Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.23607 | −0.912871 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.23607 | 0.645497 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.23607 | −0.577350 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.23607 | 0.784862 | 0.392431 | − | 0.919781i | \(-0.371634\pi\) | ||||
0.392431 | + | 0.919781i | \(0.371634\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | 2.23607 | 0.512989 | 0.256495 | − | 0.966546i | \(-0.417432\pi\) | ||||
0.256495 | + | 0.966546i | \(0.417432\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.23607 | 0.487950 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.23607 | −1.71734 | −0.858669 | − | 0.512530i | \(-0.828708\pi\) | ||||
−0.858669 | + | 0.512530i | \(0.828708\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 2.23607 | 0.408248 | ||||||||
\(31\) | −0.763932 | −0.137206 | −0.0686031 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686031 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.23607 | −0.554981 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | −8.94427 | −1.47043 | −0.735215 | − | 0.677834i | \(-0.762919\pi\) | ||||
−0.735215 | + | 0.677834i | \(0.762919\pi\) | |||||||
\(38\) | −2.23607 | −0.362738 | ||||||||
\(39\) | 2.23607 | 0.358057 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.76393 | −0.431654 | −0.215827 | − | 0.976432i | \(-0.569245\pi\) | ||||
−0.215827 | + | 0.976432i | \(0.569245\pi\) | |||||||
\(42\) | −2.23607 | −0.345033 | ||||||||
\(43\) | −1.23607 | −0.188499 | −0.0942493 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942493 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 8.23607 | 1.21434 | ||||||||
\(47\) | −5.70820 | −0.832627 | −0.416314 | − | 0.909221i | \(-0.636678\pi\) | ||||
−0.416314 | + | 0.909221i | \(0.636678\pi\) | |||||||
\(48\) | 2.23607 | 0.322749 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 7.23607 | 1.01325 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 7.70820 | 1.05880 | 0.529402 | − | 0.848371i | \(-0.322416\pi\) | ||||
0.529402 | + | 0.848371i | \(0.322416\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | −8.70820 | −1.13371 | −0.566856 | − | 0.823817i | \(-0.691840\pi\) | ||||
−0.566856 | + | 0.823817i | \(0.691840\pi\) | |||||||
\(60\) | −2.23607 | −0.288675 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0.763932 | 0.0970195 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.76393 | −0.337668 | −0.168834 | − | 0.985644i | \(-0.554000\pi\) | ||||
−0.168834 | + | 0.985644i | \(0.554000\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | −18.4164 | −2.21707 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −10.4721 | −1.24281 | −0.621407 | − | 0.783488i | \(-0.713439\pi\) | ||||
−0.621407 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(72\) | −2.00000 | −0.235702 | ||||||||
\(73\) | −2.76393 | −0.323494 | −0.161747 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161747 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(74\) | 8.94427 | 1.03975 | ||||||||
\(75\) | 2.23607 | 0.258199 | ||||||||
\(76\) | 2.23607 | 0.256495 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.23607 | −0.253185 | ||||||||
\(79\) | 5.76393 | 0.648493 | 0.324247 | − | 0.945973i | \(-0.394889\pi\) | ||||
0.324247 | + | 0.945973i | \(0.394889\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 2.76393 | 0.305225 | ||||||||
\(83\) | 4.23607 | 0.464969 | 0.232484 | − | 0.972600i | \(-0.425315\pi\) | ||||
0.232484 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(84\) | 2.23607 | 0.243975 | ||||||||
\(85\) | −3.23607 | −0.351001 | ||||||||
\(86\) | 1.23607 | 0.133289 | ||||||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7639 | −1.35297 | −0.676487 | − | 0.736455i | \(-0.736499\pi\) | ||||
−0.676487 | + | 0.736455i | \(0.736499\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −8.23607 | −0.858669 | ||||||||
\(93\) | −1.70820 | −0.177132 | ||||||||
\(94\) | 5.70820 | 0.588756 | ||||||||
\(95\) | −2.23607 | −0.229416 | ||||||||
\(96\) | −2.23607 | −0.228218 | ||||||||
\(97\) | 12.4721 | 1.26635 | 0.633177 | − | 0.774007i | \(-0.281751\pi\) | ||||
0.633177 | + | 0.774007i | \(0.281751\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.00000 | −0.0995037 | −0.0497519 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497519 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(102\) | −7.23607 | −0.716477 | ||||||||
\(103\) | −8.18034 | −0.806033 | −0.403016 | − | 0.915193i | \(-0.632038\pi\) | ||||
−0.403016 | + | 0.915193i | \(0.632038\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −2.23607 | −0.218218 | ||||||||
\(106\) | −7.70820 | −0.748687 | ||||||||
\(107\) | 6.47214 | 0.625685 | 0.312842 | − | 0.949805i | \(-0.398719\pi\) | ||||
0.312842 | + | 0.949805i | \(0.398719\pi\) | |||||||
\(108\) | −2.23607 | −0.215166 | ||||||||
\(109\) | 9.70820 | 0.929877 | 0.464939 | − | 0.885343i | \(-0.346076\pi\) | ||||
0.464939 | + | 0.885343i | \(0.346076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0000 | −1.89832 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.00000 | −0.0940721 | −0.0470360 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470360 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(114\) | −5.00000 | −0.468293 | ||||||||
\(115\) | 8.23607 | 0.768017 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 8.70820 | 0.801655 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 2.23607 | 0.204124 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 12.4721 | 1.12917 | ||||||||
\(123\) | −6.18034 | −0.557262 | ||||||||
\(124\) | −0.763932 | −0.0686031 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 1.76393 | 0.156524 | 0.0782618 | − | 0.996933i | \(-0.475063\pi\) | ||||
0.0782618 | + | 0.996933i | \(0.475063\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.76393 | −0.243351 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | 19.1803 | 1.67579 | 0.837897 | − | 0.545828i | \(-0.183785\pi\) | ||||
0.837897 | + | 0.545828i | \(0.183785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.23607 | 0.193892 | ||||||||
\(134\) | 2.76393 | 0.238767 | ||||||||
\(135\) | 2.23607 | 0.192450 | ||||||||
\(136\) | −3.23607 | −0.277491 | ||||||||
\(137\) | 4.52786 | 0.386842 | 0.193421 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193421 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(138\) | 18.4164 | 1.56771 | ||||||||
\(139\) | −0.236068 | −0.0200230 | −0.0100115 | − | 0.999950i | \(-0.503187\pi\) | ||||
−0.0100115 | + | 0.999950i | \(0.503187\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −12.7639 | −1.07492 | ||||||||
\(142\) | 10.4721 | 0.878802 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | 4.47214 | 0.371391 | ||||||||
\(146\) | 2.76393 | 0.228745 | ||||||||
\(147\) | 2.23607 | 0.184428 | ||||||||
\(148\) | −8.94427 | −0.735215 | ||||||||
\(149\) | 4.00000 | 0.327693 | 0.163846 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163846 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(150\) | −2.23607 | −0.182574 | ||||||||
\(151\) | 7.76393 | 0.631820 | 0.315910 | − | 0.948789i | \(-0.397690\pi\) | ||||
0.315910 | + | 0.948789i | \(0.397690\pi\) | |||||||
\(152\) | −2.23607 | −0.181369 | ||||||||
\(153\) | 6.47214 | 0.523241 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.763932 | 0.0613605 | ||||||||
\(156\) | 2.23607 | 0.179029 | ||||||||
\(157\) | 17.4721 | 1.39443 | 0.697214 | − | 0.716863i | \(-0.254423\pi\) | ||||
0.697214 | + | 0.716863i | \(0.254423\pi\) | |||||||
\(158\) | −5.76393 | −0.458554 | ||||||||
\(159\) | 17.2361 | 1.36691 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −8.23607 | −0.649093 | ||||||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | −2.76393 | −0.215827 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.23607 | −0.328783 | ||||||||
\(167\) | −11.7082 | −0.906008 | −0.453004 | − | 0.891508i | \(-0.649648\pi\) | ||||
−0.453004 | + | 0.891508i | \(0.649648\pi\) | |||||||
\(168\) | −2.23607 | −0.172516 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 3.23607 | 0.248195 | ||||||||
\(171\) | 4.47214 | 0.341993 | ||||||||
\(172\) | −1.23607 | −0.0942493 | ||||||||
\(173\) | −15.8885 | −1.20798 | −0.603992 | − | 0.796991i | \(-0.706424\pi\) | ||||
−0.603992 | + | 0.796991i | \(0.706424\pi\) | |||||||
\(174\) | 10.0000 | 0.758098 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.4721 | −1.46362 | ||||||||
\(178\) | 12.7639 | 0.956697 | ||||||||
\(179\) | −6.76393 | −0.505560 | −0.252780 | − | 0.967524i | \(-0.581345\pi\) | ||||
−0.252780 | + | 0.967524i | \(0.581345\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | −1.00000 | −0.0741249 | ||||||||
\(183\) | −27.8885 | −2.06158 | ||||||||
\(184\) | 8.23607 | 0.607171 | ||||||||
\(185\) | 8.94427 | 0.657596 | ||||||||
\(186\) | 1.70820 | 0.125252 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.70820 | −0.416314 | ||||||||
\(189\) | −2.23607 | −0.162650 | ||||||||
\(190\) | 2.23607 | 0.162221 | ||||||||
\(191\) | 2.81966 | 0.204023 | 0.102012 | − | 0.994783i | \(-0.467472\pi\) | ||||
0.102012 | + | 0.994783i | \(0.467472\pi\) | |||||||
\(192\) | 2.23607 | 0.161374 | ||||||||
\(193\) | −9.94427 | −0.715804 | −0.357902 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357902 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(194\) | −12.4721 | −0.895447 | ||||||||
\(195\) | −2.23607 | −0.160128 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −16.4721 | −1.17359 | −0.586796 | − | 0.809735i | \(-0.699611\pi\) | ||||
−0.586796 | + | 0.809735i | \(0.699611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.47214 | 0.317021 | 0.158511 | − | 0.987357i | \(-0.449331\pi\) | ||||
0.158511 | + | 0.987357i | \(0.449331\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.18034 | −0.435928 | ||||||||
\(202\) | 1.00000 | 0.0703598 | ||||||||
\(203\) | −4.47214 | −0.313882 | ||||||||
\(204\) | 7.23607 | 0.506626 | ||||||||
\(205\) | 2.76393 | 0.193041 | ||||||||
\(206\) | 8.18034 | 0.569951 | ||||||||
\(207\) | −16.4721 | −1.14489 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.23607 | 0.154303 | ||||||||
\(211\) | 12.4721 | 0.858617 | 0.429309 | − | 0.903158i | \(-0.358757\pi\) | ||||
0.429309 | + | 0.903158i | \(0.358757\pi\) | |||||||
\(212\) | 7.70820 | 0.529402 | ||||||||
\(213\) | −23.4164 | −1.60447 | ||||||||
\(214\) | −6.47214 | −0.442426 | ||||||||
\(215\) | 1.23607 | 0.0842991 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −0.763932 | −0.0518591 | ||||||||
\(218\) | −9.70820 | −0.657523 | ||||||||
\(219\) | −6.18034 | −0.417629 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.23607 | 0.217681 | ||||||||
\(222\) | 20.0000 | 1.34231 | ||||||||
\(223\) | 14.1803 | 0.949586 | 0.474793 | − | 0.880098i | \(-0.342523\pi\) | ||||
0.474793 | + | 0.880098i | \(0.342523\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 1.00000 | 0.0665190 | ||||||||
\(227\) | 19.4164 | 1.28871 | 0.644356 | − | 0.764726i | \(-0.277125\pi\) | ||||
0.644356 | + | 0.764726i | \(0.277125\pi\) | |||||||
\(228\) | 5.00000 | 0.331133 | ||||||||
\(229\) | −10.9443 | −0.723218 | −0.361609 | − | 0.932330i | \(-0.617772\pi\) | ||||
−0.361609 | + | 0.932330i | \(0.617772\pi\) | |||||||
\(230\) | −8.23607 | −0.543070 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | −16.4164 | −1.07547 | −0.537737 | − | 0.843112i | \(-0.680721\pi\) | ||||
−0.537737 | + | 0.843112i | \(0.680721\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 5.70820 | 0.372362 | ||||||||
\(236\) | −8.70820 | −0.566856 | ||||||||
\(237\) | 12.8885 | 0.837201 | ||||||||
\(238\) | −3.23607 | −0.209763 | ||||||||
\(239\) | −2.70820 | −0.175179 | −0.0875896 | − | 0.996157i | \(-0.527916\pi\) | ||||
−0.0875896 | + | 0.996157i | \(0.527916\pi\) | |||||||
\(240\) | −2.23607 | −0.144338 | ||||||||
\(241\) | 22.3607 | 1.44038 | 0.720189 | − | 0.693778i | \(-0.244055\pi\) | ||||
0.720189 | + | 0.693778i | \(0.244055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | −12.4721 | −0.798447 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 6.18034 | 0.394044 | ||||||||
\(247\) | 2.23607 | 0.142278 | ||||||||
\(248\) | 0.763932 | 0.0485097 | ||||||||
\(249\) | 9.47214 | 0.600272 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.88854 | 0.371682 | 0.185841 | − | 0.982580i | \(-0.440499\pi\) | ||||
0.185841 | + | 0.982580i | \(0.440499\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.76393 | −0.110679 | ||||||||
\(255\) | −7.23607 | −0.453140 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.23607 | −0.576130 | −0.288065 | − | 0.957611i | \(-0.593012\pi\) | ||||
−0.288065 | + | 0.957611i | \(0.593012\pi\) | |||||||
\(258\) | 2.76393 | 0.172075 | ||||||||
\(259\) | −8.94427 | −0.555770 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | −8.94427 | −0.553637 | ||||||||
\(262\) | −19.1803 | −1.18497 | ||||||||
\(263\) | −23.6525 | −1.45847 | −0.729237 | − | 0.684261i | \(-0.760125\pi\) | ||||
−0.729237 | + | 0.684261i | \(0.760125\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.70820 | −0.473511 | ||||||||
\(266\) | −2.23607 | −0.137102 | ||||||||
\(267\) | −28.5410 | −1.74668 | ||||||||
\(268\) | −2.76393 | −0.168834 | ||||||||
\(269\) | 25.8328 | 1.57505 | 0.787527 | − | 0.616280i | \(-0.211361\pi\) | ||||
0.787527 | + | 0.616280i | \(0.211361\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | −19.4164 | −1.17946 | −0.589731 | − | 0.807599i | \(-0.700766\pi\) | ||||
−0.589731 | + | 0.807599i | \(0.700766\pi\) | |||||||
\(272\) | 3.23607 | 0.196215 | ||||||||
\(273\) | 2.23607 | 0.135333 | ||||||||
\(274\) | −4.52786 | −0.273538 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.4164 | −1.10854 | ||||||||
\(277\) | −25.5967 | −1.53796 | −0.768980 | − | 0.639273i | \(-0.779235\pi\) | ||||
−0.768980 | + | 0.639273i | \(0.779235\pi\) | |||||||
\(278\) | 0.236068 | 0.0141584 | ||||||||
\(279\) | −1.52786 | −0.0914708 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −27.8328 | −1.66037 | −0.830183 | − | 0.557491i | \(-0.811764\pi\) | ||||
−0.830183 | + | 0.557491i | \(0.811764\pi\) | |||||||
\(282\) | 12.7639 | 0.760081 | ||||||||
\(283\) | 21.7639 | 1.29373 | 0.646866 | − | 0.762604i | \(-0.276079\pi\) | ||||
0.646866 | + | 0.762604i | \(0.276079\pi\) | |||||||
\(284\) | −10.4721 | −0.621407 | ||||||||
\(285\) | −5.00000 | −0.296174 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.76393 | −0.163150 | ||||||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | −4.47214 | −0.262613 | ||||||||
\(291\) | 27.8885 | 1.63486 | ||||||||
\(292\) | −2.76393 | −0.161747 | ||||||||
\(293\) | −5.00000 | −0.292103 | −0.146052 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146052 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(294\) | −2.23607 | −0.130410 | ||||||||
\(295\) | 8.70820 | 0.507011 | ||||||||
\(296\) | 8.94427 | 0.519875 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | −8.23607 | −0.476304 | ||||||||
\(300\) | 2.23607 | 0.129099 | ||||||||
\(301\) | −1.23607 | −0.0712458 | ||||||||
\(302\) | −7.76393 | −0.446764 | ||||||||
\(303\) | −2.23607 | −0.128459 | ||||||||
\(304\) | 2.23607 | 0.128247 | ||||||||
\(305\) | 12.4721 | 0.714152 | ||||||||
\(306\) | −6.47214 | −0.369987 | ||||||||
\(307\) | −15.4164 | −0.879861 | −0.439930 | − | 0.898032i | \(-0.644997\pi\) | ||||
−0.439930 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.2918 | −1.04058 | ||||||||
\(310\) | −0.763932 | −0.0433884 | ||||||||
\(311\) | 13.1246 | 0.744228 | 0.372114 | − | 0.928187i | \(-0.378633\pi\) | ||||
0.372114 | + | 0.928187i | \(0.378633\pi\) | |||||||
\(312\) | −2.23607 | −0.126592 | ||||||||
\(313\) | 28.4721 | 1.60934 | 0.804670 | − | 0.593722i | \(-0.202342\pi\) | ||||
0.804670 | + | 0.593722i | \(0.202342\pi\) | |||||||
\(314\) | −17.4721 | −0.986010 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 5.76393 | 0.324247 | ||||||||
\(317\) | −30.6525 | −1.72161 | −0.860807 | − | 0.508931i | \(-0.830041\pi\) | ||||
−0.860807 | + | 0.508931i | \(0.830041\pi\) | |||||||
\(318\) | −17.2361 | −0.966551 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 14.4721 | 0.807756 | ||||||||
\(322\) | 8.23607 | 0.458978 | ||||||||
\(323\) | 7.23607 | 0.402626 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | 21.7082 | 1.20047 | ||||||||
\(328\) | 2.76393 | 0.152613 | ||||||||
\(329\) | −5.70820 | −0.314703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.29180 | −0.455758 | −0.227879 | − | 0.973689i | \(-0.573179\pi\) | ||||
−0.227879 | + | 0.973689i | \(0.573179\pi\) | |||||||
\(332\) | 4.23607 | 0.232484 | ||||||||
\(333\) | −17.8885 | −0.980286 | ||||||||
\(334\) | 11.7082 | 0.640644 | ||||||||
\(335\) | 2.76393 | 0.151010 | ||||||||
\(336\) | 2.23607 | 0.121988 | ||||||||
\(337\) | 32.8885 | 1.79155 | 0.895777 | − | 0.444505i | \(-0.146620\pi\) | ||||
0.895777 | + | 0.444505i | \(0.146620\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | −2.23607 | −0.121447 | ||||||||
\(340\) | −3.23607 | −0.175500 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.47214 | −0.241825 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.23607 | 0.0666443 | ||||||||
\(345\) | 18.4164 | 0.991506 | ||||||||
\(346\) | 15.8885 | 0.854173 | ||||||||
\(347\) | −6.00000 | −0.322097 | −0.161048 | − | 0.986947i | \(-0.551488\pi\) | ||||
−0.161048 | + | 0.986947i | \(0.551488\pi\) | |||||||
\(348\) | −10.0000 | −0.536056 | ||||||||
\(349\) | −26.4164 | −1.41404 | −0.707019 | − | 0.707195i | \(-0.749960\pi\) | ||||
−0.707019 | + | 0.707195i | \(0.749960\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −2.23607 | −0.119352 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.23607 | −0.491586 | −0.245793 | − | 0.969322i | \(-0.579048\pi\) | ||||
−0.245793 | + | 0.969322i | \(0.579048\pi\) | |||||||
\(354\) | 19.4721 | 1.03493 | ||||||||
\(355\) | 10.4721 | 0.555803 | ||||||||
\(356\) | −12.7639 | −0.676487 | ||||||||
\(357\) | 7.23607 | 0.382973 | ||||||||
\(358\) | 6.76393 | 0.357485 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | −14.0000 | −0.736842 | ||||||||
\(362\) | −7.00000 | −0.367912 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 2.76393 | 0.144671 | ||||||||
\(366\) | 27.8885 | 1.45776 | ||||||||
\(367\) | −14.1803 | −0.740208 | −0.370104 | − | 0.928990i | \(-0.620678\pi\) | ||||
−0.370104 | + | 0.928990i | \(0.620678\pi\) | |||||||
\(368\) | −8.23607 | −0.429335 | ||||||||
\(369\) | −5.52786 | −0.287769 | ||||||||
\(370\) | −8.94427 | −0.464991 | ||||||||
\(371\) | 7.70820 | 0.400190 | ||||||||
\(372\) | −1.70820 | −0.0885662 | ||||||||
\(373\) | −14.4721 | −0.749339 | −0.374669 | − | 0.927158i | \(-0.622244\pi\) | ||||
−0.374669 | + | 0.927158i | \(0.622244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.23607 | −0.115470 | ||||||||
\(376\) | 5.70820 | 0.294378 | ||||||||
\(377\) | −4.47214 | −0.230327 | ||||||||
\(378\) | 2.23607 | 0.115011 | ||||||||
\(379\) | −15.4164 | −0.791888 | −0.395944 | − | 0.918275i | \(-0.629583\pi\) | ||||
−0.395944 | + | 0.918275i | \(0.629583\pi\) | |||||||
\(380\) | −2.23607 | −0.114708 | ||||||||
\(381\) | 3.94427 | 0.202071 | ||||||||
\(382\) | −2.81966 | −0.144266 | ||||||||
\(383\) | −12.7639 | −0.652206 | −0.326103 | − | 0.945334i | \(-0.605736\pi\) | ||||
−0.326103 | + | 0.945334i | \(0.605736\pi\) | |||||||
\(384\) | −2.23607 | −0.114109 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.94427 | 0.506150 | ||||||||
\(387\) | −2.47214 | −0.125666 | ||||||||
\(388\) | 12.4721 | 0.633177 | ||||||||
\(389\) | −31.7082 | −1.60767 | −0.803835 | − | 0.594852i | \(-0.797210\pi\) | ||||
−0.803835 | + | 0.594852i | \(0.797210\pi\) | |||||||
\(390\) | 2.23607 | 0.113228 | ||||||||
\(391\) | −26.6525 | −1.34787 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 42.8885 | 2.16344 | ||||||||
\(394\) | 16.4721 | 0.829854 | ||||||||
\(395\) | −5.76393 | −0.290015 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | −4.47214 | −0.224168 | ||||||||
\(399\) | 5.00000 | 0.250313 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 24.8328 | 1.24009 | 0.620046 | − | 0.784566i | \(-0.287114\pi\) | ||||
0.620046 | + | 0.784566i | \(0.287114\pi\) | |||||||
\(402\) | 6.18034 | 0.308247 | ||||||||
\(403\) | −0.763932 | −0.0380542 | ||||||||
\(404\) | −1.00000 | −0.0497519 | ||||||||
\(405\) | 11.0000 | 0.546594 | ||||||||
\(406\) | 4.47214 | 0.221948 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.23607 | −0.358239 | ||||||||
\(409\) | 20.4721 | 1.01228 | 0.506141 | − | 0.862451i | \(-0.331072\pi\) | ||||
0.506141 | + | 0.862451i | \(0.331072\pi\) | |||||||
\(410\) | −2.76393 | −0.136501 | ||||||||
\(411\) | 10.1246 | 0.499410 | ||||||||
\(412\) | −8.18034 | −0.403016 | ||||||||
\(413\) | −8.70820 | −0.428503 | ||||||||
\(414\) | 16.4721 | 0.809561 | ||||||||
\(415\) | −4.23607 | −0.207940 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −0.527864 | −0.0258496 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.7639 | −1.16094 | −0.580472 | − | 0.814280i | \(-0.697132\pi\) | ||||
−0.580472 | + | 0.814280i | \(0.697132\pi\) | |||||||
\(420\) | −2.23607 | −0.109109 | ||||||||
\(421\) | −20.9443 | −1.02076 | −0.510381 | − | 0.859949i | \(-0.670495\pi\) | ||||
−0.510381 | + | 0.859949i | \(0.670495\pi\) | |||||||
\(422\) | −12.4721 | −0.607134 | ||||||||
\(423\) | −11.4164 | −0.555085 | ||||||||
\(424\) | −7.70820 | −0.374343 | ||||||||
\(425\) | 3.23607 | 0.156972 | ||||||||
\(426\) | 23.4164 | 1.13453 | ||||||||
\(427\) | −12.4721 | −0.603569 | ||||||||
\(428\) | 6.47214 | 0.312842 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.23607 | −0.0596085 | ||||||||
\(431\) | −2.34752 | −0.113076 | −0.0565381 | − | 0.998400i | \(-0.518006\pi\) | ||||
−0.0565381 | + | 0.998400i | \(0.518006\pi\) | |||||||
\(432\) | −2.23607 | −0.107583 | ||||||||
\(433\) | 18.6525 | 0.896381 | 0.448190 | − | 0.893938i | \(-0.352069\pi\) | ||||
0.448190 | + | 0.893938i | \(0.352069\pi\) | |||||||
\(434\) | 0.763932 | 0.0366699 | ||||||||
\(435\) | 10.0000 | 0.479463 | ||||||||
\(436\) | 9.70820 | 0.464939 | ||||||||
\(437\) | −18.4164 | −0.880976 | ||||||||
\(438\) | 6.18034 | 0.295308 | ||||||||
\(439\) | −25.1246 | −1.19913 | −0.599566 | − | 0.800325i | \(-0.704660\pi\) | ||||
−0.599566 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | −3.23607 | −0.153924 | ||||||||
\(443\) | 20.3607 | 0.967365 | 0.483683 | − | 0.875244i | \(-0.339299\pi\) | ||||
0.483683 | + | 0.875244i | \(0.339299\pi\) | |||||||
\(444\) | −20.0000 | −0.949158 | ||||||||
\(445\) | 12.7639 | 0.605068 | ||||||||
\(446\) | −14.1803 | −0.671459 | ||||||||
\(447\) | 8.94427 | 0.423050 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −29.8328 | −1.40790 | −0.703949 | − | 0.710251i | \(-0.748582\pi\) | ||||
−0.703949 | + | 0.710251i | \(0.748582\pi\) | |||||||
\(450\) | −2.00000 | −0.0942809 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.00000 | −0.0470360 | ||||||||
\(453\) | 17.3607 | 0.815676 | ||||||||
\(454\) | −19.4164 | −0.911257 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | −9.58359 | −0.448302 | −0.224151 | − | 0.974554i | \(-0.571961\pi\) | ||||
−0.224151 | + | 0.974554i | \(0.571961\pi\) | |||||||
\(458\) | 10.9443 | 0.511392 | ||||||||
\(459\) | −7.23607 | −0.337751 | ||||||||
\(460\) | 8.23607 | 0.384009 | ||||||||
\(461\) | 11.8885 | 0.553705 | 0.276852 | − | 0.960912i | \(-0.410709\pi\) | ||||
0.276852 | + | 0.960912i | \(0.410709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70820 | −0.125861 | −0.0629305 | − | 0.998018i | \(-0.520045\pi\) | ||||
−0.0629305 | + | 0.998018i | \(0.520045\pi\) | |||||||
\(464\) | −4.47214 | −0.207614 | ||||||||
\(465\) | 1.70820 | 0.0792161 | ||||||||
\(466\) | 16.4164 | 0.760475 | ||||||||
\(467\) | −25.1803 | −1.16521 | −0.582604 | − | 0.812756i | \(-0.697966\pi\) | ||||
−0.582604 | + | 0.812756i | \(0.697966\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −2.76393 | −0.127627 | ||||||||
\(470\) | −5.70820 | −0.263300 | ||||||||
\(471\) | 39.0689 | 1.80020 | ||||||||
\(472\) | 8.70820 | 0.400828 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.8885 | −0.591990 | ||||||||
\(475\) | 2.23607 | 0.102598 | ||||||||
\(476\) | 3.23607 | 0.148325 | ||||||||
\(477\) | 15.4164 | 0.705869 | ||||||||
\(478\) | 2.70820 | 0.123870 | ||||||||
\(479\) | 21.5967 | 0.986781 | 0.493390 | − | 0.869808i | \(-0.335757\pi\) | ||||
0.493390 | + | 0.869808i | \(0.335757\pi\) | |||||||
\(480\) | 2.23607 | 0.102062 | ||||||||
\(481\) | −8.94427 | −0.407824 | ||||||||
\(482\) | −22.3607 | −1.01850 | ||||||||
\(483\) | −18.4164 | −0.837976 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.4721 | −0.566331 | ||||||||
\(486\) | 17.8885 | 0.811441 | ||||||||
\(487\) | −2.23607 | −0.101326 | −0.0506630 | − | 0.998716i | \(-0.516133\pi\) | ||||
−0.0506630 | + | 0.998716i | \(0.516133\pi\) | |||||||
\(488\) | 12.4721 | 0.564587 | ||||||||
\(489\) | −13.4164 | −0.606711 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 26.7639 | 1.20784 | 0.603920 | − | 0.797045i | \(-0.293605\pi\) | ||||
0.603920 | + | 0.797045i | \(0.293605\pi\) | |||||||
\(492\) | −6.18034 | −0.278631 | ||||||||
\(493\) | −14.4721 | −0.651792 | ||||||||
\(494\) | −2.23607 | −0.100605 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.763932 | −0.0343016 | ||||||||
\(497\) | −10.4721 | −0.469739 | ||||||||
\(498\) | −9.47214 | −0.424457 | ||||||||
\(499\) | −26.8328 | −1.20120 | −0.600601 | − | 0.799549i | \(-0.705072\pi\) | ||||
−0.600601 | + | 0.799549i | \(0.705072\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −26.1803 | −1.16965 | ||||||||
\(502\) | −5.88854 | −0.262819 | ||||||||
\(503\) | −23.5967 | −1.05213 | −0.526063 | − | 0.850445i | \(-0.676333\pi\) | ||||
−0.526063 | + | 0.850445i | \(0.676333\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 1.00000 | 0.0444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.8328 | −1.19169 | ||||||||
\(508\) | 1.76393 | 0.0782618 | ||||||||
\(509\) | −6.88854 | −0.305329 | −0.152665 | − | 0.988278i | \(-0.548785\pi\) | ||||
−0.152665 | + | 0.988278i | \(0.548785\pi\) | |||||||
\(510\) | 7.23607 | 0.320418 | ||||||||
\(511\) | −2.76393 | −0.122269 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 9.23607 | 0.407385 | ||||||||
\(515\) | 8.18034 | 0.360469 | ||||||||
\(516\) | −2.76393 | −0.121675 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.94427 | 0.392989 | ||||||||
\(519\) | −35.5279 | −1.55950 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −18.9443 | −0.829964 | −0.414982 | − | 0.909830i | \(-0.636212\pi\) | ||||
−0.414982 | + | 0.909830i | \(0.636212\pi\) | |||||||
\(522\) | 8.94427 | 0.391480 | ||||||||
\(523\) | −4.34752 | −0.190104 | −0.0950520 | − | 0.995472i | \(-0.530302\pi\) | ||||
−0.0950520 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(524\) | 19.1803 | 0.837897 | ||||||||
\(525\) | 2.23607 | 0.0975900 | ||||||||
\(526\) | 23.6525 | 1.03130 | ||||||||
\(527\) | −2.47214 | −0.107688 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 7.70820 | 0.334823 | ||||||||
\(531\) | −17.4164 | −0.755808 | ||||||||
\(532\) | 2.23607 | 0.0969458 | ||||||||
\(533\) | −2.76393 | −0.119719 | ||||||||
\(534\) | 28.5410 | 1.23509 | ||||||||
\(535\) | −6.47214 | −0.279815 | ||||||||
\(536\) | 2.76393 | 0.119384 | ||||||||
\(537\) | −15.1246 | −0.652675 | ||||||||
\(538\) | −25.8328 | −1.11373 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.23607 | 0.0962250 | ||||||||
\(541\) | 27.3050 | 1.17393 | 0.586966 | − | 0.809612i | \(-0.300322\pi\) | ||||
0.586966 | + | 0.809612i | \(0.300322\pi\) | |||||||
\(542\) | 19.4164 | 0.834006 | ||||||||
\(543\) | 15.6525 | 0.671712 | ||||||||
\(544\) | −3.23607 | −0.138745 | ||||||||
\(545\) | −9.70820 | −0.415854 | ||||||||
\(546\) | −2.23607 | −0.0956949 | ||||||||
\(547\) | −24.6525 | −1.05406 | −0.527032 | − | 0.849846i | \(-0.676695\pi\) | ||||
−0.527032 | + | 0.849846i | \(0.676695\pi\) | |||||||
\(548\) | 4.52786 | 0.193421 | ||||||||
\(549\) | −24.9443 | −1.06460 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0000 | −0.426014 | ||||||||
\(552\) | 18.4164 | 0.783854 | ||||||||
\(553\) | 5.76393 | 0.245107 | ||||||||
\(554\) | 25.5967 | 1.08750 | ||||||||
\(555\) | 20.0000 | 0.848953 | ||||||||
\(556\) | −0.236068 | −0.0100115 | ||||||||
\(557\) | 9.12461 | 0.386622 | 0.193311 | − | 0.981138i | \(-0.438077\pi\) | ||||
0.193311 | + | 0.981138i | \(0.438077\pi\) | |||||||
\(558\) | 1.52786 | 0.0646796 | ||||||||
\(559\) | −1.23607 | −0.0522801 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.8328 | 1.17406 | ||||||||
\(563\) | 12.5967 | 0.530890 | 0.265445 | − | 0.964126i | \(-0.414481\pi\) | ||||
0.265445 | + | 0.964126i | \(0.414481\pi\) | |||||||
\(564\) | −12.7639 | −0.537458 | ||||||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | −21.7639 | −0.914806 | ||||||||
\(567\) | −11.0000 | −0.461957 | ||||||||
\(568\) | 10.4721 | 0.439401 | ||||||||
\(569\) | −1.47214 | −0.0617151 | −0.0308576 | − | 0.999524i | \(-0.509824\pi\) | ||||
−0.0308576 | + | 0.999524i | \(0.509824\pi\) | |||||||
\(570\) | 5.00000 | 0.209427 | ||||||||
\(571\) | −8.36068 | −0.349884 | −0.174942 | − | 0.984579i | \(-0.555974\pi\) | ||||
−0.174942 | + | 0.984579i | \(0.555974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.30495 | 0.263393 | ||||||||
\(574\) | 2.76393 | 0.115364 | ||||||||
\(575\) | −8.23607 | −0.343468 | ||||||||
\(576\) | 2.00000 | 0.0833333 | ||||||||
\(577\) | 41.0132 | 1.70740 | 0.853700 | − | 0.520765i | \(-0.174353\pi\) | ||||
0.853700 | + | 0.520765i | \(0.174353\pi\) | |||||||
\(578\) | 6.52786 | 0.271523 | ||||||||
\(579\) | −22.2361 | −0.924099 | ||||||||
\(580\) | 4.47214 | 0.185695 | ||||||||
\(581\) | 4.23607 | 0.175742 | ||||||||
\(582\) | −27.8885 | −1.15602 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.76393 | 0.114372 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 5.00000 | 0.206548 | ||||||||
\(587\) | 35.0689 | 1.44745 | 0.723724 | − | 0.690090i | \(-0.242429\pi\) | ||||
0.723724 | + | 0.690090i | \(0.242429\pi\) | |||||||
\(588\) | 2.23607 | 0.0922139 | ||||||||
\(589\) | −1.70820 | −0.0703853 | ||||||||
\(590\) | −8.70820 | −0.358511 | ||||||||
\(591\) | −36.8328 | −1.51510 | ||||||||
\(592\) | −8.94427 | −0.367607 | ||||||||
\(593\) | 19.0557 | 0.782525 | 0.391262 | − | 0.920279i | \(-0.372038\pi\) | ||||
0.391262 | + | 0.920279i | \(0.372038\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.23607 | −0.132666 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 8.23607 | 0.336798 | ||||||||
\(599\) | −31.0689 | −1.26944 | −0.634720 | − | 0.772742i | \(-0.718885\pi\) | ||||
−0.634720 | + | 0.772742i | \(0.718885\pi\) | |||||||
\(600\) | −2.23607 | −0.0912871 | ||||||||
\(601\) | −4.65248 | −0.189778 | −0.0948892 | − | 0.995488i | \(-0.530250\pi\) | ||||
−0.0948892 | + | 0.995488i | \(0.530250\pi\) | |||||||
\(602\) | 1.23607 | 0.0503784 | ||||||||
\(603\) | −5.52786 | −0.225112 | ||||||||
\(604\) | 7.76393 | 0.315910 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.23607 | 0.0908341 | ||||||||
\(607\) | 38.9443 | 1.58070 | 0.790350 | − | 0.612656i | \(-0.209899\pi\) | ||||
0.790350 | + | 0.612656i | \(0.209899\pi\) | |||||||
\(608\) | −2.23607 | −0.0906845 | ||||||||
\(609\) | −10.0000 | −0.405220 | ||||||||
\(610\) | −12.4721 | −0.504982 | ||||||||
\(611\) | −5.70820 | −0.230929 | ||||||||
\(612\) | 6.47214 | 0.261621 | ||||||||
\(613\) | 41.1246 | 1.66101 | 0.830504 | − | 0.557013i | \(-0.188053\pi\) | ||||
0.830504 | + | 0.557013i | \(0.188053\pi\) | |||||||
\(614\) | 15.4164 | 0.622156 | ||||||||
\(615\) | 6.18034 | 0.249215 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.11146 | −0.326555 | −0.163277 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163277 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(618\) | 18.2918 | 0.735804 | ||||||||
\(619\) | 19.5410 | 0.785420 | 0.392710 | − | 0.919662i | \(-0.371538\pi\) | ||||
0.392710 | + | 0.919662i | \(0.371538\pi\) | |||||||
\(620\) | 0.763932 | 0.0306802 | ||||||||
\(621\) | 18.4164 | 0.739025 | ||||||||
\(622\) | −13.1246 | −0.526249 | ||||||||
\(623\) | −12.7639 | −0.511376 | ||||||||
\(624\) | 2.23607 | 0.0895144 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.4721 | −1.13798 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.4721 | 0.697214 | ||||||||
\(629\) | −28.9443 | −1.15408 | ||||||||
\(630\) | 2.00000 | 0.0796819 | ||||||||
\(631\) | 28.3607 | 1.12902 | 0.564510 | − | 0.825426i | \(-0.309065\pi\) | ||||
0.564510 | + | 0.825426i | \(0.309065\pi\) | |||||||
\(632\) | −5.76393 | −0.229277 | ||||||||
\(633\) | 27.8885 | 1.10847 | ||||||||
\(634\) | 30.6525 | 1.21737 | ||||||||
\(635\) | −1.76393 | −0.0699995 | ||||||||
\(636\) | 17.2361 | 0.683455 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.9443 | −0.828543 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 29.8328 | 1.17833 | 0.589163 | − | 0.808014i | \(-0.299458\pi\) | ||||
0.589163 | + | 0.808014i | \(0.299458\pi\) | |||||||
\(642\) | −14.4721 | −0.571170 | ||||||||
\(643\) | 41.8885 | 1.65192 | 0.825961 | − | 0.563727i | \(-0.190633\pi\) | ||||
0.825961 | + | 0.563727i | \(0.190633\pi\) | |||||||
\(644\) | −8.23607 | −0.324547 | ||||||||
\(645\) | 2.76393 | 0.108830 | ||||||||
\(646\) | −7.23607 | −0.284699 | ||||||||
\(647\) | −4.76393 | −0.187289 | −0.0936447 | − | 0.995606i | \(-0.529852\pi\) | ||||
−0.0936447 | + | 0.995606i | \(0.529852\pi\) | |||||||
\(648\) | 11.0000 | 0.432121 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | −1.70820 | −0.0669498 | ||||||||
\(652\) | −6.00000 | −0.234978 | ||||||||
\(653\) | 39.7082 | 1.55390 | 0.776951 | − | 0.629561i | \(-0.216765\pi\) | ||||
0.776951 | + | 0.629561i | \(0.216765\pi\) | |||||||
\(654\) | −21.7082 | −0.848858 | ||||||||
\(655\) | −19.1803 | −0.749438 | ||||||||
\(656\) | −2.76393 | −0.107913 | ||||||||
\(657\) | −5.52786 | −0.215663 | ||||||||
\(658\) | 5.70820 | 0.222529 | ||||||||
\(659\) | −25.2361 | −0.983058 | −0.491529 | − | 0.870861i | \(-0.663562\pi\) | ||||
−0.491529 | + | 0.870861i | \(0.663562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4164 | −0.871897 | −0.435949 | − | 0.899972i | \(-0.643587\pi\) | ||||
−0.435949 | + | 0.899972i | \(0.643587\pi\) | |||||||
\(662\) | 8.29180 | 0.322270 | ||||||||
\(663\) | 7.23607 | 0.281026 | ||||||||
\(664\) | −4.23607 | −0.164391 | ||||||||
\(665\) | −2.23607 | −0.0867110 | ||||||||
\(666\) | 17.8885 | 0.693167 | ||||||||
\(667\) | 36.8328 | 1.42617 | ||||||||
\(668\) | −11.7082 | −0.453004 | ||||||||
\(669\) | 31.7082 | 1.22591 | ||||||||
\(670\) | −2.76393 | −0.106780 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.23607 | −0.0862582 | ||||||||
\(673\) | −27.9443 | −1.07717 | −0.538586 | − | 0.842570i | \(-0.681041\pi\) | ||||
−0.538586 | + | 0.842570i | \(0.681041\pi\) | |||||||
\(674\) | −32.8885 | −1.26682 | ||||||||
\(675\) | −2.23607 | −0.0860663 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 7.83282 | 0.301040 | 0.150520 | − | 0.988607i | \(-0.451905\pi\) | ||||
0.150520 | + | 0.988607i | \(0.451905\pi\) | |||||||
\(678\) | 2.23607 | 0.0858757 | ||||||||
\(679\) | 12.4721 | 0.478637 | ||||||||
\(680\) | 3.23607 | 0.124098 | ||||||||
\(681\) | 43.4164 | 1.66372 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.3607 | 1.46783 | 0.733915 | − | 0.679241i | \(-0.237691\pi\) | ||||
0.733915 | + | 0.679241i | \(0.237691\pi\) | |||||||
\(684\) | 4.47214 | 0.170996 | ||||||||
\(685\) | −4.52786 | −0.173001 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −24.4721 | −0.933670 | ||||||||
\(688\) | −1.23607 | −0.0471246 | ||||||||
\(689\) | 7.70820 | 0.293659 | ||||||||
\(690\) | −18.4164 | −0.701101 | ||||||||
\(691\) | −40.0000 | −1.52167 | −0.760836 | − | 0.648944i | \(-0.775211\pi\) | ||||
−0.760836 | + | 0.648944i | \(0.775211\pi\) | |||||||
\(692\) | −15.8885 | −0.603992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 0.236068 | 0.00895457 | ||||||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | −8.94427 | −0.338788 | ||||||||
\(698\) | 26.4164 | 0.999876 | ||||||||
\(699\) | −36.7082 | −1.38843 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 31.5967 | 1.19339 | 0.596696 | − | 0.802467i | \(-0.296480\pi\) | ||||
0.596696 | + | 0.802467i | \(0.296480\pi\) | |||||||
\(702\) | 2.23607 | 0.0843949 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.7639 | 0.480717 | ||||||||
\(706\) | 9.23607 | 0.347604 | ||||||||
\(707\) | −1.00000 | −0.0376089 | ||||||||
\(708\) | −19.4721 | −0.731808 | ||||||||
\(709\) | 36.9443 | 1.38747 | 0.693736 | − | 0.720230i | \(-0.255964\pi\) | ||||
0.693736 | + | 0.720230i | \(0.255964\pi\) | |||||||
\(710\) | −10.4721 | −0.393012 | ||||||||
\(711\) | 11.5279 | 0.432329 | ||||||||
\(712\) | 12.7639 | 0.478349 | ||||||||
\(713\) | 6.29180 | 0.235630 | ||||||||
\(714\) | −7.23607 | −0.270803 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.76393 | −0.252780 | ||||||||
\(717\) | −6.05573 | −0.226155 | ||||||||
\(718\) | −16.0000 | −0.597115 | ||||||||
\(719\) | −46.8328 | −1.74657 | −0.873285 | − | 0.487210i | \(-0.838015\pi\) | ||||
−0.873285 | + | 0.487210i | \(0.838015\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | −8.18034 | −0.304652 | ||||||||
\(722\) | 14.0000 | 0.521026 | ||||||||
\(723\) | 50.0000 | 1.85952 | ||||||||
\(724\) | 7.00000 | 0.260153 | ||||||||
\(725\) | −4.47214 | −0.166091 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.3050 | 0.864333 | 0.432166 | − | 0.901794i | \(-0.357749\pi\) | ||||
0.432166 | + | 0.901794i | \(0.357749\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | −2.76393 | −0.102298 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | −27.8885 | −1.03079 | ||||||||
\(733\) | −21.5836 | −0.797208 | −0.398604 | − | 0.917123i | \(-0.630505\pi\) | ||||
−0.398604 | + | 0.917123i | \(0.630505\pi\) | |||||||
\(734\) | 14.1803 | 0.523406 | ||||||||
\(735\) | −2.23607 | −0.0824786 | ||||||||
\(736\) | 8.23607 | 0.303585 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.52786 | 0.203483 | ||||||||
\(739\) | −40.0689 | −1.47396 | −0.736979 | − | 0.675916i | \(-0.763748\pi\) | ||||
−0.736979 | + | 0.675916i | \(0.763748\pi\) | |||||||
\(740\) | 8.94427 | 0.328798 | ||||||||
\(741\) | 5.00000 | 0.183680 | ||||||||
\(742\) | −7.70820 | −0.282977 | ||||||||
\(743\) | 28.0000 | 1.02722 | 0.513610 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513610 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(744\) | 1.70820 | 0.0626258 | ||||||||
\(745\) | −4.00000 | −0.146549 | ||||||||
\(746\) | 14.4721 | 0.529863 | ||||||||
\(747\) | 8.47214 | 0.309979 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.47214 | 0.236487 | ||||||||
\(750\) | 2.23607 | 0.0816497 | ||||||||
\(751\) | 11.1803 | 0.407976 | 0.203988 | − | 0.978973i | \(-0.434610\pi\) | ||||
0.203988 | + | 0.978973i | \(0.434610\pi\) | |||||||
\(752\) | −5.70820 | −0.208157 | ||||||||
\(753\) | 13.1672 | 0.479839 | ||||||||
\(754\) | 4.47214 | 0.162866 | ||||||||
\(755\) | −7.76393 | −0.282558 | ||||||||
\(756\) | −2.23607 | −0.0813250 | ||||||||
\(757\) | −11.3475 | −0.412433 | −0.206216 | − | 0.978506i | \(-0.566115\pi\) | ||||
−0.206216 | + | 0.978506i | \(0.566115\pi\) | |||||||
\(758\) | 15.4164 | 0.559949 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.23607 | 0.0811107 | ||||||||
\(761\) | 36.5410 | 1.32461 | 0.662305 | − | 0.749234i | \(-0.269578\pi\) | ||||
0.662305 | + | 0.749234i | \(0.269578\pi\) | |||||||
\(762\) | −3.94427 | −0.142886 | ||||||||
\(763\) | 9.70820 | 0.351461 | ||||||||
\(764\) | 2.81966 | 0.102012 | ||||||||
\(765\) | −6.47214 | −0.234001 | ||||||||
\(766\) | 12.7639 | 0.461180 | ||||||||
\(767\) | −8.70820 | −0.314435 | ||||||||
\(768\) | 2.23607 | 0.0806872 | ||||||||
\(769\) | −12.0000 | −0.432731 | −0.216366 | − | 0.976312i | \(-0.569420\pi\) | ||||
−0.216366 | + | 0.976312i | \(0.569420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.6525 | −0.743781 | ||||||||
\(772\) | −9.94427 | −0.357902 | ||||||||
\(773\) | −10.0557 | −0.361679 | −0.180840 | − | 0.983513i | \(-0.557882\pi\) | ||||
−0.180840 | + | 0.983513i | \(0.557882\pi\) | |||||||
\(774\) | 2.47214 | 0.0888591 | ||||||||
\(775\) | −0.763932 | −0.0274412 | ||||||||
\(776\) | −12.4721 | −0.447724 | ||||||||
\(777\) | −20.0000 | −0.717496 | ||||||||
\(778\) | 31.7082 | 1.13679 | ||||||||
\(779\) | −6.18034 | −0.221434 | ||||||||
\(780\) | −2.23607 | −0.0800641 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.6525 | 0.953091 | ||||||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −17.4721 | −0.623607 | ||||||||
\(786\) | −42.8885 | −1.52978 | ||||||||
\(787\) | 39.7771 | 1.41790 | 0.708950 | − | 0.705259i | \(-0.249169\pi\) | ||||
0.708950 | + | 0.705259i | \(0.249169\pi\) | |||||||
\(788\) | −16.4721 | −0.586796 | ||||||||
\(789\) | −52.8885 | −1.88288 | ||||||||
\(790\) | 5.76393 | 0.205071 | ||||||||
\(791\) | −1.00000 | −0.0355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4721 | −0.442899 | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | −17.2361 | −0.611300 | ||||||||
\(796\) | 4.47214 | 0.158511 | ||||||||
\(797\) | −6.88854 | −0.244005 | −0.122002 | − | 0.992530i | \(-0.538932\pi\) | ||||
−0.122002 | + | 0.992530i | \(0.538932\pi\) | |||||||
\(798\) | −5.00000 | −0.176998 | ||||||||
\(799\) | −18.4721 | −0.653497 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −25.5279 | −0.901983 | ||||||||
\(802\) | −24.8328 | −0.876877 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.18034 | −0.217964 | ||||||||
\(805\) | 8.23607 | 0.290283 | ||||||||
\(806\) | 0.763932 | 0.0269084 | ||||||||
\(807\) | 57.7639 | 2.03339 | ||||||||
\(808\) | 1.00000 | 0.0351799 | ||||||||
\(809\) | −46.3607 | −1.62995 | −0.814977 | − | 0.579493i | \(-0.803251\pi\) | ||||
−0.814977 | + | 0.579493i | \(0.803251\pi\) | |||||||
\(810\) | −11.0000 | −0.386501 | ||||||||
\(811\) | −6.47214 | −0.227267 | −0.113634 | − | 0.993523i | \(-0.536249\pi\) | ||||
−0.113634 | + | 0.993523i | \(0.536249\pi\) | |||||||
\(812\) | −4.47214 | −0.156941 | ||||||||
\(813\) | −43.4164 | −1.52268 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 7.23607 | 0.253313 | ||||||||
\(817\) | −2.76393 | −0.0966977 | ||||||||
\(818\) | −20.4721 | −0.715791 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 2.76393 | 0.0965207 | ||||||||
\(821\) | 30.9443 | 1.07996 | 0.539981 | − | 0.841677i | \(-0.318431\pi\) | ||||
0.539981 | + | 0.841677i | \(0.318431\pi\) | |||||||
\(822\) | −10.1246 | −0.353136 | ||||||||
\(823\) | −28.3607 | −0.988591 | −0.494296 | − | 0.869294i | \(-0.664574\pi\) | ||||
−0.494296 | + | 0.869294i | \(0.664574\pi\) | |||||||
\(824\) | 8.18034 | 0.284976 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.70820 | 0.302997 | ||||||||
\(827\) | −10.1803 | −0.354005 | −0.177003 | − | 0.984210i | \(-0.556640\pi\) | ||||
−0.177003 | + | 0.984210i | \(0.556640\pi\) | |||||||
\(828\) | −16.4721 | −0.572446 | ||||||||
\(829\) | 5.94427 | 0.206453 | 0.103227 | − | 0.994658i | \(-0.467083\pi\) | ||||
0.103227 | + | 0.994658i | \(0.467083\pi\) | |||||||
\(830\) | 4.23607 | 0.147036 | ||||||||
\(831\) | −57.2361 | −1.98550 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 3.23607 | 0.112123 | ||||||||
\(834\) | 0.527864 | 0.0182784 | ||||||||
\(835\) | 11.7082 | 0.405179 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.70820 | 0.0590442 | ||||||||
\(838\) | 23.7639 | 0.820911 | ||||||||
\(839\) | 35.5967 | 1.22894 | 0.614468 | − | 0.788942i | \(-0.289371\pi\) | ||||
0.614468 | + | 0.788942i | \(0.289371\pi\) | |||||||
\(840\) | 2.23607 | 0.0771517 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 20.9443 | 0.721787 | ||||||||
\(843\) | −62.2361 | −2.14352 | ||||||||
\(844\) | 12.4721 | 0.429309 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | 11.4164 | 0.392504 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.70820 | 0.264701 | ||||||||
\(849\) | 48.6656 | 1.67020 | ||||||||
\(850\) | −3.23607 | −0.110996 | ||||||||
\(851\) | 73.6656 | 2.52523 | ||||||||
\(852\) | −23.4164 | −0.802233 | ||||||||
\(853\) | −5.47214 | −0.187362 | −0.0936812 | − | 0.995602i | \(-0.529863\pi\) | ||||
−0.0936812 | + | 0.995602i | \(0.529863\pi\) | |||||||
\(854\) | 12.4721 | 0.426788 | ||||||||
\(855\) | −4.47214 | −0.152944 | ||||||||
\(856\) | −6.47214 | −0.221213 | ||||||||
\(857\) | −42.8328 | −1.46314 | −0.731571 | − | 0.681766i | \(-0.761212\pi\) | ||||
−0.731571 | + | 0.681766i | \(0.761212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9443 | −0.578131 | −0.289066 | − | 0.957309i | \(-0.593345\pi\) | ||||
−0.289066 | + | 0.957309i | \(0.593345\pi\) | |||||||
\(860\) | 1.23607 | 0.0421496 | ||||||||
\(861\) | −6.18034 | −0.210625 | ||||||||
\(862\) | 2.34752 | 0.0799570 | ||||||||
\(863\) | 32.7214 | 1.11385 | 0.556924 | − | 0.830563i | \(-0.311981\pi\) | ||||
0.556924 | + | 0.830563i | \(0.311981\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | 15.8885 | 0.540227 | ||||||||
\(866\) | −18.6525 | −0.633837 | ||||||||
\(867\) | −14.5967 | −0.495732 | ||||||||
\(868\) | −0.763932 | −0.0259295 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.0000 | −0.339032 | ||||||||
\(871\) | −2.76393 | −0.0936523 | ||||||||
\(872\) | −9.70820 | −0.328761 | ||||||||
\(873\) | 24.9443 | 0.844236 | ||||||||
\(874\) | 18.4164 | 0.622944 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −6.18034 | −0.208814 | ||||||||
\(877\) | 41.9574 | 1.41680 | 0.708401 | − | 0.705810i | \(-0.249417\pi\) | ||||
0.708401 | + | 0.705810i | \(0.249417\pi\) | |||||||
\(878\) | 25.1246 | 0.847915 | ||||||||
\(879\) | −11.1803 | −0.377104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9443 | 0.436104 | 0.218052 | − | 0.975937i | \(-0.430030\pi\) | ||||
0.218052 | + | 0.975937i | \(0.430030\pi\) | |||||||
\(882\) | −2.00000 | −0.0673435 | ||||||||
\(883\) | −13.5279 | −0.455249 | −0.227624 | − | 0.973749i | \(-0.573096\pi\) | ||||
−0.227624 | + | 0.973749i | \(0.573096\pi\) | |||||||
\(884\) | 3.23607 | 0.108841 | ||||||||
\(885\) | 19.4721 | 0.654549 | ||||||||
\(886\) | −20.3607 | −0.684030 | ||||||||
\(887\) | 0.763932 | 0.0256503 | 0.0128252 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128252 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(888\) | 20.0000 | 0.671156 | ||||||||
\(889\) | 1.76393 | 0.0591604 | ||||||||
\(890\) | −12.7639 | −0.427848 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.1803 | 0.474793 | ||||||||
\(893\) | −12.7639 | −0.427129 | ||||||||
\(894\) | −8.94427 | −0.299141 | ||||||||
\(895\) | 6.76393 | 0.226093 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −18.4164 | −0.614906 | ||||||||
\(898\) | 29.8328 | 0.995534 | ||||||||
\(899\) | 3.41641 | 0.113944 | ||||||||
\(900\) | 2.00000 | 0.0666667 | ||||||||
\(901\) | 24.9443 | 0.831014 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.76393 | −0.0919779 | ||||||||
\(904\) | 1.00000 | 0.0332595 | ||||||||
\(905\) | −7.00000 | −0.232688 | ||||||||
\(906\) | −17.3607 | −0.576770 | ||||||||
\(907\) | −4.36068 | −0.144794 | −0.0723970 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723970 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(908\) | 19.4164 | 0.644356 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 1.00000 | 0.0331497 | ||||||||
\(911\) | −12.3475 | −0.409092 | −0.204546 | − | 0.978857i | \(-0.565572\pi\) | ||||
−0.204546 | + | 0.978857i | \(0.565572\pi\) | |||||||
\(912\) | 5.00000 | 0.165567 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.58359 | 0.316997 | ||||||||
\(915\) | 27.8885 | 0.921967 | ||||||||
\(916\) | −10.9443 | −0.361609 | ||||||||
\(917\) | 19.1803 | 0.633391 | ||||||||
\(918\) | 7.23607 | 0.238826 | ||||||||
\(919\) | −4.94427 | −0.163096 | −0.0815482 | − | 0.996669i | \(-0.525986\pi\) | ||||
−0.0815482 | + | 0.996669i | \(0.525986\pi\) | |||||||
\(920\) | −8.23607 | −0.271535 | ||||||||
\(921\) | −34.4721 | −1.13590 | ||||||||
\(922\) | −11.8885 | −0.391528 | ||||||||
\(923\) | −10.4721 | −0.344695 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.94427 | −0.294086 | ||||||||
\(926\) | 2.70820 | 0.0889971 | ||||||||
\(927\) | −16.3607 | −0.537355 | ||||||||
\(928\) | 4.47214 | 0.146805 | ||||||||
\(929\) | 10.8328 | 0.355413 | 0.177707 | − | 0.984084i | \(-0.443132\pi\) | ||||
0.177707 | + | 0.984084i | \(0.443132\pi\) | |||||||
\(930\) | −1.70820 | −0.0560142 | ||||||||
\(931\) | 2.23607 | 0.0732842 | ||||||||
\(932\) | −16.4164 | −0.537737 | ||||||||
\(933\) | 29.3475 | 0.960795 | ||||||||
\(934\) | 25.1803 | 0.823926 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 11.5279 | 0.376599 | 0.188299 | − | 0.982112i | \(-0.439702\pi\) | ||||
0.188299 | + | 0.982112i | \(0.439702\pi\) | |||||||
\(938\) | 2.76393 | 0.0902456 | ||||||||
\(939\) | 63.6656 | 2.07765 | ||||||||
\(940\) | 5.70820 | 0.186181 | ||||||||
\(941\) | −20.1115 | −0.655615 | −0.327807 | − | 0.944745i | \(-0.606310\pi\) | ||||
−0.327807 | + | 0.944745i | \(0.606310\pi\) | |||||||
\(942\) | −39.0689 | −1.27293 | ||||||||
\(943\) | 22.7639 | 0.741296 | ||||||||
\(944\) | −8.70820 | −0.283428 | ||||||||
\(945\) | 2.23607 | 0.0727393 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.0689 | −1.56203 | −0.781014 | − | 0.624513i | \(-0.785297\pi\) | ||||
−0.781014 | + | 0.624513i | \(0.785297\pi\) | |||||||
\(948\) | 12.8885 | 0.418600 | ||||||||
\(949\) | −2.76393 | −0.0897210 | ||||||||
\(950\) | −2.23607 | −0.0725476 | ||||||||
\(951\) | −68.5410 | −2.22259 | ||||||||
\(952\) | −3.23607 | −0.104882 | ||||||||
\(953\) | −10.8885 | −0.352715 | −0.176357 | − | 0.984326i | \(-0.556431\pi\) | ||||
−0.176357 | + | 0.984326i | \(0.556431\pi\) | |||||||
\(954\) | −15.4164 | −0.499125 | ||||||||
\(955\) | −2.81966 | −0.0912421 | ||||||||
\(956\) | −2.70820 | −0.0875896 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.5967 | −0.697759 | ||||||||
\(959\) | 4.52786 | 0.146212 | ||||||||
\(960\) | −2.23607 | −0.0721688 | ||||||||
\(961\) | −30.4164 | −0.981174 | ||||||||
\(962\) | 8.94427 | 0.288375 | ||||||||
\(963\) | 12.9443 | 0.417123 | ||||||||
\(964\) | 22.3607 | 0.720189 | ||||||||
\(965\) | 9.94427 | 0.320117 | ||||||||
\(966\) | 18.4164 | 0.592538 | ||||||||
\(967\) | −43.1935 | −1.38901 | −0.694505 | − | 0.719488i | \(-0.744376\pi\) | ||||
−0.694505 | + | 0.719488i | \(0.744376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.1803 | 0.519787 | ||||||||
\(970\) | 12.4721 | 0.400456 | ||||||||
\(971\) | 24.1246 | 0.774196 | 0.387098 | − | 0.922039i | \(-0.373478\pi\) | ||||
0.387098 | + | 0.922039i | \(0.373478\pi\) | |||||||
\(972\) | −17.8885 | −0.573775 | ||||||||
\(973\) | −0.236068 | −0.00756799 | ||||||||
\(974\) | 2.23607 | 0.0716482 | ||||||||
\(975\) | 2.23607 | 0.0716115 | ||||||||
\(976\) | −12.4721 | −0.399223 | ||||||||
\(977\) | −28.0557 | −0.897582 | −0.448791 | − | 0.893637i | \(-0.648145\pi\) | ||||
−0.448791 | + | 0.893637i | \(0.648145\pi\) | |||||||
\(978\) | 13.4164 | 0.429009 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 19.4164 | 0.619918 | ||||||||
\(982\) | −26.7639 | −0.854071 | ||||||||
\(983\) | −55.1935 | −1.76040 | −0.880200 | − | 0.474604i | \(-0.842591\pi\) | ||||
−0.880200 | + | 0.474604i | \(0.842591\pi\) | |||||||
\(984\) | 6.18034 | 0.197022 | ||||||||
\(985\) | 16.4721 | 0.524846 | ||||||||
\(986\) | 14.4721 | 0.460887 | ||||||||
\(987\) | −12.7639 | −0.406280 | ||||||||
\(988\) | 2.23607 | 0.0711388 | ||||||||
\(989\) | 10.1803 | 0.323716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.7082 | 1.03901 | 0.519505 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519505 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(992\) | 0.763932 | 0.0242549 | ||||||||
\(993\) | −18.5410 | −0.588381 | ||||||||
\(994\) | 10.4721 | 0.332156 | ||||||||
\(995\) | −4.47214 | −0.141776 | ||||||||
\(996\) | 9.47214 | 0.300136 | ||||||||
\(997\) | −6.16718 | −0.195317 | −0.0976583 | − | 0.995220i | \(-0.531135\pi\) | ||||
−0.0976583 | + | 0.995220i | \(0.531135\pi\) | |||||||
\(998\) | 26.8328 | 0.849378 | ||||||||
\(999\) | 20.0000 | 0.632772 |
(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 | 8470.2.a.bn.1.2 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.by.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bn.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.by.1.2 | yes | 2 | 11.10 | odd | 2 |