | ||||||||
\(299\) | 2.26130 | 0.130774 | ||||||||
\(300\) | 0.551929 | 0.0318656 | ||||||||
\(301\) | 11.7546 | 0.677524 | ||||||||
\(302\) | −15.7549 | −0.906594 | ||||||||
\(303\) | 0.0441962 | 0.00253901 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.23040 | 0.356751 | ||||||||
\(306\) | 4.93842 | 0.282310 | ||||||||
\(307\) | 30.4852 | 1.73988 | 0.869941 | − | 0.493155i | \(-0.164157\pi\) | ||||
0.869941 | + | 0.493155i | \(0.164157\pi\) | |||||||
\(308\) | −2.29128 | −0.130558 | ||||||||
\(309\) | 0.746312 | 0.0424562 | ||||||||
\(310\) | −1.84151 | −0.104591 | ||||||||
\(311\) | −11.0434 | −0.626214 | −0.313107 | − | 0.949718i | \(-0.601370\pi\) | ||||
−0.313107 | + | 0.949718i | \(0.601370\pi\) | |||||||
\(312\) | 0.0326587 | 0.00184894 | ||||||||
\(313\) | 10.4897 | 0.592914 | 0.296457 | − | 0.955046i | \(-0.404195\pi\) | ||||
0.296457 | + | 0.955046i | \(0.404195\pi\) | |||||||
\(314\) | −1.39782 | −0.0788836 | ||||||||
\(315\) | −3.41154 | −0.192219 | ||||||||
\(316\) | 14.1034 | 0.793379 | ||||||||
\(317\) | −10.5366 | −0.591795 | −0.295897 | − | 0.955220i | \(-0.595619\pi\) | ||||
−0.295897 | + | 0.955220i | \(0.595619\pi\) | |||||||
\(318\) | 1.01280 | 0.0567949 | ||||||||
\(319\) | −2.32572 | −0.130215 | ||||||||
\(320\) | −0.498551 | −0.0278699 | ||||||||
\(321\) | 1.24006 | 0.0692131 | ||||||||
\(322\) | 18.4287 | 1.02699 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.87874 | 0.493264 | ||||||||
\(325\) | −1.33588 | −0.0741013 | ||||||||
\(326\) | 16.7244 | 0.926277 | ||||||||
\(327\) | −0.704768 | −0.0389738 | ||||||||
\(328\) | −0.535174 | −0.0295500 | ||||||||
\(329\) | −24.3588 | −1.34294 | ||||||||
\(330\) | −0.0579118 | −0.00318794 | ||||||||
\(331\) | 6.07028 | 0.333653 | 0.166826 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166826 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(332\) | −15.6876 | −0.860971 | ||||||||
\(333\) | −17.5730 | −0.962996 | ||||||||
\(334\) | 9.79562 | 0.535992 | ||||||||
\(335\) | 5.84990 | 0.319614 | ||||||||
\(336\) | 0.266155 | 0.0145200 | ||||||||
\(337\) | −6.48458 | −0.353238 | −0.176619 | − | 0.984279i | \(-0.556516\pi\) | ||||
−0.176619 | + | 0.984279i | \(0.556516\pi\) | |||||||
\(338\) | 12.9210 | 0.702807 | ||||||||
\(339\) | −1.50994 | −0.0820087 | ||||||||
\(340\) | −0.824392 | −0.0447089 | ||||||||
\(341\) | −3.69373 | −0.200027 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0488 | 1.08253 | ||||||||
\(344\) | 5.13015 | 0.276599 | ||||||||
\(345\) | 0.465782 | 0.0250769 | ||||||||
\(346\) | −13.5070 | −0.726142 | ||||||||
\(347\) | 19.2179 | 1.03167 | 0.515837 | − | 0.856687i | \(-0.327481\pi\) | ||||
0.515837 | + | 0.856687i | \(0.327481\pi\) | |||||||
\(348\) | 0.270156 | 0.0144819 | ||||||||
\(349\) | 29.2730 | 1.56695 | 0.783474 | − | 0.621425i | \(-0.213446\pi\) | ||||
0.783474 | + | 0.621425i | \(0.213446\pi\) | |||||||
\(350\) | −10.8869 | −0.581929 | ||||||||
\(351\) | 0.195512 | 0.0104356 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −4.70031 | −0.250172 | −0.125086 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125086 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(354\) | −0.330144 | −0.0175470 | ||||||||
\(355\) | −2.74665 | −0.145777 | ||||||||
\(356\) | 6.41709 | 0.340105 | ||||||||
\(357\) | 0.440108 | 0.0232930 | ||||||||
\(358\) | 17.7695 | 0.939149 | ||||||||
\(359\) | −28.4846 | −1.50336 | −0.751680 | − | 0.659529i | \(-0.770756\pi\) | ||||
−0.751680 | + | 0.659529i | \(0.770756\pi\) | |||||||
\(360\) | −1.48893 | −0.0784733 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 11.3679 | 0.597484 | ||||||||
\(363\) | −0.116160 | −0.00609683 | ||||||||
\(364\) | −0.644199 | −0.0337652 | ||||||||
\(365\) | −1.18745 | −0.0621538 | ||||||||
\(366\) | −1.45165 | −0.0758792 | ||||||||
\(367\) | 1.29074 | 0.0673763 | 0.0336881 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336881 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(368\) | 8.04296 | 0.419268 | ||||||||
\(369\) | −1.59830 | −0.0832042 | ||||||||
\(370\) | 2.93354 | 0.152508 | ||||||||
\(371\) | −19.9776 | −1.03719 | ||||||||
\(372\) | 0.429064 | 0.0222459 | ||||||||
\(373\) | −8.35563 | −0.432638 | −0.216319 | − | 0.976323i | \(-0.569405\pi\) | ||||
−0.216319 | + | 0.976323i | \(0.569405\pi\) | |||||||
\(374\) | −1.65358 | −0.0855044 | ||||||||
\(375\) | −0.564724 | −0.0291622 | ||||||||
\(376\) | −10.6311 | −0.548257 | ||||||||
\(377\) | −0.653881 | −0.0336766 | ||||||||
\(378\) | 1.59334 | 0.0819526 | ||||||||
\(379\) | 11.2112 | 0.575879 | 0.287940 | − | 0.957649i | \(-0.407030\pi\) | ||||
0.287940 | + | 0.957649i | \(0.407030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.04224 | −0.104627 | ||||||||
\(382\) | 8.81314 | 0.450920 | ||||||||
\(383\) | 23.5595 | 1.20383 | 0.601917 | − | 0.798559i | \(-0.294404\pi\) | ||||
0.601917 | + | 0.798559i | \(0.294404\pi\) | |||||||
\(384\) | 0.116160 | 0.00592777 | ||||||||
\(385\) | 1.14232 | 0.0582180 | ||||||||
\(386\) | −1.62372 | −0.0826450 | ||||||||
\(387\) | 15.3212 | 0.778821 | ||||||||
\(388\) | 15.4833 | 0.786044 | ||||||||
\(389\) | 32.3109 | 1.63823 | 0.819113 | − | 0.573632i | \(-0.194466\pi\) | ||||
0.819113 | + | 0.573632i | \(0.194466\pi\) | |||||||
\(390\) | −0.0162820 | −0.000824473 0 | ||||||||
\(391\) | 13.2996 | 0.672592 | ||||||||
\(392\) | 1.75004 | 0.0883905 | ||||||||
\(393\) | −0.596279 | −0.0300783 | ||||||||
\(394\) | 20.2131 | 1.01832 | ||||||||
\(395\) | −7.03128 | −0.353782 | ||||||||
\(396\) | −2.98651 | −0.150078 | ||||||||
\(397\) | −21.6587 | −1.08702 | −0.543511 | − | 0.839402i | \(-0.682905\pi\) | ||||
−0.543511 | + | 0.839402i | \(0.682905\pi\) | |||||||
\(398\) | 17.2777 | 0.866053 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.75145 | −0.237572 | ||||||||
\(401\) | 15.2032 | 0.759210 | 0.379605 | − | 0.925149i | \(-0.376060\pi\) | ||||
0.379605 | + | 0.925149i | \(0.376060\pi\) | |||||||
\(402\) | −1.36300 | −0.0679803 | ||||||||
\(403\) | −1.03850 | −0.0517314 | ||||||||
\(404\) | −0.380477 | −0.0189294 | ||||||||
\(405\) | −4.42651 | −0.219955 | ||||||||
\(406\) | −5.32887 | −0.264467 | ||||||||
\(407\) | 5.88414 | 0.291666 | ||||||||
\(408\) | 0.192080 | 0.00950936 | ||||||||
\(409\) | −35.8741 | −1.77386 | −0.886931 | − | 0.461902i | \(-0.847167\pi\) | ||||
−0.886931 | + | 0.461902i | \(0.847167\pi\) | |||||||
\(410\) | 0.266812 | 0.0131769 | ||||||||
\(411\) | −0.350744 | −0.0173009 | ||||||||
\(412\) | −6.42485 | −0.316530 | ||||||||
\(413\) | 6.51215 | 0.320442 | ||||||||
\(414\) | 24.0204 | 1.18054 | ||||||||
\(415\) | 7.82109 | 0.383922 | ||||||||
\(416\) | −0.281152 | −0.0137846 | ||||||||
\(417\) | 0.341834 | 0.0167397 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.02288 | 0.245384 | 0.122692 | − | 0.992445i | \(-0.460847\pi\) | ||||
0.122692 | + | 0.992445i | \(0.460847\pi\) | |||||||
\(420\) | −0.132692 | −0.00647471 | ||||||||
\(421\) | 5.74864 | 0.280172 | 0.140086 | − | 0.990139i | \(-0.455262\pi\) | ||||
0.140086 | + | 0.990139i | \(0.455262\pi\) | |||||||
\(422\) | −7.33059 | −0.356848 | ||||||||
\(423\) | −31.7498 | −1.54373 | ||||||||
\(424\) | −8.71898 | −0.423431 | ||||||||
\(425\) | −7.85688 | −0.381115 | ||||||||
\(426\) | 0.639956 | 0.0310060 | ||||||||
\(427\) | 28.6341 | 1.38570 | ||||||||
\(428\) | −10.6754 | −0.516014 | ||||||||
\(429\) | −0.0326587 | −0.00157678 | ||||||||
\(430\) | −2.55764 | −0.123340 | ||||||||
\(431\) | −25.8934 | −1.24724 | −0.623622 | − | 0.781726i | \(-0.714339\pi\) | ||||
−0.623622 | + | 0.781726i | \(0.714339\pi\) | |||||||
\(432\) | 0.695394 | 0.0334571 | ||||||||
\(433\) | 9.54377 | 0.458644 | 0.229322 | − | 0.973351i | \(-0.426349\pi\) | ||||
0.229322 | + | 0.973351i | \(0.426349\pi\) | |||||||
\(434\) | −8.46336 | −0.406254 | ||||||||
\(435\) | −0.134686 | −0.00645772 | ||||||||
\(436\) | 6.06721 | 0.290567 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.276670 | 0.0132198 | ||||||||
\(439\) | 0.635179 | 0.0303154 | 0.0151577 | − | 0.999885i | \(-0.495175\pi\) | ||||
0.0151577 | + | 0.999885i | \(0.495175\pi\) | |||||||
\(440\) | 0.498551 | 0.0237675 | ||||||||
\(441\) | 5.22652 | 0.248882 | ||||||||
\(442\) | −0.464907 | −0.0221134 | ||||||||
\(443\) | 17.6440 | 0.838290 | 0.419145 | − | 0.907919i | \(-0.362330\pi\) | ||||
0.419145 | + | 0.907919i | \(0.362330\pi\) | |||||||
\(444\) | −0.683502 | −0.0324376 | ||||||||
\(445\) | −3.19925 | −0.151659 | ||||||||
\(446\) | −4.52822 | −0.214418 | ||||||||
\(447\) | −0.302233 | −0.0142951 | ||||||||
\(448\) | −2.29128 | −0.108253 | ||||||||
\(449\) | −20.9736 | −0.989808 | −0.494904 | − | 0.868948i | \(-0.664797\pi\) | ||||
−0.494904 | + | 0.868948i | \(0.664797\pi\) | |||||||
\(450\) | −14.1902 | −0.668934 | ||||||||
\(451\) | 0.535174 | 0.0252004 | ||||||||
\(452\) | 12.9988 | 0.611411 | ||||||||
\(453\) | −1.83010 | −0.0859854 | ||||||||
\(454\) | 23.3452 | 1.09564 | ||||||||
\(455\) | 0.321166 | 0.0150565 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9647 | −1.07424 | −0.537121 | − | 0.843505i | \(-0.680488\pi\) | ||||
−0.537121 | + | 0.843505i | \(0.680488\pi\) | |||||||
\(458\) | 17.7244 | 0.828206 | ||||||||
\(459\) | 1.14989 | 0.0536721 | ||||||||
\(460\) | −4.00983 | −0.186959 | ||||||||
\(461\) | −25.6578 | −1.19500 | −0.597502 | − | 0.801867i | \(-0.703840\pi\) | ||||
−0.597502 | + | 0.801867i | \(0.703840\pi\) | |||||||
\(462\) | −0.266155 | −0.0123827 | ||||||||
\(463\) | 14.4251 | 0.670393 | 0.335197 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335197 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(464\) | −2.32572 | −0.107969 | ||||||||
\(465\) | −0.213910 | −0.00991986 | ||||||||
\(466\) | 16.4045 | 0.759923 | ||||||||
\(467\) | −6.26939 | −0.290113 | −0.145056 | − | 0.989423i | \(-0.546336\pi\) | ||||
−0.145056 | + | 0.989423i | \(0.546336\pi\) | |||||||
\(468\) | −0.839664 | −0.0388135 | ||||||||
\(469\) | 26.8854 | 1.24145 | ||||||||
\(470\) | 5.30015 | 0.244477 | ||||||||
\(471\) | −0.162371 | −0.00748167 | ||||||||
\(472\) | 2.84215 | 0.130820 | ||||||||
\(473\) | −5.13015 | −0.235884 | ||||||||
\(474\) | 1.63826 | 0.0752476 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.78880 | −0.173659 | ||||||||
\(477\) | −26.0393 | −1.19226 | ||||||||
\(478\) | −18.2990 | −0.836979 | ||||||||
\(479\) | 9.22842 | 0.421657 | 0.210829 | − | 0.977523i | \(-0.432384\pi\) | ||||
0.210829 | + | 0.977523i | \(0.432384\pi\) | |||||||
\(480\) | −0.0579118 | −0.00264330 | ||||||||
\(481\) | 1.65434 | 0.0754314 | ||||||||
\(482\) | −6.06680 | −0.276335 | ||||||||
\(483\) | 2.14068 | 0.0974041 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.71920 | −0.350511 | ||||||||
\(486\) | 3.11754 | 0.141414 | ||||||||
\(487\) | −34.5755 | −1.56676 | −0.783382 | − | 0.621541i | \(-0.786507\pi\) | ||||
−0.783382 | + | 0.621541i | \(0.786507\pi\) | |||||||
\(488\) | 12.4970 | 0.565713 | ||||||||
\(489\) | 1.94270 | 0.0878521 | ||||||||
\(490\) | −0.872486 | −0.0394149 | ||||||||
\(491\) | −19.5615 | −0.882800 | −0.441400 | − | 0.897311i | \(-0.645518\pi\) | ||||
−0.441400 | + | 0.897311i | \(0.645518\pi\) | |||||||
\(492\) | −0.0621659 | −0.00280266 | ||||||||
\(493\) | −3.84575 | −0.173204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.48893 | 0.0669223 | ||||||||
\(496\) | −3.69373 | −0.165853 | ||||||||
\(497\) | −12.6232 | −0.566230 | ||||||||
\(498\) | −1.82228 | −0.0816583 | ||||||||
\(499\) | 7.82554 | 0.350319 | 0.175160 | − | 0.984540i | \(-0.443956\pi\) | ||||
0.175160 | + | 0.984540i | \(0.443956\pi\) | |||||||
\(500\) | 4.86159 | 0.217417 | ||||||||
\(501\) | 1.13786 | 0.0508359 | ||||||||
\(502\) | 17.0918 | 0.762842 | ||||||||
\(503\) | −11.2496 | −0.501595 | −0.250798 | − | 0.968040i | \(-0.580693\pi\) | ||||
−0.250798 | + | 0.968040i | \(0.580693\pi\) | |||||||
\(504\) | −6.84292 | −0.304808 | ||||||||
\(505\) | 0.189687 | 0.00844096 | ||||||||
\(506\) | −8.04296 | −0.357553 | ||||||||
\(507\) | 1.50090 | 0.0666573 | ||||||||
\(508\) | 17.5813 | 0.780043 | ||||||||
\(509\) | 15.2535 | 0.676101 | 0.338051 | − | 0.941128i | \(-0.390233\pi\) | ||||
0.338051 | + | 0.941128i | \(0.390233\pi\) | |||||||
\(510\) | −0.0957615 | −0.00424039 | ||||||||
\(511\) | −5.45735 | −0.241419 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.9996 | 1.10269 | ||||||||
\(515\) | 3.20312 | 0.141146 | ||||||||
\(516\) | 0.595919 | 0.0262339 | ||||||||
\(517\) | 10.6311 | 0.467555 | ||||||||
\(518\) | 13.4822 | 0.592374 | ||||||||
\(519\) | −1.56898 | −0.0688705 | ||||||||
\(520\) | 0.140169 | 0.00614681 | ||||||||
\(521\) | −11.6055 | −0.508446 | −0.254223 | − | 0.967146i | \(-0.581820\pi\) | ||||
−0.254223 | + | 0.967146i | \(0.581820\pi\) | |||||||
\(522\) | −6.94577 | −0.304008 | ||||||||
\(523\) | −22.2527 | −0.973043 | −0.486521 | − | 0.873669i | \(-0.661734\pi\) | ||||
−0.486521 | + | 0.873669i | \(0.661734\pi\) | |||||||
\(524\) | 5.13325 | 0.224247 | ||||||||
\(525\) | −1.26462 | −0.0551927 | ||||||||
\(526\) | −4.06122 | −0.177077 | ||||||||
\(527\) | −6.10786 | −0.266063 | ||||||||
\(528\) | −0.116160 | −0.00505522 | ||||||||
\(529\) | 41.6892 | 1.81257 | ||||||||
\(530\) | 4.34686 | 0.188815 | ||||||||
\(531\) | 8.48809 | 0.368352 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.150466 | 0.00651739 | ||||||||
\(534\) | 0.745410 | 0.0322570 | ||||||||
\(535\) | 5.32223 | 0.230100 | ||||||||
\(536\) | 11.7338 | 0.506823 | ||||||||
\(537\) | 2.06411 | 0.0890730 | ||||||||
\(538\) | −0.576207 | −0.0248421 | ||||||||
\(539\) | −1.75004 | −0.0753797 | ||||||||
\(540\) | −0.346689 | −0.0149191 | ||||||||
\(541\) | −19.8053 | −0.851495 | −0.425747 | − | 0.904842i | \(-0.639989\pi\) | ||||
−0.425747 | + | 0.904842i | \(0.639989\pi\) | |||||||
\(542\) | 26.7182 | 1.14764 | ||||||||
\(543\) | 1.32050 | 0.0566680 | ||||||||
\(544\) | −1.65358 | −0.0708965 | ||||||||
\(545\) | −3.02482 | −0.129569 | ||||||||
\(546\) | −0.0748302 | −0.00320244 | ||||||||
\(547\) | −6.19583 | −0.264914 | −0.132457 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132457 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(548\) | 3.01949 | 0.128986 | ||||||||
\(549\) | 37.3224 | 1.59288 | ||||||||
\(550\) | 4.75145 | 0.202602 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.934272 | 0.0397652 | ||||||||
\(553\) | −32.3149 | −1.37417 | ||||||||
\(554\) | 3.12741 | 0.132871 | ||||||||
\(555\) | 0.340761 | 0.0144645 | ||||||||
\(556\) | −2.94278 | −0.124802 | ||||||||
\(557\) | −10.4271 | −0.441810 | −0.220905 | − | 0.975295i | \(-0.570901\pi\) | ||||
−0.220905 | + | 0.975295i | \(0.570901\pi\) | |||||||
\(558\) | −11.0313 | −0.466994 | ||||||||
\(559\) | −1.44235 | −0.0610051 | ||||||||
\(560\) | 1.14232 | 0.0482718 | ||||||||
\(561\) | −0.192080 | −0.00810961 | ||||||||
\(562\) | 24.8620 | 1.04874 | ||||||||
\(563\) | −4.62498 | −0.194920 | −0.0974598 | − | 0.995239i | \(-0.531072\pi\) | ||||
−0.0974598 | + | 0.995239i | \(0.531072\pi\) | |||||||
\(564\) | −1.23491 | −0.0519991 | ||||||||
\(565\) | −6.48055 | −0.272639 | ||||||||
\(566\) | 1.16115 | 0.0488070 | ||||||||
\(567\) | −20.3437 | −0.854354 | ||||||||
\(568\) | −5.50926 | −0.231163 | ||||||||
\(569\) | −6.32419 | −0.265124 | −0.132562 | − | 0.991175i | \(-0.542320\pi\) | ||||
−0.132562 | + | 0.991175i | \(0.542320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.48702 | 0.0622299 | 0.0311150 | − | 0.999516i | \(-0.490094\pi\) | ||||
0.0311150 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(572\) | 0.281152 | 0.0117556 | ||||||||
\(573\) | 1.02374 | 0.0427672 | ||||||||
\(574\) | 1.22623 | 0.0511820 | ||||||||
\(575\) | −38.2157 | −1.59370 | ||||||||
\(576\) | −2.98651 | −0.124438 | ||||||||
\(577\) | −39.2241 | −1.63292 | −0.816461 | − | 0.577401i | \(-0.804067\pi\) | ||||
−0.816461 | + | 0.577401i | \(0.804067\pi\) | |||||||
\(578\) | 14.2657 | 0.593374 | ||||||||
\(579\) | −0.188611 | −0.00783841 | ||||||||
\(580\) | 1.15949 | 0.0481452 | ||||||||
\(581\) | 35.9448 | 1.49124 | ||||||||
\(582\) | 1.79854 | 0.0745519 | ||||||||
\(583\) | 8.71898 | 0.361103 | ||||||||
\(584\) | −2.38179 | −0.0985594 | ||||||||
\(585\) | 0.418615 | 0.0173076 | ||||||||
\(586\) | 26.8022 | 1.10719 | ||||||||
\(587\) | −30.0482 | −1.24022 | −0.620112 | − | 0.784513i | \(-0.712913\pi\) | ||||
−0.620112 | + | 0.784513i | \(0.712913\pi\) | |||||||
\(588\) | 0.203285 | 0.00838334 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.41695 | −0.0583351 | ||||||||
\(591\) | 2.34796 | 0.0965821 | ||||||||
\(592\) | 5.88414 | 0.241837 | ||||||||
\(593\) | −31.2053 | −1.28145 | −0.640723 | − | 0.767772i | \(-0.721365\pi\) | ||||
−0.640723 | + | 0.767772i | \(0.721365\pi\) | |||||||
\(594\) | −0.695394 | −0.0285323 | ||||||||
\(595\) | 1.88891 | 0.0774378 | ||||||||
\(596\) | 2.60187 | 0.106577 | ||||||||
\(597\) | 2.00698 | 0.0821402 | ||||||||
\(598\) | −2.26130 | −0.0924714 | ||||||||
\(599\) | 28.7348 | 1.17407 | 0.587037 | − | 0.809560i | \(-0.300294\pi\) | ||||
0.587037 | + | 0.809560i | \(0.300294\pi\) | |||||||
\(600\) | −0.551929 | −0.0225324 | ||||||||
\(601\) | 14.2810 | 0.582535 | 0.291267 | − | 0.956642i | \(-0.405923\pi\) | ||||
0.291267 | + | 0.956642i | \(0.405923\pi\) | |||||||
\(602\) | −11.7546 | −0.479082 | ||||||||
\(603\) | 35.0431 | 1.42707 | ||||||||
\(604\) | 15.7549 | 0.641059 | ||||||||
\(605\) | −0.498551 | −0.0202690 | ||||||||
\(606\) | −0.0441962 | −0.00179535 | ||||||||
\(607\) | −10.4197 | −0.422924 | −0.211462 | − | 0.977386i | \(-0.567822\pi\) | ||||
−0.211462 | + | 0.977386i | \(0.567822\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.619002 | −0.0250832 | ||||||||
\(610\) | −6.23040 | −0.252261 | ||||||||
\(611\) | 2.98896 | 0.120920 | ||||||||
\(612\) | −4.93842 | −0.199624 | ||||||||
\(613\) | −24.6139 | −0.994146 | −0.497073 | − | 0.867709i | \(-0.665592\pi\) | ||||
−0.497073 | + | 0.867709i | \(0.665592\pi\) | |||||||
\(614\) | −30.4852 | −1.23028 | ||||||||
\(615\) | 0.0309929 | 0.00124975 | ||||||||
\(616\) | 2.29128 | 0.0923182 | ||||||||
\(617\) | 32.5839 | 1.31178 | 0.655888 | − | 0.754858i | \(-0.272294\pi\) | ||||
0.655888 | + | 0.754858i | \(0.272294\pi\) | |||||||
\(618\) | −0.746312 | −0.0300211 | ||||||||
\(619\) | −13.0992 | −0.526503 | −0.263252 | − | 0.964727i | \(-0.584795\pi\) | ||||
−0.263252 | + | 0.964727i | \(0.584795\pi\) | |||||||
\(620\) | 1.84151 | 0.0739569 | ||||||||
\(621\) | 5.59302 | 0.224440 | ||||||||
\(622\) | 11.0434 | 0.442800 | ||||||||
\(623\) | −14.7033 | −0.589077 | ||||||||
\(624\) | −0.0326587 | −0.00130739 | ||||||||
\(625\) | 21.3335 | 0.853339 | ||||||||
\(626\) | −10.4897 | −0.419254 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.39782 | 0.0557791 | ||||||||
\(629\) | 9.72987 | 0.387955 | ||||||||
\(630\) | 3.41154 | 0.135919 | ||||||||
\(631\) | 15.0145 | 0.597719 | 0.298860 | − | 0.954297i | \(-0.403394\pi\) | ||||
0.298860 | + | 0.954297i | \(0.403394\pi\) | |||||||
\(632\) | −14.1034 | −0.561004 | ||||||||
\(633\) | −0.851523 | −0.0338450 | ||||||||
\(634\) | 10.5366 | 0.418462 | ||||||||
\(635\) | −8.76516 | −0.347835 | ||||||||
\(636\) | −1.01280 | −0.0401601 | ||||||||
\(637\) | −0.492029 | −0.0194949 | ||||||||
\(638\) | 2.32572 | 0.0920760 | ||||||||
\(639\) | −16.4534 | −0.650888 | ||||||||
\(640\) | 0.498551 | 0.0197070 | ||||||||
\(641\) | −10.5045 | −0.414903 | −0.207452 | − | 0.978245i | \(-0.566517\pi\) | ||||
−0.207452 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(642\) | −1.24006 | −0.0489411 | ||||||||
\(643\) | 42.9906 | 1.69538 | 0.847691 | − | 0.530490i | \(-0.177992\pi\) | ||||
0.847691 | + | 0.530490i | \(0.177992\pi\) | |||||||
\(644\) | −18.4287 | −0.726191 | ||||||||
\(645\) | −0.297096 | −0.0116981 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.291739 | −0.0114694 | −0.00573472 | − | 0.999984i | \(-0.501825\pi\) | ||||
−0.00573472 | + | 0.999984i | \(0.501825\pi\) | |||||||
\(648\) | −8.87874 | −0.348790 | ||||||||
\(649\) | −2.84215 | −0.111564 | ||||||||
\(650\) | 1.33588 | 0.0523976 | ||||||||
\(651\) | −0.983105 | −0.0385309 | ||||||||
\(652\) | −16.7244 | −0.654977 | ||||||||
\(653\) | −16.7418 | −0.655158 | −0.327579 | − | 0.944824i | \(-0.606233\pi\) | ||||
−0.327579 | + | 0.944824i | \(0.606233\pi\) | |||||||
\(654\) | 0.704768 | 0.0275586 | ||||||||
\(655\) | −2.55919 | −0.0999957 | ||||||||
\(656\) | 0.535174 | 0.0208950 | ||||||||
\(657\) | −7.11325 | −0.277514 | ||||||||
\(658\) | 24.3588 | 0.949605 | ||||||||
\(659\) | −23.3216 | −0.908480 | −0.454240 | − | 0.890879i | \(-0.650089\pi\) | ||||
−0.454240 | + | 0.890879i | \(0.650089\pi\) | |||||||
\(660\) | 0.0579118 | 0.00225421 | ||||||||
\(661\) | −41.7610 | −1.62431 | −0.812157 | − | 0.583438i | \(-0.801707\pi\) | ||||
−0.812157 | + | 0.583438i | \(0.801707\pi\) | |||||||
\(662\) | −6.07028 | −0.235928 | ||||||||
\(663\) | −0.0540037 | −0.00209733 | ||||||||
\(664\) | 15.6876 | 0.608799 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.5730 | 0.680941 | ||||||||
\(667\) | −18.7057 | −0.724286 | ||||||||
\(668\) | −9.79562 | −0.379004 | ||||||||
\(669\) | −0.525999 | −0.0203363 | ||||||||
\(670\) | −5.84990 | −0.226001 | ||||||||
\(671\) | −12.4970 | −0.482441 | ||||||||
\(672\) | −0.266155 | −0.0102672 | ||||||||
\(673\) | −14.5308 | −0.560121 | −0.280060 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280060 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(674\) | 6.48458 | 0.249777 | ||||||||
\(675\) | −3.30413 | −0.127176 | ||||||||
\(676\) | −12.9210 | −0.496960 | ||||||||
\(677\) | −10.5860 | −0.406853 | −0.203426 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203426 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(678\) | 1.50994 | 0.0579889 | ||||||||
\(679\) | −35.4765 | −1.36146 | ||||||||
\(680\) | 0.824392 | 0.0316140 | ||||||||
\(681\) | 2.71178 | 0.103916 | ||||||||
\(682\) | 3.69373 | 0.141440 | ||||||||
\(683\) | 19.6157 | 0.750575 | 0.375288 | − | 0.926908i | \(-0.377544\pi\) | ||||
0.375288 | + | 0.926908i | \(0.377544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.50537 | −0.0575172 | ||||||||
\(686\) | −20.0488 | −0.765466 | ||||||||
\(687\) | 2.05887 | 0.0785506 | ||||||||
\(688\) | −5.13015 | −0.195585 | ||||||||
\(689\) | 2.45136 | 0.0933895 | ||||||||
\(690\) | −0.465782 | −0.0177320 | ||||||||
\(691\) | 12.8441 | 0.488613 | 0.244307 | − | 0.969698i | \(-0.421440\pi\) | ||||
0.244307 | + | 0.969698i | \(0.421440\pi\) | |||||||
\(692\) | 13.5070 | 0.513460 | ||||||||
\(693\) | 6.84292 | 0.259941 | ||||||||
\(694\) | −19.2179 | −0.729503 | ||||||||
\(695\) | 1.46713 | 0.0556513 | ||||||||
\(696\) | −0.270156 | −0.0102402 | ||||||||
\(697\) | 0.884951 | 0.0335199 | ||||||||
\(698\) | −29.2730 | −1.10800 | ||||||||
\(699\) | 1.90555 | 0.0720744 | ||||||||
\(700\) | 10.8869 | 0.411486 | ||||||||
\(701\) | 27.9107 | 1.05417 | 0.527087 | − | 0.849811i | \(-0.323284\pi\) | ||||
0.527087 | + | 0.849811i | \(0.323284\pi\) | |||||||
\(702\) | −0.195512 | −0.00737911 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0.615666 | 0.0231873 | ||||||||
\(706\) | 4.70031 | 0.176898 | ||||||||
\(707\) | 0.871778 | 0.0327866 | ||||||||
\(708\) | 0.330144 | 0.0124076 | ||||||||
\(709\) | 37.0592 | 1.39179 | 0.695894 | − | 0.718145i | \(-0.255008\pi\) | ||||
0.695894 | + | 0.718145i | \(0.255008\pi\) | |||||||
\(710\) | 2.74665 | 0.103080 | ||||||||
\(711\) | −42.1200 | −1.57962 | ||||||||
\(712\) | −6.41709 | −0.240491 | ||||||||
\(713\) | −29.7085 | −1.11259 | ||||||||
\(714\) | −0.440108 | −0.0164706 | ||||||||
\(715\) | −0.140169 | −0.00524202 | ||||||||
\(716\) | −17.7695 | −0.664079 | ||||||||
\(717\) | −2.12562 | −0.0793827 | ||||||||
\(718\) | 28.4846 | 1.06304 | ||||||||
\(719\) | 34.5573 | 1.28877 | 0.644385 | − | 0.764701i | \(-0.277113\pi\) | ||||
0.644385 | + | 0.764701i | \(0.277113\pi\) | |||||||
\(720\) | 1.48893 | 0.0554890 | ||||||||
\(721\) | 14.7211 | 0.548243 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.704721 | −0.0262089 | ||||||||
\(724\) | −11.3679 | −0.422485 | ||||||||
\(725\) | 11.0505 | 0.410406 | ||||||||
\(726\) | 0.116160 | 0.00431111 | ||||||||
\(727\) | −12.5155 | −0.464174 | −0.232087 | − | 0.972695i | \(-0.574555\pi\) | ||||
−0.232087 | + | 0.972695i | \(0.574555\pi\) | |||||||
\(728\) | 0.644199 | 0.0238756 | ||||||||
\(729\) | −26.2741 | −0.973115 | ||||||||
\(730\) | 1.18745 | 0.0439494 | ||||||||
\(731\) | −8.48309 | −0.313758 | ||||||||
\(732\) | 1.45165 | 0.0536547 | ||||||||
\(733\) | 14.8661 | 0.549091 | 0.274546 | − | 0.961574i | \(-0.411473\pi\) | ||||
0.274546 | + | 0.961574i | \(0.411473\pi\) | |||||||
\(734\) | −1.29074 | −0.0476422 | ||||||||
\(735\) | −0.101348 | −0.00373828 | ||||||||
\(736\) | −8.04296 | −0.296467 | ||||||||
\(737\) | −11.7338 | −0.432220 | ||||||||
\(738\) | 1.59830 | 0.0588343 | ||||||||
\(739\) | −9.81013 | −0.360871 | −0.180436 | − | 0.983587i | \(-0.557751\pi\) | ||||
−0.180436 | + | 0.983587i | \(0.557751\pi\) | |||||||
\(740\) | −2.93354 | −0.107839 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.9776 | 0.733401 | ||||||||
\(743\) | 10.9782 | 0.402750 | 0.201375 | − | 0.979514i | \(-0.435459\pi\) | ||||
0.201375 | + | 0.979514i | \(0.435459\pi\) | |||||||
\(744\) | −0.429064 | −0.0157303 | ||||||||
\(745\) | −1.29716 | −0.0475244 | ||||||||
\(746\) | 8.35563 | 0.305921 | ||||||||
\(747\) | 46.8513 | 1.71420 | ||||||||
\(748\) | 1.65358 | 0.0604607 | ||||||||
\(749\) | 24.4603 | 0.893760 | ||||||||
\(750\) | 0.564724 | 0.0206208 | ||||||||
\(751\) | 26.2778 | 0.958891 | 0.479445 | − | 0.877572i | \(-0.340838\pi\) | ||||
0.479445 | + | 0.877572i | \(0.340838\pi\) | |||||||
\(752\) | 10.6311 | 0.387676 | ||||||||
\(753\) | 1.98538 | 0.0723513 | ||||||||
\(754\) | 0.653881 | 0.0238130 | ||||||||
\(755\) | −7.85464 | −0.285860 | ||||||||
\(756\) | −1.59334 | −0.0579492 | ||||||||
\(757\) | −45.6128 | −1.65783 | −0.828913 | − | 0.559377i | \(-0.811040\pi\) | ||||
−0.828913 | + | 0.559377i | \(0.811040\pi\) | |||||||
\(758\) | −11.2112 | −0.407208 | ||||||||
\(759\) | −0.934272 | −0.0339119 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.9343 | −1.33887 | −0.669433 | − | 0.742872i | \(-0.733463\pi\) | ||||
−0.669433 | + | 0.742872i | \(0.733463\pi\) | |||||||
\(762\) | 2.04224 | 0.0739826 | ||||||||
\(763\) | −13.9017 | −0.503274 | ||||||||
\(764\) | −8.81314 | −0.318848 | ||||||||
\(765\) | 2.46205 | 0.0890157 | ||||||||
\(766\) | −23.5595 | −0.851239 | ||||||||
\(767\) | −0.799076 | −0.0288530 | ||||||||
\(768\) | −0.116160 | −0.00419157 | ||||||||
\(769\) | 0.908733 | 0.0327697 | 0.0163849 | − | 0.999866i | \(-0.494784\pi\) | ||||
0.0163849 | + | 0.999866i | \(0.494784\pi\) | |||||||
\(770\) | −1.14232 | −0.0411663 | ||||||||
\(771\) | 2.90396 | 0.104583 | ||||||||
\(772\) | 1.62372 | 0.0584388 | ||||||||
\(773\) | 4.28492 | 0.154118 | 0.0770590 | − | 0.997027i | \(-0.475447\pi\) | ||||
0.0770590 | + | 0.997027i | \(0.475447\pi\) | |||||||
\(774\) | −15.3212 | −0.550710 | ||||||||
\(775\) | 17.5506 | 0.630435 | ||||||||
\(776\) | −15.4833 | −0.555817 | ||||||||
\(777\) | 1.56609 | 0.0561833 | ||||||||
\(778\) | −32.3109 | −1.15840 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.0162820 | 0.000582991 0 | ||||||||
\(781\) | 5.50926 | 0.197137 | ||||||||
\(782\) | −13.2996 | −0.475594 | ||||||||
\(783\) | −1.61729 | −0.0577972 | ||||||||
\(784\) | −1.75004 | −0.0625015 | ||||||||
\(785\) | −0.696885 | −0.0248729 | ||||||||
\(786\) | 0.596279 | 0.0212686 | ||||||||
\(787\) | 27.9756 | 0.997223 | 0.498612 | − | 0.866825i | \(-0.333843\pi\) | ||||
0.498612 | + | 0.866825i | \(0.333843\pi\) | |||||||
\(788\) | −20.2131 | −0.720062 | ||||||||
\(789\) | −0.471752 | −0.0167948 | ||||||||
\(790\) | 7.03128 | 0.250162 | ||||||||
\(791\) | −29.7838 | −1.05899 | ||||||||
\(792\) | 2.98651 | 0.106121 | ||||||||
\(793\) | −3.51356 | −0.124770 | ||||||||
\(794\) | 21.6587 | 0.768640 | ||||||||
\(795\) | 0.504932 | 0.0179081 | ||||||||
\(796\) | −17.2777 | −0.612392 | ||||||||
\(797\) | −51.6959 | −1.83116 | −0.915581 | − | 0.402135i | \(-0.868268\pi\) | ||||
−0.915581 | + | 0.402135i | \(0.868268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.5793 | 0.621912 | ||||||||
\(800\) | 4.75145 | 0.167989 | ||||||||
\(801\) | −19.1647 | −0.677151 | ||||||||
\(802\) | −15.2032 | −0.536842 | ||||||||
\(803\) | 2.38179 | 0.0840517 | ||||||||
\(804\) | 1.36300 | 0.0480693 | ||||||||
\(805\) | 9.18763 | 0.323821 | ||||||||
\(806\) | 1.03850 | 0.0365796 | ||||||||
\(807\) | −0.0669323 | −0.00235613 | ||||||||
\(808\) | 0.380477 | 0.0133851 | ||||||||
\(809\) | 16.2645 | 0.571828 | 0.285914 | − | 0.958255i | \(-0.407703\pi\) | ||||
0.285914 | + | 0.958255i | \(0.407703\pi\) | |||||||
\(810\) | 4.42651 | 0.155532 | ||||||||
\(811\) | 46.9741 | 1.64948 | 0.824742 | − | 0.565509i | \(-0.191320\pi\) | ||||
0.824742 | + | 0.565509i | \(0.191320\pi\) | |||||||
\(812\) | 5.32887 | 0.187007 | ||||||||
\(813\) | 3.10359 | 0.108848 | ||||||||
\(814\) | −5.88414 | −0.206239 | ||||||||
\(815\) | 8.33795 | 0.292066 | ||||||||
\(816\) | −0.192080 | −0.00672413 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 35.8741 | 1.25431 | ||||||||
\(819\) | 1.92390 | 0.0672266 | ||||||||
\(820\) | −0.266812 | −0.00931747 | ||||||||
\(821\) | −25.0551 | −0.874430 | −0.437215 | − | 0.899357i | \(-0.644035\pi\) | ||||
−0.437215 | + | 0.899357i | \(0.644035\pi\) | |||||||
\(822\) | 0.350744 | 0.0122336 | ||||||||
\(823\) | −42.3112 | −1.47488 | −0.737438 | − | 0.675415i | \(-0.763964\pi\) | ||||
−0.737438 | + | 0.675415i | \(0.763964\pi\) | |||||||
\(824\) | 6.42485 | 0.223820 | ||||||||
\(825\) | 0.551929 | 0.0192157 | ||||||||
\(826\) | −6.51215 | −0.226587 | ||||||||
\(827\) | 13.9959 | 0.486686 | 0.243343 | − | 0.969940i | \(-0.421756\pi\) | ||||
0.243343 | + | 0.969940i | \(0.421756\pi\) | |||||||
\(828\) | −24.0204 | −0.834765 | ||||||||
\(829\) | −11.7480 | −0.408025 | −0.204012 | − | 0.978968i | \(-0.565398\pi\) | ||||
−0.204012 | + | 0.978968i | \(0.565398\pi\) | |||||||
\(830\) | −7.82109 | −0.271474 | ||||||||
\(831\) | 0.363280 | 0.0126020 | ||||||||
\(832\) | 0.281152 | 0.00974721 | ||||||||
\(833\) | −2.89383 | −0.100265 | ||||||||
\(834\) | −0.341834 | −0.0118367 | ||||||||
\(835\) | 4.88362 | 0.169004 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.56860 | −0.0887836 | ||||||||
\(838\) | −5.02288 | −0.173512 | ||||||||
\(839\) | −20.5061 | −0.707948 | −0.353974 | − | 0.935255i | \(-0.615170\pi\) | ||||
−0.353974 | + | 0.935255i | \(0.615170\pi\) | |||||||
\(840\) | 0.132692 | 0.00457831 | ||||||||
\(841\) | −23.5910 | −0.813484 | ||||||||
\(842\) | −5.74864 | −0.198111 | ||||||||
\(843\) | 2.88798 | 0.0994672 | ||||||||
\(844\) | 7.33059 | 0.252329 | ||||||||
\(845\) | 6.44176 | 0.221603 | ||||||||
\(846\) | 31.7498 | 1.09158 | ||||||||
\(847\) | −2.29128 | −0.0787293 | ||||||||
\(848\) | 8.71898 | 0.299411 | ||||||||
\(849\) | 0.134880 | 0.00462907 | ||||||||
\(850\) | 7.85688 | 0.269489 | ||||||||
\(851\) | 47.3259 | 1.62231 | ||||||||
\(852\) | −0.639956 | −0.0219245 | ||||||||
\(853\) | −55.5880 | −1.90330 | −0.951648 | − | 0.307191i | \(-0.900611\pi\) | ||||
−0.951648 | + | 0.307191i | \(0.900611\pi\) | |||||||
\(854\) | −28.6341 | −0.979839 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.6754 | 0.364877 | ||||||||
\(857\) | 40.9286 | 1.39809 | 0.699047 | − | 0.715076i | \(-0.253608\pi\) | ||||
0.699047 | + | 0.715076i | \(0.253608\pi\) | |||||||
\(858\) | 0.0326587 | 0.00111495 | ||||||||
\(859\) | −1.62330 | −0.0553864 | −0.0276932 | − | 0.999616i | \(-0.508816\pi\) | ||||
−0.0276932 | + | 0.999616i | \(0.508816\pi\) | |||||||
\(860\) | 2.55764 | 0.0872148 | ||||||||
\(861\) | 0.142439 | 0.00485432 | ||||||||
\(862\) | 25.8934 | 0.881934 | ||||||||
\(863\) | 28.6326 | 0.974665 | 0.487332 | − | 0.873217i | \(-0.337970\pi\) | ||||
0.487332 | + | 0.873217i | \(0.337970\pi\) | |||||||
\(864\) | −0.695394 | −0.0236578 | ||||||||
\(865\) | −6.73395 | −0.228961 | ||||||||
\(866\) | −9.54377 | −0.324311 | ||||||||
\(867\) | 1.65710 | 0.0562782 | ||||||||
\(868\) | 8.46336 | 0.287265 | ||||||||
\(869\) | 14.1034 | 0.478426 | ||||||||
\(870\) | 0.134686 | 0.00456630 | ||||||||
\(871\) | −3.29899 | −0.111782 | ||||||||
\(872\) | −6.06721 | −0.205462 | ||||||||
\(873\) | −46.2409 | −1.56502 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1393 | −0.376576 | ||||||||
\(876\) | −0.276670 | −0.00934780 | ||||||||
\(877\) | −17.7920 | −0.600793 | −0.300397 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300397 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(878\) | −0.635179 | −0.0214363 | ||||||||
\(879\) | 3.11335 | 0.105011 | ||||||||
\(880\) | −0.498551 | −0.0168062 | ||||||||
\(881\) | 16.4217 | 0.553262 | 0.276631 | − | 0.960976i | \(-0.410782\pi\) | ||||
0.276631 | + | 0.960976i | \(0.410782\pi\) | |||||||
\(882\) | −5.22652 | −0.175986 | ||||||||
\(883\) | 26.0571 | 0.876892 | 0.438446 | − | 0.898757i | \(-0.355529\pi\) | ||||
0.438446 | + | 0.898757i | \(0.355529\pi\) | |||||||
\(884\) | 0.464907 | 0.0156365 | ||||||||
\(885\) | −0.164594 | −0.00553276 | ||||||||
\(886\) | −17.6440 | −0.592760 | ||||||||
\(887\) | −44.6815 | −1.50026 | −0.750130 | − | 0.661291i | \(-0.770009\pi\) | ||||
−0.750130 | + | 0.661291i | \(0.770009\pi\) | |||||||
\(888\) | 0.683502 | 0.0229368 | ||||||||
\(889\) | −40.2836 | −1.35107 | ||||||||
\(890\) | 3.19925 | 0.107239 | ||||||||
\(891\) | 8.87874 | 0.297449 | ||||||||
\(892\) | 4.52822 | 0.151616 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.302233 | 0.0101082 | ||||||||
\(895\) | 8.85902 | 0.296125 | ||||||||
\(896\) | 2.29128 | 0.0765462 | ||||||||
\(897\) | −0.262673 | −0.00877039 | ||||||||
\(898\) | 20.9736 | 0.699900 | ||||||||
\(899\) | 8.59057 | 0.286512 | ||||||||
\(900\) | 14.1902 | 0.473008 | ||||||||
\(901\) | 14.4175 | 0.480316 | ||||||||
\(902\) | −0.535174 | −0.0178193 | ||||||||
\(903\) | −1.36542 | −0.0454382 | ||||||||
\(904\) | −12.9988 | −0.432333 | ||||||||
\(905\) | 5.66748 | 0.188393 | ||||||||
\(906\) | 1.83010 | 0.0608008 | ||||||||
\(907\) | −19.9543 | −0.662570 | −0.331285 | − | 0.943531i | \(-0.607482\pi\) | ||||
−0.331285 | + | 0.943531i | \(0.607482\pi\) | |||||||
\(908\) | −23.3452 | −0.774737 | ||||||||
\(909\) | 1.13630 | 0.0376886 | ||||||||
\(910\) | −0.321166 | −0.0106465 | ||||||||
\(911\) | 3.88096 | 0.128582 | 0.0642910 | − | 0.997931i | \(-0.479521\pi\) | ||||
0.0642910 | + | 0.997931i | \(0.479521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.6876 | −0.519185 | ||||||||
\(914\) | 22.9647 | 0.759604 | ||||||||
\(915\) | −0.723724 | −0.0239256 | ||||||||
\(916\) | −17.7244 | −0.585630 | ||||||||
\(917\) | −11.7617 | −0.388405 | ||||||||
\(918\) | −1.14989 | −0.0379519 | ||||||||
\(919\) | 18.4756 | 0.609454 | 0.304727 | − | 0.952440i | \(-0.401435\pi\) | ||||
0.304727 | + | 0.952440i | \(0.401435\pi\) | |||||||
\(920\) | 4.00983 | 0.132200 | ||||||||
\(921\) | −3.54117 | −0.116685 | ||||||||
\(922\) | 25.6578 | 0.844995 | ||||||||
\(923\) | 1.54894 | 0.0509840 | ||||||||
\(924\) | 0.266155 | 0.00875586 | ||||||||
\(925\) | −27.9582 | −0.919259 | ||||||||
\(926\) | −14.4251 | −0.474040 | ||||||||
\(927\) | 19.1879 | 0.630212 | ||||||||
\(928\) | 2.32572 | 0.0763454 | ||||||||
\(929\) | 40.8696 | 1.34089 | 0.670444 | − | 0.741960i | \(-0.266104\pi\) | ||||
0.670444 | + | 0.741960i | \(0.266104\pi\) | |||||||
\(930\) | 0.213910 | 0.00701440 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.4045 | −0.537347 | ||||||||
\(933\) | 1.28280 | 0.0419971 | ||||||||
\(934\) | 6.26939 | 0.205141 | ||||||||
\(935\) | −0.824392 | −0.0269605 | ||||||||
\(936\) | 0.839664 | 0.0274453 | ||||||||
\(937\) | −45.2015 | −1.47667 | −0.738335 | − | 0.674435i | \(-0.764387\pi\) | ||||
−0.738335 | + | 0.674435i | \(0.764387\pi\) | |||||||
\(938\) | −26.8854 | −0.877840 | ||||||||
\(939\) | −1.21849 | −0.0397638 | ||||||||
\(940\) | −5.30015 | −0.172872 | ||||||||
\(941\) | 10.4566 | 0.340876 | 0.170438 | − | 0.985368i | \(-0.445482\pi\) | ||||
0.170438 | + | 0.985368i | \(0.445482\pi\) | |||||||
\(942\) | 0.162371 | 0.00529034 | ||||||||
\(943\) | 4.30438 | 0.140170 | ||||||||
\(944\) | −2.84215 | −0.0925040 | ||||||||
\(945\) | 0.794362 | 0.0258406 | ||||||||
\(946\) | 5.13015 | 0.166795 | ||||||||
\(947\) | −37.2519 | −1.21052 | −0.605262 | − | 0.796026i | \(-0.706932\pi\) | ||||
−0.605262 | + | 0.796026i | \(0.706932\pi\) | |||||||
\(948\) | −1.63826 | −0.0532081 | ||||||||
\(949\) | 0.669647 | 0.0217377 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.22393 | 0.0396888 | ||||||||
\(952\) | 3.78880 | 0.122796 | ||||||||
\(953\) | −21.3523 | −0.691668 | −0.345834 | − | 0.938296i | \(-0.612404\pi\) | ||||
−0.345834 | + | 0.938296i | \(0.612404\pi\) | |||||||
\(954\) | 26.0393 | 0.843053 | ||||||||
\(955\) | 4.39380 | 0.142180 | ||||||||
\(956\) | 18.2990 | 0.591833 | ||||||||
\(957\) | 0.270156 | 0.00873289 | ||||||||
\(958\) | −9.22842 | −0.298157 | ||||||||
\(959\) | −6.91849 | −0.223410 | ||||||||
\(960\) | 0.0579118 | 0.00186909 | ||||||||
\(961\) | −17.3564 | −0.559883 | ||||||||
\(962\) | −1.65434 | −0.0533381 | ||||||||
\(963\) | 31.8821 | 1.02739 | ||||||||
\(964\) | 6.06680 | 0.195399 | ||||||||
\(965\) | −0.809505 | −0.0260589 | ||||||||
\(966\) | −2.14068 | −0.0688751 | ||||||||
\(967\) | 23.5891 | 0.758575 | 0.379287 | − | 0.925279i | \(-0.376169\pi\) | ||||
0.379287 | + | 0.925279i | \(0.376169\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.71920 | 0.247849 | ||||||||
\(971\) | 20.2354 | 0.649385 | 0.324692 | − | 0.945820i | \(-0.394739\pi\) | ||||
0.324692 | + | 0.945820i | \(0.394739\pi\) | |||||||
\(972\) | −3.11754 | −0.0999950 | ||||||||
\(973\) | 6.74273 | 0.216162 | ||||||||
\(974\) | 34.5755 | 1.10787 | ||||||||
\(975\) | 0.155176 | 0.00496961 | ||||||||
\(976\) | −12.4970 | −0.400019 | ||||||||
\(977\) | 5.21980 | 0.166996 | 0.0834980 | − | 0.996508i | \(-0.473391\pi\) | ||||
0.0834980 | + | 0.996508i | \(0.473391\pi\) | |||||||
\(978\) | −1.94270 | −0.0621209 | ||||||||
\(979\) | 6.41709 | 0.205091 | ||||||||
\(980\) | 0.872486 | 0.0278705 | ||||||||
\(981\) | −18.1198 | −0.578520 | ||||||||
\(982\) | 19.5615 | 0.624234 | ||||||||
\(983\) | −40.5282 | −1.29265 | −0.646325 | − | 0.763062i | \(-0.723695\pi\) | ||||
−0.646325 | + | 0.763062i | \(0.723695\pi\) | |||||||
\(984\) | 0.0621659 | 0.00198178 | ||||||||
\(985\) | 10.0773 | 0.321088 | ||||||||
\(986\) | 3.84575 | 0.122474 | ||||||||
\(987\) | 2.82952 | 0.0900647 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.2616 | −1.31204 | ||||||||
\(990\) | −1.48893 | −0.0473212 | ||||||||
\(991\) | −3.36817 | −0.106993 | −0.0534967 | − | 0.998568i | \(-0.517037\pi\) | ||||
−0.0534967 | + | 0.998568i | \(0.517037\pi\) | |||||||
\(992\) | 3.69373 | 0.117276 | ||||||||
\(993\) | −0.705125 | −0.0223765 | ||||||||
\(994\) | 12.6232 | 0.400385 | ||||||||
\(995\) | 8.61382 | 0.273076 | ||||||||
\(996\) | 1.82228 | 0.0577411 | ||||||||
\(997\) | −25.3751 | −0.803638 | −0.401819 | − | 0.915719i | \(-0.631622\pi\) | ||||
−0.401819 | + | 0.915719i | \(0.631622\pi\) | |||||||
\(998\) | −7.82554 | −0.247713 | ||||||||
\(999\) | 4.09179 | 0.129459 |
(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 | 7942.2.a.bs.1.6 | 12 | ||
19.14 | odd | 18 | 418.2.j.b.177.2 | yes | 24 | ||
19.15 | odd | 18 | 418.2.j.b.111.2 | ✓ | 24 | ||
19.18 | odd | 2 | 7942.2.a.bw.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.j.b.111.2 | ✓ | 24 | 19.15 | odd | 18 | ||
418.2.j.b.177.2 | yes | 24 | 19.14 | odd | 18 | ||
7942.2.a.bs.1.6 | 12 | 1.1 | even | 1 | trivial | ||
7942.2.a.bw.1.7 | 12 | 19.18 | odd | 2 |