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: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.93185\) 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 | ||||||||
\(3\) | 0.414214 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.414214 | 0.119573 | ||||||||
\(13\) | 2.13165 | 0.591214 | 0.295607 | − | 0.955310i | \(-0.404478\pi\) | ||||
0.295607 | + | 0.955310i | \(0.404478\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.44949 | 1.07916 | 0.539580 | − | 0.841934i | \(-0.318583\pi\) | ||||
0.539580 | + | 0.841934i | \(0.318583\pi\) | |||||||
\(18\) | −2.82843 | −0.666667 | ||||||||
\(19\) | −8.27792 | −1.89908 | −0.949542 | − | 0.313639i | \(-0.898452\pi\) | ||||
−0.949542 | + | 0.313639i | \(0.898452\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.414214 | −0.0903888 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.646887 | −0.134885 | −0.0674426 | − | 0.997723i | \(-0.521484\pi\) | ||||
−0.0674426 | + | 0.997723i | \(0.521484\pi\) | |||||||
\(24\) | 0.414214 | 0.0845510 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.13165 | 0.418051 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 0.428825 | 0.0796309 | 0.0398154 | − | 0.999207i | \(-0.487323\pi\) | ||||
0.0398154 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(30\) | 0.414214 | 0.0756247 | ||||||||
\(31\) | −4.52004 | −0.811824 | −0.405912 | − | 0.913912i | \(-0.633046\pi\) | ||||
−0.405912 | + | 0.913912i | \(0.633046\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.44949 | 0.763081 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | −8.49938 | −1.39729 | −0.698645 | − | 0.715469i | \(-0.746213\pi\) | ||||
−0.698645 | + | 0.715469i | \(0.746213\pi\) | |||||||
\(38\) | −8.27792 | −1.34286 | ||||||||
\(39\) | 0.882959 | 0.141387 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.6057 | −1.65634 | −0.828168 | − | 0.560480i | \(-0.810617\pi\) | ||||
−0.828168 | + | 0.560480i | \(0.810617\pi\) | |||||||
\(42\) | −0.414214 | −0.0639145 | ||||||||
\(43\) | −2.65634 | −0.405088 | −0.202544 | − | 0.979273i | \(-0.564921\pi\) | ||||
−0.202544 | + | 0.979273i | \(0.564921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | −0.646887 | −0.0953782 | ||||||||
\(47\) | 4.34242 | 0.633407 | 0.316703 | − | 0.948525i | \(-0.397424\pi\) | ||||
0.316703 | + | 0.948525i | \(0.397424\pi\) | |||||||
\(48\) | 0.414214 | 0.0597866 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.84304 | 0.258077 | ||||||||
\(52\) | 2.13165 | 0.295607 | ||||||||
\(53\) | 0.0206643 | 0.00283846 | 0.00141923 | − | 0.999999i | \(-0.499548\pi\) | ||||
0.00141923 | + | 0.999999i | \(0.499548\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.42883 | −0.454159 | ||||||||
\(58\) | 0.428825 | 0.0563075 | ||||||||
\(59\) | −4.51059 | −0.587229 | −0.293614 | − | 0.955924i | \(-0.594858\pi\) | ||||
−0.293614 | + | 0.955924i | \(0.594858\pi\) | |||||||
\(60\) | 0.414214 | 0.0534747 | ||||||||
\(61\) | −1.36433 | −0.174684 | −0.0873420 | − | 0.996178i | \(-0.527837\pi\) | ||||
−0.0873420 | + | 0.996178i | \(0.527837\pi\) | |||||||
\(62\) | −4.52004 | −0.574046 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.13165 | 0.264399 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.68556 | −0.328094 | −0.164047 | − | 0.986453i | \(-0.552455\pi\) | ||||
−0.164047 | + | 0.986453i | \(0.552455\pi\) | |||||||
\(68\) | 4.44949 | 0.539580 | ||||||||
\(69\) | −0.267949 | −0.0322573 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −9.05040 | −1.07409 | −0.537043 | − | 0.843555i | \(-0.680459\pi\) | ||||
−0.537043 | + | 0.843555i | \(0.680459\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | 0.585786 | 0.0685611 | 0.0342806 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342806 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(74\) | −8.49938 | −0.988033 | ||||||||
\(75\) | 0.414214 | 0.0478293 | ||||||||
\(76\) | −8.27792 | −0.949542 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.882959 | 0.0999755 | ||||||||
\(79\) | −4.24728 | −0.477857 | −0.238928 | − | 0.971037i | \(-0.576796\pi\) | ||||
−0.238928 | + | 0.971037i | \(0.576796\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −10.6057 | −1.17121 | ||||||||
\(83\) | 4.62446 | 0.507601 | 0.253800 | − | 0.967257i | \(-0.418319\pi\) | ||||
0.253800 | + | 0.967257i | \(0.418319\pi\) | |||||||
\(84\) | −0.414214 | −0.0451944 | ||||||||
\(85\) | 4.44949 | 0.482615 | ||||||||
\(86\) | −2.65634 | −0.286440 | ||||||||
\(87\) | 0.177625 | 0.0190434 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.17209 | −0.230241 | −0.115120 | − | 0.993352i | \(-0.536725\pi\) | ||||
−0.115120 | + | 0.993352i | \(0.536725\pi\) | |||||||
\(90\) | −2.82843 | −0.298142 | ||||||||
\(91\) | −2.13165 | −0.223458 | ||||||||
\(92\) | −0.646887 | −0.0674426 | ||||||||
\(93\) | −1.87226 | −0.194145 | ||||||||
\(94\) | 4.34242 | 0.447886 | ||||||||
\(95\) | −8.27792 | −0.849296 | ||||||||
\(96\) | 0.414214 | 0.0422755 | ||||||||
\(97\) | 13.0552 | 1.32556 | 0.662778 | − | 0.748816i | \(-0.269377\pi\) | ||||
0.662778 | + | 0.748816i | \(0.269377\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.46410 | 0.643202 | 0.321601 | − | 0.946875i | \(-0.395779\pi\) | ||||
0.321601 | + | 0.946875i | \(0.395779\pi\) | |||||||
\(102\) | 1.84304 | 0.182488 | ||||||||
\(103\) | −12.4495 | −1.22668 | −0.613342 | − | 0.789817i | \(-0.710175\pi\) | ||||
−0.613342 | + | 0.789817i | \(0.710175\pi\) | |||||||
\(104\) | 2.13165 | 0.209026 | ||||||||
\(105\) | −0.414214 | −0.0404231 | ||||||||
\(106\) | 0.0206643 | 0.00200710 | ||||||||
\(107\) | 10.0048 | 0.967201 | 0.483601 | − | 0.875289i | \(-0.339329\pi\) | ||||
0.483601 | + | 0.875289i | \(0.339329\pi\) | |||||||
\(108\) | −2.41421 | −0.232308 | ||||||||
\(109\) | −5.91359 | −0.566419 | −0.283210 | − | 0.959058i | \(-0.591399\pi\) | ||||
−0.283210 | + | 0.959058i | \(0.591399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.52056 | −0.334157 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −3.76857 | −0.354517 | −0.177259 | − | 0.984164i | \(-0.556723\pi\) | ||||
−0.177259 | + | 0.984164i | \(0.556723\pi\) | |||||||
\(114\) | −3.42883 | −0.321139 | ||||||||
\(115\) | −0.646887 | −0.0603225 | ||||||||
\(116\) | 0.428825 | 0.0398154 | ||||||||
\(117\) | −6.02922 | −0.557402 | ||||||||
\(118\) | −4.51059 | −0.415233 | ||||||||
\(119\) | −4.44949 | −0.407884 | ||||||||
\(120\) | 0.414214 | 0.0378124 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.36433 | −0.123520 | ||||||||
\(123\) | −4.39303 | −0.396107 | ||||||||
\(124\) | −4.52004 | −0.405912 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.82843 | 0.251976 | ||||||||
\(127\) | 8.56564 | 0.760077 | 0.380039 | − | 0.924971i | \(-0.375911\pi\) | ||||
0.380039 | + | 0.924971i | \(0.375911\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.10029 | −0.0968753 | ||||||||
\(130\) | 2.13165 | 0.186958 | ||||||||
\(131\) | 5.64224 | 0.492965 | 0.246483 | − | 0.969147i | \(-0.420725\pi\) | ||||
0.246483 | + | 0.969147i | \(0.420725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.27792 | 0.717786 | ||||||||
\(134\) | −2.68556 | −0.231997 | ||||||||
\(135\) | −2.41421 | −0.207782 | ||||||||
\(136\) | 4.44949 | 0.381541 | ||||||||
\(137\) | −1.64637 | −0.140659 | −0.0703295 | − | 0.997524i | \(-0.522405\pi\) | ||||
−0.0703295 | + | 0.997524i | \(0.522405\pi\) | |||||||
\(138\) | −0.267949 | −0.0228093 | ||||||||
\(139\) | −16.3071 | −1.38315 | −0.691577 | − | 0.722303i | \(-0.743084\pi\) | ||||
−0.691577 | + | 0.722303i | \(0.743084\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 1.79869 | 0.151477 | ||||||||
\(142\) | −9.05040 | −0.759493 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.82843 | −0.235702 | ||||||||
\(145\) | 0.428825 | 0.0356120 | ||||||||
\(146\) | 0.585786 | 0.0484800 | ||||||||
\(147\) | 0.414214 | 0.0341638 | ||||||||
\(148\) | −8.49938 | −0.698645 | ||||||||
\(149\) | −4.12701 | −0.338098 | −0.169049 | − | 0.985608i | \(-0.554070\pi\) | ||||
−0.169049 | + | 0.985608i | \(0.554070\pi\) | |||||||
\(150\) | 0.414214 | 0.0338204 | ||||||||
\(151\) | 11.8949 | 0.967989 | 0.483995 | − | 0.875071i | \(-0.339185\pi\) | ||||
0.483995 | + | 0.875071i | \(0.339185\pi\) | |||||||
\(152\) | −8.27792 | −0.671428 | ||||||||
\(153\) | −12.5851 | −1.01744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.52004 | −0.363059 | ||||||||
\(156\) | 0.882959 | 0.0706933 | ||||||||
\(157\) | 10.6617 | 0.850893 | 0.425447 | − | 0.904984i | \(-0.360117\pi\) | ||||
0.425447 | + | 0.904984i | \(0.360117\pi\) | |||||||
\(158\) | −4.24728 | −0.337896 | ||||||||
\(159\) | 0.00855944 | 0.000678807 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.646887 | 0.0509818 | ||||||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | −19.0917 | −1.49538 | −0.747690 | − | 0.664048i | \(-0.768837\pi\) | ||||
−0.747690 | + | 0.664048i | \(0.768837\pi\) | |||||||
\(164\) | −10.6057 | −0.828168 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.62446 | 0.358928 | ||||||||
\(167\) | 13.3684 | 1.03448 | 0.517239 | − | 0.855841i | \(-0.326960\pi\) | ||||
0.517239 | + | 0.855841i | \(0.326960\pi\) | |||||||
\(168\) | −0.414214 | −0.0319573 | ||||||||
\(169\) | −8.45606 | −0.650466 | ||||||||
\(170\) | 4.44949 | 0.341260 | ||||||||
\(171\) | 23.4135 | 1.79047 | ||||||||
\(172\) | −2.65634 | −0.202544 | ||||||||
\(173\) | −2.38551 | −0.181367 | −0.0906833 | − | 0.995880i | \(-0.528905\pi\) | ||||
−0.0906833 | + | 0.995880i | \(0.528905\pi\) | |||||||
\(174\) | 0.177625 | 0.0134657 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.86835 | −0.140434 | ||||||||
\(178\) | −2.17209 | −0.162805 | ||||||||
\(179\) | −3.68681 | −0.275565 | −0.137782 | − | 0.990463i | \(-0.543997\pi\) | ||||
−0.137782 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(180\) | −2.82843 | −0.210819 | ||||||||
\(181\) | −9.53001 | −0.708360 | −0.354180 | − | 0.935177i | \(-0.615240\pi\) | ||||
−0.354180 | + | 0.935177i | \(0.615240\pi\) | |||||||
\(182\) | −2.13165 | −0.158009 | ||||||||
\(183\) | −0.565122 | −0.0417750 | ||||||||
\(184\) | −0.646887 | −0.0476891 | ||||||||
\(185\) | −8.49938 | −0.624887 | ||||||||
\(186\) | −1.87226 | −0.137281 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.34242 | 0.316703 | ||||||||
\(189\) | 2.41421 | 0.175608 | ||||||||
\(190\) | −8.27792 | −0.600543 | ||||||||
\(191\) | −13.3789 | −0.968066 | −0.484033 | − | 0.875050i | \(-0.660829\pi\) | ||||
−0.484033 | + | 0.875050i | \(0.660829\pi\) | |||||||
\(192\) | 0.414214 | 0.0298933 | ||||||||
\(193\) | 6.52985 | 0.470029 | 0.235014 | − | 0.971992i | \(-0.424486\pi\) | ||||
0.235014 | + | 0.971992i | \(0.424486\pi\) | |||||||
\(194\) | 13.0552 | 0.937310 | ||||||||
\(195\) | 0.882959 | 0.0632300 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 26.1056 | 1.85995 | 0.929974 | − | 0.367625i | \(-0.119829\pi\) | ||||
0.929974 | + | 0.367625i | \(0.119829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8917 | −1.33920 | −0.669598 | − | 0.742724i | \(-0.733534\pi\) | ||||
−0.669598 | + | 0.742724i | \(0.733534\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.11240 | −0.0784624 | ||||||||
\(202\) | 6.46410 | 0.454813 | ||||||||
\(203\) | −0.428825 | −0.0300976 | ||||||||
\(204\) | 1.84304 | 0.129039 | ||||||||
\(205\) | −10.6057 | −0.740736 | ||||||||
\(206\) | −12.4495 | −0.867397 | ||||||||
\(207\) | 1.82967 | 0.127171 | ||||||||
\(208\) | 2.13165 | 0.147804 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.414214 | −0.0285835 | ||||||||
\(211\) | −16.7627 | −1.15399 | −0.576995 | − | 0.816747i | \(-0.695775\pi\) | ||||
−0.576995 | + | 0.816747i | \(0.695775\pi\) | |||||||
\(212\) | 0.0206643 | 0.00141923 | ||||||||
\(213\) | −3.74880 | −0.256864 | ||||||||
\(214\) | 10.0048 | 0.683915 | ||||||||
\(215\) | −2.65634 | −0.181161 | ||||||||
\(216\) | −2.41421 | −0.164266 | ||||||||
\(217\) | 4.52004 | 0.306840 | ||||||||
\(218\) | −5.91359 | −0.400519 | ||||||||
\(219\) | 0.242641 | 0.0163961 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48477 | 0.638014 | ||||||||
\(222\) | −3.52056 | −0.236284 | ||||||||
\(223\) | −17.0053 | −1.13876 | −0.569380 | − | 0.822074i | \(-0.692817\pi\) | ||||
−0.569380 | + | 0.822074i | \(0.692817\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | −3.76857 | −0.250682 | ||||||||
\(227\) | −14.0613 | −0.933279 | −0.466639 | − | 0.884448i | \(-0.654535\pi\) | ||||
−0.466639 | + | 0.884448i | \(0.654535\pi\) | |||||||
\(228\) | −3.42883 | −0.227080 | ||||||||
\(229\) | −27.7673 | −1.83491 | −0.917457 | − | 0.397836i | \(-0.869761\pi\) | ||||
−0.917457 | + | 0.397836i | \(0.869761\pi\) | |||||||
\(230\) | −0.646887 | −0.0426544 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.428825 | 0.0281538 | ||||||||
\(233\) | −9.82113 | −0.643404 | −0.321702 | − | 0.946841i | \(-0.604255\pi\) | ||||
−0.321702 | + | 0.946841i | \(0.604255\pi\) | |||||||
\(234\) | −6.02922 | −0.394143 | ||||||||
\(235\) | 4.34242 | 0.283268 | ||||||||
\(236\) | −4.51059 | −0.293614 | ||||||||
\(237\) | −1.75928 | −0.114278 | ||||||||
\(238\) | −4.44949 | −0.288418 | ||||||||
\(239\) | 4.28964 | 0.277474 | 0.138737 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138737 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(240\) | 0.414214 | 0.0267374 | ||||||||
\(241\) | −5.13505 | −0.330778 | −0.165389 | − | 0.986228i | \(-0.552888\pi\) | ||||
−0.165389 | + | 0.986228i | \(0.552888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3431 | 0.663513 | ||||||||
\(244\) | −1.36433 | −0.0873420 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −4.39303 | −0.280090 | ||||||||
\(247\) | −17.6456 | −1.12277 | ||||||||
\(248\) | −4.52004 | −0.287023 | ||||||||
\(249\) | 1.91552 | 0.121391 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.5851 | −0.668123 | −0.334061 | − | 0.942551i | \(-0.608419\pi\) | ||||
−0.334061 | + | 0.942551i | \(0.608419\pi\) | |||||||
\(252\) | 2.82843 | 0.178174 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.56564 | 0.537456 | ||||||||
\(255\) | 1.84304 | 0.115416 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.27667 | −0.266771 | −0.133386 | − | 0.991064i | \(-0.542585\pi\) | ||||
−0.133386 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(258\) | −1.10029 | −0.0685012 | ||||||||
\(259\) | 8.49938 | 0.528126 | ||||||||
\(260\) | 2.13165 | 0.132199 | ||||||||
\(261\) | −1.21290 | −0.0750767 | ||||||||
\(262\) | 5.64224 | 0.348579 | ||||||||
\(263\) | 12.7773 | 0.787882 | 0.393941 | − | 0.919136i | \(-0.371111\pi\) | ||||
0.393941 | + | 0.919136i | \(0.371111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0206643 | 0.00126940 | ||||||||
\(266\) | 8.27792 | 0.507552 | ||||||||
\(267\) | −0.899708 | −0.0550613 | ||||||||
\(268\) | −2.68556 | −0.164047 | ||||||||
\(269\) | −6.94495 | −0.423441 | −0.211721 | − | 0.977330i | \(-0.567907\pi\) | ||||
−0.211721 | + | 0.977330i | \(0.567907\pi\) | |||||||
\(270\) | −2.41421 | −0.146924 | ||||||||
\(271\) | −29.3911 | −1.78538 | −0.892690 | − | 0.450671i | \(-0.851185\pi\) | ||||
−0.892690 | + | 0.450671i | \(0.851185\pi\) | |||||||
\(272\) | 4.44949 | 0.269790 | ||||||||
\(273\) | −0.882959 | −0.0534391 | ||||||||
\(274\) | −1.64637 | −0.0994609 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.267949 | −0.0161286 | ||||||||
\(277\) | 9.99927 | 0.600798 | 0.300399 | − | 0.953814i | \(-0.402880\pi\) | ||||
0.300399 | + | 0.953814i | \(0.402880\pi\) | |||||||
\(278\) | −16.3071 | −0.978037 | ||||||||
\(279\) | 12.7846 | 0.765395 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 21.5792 | 1.28731 | 0.643653 | − | 0.765318i | \(-0.277418\pi\) | ||||
0.643653 | + | 0.765318i | \(0.277418\pi\) | |||||||
\(282\) | 1.79869 | 0.107110 | ||||||||
\(283\) | 11.2319 | 0.667670 | 0.333835 | − | 0.942632i | \(-0.391657\pi\) | ||||
0.333835 | + | 0.942632i | \(0.391657\pi\) | |||||||
\(284\) | −9.05040 | −0.537043 | ||||||||
\(285\) | −3.42883 | −0.203106 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6057 | 0.626036 | ||||||||
\(288\) | −2.82843 | −0.166667 | ||||||||
\(289\) | 2.79796 | 0.164586 | ||||||||
\(290\) | 0.428825 | 0.0251815 | ||||||||
\(291\) | 5.40765 | 0.317002 | ||||||||
\(292\) | 0.585786 | 0.0342806 | ||||||||
\(293\) | 16.7673 | 0.979558 | 0.489779 | − | 0.871847i | \(-0.337078\pi\) | ||||
0.489779 | + | 0.871847i | \(0.337078\pi\) | |||||||
\(294\) | 0.414214 | 0.0241574 | ||||||||
\(295\) | −4.51059 | −0.262617 | ||||||||
\(296\) | −8.49938 | −0.494016 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.12701 | −0.239071 | ||||||||
\(299\) | −1.37894 | −0.0797460 | ||||||||
\(300\) | 0.414214 | 0.0239146 | ||||||||
\(301\) | 2.65634 | 0.153109 | ||||||||
\(302\) | 11.8949 | 0.684472 | ||||||||
\(303\) | 2.67752 | 0.153819 | ||||||||
\(304\) | −8.27792 | −0.474771 | ||||||||
\(305\) | −1.36433 | −0.0781211 | ||||||||
\(306\) | −12.5851 | −0.719440 | ||||||||
\(307\) | −12.5840 | −0.718208 | −0.359104 | − | 0.933297i | \(-0.616918\pi\) | ||||
−0.359104 | + | 0.933297i | \(0.616918\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.15675 | −0.293357 | ||||||||
\(310\) | −4.52004 | −0.256721 | ||||||||
\(311\) | −21.3223 | −1.20907 | −0.604537 | − | 0.796577i | \(-0.706642\pi\) | ||||
−0.604537 | + | 0.796577i | \(0.706642\pi\) | |||||||
\(312\) | 0.882959 | 0.0499877 | ||||||||
\(313\) | 24.9895 | 1.41249 | 0.706244 | − | 0.707968i | \(-0.250388\pi\) | ||||
0.706244 | + | 0.707968i | \(0.250388\pi\) | |||||||
\(314\) | 10.6617 | 0.601672 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | −4.24728 | −0.238928 | ||||||||
\(317\) | 3.33636 | 0.187389 | 0.0936944 | − | 0.995601i | \(-0.470132\pi\) | ||||
0.0936944 | + | 0.995601i | \(0.470132\pi\) | |||||||
\(318\) | 0.00855944 | 0.000479989 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 4.14413 | 0.231303 | ||||||||
\(322\) | 0.646887 | 0.0360496 | ||||||||
\(323\) | −36.8325 | −2.04942 | ||||||||
\(324\) | 7.48528 | 0.415849 | ||||||||
\(325\) | 2.13165 | 0.118243 | ||||||||
\(326\) | −19.0917 | −1.05739 | ||||||||
\(327\) | −2.44949 | −0.135457 | ||||||||
\(328\) | −10.6057 | −0.585603 | ||||||||
\(329\) | −4.34242 | −0.239405 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.12044 | 0.446340 | 0.223170 | − | 0.974780i | \(-0.428360\pi\) | ||||
0.223170 | + | 0.974780i | \(0.428360\pi\) | |||||||
\(332\) | 4.62446 | 0.253800 | ||||||||
\(333\) | 24.0399 | 1.31738 | ||||||||
\(334\) | 13.3684 | 0.731487 | ||||||||
\(335\) | −2.68556 | −0.146728 | ||||||||
\(336\) | −0.414214 | −0.0225972 | ||||||||
\(337\) | −30.2961 | −1.65033 | −0.825167 | − | 0.564889i | \(-0.808919\pi\) | ||||
−0.825167 | + | 0.564889i | \(0.808919\pi\) | |||||||
\(338\) | −8.45606 | −0.459949 | ||||||||
\(339\) | −1.56099 | −0.0847815 | ||||||||
\(340\) | 4.44949 | 0.241307 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 23.4135 | 1.26606 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.65634 | −0.143220 | ||||||||
\(345\) | −0.267949 | −0.0144259 | ||||||||
\(346\) | −2.38551 | −0.128246 | ||||||||
\(347\) | 21.5745 | 1.15818 | 0.579091 | − | 0.815263i | \(-0.303408\pi\) | ||||
0.579091 | + | 0.815263i | \(0.303408\pi\) | |||||||
\(348\) | 0.177625 | 0.00952172 | ||||||||
\(349\) | 29.4536 | 1.57661 | 0.788307 | − | 0.615282i | \(-0.210958\pi\) | ||||
0.788307 | + | 0.615282i | \(0.210958\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −5.14626 | −0.274687 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.2578 | 0.545966 | 0.272983 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272983 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(354\) | −1.86835 | −0.0993015 | ||||||||
\(355\) | −9.05040 | −0.480346 | ||||||||
\(356\) | −2.17209 | −0.115120 | ||||||||
\(357\) | −1.84304 | −0.0975440 | ||||||||
\(358\) | −3.68681 | −0.194854 | ||||||||
\(359\) | −31.9893 | −1.68833 | −0.844164 | − | 0.536085i | \(-0.819903\pi\) | ||||
−0.844164 | + | 0.536085i | \(0.819903\pi\) | |||||||
\(360\) | −2.82843 | −0.149071 | ||||||||
\(361\) | 49.5239 | 2.60652 | ||||||||
\(362\) | −9.53001 | −0.500886 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.13165 | −0.111729 | ||||||||
\(365\) | 0.585786 | 0.0306615 | ||||||||
\(366\) | −0.565122 | −0.0295394 | ||||||||
\(367\) | 21.2734 | 1.11046 | 0.555232 | − | 0.831695i | \(-0.312629\pi\) | ||||
0.555232 | + | 0.831695i | \(0.312629\pi\) | |||||||
\(368\) | −0.646887 | −0.0337213 | ||||||||
\(369\) | 29.9975 | 1.56161 | ||||||||
\(370\) | −8.49938 | −0.441862 | ||||||||
\(371\) | −0.0206643 | −0.00107284 | ||||||||
\(372\) | −1.87226 | −0.0970723 | ||||||||
\(373\) | −21.6695 | −1.12200 | −0.561002 | − | 0.827815i | \(-0.689584\pi\) | ||||
−0.561002 | + | 0.827815i | \(0.689584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.414214 | 0.0213899 | ||||||||
\(376\) | 4.34242 | 0.223943 | ||||||||
\(377\) | 0.914107 | 0.0470789 | ||||||||
\(378\) | 2.41421 | 0.124174 | ||||||||
\(379\) | −15.6617 | −0.804486 | −0.402243 | − | 0.915533i | \(-0.631769\pi\) | ||||
−0.402243 | + | 0.915533i | \(0.631769\pi\) | |||||||
\(380\) | −8.27792 | −0.424648 | ||||||||
\(381\) | 3.54800 | 0.181770 | ||||||||
\(382\) | −13.3789 | −0.684526 | ||||||||
\(383\) | 17.5412 | 0.896315 | 0.448157 | − | 0.893955i | \(-0.352080\pi\) | ||||
0.448157 | + | 0.893955i | \(0.352080\pi\) | |||||||
\(384\) | 0.414214 | 0.0211377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.52985 | 0.332360 | ||||||||
\(387\) | 7.51326 | 0.381921 | ||||||||
\(388\) | 13.0552 | 0.662778 | ||||||||
\(389\) | −19.6118 | −0.994356 | −0.497178 | − | 0.867648i | \(-0.665630\pi\) | ||||
−0.497178 | + | 0.867648i | \(0.665630\pi\) | |||||||
\(390\) | 0.882959 | 0.0447104 | ||||||||
\(391\) | −2.87832 | −0.145563 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 2.33709 | 0.117891 | ||||||||
\(394\) | 26.1056 | 1.31518 | ||||||||
\(395\) | −4.24728 | −0.213704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.78482 | −0.0895777 | −0.0447889 | − | 0.998996i | \(-0.514262\pi\) | ||||
−0.0447889 | + | 0.998996i | \(0.514262\pi\) | |||||||
\(398\) | −18.8917 | −0.946954 | ||||||||
\(399\) | 3.42883 | 0.171656 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −27.8471 | −1.39062 | −0.695309 | − | 0.718711i | \(-0.744733\pi\) | ||||
−0.695309 | + | 0.718711i | \(0.744733\pi\) | |||||||
\(402\) | −1.11240 | −0.0554813 | ||||||||
\(403\) | −9.63516 | −0.479961 | ||||||||
\(404\) | 6.46410 | 0.321601 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | −0.428825 | −0.0212822 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.84304 | 0.0912440 | ||||||||
\(409\) | −17.0071 | −0.840946 | −0.420473 | − | 0.907305i | \(-0.638136\pi\) | ||||
−0.420473 | + | 0.907305i | \(0.638136\pi\) | |||||||
\(410\) | −10.6057 | −0.523779 | ||||||||
\(411\) | −0.681949 | −0.0336381 | ||||||||
\(412\) | −12.4495 | −0.613342 | ||||||||
\(413\) | 4.51059 | 0.221952 | ||||||||
\(414\) | 1.82967 | 0.0899235 | ||||||||
\(415\) | 4.62446 | 0.227006 | ||||||||
\(416\) | 2.13165 | 0.104513 | ||||||||
\(417\) | −6.75464 | −0.330776 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.35112 | 0.359126 | 0.179563 | − | 0.983746i | \(-0.442532\pi\) | ||||
0.179563 | + | 0.983746i | \(0.442532\pi\) | |||||||
\(420\) | −0.414214 | −0.0202116 | ||||||||
\(421\) | 20.0267 | 0.976043 | 0.488022 | − | 0.872832i | \(-0.337719\pi\) | ||||
0.488022 | + | 0.872832i | \(0.337719\pi\) | |||||||
\(422\) | −16.7627 | −0.815995 | ||||||||
\(423\) | −12.2822 | −0.597181 | ||||||||
\(424\) | 0.0206643 | 0.00100355 | ||||||||
\(425\) | 4.44949 | 0.215832 | ||||||||
\(426\) | −3.74880 | −0.181630 | ||||||||
\(427\) | 1.36433 | 0.0660243 | ||||||||
\(428\) | 10.0048 | 0.483601 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.65634 | −0.128100 | ||||||||
\(431\) | 5.14626 | 0.247887 | 0.123943 | − | 0.992289i | \(-0.460446\pi\) | ||||
0.123943 | + | 0.992289i | \(0.460446\pi\) | |||||||
\(432\) | −2.41421 | −0.116154 | ||||||||
\(433\) | −41.3976 | −1.98944 | −0.994722 | − | 0.102611i | \(-0.967280\pi\) | ||||
−0.994722 | + | 0.102611i | \(0.967280\pi\) | |||||||
\(434\) | 4.52004 | 0.216969 | ||||||||
\(435\) | 0.177625 | 0.00851648 | ||||||||
\(436\) | −5.91359 | −0.283210 | ||||||||
\(437\) | 5.35487 | 0.256158 | ||||||||
\(438\) | 0.242641 | 0.0115938 | ||||||||
\(439\) | −21.6609 | −1.03382 | −0.516910 | − | 0.856040i | \(-0.672918\pi\) | ||||
−0.516910 | + | 0.856040i | \(0.672918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.82843 | −0.134687 | ||||||||
\(442\) | 9.48477 | 0.451144 | ||||||||
\(443\) | 21.0771 | 1.00141 | 0.500703 | − | 0.865619i | \(-0.333075\pi\) | ||||
0.500703 | + | 0.865619i | \(0.333075\pi\) | |||||||
\(444\) | −3.52056 | −0.167078 | ||||||||
\(445\) | −2.17209 | −0.102967 | ||||||||
\(446\) | −17.0053 | −0.805225 | ||||||||
\(447\) | −1.70946 | −0.0808548 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 40.9893 | 1.93440 | 0.967201 | − | 0.254011i | \(-0.0817501\pi\) | ||||
0.967201 | + | 0.254011i | \(0.0817501\pi\) | |||||||
\(450\) | −2.82843 | −0.133333 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.76857 | −0.177259 | ||||||||
\(453\) | 4.92701 | 0.231491 | ||||||||
\(454\) | −14.0613 | −0.659928 | ||||||||
\(455\) | −2.13165 | −0.0999334 | ||||||||
\(456\) | −3.42883 | −0.160569 | ||||||||
\(457\) | −18.3784 | −0.859706 | −0.429853 | − | 0.902899i | \(-0.641435\pi\) | ||||
−0.429853 | + | 0.902899i | \(0.641435\pi\) | |||||||
\(458\) | −27.7673 | −1.29748 | ||||||||
\(459\) | −10.7420 | −0.501394 | ||||||||
\(460\) | −0.646887 | −0.0301612 | ||||||||
\(461\) | −15.0383 | −0.700403 | −0.350202 | − | 0.936674i | \(-0.613887\pi\) | ||||
−0.350202 | + | 0.936674i | \(0.613887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6376 | −1.33090 | −0.665451 | − | 0.746442i | \(-0.731761\pi\) | ||||
−0.665451 | + | 0.746442i | \(0.731761\pi\) | |||||||
\(464\) | 0.428825 | 0.0199077 | ||||||||
\(465\) | −1.87226 | −0.0868241 | ||||||||
\(466\) | −9.82113 | −0.454955 | ||||||||
\(467\) | 9.16960 | 0.424318 | 0.212159 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212159 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(468\) | −6.02922 | −0.278701 | ||||||||
\(469\) | 2.68556 | 0.124008 | ||||||||
\(470\) | 4.34242 | 0.200301 | ||||||||
\(471\) | 4.41621 | 0.203488 | ||||||||
\(472\) | −4.51059 | −0.207617 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.75928 | −0.0808065 | ||||||||
\(475\) | −8.27792 | −0.379817 | ||||||||
\(476\) | −4.44949 | −0.203942 | ||||||||
\(477\) | −0.0584475 | −0.00267613 | ||||||||
\(478\) | 4.28964 | 0.196204 | ||||||||
\(479\) | 33.8489 | 1.54659 | 0.773297 | − | 0.634044i | \(-0.218606\pi\) | ||||
0.773297 | + | 0.634044i | \(0.218606\pi\) | |||||||
\(480\) | 0.414214 | 0.0189062 | ||||||||
\(481\) | −18.1177 | −0.826097 | ||||||||
\(482\) | −5.13505 | −0.233895 | ||||||||
\(483\) | 0.267949 | 0.0121921 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.0552 | 0.592807 | ||||||||
\(486\) | 10.3431 | 0.469175 | ||||||||
\(487\) | −27.2216 | −1.23353 | −0.616765 | − | 0.787148i | \(-0.711557\pi\) | ||||
−0.616765 | + | 0.787148i | \(0.711557\pi\) | |||||||
\(488\) | −1.36433 | −0.0617601 | ||||||||
\(489\) | −7.90805 | −0.357615 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 33.7879 | 1.52483 | 0.762414 | − | 0.647089i | \(-0.224014\pi\) | ||||
0.762414 | + | 0.647089i | \(0.224014\pi\) | |||||||
\(492\) | −4.39303 | −0.198053 | ||||||||
\(493\) | 1.90805 | 0.0859344 | ||||||||
\(494\) | −17.6456 | −0.793915 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.52004 | −0.202956 | ||||||||
\(497\) | 9.05040 | 0.405966 | ||||||||
\(498\) | 1.91552 | 0.0858363 | ||||||||
\(499\) | 14.6347 | 0.655140 | 0.327570 | − | 0.944827i | \(-0.393770\pi\) | ||||
0.327570 | + | 0.944827i | \(0.393770\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 5.53737 | 0.247392 | ||||||||
\(502\) | −10.5851 | −0.472434 | ||||||||
\(503\) | 23.0486 | 1.02769 | 0.513844 | − | 0.857884i | \(-0.328221\pi\) | ||||
0.513844 | + | 0.857884i | \(0.328221\pi\) | |||||||
\(504\) | 2.82843 | 0.125988 | ||||||||
\(505\) | 6.46410 | 0.287649 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.50261 | −0.155557 | ||||||||
\(508\) | 8.56564 | 0.380039 | ||||||||
\(509\) | 2.55368 | 0.113190 | 0.0565949 | − | 0.998397i | \(-0.481976\pi\) | ||||
0.0565949 | + | 0.998397i | \(0.481976\pi\) | |||||||
\(510\) | 1.84304 | 0.0816111 | ||||||||
\(511\) | −0.585786 | −0.0259137 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 19.9847 | 0.882344 | ||||||||
\(514\) | −4.27667 | −0.188636 | ||||||||
\(515\) | −12.4495 | −0.548590 | ||||||||
\(516\) | −1.10029 | −0.0484376 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.49938 | 0.373441 | ||||||||
\(519\) | −0.988109 | −0.0433732 | ||||||||
\(520\) | 2.13165 | 0.0934791 | ||||||||
\(521\) | 9.67198 | 0.423737 | 0.211869 | − | 0.977298i | \(-0.432045\pi\) | ||||
0.211869 | + | 0.977298i | \(0.432045\pi\) | |||||||
\(522\) | −1.21290 | −0.0530873 | ||||||||
\(523\) | 26.0501 | 1.13909 | 0.569545 | − | 0.821960i | \(-0.307120\pi\) | ||||
0.569545 | + | 0.821960i | \(0.307120\pi\) | |||||||
\(524\) | 5.64224 | 0.246483 | ||||||||
\(525\) | −0.414214 | −0.0180778 | ||||||||
\(526\) | 12.7773 | 0.557117 | ||||||||
\(527\) | −20.1119 | −0.876087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5815 | −0.981806 | ||||||||
\(530\) | 0.0206643 | 0.000897600 0 | ||||||||
\(531\) | 12.7579 | 0.553645 | ||||||||
\(532\) | 8.27792 | 0.358893 | ||||||||
\(533\) | −22.6077 | −0.979249 | ||||||||
\(534\) | −0.899708 | −0.0389342 | ||||||||
\(535\) | 10.0048 | 0.432546 | ||||||||
\(536\) | −2.68556 | −0.115999 | ||||||||
\(537\) | −1.52713 | −0.0659003 | ||||||||
\(538\) | −6.94495 | −0.299418 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.41421 | −0.103891 | ||||||||
\(541\) | 40.9549 | 1.76079 | 0.880395 | − | 0.474241i | \(-0.157277\pi\) | ||||
0.880395 | + | 0.474241i | \(0.157277\pi\) | |||||||
\(542\) | −29.3911 | −1.26245 | ||||||||
\(543\) | −3.94746 | −0.169402 | ||||||||
\(544\) | 4.44949 | 0.190770 | ||||||||
\(545\) | −5.91359 | −0.253310 | ||||||||
\(546\) | −0.882959 | −0.0377872 | ||||||||
\(547\) | −26.8345 | −1.14736 | −0.573680 | − | 0.819079i | \(-0.694485\pi\) | ||||
−0.573680 | + | 0.819079i | \(0.694485\pi\) | |||||||
\(548\) | −1.64637 | −0.0703295 | ||||||||
\(549\) | 3.85890 | 0.164694 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.54978 | −0.151226 | ||||||||
\(552\) | −0.267949 | −0.0114047 | ||||||||
\(553\) | 4.24728 | 0.180613 | ||||||||
\(554\) | 9.99927 | 0.424828 | ||||||||
\(555\) | −3.52056 | −0.149439 | ||||||||
\(556\) | −16.3071 | −0.691577 | ||||||||
\(557\) | −19.9262 | −0.844301 | −0.422151 | − | 0.906526i | \(-0.638725\pi\) | ||||
−0.422151 | + | 0.906526i | \(0.638725\pi\) | |||||||
\(558\) | 12.7846 | 0.541216 | ||||||||
\(559\) | −5.66239 | −0.239494 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.5792 | 0.910262 | ||||||||
\(563\) | −8.40103 | −0.354061 | −0.177031 | − | 0.984205i | \(-0.556649\pi\) | ||||
−0.177031 | + | 0.984205i | \(0.556649\pi\) | |||||||
\(564\) | 1.79869 | 0.0757384 | ||||||||
\(565\) | −3.76857 | −0.158545 | ||||||||
\(566\) | 11.2319 | 0.472114 | ||||||||
\(567\) | −7.48528 | −0.314352 | ||||||||
\(568\) | −9.05040 | −0.379746 | ||||||||
\(569\) | 29.5592 | 1.23919 | 0.619594 | − | 0.784923i | \(-0.287297\pi\) | ||||
0.619594 | + | 0.784923i | \(0.287297\pi\) | |||||||
\(570\) | −3.42883 | −0.143618 | ||||||||
\(571\) | 23.2036 | 0.971041 | 0.485520 | − | 0.874225i | \(-0.338630\pi\) | ||||
0.485520 | + | 0.874225i | \(0.338630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.54174 | −0.231509 | ||||||||
\(574\) | 10.6057 | 0.442674 | ||||||||
\(575\) | −0.646887 | −0.0269770 | ||||||||
\(576\) | −2.82843 | −0.117851 | ||||||||
\(577\) | 9.45408 | 0.393579 | 0.196789 | − | 0.980446i | \(-0.436948\pi\) | ||||
0.196789 | + | 0.980446i | \(0.436948\pi\) | |||||||
\(578\) | 2.79796 | 0.116380 | ||||||||
\(579\) | 2.70475 | 0.112406 | ||||||||
\(580\) | 0.428825 | 0.0178060 | ||||||||
\(581\) | −4.62446 | −0.191855 | ||||||||
\(582\) | 5.40765 | 0.224154 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.585786 | 0.0242400 | ||||||||
\(585\) | −6.02922 | −0.249278 | ||||||||
\(586\) | 16.7673 | 0.692652 | ||||||||
\(587\) | 20.1626 | 0.832199 | 0.416100 | − | 0.909319i | \(-0.363397\pi\) | ||||
0.416100 | + | 0.909319i | \(0.363397\pi\) | |||||||
\(588\) | 0.414214 | 0.0170819 | ||||||||
\(589\) | 37.4165 | 1.54172 | ||||||||
\(590\) | −4.51059 | −0.185698 | ||||||||
\(591\) | 10.8133 | 0.444800 | ||||||||
\(592\) | −8.49938 | −0.349322 | ||||||||
\(593\) | 34.9585 | 1.43557 | 0.717786 | − | 0.696264i | \(-0.245156\pi\) | ||||
0.717786 | + | 0.696264i | \(0.245156\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.44949 | −0.182411 | ||||||||
\(596\) | −4.12701 | −0.169049 | ||||||||
\(597\) | −7.82519 | −0.320264 | ||||||||
\(598\) | −1.37894 | −0.0563889 | ||||||||
\(599\) | 24.4400 | 0.998591 | 0.499295 | − | 0.866432i | \(-0.333592\pi\) | ||||
0.499295 | + | 0.866432i | \(0.333592\pi\) | |||||||
\(600\) | 0.414214 | 0.0169102 | ||||||||
\(601\) | 9.94812 | 0.405792 | 0.202896 | − | 0.979200i | \(-0.434965\pi\) | ||||
0.202896 | + | 0.979200i | \(0.434965\pi\) | |||||||
\(602\) | 2.65634 | 0.108264 | ||||||||
\(603\) | 7.59592 | 0.309330 | ||||||||
\(604\) | 11.8949 | 0.483995 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.67752 | 0.108767 | ||||||||
\(607\) | 32.6542 | 1.32539 | 0.662696 | − | 0.748889i | \(-0.269412\pi\) | ||||
0.662696 | + | 0.748889i | \(0.269412\pi\) | |||||||
\(608\) | −8.27792 | −0.335714 | ||||||||
\(609\) | −0.177625 | −0.00719774 | ||||||||
\(610\) | −1.36433 | −0.0552399 | ||||||||
\(611\) | 9.25652 | 0.374479 | ||||||||
\(612\) | −12.5851 | −0.508721 | ||||||||
\(613\) | 39.0744 | 1.57820 | 0.789100 | − | 0.614264i | \(-0.210547\pi\) | ||||
0.789100 | + | 0.614264i | \(0.210547\pi\) | |||||||
\(614\) | −12.5840 | −0.507850 | ||||||||
\(615\) | −4.39303 | −0.177144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.10384 | −0.205473 | −0.102736 | − | 0.994709i | \(-0.532760\pi\) | ||||
−0.102736 | + | 0.994709i | \(0.532760\pi\) | |||||||
\(618\) | −5.15675 | −0.207435 | ||||||||
\(619\) | 8.03596 | 0.322992 | 0.161496 | − | 0.986873i | \(-0.448368\pi\) | ||||
0.161496 | + | 0.986873i | \(0.448368\pi\) | |||||||
\(620\) | −4.52004 | −0.181529 | ||||||||
\(621\) | 1.56172 | 0.0626698 | ||||||||
\(622\) | −21.3223 | −0.854945 | ||||||||
\(623\) | 2.17209 | 0.0870229 | ||||||||
\(624\) | 0.882959 | 0.0353467 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.9895 | 0.998780 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.6617 | 0.425447 | ||||||||
\(629\) | −37.8179 | −1.50790 | ||||||||
\(630\) | 2.82843 | 0.112687 | ||||||||
\(631\) | 2.37486 | 0.0945416 | 0.0472708 | − | 0.998882i | \(-0.484948\pi\) | ||||
0.0472708 | + | 0.998882i | \(0.484948\pi\) | |||||||
\(632\) | −4.24728 | −0.168948 | ||||||||
\(633\) | −6.94333 | −0.275973 | ||||||||
\(634\) | 3.33636 | 0.132504 | ||||||||
\(635\) | 8.56564 | 0.339917 | ||||||||
\(636\) | 0.00855944 | 0.000339404 0 | ||||||||
\(637\) | 2.13165 | 0.0844591 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.5984 | 1.01266 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −41.6595 | −1.64545 | −0.822725 | − | 0.568440i | \(-0.807547\pi\) | ||||
−0.822725 | + | 0.568440i | \(0.807547\pi\) | |||||||
\(642\) | 4.14413 | 0.163556 | ||||||||
\(643\) | 36.9681 | 1.45788 | 0.728939 | − | 0.684578i | \(-0.240014\pi\) | ||||
0.728939 | + | 0.684578i | \(0.240014\pi\) | |||||||
\(644\) | 0.646887 | 0.0254909 | ||||||||
\(645\) | −1.10029 | −0.0433239 | ||||||||
\(646\) | −36.8325 | −1.44916 | ||||||||
\(647\) | −14.5229 | −0.570952 | −0.285476 | − | 0.958386i | \(-0.592152\pi\) | ||||
−0.285476 | + | 0.958386i | \(0.592152\pi\) | |||||||
\(648\) | 7.48528 | 0.294050 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.13165 | 0.0836103 | ||||||||
\(651\) | 1.87226 | 0.0733798 | ||||||||
\(652\) | −19.0917 | −0.747690 | ||||||||
\(653\) | −49.0424 | −1.91918 | −0.959588 | − | 0.281408i | \(-0.909199\pi\) | ||||
−0.959588 | + | 0.281408i | \(0.909199\pi\) | |||||||
\(654\) | −2.44949 | −0.0957826 | ||||||||
\(655\) | 5.64224 | 0.220461 | ||||||||
\(656\) | −10.6057 | −0.414084 | ||||||||
\(657\) | −1.65685 | −0.0646400 | ||||||||
\(658\) | −4.34242 | −0.169285 | ||||||||
\(659\) | −14.0139 | −0.545903 | −0.272951 | − | 0.962028i | \(-0.588000\pi\) | ||||
−0.272951 | + | 0.962028i | \(0.588000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.9342 | 1.74774 | 0.873869 | − | 0.486161i | \(-0.161603\pi\) | ||||
0.873869 | + | 0.486161i | \(0.161603\pi\) | |||||||
\(662\) | 8.12044 | 0.315610 | ||||||||
\(663\) | 3.92872 | 0.152579 | ||||||||
\(664\) | 4.62446 | 0.179464 | ||||||||
\(665\) | 8.27792 | 0.321004 | ||||||||
\(666\) | 24.0399 | 0.931526 | ||||||||
\(667\) | −0.277401 | −0.0107410 | ||||||||
\(668\) | 13.3684 | 0.517239 | ||||||||
\(669\) | −7.04384 | −0.272330 | ||||||||
\(670\) | −2.68556 | −0.103752 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.414214 | −0.0159786 | ||||||||
\(673\) | 43.1679 | 1.66400 | 0.832000 | − | 0.554775i | \(-0.187196\pi\) | ||||
0.832000 | + | 0.554775i | \(0.187196\pi\) | |||||||
\(674\) | −30.2961 | −1.16696 | ||||||||
\(675\) | −2.41421 | −0.0929231 | ||||||||
\(676\) | −8.45606 | −0.325233 | ||||||||
\(677\) | 7.26720 | 0.279301 | 0.139651 | − | 0.990201i | \(-0.455402\pi\) | ||||
0.139651 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(678\) | −1.56099 | −0.0599496 | ||||||||
\(679\) | −13.0552 | −0.501013 | ||||||||
\(680\) | 4.44949 | 0.170630 | ||||||||
\(681\) | −5.82437 | −0.223190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.44196 | 0.323023 | 0.161511 | − | 0.986871i | \(-0.448363\pi\) | ||||
0.161511 | + | 0.986871i | \(0.448363\pi\) | |||||||
\(684\) | 23.4135 | 0.895237 | ||||||||
\(685\) | −1.64637 | −0.0629046 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −11.5016 | −0.438813 | ||||||||
\(688\) | −2.65634 | −0.101272 | ||||||||
\(689\) | 0.0440491 | 0.00167814 | ||||||||
\(690\) | −0.267949 | −0.0102007 | ||||||||
\(691\) | 42.7272 | 1.62542 | 0.812710 | − | 0.582669i | \(-0.197992\pi\) | ||||
0.812710 | + | 0.582669i | \(0.197992\pi\) | |||||||
\(692\) | −2.38551 | −0.0906833 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.5745 | 0.818958 | ||||||||
\(695\) | −16.3071 | −0.618565 | ||||||||
\(696\) | 0.177625 | 0.00673287 | ||||||||
\(697\) | −47.1901 | −1.78745 | ||||||||
\(698\) | 29.4536 | 1.11483 | ||||||||
\(699\) | −4.06805 | −0.153868 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −32.9814 | −1.24569 | −0.622846 | − | 0.782345i | \(-0.714024\pi\) | ||||
−0.622846 | + | 0.782345i | \(0.714024\pi\) | |||||||
\(702\) | −5.14626 | −0.194233 | ||||||||
\(703\) | 70.3571 | 2.65357 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.79869 | 0.0677425 | ||||||||
\(706\) | 10.2578 | 0.386056 | ||||||||
\(707\) | −6.46410 | −0.243108 | ||||||||
\(708\) | −1.86835 | −0.0702168 | ||||||||
\(709\) | 19.1550 | 0.719381 | 0.359690 | − | 0.933072i | \(-0.382882\pi\) | ||||
0.359690 | + | 0.933072i | \(0.382882\pi\) | |||||||
\(710\) | −9.05040 | −0.339656 | ||||||||
\(711\) | 12.0131 | 0.450528 | ||||||||
\(712\) | −2.17209 | −0.0814025 | ||||||||
\(713\) | 2.92395 | 0.109503 | ||||||||
\(714\) | −1.84304 | −0.0689740 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.68681 | −0.137782 | ||||||||
\(717\) | 1.77683 | 0.0663569 | ||||||||
\(718\) | −31.9893 | −1.19383 | ||||||||
\(719\) | 39.4644 | 1.47177 | 0.735887 | − | 0.677104i | \(-0.236765\pi\) | ||||
0.735887 | + | 0.677104i | \(0.236765\pi\) | |||||||
\(720\) | −2.82843 | −0.105409 | ||||||||
\(721\) | 12.4495 | 0.463643 | ||||||||
\(722\) | 49.5239 | 1.84309 | ||||||||
\(723\) | −2.12701 | −0.0791043 | ||||||||
\(724\) | −9.53001 | −0.354180 | ||||||||
\(725\) | 0.428825 | 0.0159262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9129 | −0.961055 | −0.480527 | − | 0.876980i | \(-0.659555\pi\) | ||||
−0.480527 | + | 0.876980i | \(0.659555\pi\) | |||||||
\(728\) | −2.13165 | −0.0790043 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0.585786 | 0.0216809 | ||||||||
\(731\) | −11.8194 | −0.437155 | ||||||||
\(732\) | −0.565122 | −0.0208875 | ||||||||
\(733\) | −47.2935 | −1.74683 | −0.873413 | − | 0.486981i | \(-0.838098\pi\) | ||||
−0.873413 | + | 0.486981i | \(0.838098\pi\) | |||||||
\(734\) | 21.2734 | 0.785217 | ||||||||
\(735\) | 0.414214 | 0.0152785 | ||||||||
\(736\) | −0.646887 | −0.0238446 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 29.9975 | 1.10422 | ||||||||
\(739\) | −34.1019 | −1.25446 | −0.627229 | − | 0.778835i | \(-0.715811\pi\) | ||||
−0.627229 | + | 0.778835i | \(0.715811\pi\) | |||||||
\(740\) | −8.49938 | −0.312443 | ||||||||
\(741\) | −7.30906 | −0.268505 | ||||||||
\(742\) | −0.0206643 | −0.000758611 0 | ||||||||
\(743\) | −37.2951 | −1.36823 | −0.684113 | − | 0.729376i | \(-0.739810\pi\) | ||||
−0.684113 | + | 0.729376i | \(0.739810\pi\) | |||||||
\(744\) | −1.87226 | −0.0686405 | ||||||||
\(745\) | −4.12701 | −0.151202 | ||||||||
\(746\) | −21.6695 | −0.793376 | ||||||||
\(747\) | −13.0800 | −0.478571 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.0048 | −0.365568 | ||||||||
\(750\) | 0.414214 | 0.0151249 | ||||||||
\(751\) | 27.1160 | 0.989475 | 0.494738 | − | 0.869042i | \(-0.335264\pi\) | ||||
0.494738 | + | 0.869042i | \(0.335264\pi\) | |||||||
\(752\) | 4.34242 | 0.158352 | ||||||||
\(753\) | −4.38447 | −0.159779 | ||||||||
\(754\) | 0.914107 | 0.0332898 | ||||||||
\(755\) | 11.8949 | 0.432898 | ||||||||
\(756\) | 2.41421 | 0.0878041 | ||||||||
\(757\) | 1.81278 | 0.0658868 | 0.0329434 | − | 0.999457i | \(-0.489512\pi\) | ||||
0.0329434 | + | 0.999457i | \(0.489512\pi\) | |||||||
\(758\) | −15.6617 | −0.568857 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.27792 | −0.300272 | ||||||||
\(761\) | 31.5856 | 1.14498 | 0.572488 | − | 0.819913i | \(-0.305978\pi\) | ||||
0.572488 | + | 0.819913i | \(0.305978\pi\) | |||||||
\(762\) | 3.54800 | 0.128531 | ||||||||
\(763\) | 5.91359 | 0.214086 | ||||||||
\(764\) | −13.3789 | −0.484033 | ||||||||
\(765\) | −12.5851 | −0.455014 | ||||||||
\(766\) | 17.5412 | 0.633790 | ||||||||
\(767\) | −9.61501 | −0.347178 | ||||||||
\(768\) | 0.414214 | 0.0149466 | ||||||||
\(769\) | −33.4286 | −1.20547 | −0.602733 | − | 0.797943i | \(-0.705922\pi\) | ||||
−0.602733 | + | 0.797943i | \(0.705922\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.77146 | −0.0637974 | ||||||||
\(772\) | 6.52985 | 0.235014 | ||||||||
\(773\) | −47.6294 | −1.71311 | −0.856555 | − | 0.516055i | \(-0.827400\pi\) | ||||
−0.856555 | + | 0.516055i | \(0.827400\pi\) | |||||||
\(774\) | 7.51326 | 0.270059 | ||||||||
\(775\) | −4.52004 | −0.162365 | ||||||||
\(776\) | 13.0552 | 0.468655 | ||||||||
\(777\) | 3.52056 | 0.126299 | ||||||||
\(778\) | −19.6118 | −0.703116 | ||||||||
\(779\) | 87.7933 | 3.14552 | ||||||||
\(780\) | 0.882959 | 0.0316150 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.87832 | −0.102928 | ||||||||
\(783\) | −1.03528 | −0.0369978 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.6617 | 0.380531 | ||||||||
\(786\) | 2.33709 | 0.0833614 | ||||||||
\(787\) | 35.3497 | 1.26008 | 0.630041 | − | 0.776562i | \(-0.283038\pi\) | ||||
0.630041 | + | 0.776562i | \(0.283038\pi\) | |||||||
\(788\) | 26.1056 | 0.929974 | ||||||||
\(789\) | 5.29253 | 0.188419 | ||||||||
\(790\) | −4.24728 | −0.151112 | ||||||||
\(791\) | 3.76857 | 0.133995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.90827 | −0.103276 | ||||||||
\(794\) | −1.78482 | −0.0633410 | ||||||||
\(795\) | 0.00855944 | 0.000303572 0 | ||||||||
\(796\) | −18.8917 | −0.669598 | ||||||||
\(797\) | −11.6576 | −0.412933 | −0.206467 | − | 0.978454i | \(-0.566197\pi\) | ||||
−0.206467 | + | 0.978454i | \(0.566197\pi\) | |||||||
\(798\) | 3.42883 | 0.121379 | ||||||||
\(799\) | 19.3215 | 0.683547 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 6.14359 | 0.217073 | ||||||||
\(802\) | −27.8471 | −0.983316 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.11240 | −0.0392312 | ||||||||
\(805\) | 0.646887 | 0.0227998 | ||||||||
\(806\) | −9.63516 | −0.339384 | ||||||||
\(807\) | −2.87669 | −0.101264 | ||||||||
\(808\) | 6.46410 | 0.227406 | ||||||||
\(809\) | −14.5052 | −0.509976 | −0.254988 | − | 0.966944i | \(-0.582072\pi\) | ||||
−0.254988 | + | 0.966944i | \(0.582072\pi\) | |||||||
\(810\) | 7.48528 | 0.263006 | ||||||||
\(811\) | 30.8587 | 1.08359 | 0.541797 | − | 0.840509i | \(-0.317744\pi\) | ||||
0.541797 | + | 0.840509i | \(0.317744\pi\) | |||||||
\(812\) | −0.428825 | −0.0150488 | ||||||||
\(813\) | −12.1742 | −0.426967 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.0917 | −0.668754 | ||||||||
\(816\) | 1.84304 | 0.0645193 | ||||||||
\(817\) | 21.9890 | 0.769296 | ||||||||
\(818\) | −17.0071 | −0.594639 | ||||||||
\(819\) | 6.02922 | 0.210678 | ||||||||
\(820\) | −10.6057 | −0.370368 | ||||||||
\(821\) | −8.11042 | −0.283056 | −0.141528 | − | 0.989934i | \(-0.545201\pi\) | ||||
−0.141528 | + | 0.989934i | \(0.545201\pi\) | |||||||
\(822\) | −0.681949 | −0.0237857 | ||||||||
\(823\) | −46.4122 | −1.61783 | −0.808914 | − | 0.587926i | \(-0.799944\pi\) | ||||
−0.808914 | + | 0.587926i | \(0.799944\pi\) | |||||||
\(824\) | −12.4495 | −0.433699 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.51059 | 0.156943 | ||||||||
\(827\) | −22.7819 | −0.792204 | −0.396102 | − | 0.918207i | \(-0.629637\pi\) | ||||
−0.396102 | + | 0.918207i | \(0.629637\pi\) | |||||||
\(828\) | 1.82967 | 0.0635855 | ||||||||
\(829\) | −6.20021 | −0.215342 | −0.107671 | − | 0.994187i | \(-0.534339\pi\) | ||||
−0.107671 | + | 0.994187i | \(0.534339\pi\) | |||||||
\(830\) | 4.62446 | 0.160517 | ||||||||
\(831\) | 4.14183 | 0.143679 | ||||||||
\(832\) | 2.13165 | 0.0739018 | ||||||||
\(833\) | 4.44949 | 0.154166 | ||||||||
\(834\) | −6.75464 | −0.233894 | ||||||||
\(835\) | 13.3684 | 0.462633 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.9123 | 0.377186 | ||||||||
\(838\) | 7.35112 | 0.253940 | ||||||||
\(839\) | −4.54727 | −0.156989 | −0.0784947 | − | 0.996915i | \(-0.525011\pi\) | ||||
−0.0784947 | + | 0.996915i | \(0.525011\pi\) | |||||||
\(840\) | −0.414214 | −0.0142917 | ||||||||
\(841\) | −28.8161 | −0.993659 | ||||||||
\(842\) | 20.0267 | 0.690167 | ||||||||
\(843\) | 8.93838 | 0.307854 | ||||||||
\(844\) | −16.7627 | −0.576995 | ||||||||
\(845\) | −8.45606 | −0.290897 | ||||||||
\(846\) | −12.2822 | −0.422271 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.0206643 | 0.000709615 0 | ||||||||
\(849\) | 4.65242 | 0.159671 | ||||||||
\(850\) | 4.44949 | 0.152616 | ||||||||
\(851\) | 5.49813 | 0.188474 | ||||||||
\(852\) | −3.74880 | −0.128432 | ||||||||
\(853\) | −26.8475 | −0.919241 | −0.459620 | − | 0.888115i | \(-0.652015\pi\) | ||||
−0.459620 | + | 0.888115i | \(0.652015\pi\) | |||||||
\(854\) | 1.36433 | 0.0466863 | ||||||||
\(855\) | 23.4135 | 0.800724 | ||||||||
\(856\) | 10.0048 | 0.341957 | ||||||||
\(857\) | 40.8363 | 1.39494 | 0.697470 | − | 0.716614i | \(-0.254309\pi\) | ||||
0.697470 | + | 0.716614i | \(0.254309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.34824 | 0.0460013 | 0.0230006 | − | 0.999735i | \(-0.492678\pi\) | ||||
0.0230006 | + | 0.999735i | \(0.492678\pi\) | |||||||
\(860\) | −2.65634 | −0.0905804 | ||||||||
\(861\) | 4.39303 | 0.149714 | ||||||||
\(862\) | 5.14626 | 0.175282 | ||||||||
\(863\) | −40.8376 | −1.39013 | −0.695064 | − | 0.718948i | \(-0.744624\pi\) | ||||
−0.695064 | + | 0.718948i | \(0.744624\pi\) | |||||||
\(864\) | −2.41421 | −0.0821332 | ||||||||
\(865\) | −2.38551 | −0.0811096 | ||||||||
\(866\) | −41.3976 | −1.40675 | ||||||||
\(867\) | 1.15895 | 0.0393601 | ||||||||
\(868\) | 4.52004 | 0.153420 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.177625 | 0.00602206 | ||||||||
\(871\) | −5.72469 | −0.193974 | ||||||||
\(872\) | −5.91359 | −0.200259 | ||||||||
\(873\) | −36.9257 | −1.24975 | ||||||||
\(874\) | 5.35487 | 0.181131 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0.242641 | 0.00819807 | ||||||||
\(877\) | 4.52485 | 0.152793 | 0.0763967 | − | 0.997078i | \(-0.475658\pi\) | ||||
0.0763967 | + | 0.997078i | \(0.475658\pi\) | |||||||
\(878\) | −21.6609 | −0.731021 | ||||||||
\(879\) | 6.94525 | 0.234258 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.7841 | −0.632852 | −0.316426 | − | 0.948617i | \(-0.602483\pi\) | ||||
−0.316426 | + | 0.948617i | \(0.602483\pi\) | |||||||
\(882\) | −2.82843 | −0.0952381 | ||||||||
\(883\) | −27.8159 | −0.936080 | −0.468040 | − | 0.883707i | \(-0.655040\pi\) | ||||
−0.468040 | + | 0.883707i | \(0.655040\pi\) | |||||||
\(884\) | 9.48477 | 0.319007 | ||||||||
\(885\) | −1.86835 | −0.0628038 | ||||||||
\(886\) | 21.0771 | 0.708100 | ||||||||
\(887\) | 1.97830 | 0.0664250 | 0.0332125 | − | 0.999448i | \(-0.489426\pi\) | ||||
0.0332125 | + | 0.999448i | \(0.489426\pi\) | |||||||
\(888\) | −3.52056 | −0.118142 | ||||||||
\(889\) | −8.56564 | −0.287282 | ||||||||
\(890\) | −2.17209 | −0.0728086 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.0053 | −0.569380 | ||||||||
\(893\) | −35.9462 | −1.20289 | ||||||||
\(894\) | −1.70946 | −0.0571730 | ||||||||
\(895\) | −3.68681 | −0.123236 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.571175 | −0.0190710 | ||||||||
\(898\) | 40.9893 | 1.36783 | ||||||||
\(899\) | −1.93831 | −0.0646462 | ||||||||
\(900\) | −2.82843 | −0.0942809 | ||||||||
\(901\) | 0.0919456 | 0.00306315 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.10029 | 0.0366154 | ||||||||
\(904\) | −3.76857 | −0.125341 | ||||||||
\(905\) | −9.53001 | −0.316788 | ||||||||
\(906\) | 4.92701 | 0.163689 | ||||||||
\(907\) | 29.2382 | 0.970838 | 0.485419 | − | 0.874282i | \(-0.338667\pi\) | ||||
0.485419 | + | 0.874282i | \(0.338667\pi\) | |||||||
\(908\) | −14.0613 | −0.466639 | ||||||||
\(909\) | −18.2832 | −0.606417 | ||||||||
\(910\) | −2.13165 | −0.0706636 | ||||||||
\(911\) | 7.11563 | 0.235751 | 0.117876 | − | 0.993028i | \(-0.462392\pi\) | ||||
0.117876 | + | 0.993028i | \(0.462392\pi\) | |||||||
\(912\) | −3.42883 | −0.113540 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −18.3784 | −0.607904 | ||||||||
\(915\) | −0.565122 | −0.0186824 | ||||||||
\(916\) | −27.7673 | −0.917457 | ||||||||
\(917\) | −5.64224 | −0.186323 | ||||||||
\(918\) | −10.7420 | −0.354539 | ||||||||
\(919\) | −48.4518 | −1.59828 | −0.799138 | − | 0.601147i | \(-0.794711\pi\) | ||||
−0.799138 | + | 0.601147i | \(0.794711\pi\) | |||||||
\(920\) | −0.646887 | −0.0213272 | ||||||||
\(921\) | −5.21247 | −0.171757 | ||||||||
\(922\) | −15.0383 | −0.495260 | ||||||||
\(923\) | −19.2923 | −0.635014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.49938 | −0.279458 | ||||||||
\(926\) | −28.6376 | −0.941090 | ||||||||
\(927\) | 35.2125 | 1.15653 | ||||||||
\(928\) | 0.428825 | 0.0140769 | ||||||||
\(929\) | 14.8869 | 0.488423 | 0.244211 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244211 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(930\) | −1.87226 | −0.0613939 | ||||||||
\(931\) | −8.27792 | −0.271298 | ||||||||
\(932\) | −9.82113 | −0.321702 | ||||||||
\(933\) | −8.83197 | −0.289146 | ||||||||
\(934\) | 9.16960 | 0.300038 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.02922 | −0.197071 | ||||||||
\(937\) | 4.76268 | 0.155590 | 0.0777950 | − | 0.996969i | \(-0.475212\pi\) | ||||
0.0777950 | + | 0.996969i | \(0.475212\pi\) | |||||||
\(938\) | 2.68556 | 0.0876867 | ||||||||
\(939\) | 10.3510 | 0.337791 | ||||||||
\(940\) | 4.34242 | 0.141634 | ||||||||
\(941\) | 25.4100 | 0.828341 | 0.414171 | − | 0.910199i | \(-0.364072\pi\) | ||||
0.414171 | + | 0.910199i | \(0.364072\pi\) | |||||||
\(942\) | 4.41621 | 0.143888 | ||||||||
\(943\) | 6.86070 | 0.223415 | ||||||||
\(944\) | −4.51059 | −0.146807 | ||||||||
\(945\) | 2.41421 | 0.0785344 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.0379 | −1.91847 | −0.959237 | − | 0.282603i | \(-0.908802\pi\) | ||||
−0.959237 | + | 0.282603i | \(0.908802\pi\) | |||||||
\(948\) | −1.75928 | −0.0571389 | ||||||||
\(949\) | 1.24869 | 0.0405343 | ||||||||
\(950\) | −8.27792 | −0.268571 | ||||||||
\(951\) | 1.38197 | 0.0448134 | ||||||||
\(952\) | −4.44949 | −0.144209 | ||||||||
\(953\) | 28.2159 | 0.914003 | 0.457002 | − | 0.889466i | \(-0.348923\pi\) | ||||
0.457002 | + | 0.889466i | \(0.348923\pi\) | |||||||
\(954\) | −0.0584475 | −0.00189231 | ||||||||
\(955\) | −13.3789 | −0.432932 | ||||||||
\(956\) | 4.28964 | 0.138737 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.8489 | 1.09361 | ||||||||
\(959\) | 1.64637 | 0.0531641 | ||||||||
\(960\) | 0.414214 | 0.0133687 | ||||||||
\(961\) | −10.5692 | −0.340943 | ||||||||
\(962\) | −18.1177 | −0.584139 | ||||||||
\(963\) | −28.2979 | −0.911886 | ||||||||
\(964\) | −5.13505 | −0.165389 | ||||||||
\(965\) | 6.52985 | 0.210203 | ||||||||
\(966\) | 0.267949 | 0.00862112 | ||||||||
\(967\) | −27.6194 | −0.888179 | −0.444090 | − | 0.895982i | \(-0.646473\pi\) | ||||
−0.444090 | + | 0.895982i | \(0.646473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.2565 | −0.490110 | ||||||||
\(970\) | 13.0552 | 0.419178 | ||||||||
\(971\) | 30.2501 | 0.970772 | 0.485386 | − | 0.874300i | \(-0.338679\pi\) | ||||
0.485386 | + | 0.874300i | \(0.338679\pi\) | |||||||
\(972\) | 10.3431 | 0.331757 | ||||||||
\(973\) | 16.3071 | 0.522783 | ||||||||
\(974\) | −27.2216 | −0.872237 | ||||||||
\(975\) | 0.882959 | 0.0282773 | ||||||||
\(976\) | −1.36433 | −0.0436710 | ||||||||
\(977\) | 41.5134 | 1.32813 | 0.664066 | − | 0.747674i | \(-0.268829\pi\) | ||||
0.664066 | + | 0.747674i | \(0.268829\pi\) | |||||||
\(978\) | −7.90805 | −0.252872 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 16.7262 | 0.534025 | ||||||||
\(982\) | 33.7879 | 1.07822 | ||||||||
\(983\) | 10.6312 | 0.339082 | 0.169541 | − | 0.985523i | \(-0.445771\pi\) | ||||
0.169541 | + | 0.985523i | \(0.445771\pi\) | |||||||
\(984\) | −4.39303 | −0.140045 | ||||||||
\(985\) | 26.1056 | 0.831794 | ||||||||
\(986\) | 1.90805 | 0.0607648 | ||||||||
\(987\) | −1.79869 | −0.0572529 | ||||||||
\(988\) | −17.6456 | −0.561383 | ||||||||
\(989\) | 1.71835 | 0.0546403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.8815 | −1.42571 | −0.712853 | − | 0.701313i | \(-0.752597\pi\) | ||||
−0.712853 | + | 0.701313i | \(0.752597\pi\) | |||||||
\(992\) | −4.52004 | −0.143511 | ||||||||
\(993\) | 3.36360 | 0.106741 | ||||||||
\(994\) | 9.05040 | 0.287061 | ||||||||
\(995\) | −18.8917 | −0.598907 | ||||||||
\(996\) | 1.91552 | 0.0606954 | ||||||||
\(997\) | 30.7930 | 0.975225 | 0.487613 | − | 0.873060i | \(-0.337868\pi\) | ||||
0.487613 | + | 0.873060i | \(0.337868\pi\) | |||||||
\(998\) | 14.6347 | 0.463254 | ||||||||
\(999\) | 20.5193 | 0.649202 |
(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.cr.1.4 | yes | 4 | |
11.10 | odd | 2 | 8470.2.a.cp.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cp.1.3 | ✓ | 4 | 11.10 | odd | 2 | ||
8470.2.a.cr.1.4 | yes | 4 | 1.1 | even | 1 | trivial |