Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.343018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.343018 | −0.153402 | −0.0767010 | − | 0.997054i | \(-0.524439\pi\) | ||||
−0.0767010 | + | 0.997054i | \(0.524439\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.39676 | 0.905889 | 0.452945 | − | 0.891539i | \(-0.350373\pi\) | ||||
0.452945 | + | 0.891539i | \(0.350373\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.343018 | 0.108472 | ||||||||
\(11\) | 1.78117 | 0.537044 | 0.268522 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268522 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.39676 | −0.640561 | ||||||||
\(15\) | 0.343018 | 0.0885667 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.22357 | 1.26690 | 0.633451 | − | 0.773783i | \(-0.281638\pi\) | ||||
0.633451 | + | 0.773783i | \(0.281638\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.94679 | −0.905456 | −0.452728 | − | 0.891649i | \(-0.649549\pi\) | ||||
−0.452728 | + | 0.891649i | \(0.649549\pi\) | |||||||
\(20\) | −0.343018 | −0.0767010 | ||||||||
\(21\) | −2.39676 | −0.523016 | ||||||||
\(22\) | −1.78117 | −0.379748 | ||||||||
\(23\) | 2.02924 | 0.423125 | 0.211562 | − | 0.977364i | \(-0.432145\pi\) | ||||
0.211562 | + | 0.977364i | \(0.432145\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.88234 | −0.976468 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.39676 | 0.452945 | ||||||||
\(29\) | −7.94406 | −1.47518 | −0.737588 | − | 0.675251i | \(-0.764035\pi\) | ||||
−0.737588 | + | 0.675251i | \(0.764035\pi\) | |||||||
\(30\) | −0.343018 | −0.0626261 | ||||||||
\(31\) | 2.26086 | 0.406063 | 0.203031 | − | 0.979172i | \(-0.434921\pi\) | ||||
0.203031 | + | 0.979172i | \(0.434921\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.78117 | −0.310063 | ||||||||
\(34\) | −5.22357 | −0.895835 | ||||||||
\(35\) | −0.822130 | −0.138965 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.14049 | 1.33829 | 0.669144 | − | 0.743133i | \(-0.266661\pi\) | ||||
0.669144 | + | 0.743133i | \(0.266661\pi\) | |||||||
\(38\) | 3.94679 | 0.640254 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.343018 | 0.0542358 | ||||||||
\(41\) | −0.158645 | −0.0247762 | −0.0123881 | − | 0.999923i | \(-0.503943\pi\) | ||||
−0.0123881 | + | 0.999923i | \(0.503943\pi\) | |||||||
\(42\) | 2.39676 | 0.369828 | ||||||||
\(43\) | 2.52136 | 0.384504 | 0.192252 | − | 0.981346i | \(-0.438421\pi\) | ||||
0.192252 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(44\) | 1.78117 | 0.268522 | ||||||||
\(45\) | −0.343018 | −0.0511340 | ||||||||
\(46\) | −2.02924 | −0.299194 | ||||||||
\(47\) | 7.07689 | 1.03227 | 0.516135 | − | 0.856507i | \(-0.327370\pi\) | ||||
0.516135 | + | 0.856507i | \(0.327370\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.25555 | −0.179364 | ||||||||
\(50\) | 4.88234 | 0.690467 | ||||||||
\(51\) | −5.22357 | −0.731446 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 6.10766 | 0.838951 | 0.419476 | − | 0.907767i | \(-0.362214\pi\) | ||||
0.419476 | + | 0.907767i | \(0.362214\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.610974 | −0.0823837 | ||||||||
\(56\) | −2.39676 | −0.320280 | ||||||||
\(57\) | 3.94679 | 0.522765 | ||||||||
\(58\) | 7.94406 | 1.04311 | ||||||||
\(59\) | −8.74158 | −1.13806 | −0.569028 | − | 0.822318i | \(-0.692681\pi\) | ||||
−0.569028 | + | 0.822318i | \(0.692681\pi\) | |||||||
\(60\) | 0.343018 | 0.0442834 | ||||||||
\(61\) | 3.19752 | 0.409400 | 0.204700 | − | 0.978825i | \(-0.434378\pi\) | ||||
0.204700 | + | 0.978825i | \(0.434378\pi\) | |||||||
\(62\) | −2.26086 | −0.287130 | ||||||||
\(63\) | 2.39676 | 0.301963 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.343018 | −0.0425461 | ||||||||
\(66\) | 1.78117 | 0.219247 | ||||||||
\(67\) | 7.84847 | 0.958843 | 0.479422 | − | 0.877585i | \(-0.340846\pi\) | ||||
0.479422 | + | 0.877585i | \(0.340846\pi\) | |||||||
\(68\) | 5.22357 | 0.633451 | ||||||||
\(69\) | −2.02924 | −0.244291 | ||||||||
\(70\) | 0.822130 | 0.0982633 | ||||||||
\(71\) | 7.09487 | 0.842006 | 0.421003 | − | 0.907059i | \(-0.361678\pi\) | ||||
0.421003 | + | 0.907059i | \(0.361678\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 17.0401 | 1.99439 | 0.997197 | − | 0.0748173i | \(-0.0238374\pi\) | ||||
0.997197 | + | 0.0748173i | \(0.0238374\pi\) | |||||||
\(74\) | −8.14049 | −0.946312 | ||||||||
\(75\) | 4.88234 | 0.563764 | ||||||||
\(76\) | −3.94679 | −0.452728 | ||||||||
\(77\) | 4.26904 | 0.486503 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −3.08307 | −0.346873 | −0.173436 | − | 0.984845i | \(-0.555487\pi\) | ||||
−0.173436 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(80\) | −0.343018 | −0.0383505 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.158645 | 0.0175194 | ||||||||
\(83\) | −9.65424 | −1.05969 | −0.529845 | − | 0.848094i | \(-0.677750\pi\) | ||||
−0.529845 | + | 0.848094i | \(0.677750\pi\) | |||||||
\(84\) | −2.39676 | −0.261508 | ||||||||
\(85\) | −1.79178 | −0.194345 | ||||||||
\(86\) | −2.52136 | −0.271885 | ||||||||
\(87\) | 7.94406 | 0.851693 | ||||||||
\(88\) | −1.78117 | −0.189874 | ||||||||
\(89\) | 6.89933 | 0.731327 | 0.365664 | − | 0.930747i | \(-0.380842\pi\) | ||||
0.365664 | + | 0.930747i | \(0.380842\pi\) | |||||||
\(90\) | 0.343018 | 0.0361572 | ||||||||
\(91\) | 2.39676 | 0.251249 | ||||||||
\(92\) | 2.02924 | 0.211562 | ||||||||
\(93\) | −2.26086 | −0.234440 | ||||||||
\(94\) | −7.07689 | −0.729925 | ||||||||
\(95\) | 1.35382 | 0.138899 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.83476 | 0.795499 | 0.397750 | − | 0.917494i | \(-0.369791\pi\) | ||||
0.397750 | + | 0.917494i | \(0.369791\pi\) | |||||||
\(98\) | 1.25555 | 0.126830 | ||||||||
\(99\) | 1.78117 | 0.179015 | ||||||||
\(100\) | −4.88234 | −0.488234 | ||||||||
\(101\) | −5.96014 | −0.593056 | −0.296528 | − | 0.955024i | \(-0.595829\pi\) | ||||
−0.296528 | + | 0.955024i | \(0.595829\pi\) | |||||||
\(102\) | 5.22357 | 0.517211 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0.822130 | 0.0802317 | ||||||||
\(106\) | −6.10766 | −0.593228 | ||||||||
\(107\) | 0.562160 | 0.0543461 | 0.0271730 | − | 0.999631i | \(-0.491349\pi\) | ||||
0.0271730 | + | 0.999631i | \(0.491349\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.55415 | −0.723557 | −0.361778 | − | 0.932264i | \(-0.617830\pi\) | ||||
−0.361778 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(110\) | 0.610974 | 0.0582541 | ||||||||
\(111\) | −8.14049 | −0.772661 | ||||||||
\(112\) | 2.39676 | 0.226472 | ||||||||
\(113\) | −6.21659 | −0.584807 | −0.292404 | − | 0.956295i | \(-0.594455\pi\) | ||||
−0.292404 | + | 0.956295i | \(0.594455\pi\) | |||||||
\(114\) | −3.94679 | −0.369651 | ||||||||
\(115\) | −0.696063 | −0.0649082 | ||||||||
\(116\) | −7.94406 | −0.737588 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 8.74158 | 0.804728 | ||||||||
\(119\) | 12.5196 | 1.14767 | ||||||||
\(120\) | −0.343018 | −0.0313131 | ||||||||
\(121\) | −7.82742 | −0.711583 | ||||||||
\(122\) | −3.19752 | −0.289490 | ||||||||
\(123\) | 0.158645 | 0.0143045 | ||||||||
\(124\) | 2.26086 | 0.203031 | ||||||||
\(125\) | 3.38982 | 0.303194 | ||||||||
\(126\) | −2.39676 | −0.213520 | ||||||||
\(127\) | 13.9651 | 1.23920 | 0.619600 | − | 0.784918i | \(-0.287295\pi\) | ||||
0.619600 | + | 0.784918i | \(0.287295\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.52136 | −0.221993 | ||||||||
\(130\) | 0.343018 | 0.0300846 | ||||||||
\(131\) | −3.65169 | −0.319050 | −0.159525 | − | 0.987194i | \(-0.550996\pi\) | ||||
−0.159525 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(132\) | −1.78117 | −0.155031 | ||||||||
\(133\) | −9.45951 | −0.820243 | ||||||||
\(134\) | −7.84847 | −0.678004 | ||||||||
\(135\) | 0.343018 | 0.0295222 | ||||||||
\(136\) | −5.22357 | −0.447918 | ||||||||
\(137\) | −0.558208 | −0.0476909 | −0.0238454 | − | 0.999716i | \(-0.507591\pi\) | ||||
−0.0238454 | + | 0.999716i | \(0.507591\pi\) | |||||||
\(138\) | 2.02924 | 0.172740 | ||||||||
\(139\) | 19.2351 | 1.63150 | 0.815748 | − | 0.578407i | \(-0.196325\pi\) | ||||
0.815748 | + | 0.578407i | \(0.196325\pi\) | |||||||
\(140\) | −0.822130 | −0.0694827 | ||||||||
\(141\) | −7.07689 | −0.595982 | ||||||||
\(142\) | −7.09487 | −0.595388 | ||||||||
\(143\) | 1.78117 | 0.148949 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.72495 | 0.226295 | ||||||||
\(146\) | −17.0401 | −1.41025 | ||||||||
\(147\) | 1.25555 | 0.103556 | ||||||||
\(148\) | 8.14049 | 0.669144 | ||||||||
\(149\) | −23.8755 | −1.95596 | −0.977980 | − | 0.208698i | \(-0.933077\pi\) | ||||
−0.977980 | + | 0.208698i | \(0.933077\pi\) | |||||||
\(150\) | −4.88234 | −0.398641 | ||||||||
\(151\) | 2.70857 | 0.220420 | 0.110210 | − | 0.993908i | \(-0.464848\pi\) | ||||
0.110210 | + | 0.993908i | \(0.464848\pi\) | |||||||
\(152\) | 3.94679 | 0.320127 | ||||||||
\(153\) | 5.22357 | 0.422301 | ||||||||
\(154\) | −4.26904 | −0.344009 | ||||||||
\(155\) | −0.775515 | −0.0622909 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −7.82902 | −0.624824 | −0.312412 | − | 0.949947i | \(-0.601137\pi\) | ||||
−0.312412 | + | 0.949947i | \(0.601137\pi\) | |||||||
\(158\) | 3.08307 | 0.245276 | ||||||||
\(159\) | −6.10766 | −0.484369 | ||||||||
\(160\) | 0.343018 | 0.0271179 | ||||||||
\(161\) | 4.86359 | 0.383304 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −6.11690 | −0.479112 | −0.239556 | − | 0.970882i | \(-0.577002\pi\) | ||||
−0.239556 | + | 0.970882i | \(0.577002\pi\) | |||||||
\(164\) | −0.158645 | −0.0123881 | ||||||||
\(165\) | 0.610974 | 0.0475643 | ||||||||
\(166\) | 9.65424 | 0.749314 | ||||||||
\(167\) | −0.442298 | −0.0342261 | −0.0171130 | − | 0.999854i | \(-0.505448\pi\) | ||||
−0.0171130 | + | 0.999854i | \(0.505448\pi\) | |||||||
\(168\) | 2.39676 | 0.184914 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.79178 | 0.137423 | ||||||||
\(171\) | −3.94679 | −0.301819 | ||||||||
\(172\) | 2.52136 | 0.192252 | ||||||||
\(173\) | 8.46037 | 0.643230 | 0.321615 | − | 0.946871i | \(-0.395774\pi\) | ||||
0.321615 | + | 0.946871i | \(0.395774\pi\) | |||||||
\(174\) | −7.94406 | −0.602238 | ||||||||
\(175\) | −11.7018 | −0.884572 | ||||||||
\(176\) | 1.78117 | 0.134261 | ||||||||
\(177\) | 8.74158 | 0.657057 | ||||||||
\(178\) | −6.89933 | −0.517127 | ||||||||
\(179\) | −15.7783 | −1.17933 | −0.589663 | − | 0.807649i | \(-0.700739\pi\) | ||||
−0.589663 | + | 0.807649i | \(0.700739\pi\) | |||||||
\(180\) | −0.343018 | −0.0255670 | ||||||||
\(181\) | 24.0105 | 1.78469 | 0.892343 | − | 0.451358i | \(-0.149060\pi\) | ||||
0.892343 | + | 0.451358i | \(0.149060\pi\) | |||||||
\(182\) | −2.39676 | −0.177660 | ||||||||
\(183\) | −3.19752 | −0.236367 | ||||||||
\(184\) | −2.02924 | −0.149597 | ||||||||
\(185\) | −2.79233 | −0.205296 | ||||||||
\(186\) | 2.26086 | 0.165774 | ||||||||
\(187\) | 9.30409 | 0.680383 | ||||||||
\(188\) | 7.07689 | 0.516135 | ||||||||
\(189\) | −2.39676 | −0.174339 | ||||||||
\(190\) | −1.35382 | −0.0982163 | ||||||||
\(191\) | −9.36830 | −0.677866 | −0.338933 | − | 0.940811i | \(-0.610066\pi\) | ||||
−0.338933 | + | 0.940811i | \(0.610066\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 9.10133 | 0.655128 | 0.327564 | − | 0.944829i | \(-0.393772\pi\) | ||||
0.327564 | + | 0.944829i | \(0.393772\pi\) | |||||||
\(194\) | −7.83476 | −0.562503 | ||||||||
\(195\) | 0.343018 | 0.0245640 | ||||||||
\(196\) | −1.25555 | −0.0896821 | ||||||||
\(197\) | −17.7399 | −1.26391 | −0.631956 | − | 0.775004i | \(-0.717748\pi\) | ||||
−0.631956 | + | 0.775004i | \(0.717748\pi\) | |||||||
\(198\) | −1.78117 | −0.126583 | ||||||||
\(199\) | 3.44401 | 0.244139 | 0.122070 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122070 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(200\) | 4.88234 | 0.345234 | ||||||||
\(201\) | −7.84847 | −0.553588 | ||||||||
\(202\) | 5.96014 | 0.419354 | ||||||||
\(203\) | −19.0400 | −1.33635 | ||||||||
\(204\) | −5.22357 | −0.365723 | ||||||||
\(205\) | 0.0544180 | 0.00380072 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 2.02924 | 0.141042 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −7.02993 | −0.486270 | ||||||||
\(210\) | −0.822130 | −0.0567324 | ||||||||
\(211\) | 16.1940 | 1.11484 | 0.557419 | − | 0.830231i | \(-0.311792\pi\) | ||||
0.557419 | + | 0.830231i | \(0.311792\pi\) | |||||||
\(212\) | 6.10766 | 0.419476 | ||||||||
\(213\) | −7.09487 | −0.486133 | ||||||||
\(214\) | −0.562160 | −0.0384285 | ||||||||
\(215\) | −0.864871 | −0.0589837 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 5.41874 | 0.367848 | ||||||||
\(218\) | 7.55415 | 0.511632 | ||||||||
\(219\) | −17.0401 | −1.15146 | ||||||||
\(220\) | −0.610974 | −0.0411919 | ||||||||
\(221\) | 5.22357 | 0.351375 | ||||||||
\(222\) | 8.14049 | 0.546354 | ||||||||
\(223\) | 2.60140 | 0.174202 | 0.0871012 | − | 0.996199i | \(-0.472240\pi\) | ||||
0.0871012 | + | 0.996199i | \(0.472240\pi\) | |||||||
\(224\) | −2.39676 | −0.160140 | ||||||||
\(225\) | −4.88234 | −0.325489 | ||||||||
\(226\) | 6.21659 | 0.413521 | ||||||||
\(227\) | 0.153884 | 0.0102136 | 0.00510682 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510682 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(228\) | 3.94679 | 0.261383 | ||||||||
\(229\) | 10.5875 | 0.699640 | 0.349820 | − | 0.936817i | \(-0.386243\pi\) | ||||
0.349820 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(230\) | 0.696063 | 0.0458971 | ||||||||
\(231\) | −4.26904 | −0.280883 | ||||||||
\(232\) | 7.94406 | 0.521553 | ||||||||
\(233\) | 12.4251 | 0.813996 | 0.406998 | − | 0.913429i | \(-0.366576\pi\) | ||||
0.406998 | + | 0.913429i | \(0.366576\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −2.42750 | −0.158352 | ||||||||
\(236\) | −8.74158 | −0.569028 | ||||||||
\(237\) | 3.08307 | 0.200267 | ||||||||
\(238\) | −12.5196 | −0.811528 | ||||||||
\(239\) | −10.7307 | −0.694114 | −0.347057 | − | 0.937844i | \(-0.612819\pi\) | ||||
−0.347057 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(240\) | 0.343018 | 0.0221417 | ||||||||
\(241\) | −8.36037 | −0.538539 | −0.269269 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269269 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(242\) | 7.82742 | 0.503165 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.19752 | 0.204700 | ||||||||
\(245\) | 0.430676 | 0.0275149 | ||||||||
\(246\) | −0.158645 | −0.0101148 | ||||||||
\(247\) | −3.94679 | −0.251128 | ||||||||
\(248\) | −2.26086 | −0.143565 | ||||||||
\(249\) | 9.65424 | 0.611812 | ||||||||
\(250\) | −3.38982 | −0.214391 | ||||||||
\(251\) | −5.05823 | −0.319273 | −0.159636 | − | 0.987176i | \(-0.551032\pi\) | ||||
−0.159636 | + | 0.987176i | \(0.551032\pi\) | |||||||
\(252\) | 2.39676 | 0.150982 | ||||||||
\(253\) | 3.61442 | 0.227237 | ||||||||
\(254\) | −13.9651 | −0.876247 | ||||||||
\(255\) | 1.79178 | 0.112205 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.1908 | 0.635684 | 0.317842 | − | 0.948144i | \(-0.397042\pi\) | ||||
0.317842 | + | 0.948144i | \(0.397042\pi\) | |||||||
\(258\) | 2.52136 | 0.156973 | ||||||||
\(259\) | 19.5108 | 1.21234 | ||||||||
\(260\) | −0.343018 | −0.0212730 | ||||||||
\(261\) | −7.94406 | −0.491725 | ||||||||
\(262\) | 3.65169 | 0.225602 | ||||||||
\(263\) | −17.1554 | −1.05784 | −0.528922 | − | 0.848670i | \(-0.677404\pi\) | ||||
−0.528922 | + | 0.848670i | \(0.677404\pi\) | |||||||
\(264\) | 1.78117 | 0.109624 | ||||||||
\(265\) | −2.09503 | −0.128697 | ||||||||
\(266\) | 9.45951 | 0.580000 | ||||||||
\(267\) | −6.89933 | −0.422232 | ||||||||
\(268\) | 7.84847 | 0.479422 | ||||||||
\(269\) | −0.814999 | −0.0496913 | −0.0248457 | − | 0.999691i | \(-0.507909\pi\) | ||||
−0.0248457 | + | 0.999691i | \(0.507909\pi\) | |||||||
\(270\) | −0.343018 | −0.0208754 | ||||||||
\(271\) | 9.45379 | 0.574277 | 0.287138 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287138 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(272\) | 5.22357 | 0.316726 | ||||||||
\(273\) | −2.39676 | −0.145058 | ||||||||
\(274\) | 0.558208 | 0.0337226 | ||||||||
\(275\) | −8.69630 | −0.524406 | ||||||||
\(276\) | −2.02924 | −0.122146 | ||||||||
\(277\) | −1.05069 | −0.0631299 | −0.0315650 | − | 0.999502i | \(-0.510049\pi\) | ||||
−0.0315650 | + | 0.999502i | \(0.510049\pi\) | |||||||
\(278\) | −19.2351 | −1.15364 | ||||||||
\(279\) | 2.26086 | 0.135354 | ||||||||
\(280\) | 0.822130 | 0.0491317 | ||||||||
\(281\) | 31.5105 | 1.87976 | 0.939879 | − | 0.341508i | \(-0.110938\pi\) | ||||
0.939879 | + | 0.341508i | \(0.110938\pi\) | |||||||
\(282\) | 7.07689 | 0.421423 | ||||||||
\(283\) | −10.4757 | −0.622714 | −0.311357 | − | 0.950293i | \(-0.600784\pi\) | ||||
−0.311357 | + | 0.950293i | \(0.600784\pi\) | |||||||
\(284\) | 7.09487 | 0.421003 | ||||||||
\(285\) | −1.35382 | −0.0801933 | ||||||||
\(286\) | −1.78117 | −0.105323 | ||||||||
\(287\) | −0.380234 | −0.0224445 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.2857 | 0.605041 | ||||||||
\(290\) | −2.72495 | −0.160015 | ||||||||
\(291\) | −7.83476 | −0.459282 | ||||||||
\(292\) | 17.0401 | 0.997197 | ||||||||
\(293\) | −4.79493 | −0.280123 | −0.140061 | − | 0.990143i | \(-0.544730\pi\) | ||||
−0.140061 | + | 0.990143i | \(0.544730\pi\) | |||||||
\(294\) | −1.25555 | −0.0732252 | ||||||||
\(295\) | 2.99851 | 0.174580 | ||||||||
\(296\) | −8.14049 | −0.473156 | ||||||||
\(297\) | −1.78117 | −0.103354 | ||||||||
\(298\) | 23.8755 | 1.38307 | ||||||||
\(299\) | 2.02924 | 0.117354 | ||||||||
\(300\) | 4.88234 | 0.281882 | ||||||||
\(301\) | 6.04309 | 0.348318 | ||||||||
\(302\) | −2.70857 | −0.155861 | ||||||||
\(303\) | 5.96014 | 0.342401 | ||||||||
\(304\) | −3.94679 | −0.226364 | ||||||||
\(305\) | −1.09681 | −0.0628029 | ||||||||
\(306\) | −5.22357 | −0.298612 | ||||||||
\(307\) | 19.2898 | 1.10092 | 0.550462 | − | 0.834860i | \(-0.314452\pi\) | ||||
0.550462 | + | 0.834860i | \(0.314452\pi\) | |||||||
\(308\) | 4.26904 | 0.243251 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0.775515 | 0.0440463 | ||||||||
\(311\) | 21.2835 | 1.20687 | 0.603437 | − | 0.797411i | \(-0.293797\pi\) | ||||
0.603437 | + | 0.797411i | \(0.293797\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −11.9002 | −0.672637 | −0.336318 | − | 0.941748i | \(-0.609182\pi\) | ||||
−0.336318 | + | 0.941748i | \(0.609182\pi\) | |||||||
\(314\) | 7.82902 | 0.441817 | ||||||||
\(315\) | −0.822130 | −0.0463218 | ||||||||
\(316\) | −3.08307 | −0.173436 | ||||||||
\(317\) | −21.6584 | −1.21646 | −0.608229 | − | 0.793761i | \(-0.708120\pi\) | ||||
−0.608229 | + | 0.793761i | \(0.708120\pi\) | |||||||
\(318\) | 6.10766 | 0.342500 | ||||||||
\(319\) | −14.1498 | −0.792234 | ||||||||
\(320\) | −0.343018 | −0.0191753 | ||||||||
\(321\) | −0.562160 | −0.0313767 | ||||||||
\(322\) | −4.86359 | −0.271037 | ||||||||
\(323\) | −20.6163 | −1.14712 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.88234 | −0.270823 | ||||||||
\(326\) | 6.11690 | 0.338784 | ||||||||
\(327\) | 7.55415 | 0.417746 | ||||||||
\(328\) | 0.158645 | 0.00875971 | ||||||||
\(329\) | 16.9616 | 0.935123 | ||||||||
\(330\) | −0.610974 | −0.0336330 | ||||||||
\(331\) | 26.4528 | 1.45398 | 0.726989 | − | 0.686650i | \(-0.240919\pi\) | ||||
0.726989 | + | 0.686650i | \(0.240919\pi\) | |||||||
\(332\) | −9.65424 | −0.529845 | ||||||||
\(333\) | 8.14049 | 0.446096 | ||||||||
\(334\) | 0.442298 | 0.0242015 | ||||||||
\(335\) | −2.69216 | −0.147089 | ||||||||
\(336\) | −2.39676 | −0.130754 | ||||||||
\(337\) | 12.3203 | 0.671127 | 0.335564 | − | 0.942018i | \(-0.391073\pi\) | ||||
0.335564 | + | 0.942018i | \(0.391073\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 6.21659 | 0.337639 | ||||||||
\(340\) | −1.79178 | −0.0971727 | ||||||||
\(341\) | 4.02699 | 0.218074 | ||||||||
\(342\) | 3.94679 | 0.213418 | ||||||||
\(343\) | −19.7866 | −1.06837 | ||||||||
\(344\) | −2.52136 | −0.135943 | ||||||||
\(345\) | 0.696063 | 0.0374748 | ||||||||
\(346\) | −8.46037 | −0.454832 | ||||||||
\(347\) | 7.66523 | 0.411491 | 0.205746 | − | 0.978606i | \(-0.434038\pi\) | ||||
0.205746 | + | 0.978606i | \(0.434038\pi\) | |||||||
\(348\) | 7.94406 | 0.425846 | ||||||||
\(349\) | 18.8662 | 1.00988 | 0.504942 | − | 0.863153i | \(-0.331514\pi\) | ||||
0.504942 | + | 0.863153i | \(0.331514\pi\) | |||||||
\(350\) | 11.7018 | 0.625487 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.78117 | −0.0949369 | ||||||||
\(353\) | −1.98763 | −0.105791 | −0.0528954 | − | 0.998600i | \(-0.516845\pi\) | ||||
−0.0528954 | + | 0.998600i | \(0.516845\pi\) | |||||||
\(354\) | −8.74158 | −0.464610 | ||||||||
\(355\) | −2.43367 | −0.129166 | ||||||||
\(356\) | 6.89933 | 0.365664 | ||||||||
\(357\) | −12.5196 | −0.662609 | ||||||||
\(358\) | 15.7783 | 0.833910 | ||||||||
\(359\) | 32.8713 | 1.73488 | 0.867439 | − | 0.497543i | \(-0.165764\pi\) | ||||
0.867439 | + | 0.497543i | \(0.165764\pi\) | |||||||
\(360\) | 0.343018 | 0.0180786 | ||||||||
\(361\) | −3.42283 | −0.180149 | ||||||||
\(362\) | −24.0105 | −1.26196 | ||||||||
\(363\) | 7.82742 | 0.410833 | ||||||||
\(364\) | 2.39676 | 0.125624 | ||||||||
\(365\) | −5.84506 | −0.305944 | ||||||||
\(366\) | 3.19752 | 0.167137 | ||||||||
\(367\) | 3.74369 | 0.195419 | 0.0977095 | − | 0.995215i | \(-0.468848\pi\) | ||||
0.0977095 | + | 0.995215i | \(0.468848\pi\) | |||||||
\(368\) | 2.02924 | 0.105781 | ||||||||
\(369\) | −0.158645 | −0.00825873 | ||||||||
\(370\) | 2.79233 | 0.145166 | ||||||||
\(371\) | 14.6386 | 0.759997 | ||||||||
\(372\) | −2.26086 | −0.117220 | ||||||||
\(373\) | −0.977914 | −0.0506345 | −0.0253172 | − | 0.999679i | \(-0.508060\pi\) | ||||
−0.0253172 | + | 0.999679i | \(0.508060\pi\) | |||||||
\(374\) | −9.30409 | −0.481103 | ||||||||
\(375\) | −3.38982 | −0.175049 | ||||||||
\(376\) | −7.07689 | −0.364963 | ||||||||
\(377\) | −7.94406 | −0.409140 | ||||||||
\(378\) | 2.39676 | 0.123276 | ||||||||
\(379\) | −15.2708 | −0.784410 | −0.392205 | − | 0.919878i | \(-0.628288\pi\) | ||||
−0.392205 | + | 0.919878i | \(0.628288\pi\) | |||||||
\(380\) | 1.35382 | 0.0694494 | ||||||||
\(381\) | −13.9651 | −0.715452 | ||||||||
\(382\) | 9.36830 | 0.479324 | ||||||||
\(383\) | −25.2275 | −1.28907 | −0.644533 | − | 0.764576i | \(-0.722948\pi\) | ||||
−0.644533 | + | 0.764576i | \(0.722948\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.46436 | −0.0746305 | ||||||||
\(386\) | −9.10133 | −0.463245 | ||||||||
\(387\) | 2.52136 | 0.128168 | ||||||||
\(388\) | 7.83476 | 0.397750 | ||||||||
\(389\) | 23.3407 | 1.18342 | 0.591711 | − | 0.806151i | \(-0.298453\pi\) | ||||
0.591711 | + | 0.806151i | \(0.298453\pi\) | |||||||
\(390\) | −0.343018 | −0.0173694 | ||||||||
\(391\) | 10.5999 | 0.536058 | ||||||||
\(392\) | 1.25555 | 0.0634148 | ||||||||
\(393\) | 3.65169 | 0.184204 | ||||||||
\(394\) | 17.7399 | 0.893721 | ||||||||
\(395\) | 1.05755 | 0.0532110 | ||||||||
\(396\) | 1.78117 | 0.0895074 | ||||||||
\(397\) | −33.7019 | −1.69145 | −0.845726 | − | 0.533617i | \(-0.820832\pi\) | ||||
−0.845726 | + | 0.533617i | \(0.820832\pi\) | |||||||
\(398\) | −3.44401 | −0.172633 | ||||||||
\(399\) | 9.45951 | 0.473568 | ||||||||
\(400\) | −4.88234 | −0.244117 | ||||||||
\(401\) | −17.7330 | −0.885543 | −0.442772 | − | 0.896634i | \(-0.646005\pi\) | ||||
−0.442772 | + | 0.896634i | \(0.646005\pi\) | |||||||
\(402\) | 7.84847 | 0.391446 | ||||||||
\(403\) | 2.26086 | 0.112622 | ||||||||
\(404\) | −5.96014 | −0.296528 | ||||||||
\(405\) | −0.343018 | −0.0170447 | ||||||||
\(406\) | 19.0400 | 0.944939 | ||||||||
\(407\) | 14.4996 | 0.718720 | ||||||||
\(408\) | 5.22357 | 0.258605 | ||||||||
\(409\) | 0.866427 | 0.0428420 | 0.0214210 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214210 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(410\) | −0.0544180 | −0.00268752 | ||||||||
\(411\) | 0.558208 | 0.0275343 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −20.9515 | −1.03095 | ||||||||
\(414\) | −2.02924 | −0.0997315 | ||||||||
\(415\) | 3.31157 | 0.162559 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −19.2351 | −0.941945 | ||||||||
\(418\) | 7.02993 | 0.343845 | ||||||||
\(419\) | 4.23789 | 0.207035 | 0.103517 | − | 0.994628i | \(-0.466990\pi\) | ||||
0.103517 | + | 0.994628i | \(0.466990\pi\) | |||||||
\(420\) | 0.822130 | 0.0401158 | ||||||||
\(421\) | 12.9281 | 0.630075 | 0.315038 | − | 0.949079i | \(-0.397983\pi\) | ||||
0.315038 | + | 0.949079i | \(0.397983\pi\) | |||||||
\(422\) | −16.1940 | −0.788310 | ||||||||
\(423\) | 7.07689 | 0.344090 | ||||||||
\(424\) | −6.10766 | −0.296614 | ||||||||
\(425\) | −25.5032 | −1.23709 | ||||||||
\(426\) | 7.09487 | 0.343748 | ||||||||
\(427\) | 7.66368 | 0.370872 | ||||||||
\(428\) | 0.562160 | 0.0271730 | ||||||||
\(429\) | −1.78117 | −0.0859959 | ||||||||
\(430\) | 0.864871 | 0.0417078 | ||||||||
\(431\) | 2.33069 | 0.112266 | 0.0561328 | − | 0.998423i | \(-0.482123\pi\) | ||||
0.0561328 | + | 0.998423i | \(0.482123\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 11.0775 | 0.532350 | 0.266175 | − | 0.963925i | \(-0.414240\pi\) | ||||
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(434\) | −5.41874 | −0.260108 | ||||||||
\(435\) | −2.72495 | −0.130651 | ||||||||
\(436\) | −7.55415 | −0.361778 | ||||||||
\(437\) | −8.00897 | −0.383121 | ||||||||
\(438\) | 17.0401 | 0.814208 | ||||||||
\(439\) | −22.3671 | −1.06752 | −0.533761 | − | 0.845635i | \(-0.679222\pi\) | ||||
−0.533761 | + | 0.845635i | \(0.679222\pi\) | |||||||
\(440\) | 0.610974 | 0.0291270 | ||||||||
\(441\) | −1.25555 | −0.0597881 | ||||||||
\(442\) | −5.22357 | −0.248460 | ||||||||
\(443\) | −0.372988 | −0.0177212 | −0.00886060 | − | 0.999961i | \(-0.502820\pi\) | ||||
−0.00886060 | + | 0.999961i | \(0.502820\pi\) | |||||||
\(444\) | −8.14049 | −0.386330 | ||||||||
\(445\) | −2.36659 | −0.112187 | ||||||||
\(446\) | −2.60140 | −0.123180 | ||||||||
\(447\) | 23.8755 | 1.12927 | ||||||||
\(448\) | 2.39676 | 0.113236 | ||||||||
\(449\) | −9.55036 | −0.450709 | −0.225355 | − | 0.974277i | \(-0.572354\pi\) | ||||
−0.225355 | + | 0.974277i | \(0.572354\pi\) | |||||||
\(450\) | 4.88234 | 0.230156 | ||||||||
\(451\) | −0.282575 | −0.0133059 | ||||||||
\(452\) | −6.21659 | −0.292404 | ||||||||
\(453\) | −2.70857 | −0.127260 | ||||||||
\(454\) | −0.153884 | −0.00722213 | ||||||||
\(455\) | −0.822130 | −0.0385421 | ||||||||
\(456\) | −3.94679 | −0.184825 | ||||||||
\(457\) | 8.43762 | 0.394695 | 0.197348 | − | 0.980334i | \(-0.436767\pi\) | ||||
0.197348 | + | 0.980334i | \(0.436767\pi\) | |||||||
\(458\) | −10.5875 | −0.494720 | ||||||||
\(459\) | −5.22357 | −0.243815 | ||||||||
\(460\) | −0.696063 | −0.0324541 | ||||||||
\(461\) | 0.632681 | 0.0294669 | 0.0147335 | − | 0.999891i | \(-0.495310\pi\) | ||||
0.0147335 | + | 0.999891i | \(0.495310\pi\) | |||||||
\(462\) | 4.26904 | 0.198614 | ||||||||
\(463\) | −18.6646 | −0.867417 | −0.433709 | − | 0.901053i | \(-0.642795\pi\) | ||||
−0.433709 | + | 0.901053i | \(0.642795\pi\) | |||||||
\(464\) | −7.94406 | −0.368794 | ||||||||
\(465\) | 0.775515 | 0.0359636 | ||||||||
\(466\) | −12.4251 | −0.575582 | ||||||||
\(467\) | 30.1881 | 1.39694 | 0.698470 | − | 0.715639i | \(-0.253864\pi\) | ||||
0.698470 | + | 0.715639i | \(0.253864\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 18.8109 | 0.868606 | ||||||||
\(470\) | 2.42750 | 0.111972 | ||||||||
\(471\) | 7.82902 | 0.360742 | ||||||||
\(472\) | 8.74158 | 0.402364 | ||||||||
\(473\) | 4.49098 | 0.206496 | ||||||||
\(474\) | −3.08307 | −0.141610 | ||||||||
\(475\) | 19.2696 | 0.884149 | ||||||||
\(476\) | 12.5196 | 0.573837 | ||||||||
\(477\) | 6.10766 | 0.279650 | ||||||||
\(478\) | 10.7307 | 0.490812 | ||||||||
\(479\) | 3.54195 | 0.161836 | 0.0809179 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809179 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(480\) | −0.343018 | −0.0156565 | ||||||||
\(481\) | 8.14049 | 0.371174 | ||||||||
\(482\) | 8.36037 | 0.380804 | ||||||||
\(483\) | −4.86359 | −0.221301 | ||||||||
\(484\) | −7.82742 | −0.355792 | ||||||||
\(485\) | −2.68746 | −0.122031 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 23.7808 | 1.07761 | 0.538805 | − | 0.842431i | \(-0.318876\pi\) | ||||
0.538805 | + | 0.842431i | \(0.318876\pi\) | |||||||
\(488\) | −3.19752 | −0.144745 | ||||||||
\(489\) | 6.11690 | 0.276616 | ||||||||
\(490\) | −0.430676 | −0.0194559 | ||||||||
\(491\) | 21.9035 | 0.988491 | 0.494246 | − | 0.869322i | \(-0.335444\pi\) | ||||
0.494246 | + | 0.869322i | \(0.335444\pi\) | |||||||
\(492\) | 0.158645 | 0.00715227 | ||||||||
\(493\) | −41.4964 | −1.86890 | ||||||||
\(494\) | 3.94679 | 0.177575 | ||||||||
\(495\) | −0.610974 | −0.0274612 | ||||||||
\(496\) | 2.26086 | 0.101516 | ||||||||
\(497\) | 17.0047 | 0.762765 | ||||||||
\(498\) | −9.65424 | −0.432617 | ||||||||
\(499\) | 12.0837 | 0.540939 | 0.270470 | − | 0.962728i | \(-0.412821\pi\) | ||||
0.270470 | + | 0.962728i | \(0.412821\pi\) | |||||||
\(500\) | 3.38982 | 0.151597 | ||||||||
\(501\) | 0.442298 | 0.0197604 | ||||||||
\(502\) | 5.05823 | 0.225760 | ||||||||
\(503\) | −9.05121 | −0.403574 | −0.201787 | − | 0.979429i | \(-0.564675\pi\) | ||||
−0.201787 | + | 0.979429i | \(0.564675\pi\) | |||||||
\(504\) | −2.39676 | −0.106760 | ||||||||
\(505\) | 2.04443 | 0.0909761 | ||||||||
\(506\) | −3.61442 | −0.160681 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 13.9651 | 0.619600 | ||||||||
\(509\) | −40.8400 | −1.81020 | −0.905100 | − | 0.425200i | \(-0.860204\pi\) | ||||
−0.905100 | + | 0.425200i | \(0.860204\pi\) | |||||||
\(510\) | −1.79178 | −0.0793412 | ||||||||
\(511\) | 40.8410 | 1.80670 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.94679 | 0.174255 | ||||||||
\(514\) | −10.1908 | −0.449496 | ||||||||
\(515\) | 0.343018 | 0.0151152 | ||||||||
\(516\) | −2.52136 | −0.110997 | ||||||||
\(517\) | 12.6052 | 0.554375 | ||||||||
\(518\) | −19.5108 | −0.857254 | ||||||||
\(519\) | −8.46037 | −0.371369 | ||||||||
\(520\) | 0.343018 | 0.0150423 | ||||||||
\(521\) | −2.46115 | −0.107825 | −0.0539126 | − | 0.998546i | \(-0.517169\pi\) | ||||
−0.0539126 | + | 0.998546i | \(0.517169\pi\) | |||||||
\(522\) | 7.94406 | 0.347702 | ||||||||
\(523\) | 0.745614 | 0.0326034 | 0.0163017 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0163017 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(524\) | −3.65169 | −0.159525 | ||||||||
\(525\) | 11.7018 | 0.510708 | ||||||||
\(526\) | 17.1554 | 0.748009 | ||||||||
\(527\) | 11.8098 | 0.514442 | ||||||||
\(528\) | −1.78117 | −0.0775157 | ||||||||
\(529\) | −18.8822 | −0.820965 | ||||||||
\(530\) | 2.09503 | 0.0910024 | ||||||||
\(531\) | −8.74158 | −0.379352 | ||||||||
\(532\) | −9.45951 | −0.410122 | ||||||||
\(533\) | −0.158645 | −0.00687168 | ||||||||
\(534\) | 6.89933 | 0.298563 | ||||||||
\(535\) | −0.192831 | −0.00833680 | ||||||||
\(536\) | −7.84847 | −0.339002 | ||||||||
\(537\) | 15.7783 | 0.680884 | ||||||||
\(538\) | 0.814999 | 0.0351371 | ||||||||
\(539\) | −2.23635 | −0.0963266 | ||||||||
\(540\) | 0.343018 | 0.0147611 | ||||||||
\(541\) | 21.4494 | 0.922180 | 0.461090 | − | 0.887353i | \(-0.347459\pi\) | ||||
0.461090 | + | 0.887353i | \(0.347459\pi\) | |||||||
\(542\) | −9.45379 | −0.406075 | ||||||||
\(543\) | −24.0105 | −1.03039 | ||||||||
\(544\) | −5.22357 | −0.223959 | ||||||||
\(545\) | 2.59121 | 0.110995 | ||||||||
\(546\) | 2.39676 | 0.102572 | ||||||||
\(547\) | 6.04582 | 0.258500 | 0.129250 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129250 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(548\) | −0.558208 | −0.0238454 | ||||||||
\(549\) | 3.19752 | 0.136467 | ||||||||
\(550\) | 8.69630 | 0.370811 | ||||||||
\(551\) | 31.3536 | 1.33571 | ||||||||
\(552\) | 2.02924 | 0.0863700 | ||||||||
\(553\) | −7.38938 | −0.314228 | ||||||||
\(554\) | 1.05069 | 0.0446396 | ||||||||
\(555\) | 2.79233 | 0.118528 | ||||||||
\(556\) | 19.2351 | 0.815748 | ||||||||
\(557\) | 26.3842 | 1.11793 | 0.558967 | − | 0.829190i | \(-0.311198\pi\) | ||||
0.558967 | + | 0.829190i | \(0.311198\pi\) | |||||||
\(558\) | −2.26086 | −0.0957099 | ||||||||
\(559\) | 2.52136 | 0.106642 | ||||||||
\(560\) | −0.822130 | −0.0347413 | ||||||||
\(561\) | −9.30409 | −0.392819 | ||||||||
\(562\) | −31.5105 | −1.32919 | ||||||||
\(563\) | 21.6247 | 0.911374 | 0.455687 | − | 0.890140i | \(-0.349394\pi\) | ||||
0.455687 | + | 0.890140i | \(0.349394\pi\) | |||||||
\(564\) | −7.07689 | −0.297991 | ||||||||
\(565\) | 2.13240 | 0.0897107 | ||||||||
\(566\) | 10.4757 | 0.440325 | ||||||||
\(567\) | 2.39676 | 0.100654 | ||||||||
\(568\) | −7.09487 | −0.297694 | ||||||||
\(569\) | 23.8137 | 0.998322 | 0.499161 | − | 0.866509i | \(-0.333642\pi\) | ||||
0.499161 | + | 0.866509i | \(0.333642\pi\) | |||||||
\(570\) | 1.35382 | 0.0567052 | ||||||||
\(571\) | 18.1098 | 0.757870 | 0.378935 | − | 0.925423i | \(-0.376290\pi\) | ||||
0.378935 | + | 0.925423i | \(0.376290\pi\) | |||||||
\(572\) | 1.78117 | 0.0744746 | ||||||||
\(573\) | 9.36830 | 0.391366 | ||||||||
\(574\) | 0.380234 | 0.0158707 | ||||||||
\(575\) | −9.90742 | −0.413168 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 31.1375 | 1.29627 | 0.648136 | − | 0.761525i | \(-0.275549\pi\) | ||||
0.648136 | + | 0.761525i | \(0.275549\pi\) | |||||||
\(578\) | −10.2857 | −0.427828 | ||||||||
\(579\) | −9.10133 | −0.378238 | ||||||||
\(580\) | 2.72495 | 0.113147 | ||||||||
\(581\) | −23.1389 | −0.959962 | ||||||||
\(582\) | 7.83476 | 0.324761 | ||||||||
\(583\) | 10.8788 | 0.450554 | ||||||||
\(584\) | −17.0401 | −0.705125 | ||||||||
\(585\) | −0.343018 | −0.0141820 | ||||||||
\(586\) | 4.79493 | 0.198077 | ||||||||
\(587\) | −14.5846 | −0.601969 | −0.300985 | − | 0.953629i | \(-0.597315\pi\) | ||||
−0.300985 | + | 0.953629i | \(0.597315\pi\) | |||||||
\(588\) | 1.25555 | 0.0517780 | ||||||||
\(589\) | −8.92315 | −0.367672 | ||||||||
\(590\) | −2.99851 | −0.123447 | ||||||||
\(591\) | 17.7399 | 0.729720 | ||||||||
\(592\) | 8.14049 | 0.334572 | ||||||||
\(593\) | 0.370789 | 0.0152265 | 0.00761324 | − | 0.999971i | \(-0.497577\pi\) | ||||
0.00761324 | + | 0.999971i | \(0.497577\pi\) | |||||||
\(594\) | 1.78117 | 0.0730825 | ||||||||
\(595\) | −4.29445 | −0.176055 | ||||||||
\(596\) | −23.8755 | −0.977980 | ||||||||
\(597\) | −3.44401 | −0.140954 | ||||||||
\(598\) | −2.02924 | −0.0829816 | ||||||||
\(599\) | 14.1950 | 0.579993 | 0.289997 | − | 0.957028i | \(-0.406346\pi\) | ||||
0.289997 | + | 0.957028i | \(0.406346\pi\) | |||||||
\(600\) | −4.88234 | −0.199321 | ||||||||
\(601\) | −6.50391 | −0.265300 | −0.132650 | − | 0.991163i | \(-0.542349\pi\) | ||||
−0.132650 | + | 0.991163i | \(0.542349\pi\) | |||||||
\(602\) | −6.04309 | −0.246298 | ||||||||
\(603\) | 7.84847 | 0.319614 | ||||||||
\(604\) | 2.70857 | 0.110210 | ||||||||
\(605\) | 2.68494 | 0.109158 | ||||||||
\(606\) | −5.96014 | −0.242114 | ||||||||
\(607\) | 24.1093 | 0.978566 | 0.489283 | − | 0.872125i | \(-0.337259\pi\) | ||||
0.489283 | + | 0.872125i | \(0.337259\pi\) | |||||||
\(608\) | 3.94679 | 0.160064 | ||||||||
\(609\) | 19.0400 | 0.771540 | ||||||||
\(610\) | 1.09681 | 0.0444083 | ||||||||
\(611\) | 7.07689 | 0.286300 | ||||||||
\(612\) | 5.22357 | 0.211150 | ||||||||
\(613\) | −1.14964 | −0.0464333 | −0.0232167 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232167 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(614\) | −19.2898 | −0.778471 | ||||||||
\(615\) | −0.0544180 | −0.00219435 | ||||||||
\(616\) | −4.26904 | −0.172005 | ||||||||
\(617\) | −4.66642 | −0.187863 | −0.0939315 | − | 0.995579i | \(-0.529943\pi\) | ||||
−0.0939315 | + | 0.995579i | \(0.529943\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 11.0487 | 0.444085 | 0.222043 | − | 0.975037i | \(-0.428728\pi\) | ||||
0.222043 | + | 0.975037i | \(0.428728\pi\) | |||||||
\(620\) | −0.775515 | −0.0311454 | ||||||||
\(621\) | −2.02924 | −0.0814304 | ||||||||
\(622\) | −21.2835 | −0.853389 | ||||||||
\(623\) | 16.5360 | 0.662502 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 23.2489 | 0.929957 | ||||||||
\(626\) | 11.9002 | 0.475626 | ||||||||
\(627\) | 7.02993 | 0.280748 | ||||||||
\(628\) | −7.82902 | −0.312412 | ||||||||
\(629\) | 42.5224 | 1.69548 | ||||||||
\(630\) | 0.822130 | 0.0327544 | ||||||||
\(631\) | 36.5947 | 1.45681 | 0.728405 | − | 0.685146i | \(-0.240262\pi\) | ||||
0.728405 | + | 0.685146i | \(0.240262\pi\) | |||||||
\(632\) | 3.08307 | 0.122638 | ||||||||
\(633\) | −16.1940 | −0.643653 | ||||||||
\(634\) | 21.6584 | 0.860166 | ||||||||
\(635\) | −4.79026 | −0.190096 | ||||||||
\(636\) | −6.10766 | −0.242184 | ||||||||
\(637\) | −1.25555 | −0.0497467 | ||||||||
\(638\) | 14.1498 | 0.560194 | ||||||||
\(639\) | 7.09487 | 0.280669 | ||||||||
\(640\) | 0.343018 | 0.0135590 | ||||||||
\(641\) | 14.3213 | 0.565657 | 0.282828 | − | 0.959171i | \(-0.408727\pi\) | ||||
0.282828 | + | 0.959171i | \(0.408727\pi\) | |||||||
\(642\) | 0.562160 | 0.0221867 | ||||||||
\(643\) | 42.7131 | 1.68444 | 0.842220 | − | 0.539135i | \(-0.181249\pi\) | ||||
0.842220 | + | 0.539135i | \(0.181249\pi\) | |||||||
\(644\) | 4.86359 | 0.191652 | ||||||||
\(645\) | 0.864871 | 0.0340543 | ||||||||
\(646\) | 20.6163 | 0.811139 | ||||||||
\(647\) | 14.3611 | 0.564592 | 0.282296 | − | 0.959327i | \(-0.408904\pi\) | ||||
0.282296 | + | 0.959327i | \(0.408904\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −15.5703 | −0.611187 | ||||||||
\(650\) | 4.88234 | 0.191501 | ||||||||
\(651\) | −5.41874 | −0.212377 | ||||||||
\(652\) | −6.11690 | −0.239556 | ||||||||
\(653\) | 45.2621 | 1.77124 | 0.885621 | − | 0.464409i | \(-0.153733\pi\) | ||||
0.885621 | + | 0.464409i | \(0.153733\pi\) | |||||||
\(654\) | −7.55415 | −0.295391 | ||||||||
\(655\) | 1.25260 | 0.0489429 | ||||||||
\(656\) | −0.158645 | −0.00619405 | ||||||||
\(657\) | 17.0401 | 0.664798 | ||||||||
\(658\) | −16.9616 | −0.661232 | ||||||||
\(659\) | 35.4677 | 1.38163 | 0.690813 | − | 0.723033i | \(-0.257253\pi\) | ||||
0.690813 | + | 0.723033i | \(0.257253\pi\) | |||||||
\(660\) | 0.610974 | 0.0237821 | ||||||||
\(661\) | −17.9913 | −0.699780 | −0.349890 | − | 0.936791i | \(-0.613781\pi\) | ||||
−0.349890 | + | 0.936791i | \(0.613781\pi\) | |||||||
\(662\) | −26.4528 | −1.02812 | ||||||||
\(663\) | −5.22357 | −0.202867 | ||||||||
\(664\) | 9.65424 | 0.374657 | ||||||||
\(665\) | 3.24478 | 0.125827 | ||||||||
\(666\) | −8.14049 | −0.315437 | ||||||||
\(667\) | −16.1204 | −0.624183 | ||||||||
\(668\) | −0.442298 | −0.0171130 | ||||||||
\(669\) | −2.60140 | −0.100576 | ||||||||
\(670\) | 2.69216 | 0.104007 | ||||||||
\(671\) | 5.69534 | 0.219866 | ||||||||
\(672\) | 2.39676 | 0.0924570 | ||||||||
\(673\) | −7.41406 | −0.285791 | −0.142895 | − | 0.989738i | \(-0.545641\pi\) | ||||
−0.142895 | + | 0.989738i | \(0.545641\pi\) | |||||||
\(674\) | −12.3203 | −0.474558 | ||||||||
\(675\) | 4.88234 | 0.187921 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 0.502213 | 0.0193016 | 0.00965080 | − | 0.999953i | \(-0.496928\pi\) | ||||
0.00965080 | + | 0.999953i | \(0.496928\pi\) | |||||||
\(678\) | −6.21659 | −0.238747 | ||||||||
\(679\) | 18.7780 | 0.720634 | ||||||||
\(680\) | 1.79178 | 0.0687115 | ||||||||
\(681\) | −0.153884 | −0.00589684 | ||||||||
\(682\) | −4.02699 | −0.154201 | ||||||||
\(683\) | 17.8495 | 0.682991 | 0.341495 | − | 0.939883i | \(-0.389067\pi\) | ||||
0.341495 | + | 0.939883i | \(0.389067\pi\) | |||||||
\(684\) | −3.94679 | −0.150909 | ||||||||
\(685\) | 0.191475 | 0.00731588 | ||||||||
\(686\) | 19.7866 | 0.755454 | ||||||||
\(687\) | −10.5875 | −0.403937 | ||||||||
\(688\) | 2.52136 | 0.0961260 | ||||||||
\(689\) | 6.10766 | 0.232683 | ||||||||
\(690\) | −0.696063 | −0.0264987 | ||||||||
\(691\) | −28.8752 | −1.09846 | −0.549232 | − | 0.835670i | \(-0.685080\pi\) | ||||
−0.549232 | + | 0.835670i | \(0.685080\pi\) | |||||||
\(692\) | 8.46037 | 0.321615 | ||||||||
\(693\) | 4.26904 | 0.162168 | ||||||||
\(694\) | −7.66523 | −0.290968 | ||||||||
\(695\) | −6.59796 | −0.250275 | ||||||||
\(696\) | −7.94406 | −0.301119 | ||||||||
\(697\) | −0.828694 | −0.0313890 | ||||||||
\(698\) | −18.8662 | −0.714096 | ||||||||
\(699\) | −12.4251 | −0.469961 | ||||||||
\(700\) | −11.7018 | −0.442286 | ||||||||
\(701\) | 24.3254 | 0.918758 | 0.459379 | − | 0.888240i | \(-0.348072\pi\) | ||||
0.459379 | + | 0.888240i | \(0.348072\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −32.1288 | −1.21176 | ||||||||
\(704\) | 1.78117 | 0.0671305 | ||||||||
\(705\) | 2.42750 | 0.0914248 | ||||||||
\(706\) | 1.98763 | 0.0748054 | ||||||||
\(707\) | −14.2850 | −0.537244 | ||||||||
\(708\) | 8.74158 | 0.328529 | ||||||||
\(709\) | −33.8429 | −1.27100 | −0.635499 | − | 0.772102i | \(-0.719206\pi\) | ||||
−0.635499 | + | 0.772102i | \(0.719206\pi\) | |||||||
\(710\) | 2.43367 | 0.0913338 | ||||||||
\(711\) | −3.08307 | −0.115624 | ||||||||
\(712\) | −6.89933 | −0.258563 | ||||||||
\(713\) | 4.58782 | 0.171815 | ||||||||
\(714\) | 12.5196 | 0.468536 | ||||||||
\(715\) | −0.610974 | −0.0228491 | ||||||||
\(716\) | −15.7783 | −0.589663 | ||||||||
\(717\) | 10.7307 | 0.400747 | ||||||||
\(718\) | −32.8713 | −1.22674 | ||||||||
\(719\) | −47.6357 | −1.77651 | −0.888256 | − | 0.459348i | \(-0.848083\pi\) | ||||
−0.888256 | + | 0.459348i | \(0.848083\pi\) | |||||||
\(720\) | −0.343018 | −0.0127835 | ||||||||
\(721\) | −2.39676 | −0.0892599 | ||||||||
\(722\) | 3.42283 | 0.127385 | ||||||||
\(723\) | 8.36037 | 0.310925 | ||||||||
\(724\) | 24.0105 | 0.892343 | ||||||||
\(725\) | 38.7856 | 1.44046 | ||||||||
\(726\) | −7.82742 | −0.290503 | ||||||||
\(727\) | −31.8772 | −1.18226 | −0.591130 | − | 0.806576i | \(-0.701318\pi\) | ||||
−0.591130 | + | 0.806576i | \(0.701318\pi\) | |||||||
\(728\) | −2.39676 | −0.0888298 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.84506 | 0.216335 | ||||||||
\(731\) | 13.1705 | 0.487129 | ||||||||
\(732\) | −3.19752 | −0.118184 | ||||||||
\(733\) | 3.97359 | 0.146768 | 0.0733840 | − | 0.997304i | \(-0.476620\pi\) | ||||
0.0733840 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(734\) | −3.74369 | −0.138182 | ||||||||
\(735\) | −0.430676 | −0.0158857 | ||||||||
\(736\) | −2.02924 | −0.0747986 | ||||||||
\(737\) | 13.9795 | 0.514941 | ||||||||
\(738\) | 0.158645 | 0.00583981 | ||||||||
\(739\) | 15.9452 | 0.586555 | 0.293278 | − | 0.956027i | \(-0.405254\pi\) | ||||
0.293278 | + | 0.956027i | \(0.405254\pi\) | |||||||
\(740\) | −2.79233 | −0.102648 | ||||||||
\(741\) | 3.94679 | 0.144989 | ||||||||
\(742\) | −14.6386 | −0.537399 | ||||||||
\(743\) | 35.0364 | 1.28536 | 0.642680 | − | 0.766134i | \(-0.277822\pi\) | ||||
0.642680 | + | 0.766134i | \(0.277822\pi\) | |||||||
\(744\) | 2.26086 | 0.0828872 | ||||||||
\(745\) | 8.18973 | 0.300048 | ||||||||
\(746\) | 0.977914 | 0.0358040 | ||||||||
\(747\) | −9.65424 | −0.353230 | ||||||||
\(748\) | 9.30409 | 0.340191 | ||||||||
\(749\) | 1.34736 | 0.0492315 | ||||||||
\(750\) | 3.38982 | 0.123779 | ||||||||
\(751\) | 13.8824 | 0.506576 | 0.253288 | − | 0.967391i | \(-0.418488\pi\) | ||||
0.253288 | + | 0.967391i | \(0.418488\pi\) | |||||||
\(752\) | 7.07689 | 0.258068 | ||||||||
\(753\) | 5.05823 | 0.184332 | ||||||||
\(754\) | 7.94406 | 0.289306 | ||||||||
\(755\) | −0.929086 | −0.0338129 | ||||||||
\(756\) | −2.39676 | −0.0871693 | ||||||||
\(757\) | −37.8619 | −1.37611 | −0.688057 | − | 0.725657i | \(-0.741536\pi\) | ||||
−0.688057 | + | 0.725657i | \(0.741536\pi\) | |||||||
\(758\) | 15.2708 | 0.554662 | ||||||||
\(759\) | −3.61442 | −0.131195 | ||||||||
\(760\) | −1.35382 | −0.0491082 | ||||||||
\(761\) | 22.2610 | 0.806961 | 0.403481 | − | 0.914988i | \(-0.367800\pi\) | ||||
0.403481 | + | 0.914988i | \(0.367800\pi\) | |||||||
\(762\) | 13.9651 | 0.505901 | ||||||||
\(763\) | −18.1055 | −0.655462 | ||||||||
\(764\) | −9.36830 | −0.338933 | ||||||||
\(765\) | −1.79178 | −0.0647818 | ||||||||
\(766\) | 25.2275 | 0.911508 | ||||||||
\(767\) | −8.74158 | −0.315640 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 0.172135 | 0.00620734 | 0.00310367 | − | 0.999995i | \(-0.499012\pi\) | ||||
0.00310367 | + | 0.999995i | \(0.499012\pi\) | |||||||
\(770\) | 1.46436 | 0.0527718 | ||||||||
\(771\) | −10.1908 | −0.367012 | ||||||||
\(772\) | 9.10133 | 0.327564 | ||||||||
\(773\) | −6.30578 | −0.226803 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(774\) | −2.52136 | −0.0906285 | ||||||||
\(775\) | −11.0383 | −0.396507 | ||||||||
\(776\) | −7.83476 | −0.281251 | ||||||||
\(777\) | −19.5108 | −0.699945 | ||||||||
\(778\) | −23.3407 | −0.836805 | ||||||||
\(779\) | 0.626139 | 0.0224338 | ||||||||
\(780\) | 0.343018 | 0.0122820 | ||||||||
\(781\) | 12.6372 | 0.452195 | ||||||||
\(782\) | −10.5999 | −0.379050 | ||||||||
\(783\) | 7.94406 | 0.283898 | ||||||||
\(784\) | −1.25555 | −0.0448411 | ||||||||
\(785\) | 2.68549 | 0.0958493 | ||||||||
\(786\) | −3.65169 | −0.130252 | ||||||||
\(787\) | −37.3651 | −1.33192 | −0.665961 | − | 0.745986i | \(-0.731978\pi\) | ||||
−0.665961 | + | 0.745986i | \(0.731978\pi\) | |||||||
\(788\) | −17.7399 | −0.631956 | ||||||||
\(789\) | 17.1554 | 0.610747 | ||||||||
\(790\) | −1.05755 | −0.0376258 | ||||||||
\(791\) | −14.8997 | −0.529771 | ||||||||
\(792\) | −1.78117 | −0.0632913 | ||||||||
\(793\) | 3.19752 | 0.113547 | ||||||||
\(794\) | 33.7019 | 1.19604 | ||||||||
\(795\) | 2.09503 | 0.0743032 | ||||||||
\(796\) | 3.44401 | 0.122070 | ||||||||
\(797\) | 16.4811 | 0.583791 | 0.291896 | − | 0.956450i | \(-0.405714\pi\) | ||||
0.291896 | + | 0.956450i | \(0.405714\pi\) | |||||||
\(798\) | −9.45951 | −0.334863 | ||||||||
\(799\) | 36.9666 | 1.30779 | ||||||||
\(800\) | 4.88234 | 0.172617 | ||||||||
\(801\) | 6.89933 | 0.243776 | ||||||||
\(802\) | 17.7330 | 0.626174 | ||||||||
\(803\) | 30.3514 | 1.07108 | ||||||||
\(804\) | −7.84847 | −0.276794 | ||||||||
\(805\) | −1.66830 | −0.0587997 | ||||||||
\(806\) | −2.26086 | −0.0796354 | ||||||||
\(807\) | 0.814999 | 0.0286893 | ||||||||
\(808\) | 5.96014 | 0.209677 | ||||||||
\(809\) | −0.895485 | −0.0314836 | −0.0157418 | − | 0.999876i | \(-0.505011\pi\) | ||||
−0.0157418 | + | 0.999876i | \(0.505011\pi\) | |||||||
\(810\) | 0.343018 | 0.0120524 | ||||||||
\(811\) | −36.3541 | −1.27657 | −0.638283 | − | 0.769802i | \(-0.720355\pi\) | ||||
−0.638283 | + | 0.769802i | \(0.720355\pi\) | |||||||
\(812\) | −19.0400 | −0.668173 | ||||||||
\(813\) | −9.45379 | −0.331559 | ||||||||
\(814\) | −14.4996 | −0.508212 | ||||||||
\(815\) | 2.09820 | 0.0734969 | ||||||||
\(816\) | −5.22357 | −0.182862 | ||||||||
\(817\) | −9.95129 | −0.348152 | ||||||||
\(818\) | −0.866427 | −0.0302939 | ||||||||
\(819\) | 2.39676 | 0.0837495 | ||||||||
\(820\) | 0.0544180 | 0.00190036 | ||||||||
\(821\) | −23.6636 | −0.825867 | −0.412934 | − | 0.910761i | \(-0.635496\pi\) | ||||
−0.412934 | + | 0.910761i | \(0.635496\pi\) | |||||||
\(822\) | −0.558208 | −0.0194697 | ||||||||
\(823\) | −12.6850 | −0.442172 | −0.221086 | − | 0.975254i | \(-0.570960\pi\) | ||||
−0.221086 | + | 0.975254i | \(0.570960\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 8.69630 | 0.302766 | ||||||||
\(826\) | 20.9515 | 0.728994 | ||||||||
\(827\) | 2.08401 | 0.0724680 | 0.0362340 | − | 0.999343i | \(-0.488464\pi\) | ||||
0.0362340 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(828\) | 2.02924 | 0.0705208 | ||||||||
\(829\) | 15.9265 | 0.553149 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(830\) | −3.31157 | −0.114946 | ||||||||
\(831\) | 1.05069 | 0.0364481 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −6.55845 | −0.227237 | ||||||||
\(834\) | 19.2351 | 0.666056 | ||||||||
\(835\) | 0.151716 | 0.00525035 | ||||||||
\(836\) | −7.02993 | −0.243135 | ||||||||
\(837\) | −2.26086 | −0.0781468 | ||||||||
\(838\) | −4.23789 | −0.146396 | ||||||||
\(839\) | 52.0067 | 1.79547 | 0.897736 | − | 0.440534i | \(-0.145211\pi\) | ||||
0.897736 | + | 0.440534i | \(0.145211\pi\) | |||||||
\(840\) | −0.822130 | −0.0283662 | ||||||||
\(841\) | 34.1081 | 1.17614 | ||||||||
\(842\) | −12.9281 | −0.445530 | ||||||||
\(843\) | −31.5105 | −1.08528 | ||||||||
\(844\) | 16.1940 | 0.557419 | ||||||||
\(845\) | −0.343018 | −0.0118002 | ||||||||
\(846\) | −7.07689 | −0.243308 | ||||||||
\(847\) | −18.7604 | −0.644616 | ||||||||
\(848\) | 6.10766 | 0.209738 | ||||||||
\(849\) | 10.4757 | 0.359524 | ||||||||
\(850\) | 25.5032 | 0.874754 | ||||||||
\(851\) | 16.5190 | 0.566263 | ||||||||
\(852\) | −7.09487 | −0.243066 | ||||||||
\(853\) | 1.52195 | 0.0521107 | 0.0260553 | − | 0.999661i | \(-0.491705\pi\) | ||||
0.0260553 | + | 0.999661i | \(0.491705\pi\) | |||||||
\(854\) | −7.66368 | −0.262246 | ||||||||
\(855\) | 1.35382 | 0.0462996 | ||||||||
\(856\) | −0.562160 | −0.0192142 | ||||||||
\(857\) | −0.192010 | −0.00655892 | −0.00327946 | − | 0.999995i | \(-0.501044\pi\) | ||||
−0.00327946 | + | 0.999995i | \(0.501044\pi\) | |||||||
\(858\) | 1.78117 | 0.0608083 | ||||||||
\(859\) | 20.9645 | 0.715299 | 0.357649 | − | 0.933856i | \(-0.383578\pi\) | ||||
0.357649 | + | 0.933856i | \(0.383578\pi\) | |||||||
\(860\) | −0.864871 | −0.0294919 | ||||||||
\(861\) | 0.380234 | 0.0129583 | ||||||||
\(862\) | −2.33069 | −0.0793838 | ||||||||
\(863\) | 20.7125 | 0.705060 | 0.352530 | − | 0.935800i | \(-0.385321\pi\) | ||||
0.352530 | + | 0.935800i | \(0.385321\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.90205 | −0.0986728 | ||||||||
\(866\) | −11.0775 | −0.376428 | ||||||||
\(867\) | −10.2857 | −0.349320 | ||||||||
\(868\) | 5.41874 | 0.183924 | ||||||||
\(869\) | −5.49149 | −0.186286 | ||||||||
\(870\) | 2.72495 | 0.0923845 | ||||||||
\(871\) | 7.84847 | 0.265935 | ||||||||
\(872\) | 7.55415 | 0.255816 | ||||||||
\(873\) | 7.83476 | 0.265166 | ||||||||
\(874\) | 8.00897 | 0.270907 | ||||||||
\(875\) | 8.12457 | 0.274661 | ||||||||
\(876\) | −17.0401 | −0.575732 | ||||||||
\(877\) | 44.6845 | 1.50889 | 0.754445 | − | 0.656363i | \(-0.227906\pi\) | ||||
0.754445 | + | 0.656363i | \(0.227906\pi\) | |||||||
\(878\) | 22.3671 | 0.754852 | ||||||||
\(879\) | 4.79493 | 0.161729 | ||||||||
\(880\) | −0.610974 | −0.0205959 | ||||||||
\(881\) | −7.06710 | −0.238097 | −0.119048 | − | 0.992888i | \(-0.537984\pi\) | ||||
−0.119048 | + | 0.992888i | \(0.537984\pi\) | |||||||
\(882\) | 1.25555 | 0.0422766 | ||||||||
\(883\) | 0.499721 | 0.0168170 | 0.00840848 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00840848 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(884\) | 5.22357 | 0.175688 | ||||||||
\(885\) | −2.99851 | −0.100794 | ||||||||
\(886\) | 0.372988 | 0.0125308 | ||||||||
\(887\) | −38.7309 | −1.30046 | −0.650228 | − | 0.759739i | \(-0.725327\pi\) | ||||
−0.650228 | + | 0.759739i | \(0.725327\pi\) | |||||||
\(888\) | 8.14049 | 0.273177 | ||||||||
\(889\) | 33.4709 | 1.12258 | ||||||||
\(890\) | 2.36659 | 0.0793283 | ||||||||
\(891\) | 1.78117 | 0.0596716 | ||||||||
\(892\) | 2.60140 | 0.0871012 | ||||||||
\(893\) | −27.9310 | −0.934676 | ||||||||
\(894\) | −23.8755 | −0.798517 | ||||||||
\(895\) | 5.41224 | 0.180911 | ||||||||
\(896\) | −2.39676 | −0.0800701 | ||||||||
\(897\) | −2.02924 | −0.0677542 | ||||||||
\(898\) | 9.55036 | 0.318700 | ||||||||
\(899\) | −17.9604 | −0.599014 | ||||||||
\(900\) | −4.88234 | −0.162745 | ||||||||
\(901\) | 31.9038 | 1.06287 | ||||||||
\(902\) | 0.282575 | 0.00940871 | ||||||||
\(903\) | −6.04309 | −0.201102 | ||||||||
\(904\) | 6.21659 | 0.206761 | ||||||||
\(905\) | −8.23602 | −0.273775 | ||||||||
\(906\) | 2.70857 | 0.0899861 | ||||||||
\(907\) | 21.6452 | 0.718718 | 0.359359 | − | 0.933199i | \(-0.382995\pi\) | ||||
0.359359 | + | 0.933199i | \(0.382995\pi\) | |||||||
\(908\) | 0.153884 | 0.00510682 | ||||||||
\(909\) | −5.96014 | −0.197685 | ||||||||
\(910\) | 0.822130 | 0.0272533 | ||||||||
\(911\) | −6.10346 | −0.202217 | −0.101108 | − | 0.994875i | \(-0.532239\pi\) | ||||
−0.101108 | + | 0.994875i | \(0.532239\pi\) | |||||||
\(912\) | 3.94679 | 0.130691 | ||||||||
\(913\) | −17.1959 | −0.569101 | ||||||||
\(914\) | −8.43762 | −0.279092 | ||||||||
\(915\) | 1.09681 | 0.0362593 | ||||||||
\(916\) | 10.5875 | 0.349820 | ||||||||
\(917\) | −8.75223 | −0.289024 | ||||||||
\(918\) | 5.22357 | 0.172404 | ||||||||
\(919\) | 48.6005 | 1.60318 | 0.801591 | − | 0.597873i | \(-0.203987\pi\) | ||||
0.801591 | + | 0.597873i | \(0.203987\pi\) | |||||||
\(920\) | 0.696063 | 0.0229485 | ||||||||
\(921\) | −19.2898 | −0.635619 | ||||||||
\(922\) | −0.632681 | −0.0208363 | ||||||||
\(923\) | 7.09487 | 0.233531 | ||||||||
\(924\) | −4.26904 | −0.140441 | ||||||||
\(925\) | −39.7446 | −1.30679 | ||||||||
\(926\) | 18.6646 | 0.613357 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 7.94406 | 0.260777 | ||||||||
\(929\) | 40.9361 | 1.34307 | 0.671535 | − | 0.740972i | \(-0.265635\pi\) | ||||
0.671535 | + | 0.740972i | \(0.265635\pi\) | |||||||
\(930\) | −0.775515 | −0.0254301 | ||||||||
\(931\) | 4.95539 | 0.162406 | ||||||||
\(932\) | 12.4251 | 0.406998 | ||||||||
\(933\) | −21.2835 | −0.696789 | ||||||||
\(934\) | −30.1881 | −0.987786 | ||||||||
\(935\) | −3.19147 | −0.104372 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −20.7616 | −0.678253 | −0.339126 | − | 0.940741i | \(-0.610131\pi\) | ||||
−0.339126 | + | 0.940741i | \(0.610131\pi\) | |||||||
\(938\) | −18.8109 | −0.614197 | ||||||||
\(939\) | 11.9002 | 0.388347 | ||||||||
\(940\) | −2.42750 | −0.0791762 | ||||||||
\(941\) | −32.0125 | −1.04358 | −0.521789 | − | 0.853075i | \(-0.674735\pi\) | ||||
−0.521789 | + | 0.853075i | \(0.674735\pi\) | |||||||
\(942\) | −7.82902 | −0.255083 | ||||||||
\(943\) | −0.321928 | −0.0104834 | ||||||||
\(944\) | −8.74158 | −0.284514 | ||||||||
\(945\) | 0.822130 | 0.0267439 | ||||||||
\(946\) | −4.49098 | −0.146014 | ||||||||
\(947\) | −4.85737 | −0.157843 | −0.0789216 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789216 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(948\) | 3.08307 | 0.100133 | ||||||||
\(949\) | 17.0401 | 0.553146 | ||||||||
\(950\) | −19.2696 | −0.625188 | ||||||||
\(951\) | 21.6584 | 0.702323 | ||||||||
\(952\) | −12.5196 | −0.405764 | ||||||||
\(953\) | 4.91973 | 0.159366 | 0.0796828 | − | 0.996820i | \(-0.474609\pi\) | ||||
0.0796828 | + | 0.996820i | \(0.474609\pi\) | |||||||
\(954\) | −6.10766 | −0.197743 | ||||||||
\(955\) | 3.21349 | 0.103986 | ||||||||
\(956\) | −10.7307 | −0.347057 | ||||||||
\(957\) | 14.1498 | 0.457397 | ||||||||
\(958\) | −3.54195 | −0.114435 | ||||||||
\(959\) | −1.33789 | −0.0432027 | ||||||||
\(960\) | 0.343018 | 0.0110708 | ||||||||
\(961\) | −25.8885 | −0.835113 | ||||||||
\(962\) | −8.14049 | −0.262460 | ||||||||
\(963\) | 0.562160 | 0.0181154 | ||||||||
\(964\) | −8.36037 | −0.269269 | ||||||||
\(965\) | −3.12192 | −0.100498 | ||||||||
\(966\) | 4.86359 | 0.156483 | ||||||||
\(967\) | −37.5026 | −1.20600 | −0.603001 | − | 0.797741i | \(-0.706028\pi\) | ||||
−0.603001 | + | 0.797741i | \(0.706028\pi\) | |||||||
\(968\) | 7.82742 | 0.251583 | ||||||||
\(969\) | 20.6163 | 0.662293 | ||||||||
\(970\) | 2.68746 | 0.0862891 | ||||||||
\(971\) | −18.4820 | −0.593114 | −0.296557 | − | 0.955015i | \(-0.595839\pi\) | ||||
−0.296557 | + | 0.955015i | \(0.595839\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 46.1018 | 1.47796 | ||||||||
\(974\) | −23.7808 | −0.761985 | ||||||||
\(975\) | 4.88234 | 0.156360 | ||||||||
\(976\) | 3.19752 | 0.102350 | ||||||||
\(977\) | 10.7816 | 0.344934 | 0.172467 | − | 0.985015i | \(-0.444826\pi\) | ||||
0.172467 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(978\) | −6.11690 | −0.195597 | ||||||||
\(979\) | 12.2889 | 0.392755 | ||||||||
\(980\) | 0.430676 | 0.0137574 | ||||||||
\(981\) | −7.55415 | −0.241186 | ||||||||
\(982\) | −21.9035 | −0.698969 | ||||||||
\(983\) | 47.5111 | 1.51537 | 0.757684 | − | 0.652622i | \(-0.226331\pi\) | ||||
0.757684 | + | 0.652622i | \(0.226331\pi\) | |||||||
\(984\) | −0.158645 | −0.00505742 | ||||||||
\(985\) | 6.08508 | 0.193887 | ||||||||
\(986\) | 41.4964 | 1.32151 | ||||||||
\(987\) | −16.9616 | −0.539893 | ||||||||
\(988\) | −3.94679 | −0.125564 | ||||||||
\(989\) | 5.11644 | 0.162693 | ||||||||
\(990\) | 0.610974 | 0.0194180 | ||||||||
\(991\) | 36.7868 | 1.16857 | 0.584285 | − | 0.811549i | \(-0.301375\pi\) | ||||
0.584285 | + | 0.811549i | \(0.301375\pi\) | |||||||
\(992\) | −2.26086 | −0.0717824 | ||||||||
\(993\) | −26.4528 | −0.839454 | ||||||||
\(994\) | −17.0047 | −0.539356 | ||||||||
\(995\) | −1.18136 | −0.0374515 | ||||||||
\(996\) | 9.65424 | 0.305906 | ||||||||
\(997\) | 5.44037 | 0.172298 | 0.0861491 | − | 0.996282i | \(-0.472544\pi\) | ||||
0.0861491 | + | 0.996282i | \(0.472544\pi\) | |||||||
\(998\) | −12.0837 | −0.382502 | ||||||||
\(999\) | −8.14049 | −0.257554 |
(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 | 8034.2.a.z.1.8 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.8 | ✓ | 14 | 1.1 | even | 1 | trivial |