Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
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: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.38197 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 0.236068 | 0.0892253 | 0.0446127 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446127 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | −1.38197 | −0.437016 | ||||||||
\(11\) | −4.23607 | −1.27722 | −0.638611 | − | 0.769529i | \(-0.720491\pi\) | ||||
−0.638611 | + | 0.769529i | \(0.720491\pi\) | |||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0.236068 | 0.0630918 | ||||||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.23607 | −1.02740 | −0.513699 | − | 0.857971i | \(-0.671725\pi\) | ||||
−0.513699 | + | 0.857971i | \(0.671725\pi\) | |||||||
\(18\) | −0.381966 | −0.0900303 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.38197 | −0.309017 | ||||||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | −4.23607 | −0.903133 | ||||||||
\(23\) | −3.76393 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(24\) | −1.61803 | −0.330280 | ||||||||
\(25\) | −3.09017 | −0.618034 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0.236068 | 0.0446127 | ||||||||
\(29\) | −5.85410 | −1.08708 | −0.543540 | − | 0.839383i | \(-0.682916\pi\) | ||||
−0.543540 | + | 0.839383i | \(0.682916\pi\) | |||||||
\(30\) | 2.23607 | 0.408248 | ||||||||
\(31\) | −1.47214 | −0.264403 | −0.132202 | − | 0.991223i | \(-0.542205\pi\) | ||||
−0.132202 | + | 0.991223i | \(0.542205\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.85410 | 1.19315 | ||||||||
\(34\) | −4.23607 | −0.726480 | ||||||||
\(35\) | −0.326238 | −0.0551443 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | 4.70820 | 0.774024 | 0.387012 | − | 0.922075i | \(-0.373507\pi\) | ||||
0.387012 | + | 0.922075i | \(0.373507\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 1.61803 | 0.259093 | ||||||||
\(40\) | −1.38197 | −0.218508 | ||||||||
\(41\) | −5.70820 | −0.891472 | −0.445736 | − | 0.895165i | \(-0.647058\pi\) | ||||
−0.445736 | + | 0.895165i | \(0.647058\pi\) | |||||||
\(42\) | −0.381966 | −0.0589386 | ||||||||
\(43\) | −2.23607 | −0.340997 | −0.170499 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170499 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(44\) | −4.23607 | −0.638611 | ||||||||
\(45\) | 0.527864 | 0.0786893 | ||||||||
\(46\) | −3.76393 | −0.554962 | ||||||||
\(47\) | −0.145898 | −0.0212814 | −0.0106407 | − | 0.999943i | \(-0.503387\pi\) | ||||
−0.0106407 | + | 0.999943i | \(0.503387\pi\) | |||||||
\(48\) | −1.61803 | −0.233543 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | −3.09017 | −0.437016 | ||||||||
\(51\) | 6.85410 | 0.959766 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 5.85410 | 0.789367 | ||||||||
\(56\) | 0.236068 | 0.0315459 | ||||||||
\(57\) | −3.23607 | −0.428628 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | 13.5623 | 1.76566 | 0.882831 | − | 0.469691i | \(-0.155635\pi\) | ||||
0.882831 | + | 0.469691i | \(0.155635\pi\) | |||||||
\(60\) | 2.23607 | 0.288675 | ||||||||
\(61\) | 3.47214 | 0.444561 | 0.222281 | − | 0.974983i | \(-0.428650\pi\) | ||||
0.222281 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(62\) | −1.47214 | −0.186961 | ||||||||
\(63\) | −0.0901699 | −0.0113603 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.38197 | 0.171412 | ||||||||
\(66\) | 6.85410 | 0.843682 | ||||||||
\(67\) | 6.23607 | 0.761857 | 0.380928 | − | 0.924605i | \(-0.375604\pi\) | ||||
0.380928 | + | 0.924605i | \(0.375604\pi\) | |||||||
\(68\) | −4.23607 | −0.513699 | ||||||||
\(69\) | 6.09017 | 0.733170 | ||||||||
\(70\) | −0.326238 | −0.0389929 | ||||||||
\(71\) | −3.70820 | −0.440083 | −0.220041 | − | 0.975491i | \(-0.570619\pi\) | ||||
−0.220041 | + | 0.975491i | \(0.570619\pi\) | |||||||
\(72\) | −0.381966 | −0.0450151 | ||||||||
\(73\) | 2.70820 | 0.316971 | 0.158486 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158486 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(74\) | 4.70820 | 0.547318 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 1.61803 | 0.183206 | ||||||||
\(79\) | 10.7984 | 1.21491 | 0.607456 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607456 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(80\) | −1.38197 | −0.154508 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | −5.70820 | −0.630366 | ||||||||
\(83\) | −0.763932 | −0.0838524 | −0.0419262 | − | 0.999121i | \(-0.513349\pi\) | ||||
−0.0419262 | + | 0.999121i | \(0.513349\pi\) | |||||||
\(84\) | −0.381966 | −0.0416759 | ||||||||
\(85\) | 5.85410 | 0.634967 | ||||||||
\(86\) | −2.23607 | −0.241121 | ||||||||
\(87\) | 9.47214 | 1.01552 | ||||||||
\(88\) | −4.23607 | −0.451566 | ||||||||
\(89\) | 14.7984 | 1.56862 | 0.784312 | − | 0.620366i | \(-0.213016\pi\) | ||||
0.784312 | + | 0.620366i | \(0.213016\pi\) | |||||||
\(90\) | 0.527864 | 0.0556418 | ||||||||
\(91\) | −0.236068 | −0.0247466 | ||||||||
\(92\) | −3.76393 | −0.392417 | ||||||||
\(93\) | 2.38197 | 0.246998 | ||||||||
\(94\) | −0.145898 | −0.0150482 | ||||||||
\(95\) | −2.76393 | −0.283573 | ||||||||
\(96\) | −1.61803 | −0.165140 | ||||||||
\(97\) | −18.6525 | −1.89387 | −0.946936 | − | 0.321422i | \(-0.895839\pi\) | ||||
−0.946936 | + | 0.321422i | \(0.895839\pi\) | |||||||
\(98\) | −6.94427 | −0.701477 | ||||||||
\(99\) | 1.61803 | 0.162619 | ||||||||
\(100\) | −3.09017 | −0.309017 | ||||||||
\(101\) | 6.09017 | 0.605995 | 0.302997 | − | 0.952991i | \(-0.402013\pi\) | ||||
0.302997 | + | 0.952991i | \(0.402013\pi\) | |||||||
\(102\) | 6.85410 | 0.678657 | ||||||||
\(103\) | 4.14590 | 0.408507 | 0.204254 | − | 0.978918i | \(-0.434523\pi\) | ||||
0.204254 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0.527864 | 0.0515143 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.76393 | −0.750568 | −0.375284 | − | 0.926910i | \(-0.622455\pi\) | ||||
−0.375284 | + | 0.926910i | \(0.622455\pi\) | |||||||
\(108\) | 5.47214 | 0.526557 | ||||||||
\(109\) | 8.70820 | 0.834095 | 0.417047 | − | 0.908885i | \(-0.363065\pi\) | ||||
0.417047 | + | 0.908885i | \(0.363065\pi\) | |||||||
\(110\) | 5.85410 | 0.558167 | ||||||||
\(111\) | −7.61803 | −0.723072 | ||||||||
\(112\) | 0.236068 | 0.0223063 | ||||||||
\(113\) | −17.6180 | −1.65737 | −0.828683 | − | 0.559719i | \(-0.810909\pi\) | ||||
−0.828683 | + | 0.559719i | \(0.810909\pi\) | |||||||
\(114\) | −3.23607 | −0.303086 | ||||||||
\(115\) | 5.20163 | 0.485054 | ||||||||
\(116\) | −5.85410 | −0.543540 | ||||||||
\(117\) | 0.381966 | 0.0353128 | ||||||||
\(118\) | 13.5623 | 1.24851 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 2.23607 | 0.204124 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | 3.47214 | 0.314352 | ||||||||
\(123\) | 9.23607 | 0.832788 | ||||||||
\(124\) | −1.47214 | −0.132202 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | −0.0901699 | −0.00803298 | ||||||||
\(127\) | −3.79837 | −0.337051 | −0.168526 | − | 0.985697i | \(-0.553901\pi\) | ||||
−0.168526 | + | 0.985697i | \(0.553901\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.61803 | 0.318550 | ||||||||
\(130\) | 1.38197 | 0.121206 | ||||||||
\(131\) | 7.23607 | 0.632218 | 0.316109 | − | 0.948723i | \(-0.397623\pi\) | ||||
0.316109 | + | 0.948723i | \(0.397623\pi\) | |||||||
\(132\) | 6.85410 | 0.596573 | ||||||||
\(133\) | 0.472136 | 0.0409394 | ||||||||
\(134\) | 6.23607 | 0.538714 | ||||||||
\(135\) | −7.56231 | −0.650860 | ||||||||
\(136\) | −4.23607 | −0.363240 | ||||||||
\(137\) | −13.3820 | −1.14330 | −0.571649 | − | 0.820498i | \(-0.693696\pi\) | ||||
−0.571649 | + | 0.820498i | \(0.693696\pi\) | |||||||
\(138\) | 6.09017 | 0.518430 | ||||||||
\(139\) | −9.56231 | −0.811064 | −0.405532 | − | 0.914081i | \(-0.632914\pi\) | ||||
−0.405532 | + | 0.914081i | \(0.632914\pi\) | |||||||
\(140\) | −0.326238 | −0.0275721 | ||||||||
\(141\) | 0.236068 | 0.0198805 | ||||||||
\(142\) | −3.70820 | −0.311186 | ||||||||
\(143\) | 4.23607 | 0.354238 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 8.09017 | 0.671852 | ||||||||
\(146\) | 2.70820 | 0.224133 | ||||||||
\(147\) | 11.2361 | 0.926735 | ||||||||
\(148\) | 4.70820 | 0.387012 | ||||||||
\(149\) | −15.3262 | −1.25557 | −0.627787 | − | 0.778385i | \(-0.716039\pi\) | ||||
−0.627787 | + | 0.778385i | \(0.716039\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | 7.94427 | 0.646496 | 0.323248 | − | 0.946314i | \(-0.395225\pi\) | ||||
0.323248 | + | 0.946314i | \(0.395225\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 1.61803 | 0.130810 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 2.03444 | 0.163410 | ||||||||
\(156\) | 1.61803 | 0.129546 | ||||||||
\(157\) | −8.65248 | −0.690543 | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||||
−0.345271 | + | 0.938503i | \(0.612213\pi\) | |||||||
\(158\) | 10.7984 | 0.859072 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.38197 | −0.109254 | ||||||||
\(161\) | −0.888544 | −0.0700271 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | 1.67376 | 0.131099 | 0.0655496 | − | 0.997849i | \(-0.479120\pi\) | ||||
0.0655496 | + | 0.997849i | \(0.479120\pi\) | |||||||
\(164\) | −5.70820 | −0.445736 | ||||||||
\(165\) | −9.47214 | −0.737405 | ||||||||
\(166\) | −0.763932 | −0.0592926 | ||||||||
\(167\) | 1.38197 | 0.106940 | 0.0534699 | − | 0.998569i | \(-0.482972\pi\) | ||||
0.0534699 | + | 0.998569i | \(0.482972\pi\) | |||||||
\(168\) | −0.381966 | −0.0294693 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 5.85410 | 0.448989 | ||||||||
\(171\) | −0.763932 | −0.0584193 | ||||||||
\(172\) | −2.23607 | −0.170499 | ||||||||
\(173\) | 1.47214 | 0.111924 | 0.0559622 | − | 0.998433i | \(-0.482177\pi\) | ||||
0.0559622 | + | 0.998433i | \(0.482177\pi\) | |||||||
\(174\) | 9.47214 | 0.718081 | ||||||||
\(175\) | −0.729490 | −0.0551443 | ||||||||
\(176\) | −4.23607 | −0.319306 | ||||||||
\(177\) | −21.9443 | −1.64943 | ||||||||
\(178\) | 14.7984 | 1.10919 | ||||||||
\(179\) | 5.29180 | 0.395527 | 0.197764 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197764 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(180\) | 0.527864 | 0.0393447 | ||||||||
\(181\) | −7.41641 | −0.551257 | −0.275629 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275629 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(182\) | −0.236068 | −0.0174985 | ||||||||
\(183\) | −5.61803 | −0.415297 | ||||||||
\(184\) | −3.76393 | −0.277481 | ||||||||
\(185\) | −6.50658 | −0.478373 | ||||||||
\(186\) | 2.38197 | 0.174654 | ||||||||
\(187\) | 17.9443 | 1.31222 | ||||||||
\(188\) | −0.145898 | −0.0106407 | ||||||||
\(189\) | 1.29180 | 0.0939643 | ||||||||
\(190\) | −2.76393 | −0.200517 | ||||||||
\(191\) | −22.9443 | −1.66019 | −0.830095 | − | 0.557623i | \(-0.811714\pi\) | ||||
−0.830095 | + | 0.557623i | \(0.811714\pi\) | |||||||
\(192\) | −1.61803 | −0.116772 | ||||||||
\(193\) | −3.76393 | −0.270934 | −0.135467 | − | 0.990782i | \(-0.543253\pi\) | ||||
−0.135467 | + | 0.990782i | \(0.543253\pi\) | |||||||
\(194\) | −18.6525 | −1.33917 | ||||||||
\(195\) | −2.23607 | −0.160128 | ||||||||
\(196\) | −6.94427 | −0.496019 | ||||||||
\(197\) | −24.6180 | −1.75396 | −0.876981 | − | 0.480525i | \(-0.840446\pi\) | ||||
−0.876981 | + | 0.480525i | \(0.840446\pi\) | |||||||
\(198\) | 1.61803 | 0.114989 | ||||||||
\(199\) | −7.61803 | −0.540028 | −0.270014 | − | 0.962856i | \(-0.587028\pi\) | ||||
−0.270014 | + | 0.962856i | \(0.587028\pi\) | |||||||
\(200\) | −3.09017 | −0.218508 | ||||||||
\(201\) | −10.0902 | −0.711706 | ||||||||
\(202\) | 6.09017 | 0.428503 | ||||||||
\(203\) | −1.38197 | −0.0969950 | ||||||||
\(204\) | 6.85410 | 0.479883 | ||||||||
\(205\) | 7.88854 | 0.550960 | ||||||||
\(206\) | 4.14590 | 0.288858 | ||||||||
\(207\) | 1.43769 | 0.0999266 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −8.47214 | −0.586030 | ||||||||
\(210\) | 0.527864 | 0.0364261 | ||||||||
\(211\) | −5.85410 | −0.403013 | −0.201506 | − | 0.979487i | \(-0.564584\pi\) | ||||
−0.201506 | + | 0.979487i | \(0.564584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | −7.76393 | −0.530731 | ||||||||
\(215\) | 3.09017 | 0.210748 | ||||||||
\(216\) | 5.47214 | 0.372332 | ||||||||
\(217\) | −0.347524 | −0.0235915 | ||||||||
\(218\) | 8.70820 | 0.589794 | ||||||||
\(219\) | −4.38197 | −0.296106 | ||||||||
\(220\) | 5.85410 | 0.394683 | ||||||||
\(221\) | 4.23607 | 0.284949 | ||||||||
\(222\) | −7.61803 | −0.511289 | ||||||||
\(223\) | 10.3262 | 0.691496 | 0.345748 | − | 0.938327i | \(-0.387625\pi\) | ||||
0.345748 | + | 0.938327i | \(0.387625\pi\) | |||||||
\(224\) | 0.236068 | 0.0157730 | ||||||||
\(225\) | 1.18034 | 0.0786893 | ||||||||
\(226\) | −17.6180 | −1.17193 | ||||||||
\(227\) | 5.03444 | 0.334148 | 0.167074 | − | 0.985944i | \(-0.446568\pi\) | ||||
0.167074 | + | 0.985944i | \(0.446568\pi\) | |||||||
\(228\) | −3.23607 | −0.214314 | ||||||||
\(229\) | 2.70820 | 0.178963 | 0.0894816 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894816 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(230\) | 5.20163 | 0.342985 | ||||||||
\(231\) | 1.61803 | 0.106459 | ||||||||
\(232\) | −5.85410 | −0.384341 | ||||||||
\(233\) | −0.236068 | −0.0154653 | −0.00773266 | − | 0.999970i | \(-0.502461\pi\) | ||||
−0.00773266 | + | 0.999970i | \(0.502461\pi\) | |||||||
\(234\) | 0.381966 | 0.0249699 | ||||||||
\(235\) | 0.201626 | 0.0131526 | ||||||||
\(236\) | 13.5623 | 0.882831 | ||||||||
\(237\) | −17.4721 | −1.13494 | ||||||||
\(238\) | −1.00000 | −0.0648204 | ||||||||
\(239\) | 14.2705 | 0.923083 | 0.461541 | − | 0.887119i | \(-0.347297\pi\) | ||||
0.461541 | + | 0.887119i | \(0.347297\pi\) | |||||||
\(240\) | 2.23607 | 0.144338 | ||||||||
\(241\) | 8.70820 | 0.560945 | 0.280472 | − | 0.959862i | \(-0.409509\pi\) | ||||
0.280472 | + | 0.959862i | \(0.409509\pi\) | |||||||
\(242\) | 6.94427 | 0.446395 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 3.47214 | 0.222281 | ||||||||
\(245\) | 9.59675 | 0.613114 | ||||||||
\(246\) | 9.23607 | 0.588870 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | −1.47214 | −0.0934807 | ||||||||
\(249\) | 1.23607 | 0.0783326 | ||||||||
\(250\) | 11.1803 | 0.707107 | ||||||||
\(251\) | 12.9098 | 0.814861 | 0.407431 | − | 0.913236i | \(-0.366425\pi\) | ||||
0.407431 | + | 0.913236i | \(0.366425\pi\) | |||||||
\(252\) | −0.0901699 | −0.00568017 | ||||||||
\(253\) | 15.9443 | 1.00241 | ||||||||
\(254\) | −3.79837 | −0.238331 | ||||||||
\(255\) | −9.47214 | −0.593168 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.47214 | 0.216586 | 0.108293 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108293 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(258\) | 3.61803 | 0.225249 | ||||||||
\(259\) | 1.11146 | 0.0690625 | ||||||||
\(260\) | 1.38197 | 0.0857059 | ||||||||
\(261\) | 2.23607 | 0.138409 | ||||||||
\(262\) | 7.23607 | 0.447046 | ||||||||
\(263\) | −10.2705 | −0.633307 | −0.316653 | − | 0.948541i | \(-0.602559\pi\) | ||||
−0.316653 | + | 0.948541i | \(0.602559\pi\) | |||||||
\(264\) | 6.85410 | 0.421841 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.472136 | 0.0289485 | ||||||||
\(267\) | −23.9443 | −1.46537 | ||||||||
\(268\) | 6.23607 | 0.380928 | ||||||||
\(269\) | 1.00000 | 0.0609711 | ||||||||
\(270\) | −7.56231 | −0.460227 | ||||||||
\(271\) | −16.1246 | −0.979500 | −0.489750 | − | 0.871863i | \(-0.662912\pi\) | ||||
−0.489750 | + | 0.871863i | \(0.662912\pi\) | |||||||
\(272\) | −4.23607 | −0.256849 | ||||||||
\(273\) | 0.381966 | 0.0231176 | ||||||||
\(274\) | −13.3820 | −0.808434 | ||||||||
\(275\) | 13.0902 | 0.789367 | ||||||||
\(276\) | 6.09017 | 0.366585 | ||||||||
\(277\) | −23.6180 | −1.41907 | −0.709535 | − | 0.704670i | \(-0.751095\pi\) | ||||
−0.709535 | + | 0.704670i | \(0.751095\pi\) | |||||||
\(278\) | −9.56231 | −0.573509 | ||||||||
\(279\) | 0.562306 | 0.0336644 | ||||||||
\(280\) | −0.326238 | −0.0194964 | ||||||||
\(281\) | −6.81966 | −0.406827 | −0.203413 | − | 0.979093i | \(-0.565204\pi\) | ||||
−0.203413 | + | 0.979093i | \(0.565204\pi\) | |||||||
\(282\) | 0.236068 | 0.0140576 | ||||||||
\(283\) | 10.2361 | 0.608471 | 0.304236 | − | 0.952597i | \(-0.401599\pi\) | ||||
0.304236 | + | 0.952597i | \(0.401599\pi\) | |||||||
\(284\) | −3.70820 | −0.220041 | ||||||||
\(285\) | 4.47214 | 0.264906 | ||||||||
\(286\) | 4.23607 | 0.250484 | ||||||||
\(287\) | −1.34752 | −0.0795418 | ||||||||
\(288\) | −0.381966 | −0.0225076 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | 8.09017 | 0.475071 | ||||||||
\(291\) | 30.1803 | 1.76920 | ||||||||
\(292\) | 2.70820 | 0.158486 | ||||||||
\(293\) | 16.4721 | 0.962312 | 0.481156 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481156 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(294\) | 11.2361 | 0.655301 | ||||||||
\(295\) | −18.7426 | −1.09124 | ||||||||
\(296\) | 4.70820 | 0.273659 | ||||||||
\(297\) | −23.1803 | −1.34506 | ||||||||
\(298\) | −15.3262 | −0.887825 | ||||||||
\(299\) | 3.76393 | 0.217674 | ||||||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | −0.527864 | −0.0304256 | ||||||||
\(302\) | 7.94427 | 0.457141 | ||||||||
\(303\) | −9.85410 | −0.566103 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −4.79837 | −0.274754 | ||||||||
\(306\) | 1.61803 | 0.0924968 | ||||||||
\(307\) | −8.12461 | −0.463696 | −0.231848 | − | 0.972752i | \(-0.574477\pi\) | ||||
−0.231848 | + | 0.972752i | \(0.574477\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | −6.70820 | −0.381616 | ||||||||
\(310\) | 2.03444 | 0.115549 | ||||||||
\(311\) | −12.7639 | −0.723776 | −0.361888 | − | 0.932222i | \(-0.617868\pi\) | ||||
−0.361888 | + | 0.932222i | \(0.617868\pi\) | |||||||
\(312\) | 1.61803 | 0.0916031 | ||||||||
\(313\) | 19.8541 | 1.12222 | 0.561110 | − | 0.827741i | \(-0.310374\pi\) | ||||
0.561110 | + | 0.827741i | \(0.310374\pi\) | |||||||
\(314\) | −8.65248 | −0.488287 | ||||||||
\(315\) | 0.124612 | 0.00702108 | ||||||||
\(316\) | 10.7984 | 0.607456 | ||||||||
\(317\) | −25.7639 | −1.44705 | −0.723523 | − | 0.690300i | \(-0.757479\pi\) | ||||
−0.723523 | + | 0.690300i | \(0.757479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.7984 | 1.38844 | ||||||||
\(320\) | −1.38197 | −0.0772542 | ||||||||
\(321\) | 12.5623 | 0.701160 | ||||||||
\(322\) | −0.888544 | −0.0495166 | ||||||||
\(323\) | −8.47214 | −0.471402 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | 3.09017 | 0.171412 | ||||||||
\(326\) | 1.67376 | 0.0927011 | ||||||||
\(327\) | −14.0902 | −0.779188 | ||||||||
\(328\) | −5.70820 | −0.315183 | ||||||||
\(329\) | −0.0344419 | −0.00189884 | ||||||||
\(330\) | −9.47214 | −0.521424 | ||||||||
\(331\) | 23.1803 | 1.27411 | 0.637053 | − | 0.770820i | \(-0.280153\pi\) | ||||
0.637053 | + | 0.770820i | \(0.280153\pi\) | |||||||
\(332\) | −0.763932 | −0.0419262 | ||||||||
\(333\) | −1.79837 | −0.0985503 | ||||||||
\(334\) | 1.38197 | 0.0756178 | ||||||||
\(335\) | −8.61803 | −0.470853 | ||||||||
\(336\) | −0.381966 | −0.0208380 | ||||||||
\(337\) | 18.9787 | 1.03384 | 0.516918 | − | 0.856035i | \(-0.327079\pi\) | ||||
0.516918 | + | 0.856035i | \(0.327079\pi\) | |||||||
\(338\) | −12.0000 | −0.652714 | ||||||||
\(339\) | 28.5066 | 1.54826 | ||||||||
\(340\) | 5.85410 | 0.317483 | ||||||||
\(341\) | 6.23607 | 0.337702 | ||||||||
\(342\) | −0.763932 | −0.0413087 | ||||||||
\(343\) | −3.29180 | −0.177740 | ||||||||
\(344\) | −2.23607 | −0.120561 | ||||||||
\(345\) | −8.41641 | −0.453124 | ||||||||
\(346\) | 1.47214 | 0.0791425 | ||||||||
\(347\) | −31.3607 | −1.68353 | −0.841765 | − | 0.539845i | \(-0.818483\pi\) | ||||
−0.841765 | + | 0.539845i | \(0.818483\pi\) | |||||||
\(348\) | 9.47214 | 0.507760 | ||||||||
\(349\) | −12.2705 | −0.656825 | −0.328413 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328413 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(350\) | −0.729490 | −0.0389929 | ||||||||
\(351\) | −5.47214 | −0.292081 | ||||||||
\(352\) | −4.23607 | −0.225783 | ||||||||
\(353\) | −3.14590 | −0.167439 | −0.0837196 | − | 0.996489i | \(-0.526680\pi\) | ||||
−0.0837196 | + | 0.996489i | \(0.526680\pi\) | |||||||
\(354\) | −21.9443 | −1.16632 | ||||||||
\(355\) | 5.12461 | 0.271986 | ||||||||
\(356\) | 14.7984 | 0.784312 | ||||||||
\(357\) | 1.61803 | 0.0856354 | ||||||||
\(358\) | 5.29180 | 0.279680 | ||||||||
\(359\) | 0.944272 | 0.0498368 | 0.0249184 | − | 0.999689i | \(-0.492067\pi\) | ||||
0.0249184 | + | 0.999689i | \(0.492067\pi\) | |||||||
\(360\) | 0.527864 | 0.0278209 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −7.41641 | −0.389798 | ||||||||
\(363\) | −11.2361 | −0.589741 | ||||||||
\(364\) | −0.236068 | −0.0123733 | ||||||||
\(365\) | −3.74265 | −0.195899 | ||||||||
\(366\) | −5.61803 | −0.293659 | ||||||||
\(367\) | −33.7984 | −1.76426 | −0.882130 | − | 0.471005i | \(-0.843891\pi\) | ||||
−0.882130 | + | 0.471005i | \(0.843891\pi\) | |||||||
\(368\) | −3.76393 | −0.196209 | ||||||||
\(369\) | 2.18034 | 0.113504 | ||||||||
\(370\) | −6.50658 | −0.338261 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.38197 | 0.123499 | ||||||||
\(373\) | −10.9443 | −0.566673 | −0.283336 | − | 0.959021i | \(-0.591441\pi\) | ||||
−0.283336 | + | 0.959021i | \(0.591441\pi\) | |||||||
\(374\) | 17.9443 | 0.927876 | ||||||||
\(375\) | −18.0902 | −0.934172 | ||||||||
\(376\) | −0.145898 | −0.00752412 | ||||||||
\(377\) | 5.85410 | 0.301502 | ||||||||
\(378\) | 1.29180 | 0.0664428 | ||||||||
\(379\) | 12.8541 | 0.660271 | 0.330135 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330135 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(380\) | −2.76393 | −0.141787 | ||||||||
\(381\) | 6.14590 | 0.314864 | ||||||||
\(382\) | −22.9443 | −1.17393 | ||||||||
\(383\) | −19.6180 | −1.00243 | −0.501217 | − | 0.865321i | \(-0.667114\pi\) | ||||
−0.501217 | + | 0.865321i | \(0.667114\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | 1.38197 | 0.0704315 | ||||||||
\(386\) | −3.76393 | −0.191579 | ||||||||
\(387\) | 0.854102 | 0.0434164 | ||||||||
\(388\) | −18.6525 | −0.946936 | ||||||||
\(389\) | 11.0557 | 0.560548 | 0.280274 | − | 0.959920i | \(-0.409575\pi\) | ||||
0.280274 | + | 0.959920i | \(0.409575\pi\) | |||||||
\(390\) | −2.23607 | −0.113228 | ||||||||
\(391\) | 15.9443 | 0.806336 | ||||||||
\(392\) | −6.94427 | −0.350739 | ||||||||
\(393\) | −11.7082 | −0.590601 | ||||||||
\(394\) | −24.6180 | −1.24024 | ||||||||
\(395\) | −14.9230 | −0.750857 | ||||||||
\(396\) | 1.61803 | 0.0813093 | ||||||||
\(397\) | −0.729490 | −0.0366121 | −0.0183060 | − | 0.999832i | \(-0.505827\pi\) | ||||
−0.0183060 | + | 0.999832i | \(0.505827\pi\) | |||||||
\(398\) | −7.61803 | −0.381858 | ||||||||
\(399\) | −0.763932 | −0.0382444 | ||||||||
\(400\) | −3.09017 | −0.154508 | ||||||||
\(401\) | 29.2705 | 1.46170 | 0.730850 | − | 0.682538i | \(-0.239124\pi\) | ||||
0.730850 | + | 0.682538i | \(0.239124\pi\) | |||||||
\(402\) | −10.0902 | −0.503252 | ||||||||
\(403\) | 1.47214 | 0.0733323 | ||||||||
\(404\) | 6.09017 | 0.302997 | ||||||||
\(405\) | 10.6525 | 0.529326 | ||||||||
\(406\) | −1.38197 | −0.0685858 | ||||||||
\(407\) | −19.9443 | −0.988601 | ||||||||
\(408\) | 6.85410 | 0.339329 | ||||||||
\(409\) | 19.6525 | 0.971752 | 0.485876 | − | 0.874028i | \(-0.338501\pi\) | ||||
0.485876 | + | 0.874028i | \(0.338501\pi\) | |||||||
\(410\) | 7.88854 | 0.389587 | ||||||||
\(411\) | 21.6525 | 1.06804 | ||||||||
\(412\) | 4.14590 | 0.204254 | ||||||||
\(413\) | 3.20163 | 0.157542 | ||||||||
\(414\) | 1.43769 | 0.0706588 | ||||||||
\(415\) | 1.05573 | 0.0518237 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 15.4721 | 0.757674 | ||||||||
\(418\) | −8.47214 | −0.414386 | ||||||||
\(419\) | −37.5623 | −1.83504 | −0.917519 | − | 0.397691i | \(-0.869812\pi\) | ||||
−0.917519 | + | 0.397691i | \(0.869812\pi\) | |||||||
\(420\) | 0.527864 | 0.0257571 | ||||||||
\(421\) | 2.52786 | 0.123201 | 0.0616003 | − | 0.998101i | \(-0.480380\pi\) | ||||
0.0616003 | + | 0.998101i | \(0.480380\pi\) | |||||||
\(422\) | −5.85410 | −0.284973 | ||||||||
\(423\) | 0.0557281 | 0.00270959 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0902 | 0.634967 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0.819660 | 0.0396661 | ||||||||
\(428\) | −7.76393 | −0.375284 | ||||||||
\(429\) | −6.85410 | −0.330919 | ||||||||
\(430\) | 3.09017 | 0.149021 | ||||||||
\(431\) | −6.52786 | −0.314436 | −0.157218 | − | 0.987564i | \(-0.550253\pi\) | ||||
−0.157218 | + | 0.987564i | \(0.550253\pi\) | |||||||
\(432\) | 5.47214 | 0.263278 | ||||||||
\(433\) | 36.7984 | 1.76842 | 0.884208 | − | 0.467092i | \(-0.154698\pi\) | ||||
0.884208 | + | 0.467092i | \(0.154698\pi\) | |||||||
\(434\) | −0.347524 | −0.0166817 | ||||||||
\(435\) | −13.0902 | −0.627626 | ||||||||
\(436\) | 8.70820 | 0.417047 | ||||||||
\(437\) | −7.52786 | −0.360107 | ||||||||
\(438\) | −4.38197 | −0.209378 | ||||||||
\(439\) | 25.8541 | 1.23395 | 0.616974 | − | 0.786983i | \(-0.288358\pi\) | ||||
0.616974 | + | 0.786983i | \(0.288358\pi\) | |||||||
\(440\) | 5.85410 | 0.279083 | ||||||||
\(441\) | 2.65248 | 0.126308 | ||||||||
\(442\) | 4.23607 | 0.201489 | ||||||||
\(443\) | 6.58359 | 0.312796 | 0.156398 | − | 0.987694i | \(-0.450012\pi\) | ||||
0.156398 | + | 0.987694i | \(0.450012\pi\) | |||||||
\(444\) | −7.61803 | −0.361536 | ||||||||
\(445\) | −20.4508 | −0.969463 | ||||||||
\(446\) | 10.3262 | 0.488962 | ||||||||
\(447\) | 24.7984 | 1.17292 | ||||||||
\(448\) | 0.236068 | 0.0111532 | ||||||||
\(449\) | 14.0902 | 0.664956 | 0.332478 | − | 0.943111i | \(-0.392115\pi\) | ||||
0.332478 | + | 0.943111i | \(0.392115\pi\) | |||||||
\(450\) | 1.18034 | 0.0556418 | ||||||||
\(451\) | 24.1803 | 1.13861 | ||||||||
\(452\) | −17.6180 | −0.828683 | ||||||||
\(453\) | −12.8541 | −0.603938 | ||||||||
\(454\) | 5.03444 | 0.236278 | ||||||||
\(455\) | 0.326238 | 0.0152943 | ||||||||
\(456\) | −3.23607 | −0.151543 | ||||||||
\(457\) | 2.20163 | 0.102988 | 0.0514939 | − | 0.998673i | \(-0.483602\pi\) | ||||
0.0514939 | + | 0.998673i | \(0.483602\pi\) | |||||||
\(458\) | 2.70820 | 0.126546 | ||||||||
\(459\) | −23.1803 | −1.08197 | ||||||||
\(460\) | 5.20163 | 0.242527 | ||||||||
\(461\) | −19.1246 | −0.890722 | −0.445361 | − | 0.895351i | \(-0.646925\pi\) | ||||
−0.445361 | + | 0.895351i | \(0.646925\pi\) | |||||||
\(462\) | 1.61803 | 0.0752778 | ||||||||
\(463\) | −8.90983 | −0.414075 | −0.207037 | − | 0.978333i | \(-0.566382\pi\) | ||||
−0.207037 | + | 0.978333i | \(0.566382\pi\) | |||||||
\(464\) | −5.85410 | −0.271770 | ||||||||
\(465\) | −3.29180 | −0.152653 | ||||||||
\(466\) | −0.236068 | −0.0109356 | ||||||||
\(467\) | −33.4164 | −1.54633 | −0.773163 | − | 0.634207i | \(-0.781327\pi\) | ||||
−0.773163 | + | 0.634207i | \(0.781327\pi\) | |||||||
\(468\) | 0.381966 | 0.0176564 | ||||||||
\(469\) | 1.47214 | 0.0679769 | ||||||||
\(470\) | 0.201626 | 0.00930032 | ||||||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | 13.5623 | 0.624256 | ||||||||
\(473\) | 9.47214 | 0.435529 | ||||||||
\(474\) | −17.4721 | −0.802522 | ||||||||
\(475\) | −6.18034 | −0.283573 | ||||||||
\(476\) | −1.00000 | −0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.2705 | 0.652718 | ||||||||
\(479\) | 12.5967 | 0.575560 | 0.287780 | − | 0.957697i | \(-0.407083\pi\) | ||||
0.287780 | + | 0.957697i | \(0.407083\pi\) | |||||||
\(480\) | 2.23607 | 0.102062 | ||||||||
\(481\) | −4.70820 | −0.214676 | ||||||||
\(482\) | 8.70820 | 0.396648 | ||||||||
\(483\) | 1.43769 | 0.0654173 | ||||||||
\(484\) | 6.94427 | 0.315649 | ||||||||
\(485\) | 25.7771 | 1.17048 | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 38.8328 | 1.75968 | 0.879841 | − | 0.475267i | \(-0.157649\pi\) | ||||
0.879841 | + | 0.475267i | \(0.157649\pi\) | |||||||
\(488\) | 3.47214 | 0.157176 | ||||||||
\(489\) | −2.70820 | −0.122469 | ||||||||
\(490\) | 9.59675 | 0.433537 | ||||||||
\(491\) | 11.2361 | 0.507077 | 0.253538 | − | 0.967325i | \(-0.418406\pi\) | ||||
0.253538 | + | 0.967325i | \(0.418406\pi\) | |||||||
\(492\) | 9.23607 | 0.416394 | ||||||||
\(493\) | 24.7984 | 1.11686 | ||||||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | −2.23607 | −0.100504 | ||||||||
\(496\) | −1.47214 | −0.0661009 | ||||||||
\(497\) | −0.875388 | −0.0392665 | ||||||||
\(498\) | 1.23607 | 0.0553895 | ||||||||
\(499\) | −5.94427 | −0.266102 | −0.133051 | − | 0.991109i | \(-0.542477\pi\) | ||||
−0.133051 | + | 0.991109i | \(0.542477\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | −2.23607 | −0.0999001 | ||||||||
\(502\) | 12.9098 | 0.576194 | ||||||||
\(503\) | −10.3607 | −0.461960 | −0.230980 | − | 0.972959i | \(-0.574193\pi\) | ||||
−0.230980 | + | 0.972959i | \(0.574193\pi\) | |||||||
\(504\) | −0.0901699 | −0.00401649 | ||||||||
\(505\) | −8.41641 | −0.374525 | ||||||||
\(506\) | 15.9443 | 0.708809 | ||||||||
\(507\) | 19.4164 | 0.862313 | ||||||||
\(508\) | −3.79837 | −0.168526 | ||||||||
\(509\) | 42.3262 | 1.87608 | 0.938039 | − | 0.346530i | \(-0.112640\pi\) | ||||
0.938039 | + | 0.346530i | \(0.112640\pi\) | |||||||
\(510\) | −9.47214 | −0.419433 | ||||||||
\(511\) | 0.639320 | 0.0282819 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.9443 | 0.483201 | ||||||||
\(514\) | 3.47214 | 0.153149 | ||||||||
\(515\) | −5.72949 | −0.252472 | ||||||||
\(516\) | 3.61803 | 0.159275 | ||||||||
\(517\) | 0.618034 | 0.0271811 | ||||||||
\(518\) | 1.11146 | 0.0488346 | ||||||||
\(519\) | −2.38197 | −0.104557 | ||||||||
\(520\) | 1.38197 | 0.0606032 | ||||||||
\(521\) | 3.58359 | 0.157000 | 0.0785000 | − | 0.996914i | \(-0.474987\pi\) | ||||
0.0785000 | + | 0.996914i | \(0.474987\pi\) | |||||||
\(522\) | 2.23607 | 0.0978700 | ||||||||
\(523\) | 25.3820 | 1.10988 | 0.554938 | − | 0.831892i | \(-0.312742\pi\) | ||||
0.554938 | + | 0.831892i | \(0.312742\pi\) | |||||||
\(524\) | 7.23607 | 0.316109 | ||||||||
\(525\) | 1.18034 | 0.0515143 | ||||||||
\(526\) | −10.2705 | −0.447816 | ||||||||
\(527\) | 6.23607 | 0.271647 | ||||||||
\(528\) | 6.85410 | 0.298287 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.18034 | −0.224808 | ||||||||
\(532\) | 0.472136 | 0.0204697 | ||||||||
\(533\) | 5.70820 | 0.247250 | ||||||||
\(534\) | −23.9443 | −1.03617 | ||||||||
\(535\) | 10.7295 | 0.463876 | ||||||||
\(536\) | 6.23607 | 0.269357 | ||||||||
\(537\) | −8.56231 | −0.369491 | ||||||||
\(538\) | 1.00000 | 0.0431131 | ||||||||
\(539\) | 29.4164 | 1.26705 | ||||||||
\(540\) | −7.56231 | −0.325430 | ||||||||
\(541\) | 11.5279 | 0.495622 | 0.247811 | − | 0.968808i | \(-0.420289\pi\) | ||||
0.247811 | + | 0.968808i | \(0.420289\pi\) | |||||||
\(542\) | −16.1246 | −0.692611 | ||||||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | −4.23607 | −0.181620 | ||||||||
\(545\) | −12.0344 | −0.515499 | ||||||||
\(546\) | 0.381966 | 0.0163466 | ||||||||
\(547\) | 27.7984 | 1.18857 | 0.594286 | − | 0.804254i | \(-0.297435\pi\) | ||||
0.594286 | + | 0.804254i | \(0.297435\pi\) | |||||||
\(548\) | −13.3820 | −0.571649 | ||||||||
\(549\) | −1.32624 | −0.0566025 | ||||||||
\(550\) | 13.0902 | 0.558167 | ||||||||
\(551\) | −11.7082 | −0.498786 | ||||||||
\(552\) | 6.09017 | 0.259215 | ||||||||
\(553\) | 2.54915 | 0.108401 | ||||||||
\(554\) | −23.6180 | −1.00343 | ||||||||
\(555\) | 10.5279 | 0.446883 | ||||||||
\(556\) | −9.56231 | −0.405532 | ||||||||
\(557\) | 41.7082 | 1.76723 | 0.883617 | − | 0.468211i | \(-0.155101\pi\) | ||||
0.883617 | + | 0.468211i | \(0.155101\pi\) | |||||||
\(558\) | 0.562306 | 0.0238043 | ||||||||
\(559\) | 2.23607 | 0.0945756 | ||||||||
\(560\) | −0.326238 | −0.0137861 | ||||||||
\(561\) | −29.0344 | −1.22584 | ||||||||
\(562\) | −6.81966 | −0.287670 | ||||||||
\(563\) | 20.7082 | 0.872747 | 0.436373 | − | 0.899766i | \(-0.356263\pi\) | ||||
0.436373 | + | 0.899766i | \(0.356263\pi\) | |||||||
\(564\) | 0.236068 | 0.00994026 | ||||||||
\(565\) | 24.3475 | 1.02431 | ||||||||
\(566\) | 10.2361 | 0.430254 | ||||||||
\(567\) | −1.81966 | −0.0764185 | ||||||||
\(568\) | −3.70820 | −0.155593 | ||||||||
\(569\) | −17.0902 | −0.716457 | −0.358229 | − | 0.933634i | \(-0.616619\pi\) | ||||
−0.358229 | + | 0.933634i | \(0.616619\pi\) | |||||||
\(570\) | 4.47214 | 0.187317 | ||||||||
\(571\) | 10.0000 | 0.418487 | 0.209243 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(572\) | 4.23607 | 0.177119 | ||||||||
\(573\) | 37.1246 | 1.55090 | ||||||||
\(574\) | −1.34752 | −0.0562446 | ||||||||
\(575\) | 11.6312 | 0.485054 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | 3.00000 | 0.124892 | 0.0624458 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | 0.944272 | 0.0392765 | ||||||||
\(579\) | 6.09017 | 0.253099 | ||||||||
\(580\) | 8.09017 | 0.335926 | ||||||||
\(581\) | −0.180340 | −0.00748176 | ||||||||
\(582\) | 30.1803 | 1.25102 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.70820 | 0.112066 | ||||||||
\(585\) | −0.527864 | −0.0218245 | ||||||||
\(586\) | 16.4721 | 0.680458 | ||||||||
\(587\) | −26.3262 | −1.08660 | −0.543300 | − | 0.839539i | \(-0.682825\pi\) | ||||
−0.543300 | + | 0.839539i | \(0.682825\pi\) | |||||||
\(588\) | 11.2361 | 0.463368 | ||||||||
\(589\) | −2.94427 | −0.121317 | ||||||||
\(590\) | −18.7426 | −0.771623 | ||||||||
\(591\) | 39.8328 | 1.63850 | ||||||||
\(592\) | 4.70820 | 0.193506 | ||||||||
\(593\) | −27.4164 | −1.12586 | −0.562928 | − | 0.826506i | \(-0.690325\pi\) | ||||
−0.562928 | + | 0.826506i | \(0.690325\pi\) | |||||||
\(594\) | −23.1803 | −0.951101 | ||||||||
\(595\) | 1.38197 | 0.0566551 | ||||||||
\(596\) | −15.3262 | −0.627787 | ||||||||
\(597\) | 12.3262 | 0.504479 | ||||||||
\(598\) | 3.76393 | 0.153919 | ||||||||
\(599\) | 33.5967 | 1.37273 | 0.686363 | − | 0.727259i | \(-0.259206\pi\) | ||||
0.686363 | + | 0.727259i | \(0.259206\pi\) | |||||||
\(600\) | 5.00000 | 0.204124 | ||||||||
\(601\) | 34.6869 | 1.41491 | 0.707454 | − | 0.706759i | \(-0.249843\pi\) | ||||
0.707454 | + | 0.706759i | \(0.249843\pi\) | |||||||
\(602\) | −0.527864 | −0.0215141 | ||||||||
\(603\) | −2.38197 | −0.0970012 | ||||||||
\(604\) | 7.94427 | 0.323248 | ||||||||
\(605\) | −9.59675 | −0.390163 | ||||||||
\(606\) | −9.85410 | −0.400296 | ||||||||
\(607\) | −48.5755 | −1.97162 | −0.985809 | − | 0.167873i | \(-0.946310\pi\) | ||||
−0.985809 | + | 0.167873i | \(0.946310\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 2.23607 | 0.0906100 | ||||||||
\(610\) | −4.79837 | −0.194280 | ||||||||
\(611\) | 0.145898 | 0.00590240 | ||||||||
\(612\) | 1.61803 | 0.0654051 | ||||||||
\(613\) | −35.4721 | −1.43271 | −0.716353 | − | 0.697738i | \(-0.754190\pi\) | ||||
−0.716353 | + | 0.697738i | \(0.754190\pi\) | |||||||
\(614\) | −8.12461 | −0.327883 | ||||||||
\(615\) | −12.7639 | −0.514691 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | −33.1591 | −1.33493 | −0.667467 | − | 0.744640i | \(-0.732621\pi\) | ||||
−0.667467 | + | 0.744640i | \(0.732621\pi\) | |||||||
\(618\) | −6.70820 | −0.269844 | ||||||||
\(619\) | 12.8328 | 0.515794 | 0.257897 | − | 0.966172i | \(-0.416970\pi\) | ||||
0.257897 | + | 0.966172i | \(0.416970\pi\) | |||||||
\(620\) | 2.03444 | 0.0817052 | ||||||||
\(621\) | −20.5967 | −0.826519 | ||||||||
\(622\) | −12.7639 | −0.511787 | ||||||||
\(623\) | 3.49342 | 0.139961 | ||||||||
\(624\) | 1.61803 | 0.0647732 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.8541 | 0.793530 | ||||||||
\(627\) | 13.7082 | 0.547453 | ||||||||
\(628\) | −8.65248 | −0.345271 | ||||||||
\(629\) | −19.9443 | −0.795230 | ||||||||
\(630\) | 0.124612 | 0.00496465 | ||||||||
\(631\) | 29.7984 | 1.18625 | 0.593127 | − | 0.805109i | \(-0.297893\pi\) | ||||
0.593127 | + | 0.805109i | \(0.297893\pi\) | |||||||
\(632\) | 10.7984 | 0.429536 | ||||||||
\(633\) | 9.47214 | 0.376484 | ||||||||
\(634\) | −25.7639 | −1.02322 | ||||||||
\(635\) | 5.24922 | 0.208309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.94427 | 0.275142 | ||||||||
\(638\) | 24.7984 | 0.981777 | ||||||||
\(639\) | 1.41641 | 0.0560322 | ||||||||
\(640\) | −1.38197 | −0.0546270 | ||||||||
\(641\) | −19.1803 | −0.757578 | −0.378789 | − | 0.925483i | \(-0.623659\pi\) | ||||
−0.378789 | + | 0.925483i | \(0.623659\pi\) | |||||||
\(642\) | 12.5623 | 0.495795 | ||||||||
\(643\) | −10.8541 | −0.428044 | −0.214022 | − | 0.976829i | \(-0.568656\pi\) | ||||
−0.214022 | + | 0.976829i | \(0.568656\pi\) | |||||||
\(644\) | −0.888544 | −0.0350135 | ||||||||
\(645\) | −5.00000 | −0.196875 | ||||||||
\(646\) | −8.47214 | −0.333332 | ||||||||
\(647\) | −25.1803 | −0.989941 | −0.494971 | − | 0.868910i | \(-0.664821\pi\) | ||||
−0.494971 | + | 0.868910i | \(0.664821\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | −57.4508 | −2.25514 | ||||||||
\(650\) | 3.09017 | 0.121206 | ||||||||
\(651\) | 0.562306 | 0.0220385 | ||||||||
\(652\) | 1.67376 | 0.0655496 | ||||||||
\(653\) | 39.5410 | 1.54736 | 0.773680 | − | 0.633577i | \(-0.218414\pi\) | ||||
0.773680 | + | 0.633577i | \(0.218414\pi\) | |||||||
\(654\) | −14.0902 | −0.550969 | ||||||||
\(655\) | −10.0000 | −0.390732 | ||||||||
\(656\) | −5.70820 | −0.222868 | ||||||||
\(657\) | −1.03444 | −0.0403574 | ||||||||
\(658\) | −0.0344419 | −0.00134268 | ||||||||
\(659\) | −15.6738 | −0.610563 | −0.305282 | − | 0.952262i | \(-0.598751\pi\) | ||||
−0.305282 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(660\) | −9.47214 | −0.368702 | ||||||||
\(661\) | −14.1459 | −0.550212 | −0.275106 | − | 0.961414i | \(-0.588713\pi\) | ||||
−0.275106 | + | 0.961414i | \(0.588713\pi\) | |||||||
\(662\) | 23.1803 | 0.900929 | ||||||||
\(663\) | −6.85410 | −0.266191 | ||||||||
\(664\) | −0.763932 | −0.0296463 | ||||||||
\(665\) | −0.652476 | −0.0253019 | ||||||||
\(666\) | −1.79837 | −0.0696856 | ||||||||
\(667\) | 22.0344 | 0.853177 | ||||||||
\(668\) | 1.38197 | 0.0534699 | ||||||||
\(669\) | −16.7082 | −0.645976 | ||||||||
\(670\) | −8.61803 | −0.332944 | ||||||||
\(671\) | −14.7082 | −0.567804 | ||||||||
\(672\) | −0.381966 | −0.0147347 | ||||||||
\(673\) | −2.70820 | −0.104394 | −0.0521968 | − | 0.998637i | \(-0.516622\pi\) | ||||
−0.0521968 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(674\) | 18.9787 | 0.731033 | ||||||||
\(675\) | −16.9098 | −0.650860 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −37.5623 | −1.44364 | −0.721818 | − | 0.692083i | \(-0.756693\pi\) | ||||
−0.721818 | + | 0.692083i | \(0.756693\pi\) | |||||||
\(678\) | 28.5066 | 1.09479 | ||||||||
\(679\) | −4.40325 | −0.168981 | ||||||||
\(680\) | 5.85410 | 0.224495 | ||||||||
\(681\) | −8.14590 | −0.312151 | ||||||||
\(682\) | 6.23607 | 0.238791 | ||||||||
\(683\) | −16.7639 | −0.641454 | −0.320727 | − | 0.947172i | \(-0.603927\pi\) | ||||
−0.320727 | + | 0.947172i | \(0.603927\pi\) | |||||||
\(684\) | −0.763932 | −0.0292097 | ||||||||
\(685\) | 18.4934 | 0.706597 | ||||||||
\(686\) | −3.29180 | −0.125681 | ||||||||
\(687\) | −4.38197 | −0.167182 | ||||||||
\(688\) | −2.23607 | −0.0852493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.41641 | −0.320407 | ||||||||
\(691\) | 25.1246 | 0.955785 | 0.477893 | − | 0.878418i | \(-0.341401\pi\) | ||||
0.477893 | + | 0.878418i | \(0.341401\pi\) | |||||||
\(692\) | 1.47214 | 0.0559622 | ||||||||
\(693\) | 0.381966 | 0.0145097 | ||||||||
\(694\) | −31.3607 | −1.19044 | ||||||||
\(695\) | 13.2148 | 0.501265 | ||||||||
\(696\) | 9.47214 | 0.359040 | ||||||||
\(697\) | 24.1803 | 0.915896 | ||||||||
\(698\) | −12.2705 | −0.464446 | ||||||||
\(699\) | 0.381966 | 0.0144473 | ||||||||
\(700\) | −0.729490 | −0.0275721 | ||||||||
\(701\) | 35.9787 | 1.35890 | 0.679449 | − | 0.733723i | \(-0.262219\pi\) | ||||
0.679449 | + | 0.733723i | \(0.262219\pi\) | |||||||
\(702\) | −5.47214 | −0.206532 | ||||||||
\(703\) | 9.41641 | 0.355147 | ||||||||
\(704\) | −4.23607 | −0.159653 | ||||||||
\(705\) | −0.326238 | −0.0122868 | ||||||||
\(706\) | −3.14590 | −0.118397 | ||||||||
\(707\) | 1.43769 | 0.0540701 | ||||||||
\(708\) | −21.9443 | −0.824716 | ||||||||
\(709\) | −20.0557 | −0.753209 | −0.376604 | − | 0.926374i | \(-0.622908\pi\) | ||||
−0.376604 | + | 0.926374i | \(0.622908\pi\) | |||||||
\(710\) | 5.12461 | 0.192323 | ||||||||
\(711\) | −4.12461 | −0.154685 | ||||||||
\(712\) | 14.7984 | 0.554593 | ||||||||
\(713\) | 5.54102 | 0.207513 | ||||||||
\(714\) | 1.61803 | 0.0605534 | ||||||||
\(715\) | −5.85410 | −0.218931 | ||||||||
\(716\) | 5.29180 | 0.197764 | ||||||||
\(717\) | −23.0902 | −0.862318 | ||||||||
\(718\) | 0.944272 | 0.0352399 | ||||||||
\(719\) | 19.8197 | 0.739149 | 0.369574 | − | 0.929201i | \(-0.379504\pi\) | ||||
0.369574 | + | 0.929201i | \(0.379504\pi\) | |||||||
\(720\) | 0.527864 | 0.0196723 | ||||||||
\(721\) | 0.978714 | 0.0364492 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −14.0902 | −0.524019 | ||||||||
\(724\) | −7.41641 | −0.275629 | ||||||||
\(725\) | 18.0902 | 0.671852 | ||||||||
\(726\) | −11.2361 | −0.417010 | ||||||||
\(727\) | −31.2918 | −1.16055 | −0.580274 | − | 0.814421i | \(-0.697055\pi\) | ||||
−0.580274 | + | 0.814421i | \(0.697055\pi\) | |||||||
\(728\) | −0.236068 | −0.00874926 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | −3.74265 | −0.138522 | ||||||||
\(731\) | 9.47214 | 0.350340 | ||||||||
\(732\) | −5.61803 | −0.207649 | ||||||||
\(733\) | 11.3607 | 0.419616 | 0.209808 | − | 0.977743i | \(-0.432716\pi\) | ||||
0.209808 | + | 0.977743i | \(0.432716\pi\) | |||||||
\(734\) | −33.7984 | −1.24752 | ||||||||
\(735\) | −15.5279 | −0.572754 | ||||||||
\(736\) | −3.76393 | −0.138740 | ||||||||
\(737\) | −26.4164 | −0.973061 | ||||||||
\(738\) | 2.18034 | 0.0802594 | ||||||||
\(739\) | 5.96556 | 0.219447 | 0.109723 | − | 0.993962i | \(-0.465004\pi\) | ||||
0.109723 | + | 0.993962i | \(0.465004\pi\) | |||||||
\(740\) | −6.50658 | −0.239187 | ||||||||
\(741\) | 3.23607 | 0.118880 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.7984 | −1.23994 | −0.619971 | − | 0.784625i | \(-0.712856\pi\) | ||||
−0.619971 | + | 0.784625i | \(0.712856\pi\) | |||||||
\(744\) | 2.38197 | 0.0873271 | ||||||||
\(745\) | 21.1803 | 0.775988 | ||||||||
\(746\) | −10.9443 | −0.400698 | ||||||||
\(747\) | 0.291796 | 0.0106763 | ||||||||
\(748\) | 17.9443 | 0.656108 | ||||||||
\(749\) | −1.83282 | −0.0669696 | ||||||||
\(750\) | −18.0902 | −0.660560 | ||||||||
\(751\) | −42.8673 | −1.56425 | −0.782124 | − | 0.623123i | \(-0.785864\pi\) | ||||
−0.782124 | + | 0.623123i | \(0.785864\pi\) | |||||||
\(752\) | −0.145898 | −0.00532035 | ||||||||
\(753\) | −20.8885 | −0.761221 | ||||||||
\(754\) | 5.85410 | 0.213194 | ||||||||
\(755\) | −10.9787 | −0.399556 | ||||||||
\(756\) | 1.29180 | 0.0469822 | ||||||||
\(757\) | −21.0557 | −0.765283 | −0.382642 | − | 0.923897i | \(-0.624986\pi\) | ||||
−0.382642 | + | 0.923897i | \(0.624986\pi\) | |||||||
\(758\) | 12.8541 | 0.466882 | ||||||||
\(759\) | −25.7984 | −0.936422 | ||||||||
\(760\) | −2.76393 | −0.100258 | ||||||||
\(761\) | 25.4164 | 0.921344 | 0.460672 | − | 0.887570i | \(-0.347608\pi\) | ||||
0.460672 | + | 0.887570i | \(0.347608\pi\) | |||||||
\(762\) | 6.14590 | 0.222642 | ||||||||
\(763\) | 2.05573 | 0.0744224 | ||||||||
\(764\) | −22.9443 | −0.830095 | ||||||||
\(765\) | −2.23607 | −0.0808452 | ||||||||
\(766\) | −19.6180 | −0.708828 | ||||||||
\(767\) | −13.5623 | −0.489706 | ||||||||
\(768\) | −1.61803 | −0.0583858 | ||||||||
\(769\) | −17.6738 | −0.637332 | −0.318666 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318666 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(770\) | 1.38197 | 0.0498026 | ||||||||
\(771\) | −5.61803 | −0.202329 | ||||||||
\(772\) | −3.76393 | −0.135467 | ||||||||
\(773\) | −1.59675 | −0.0574310 | −0.0287155 | − | 0.999588i | \(-0.509142\pi\) | ||||
−0.0287155 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(774\) | 0.854102 | 0.0307001 | ||||||||
\(775\) | 4.54915 | 0.163410 | ||||||||
\(776\) | −18.6525 | −0.669585 | ||||||||
\(777\) | −1.79837 | −0.0645163 | ||||||||
\(778\) | 11.0557 | 0.396367 | ||||||||
\(779\) | −11.4164 | −0.409035 | ||||||||
\(780\) | −2.23607 | −0.0800641 | ||||||||
\(781\) | 15.7082 | 0.562084 | ||||||||
\(782\) | 15.9443 | 0.570166 | ||||||||
\(783\) | −32.0344 | −1.14482 | ||||||||
\(784\) | −6.94427 | −0.248010 | ||||||||
\(785\) | 11.9574 | 0.426779 | ||||||||
\(786\) | −11.7082 | −0.417618 | ||||||||
\(787\) | −33.6525 | −1.19958 | −0.599791 | − | 0.800157i | \(-0.704749\pi\) | ||||
−0.599791 | + | 0.800157i | \(0.704749\pi\) | |||||||
\(788\) | −24.6180 | −0.876981 | ||||||||
\(789\) | 16.6180 | 0.591618 | ||||||||
\(790\) | −14.9230 | −0.530936 | ||||||||
\(791\) | −4.15905 | −0.147879 | ||||||||
\(792\) | 1.61803 | 0.0574943 | ||||||||
\(793\) | −3.47214 | −0.123299 | ||||||||
\(794\) | −0.729490 | −0.0258886 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.61803 | −0.270014 | ||||||||
\(797\) | 37.7984 | 1.33889 | 0.669444 | − | 0.742863i | \(-0.266533\pi\) | ||||
0.669444 | + | 0.742863i | \(0.266533\pi\) | |||||||
\(798\) | −0.763932 | −0.0270429 | ||||||||
\(799\) | 0.618034 | 0.0218645 | ||||||||
\(800\) | −3.09017 | −0.109254 | ||||||||
\(801\) | −5.65248 | −0.199720 | ||||||||
\(802\) | 29.2705 | 1.03358 | ||||||||
\(803\) | −11.4721 | −0.404843 | ||||||||
\(804\) | −10.0902 | −0.355853 | ||||||||
\(805\) | 1.22794 | 0.0432791 | ||||||||
\(806\) | 1.47214 | 0.0518538 | ||||||||
\(807\) | −1.61803 | −0.0569575 | ||||||||
\(808\) | 6.09017 | 0.214251 | ||||||||
\(809\) | 24.4721 | 0.860394 | 0.430197 | − | 0.902735i | \(-0.358444\pi\) | ||||
0.430197 | + | 0.902735i | \(0.358444\pi\) | |||||||
\(810\) | 10.6525 | 0.374290 | ||||||||
\(811\) | 1.59675 | 0.0560694 | 0.0280347 | − | 0.999607i | \(-0.491075\pi\) | ||||
0.0280347 | + | 0.999607i | \(0.491075\pi\) | |||||||
\(812\) | −1.38197 | −0.0484975 | ||||||||
\(813\) | 26.0902 | 0.915022 | ||||||||
\(814\) | −19.9443 | −0.699046 | ||||||||
\(815\) | −2.31308 | −0.0810237 | ||||||||
\(816\) | 6.85410 | 0.239942 | ||||||||
\(817\) | −4.47214 | −0.156460 | ||||||||
\(818\) | 19.6525 | 0.687133 | ||||||||
\(819\) | 0.0901699 | 0.00315079 | ||||||||
\(820\) | 7.88854 | 0.275480 | ||||||||
\(821\) | −6.36068 | −0.221989 | −0.110995 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110995 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(822\) | 21.6525 | 0.755217 | ||||||||
\(823\) | −15.1115 | −0.526752 | −0.263376 | − | 0.964693i | \(-0.584836\pi\) | ||||
−0.263376 | + | 0.964693i | \(0.584836\pi\) | |||||||
\(824\) | 4.14590 | 0.144429 | ||||||||
\(825\) | −21.1803 | −0.737405 | ||||||||
\(826\) | 3.20163 | 0.111399 | ||||||||
\(827\) | 4.74265 | 0.164918 | 0.0824590 | − | 0.996594i | \(-0.473723\pi\) | ||||
0.0824590 | + | 0.996594i | \(0.473723\pi\) | |||||||
\(828\) | 1.43769 | 0.0499633 | ||||||||
\(829\) | 19.2016 | 0.666900 | 0.333450 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333450 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(830\) | 1.05573 | 0.0366449 | ||||||||
\(831\) | 38.2148 | 1.32566 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 29.4164 | 1.01922 | ||||||||
\(834\) | 15.4721 | 0.535756 | ||||||||
\(835\) | −1.90983 | −0.0660924 | ||||||||
\(836\) | −8.47214 | −0.293015 | ||||||||
\(837\) | −8.05573 | −0.278447 | ||||||||
\(838\) | −37.5623 | −1.29757 | ||||||||
\(839\) | −41.4508 | −1.43104 | −0.715521 | − | 0.698591i | \(-0.753811\pi\) | ||||
−0.715521 | + | 0.698591i | \(0.753811\pi\) | |||||||
\(840\) | 0.527864 | 0.0182130 | ||||||||
\(841\) | 5.27051 | 0.181742 | ||||||||
\(842\) | 2.52786 | 0.0871159 | ||||||||
\(843\) | 11.0344 | 0.380046 | ||||||||
\(844\) | −5.85410 | −0.201506 | ||||||||
\(845\) | 16.5836 | 0.570493 | ||||||||
\(846\) | 0.0557281 | 0.00191597 | ||||||||
\(847\) | 1.63932 | 0.0563277 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.5623 | −0.568417 | ||||||||
\(850\) | 13.0902 | 0.448989 | ||||||||
\(851\) | −17.7214 | −0.607480 | ||||||||
\(852\) | 6.00000 | 0.205557 | ||||||||
\(853\) | −48.8115 | −1.67127 | −0.835637 | − | 0.549281i | \(-0.814902\pi\) | ||||
−0.835637 | + | 0.549281i | \(0.814902\pi\) | |||||||
\(854\) | 0.819660 | 0.0280482 | ||||||||
\(855\) | 1.05573 | 0.0361051 | ||||||||
\(856\) | −7.76393 | −0.265366 | ||||||||
\(857\) | 16.0689 | 0.548903 | 0.274451 | − | 0.961601i | \(-0.411504\pi\) | ||||
0.274451 | + | 0.961601i | \(0.411504\pi\) | |||||||
\(858\) | −6.85410 | −0.233995 | ||||||||
\(859\) | 29.7426 | 1.01481 | 0.507403 | − | 0.861709i | \(-0.330606\pi\) | ||||
0.507403 | + | 0.861709i | \(0.330606\pi\) | |||||||
\(860\) | 3.09017 | 0.105374 | ||||||||
\(861\) | 2.18034 | 0.0743058 | ||||||||
\(862\) | −6.52786 | −0.222340 | ||||||||
\(863\) | 1.67376 | 0.0569755 | 0.0284878 | − | 0.999594i | \(-0.490931\pi\) | ||||
0.0284878 | + | 0.999594i | \(0.490931\pi\) | |||||||
\(864\) | 5.47214 | 0.186166 | ||||||||
\(865\) | −2.03444 | −0.0691731 | ||||||||
\(866\) | 36.7984 | 1.25046 | ||||||||
\(867\) | −1.52786 | −0.0518890 | ||||||||
\(868\) | −0.347524 | −0.0117957 | ||||||||
\(869\) | −45.7426 | −1.55171 | ||||||||
\(870\) | −13.0902 | −0.443798 | ||||||||
\(871\) | −6.23607 | −0.211301 | ||||||||
\(872\) | 8.70820 | 0.294897 | ||||||||
\(873\) | 7.12461 | 0.241132 | ||||||||
\(874\) | −7.52786 | −0.254634 | ||||||||
\(875\) | 2.63932 | 0.0892253 | ||||||||
\(876\) | −4.38197 | −0.148053 | ||||||||
\(877\) | −53.5755 | −1.80911 | −0.904557 | − | 0.426352i | \(-0.859799\pi\) | ||||
−0.904557 | + | 0.426352i | \(0.859799\pi\) | |||||||
\(878\) | 25.8541 | 0.872534 | ||||||||
\(879\) | −26.6525 | −0.898966 | ||||||||
\(880\) | 5.85410 | 0.197342 | ||||||||
\(881\) | −6.49342 | −0.218769 | −0.109384 | − | 0.994000i | \(-0.534888\pi\) | ||||
−0.109384 | + | 0.994000i | \(0.534888\pi\) | |||||||
\(882\) | 2.65248 | 0.0893135 | ||||||||
\(883\) | 48.1935 | 1.62184 | 0.810920 | − | 0.585157i | \(-0.198967\pi\) | ||||
0.810920 | + | 0.585157i | \(0.198967\pi\) | |||||||
\(884\) | 4.23607 | 0.142474 | ||||||||
\(885\) | 30.3262 | 1.01941 | ||||||||
\(886\) | 6.58359 | 0.221180 | ||||||||
\(887\) | 39.8328 | 1.33746 | 0.668728 | − | 0.743508i | \(-0.266839\pi\) | ||||
0.668728 | + | 0.743508i | \(0.266839\pi\) | |||||||
\(888\) | −7.61803 | −0.255644 | ||||||||
\(889\) | −0.896674 | −0.0300735 | ||||||||
\(890\) | −20.4508 | −0.685514 | ||||||||
\(891\) | 32.6525 | 1.09390 | ||||||||
\(892\) | 10.3262 | 0.345748 | ||||||||
\(893\) | −0.291796 | −0.00976458 | ||||||||
\(894\) | 24.7984 | 0.829382 | ||||||||
\(895\) | −7.31308 | −0.244449 | ||||||||
\(896\) | 0.236068 | 0.00788648 | ||||||||
\(897\) | −6.09017 | −0.203345 | ||||||||
\(898\) | 14.0902 | 0.470195 | ||||||||
\(899\) | 8.61803 | 0.287428 | ||||||||
\(900\) | 1.18034 | 0.0393447 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 24.1803 | 0.805117 | ||||||||
\(903\) | 0.854102 | 0.0284227 | ||||||||
\(904\) | −17.6180 | −0.585967 | ||||||||
\(905\) | 10.2492 | 0.340696 | ||||||||
\(906\) | −12.8541 | −0.427049 | ||||||||
\(907\) | 26.1246 | 0.867453 | 0.433727 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433727 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(908\) | 5.03444 | 0.167074 | ||||||||
\(909\) | −2.32624 | −0.0771564 | ||||||||
\(910\) | 0.326238 | 0.0108147 | ||||||||
\(911\) | −44.3394 | −1.46903 | −0.734515 | − | 0.678593i | \(-0.762590\pi\) | ||||
−0.734515 | + | 0.678593i | \(0.762590\pi\) | |||||||
\(912\) | −3.23607 | −0.107157 | ||||||||
\(913\) | 3.23607 | 0.107098 | ||||||||
\(914\) | 2.20163 | 0.0728233 | ||||||||
\(915\) | 7.76393 | 0.256668 | ||||||||
\(916\) | 2.70820 | 0.0894816 | ||||||||
\(917\) | 1.70820 | 0.0564099 | ||||||||
\(918\) | −23.1803 | −0.765065 | ||||||||
\(919\) | −36.6525 | −1.20905 | −0.604527 | − | 0.796585i | \(-0.706638\pi\) | ||||
−0.604527 | + | 0.796585i | \(0.706638\pi\) | |||||||
\(920\) | 5.20163 | 0.171493 | ||||||||
\(921\) | 13.1459 | 0.433172 | ||||||||
\(922\) | −19.1246 | −0.629836 | ||||||||
\(923\) | 3.70820 | 0.122057 | ||||||||
\(924\) | 1.61803 | 0.0532294 | ||||||||
\(925\) | −14.5492 | −0.478373 | ||||||||
\(926\) | −8.90983 | −0.292795 | ||||||||
\(927\) | −1.58359 | −0.0520120 | ||||||||
\(928\) | −5.85410 | −0.192170 | ||||||||
\(929\) | 40.1803 | 1.31827 | 0.659137 | − | 0.752023i | \(-0.270922\pi\) | ||||
0.659137 | + | 0.752023i | \(0.270922\pi\) | |||||||
\(930\) | −3.29180 | −0.107942 | ||||||||
\(931\) | −13.8885 | −0.455179 | ||||||||
\(932\) | −0.236068 | −0.00773266 | ||||||||
\(933\) | 20.6525 | 0.676132 | ||||||||
\(934\) | −33.4164 | −1.09342 | ||||||||
\(935\) | −24.7984 | −0.810994 | ||||||||
\(936\) | 0.381966 | 0.0124849 | ||||||||
\(937\) | −21.9098 | −0.715763 | −0.357881 | − | 0.933767i | \(-0.616501\pi\) | ||||
−0.357881 | + | 0.933767i | \(0.616501\pi\) | |||||||
\(938\) | 1.47214 | 0.0480669 | ||||||||
\(939\) | −32.1246 | −1.04835 | ||||||||
\(940\) | 0.201626 | 0.00657632 | ||||||||
\(941\) | −0.0212862 | −0.000693911 0 | −0.000346956 | − | 1.00000i | \(-0.500110\pi\) | ||||
−0.000346956 | 1.00000i | \(0.500110\pi\) | ||||||||
\(942\) | 14.0000 | 0.456145 | ||||||||
\(943\) | 21.4853 | 0.699657 | ||||||||
\(944\) | 13.5623 | 0.441415 | ||||||||
\(945\) | −1.78522 | −0.0580732 | ||||||||
\(946\) | 9.47214 | 0.307966 | ||||||||
\(947\) | 1.21478 | 0.0394751 | 0.0197376 | − | 0.999805i | \(-0.493717\pi\) | ||||
0.0197376 | + | 0.999805i | \(0.493717\pi\) | |||||||
\(948\) | −17.4721 | −0.567469 | ||||||||
\(949\) | −2.70820 | −0.0879120 | ||||||||
\(950\) | −6.18034 | −0.200517 | ||||||||
\(951\) | 41.6869 | 1.35179 | ||||||||
\(952\) | −1.00000 | −0.0324102 | ||||||||
\(953\) | −37.3050 | −1.20843 | −0.604213 | − | 0.796823i | \(-0.706512\pi\) | ||||
−0.604213 | + | 0.796823i | \(0.706512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.7082 | 1.02605 | ||||||||
\(956\) | 14.2705 | 0.461541 | ||||||||
\(957\) | −40.1246 | −1.29704 | ||||||||
\(958\) | 12.5967 | 0.406982 | ||||||||
\(959\) | −3.15905 | −0.102011 | ||||||||
\(960\) | 2.23607 | 0.0721688 | ||||||||
\(961\) | −28.8328 | −0.930091 | ||||||||
\(962\) | −4.70820 | −0.151799 | ||||||||
\(963\) | 2.96556 | 0.0955638 | ||||||||
\(964\) | 8.70820 | 0.280472 | ||||||||
\(965\) | 5.20163 | 0.167446 | ||||||||
\(966\) | 1.43769 | 0.0462570 | ||||||||
\(967\) | −4.85410 | −0.156097 | −0.0780487 | − | 0.996950i | \(-0.524869\pi\) | ||||
−0.0780487 | + | 0.996950i | \(0.524869\pi\) | |||||||
\(968\) | 6.94427 | 0.223197 | ||||||||
\(969\) | 13.7082 | 0.440371 | ||||||||
\(970\) | 25.7771 | 0.827652 | ||||||||
\(971\) | 30.6525 | 0.983685 | 0.491842 | − | 0.870684i | \(-0.336324\pi\) | ||||
0.491842 | + | 0.870684i | \(0.336324\pi\) | |||||||
\(972\) | −3.94427 | −0.126513 | ||||||||
\(973\) | −2.25735 | −0.0723675 | ||||||||
\(974\) | 38.8328 | 1.24428 | ||||||||
\(975\) | −5.00000 | −0.160128 | ||||||||
\(976\) | 3.47214 | 0.111140 | ||||||||
\(977\) | 37.8541 | 1.21106 | 0.605530 | − | 0.795822i | \(-0.292961\pi\) | ||||
0.605530 | + | 0.795822i | \(0.292961\pi\) | |||||||
\(978\) | −2.70820 | −0.0865988 | ||||||||
\(979\) | −62.6869 | −2.00348 | ||||||||
\(980\) | 9.59675 | 0.306557 | ||||||||
\(981\) | −3.32624 | −0.106199 | ||||||||
\(982\) | 11.2361 | 0.358557 | ||||||||
\(983\) | −51.5623 | −1.64458 | −0.822291 | − | 0.569067i | \(-0.807304\pi\) | ||||
−0.822291 | + | 0.569067i | \(0.807304\pi\) | |||||||
\(984\) | 9.23607 | 0.294435 | ||||||||
\(985\) | 34.0213 | 1.08401 | ||||||||
\(986\) | 24.7984 | 0.789741 | ||||||||
\(987\) | 0.0557281 | 0.00177384 | ||||||||
\(988\) | −2.00000 | −0.0636285 | ||||||||
\(989\) | 8.41641 | 0.267626 | ||||||||
\(990\) | −2.23607 | −0.0710669 | ||||||||
\(991\) | −18.6180 | −0.591421 | −0.295711 | − | 0.955278i | \(-0.595556\pi\) | ||||
−0.295711 | + | 0.955278i | \(0.595556\pi\) | |||||||
\(992\) | −1.47214 | −0.0467404 | ||||||||
\(993\) | −37.5066 | −1.19024 | ||||||||
\(994\) | −0.875388 | −0.0277656 | ||||||||
\(995\) | 10.5279 | 0.333756 | ||||||||
\(996\) | 1.23607 | 0.0391663 | ||||||||
\(997\) | −44.4164 | −1.40668 | −0.703341 | − | 0.710853i | \(-0.748309\pi\) | ||||
−0.703341 | + | 0.710853i | \(0.748309\pi\) | |||||||
\(998\) | −5.94427 | −0.188163 | ||||||||
\(999\) | 25.7639 | 0.815135 |
(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 | 538.2.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 4842.2.a.f.1.1 | 2 | |||
4.3 | odd | 2 | 4304.2.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4304.2.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
4842.2.a.f.1.1 | 2 | 3.2 | odd | 2 |