Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(1,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.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: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.36147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36147 | −1.66981 | −0.834905 | − | 0.550394i | \(-0.814478\pi\) | ||||
−0.834905 | + | 0.550394i | \(0.814478\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.57653 | 1.78827 | ||||||||
\(5\) | −3.93800 | −1.76113 | −0.880564 | − | 0.473927i | \(-0.842836\pi\) | ||||
−0.880564 | + | 0.473927i | \(0.842836\pi\) | |||||||
\(6\) | 2.36147 | 0.964066 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.72294 | −1.31626 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.29947 | 2.94075 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.57653 | −1.03246 | ||||||||
\(13\) | −3.93800 | −1.09221 | −0.546103 | − | 0.837718i | \(-0.683889\pi\) | ||||
−0.546103 | + | 0.837718i | \(0.683889\pi\) | |||||||
\(14\) | 2.36147 | 0.631129 | ||||||||
\(15\) | 3.93800 | 1.01679 | ||||||||
\(16\) | 1.63853 | 0.409633 | ||||||||
\(17\) | 4.72294 | 1.14548 | 0.572740 | − | 0.819737i | \(-0.305880\pi\) | ||||
0.572740 | + | 0.819737i | \(0.305880\pi\) | |||||||
\(18\) | −2.36147 | −0.556604 | ||||||||
\(19\) | 4.78493 | 1.09774 | 0.548870 | − | 0.835908i | \(-0.315058\pi\) | ||||
0.548870 | + | 0.835908i | \(0.315058\pi\) | |||||||
\(20\) | −14.0844 | −3.14937 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.36147 | −0.503467 | ||||||||
\(23\) | 2.72294 | 0.567772 | 0.283886 | − | 0.958858i | \(-0.408376\pi\) | ||||
0.283886 | + | 0.958858i | \(0.408376\pi\) | |||||||
\(24\) | 3.72294 | 0.759941 | ||||||||
\(25\) | 10.5079 | 2.10157 | ||||||||
\(26\) | 9.29947 | 1.82378 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.57653 | −0.675902 | ||||||||
\(29\) | 7.93800 | 1.47405 | 0.737025 | − | 0.675865i | \(-0.236230\pi\) | ||||
0.737025 | + | 0.675865i | \(0.236230\pi\) | |||||||
\(30\) | −9.29947 | −1.69784 | ||||||||
\(31\) | 1.15307 | 0.207097 | 0.103549 | − | 0.994624i | \(-0.466980\pi\) | ||||
0.103549 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(32\) | 3.57653 | 0.632248 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −11.1531 | −1.91274 | ||||||||
\(35\) | 3.93800 | 0.665644 | ||||||||
\(36\) | 3.57653 | 0.596089 | ||||||||
\(37\) | −5.50787 | −0.905489 | −0.452744 | − | 0.891640i | \(-0.649555\pi\) | ||||
−0.452744 | + | 0.891640i | \(0.649555\pi\) | |||||||
\(38\) | −11.2995 | −1.83302 | ||||||||
\(39\) | 3.93800 | 0.630585 | ||||||||
\(40\) | 14.6609 | 2.31810 | ||||||||
\(41\) | 0.430132 | 0.0671753 | 0.0335877 | − | 0.999436i | \(-0.489307\pi\) | ||||
0.0335877 | + | 0.999436i | \(0.489307\pi\) | |||||||
\(42\) | −2.36147 | −0.364383 | ||||||||
\(43\) | 6.72294 | 1.02524 | 0.512619 | − | 0.858616i | \(-0.328675\pi\) | ||||
0.512619 | + | 0.858616i | \(0.328675\pi\) | |||||||
\(44\) | 3.57653 | 0.539183 | ||||||||
\(45\) | −3.93800 | −0.587043 | ||||||||
\(46\) | −6.43013 | −0.948071 | ||||||||
\(47\) | −8.78493 | −1.28141 | −0.640707 | − | 0.767785i | \(-0.721359\pi\) | ||||
−0.640707 | + | 0.767785i | \(0.721359\pi\) | |||||||
\(48\) | −1.63853 | −0.236502 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −24.8140 | −3.50923 | ||||||||
\(51\) | −4.72294 | −0.661344 | ||||||||
\(52\) | −14.0844 | −1.95316 | ||||||||
\(53\) | −3.15307 | −0.433107 | −0.216554 | − | 0.976271i | \(-0.569482\pi\) | ||||
−0.216554 | + | 0.976271i | \(0.569482\pi\) | |||||||
\(54\) | 2.36147 | 0.321355 | ||||||||
\(55\) | −3.93800 | −0.531000 | ||||||||
\(56\) | 3.72294 | 0.497498 | ||||||||
\(57\) | −4.78493 | −0.633780 | ||||||||
\(58\) | −18.7453 | −2.46138 | ||||||||
\(59\) | −15.0911 | −1.96469 | −0.982345 | − | 0.187077i | \(-0.940098\pi\) | ||||
−0.982345 | + | 0.187077i | \(0.940098\pi\) | |||||||
\(60\) | 14.0844 | 1.81829 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −2.72294 | −0.345813 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −11.7229 | −1.46537 | ||||||||
\(65\) | 15.5079 | 1.92351 | ||||||||
\(66\) | 2.36147 | 0.290677 | ||||||||
\(67\) | 3.21507 | 0.392783 | 0.196391 | − | 0.980526i | \(-0.437078\pi\) | ||||
0.196391 | + | 0.980526i | \(0.437078\pi\) | |||||||
\(68\) | 16.8918 | 2.04843 | ||||||||
\(69\) | −2.72294 | −0.327803 | ||||||||
\(70\) | −9.29947 | −1.11150 | ||||||||
\(71\) | 13.4459 | 1.59573 | 0.797866 | − | 0.602835i | \(-0.205962\pi\) | ||||
0.797866 | + | 0.602835i | \(0.205962\pi\) | |||||||
\(72\) | −3.72294 | −0.438752 | ||||||||
\(73\) | 11.9380 | 1.39724 | 0.698619 | − | 0.715494i | \(-0.253798\pi\) | ||||
0.698619 | + | 0.715494i | \(0.253798\pi\) | |||||||
\(74\) | 13.0067 | 1.51199 | ||||||||
\(75\) | −10.5079 | −1.21334 | ||||||||
\(76\) | 17.1135 | 1.96305 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −9.29947 | −1.05296 | ||||||||
\(79\) | −5.44588 | −0.612709 | −0.306354 | − | 0.951918i | \(-0.599109\pi\) | ||||
−0.306354 | + | 0.951918i | \(0.599109\pi\) | |||||||
\(80\) | −6.45254 | −0.721416 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.01574 | −0.112170 | ||||||||
\(83\) | −2.84693 | −0.312491 | −0.156246 | − | 0.987718i | \(-0.549939\pi\) | ||||
−0.156246 | + | 0.987718i | \(0.549939\pi\) | |||||||
\(84\) | 3.57653 | 0.390232 | ||||||||
\(85\) | −18.5989 | −2.01734 | ||||||||
\(86\) | −15.8760 | −1.71195 | ||||||||
\(87\) | −7.93800 | −0.851043 | ||||||||
\(88\) | −3.72294 | −0.396866 | ||||||||
\(89\) | 12.3061 | 1.30445 | 0.652224 | − | 0.758026i | \(-0.273836\pi\) | ||||
0.652224 | + | 0.758026i | \(0.273836\pi\) | |||||||
\(90\) | 9.29947 | 0.980250 | ||||||||
\(91\) | 3.93800 | 0.412815 | ||||||||
\(92\) | 9.73868 | 1.01533 | ||||||||
\(93\) | −1.15307 | −0.119568 | ||||||||
\(94\) | 20.7453 | 2.13972 | ||||||||
\(95\) | −18.8431 | −1.93326 | ||||||||
\(96\) | −3.57653 | −0.365029 | ||||||||
\(97\) | 11.1531 | 1.13242 | 0.566211 | − | 0.824260i | \(-0.308409\pi\) | ||||
0.566211 | + | 0.824260i | \(0.308409\pi\) | |||||||
\(98\) | −2.36147 | −0.238544 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 37.5818 | 3.75818 | ||||||||
\(101\) | 16.4750 | 1.63932 | 0.819659 | − | 0.572851i | \(-0.194163\pi\) | ||||
0.819659 | + | 0.572851i | \(0.194163\pi\) | |||||||
\(102\) | 11.1531 | 1.10432 | ||||||||
\(103\) | −1.56987 | −0.154684 | −0.0773418 | − | 0.997005i | \(-0.524643\pi\) | ||||
−0.0773418 | + | 0.997005i | \(0.524643\pi\) | |||||||
\(104\) | 14.6609 | 1.43762 | ||||||||
\(105\) | −3.93800 | −0.384310 | ||||||||
\(106\) | 7.44588 | 0.723207 | ||||||||
\(107\) | −4.78493 | −0.462577 | −0.231289 | − | 0.972885i | \(-0.574294\pi\) | ||||
−0.231289 | + | 0.972885i | \(0.574294\pi\) | |||||||
\(108\) | −3.57653 | −0.344152 | ||||||||
\(109\) | −15.0291 | −1.43952 | −0.719762 | − | 0.694221i | \(-0.755749\pi\) | ||||
−0.719762 | + | 0.694221i | \(0.755749\pi\) | |||||||
\(110\) | 9.29947 | 0.886670 | ||||||||
\(111\) | 5.50787 | 0.522784 | ||||||||
\(112\) | −1.63853 | −0.154827 | ||||||||
\(113\) | 7.44588 | 0.700449 | 0.350225 | − | 0.936666i | \(-0.386105\pi\) | ||||
0.350225 | + | 0.936666i | \(0.386105\pi\) | |||||||
\(114\) | 11.2995 | 1.05829 | ||||||||
\(115\) | −10.7229 | −0.999919 | ||||||||
\(116\) | 28.3905 | 2.63600 | ||||||||
\(117\) | −3.93800 | −0.364069 | ||||||||
\(118\) | 35.6371 | 3.28066 | ||||||||
\(119\) | −4.72294 | −0.432951 | ||||||||
\(120\) | −14.6609 | −1.33835 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.1688 | −1.28278 | ||||||||
\(123\) | −0.430132 | −0.0387837 | ||||||||
\(124\) | 4.12399 | 0.370346 | ||||||||
\(125\) | −21.6900 | −1.94001 | ||||||||
\(126\) | 2.36147 | 0.210376 | ||||||||
\(127\) | 12.2928 | 1.09081 | 0.545405 | − | 0.838173i | \(-0.316376\pi\) | ||||
0.545405 | + | 0.838173i | \(0.316376\pi\) | |||||||
\(128\) | 20.5303 | 1.81464 | ||||||||
\(129\) | −6.72294 | −0.591922 | ||||||||
\(130\) | −36.6214 | −3.21191 | ||||||||
\(131\) | 7.13974 | 0.623802 | 0.311901 | − | 0.950115i | \(-0.399034\pi\) | ||||
0.311901 | + | 0.950115i | \(0.399034\pi\) | |||||||
\(132\) | −3.57653 | −0.311297 | ||||||||
\(133\) | −4.78493 | −0.414906 | ||||||||
\(134\) | −7.59228 | −0.655873 | ||||||||
\(135\) | 3.93800 | 0.338929 | ||||||||
\(136\) | −17.5832 | −1.50775 | ||||||||
\(137\) | 1.58320 | 0.135262 | 0.0676310 | − | 0.997710i | \(-0.478456\pi\) | ||||
0.0676310 | + | 0.997710i | \(0.478456\pi\) | |||||||
\(138\) | 6.43013 | 0.547369 | ||||||||
\(139\) | −17.1979 | −1.45871 | −0.729353 | − | 0.684138i | \(-0.760179\pi\) | ||||
−0.729353 | + | 0.684138i | \(0.760179\pi\) | |||||||
\(140\) | 14.0844 | 1.19035 | ||||||||
\(141\) | 8.78493 | 0.739825 | ||||||||
\(142\) | −31.7520 | −2.66457 | ||||||||
\(143\) | −3.93800 | −0.329312 | ||||||||
\(144\) | 1.63853 | 0.136544 | ||||||||
\(145\) | −31.2599 | −2.59599 | ||||||||
\(146\) | −28.1912 | −2.33312 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −19.6991 | −1.61926 | ||||||||
\(149\) | 15.9380 | 1.30569 | 0.652846 | − | 0.757491i | \(-0.273575\pi\) | ||||
0.652846 | + | 0.757491i | \(0.273575\pi\) | |||||||
\(150\) | 24.8140 | 2.02606 | ||||||||
\(151\) | 6.59894 | 0.537014 | 0.268507 | − | 0.963278i | \(-0.413470\pi\) | ||||
0.268507 | + | 0.963278i | \(0.413470\pi\) | |||||||
\(152\) | −17.8140 | −1.44491 | ||||||||
\(153\) | 4.72294 | 0.381827 | ||||||||
\(154\) | 2.36147 | 0.190293 | ||||||||
\(155\) | −4.54079 | −0.364725 | ||||||||
\(156\) | 14.0844 | 1.12765 | ||||||||
\(157\) | 7.32188 | 0.584350 | 0.292175 | − | 0.956365i | \(-0.405621\pi\) | ||||
0.292175 | + | 0.956365i | \(0.405621\pi\) | |||||||
\(158\) | 12.8603 | 1.02311 | ||||||||
\(159\) | 3.15307 | 0.250055 | ||||||||
\(160\) | −14.0844 | −1.11347 | ||||||||
\(161\) | −2.72294 | −0.214598 | ||||||||
\(162\) | −2.36147 | −0.185535 | ||||||||
\(163\) | 14.1068 | 1.10493 | 0.552466 | − | 0.833536i | \(-0.313687\pi\) | ||||
0.552466 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(164\) | 1.53838 | 0.120127 | ||||||||
\(165\) | 3.93800 | 0.306573 | ||||||||
\(166\) | 6.72294 | 0.521801 | ||||||||
\(167\) | −0.416799 | −0.0322528 | −0.0161264 | − | 0.999870i | \(-0.505133\pi\) | ||||
−0.0161264 | + | 0.999870i | \(0.505133\pi\) | |||||||
\(168\) | −3.72294 | −0.287231 | ||||||||
\(169\) | 2.50787 | 0.192913 | ||||||||
\(170\) | 43.9208 | 3.36857 | ||||||||
\(171\) | 4.78493 | 0.365913 | ||||||||
\(172\) | 24.0448 | 1.83340 | ||||||||
\(173\) | −8.43013 | −0.640931 | −0.320466 | − | 0.947260i | \(-0.603839\pi\) | ||||
−0.320466 | + | 0.947260i | \(0.603839\pi\) | |||||||
\(174\) | 18.7453 | 1.42108 | ||||||||
\(175\) | −10.5079 | −0.794320 | ||||||||
\(176\) | 1.63853 | 0.123509 | ||||||||
\(177\) | 15.0911 | 1.13431 | ||||||||
\(178\) | −29.0606 | −2.17818 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −14.0844 | −1.04979 | ||||||||
\(181\) | 20.5989 | 1.53111 | 0.765554 | − | 0.643372i | \(-0.222465\pi\) | ||||
0.765554 | + | 0.643372i | \(0.222465\pi\) | |||||||
\(182\) | −9.29947 | −0.689323 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −10.1373 | −0.747334 | ||||||||
\(185\) | 21.6900 | 1.59468 | ||||||||
\(186\) | 2.72294 | 0.199655 | ||||||||
\(187\) | 4.72294 | 0.345375 | ||||||||
\(188\) | −31.4196 | −2.29151 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 44.4974 | 3.22818 | ||||||||
\(191\) | −14.5989 | −1.05634 | −0.528171 | − | 0.849138i | \(-0.677122\pi\) | ||||
−0.528171 | + | 0.849138i | \(0.677122\pi\) | |||||||
\(192\) | 11.7229 | 0.846030 | ||||||||
\(193\) | 13.4592 | 0.968815 | 0.484408 | − | 0.874842i | \(-0.339035\pi\) | ||||
0.484408 | + | 0.874842i | \(0.339035\pi\) | |||||||
\(194\) | −26.3376 | −1.89093 | ||||||||
\(195\) | −15.5079 | −1.11054 | ||||||||
\(196\) | 3.57653 | 0.255467 | ||||||||
\(197\) | 11.4459 | 0.815485 | 0.407742 | − | 0.913097i | \(-0.366316\pi\) | ||||
0.407742 | + | 0.913097i | \(0.366316\pi\) | |||||||
\(198\) | −2.36147 | −0.167822 | ||||||||
\(199\) | −13.0291 | −0.923607 | −0.461803 | − | 0.886982i | \(-0.652797\pi\) | ||||
−0.461803 | + | 0.886982i | \(0.652797\pi\) | |||||||
\(200\) | −39.1201 | −2.76621 | ||||||||
\(201\) | −3.21507 | −0.226773 | ||||||||
\(202\) | −38.9051 | −2.73735 | ||||||||
\(203\) | −7.93800 | −0.557139 | ||||||||
\(204\) | −16.8918 | −1.18266 | ||||||||
\(205\) | −1.69386 | −0.118304 | ||||||||
\(206\) | 3.70719 | 0.258292 | ||||||||
\(207\) | 2.72294 | 0.189257 | ||||||||
\(208\) | −6.45254 | −0.447403 | ||||||||
\(209\) | 4.78493 | 0.330981 | ||||||||
\(210\) | 9.29947 | 0.641725 | ||||||||
\(211\) | 2.43013 | 0.167297 | 0.0836486 | − | 0.996495i | \(-0.473343\pi\) | ||||
0.0836486 | + | 0.996495i | \(0.473343\pi\) | |||||||
\(212\) | −11.2771 | −0.774512 | ||||||||
\(213\) | −13.4459 | −0.921296 | ||||||||
\(214\) | 11.2995 | 0.772416 | ||||||||
\(215\) | −26.4750 | −1.80558 | ||||||||
\(216\) | 3.72294 | 0.253314 | ||||||||
\(217\) | −1.15307 | −0.0782755 | ||||||||
\(218\) | 35.4907 | 2.40373 | ||||||||
\(219\) | −11.9380 | −0.806696 | ||||||||
\(220\) | −14.0844 | −0.949570 | ||||||||
\(221\) | −18.5989 | −1.25110 | ||||||||
\(222\) | −13.0067 | −0.872950 | ||||||||
\(223\) | 22.7678 | 1.52464 | 0.762321 | − | 0.647199i | \(-0.224060\pi\) | ||||
0.762321 | + | 0.647199i | \(0.224060\pi\) | |||||||
\(224\) | −3.57653 | −0.238967 | ||||||||
\(225\) | 10.5079 | 0.700525 | ||||||||
\(226\) | −17.5832 | −1.16962 | ||||||||
\(227\) | −15.8760 | −1.05373 | −0.526864 | − | 0.849950i | \(-0.676632\pi\) | ||||
−0.526864 | + | 0.849950i | \(0.676632\pi\) | |||||||
\(228\) | −17.1135 | −1.13337 | ||||||||
\(229\) | −3.15307 | −0.208361 | −0.104180 | − | 0.994558i | \(-0.533222\pi\) | ||||
−0.104180 | + | 0.994558i | \(0.533222\pi\) | |||||||
\(230\) | 25.3219 | 1.66968 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −29.5527 | −1.94023 | ||||||||
\(233\) | 13.1397 | 0.860813 | 0.430406 | − | 0.902635i | \(-0.358370\pi\) | ||||
0.430406 | + | 0.902635i | \(0.358370\pi\) | |||||||
\(234\) | 9.29947 | 0.607926 | ||||||||
\(235\) | 34.5951 | 2.25674 | ||||||||
\(236\) | −53.9737 | −3.51339 | ||||||||
\(237\) | 5.44588 | 0.353748 | ||||||||
\(238\) | 11.1531 | 0.722946 | ||||||||
\(239\) | −10.1068 | −0.653756 | −0.326878 | − | 0.945067i | \(-0.605997\pi\) | ||||
−0.326878 | + | 0.945067i | \(0.605997\pi\) | |||||||
\(240\) | 6.45254 | 0.416510 | ||||||||
\(241\) | 2.36814 | 0.152545 | 0.0762725 | − | 0.997087i | \(-0.475698\pi\) | ||||
0.0762725 | + | 0.997087i | \(0.475698\pi\) | |||||||
\(242\) | −2.36147 | −0.151801 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 21.4592 | 1.37379 | ||||||||
\(245\) | −3.93800 | −0.251590 | ||||||||
\(246\) | 1.01574 | 0.0647614 | ||||||||
\(247\) | −18.8431 | −1.19896 | ||||||||
\(248\) | −4.29281 | −0.272593 | ||||||||
\(249\) | 2.84693 | 0.180417 | ||||||||
\(250\) | 51.2203 | 3.23946 | ||||||||
\(251\) | 10.2308 | 0.645763 | 0.322881 | − | 0.946439i | \(-0.395348\pi\) | ||||
0.322881 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(252\) | −3.57653 | −0.225301 | ||||||||
\(253\) | 2.72294 | 0.171190 | ||||||||
\(254\) | −29.0291 | −1.82145 | ||||||||
\(255\) | 18.5989 | 1.16471 | ||||||||
\(256\) | −25.0357 | −1.56473 | ||||||||
\(257\) | −11.0777 | −0.691010 | −0.345505 | − | 0.938417i | \(-0.612292\pi\) | ||||
−0.345505 | + | 0.938417i | \(0.612292\pi\) | |||||||
\(258\) | 15.8760 | 0.988397 | ||||||||
\(259\) | 5.50787 | 0.342242 | ||||||||
\(260\) | 55.4644 | 3.43976 | ||||||||
\(261\) | 7.93800 | 0.491350 | ||||||||
\(262\) | −16.8603 | −1.04163 | ||||||||
\(263\) | −8.78493 | −0.541702 | −0.270851 | − | 0.962621i | \(-0.587305\pi\) | ||||
−0.270851 | + | 0.962621i | \(0.587305\pi\) | |||||||
\(264\) | 3.72294 | 0.229131 | ||||||||
\(265\) | 12.4168 | 0.762758 | ||||||||
\(266\) | 11.2995 | 0.692815 | ||||||||
\(267\) | −12.3061 | −0.753123 | ||||||||
\(268\) | 11.4988 | 0.702401 | ||||||||
\(269\) | 5.75201 | 0.350706 | 0.175353 | − | 0.984506i | \(-0.443893\pi\) | ||||
0.175353 | + | 0.984506i | \(0.443893\pi\) | |||||||
\(270\) | −9.29947 | −0.565948 | ||||||||
\(271\) | 0.784934 | 0.0476813 | 0.0238407 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238407 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(272\) | 7.73868 | 0.469226 | ||||||||
\(273\) | −3.93800 | −0.238339 | ||||||||
\(274\) | −3.73868 | −0.225862 | ||||||||
\(275\) | 10.5079 | 0.633648 | ||||||||
\(276\) | −9.73868 | −0.586200 | ||||||||
\(277\) | −11.5699 | −0.695166 | −0.347583 | − | 0.937649i | \(-0.612998\pi\) | ||||
−0.347583 | + | 0.937649i | \(0.612998\pi\) | |||||||
\(278\) | 40.6123 | 2.43576 | ||||||||
\(279\) | 1.15307 | 0.0690325 | ||||||||
\(280\) | −14.6609 | −0.876159 | ||||||||
\(281\) | −25.2599 | −1.50688 | −0.753439 | − | 0.657518i | \(-0.771607\pi\) | ||||
−0.753439 | + | 0.657518i | \(0.771607\pi\) | |||||||
\(282\) | −20.7453 | −1.23537 | ||||||||
\(283\) | −10.9671 | −0.651925 | −0.325963 | − | 0.945383i | \(-0.605688\pi\) | ||||
−0.325963 | + | 0.945383i | \(0.605688\pi\) | |||||||
\(284\) | 48.0896 | 2.85360 | ||||||||
\(285\) | 18.8431 | 1.11617 | ||||||||
\(286\) | 9.29947 | 0.549889 | ||||||||
\(287\) | −0.430132 | −0.0253899 | ||||||||
\(288\) | 3.57653 | 0.210749 | ||||||||
\(289\) | 5.30614 | 0.312126 | ||||||||
\(290\) | 73.8192 | 4.33482 | ||||||||
\(291\) | −11.1531 | −0.653805 | ||||||||
\(292\) | 42.6967 | 2.49863 | ||||||||
\(293\) | 14.7363 | 0.860902 | 0.430451 | − | 0.902614i | \(-0.358355\pi\) | ||||
0.430451 | + | 0.902614i | \(0.358355\pi\) | |||||||
\(294\) | 2.36147 | 0.137724 | ||||||||
\(295\) | 59.4287 | 3.46007 | ||||||||
\(296\) | 20.5055 | 1.19186 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −37.6371 | −2.18026 | ||||||||
\(299\) | −10.7229 | −0.620123 | ||||||||
\(300\) | −37.5818 | −2.16978 | ||||||||
\(301\) | −6.72294 | −0.387504 | ||||||||
\(302\) | −15.5832 | −0.896712 | ||||||||
\(303\) | −16.4750 | −0.946461 | ||||||||
\(304\) | 7.84026 | 0.449670 | ||||||||
\(305\) | −23.6280 | −1.35294 | ||||||||
\(306\) | −11.1531 | −0.637579 | ||||||||
\(307\) | 0.860264 | 0.0490979 | 0.0245489 | − | 0.999699i | \(-0.492185\pi\) | ||||
0.0245489 | + | 0.999699i | \(0.492185\pi\) | |||||||
\(308\) | −3.57653 | −0.203792 | ||||||||
\(309\) | 1.56987 | 0.0893067 | ||||||||
\(310\) | 10.7229 | 0.609022 | ||||||||
\(311\) | 26.8918 | 1.52489 | 0.762446 | − | 0.647052i | \(-0.223998\pi\) | ||||
0.762446 | + | 0.647052i | \(0.223998\pi\) | |||||||
\(312\) | −14.6609 | −0.830012 | ||||||||
\(313\) | 10.1688 | 0.574775 | 0.287388 | − | 0.957814i | \(-0.407213\pi\) | ||||
0.287388 | + | 0.957814i | \(0.407213\pi\) | |||||||
\(314\) | −17.2904 | −0.975753 | ||||||||
\(315\) | 3.93800 | 0.221881 | ||||||||
\(316\) | −19.4774 | −1.09569 | ||||||||
\(317\) | −27.4907 | −1.54403 | −0.772016 | − | 0.635604i | \(-0.780751\pi\) | ||||
−0.772016 | + | 0.635604i | \(0.780751\pi\) | |||||||
\(318\) | −7.44588 | −0.417544 | ||||||||
\(319\) | 7.93800 | 0.444443 | ||||||||
\(320\) | 46.1650 | 2.58070 | ||||||||
\(321\) | 4.78493 | 0.267069 | ||||||||
\(322\) | 6.43013 | 0.358337 | ||||||||
\(323\) | 22.5989 | 1.25744 | ||||||||
\(324\) | 3.57653 | 0.198696 | ||||||||
\(325\) | −41.3800 | −2.29535 | ||||||||
\(326\) | −33.3128 | −1.84503 | ||||||||
\(327\) | 15.0291 | 0.831110 | ||||||||
\(328\) | −1.60135 | −0.0884200 | ||||||||
\(329\) | 8.78493 | 0.484329 | ||||||||
\(330\) | −9.29947 | −0.511919 | ||||||||
\(331\) | −17.1979 | −0.945281 | −0.472641 | − | 0.881255i | \(-0.656699\pi\) | ||||
−0.472641 | + | 0.881255i | \(0.656699\pi\) | |||||||
\(332\) | −10.1821 | −0.558818 | ||||||||
\(333\) | −5.50787 | −0.301830 | ||||||||
\(334\) | 0.984257 | 0.0538561 | ||||||||
\(335\) | −12.6609 | −0.691741 | ||||||||
\(336\) | 1.63853 | 0.0893892 | ||||||||
\(337\) | 19.7387 | 1.07523 | 0.537617 | − | 0.843189i | \(-0.319325\pi\) | ||||
0.537617 | + | 0.843189i | \(0.319325\pi\) | |||||||
\(338\) | −5.92226 | −0.322128 | ||||||||
\(339\) | −7.44588 | −0.404404 | ||||||||
\(340\) | −66.5198 | −3.60754 | ||||||||
\(341\) | 1.15307 | 0.0624422 | ||||||||
\(342\) | −11.2995 | −0.611005 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −25.0291 | −1.34948 | ||||||||
\(345\) | 10.7229 | 0.577304 | ||||||||
\(346\) | 19.9075 | 1.07023 | ||||||||
\(347\) | 16.6123 | 0.891794 | 0.445897 | − | 0.895084i | \(-0.352885\pi\) | ||||
0.445897 | + | 0.895084i | \(0.352885\pi\) | |||||||
\(348\) | −28.3905 | −1.52189 | ||||||||
\(349\) | 6.95375 | 0.372226 | 0.186113 | − | 0.982528i | \(-0.440411\pi\) | ||||
0.186113 | + | 0.982528i | \(0.440411\pi\) | |||||||
\(350\) | 24.8140 | 1.32636 | ||||||||
\(351\) | 3.93800 | 0.210195 | ||||||||
\(352\) | 3.57653 | 0.190630 | ||||||||
\(353\) | −3.22840 | −0.171830 | −0.0859152 | − | 0.996302i | \(-0.527381\pi\) | ||||
−0.0859152 | + | 0.996302i | \(0.527381\pi\) | |||||||
\(354\) | −35.6371 | −1.89409 | ||||||||
\(355\) | −52.9499 | −2.81029 | ||||||||
\(356\) | 44.0133 | 2.33270 | ||||||||
\(357\) | 4.72294 | 0.249964 | ||||||||
\(358\) | 28.3376 | 1.49769 | ||||||||
\(359\) | 10.3061 | 0.543937 | 0.271969 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271969 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(360\) | 14.6609 | 0.772699 | ||||||||
\(361\) | 3.89559 | 0.205031 | ||||||||
\(362\) | −48.6438 | −2.55666 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 14.0844 | 0.738223 | ||||||||
\(365\) | −47.0119 | −2.46072 | ||||||||
\(366\) | 14.1688 | 0.740616 | ||||||||
\(367\) | −11.8760 | −0.619923 | −0.309961 | − | 0.950749i | \(-0.600316\pi\) | ||||
−0.309961 | + | 0.950749i | \(0.600316\pi\) | |||||||
\(368\) | 4.46162 | 0.232578 | ||||||||
\(369\) | 0.430132 | 0.0223918 | ||||||||
\(370\) | −51.2203 | −2.66282 | ||||||||
\(371\) | 3.15307 | 0.163699 | ||||||||
\(372\) | −4.12399 | −0.213819 | ||||||||
\(373\) | 16.7229 | 0.865881 | 0.432940 | − | 0.901423i | \(-0.357476\pi\) | ||||
0.432940 | + | 0.901423i | \(0.357476\pi\) | |||||||
\(374\) | −11.1531 | −0.576711 | ||||||||
\(375\) | 21.6900 | 1.12007 | ||||||||
\(376\) | 32.7058 | 1.68667 | ||||||||
\(377\) | −31.2599 | −1.60997 | ||||||||
\(378\) | −2.36147 | −0.121461 | ||||||||
\(379\) | −10.9671 | −0.563341 | −0.281671 | − | 0.959511i | \(-0.590889\pi\) | ||||
−0.281671 | + | 0.959511i | \(0.590889\pi\) | |||||||
\(380\) | −67.3930 | −3.45719 | ||||||||
\(381\) | −12.2928 | −0.629780 | ||||||||
\(382\) | 34.4750 | 1.76389 | ||||||||
\(383\) | 15.7520 | 0.804890 | 0.402445 | − | 0.915444i | \(-0.368160\pi\) | ||||
0.402445 | + | 0.915444i | \(0.368160\pi\) | |||||||
\(384\) | −20.5303 | −1.04768 | ||||||||
\(385\) | 3.93800 | 0.200699 | ||||||||
\(386\) | −31.7835 | −1.61774 | ||||||||
\(387\) | 6.72294 | 0.341746 | ||||||||
\(388\) | 39.8893 | 2.02507 | ||||||||
\(389\) | 36.7678 | 1.86420 | 0.932100 | − | 0.362202i | \(-0.117975\pi\) | ||||
0.932100 | + | 0.362202i | \(0.117975\pi\) | |||||||
\(390\) | 36.6214 | 1.85439 | ||||||||
\(391\) | 12.8603 | 0.650371 | ||||||||
\(392\) | −3.72294 | −0.188037 | ||||||||
\(393\) | −7.13974 | −0.360152 | ||||||||
\(394\) | −27.0291 | −1.36171 | ||||||||
\(395\) | 21.4459 | 1.07906 | ||||||||
\(396\) | 3.57653 | 0.179728 | ||||||||
\(397\) | 11.8627 | 0.595371 | 0.297685 | − | 0.954664i | \(-0.403785\pi\) | ||||
0.297685 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(398\) | 30.7678 | 1.54225 | ||||||||
\(399\) | 4.78493 | 0.239546 | ||||||||
\(400\) | 17.2175 | 0.860874 | ||||||||
\(401\) | 3.40106 | 0.169841 | 0.0849203 | − | 0.996388i | \(-0.472936\pi\) | ||||
0.0849203 | + | 0.996388i | \(0.472936\pi\) | |||||||
\(402\) | 7.59228 | 0.378668 | ||||||||
\(403\) | −4.54079 | −0.226193 | ||||||||
\(404\) | 58.9232 | 2.93154 | ||||||||
\(405\) | −3.93800 | −0.195681 | ||||||||
\(406\) | 18.7453 | 0.930316 | ||||||||
\(407\) | −5.50787 | −0.273015 | ||||||||
\(408\) | 17.5832 | 0.870498 | ||||||||
\(409\) | −28.0315 | −1.38607 | −0.693034 | − | 0.720905i | \(-0.743726\pi\) | ||||
−0.693034 | + | 0.720905i | \(0.743726\pi\) | |||||||
\(410\) | 4.00000 | 0.197546 | ||||||||
\(411\) | −1.58320 | −0.0780936 | ||||||||
\(412\) | −5.61469 | −0.276616 | ||||||||
\(413\) | 15.0911 | 0.742583 | ||||||||
\(414\) | −6.43013 | −0.316024 | ||||||||
\(415\) | 11.2112 | 0.550337 | ||||||||
\(416\) | −14.0844 | −0.690545 | ||||||||
\(417\) | 17.1979 | 0.842184 | ||||||||
\(418\) | −11.2995 | −0.552675 | ||||||||
\(419\) | 28.2890 | 1.38201 | 0.691003 | − | 0.722852i | \(-0.257169\pi\) | ||||
0.691003 | + | 0.722852i | \(0.257169\pi\) | |||||||
\(420\) | −14.0844 | −0.687249 | ||||||||
\(421\) | −14.4921 | −0.706303 | −0.353152 | − | 0.935566i | \(-0.614890\pi\) | ||||
−0.353152 | + | 0.935566i | \(0.614890\pi\) | |||||||
\(422\) | −5.73868 | −0.279355 | ||||||||
\(423\) | −8.78493 | −0.427138 | ||||||||
\(424\) | 11.7387 | 0.570081 | ||||||||
\(425\) | 49.6280 | 2.40731 | ||||||||
\(426\) | 31.7520 | 1.53839 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | −17.1135 | −0.827211 | ||||||||
\(429\) | 3.93800 | 0.190129 | ||||||||
\(430\) | 62.5198 | 3.01497 | ||||||||
\(431\) | −24.5369 | −1.18190 | −0.590952 | − | 0.806707i | \(-0.701248\pi\) | ||||
−0.590952 | + | 0.806707i | \(0.701248\pi\) | |||||||
\(432\) | −1.63853 | −0.0788339 | ||||||||
\(433\) | −7.32188 | −0.351867 | −0.175934 | − | 0.984402i | \(-0.556294\pi\) | ||||
−0.175934 | + | 0.984402i | \(0.556294\pi\) | |||||||
\(434\) | 2.72294 | 0.130705 | ||||||||
\(435\) | 31.2599 | 1.49880 | ||||||||
\(436\) | −53.7520 | −2.57425 | ||||||||
\(437\) | 13.0291 | 0.623265 | ||||||||
\(438\) | 28.1912 | 1.34703 | ||||||||
\(439\) | 16.5369 | 0.789265 | 0.394633 | − | 0.918839i | \(-0.370872\pi\) | ||||
0.394633 | + | 0.918839i | \(0.370872\pi\) | |||||||
\(440\) | 14.6609 | 0.698933 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 43.9208 | 2.08910 | ||||||||
\(443\) | 25.1979 | 1.19719 | 0.598594 | − | 0.801053i | \(-0.295726\pi\) | ||||
0.598594 | + | 0.801053i | \(0.295726\pi\) | |||||||
\(444\) | 19.6991 | 0.934878 | ||||||||
\(445\) | −48.4616 | −2.29730 | ||||||||
\(446\) | −53.7653 | −2.54586 | ||||||||
\(447\) | −15.9380 | −0.753842 | ||||||||
\(448\) | 11.7229 | 0.553857 | ||||||||
\(449\) | −36.5198 | −1.72347 | −0.861737 | − | 0.507355i | \(-0.830623\pi\) | ||||
−0.861737 | + | 0.507355i | \(0.830623\pi\) | |||||||
\(450\) | −24.8140 | −1.16974 | ||||||||
\(451\) | 0.430132 | 0.0202541 | ||||||||
\(452\) | 26.6304 | 1.25259 | ||||||||
\(453\) | −6.59894 | −0.310045 | ||||||||
\(454\) | 37.4907 | 1.75953 | ||||||||
\(455\) | −15.5079 | −0.727020 | ||||||||
\(456\) | 17.8140 | 0.834217 | ||||||||
\(457\) | 3.15307 | 0.147494 | 0.0737472 | − | 0.997277i | \(-0.476504\pi\) | ||||
0.0737472 | + | 0.997277i | \(0.476504\pi\) | |||||||
\(458\) | 7.44588 | 0.347923 | ||||||||
\(459\) | −4.72294 | −0.220448 | ||||||||
\(460\) | −38.3510 | −1.78812 | ||||||||
\(461\) | −24.7678 | −1.15355 | −0.576775 | − | 0.816903i | \(-0.695689\pi\) | ||||
−0.576775 | + | 0.816903i | \(0.695689\pi\) | |||||||
\(462\) | −2.36147 | −0.109865 | ||||||||
\(463\) | −35.4287 | −1.64651 | −0.823256 | − | 0.567671i | \(-0.807845\pi\) | ||||
−0.823256 | + | 0.567671i | \(0.807845\pi\) | |||||||
\(464\) | 13.0067 | 0.603819 | ||||||||
\(465\) | 4.54079 | 0.210574 | ||||||||
\(466\) | −31.0291 | −1.43739 | ||||||||
\(467\) | −23.9247 | −1.10710 | −0.553551 | − | 0.832815i | \(-0.686728\pi\) | ||||
−0.553551 | + | 0.832815i | \(0.686728\pi\) | |||||||
\(468\) | −14.0844 | −0.651052 | ||||||||
\(469\) | −3.21507 | −0.148458 | ||||||||
\(470\) | −81.6953 | −3.76832 | ||||||||
\(471\) | −7.32188 | −0.337375 | ||||||||
\(472\) | 56.1831 | 2.58604 | ||||||||
\(473\) | 6.72294 | 0.309121 | ||||||||
\(474\) | −12.8603 | −0.590691 | ||||||||
\(475\) | 50.2795 | 2.30698 | ||||||||
\(476\) | −16.8918 | −0.774232 | ||||||||
\(477\) | −3.15307 | −0.144369 | ||||||||
\(478\) | 23.8669 | 1.09165 | ||||||||
\(479\) | 4.54079 | 0.207474 | 0.103737 | − | 0.994605i | \(-0.466920\pi\) | ||||
0.103737 | + | 0.994605i | \(0.466920\pi\) | |||||||
\(480\) | 14.0844 | 0.642862 | ||||||||
\(481\) | 21.6900 | 0.988980 | ||||||||
\(482\) | −5.59228 | −0.254721 | ||||||||
\(483\) | 2.72294 | 0.123898 | ||||||||
\(484\) | 3.57653 | 0.162570 | ||||||||
\(485\) | −43.9208 | −1.99434 | ||||||||
\(486\) | 2.36147 | 0.107118 | ||||||||
\(487\) | 27.1397 | 1.22982 | 0.614909 | − | 0.788598i | \(-0.289193\pi\) | ||||
0.614909 | + | 0.788598i | \(0.289193\pi\) | |||||||
\(488\) | −22.3376 | −1.01118 | ||||||||
\(489\) | −14.1068 | −0.637932 | ||||||||
\(490\) | 9.29947 | 0.420107 | ||||||||
\(491\) | 3.46305 | 0.156285 | 0.0781427 | − | 0.996942i | \(-0.475101\pi\) | ||||
0.0781427 | + | 0.996942i | \(0.475101\pi\) | |||||||
\(492\) | −1.53838 | −0.0693556 | ||||||||
\(493\) | 37.4907 | 1.68850 | ||||||||
\(494\) | 44.4974 | 2.00203 | ||||||||
\(495\) | −3.93800 | −0.177000 | ||||||||
\(496\) | 1.88934 | 0.0848339 | ||||||||
\(497\) | −13.4459 | −0.603130 | ||||||||
\(498\) | −6.72294 | −0.301262 | ||||||||
\(499\) | −18.9671 | −0.849083 | −0.424542 | − | 0.905408i | \(-0.639565\pi\) | ||||
−0.424542 | + | 0.905408i | \(0.639565\pi\) | |||||||
\(500\) | −77.5751 | −3.46926 | ||||||||
\(501\) | 0.416799 | 0.0186212 | ||||||||
\(502\) | −24.1597 | −1.07830 | ||||||||
\(503\) | 5.86267 | 0.261404 | 0.130702 | − | 0.991422i | \(-0.458277\pi\) | ||||
0.130702 | + | 0.991422i | \(0.458277\pi\) | |||||||
\(504\) | 3.72294 | 0.165833 | ||||||||
\(505\) | −64.8784 | −2.88705 | ||||||||
\(506\) | −6.43013 | −0.285854 | ||||||||
\(507\) | −2.50787 | −0.111378 | ||||||||
\(508\) | 43.9656 | 1.95066 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | −43.9208 | −1.94485 | ||||||||
\(511\) | −11.9380 | −0.528106 | ||||||||
\(512\) | 18.0606 | 0.798172 | ||||||||
\(513\) | −4.78493 | −0.211260 | ||||||||
\(514\) | 26.1597 | 1.15386 | ||||||||
\(515\) | 6.18215 | 0.272418 | ||||||||
\(516\) | −24.0448 | −1.05851 | ||||||||
\(517\) | −8.78493 | −0.386361 | ||||||||
\(518\) | −13.0067 | −0.571480 | ||||||||
\(519\) | 8.43013 | 0.370042 | ||||||||
\(520\) | −57.7348 | −2.53184 | ||||||||
\(521\) | −2.24414 | −0.0983177 | −0.0491588 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491588 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(522\) | −18.7453 | −0.820462 | ||||||||
\(523\) | −17.9828 | −0.786334 | −0.393167 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393167 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(524\) | 25.5355 | 1.11552 | ||||||||
\(525\) | 10.5079 | 0.458601 | ||||||||
\(526\) | 20.7453 | 0.904540 | ||||||||
\(527\) | 5.44588 | 0.237226 | ||||||||
\(528\) | −1.63853 | −0.0713079 | ||||||||
\(529\) | −15.5856 | −0.677635 | ||||||||
\(530\) | −29.3219 | −1.27366 | ||||||||
\(531\) | −15.0911 | −0.654897 | ||||||||
\(532\) | −17.1135 | −0.741964 | ||||||||
\(533\) | −1.69386 | −0.0733693 | ||||||||
\(534\) | 29.0606 | 1.25757 | ||||||||
\(535\) | 18.8431 | 0.814658 | ||||||||
\(536\) | −11.9695 | −0.517003 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | −13.5832 | −0.585613 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 14.0844 | 0.606096 | ||||||||
\(541\) | 28.7678 | 1.23682 | 0.618411 | − | 0.785855i | \(-0.287777\pi\) | ||||
0.618411 | + | 0.785855i | \(0.287777\pi\) | |||||||
\(542\) | −1.85360 | −0.0796188 | ||||||||
\(543\) | −20.5989 | −0.883985 | ||||||||
\(544\) | 16.8918 | 0.724228 | ||||||||
\(545\) | 59.1846 | 2.53519 | ||||||||
\(546\) | 9.29947 | 0.397981 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 5.66237 | 0.241885 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −24.8140 | −1.05807 | ||||||||
\(551\) | 37.9828 | 1.61812 | ||||||||
\(552\) | 10.1373 | 0.431473 | ||||||||
\(553\) | 5.44588 | 0.231582 | ||||||||
\(554\) | 27.3219 | 1.16080 | ||||||||
\(555\) | −21.6900 | −0.920690 | ||||||||
\(556\) | −61.5088 | −2.60856 | ||||||||
\(557\) | −13.5079 | −0.572347 | −0.286173 | − | 0.958178i | \(-0.592383\pi\) | ||||
−0.286173 | + | 0.958178i | \(0.592383\pi\) | |||||||
\(558\) | −2.72294 | −0.115271 | ||||||||
\(559\) | −26.4750 | −1.11977 | ||||||||
\(560\) | 6.45254 | 0.272670 | ||||||||
\(561\) | −4.72294 | −0.199403 | ||||||||
\(562\) | 59.6504 | 2.51620 | ||||||||
\(563\) | 24.7811 | 1.04440 | 0.522199 | − | 0.852824i | \(-0.325112\pi\) | ||||
0.522199 | + | 0.852824i | \(0.325112\pi\) | |||||||
\(564\) | 31.4196 | 1.32300 | ||||||||
\(565\) | −29.3219 | −1.23358 | ||||||||
\(566\) | 25.8984 | 1.08859 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −50.0582 | −2.10039 | ||||||||
\(569\) | 1.75201 | 0.0734482 | 0.0367241 | − | 0.999325i | \(-0.488308\pi\) | ||||
0.0367241 | + | 0.999325i | \(0.488308\pi\) | |||||||
\(570\) | −44.4974 | −1.86379 | ||||||||
\(571\) | −3.16640 | −0.132510 | −0.0662549 | − | 0.997803i | \(-0.521105\pi\) | ||||
−0.0662549 | + | 0.997803i | \(0.521105\pi\) | |||||||
\(572\) | −14.0844 | −0.588899 | ||||||||
\(573\) | 14.5989 | 0.609880 | ||||||||
\(574\) | 1.01574 | 0.0423963 | ||||||||
\(575\) | 28.6123 | 1.19321 | ||||||||
\(576\) | −11.7229 | −0.488456 | ||||||||
\(577\) | 20.4750 | 0.852383 | 0.426192 | − | 0.904633i | \(-0.359855\pi\) | ||||
0.426192 | + | 0.904633i | \(0.359855\pi\) | |||||||
\(578\) | −12.5303 | −0.521191 | ||||||||
\(579\) | −13.4592 | −0.559346 | ||||||||
\(580\) | −111.802 | −4.64233 | ||||||||
\(581\) | 2.84693 | 0.118111 | ||||||||
\(582\) | 26.3376 | 1.09173 | ||||||||
\(583\) | −3.15307 | −0.130587 | ||||||||
\(584\) | −44.4444 | −1.83912 | ||||||||
\(585\) | 15.5079 | 0.641172 | ||||||||
\(586\) | −34.7992 | −1.43754 | ||||||||
\(587\) | −16.6609 | −0.687671 | −0.343835 | − | 0.939030i | \(-0.611726\pi\) | ||||
−0.343835 | + | 0.939030i | \(0.611726\pi\) | |||||||
\(588\) | −3.57653 | −0.147494 | ||||||||
\(589\) | 5.51736 | 0.227339 | ||||||||
\(590\) | −140.339 | −5.77767 | ||||||||
\(591\) | −11.4459 | −0.470820 | ||||||||
\(592\) | −9.02482 | −0.370918 | ||||||||
\(593\) | 27.9075 | 1.14602 | 0.573012 | − | 0.819547i | \(-0.305775\pi\) | ||||
0.573012 | + | 0.819547i | \(0.305775\pi\) | |||||||
\(594\) | 2.36147 | 0.0968922 | ||||||||
\(595\) | 18.5989 | 0.762482 | ||||||||
\(596\) | 57.0028 | 2.33493 | ||||||||
\(597\) | 13.0291 | 0.533245 | ||||||||
\(598\) | 25.3219 | 1.03549 | ||||||||
\(599\) | −24.3376 | −0.994408 | −0.497204 | − | 0.867634i | \(-0.665640\pi\) | ||||
−0.497204 | + | 0.867634i | \(0.665640\pi\) | |||||||
\(600\) | 39.1201 | 1.59707 | ||||||||
\(601\) | −9.50787 | −0.387834 | −0.193917 | − | 0.981018i | \(-0.562119\pi\) | ||||
−0.193917 | + | 0.981018i | \(0.562119\pi\) | |||||||
\(602\) | 15.8760 | 0.647058 | ||||||||
\(603\) | 3.21507 | 0.130928 | ||||||||
\(604\) | 23.6014 | 0.960325 | ||||||||
\(605\) | −3.93800 | −0.160103 | ||||||||
\(606\) | 38.9051 | 1.58041 | ||||||||
\(607\) | 26.8431 | 1.08953 | 0.544764 | − | 0.838590i | \(-0.316619\pi\) | ||||
0.544764 | + | 0.838590i | \(0.316619\pi\) | |||||||
\(608\) | 17.1135 | 0.694043 | ||||||||
\(609\) | 7.93800 | 0.321664 | ||||||||
\(610\) | 55.7968 | 2.25915 | ||||||||
\(611\) | 34.5951 | 1.39957 | ||||||||
\(612\) | 16.8918 | 0.682809 | ||||||||
\(613\) | −23.0291 | −0.930136 | −0.465068 | − | 0.885275i | \(-0.653970\pi\) | ||||
−0.465068 | + | 0.885275i | \(0.653970\pi\) | |||||||
\(614\) | −2.03149 | −0.0819841 | ||||||||
\(615\) | 1.69386 | 0.0683031 | ||||||||
\(616\) | 3.72294 | 0.150001 | ||||||||
\(617\) | 31.4459 | 1.26596 | 0.632982 | − | 0.774167i | \(-0.281831\pi\) | ||||
0.632982 | + | 0.774167i | \(0.281831\pi\) | |||||||
\(618\) | −3.70719 | −0.149125 | ||||||||
\(619\) | 2.26132 | 0.0908901 | 0.0454450 | − | 0.998967i | \(-0.485529\pi\) | ||||
0.0454450 | + | 0.998967i | \(0.485529\pi\) | |||||||
\(620\) | −16.2403 | −0.652226 | ||||||||
\(621\) | −2.72294 | −0.109268 | ||||||||
\(622\) | −63.5040 | −2.54628 | ||||||||
\(623\) | −12.3061 | −0.493035 | ||||||||
\(624\) | 6.45254 | 0.258308 | ||||||||
\(625\) | 32.8760 | 1.31504 | ||||||||
\(626\) | −24.0133 | −0.959766 | ||||||||
\(627\) | −4.78493 | −0.191092 | ||||||||
\(628\) | 26.1870 | 1.04497 | ||||||||
\(629\) | −26.0133 | −1.03722 | ||||||||
\(630\) | −9.29947 | −0.370500 | ||||||||
\(631\) | 10.3061 | 0.410281 | 0.205140 | − | 0.978733i | \(-0.434235\pi\) | ||||
0.205140 | + | 0.978733i | \(0.434235\pi\) | |||||||
\(632\) | 20.2747 | 0.806482 | ||||||||
\(633\) | −2.43013 | −0.0965891 | ||||||||
\(634\) | 64.9184 | 2.57824 | ||||||||
\(635\) | −48.4091 | −1.92106 | ||||||||
\(636\) | 11.2771 | 0.447165 | ||||||||
\(637\) | −3.93800 | −0.156029 | ||||||||
\(638\) | −18.7453 | −0.742135 | ||||||||
\(639\) | 13.4459 | 0.531911 | ||||||||
\(640\) | −80.8483 | −3.19581 | ||||||||
\(641\) | 4.13733 | 0.163415 | 0.0817073 | − | 0.996656i | \(-0.473963\pi\) | ||||
0.0817073 | + | 0.996656i | \(0.473963\pi\) | |||||||
\(642\) | −11.2995 | −0.445955 | ||||||||
\(643\) | −8.44347 | −0.332978 | −0.166489 | − | 0.986043i | \(-0.553243\pi\) | ||||
−0.166489 | + | 0.986043i | \(0.553243\pi\) | |||||||
\(644\) | −9.73868 | −0.383758 | ||||||||
\(645\) | 26.4750 | 1.04245 | ||||||||
\(646\) | −53.3667 | −2.09968 | ||||||||
\(647\) | −25.2732 | −0.993593 | −0.496796 | − | 0.867867i | \(-0.665490\pi\) | ||||
−0.496796 | + | 0.867867i | \(0.665490\pi\) | |||||||
\(648\) | −3.72294 | −0.146251 | ||||||||
\(649\) | −15.0911 | −0.592376 | ||||||||
\(650\) | 97.7177 | 3.83280 | ||||||||
\(651\) | 1.15307 | 0.0451924 | ||||||||
\(652\) | 50.4535 | 1.97591 | ||||||||
\(653\) | 47.9075 | 1.87477 | 0.937383 | − | 0.348302i | \(-0.113241\pi\) | ||||
0.937383 | + | 0.348302i | \(0.113241\pi\) | |||||||
\(654\) | −35.4907 | −1.38780 | ||||||||
\(655\) | −28.1163 | −1.09859 | ||||||||
\(656\) | 0.704785 | 0.0275172 | ||||||||
\(657\) | 11.9380 | 0.465746 | ||||||||
\(658\) | −20.7453 | −0.808738 | ||||||||
\(659\) | −28.2890 | −1.10198 | −0.550991 | − | 0.834511i | \(-0.685750\pi\) | ||||
−0.550991 | + | 0.834511i | \(0.685750\pi\) | |||||||
\(660\) | 14.0844 | 0.548235 | ||||||||
\(661\) | 19.7653 | 0.768783 | 0.384391 | − | 0.923170i | \(-0.374411\pi\) | ||||
0.384391 | + | 0.923170i | \(0.374411\pi\) | |||||||
\(662\) | 40.6123 | 1.57844 | ||||||||
\(663\) | 18.5989 | 0.722323 | ||||||||
\(664\) | 10.5989 | 0.411319 | ||||||||
\(665\) | 18.8431 | 0.730704 | ||||||||
\(666\) | 13.0067 | 0.503998 | ||||||||
\(667\) | 21.6147 | 0.836924 | ||||||||
\(668\) | −1.49069 | −0.0576767 | ||||||||
\(669\) | −22.7678 | −0.880252 | ||||||||
\(670\) | 29.8984 | 1.15508 | ||||||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | 3.57653 | 0.137968 | ||||||||
\(673\) | −51.5174 | −1.98585 | −0.992924 | − | 0.118750i | \(-0.962111\pi\) | ||||
−0.992924 | + | 0.118750i | \(0.962111\pi\) | |||||||
\(674\) | −46.6123 | −1.79544 | ||||||||
\(675\) | −10.5079 | −0.404448 | ||||||||
\(676\) | 8.96949 | 0.344980 | ||||||||
\(677\) | 46.3376 | 1.78090 | 0.890450 | − | 0.455081i | \(-0.150390\pi\) | ||||
0.890450 | + | 0.455081i | \(0.150390\pi\) | |||||||
\(678\) | 17.5832 | 0.675279 | ||||||||
\(679\) | −11.1531 | −0.428016 | ||||||||
\(680\) | 69.2427 | 2.65534 | ||||||||
\(681\) | 15.8760 | 0.608370 | ||||||||
\(682\) | −2.72294 | −0.104267 | ||||||||
\(683\) | −39.2112 | −1.50038 | −0.750188 | − | 0.661225i | \(-0.770037\pi\) | ||||
−0.750188 | + | 0.661225i | \(0.770037\pi\) | |||||||
\(684\) | 17.1135 | 0.654350 | ||||||||
\(685\) | −6.23465 | −0.238214 | ||||||||
\(686\) | 2.36147 | 0.0901613 | ||||||||
\(687\) | 3.15307 | 0.120297 | ||||||||
\(688\) | 11.0157 | 0.419971 | ||||||||
\(689\) | 12.4168 | 0.473042 | ||||||||
\(690\) | −25.3219 | −0.963988 | ||||||||
\(691\) | 7.62802 | 0.290184 | 0.145092 | − | 0.989418i | \(-0.453652\pi\) | ||||
0.145092 | + | 0.989418i | \(0.453652\pi\) | |||||||
\(692\) | −30.1507 | −1.14616 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | −39.2294 | −1.48913 | ||||||||
\(695\) | 67.7253 | 2.56897 | ||||||||
\(696\) | 29.5527 | 1.12019 | ||||||||
\(697\) | 2.03149 | 0.0769480 | ||||||||
\(698\) | −16.4211 | −0.621546 | ||||||||
\(699\) | −13.1397 | −0.496990 | ||||||||
\(700\) | −37.5818 | −1.42046 | ||||||||
\(701\) | 2.61228 | 0.0986644 | 0.0493322 | − | 0.998782i | \(-0.484291\pi\) | ||||
0.0493322 | + | 0.998782i | \(0.484291\pi\) | |||||||
\(702\) | −9.29947 | −0.350986 | ||||||||
\(703\) | −26.3548 | −0.993990 | ||||||||
\(704\) | −11.7229 | −0.441825 | ||||||||
\(705\) | −34.5951 | −1.30293 | ||||||||
\(706\) | 7.62376 | 0.286924 | ||||||||
\(707\) | −16.4750 | −0.619604 | ||||||||
\(708\) | 53.9737 | 2.02846 | ||||||||
\(709\) | 36.1516 | 1.35770 | 0.678852 | − | 0.734276i | \(-0.262478\pi\) | ||||
0.678852 | + | 0.734276i | \(0.262478\pi\) | |||||||
\(710\) | 125.040 | 4.69265 | ||||||||
\(711\) | −5.44588 | −0.204236 | ||||||||
\(712\) | −45.8150 | −1.71699 | ||||||||
\(713\) | 3.13974 | 0.117584 | ||||||||
\(714\) | −11.1531 | −0.417393 | ||||||||
\(715\) | 15.5079 | 0.579962 | ||||||||
\(716\) | −42.9184 | −1.60394 | ||||||||
\(717\) | 10.1068 | 0.377446 | ||||||||
\(718\) | −24.3376 | −0.908272 | ||||||||
\(719\) | 19.6767 | 0.733816 | 0.366908 | − | 0.930257i | \(-0.380416\pi\) | ||||
0.366908 | + | 0.930257i | \(0.380416\pi\) | |||||||
\(720\) | −6.45254 | −0.240472 | ||||||||
\(721\) | 1.56987 | 0.0584649 | ||||||||
\(722\) | −9.19932 | −0.342363 | ||||||||
\(723\) | −2.36814 | −0.0880719 | ||||||||
\(724\) | 73.6728 | 2.73803 | ||||||||
\(725\) | 83.4115 | 3.09783 | ||||||||
\(726\) | 2.36147 | 0.0876423 | ||||||||
\(727\) | 2.47495 | 0.0917909 | 0.0458954 | − | 0.998946i | \(-0.485386\pi\) | ||||
0.0458954 | + | 0.998946i | \(0.485386\pi\) | |||||||
\(728\) | −14.6609 | −0.543371 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 111.017 | 4.10893 | ||||||||
\(731\) | 31.7520 | 1.17439 | ||||||||
\(732\) | −21.4592 | −0.793155 | ||||||||
\(733\) | −40.0315 | −1.47860 | −0.739298 | − | 0.673378i | \(-0.764843\pi\) | ||||
−0.739298 | + | 0.673378i | \(0.764843\pi\) | |||||||
\(734\) | 28.0448 | 1.03515 | ||||||||
\(735\) | 3.93800 | 0.145255 | ||||||||
\(736\) | 9.73868 | 0.358973 | ||||||||
\(737\) | 3.21507 | 0.118428 | ||||||||
\(738\) | −1.01574 | −0.0373900 | ||||||||
\(739\) | 25.2771 | 0.929832 | 0.464916 | − | 0.885355i | \(-0.346085\pi\) | ||||
0.464916 | + | 0.885355i | \(0.346085\pi\) | |||||||
\(740\) | 77.5751 | 2.85172 | ||||||||
\(741\) | 18.8431 | 0.692218 | ||||||||
\(742\) | −7.44588 | −0.273347 | ||||||||
\(743\) | 2.10682 | 0.0772916 | 0.0386458 | − | 0.999253i | \(-0.487696\pi\) | ||||
0.0386458 | + | 0.999253i | \(0.487696\pi\) | |||||||
\(744\) | 4.29281 | 0.157382 | ||||||||
\(745\) | −62.7639 | −2.29949 | ||||||||
\(746\) | −39.4907 | −1.44586 | ||||||||
\(747\) | −2.84693 | −0.104164 | ||||||||
\(748\) | 16.8918 | 0.617624 | ||||||||
\(749\) | 4.78493 | 0.174838 | ||||||||
\(750\) | −51.2203 | −1.87030 | ||||||||
\(751\) | −45.9828 | −1.67794 | −0.838969 | − | 0.544180i | \(-0.816841\pi\) | ||||
−0.838969 | + | 0.544180i | \(0.816841\pi\) | |||||||
\(752\) | −14.3944 | −0.524909 | ||||||||
\(753\) | −10.2308 | −0.372831 | ||||||||
\(754\) | 73.8192 | 2.68834 | ||||||||
\(755\) | −25.9867 | −0.945752 | ||||||||
\(756\) | 3.57653 | 0.130077 | ||||||||
\(757\) | −29.2599 | −1.06347 | −0.531734 | − | 0.846911i | \(-0.678460\pi\) | ||||
−0.531734 | + | 0.846911i | \(0.678460\pi\) | |||||||
\(758\) | 25.8984 | 0.940673 | ||||||||
\(759\) | −2.72294 | −0.0988364 | ||||||||
\(760\) | 70.1516 | 2.54467 | ||||||||
\(761\) | 21.8760 | 0.793005 | 0.396502 | − | 0.918034i | \(-0.370224\pi\) | ||||
0.396502 | + | 0.918034i | \(0.370224\pi\) | |||||||
\(762\) | 29.0291 | 1.05161 | ||||||||
\(763\) | 15.0291 | 0.544089 | ||||||||
\(764\) | −52.2136 | −1.88902 | ||||||||
\(765\) | −18.5989 | −0.672446 | ||||||||
\(766\) | −37.1979 | −1.34401 | ||||||||
\(767\) | 59.4287 | 2.14585 | ||||||||
\(768\) | 25.0357 | 0.903400 | ||||||||
\(769\) | −16.2756 | −0.586914 | −0.293457 | − | 0.955972i | \(-0.594806\pi\) | ||||
−0.293457 | + | 0.955972i | \(0.594806\pi\) | |||||||
\(770\) | −9.29947 | −0.335130 | ||||||||
\(771\) | 11.0777 | 0.398955 | ||||||||
\(772\) | 48.1373 | 1.73250 | ||||||||
\(773\) | −30.4921 | −1.09673 | −0.548363 | − | 0.836241i | \(-0.684749\pi\) | ||||
−0.548363 | + | 0.836241i | \(0.684749\pi\) | |||||||
\(774\) | −15.8760 | −0.570651 | ||||||||
\(775\) | 12.1163 | 0.435231 | ||||||||
\(776\) | −41.5222 | −1.49056 | ||||||||
\(777\) | −5.50787 | −0.197594 | ||||||||
\(778\) | −86.8259 | −3.11286 | ||||||||
\(779\) | 2.05815 | 0.0737410 | ||||||||
\(780\) | −55.4644 | −1.98595 | ||||||||
\(781\) | 13.4459 | 0.481131 | ||||||||
\(782\) | −30.3691 | −1.08600 | ||||||||
\(783\) | −7.93800 | −0.283681 | ||||||||
\(784\) | 1.63853 | 0.0585190 | ||||||||
\(785\) | −28.8336 | −1.02912 | ||||||||
\(786\) | 16.8603 | 0.601386 | ||||||||
\(787\) | 35.2151 | 1.25528 | 0.627641 | − | 0.778503i | \(-0.284021\pi\) | ||||
0.627641 | + | 0.778503i | \(0.284021\pi\) | |||||||
\(788\) | 40.9366 | 1.45830 | ||||||||
\(789\) | 8.78493 | 0.312752 | ||||||||
\(790\) | −50.6438 | −1.80182 | ||||||||
\(791\) | −7.44588 | −0.264745 | ||||||||
\(792\) | −3.72294 | −0.132289 | ||||||||
\(793\) | −23.6280 | −0.839056 | ||||||||
\(794\) | −28.0133 | −0.994156 | ||||||||
\(795\) | −12.4168 | −0.440378 | ||||||||
\(796\) | −46.5989 | −1.65166 | ||||||||
\(797\) | −14.9804 | −0.530633 | −0.265317 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265317 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(798\) | −11.2995 | −0.399997 | ||||||||
\(799\) | −41.4907 | −1.46784 | ||||||||
\(800\) | 37.5818 | 1.32872 | ||||||||
\(801\) | 12.3061 | 0.434816 | ||||||||
\(802\) | −8.03149 | −0.283602 | ||||||||
\(803\) | 11.9380 | 0.421283 | ||||||||
\(804\) | −11.4988 | −0.405531 | ||||||||
\(805\) | 10.7229 | 0.377934 | ||||||||
\(806\) | 10.7229 | 0.377699 | ||||||||
\(807\) | −5.75201 | −0.202480 | ||||||||
\(808\) | −61.3352 | −2.15777 | ||||||||
\(809\) | −25.2599 | −0.888090 | −0.444045 | − | 0.896004i | \(-0.646457\pi\) | ||||
−0.444045 | + | 0.896004i | \(0.646457\pi\) | |||||||
\(810\) | 9.29947 | 0.326750 | ||||||||
\(811\) | 29.5212 | 1.03663 | 0.518315 | − | 0.855190i | \(-0.326560\pi\) | ||||
0.518315 | + | 0.855190i | \(0.326560\pi\) | |||||||
\(812\) | −28.3905 | −0.996313 | ||||||||
\(813\) | −0.784934 | −0.0275288 | ||||||||
\(814\) | 13.0067 | 0.455883 | ||||||||
\(815\) | −55.5527 | −1.94593 | ||||||||
\(816\) | −7.73868 | −0.270908 | ||||||||
\(817\) | 32.1688 | 1.12544 | ||||||||
\(818\) | 66.1955 | 2.31447 | ||||||||
\(819\) | 3.93800 | 0.137605 | ||||||||
\(820\) | −6.05815 | −0.211560 | ||||||||
\(821\) | 23.7873 | 0.830184 | 0.415092 | − | 0.909779i | \(-0.363749\pi\) | ||||
0.415092 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(822\) | 3.73868 | 0.130401 | ||||||||
\(823\) | 17.7692 | 0.619395 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(824\) | 5.84452 | 0.203604 | ||||||||
\(825\) | −10.5079 | −0.365837 | ||||||||
\(826\) | −35.6371 | −1.23997 | ||||||||
\(827\) | 8.90893 | 0.309794 | 0.154897 | − | 0.987931i | \(-0.450495\pi\) | ||||
0.154897 | + | 0.987931i | \(0.450495\pi\) | |||||||
\(828\) | 9.73868 | 0.338443 | ||||||||
\(829\) | −32.7678 | −1.13807 | −0.569036 | − | 0.822313i | \(-0.692683\pi\) | ||||
−0.569036 | + | 0.822313i | \(0.692683\pi\) | |||||||
\(830\) | −26.4750 | −0.918959 | ||||||||
\(831\) | 11.5699 | 0.401354 | ||||||||
\(832\) | 46.1650 | 1.60048 | ||||||||
\(833\) | 4.72294 | 0.163640 | ||||||||
\(834\) | −40.6123 | −1.40629 | ||||||||
\(835\) | 1.64135 | 0.0568014 | ||||||||
\(836\) | 17.1135 | 0.591882 | ||||||||
\(837\) | −1.15307 | −0.0398559 | ||||||||
\(838\) | −66.8035 | −2.30769 | ||||||||
\(839\) | 6.96708 | 0.240530 | 0.120265 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120265 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(840\) | 14.6609 | 0.505851 | ||||||||
\(841\) | 34.0119 | 1.17282 | ||||||||
\(842\) | 34.2227 | 1.17939 | ||||||||
\(843\) | 25.2599 | 0.869997 | ||||||||
\(844\) | 8.69145 | 0.299172 | ||||||||
\(845\) | −9.87601 | −0.339745 | ||||||||
\(846\) | 20.7453 | 0.713240 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −5.16640 | −0.177415 | ||||||||
\(849\) | 10.9671 | 0.376389 | ||||||||
\(850\) | −117.195 | −4.01976 | ||||||||
\(851\) | −14.9976 | −0.514111 | ||||||||
\(852\) | −48.0896 | −1.64752 | ||||||||
\(853\) | 11.1979 | 0.383408 | 0.191704 | − | 0.981453i | \(-0.438599\pi\) | ||||
0.191704 | + | 0.981453i | \(0.438599\pi\) | |||||||
\(854\) | 14.1688 | 0.484847 | ||||||||
\(855\) | −18.8431 | −0.644420 | ||||||||
\(856\) | 17.8140 | 0.608870 | ||||||||
\(857\) | −44.0315 | −1.50409 | −0.752043 | − | 0.659114i | \(-0.770932\pi\) | ||||
−0.752043 | + | 0.659114i | \(0.770932\pi\) | |||||||
\(858\) | −9.29947 | −0.317479 | ||||||||
\(859\) | 7.13974 | 0.243605 | 0.121802 | − | 0.992554i | \(-0.461133\pi\) | ||||
0.121802 | + | 0.992554i | \(0.461133\pi\) | |||||||
\(860\) | −94.6886 | −3.22885 | ||||||||
\(861\) | 0.430132 | 0.0146589 | ||||||||
\(862\) | 57.9432 | 1.97355 | ||||||||
\(863\) | −5.27706 | −0.179633 | −0.0898166 | − | 0.995958i | \(-0.528628\pi\) | ||||
−0.0898166 | + | 0.995958i | \(0.528628\pi\) | |||||||
\(864\) | −3.57653 | −0.121676 | ||||||||
\(865\) | 33.1979 | 1.12876 | ||||||||
\(866\) | 17.2904 | 0.587552 | ||||||||
\(867\) | −5.30614 | −0.180206 | ||||||||
\(868\) | −4.12399 | −0.139977 | ||||||||
\(869\) | −5.44588 | −0.184739 | ||||||||
\(870\) | −73.8192 | −2.50271 | ||||||||
\(871\) | −12.6609 | −0.429000 | ||||||||
\(872\) | 55.9523 | 1.89478 | ||||||||
\(873\) | 11.1531 | 0.377474 | ||||||||
\(874\) | −30.7678 | −1.04073 | ||||||||
\(875\) | 21.6900 | 0.733256 | ||||||||
\(876\) | −42.6967 | −1.44259 | ||||||||
\(877\) | −32.4301 | −1.09509 | −0.547544 | − | 0.836777i | \(-0.684437\pi\) | ||||
−0.547544 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(878\) | −39.0515 | −1.31792 | ||||||||
\(879\) | −14.7363 | −0.497042 | ||||||||
\(880\) | −6.45254 | −0.217515 | ||||||||
\(881\) | 39.5660 | 1.33301 | 0.666507 | − | 0.745499i | \(-0.267789\pi\) | ||||
0.666507 | + | 0.745499i | \(0.267789\pi\) | |||||||
\(882\) | −2.36147 | −0.0795148 | ||||||||
\(883\) | −24.4130 | −0.821561 | −0.410781 | − | 0.911734i | \(-0.634744\pi\) | ||||
−0.410781 | + | 0.911734i | \(0.634744\pi\) | |||||||
\(884\) | −66.5198 | −2.23730 | ||||||||
\(885\) | −59.4287 | −1.99767 | ||||||||
\(886\) | −59.5040 | −1.99908 | ||||||||
\(887\) | 36.2928 | 1.21859 | 0.609297 | − | 0.792942i | \(-0.291452\pi\) | ||||
0.609297 | + | 0.792942i | \(0.291452\pi\) | |||||||
\(888\) | −20.5055 | −0.688118 | ||||||||
\(889\) | −12.2928 | −0.412287 | ||||||||
\(890\) | 114.441 | 3.83606 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 81.4297 | 2.72647 | ||||||||
\(893\) | −42.0353 | −1.40666 | ||||||||
\(894\) | 37.6371 | 1.25877 | ||||||||
\(895\) | 47.2560 | 1.57960 | ||||||||
\(896\) | −20.5303 | −0.685869 | ||||||||
\(897\) | 10.7229 | 0.358028 | ||||||||
\(898\) | 86.2403 | 2.87788 | ||||||||
\(899\) | 9.15307 | 0.305272 | ||||||||
\(900\) | 37.5818 | 1.25273 | ||||||||
\(901\) | −14.8918 | −0.496116 | ||||||||
\(902\) | −1.01574 | −0.0338205 | ||||||||
\(903\) | 6.72294 | 0.223725 | ||||||||
\(904\) | −27.7205 | −0.921971 | ||||||||
\(905\) | −81.1187 | −2.69648 | ||||||||
\(906\) | 15.5832 | 0.517717 | ||||||||
\(907\) | −30.3958 | −1.00928 | −0.504638 | − | 0.863331i | \(-0.668374\pi\) | ||||
−0.504638 | + | 0.863331i | \(0.668374\pi\) | |||||||
\(908\) | −56.7811 | −1.88435 | ||||||||
\(909\) | 16.4750 | 0.546440 | ||||||||
\(910\) | 36.6214 | 1.21399 | ||||||||
\(911\) | −56.8259 | −1.88273 | −0.941363 | − | 0.337395i | \(-0.890454\pi\) | ||||
−0.941363 | + | 0.337395i | \(0.890454\pi\) | |||||||
\(912\) | −7.84026 | −0.259617 | ||||||||
\(913\) | −2.84693 | −0.0942196 | ||||||||
\(914\) | −7.44588 | −0.246288 | ||||||||
\(915\) | 23.6280 | 0.781118 | ||||||||
\(916\) | −11.2771 | −0.372605 | ||||||||
\(917\) | −7.13974 | −0.235775 | ||||||||
\(918\) | 11.1531 | 0.368106 | ||||||||
\(919\) | −40.1688 | −1.32505 | −0.662523 | − | 0.749041i | \(-0.730514\pi\) | ||||
−0.662523 | + | 0.749041i | \(0.730514\pi\) | |||||||
\(920\) | 39.9208 | 1.31615 | ||||||||
\(921\) | −0.860264 | −0.0283467 | ||||||||
\(922\) | 58.4883 | 1.92621 | ||||||||
\(923\) | −52.9499 | −1.74287 | ||||||||
\(924\) | 3.57653 | 0.117659 | ||||||||
\(925\) | −57.8760 | −1.90295 | ||||||||
\(926\) | 83.6638 | 2.74936 | ||||||||
\(927\) | −1.56987 | −0.0515612 | ||||||||
\(928\) | 28.3905 | 0.931965 | ||||||||
\(929\) | −27.3180 | −0.896276 | −0.448138 | − | 0.893964i | \(-0.647913\pi\) | ||||
−0.448138 | + | 0.893964i | \(0.647913\pi\) | |||||||
\(930\) | −10.7229 | −0.351619 | ||||||||
\(931\) | 4.78493 | 0.156820 | ||||||||
\(932\) | 46.9947 | 1.53936 | ||||||||
\(933\) | −26.8918 | −0.880396 | ||||||||
\(934\) | 56.4974 | 1.84865 | ||||||||
\(935\) | −18.5989 | −0.608251 | ||||||||
\(936\) | 14.6609 | 0.479208 | ||||||||
\(937\) | −5.75201 | −0.187910 | −0.0939551 | − | 0.995576i | \(-0.529951\pi\) | ||||
−0.0939551 | + | 0.995576i | \(0.529951\pi\) | |||||||
\(938\) | 7.59228 | 0.247897 | ||||||||
\(939\) | −10.1688 | −0.331847 | ||||||||
\(940\) | 123.731 | 4.03565 | ||||||||
\(941\) | −27.5699 | −0.898752 | −0.449376 | − | 0.893343i | \(-0.648354\pi\) | ||||
−0.449376 | + | 0.893343i | \(0.648354\pi\) | |||||||
\(942\) | 17.2904 | 0.563352 | ||||||||
\(943\) | 1.17122 | 0.0381402 | ||||||||
\(944\) | −24.7272 | −0.804802 | ||||||||
\(945\) | −3.93800 | −0.128103 | ||||||||
\(946\) | −15.8760 | −0.516174 | ||||||||
\(947\) | 37.0739 | 1.20474 | 0.602370 | − | 0.798217i | \(-0.294223\pi\) | ||||
0.602370 | + | 0.798217i | \(0.294223\pi\) | |||||||
\(948\) | 19.4774 | 0.632595 | ||||||||
\(949\) | −47.0119 | −1.52607 | ||||||||
\(950\) | −118.733 | −3.85222 | ||||||||
\(951\) | 27.4907 | 0.891447 | ||||||||
\(952\) | 17.5832 | 0.569875 | ||||||||
\(953\) | −12.0620 | −0.390726 | −0.195363 | − | 0.980731i | \(-0.562589\pi\) | ||||
−0.195363 | + | 0.980731i | \(0.562589\pi\) | |||||||
\(954\) | 7.44588 | 0.241069 | ||||||||
\(955\) | 57.4907 | 1.86036 | ||||||||
\(956\) | −36.1474 | −1.16909 | ||||||||
\(957\) | −7.93800 | −0.256599 | ||||||||
\(958\) | −10.7229 | −0.346442 | ||||||||
\(959\) | −1.58320 | −0.0511242 | ||||||||
\(960\) | −46.1650 | −1.48997 | ||||||||
\(961\) | −29.6704 | −0.957111 | ||||||||
\(962\) | −51.2203 | −1.65141 | ||||||||
\(963\) | −4.78493 | −0.154192 | ||||||||
\(964\) | 8.46972 | 0.272791 | ||||||||
\(965\) | −53.0024 | −1.70621 | ||||||||
\(966\) | −6.43013 | −0.206886 | ||||||||
\(967\) | 6.43013 | 0.206779 | 0.103390 | − | 0.994641i | \(-0.467031\pi\) | ||||
0.103390 | + | 0.994641i | \(0.467031\pi\) | |||||||
\(968\) | −3.72294 | −0.119660 | ||||||||
\(969\) | −22.5989 | −0.725983 | ||||||||
\(970\) | 103.718 | 3.33017 | ||||||||
\(971\) | −35.3047 | −1.13298 | −0.566491 | − | 0.824068i | \(-0.691699\pi\) | ||||
−0.566491 | + | 0.824068i | \(0.691699\pi\) | |||||||
\(972\) | −3.57653 | −0.114717 | ||||||||
\(973\) | 17.1979 | 0.551339 | ||||||||
\(974\) | −64.0896 | −2.05356 | ||||||||
\(975\) | 41.3800 | 1.32522 | ||||||||
\(976\) | 9.83119 | 0.314689 | ||||||||
\(977\) | 0.261319 | 0.00836035 | 0.00418017 | − | 0.999991i | \(-0.498669\pi\) | ||||
0.00418017 | + | 0.999991i | \(0.498669\pi\) | |||||||
\(978\) | 33.3128 | 1.06523 | ||||||||
\(979\) | 12.3061 | 0.393306 | ||||||||
\(980\) | −14.0844 | −0.449910 | ||||||||
\(981\) | −15.0291 | −0.479841 | ||||||||
\(982\) | −8.17789 | −0.260967 | ||||||||
\(983\) | −16.3376 | −0.521089 | −0.260545 | − | 0.965462i | \(-0.583902\pi\) | ||||
−0.260545 | + | 0.965462i | \(0.583902\pi\) | |||||||
\(984\) | 1.60135 | 0.0510493 | ||||||||
\(985\) | −45.0739 | −1.43617 | ||||||||
\(986\) | −88.5331 | −2.81947 | ||||||||
\(987\) | −8.78493 | −0.279628 | ||||||||
\(988\) | −67.3930 | −2.14406 | ||||||||
\(989\) | 18.3061 | 0.582101 | ||||||||
\(990\) | 9.29947 | 0.295557 | ||||||||
\(991\) | −36.2623 | −1.15191 | −0.575955 | − | 0.817481i | \(-0.695370\pi\) | ||||
−0.575955 | + | 0.817481i | \(0.695370\pi\) | |||||||
\(992\) | 4.12399 | 0.130937 | ||||||||
\(993\) | 17.1979 | 0.545759 | ||||||||
\(994\) | 31.7520 | 1.00711 | ||||||||
\(995\) | 51.3085 | 1.62659 | ||||||||
\(996\) | 10.1821 | 0.322634 | ||||||||
\(997\) | −3.47254 | −0.109977 | −0.0549883 | − | 0.998487i | \(-0.517512\pi\) | ||||
−0.0549883 | + | 0.998487i | \(0.517512\pi\) | |||||||
\(998\) | 44.7902 | 1.41781 | ||||||||
\(999\) | 5.50787 | 0.174261 |
(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 | 231.2.a.d.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 693.2.a.m.1.3 | 3 | |||
4.3 | odd | 2 | 3696.2.a.bp.1.1 | 3 | |||
5.4 | even | 2 | 5775.2.a.bw.1.3 | 3 | |||
7.6 | odd | 2 | 1617.2.a.s.1.1 | 3 | |||
11.10 | odd | 2 | 2541.2.a.bi.1.3 | 3 | |||
21.20 | even | 2 | 4851.2.a.bp.1.3 | 3 | |||
33.32 | even | 2 | 7623.2.a.cb.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.d.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
693.2.a.m.1.3 | 3 | 3.2 | odd | 2 | |||
1617.2.a.s.1.1 | 3 | 7.6 | odd | 2 | |||
2541.2.a.bi.1.3 | 3 | 11.10 | odd | 2 | |||
3696.2.a.bp.1.1 | 3 | 4.3 | odd | 2 | |||
4851.2.a.bp.1.3 | 3 | 21.20 | even | 2 | |||
5775.2.a.bw.1.3 | 3 | 5.4 | even | 2 | |||
7623.2.a.cb.1.1 | 3 | 33.32 | even | 2 |