Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.287107358976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 74x^{4} - 147x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.23950\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.683225 | 0.483113 | 0.241556 | − | 0.970387i | \(-0.422342\pi\) | ||||
0.241556 | + | 0.970387i | \(0.422342\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53320 | −0.766602 | ||||||||
\(5\) | 2.18081 | 0.975288 | 0.487644 | − | 0.873043i | \(-0.337856\pi\) | ||||
0.487644 | + | 0.873043i | \(0.337856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.85674 | −1.45771 | −0.728856 | − | 0.684667i | \(-0.759948\pi\) | ||||
−0.728856 | + | 0.684667i | \(0.759948\pi\) | |||||||
\(8\) | −2.41397 | −0.853468 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.48998 | 0.471174 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.99921 | −1.66388 | −0.831941 | − | 0.554864i | \(-0.812770\pi\) | ||||
−0.831941 | + | 0.554864i | \(0.812770\pi\) | |||||||
\(14\) | −2.63502 | −0.704239 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.41712 | 0.354280 | ||||||||
\(17\) | −3.16675 | −0.768051 | −0.384025 | − | 0.923323i | \(-0.625462\pi\) | ||||
−0.384025 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.530894 | 0.121795 | 0.0608977 | − | 0.998144i | \(-0.480604\pi\) | ||||
0.0608977 | + | 0.998144i | \(0.480604\pi\) | |||||||
\(20\) | −3.34363 | −0.747657 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.02266 | −1.46433 | −0.732163 | − | 0.681129i | \(-0.761489\pi\) | ||||
−0.732163 | + | 0.681129i | \(0.761489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.244069 | −0.0488139 | ||||||||
\(26\) | −4.09881 | −0.803843 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.91317 | 1.11748 | ||||||||
\(29\) | 7.62725 | 1.41635 | 0.708173 | − | 0.706039i | \(-0.249520\pi\) | ||||
0.708173 | + | 0.706039i | \(0.249520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.516471 | 0.0927609 | 0.0463804 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463804 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(32\) | 5.79616 | 1.02463 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.16361 | −0.371055 | ||||||||
\(35\) | −8.41082 | −1.42169 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.72760 | −0.941611 | −0.470806 | − | 0.882237i | \(-0.656037\pi\) | ||||
−0.470806 | + | 0.882237i | \(0.656037\pi\) | |||||||
\(38\) | 0.362720 | 0.0588410 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.26441 | −0.832377 | ||||||||
\(41\) | −3.61052 | −0.563868 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9656 | −1.67224 | −0.836121 | − | 0.548546i | \(-0.815182\pi\) | ||||
−0.836121 | + | 0.548546i | \(0.815182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.79806 | −0.707435 | ||||||||
\(47\) | 12.8275 | 1.87108 | 0.935542 | − | 0.353216i | \(-0.114912\pi\) | ||||
0.935542 | + | 0.353216i | \(0.114912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.87447 | 1.12492 | ||||||||
\(50\) | −0.166754 | −0.0235826 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.19802 | 1.27554 | ||||||||
\(53\) | −8.02009 | −1.10164 | −0.550822 | − | 0.834623i | \(-0.685686\pi\) | ||||
−0.550822 | + | 0.834623i | \(0.685686\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.31007 | 1.24411 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.21113 | 0.684255 | ||||||||
\(59\) | 10.6467 | 1.38608 | 0.693041 | − | 0.720898i | \(-0.256271\pi\) | ||||
0.693041 | + | 0.720898i | \(0.256271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.57377 | −0.585611 | −0.292805 | − | 0.956172i | \(-0.594589\pi\) | ||||
−0.292805 | + | 0.956172i | \(0.594589\pi\) | |||||||
\(62\) | 0.352866 | 0.0448140 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.12584 | 0.140729 | ||||||||
\(65\) | −13.0831 | −1.62276 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.38633 | −0.291537 | −0.145768 | − | 0.989319i | \(-0.546565\pi\) | ||||
−0.145768 | + | 0.989319i | \(0.546565\pi\) | |||||||
\(68\) | 4.85528 | 0.588789 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.74648 | −0.686836 | ||||||||
\(71\) | −2.94145 | −0.349086 | −0.174543 | − | 0.984650i | \(-0.555845\pi\) | ||||
−0.174543 | + | 0.984650i | \(0.555845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4664 | −1.34204 | −0.671021 | − | 0.741438i | \(-0.734144\pi\) | ||||
−0.671021 | + | 0.741438i | \(0.734144\pi\) | |||||||
\(74\) | −3.91324 | −0.454905 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.813969 | −0.0933687 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.254390 | 0.0286211 | 0.0143105 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143105 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(80\) | 3.09047 | 0.345525 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.46680 | −0.272412 | ||||||||
\(83\) | 6.81919 | 0.748503 | 0.374252 | − | 0.927327i | \(-0.377900\pi\) | ||||
0.374252 | + | 0.927327i | \(0.377900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90609 | −0.749070 | ||||||||
\(86\) | −7.49198 | −0.807881 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.5570 | 1.64904 | 0.824519 | − | 0.565835i | \(-0.191446\pi\) | ||||
0.824519 | + | 0.565835i | \(0.191446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.1374 | 2.42546 | ||||||||
\(92\) | 10.7672 | 1.12256 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.76407 | 0.903945 | ||||||||
\(95\) | 1.15778 | 0.118786 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.45274 | −0.655176 | −0.327588 | − | 0.944821i | \(-0.606236\pi\) | ||||
−0.327588 | + | 0.944821i | \(0.606236\pi\) | |||||||
\(98\) | 5.38003 | 0.543465 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.374208 | 0.0374208 | ||||||||
\(101\) | −0.974817 | −0.0969979 | −0.0484990 | − | 0.998823i | \(-0.515444\pi\) | ||||
−0.0484990 | + | 0.998823i | \(0.515444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33666 | 0.131705 | 0.0658524 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658524 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(104\) | 14.4819 | 1.42007 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.47952 | −0.532218 | ||||||||
\(107\) | 3.00315 | 0.290325 | 0.145163 | − | 0.989408i | \(-0.453629\pi\) | ||||
0.145163 | + | 0.989408i | \(0.453629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.34628 | 0.128950 | 0.0644750 | − | 0.997919i | \(-0.479463\pi\) | ||||
0.0644750 | + | 0.997919i | \(0.479463\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.46547 | −0.516439 | ||||||||
\(113\) | 15.4625 | 1.45459 | 0.727296 | − | 0.686324i | \(-0.240777\pi\) | ||||
0.727296 | + | 0.686324i | \(0.240777\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.3151 | −1.42814 | ||||||||
\(116\) | −11.6941 | −1.08577 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.27409 | 0.669634 | ||||||||
\(119\) | 12.2134 | 1.11960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.12491 | −0.282916 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.791855 | −0.0711107 | ||||||||
\(125\) | −11.4363 | −1.02290 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.73937 | −0.509287 | −0.254643 | − | 0.967035i | \(-0.581958\pi\) | ||||
−0.254643 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(128\) | −10.8231 | −0.956637 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.93873 | −0.783978 | ||||||||
\(131\) | 10.9916 | 0.960336 | 0.480168 | − | 0.877176i | \(-0.340576\pi\) | ||||
0.480168 | + | 0.877176i | \(0.340576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.04752 | −0.177543 | ||||||||
\(134\) | −1.63040 | −0.140845 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.64446 | 0.655507 | ||||||||
\(137\) | 18.2126 | 1.55600 | 0.778002 | − | 0.628261i | \(-0.216233\pi\) | ||||
0.778002 | + | 0.628261i | \(0.216233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.6108 | −1.74819 | −0.874093 | − | 0.485759i | \(-0.838543\pi\) | ||||
−0.874093 | + | 0.485759i | \(0.838543\pi\) | |||||||
\(140\) | 12.8955 | 1.08987 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.00967 | −0.168648 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.6336 | 1.38134 | ||||||||
\(146\) | −7.83414 | −0.648358 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.78158 | 0.721841 | ||||||||
\(149\) | 4.28383 | 0.350945 | 0.175473 | − | 0.984484i | \(-0.443855\pi\) | ||||
0.175473 | + | 0.984484i | \(0.443855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1954 | 0.911066 | 0.455533 | − | 0.890219i | \(-0.349449\pi\) | ||||
0.455533 | + | 0.890219i | \(0.349449\pi\) | |||||||
\(152\) | −1.28156 | −0.103949 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.12632 | 0.0904685 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.31048 | 0.583440 | 0.291720 | − | 0.956504i | \(-0.405773\pi\) | ||||
0.291720 | + | 0.956504i | \(0.405773\pi\) | |||||||
\(158\) | 0.173805 | 0.0138272 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6403 | 0.999305 | ||||||||
\(161\) | 27.0846 | 2.13457 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.9125 | −1.71632 | −0.858162 | − | 0.513380i | \(-0.828393\pi\) | ||||
−0.858162 | + | 0.513380i | \(0.828393\pi\) | |||||||
\(164\) | 5.53566 | 0.432263 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.65904 | 0.361612 | ||||||||
\(167\) | 7.22104 | 0.558781 | 0.279390 | − | 0.960178i | \(-0.409868\pi\) | ||||
0.279390 | + | 0.960178i | \(0.409868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.9906 | 1.76850 | ||||||||
\(170\) | −4.71841 | −0.361886 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.8125 | 1.28194 | ||||||||
\(173\) | −2.40767 | −0.183052 | −0.0915260 | − | 0.995803i | \(-0.529174\pi\) | ||||
−0.0915260 | + | 0.995803i | \(0.529174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.941313 | 0.0711565 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.6289 | 0.796671 | ||||||||
\(179\) | −14.6200 | −1.09275 | −0.546375 | − | 0.837540i | \(-0.683993\pi\) | ||||
−0.546375 | + | 0.837540i | \(0.683993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.900651 | 0.0669449 | 0.0334724 | − | 0.999440i | \(-0.489343\pi\) | ||||
0.0334724 | + | 0.999440i | \(0.489343\pi\) | |||||||
\(182\) | 15.8081 | 1.17177 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.9525 | 1.24976 | ||||||||
\(185\) | −12.4908 | −0.918342 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −19.6672 | −1.43438 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.791024 | 0.0573869 | ||||||||
\(191\) | 8.05453 | 0.582805 | 0.291403 | − | 0.956601i | \(-0.405878\pi\) | ||||
0.291403 | + | 0.956601i | \(0.405878\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.20116 | −0.0864611 | −0.0432306 | − | 0.999065i | \(-0.513765\pi\) | ||||
−0.0432306 | + | 0.999065i | \(0.513765\pi\) | |||||||
\(194\) | −4.40867 | −0.316524 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.0732 | −0.862369 | ||||||||
\(197\) | 25.9462 | 1.84859 | 0.924294 | − | 0.381680i | \(-0.124655\pi\) | ||||
0.924294 | + | 0.381680i | \(0.124655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.08775 | −0.431549 | −0.215775 | − | 0.976443i | \(-0.569228\pi\) | ||||
−0.215775 | + | 0.976443i | \(0.569228\pi\) | |||||||
\(200\) | 0.589177 | 0.0416611 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.666019 | −0.0468609 | ||||||||
\(203\) | −29.4164 | −2.06462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.87385 | −0.549934 | ||||||||
\(206\) | 0.913238 | 0.0636283 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.50161 | −0.589481 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.93130 | 0.614856 | 0.307428 | − | 0.951571i | \(-0.400532\pi\) | ||||
0.307428 | + | 0.951571i | \(0.400532\pi\) | |||||||
\(212\) | 12.2964 | 0.844522 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.05183 | 0.140260 | ||||||||
\(215\) | −23.9139 | −1.63092 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.99189 | −0.135219 | ||||||||
\(218\) | 0.919810 | 0.0622974 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9980 | 1.27795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.5216 | 1.77602 | 0.888009 | − | 0.459826i | \(-0.152088\pi\) | ||||
0.888009 | + | 0.459826i | \(0.152088\pi\) | |||||||
\(224\) | −22.3543 | −1.49361 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5644 | 0.702732 | ||||||||
\(227\) | −2.55624 | −0.169663 | −0.0848316 | − | 0.996395i | \(-0.527035\pi\) | ||||
−0.0848316 | + | 0.996395i | \(0.527035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2984 | 1.47352 | 0.736758 | − | 0.676156i | \(-0.236356\pi\) | ||||
0.736758 | + | 0.676156i | \(0.236356\pi\) | |||||||
\(230\) | −10.4636 | −0.689952 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.4120 | −1.20881 | ||||||||
\(233\) | 18.4651 | 1.20969 | 0.604845 | − | 0.796343i | \(-0.293235\pi\) | ||||
0.604845 | + | 0.796343i | \(0.293235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.9743 | 1.82485 | ||||||||
\(236\) | −16.3236 | −1.06257 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.34447 | 0.540892 | ||||||||
\(239\) | −6.57973 | −0.425607 | −0.212804 | − | 0.977095i | \(-0.568259\pi\) | ||||
−0.212804 | + | 0.977095i | \(0.568259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.95830 | 0.448224 | 0.224112 | − | 0.974563i | \(-0.428052\pi\) | ||||
0.224112 | + | 0.974563i | \(0.428052\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.01251 | 0.448930 | ||||||||
\(245\) | 17.1727 | 1.09712 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.18495 | −0.202653 | ||||||||
\(248\) | −1.24675 | −0.0791684 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.81358 | −0.494174 | ||||||||
\(251\) | −0.0914931 | −0.00577500 | −0.00288750 | − | 0.999996i | \(-0.500919\pi\) | ||||
−0.00288750 | + | 0.999996i | \(0.500919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.92128 | −0.246043 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.64629 | −0.602893 | ||||||||
\(257\) | −11.0833 | −0.691358 | −0.345679 | − | 0.938353i | \(-0.612351\pi\) | ||||
−0.345679 | + | 0.938353i | \(0.612351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.0899 | 1.37260 | ||||||||
\(260\) | 20.0591 | 1.24401 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.50970 | 0.463951 | ||||||||
\(263\) | −12.5347 | −0.772920 | −0.386460 | − | 0.922306i | \(-0.626302\pi\) | ||||
−0.386460 | + | 0.922306i | \(0.626302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.4903 | −1.07442 | ||||||||
\(266\) | −1.39892 | −0.0857732 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.65873 | 0.223493 | ||||||||
\(269\) | −17.3696 | −1.05904 | −0.529522 | − | 0.848296i | \(-0.677629\pi\) | ||||
−0.529522 | + | 0.848296i | \(0.677629\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5849 | −1.18970 | −0.594848 | − | 0.803838i | \(-0.702788\pi\) | ||||
−0.594848 | + | 0.803838i | \(0.702788\pi\) | |||||||
\(272\) | −4.48768 | −0.272105 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4433 | 0.751726 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2560 | 1.69774 | 0.848870 | − | 0.528601i | \(-0.177283\pi\) | ||||
0.848870 | + | 0.528601i | \(0.177283\pi\) | |||||||
\(278\) | −14.0818 | −0.844571 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20.3035 | 1.21337 | ||||||||
\(281\) | 7.89750 | 0.471125 | 0.235563 | − | 0.971859i | \(-0.424307\pi\) | ||||
0.235563 | + | 0.971859i | \(0.424307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.3792 | −1.56808 | −0.784039 | − | 0.620712i | \(-0.786844\pi\) | ||||
−0.784039 | + | 0.620712i | \(0.786844\pi\) | |||||||
\(284\) | 4.50984 | 0.267610 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.9248 | 0.821958 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.97167 | −0.410098 | ||||||||
\(290\) | 11.3645 | 0.667345 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.5804 | 1.02881 | ||||||||
\(293\) | −14.8301 | −0.866384 | −0.433192 | − | 0.901302i | \(-0.642613\pi\) | ||||
−0.433192 | + | 0.901302i | \(0.642613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.2184 | 1.35183 | ||||||||
\(296\) | 13.8263 | 0.803635 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.92682 | 0.169546 | ||||||||
\(299\) | 42.1304 | 2.43647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.2916 | 2.43765 | ||||||||
\(302\) | 7.64895 | 0.440148 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.752342 | 0.0431498 | ||||||||
\(305\) | −9.97451 | −0.571139 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.86259 | −0.277523 | −0.138761 | − | 0.990326i | \(-0.544312\pi\) | ||||
−0.138761 | + | 0.990326i | \(0.544312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.769533 | 0.0437065 | ||||||||
\(311\) | 15.2753 | 0.866182 | 0.433091 | − | 0.901350i | \(-0.357423\pi\) | ||||
0.433091 | + | 0.901350i | \(0.357423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.7228 | 1.84960 | 0.924800 | − | 0.380454i | \(-0.124232\pi\) | ||||
0.924800 | + | 0.380454i | \(0.124232\pi\) | |||||||
\(314\) | 4.99470 | 0.281867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.390031 | −0.0219410 | ||||||||
\(317\) | −3.08378 | −0.173202 | −0.0866012 | − | 0.996243i | \(-0.527601\pi\) | ||||
−0.0866012 | + | 0.996243i | \(0.527601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.45523 | 0.137252 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.5049 | 1.03124 | ||||||||
\(323\) | −1.68121 | −0.0935451 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.46422 | 0.0812205 | ||||||||
\(326\) | −14.9712 | −0.829178 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.71569 | 0.481244 | ||||||||
\(329\) | −49.4724 | −2.72750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.1750 | 1.49367 | 0.746836 | − | 0.665008i | \(-0.231572\pi\) | ||||
0.746836 | + | 0.665008i | \(0.231572\pi\) | |||||||
\(332\) | −10.4552 | −0.573804 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.93359 | 0.269954 | ||||||||
\(335\) | −5.20414 | −0.284332 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.4605 | −1.98613 | −0.993066 | − | 0.117562i | \(-0.962492\pi\) | ||||
−0.993066 | + | 0.117562i | \(0.962492\pi\) | |||||||
\(338\) | 15.7077 | 0.854387 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.5884 | 0.574239 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.37261 | −0.182104 | ||||||||
\(344\) | 26.4707 | 1.42720 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.64498 | −0.0884348 | ||||||||
\(347\) | 18.6220 | 0.999679 | 0.499839 | − | 0.866118i | \(-0.333392\pi\) | ||||
0.499839 | + | 0.866118i | \(0.333392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.6433 | −1.42618 | −0.713090 | − | 0.701072i | \(-0.752705\pi\) | ||||
−0.713090 | + | 0.701072i | \(0.752705\pi\) | |||||||
\(350\) | 0.643128 | 0.0343766 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.9338 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.41474 | −0.340459 | ||||||||
\(356\) | −23.8520 | −1.26415 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.98875 | −0.527922 | ||||||||
\(359\) | 15.7915 | 0.833446 | 0.416723 | − | 0.909034i | \(-0.363178\pi\) | ||||
0.416723 | + | 0.909034i | \(0.363178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7182 | −0.985166 | ||||||||
\(362\) | 0.615347 | 0.0323419 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −35.4744 | −1.85936 | ||||||||
\(365\) | −25.0061 | −1.30888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.63255 | 0.241817 | 0.120909 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(368\) | −9.95196 | −0.518782 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.53403 | −0.443663 | ||||||||
\(371\) | 30.9314 | 1.60588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6192 | −1.79251 | −0.896257 | − | 0.443535i | \(-0.853724\pi\) | ||||
−0.896257 | + | 0.443535i | \(0.853724\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.9652 | −1.59691 | ||||||||
\(377\) | −45.7575 | −2.35663 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.42388 | −0.227240 | −0.113620 | − | 0.993524i | \(-0.536245\pi\) | ||||
−0.113620 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(380\) | −1.77511 | −0.0910613 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.50305 | 0.281561 | ||||||||
\(383\) | 27.5705 | 1.40879 | 0.704394 | − | 0.709809i | \(-0.251219\pi\) | ||||
0.704394 | + | 0.709809i | \(0.251219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.820660 | −0.0417705 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.89337 | 0.502260 | ||||||||
\(389\) | 20.0416 | 1.01615 | 0.508074 | − | 0.861313i | \(-0.330358\pi\) | ||||
0.508074 | + | 0.861313i | \(0.330358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.2390 | 1.12468 | ||||||||
\(392\) | −19.0088 | −0.960087 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.7271 | 0.893077 | ||||||||
\(395\) | 0.554775 | 0.0279138 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.4787 | −1.22855 | −0.614275 | − | 0.789092i | \(-0.710552\pi\) | ||||
−0.614275 | + | 0.789092i | \(0.710552\pi\) | |||||||
\(398\) | −4.15930 | −0.208487 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.345876 | −0.0172938 | ||||||||
\(401\) | −15.4281 | −0.770442 | −0.385221 | − | 0.922824i | \(-0.625875\pi\) | ||||
−0.385221 | + | 0.922824i | \(0.625875\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.09842 | −0.154343 | ||||||||
\(404\) | 1.49459 | 0.0743588 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0980 | −0.997446 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50534 | 0.420562 | 0.210281 | − | 0.977641i | \(-0.432562\pi\) | ||||
0.210281 | + | 0.977641i | \(0.432562\pi\) | |||||||
\(410\) | −5.37961 | −0.265680 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.04937 | −0.100965 | ||||||||
\(413\) | −41.0616 | −2.02051 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8714 | 0.730006 | ||||||||
\(416\) | −34.7724 | −1.70486 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2348 | −0.548857 | −0.274428 | − | 0.961608i | \(-0.588489\pi\) | ||||
−0.274428 | + | 0.961608i | \(0.588489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.6185 | −1.15110 | −0.575548 | − | 0.817768i | \(-0.695211\pi\) | ||||
−0.575548 | + | 0.817768i | \(0.695211\pi\) | |||||||
\(422\) | 6.10209 | 0.297045 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.3603 | 0.940218 | ||||||||
\(425\) | 0.772907 | 0.0374915 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.6398 | 0.853652 | ||||||||
\(428\) | −4.60444 | −0.222564 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.3386 | −0.787917 | ||||||||
\(431\) | −5.55985 | −0.267808 | −0.133904 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133904 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6137 | 1.03869 | 0.519343 | − | 0.854566i | \(-0.326177\pi\) | ||||
0.519343 | + | 0.854566i | \(0.326177\pi\) | |||||||
\(434\) | −1.36091 | −0.0653259 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.06412 | −0.0988532 | ||||||||
\(437\) | −3.72829 | −0.178348 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.66239 | 0.365706 | 0.182853 | − | 0.983140i | \(-0.441467\pi\) | ||||
0.182853 | + | 0.983140i | \(0.441467\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9799 | 0.617392 | ||||||||
\(443\) | 23.9011 | 1.13558 | 0.567788 | − | 0.823175i | \(-0.307799\pi\) | ||||
0.567788 | + | 0.823175i | \(0.307799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.9268 | 1.60829 | ||||||||
\(446\) | 18.1202 | 0.858017 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.34206 | −0.205143 | ||||||||
\(449\) | 33.7817 | 1.59426 | 0.797129 | − | 0.603810i | \(-0.206351\pi\) | ||||
0.797129 | + | 0.603810i | \(0.206351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −23.7072 | −1.11509 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.74648 | −0.0819665 | ||||||||
\(455\) | 50.4583 | 2.36552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.92967 | 0.464491 | 0.232245 | − | 0.972657i | \(-0.425393\pi\) | ||||
0.232245 | + | 0.972657i | \(0.425393\pi\) | |||||||
\(458\) | 15.2348 | 0.711875 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.4811 | 1.09481 | ||||||||
\(461\) | −3.76269 | −0.175246 | −0.0876230 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876230 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4887 | 1.37045 | 0.685227 | − | 0.728329i | \(-0.259703\pi\) | ||||
0.685227 | + | 0.728329i | \(0.259703\pi\) | |||||||
\(464\) | 10.8087 | 0.501783 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.6158 | 0.584417 | ||||||||
\(467\) | −12.2272 | −0.565809 | −0.282904 | − | 0.959148i | \(-0.591298\pi\) | ||||
−0.282904 | + | 0.959148i | \(0.591298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.20347 | 0.424977 | ||||||||
\(470\) | 19.1128 | 0.881606 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.7008 | −1.18298 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.129575 | −0.00594531 | ||||||||
\(476\) | −18.7256 | −0.858285 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.49543 | −0.205616 | ||||||||
\(479\) | 31.0255 | 1.41759 | 0.708795 | − | 0.705414i | \(-0.249239\pi\) | ||||
0.708795 | + | 0.705414i | \(0.249239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.3611 | 1.56673 | ||||||||
\(482\) | 4.75408 | 0.216543 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0722 | −0.638986 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7298 | 0.622154 | 0.311077 | − | 0.950385i | \(-0.399310\pi\) | ||||
0.311077 | + | 0.950385i | \(0.399310\pi\) | |||||||
\(488\) | 11.0409 | 0.499800 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.7328 | 0.530035 | ||||||||
\(491\) | 8.43140 | 0.380504 | 0.190252 | − | 0.981735i | \(-0.439070\pi\) | ||||
0.190252 | + | 0.981735i | \(0.439070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.1536 | −1.08782 | ||||||||
\(494\) | −2.17604 | −0.0979045 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.731902 | 0.0328634 | ||||||||
\(497\) | 11.3444 | 0.508867 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7395 | −1.10749 | −0.553746 | − | 0.832686i | \(-0.686802\pi\) | ||||
−0.553746 | + | 0.832686i | \(0.686802\pi\) | |||||||
\(500\) | 17.5342 | 0.784153 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.0625104 | −0.00278997 | ||||||||
\(503\) | −16.3439 | −0.728740 | −0.364370 | − | 0.931254i | \(-0.618716\pi\) | ||||
−0.364370 | + | 0.931254i | \(0.618716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.12589 | −0.0946009 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.79962 | 0.390420 | ||||||||
\(509\) | −20.4702 | −0.907327 | −0.453664 | − | 0.891173i | \(-0.649883\pi\) | ||||
−0.453664 | + | 0.891173i | \(0.649883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.2230 | 1.95631 | ||||||||
\(512\) | 15.0556 | 0.665372 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.57239 | −0.334004 | ||||||||
\(515\) | 2.91500 | 0.128450 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15.0924 | 0.663120 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 31.5823 | 1.38498 | ||||||||
\(521\) | −40.1151 | −1.75747 | −0.878737 | − | 0.477306i | \(-0.841613\pi\) | ||||
−0.878737 | + | 0.477306i | \(0.841613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6107 | 0.770064 | 0.385032 | − | 0.922903i | \(-0.374190\pi\) | ||||
0.385032 | + | 0.922903i | \(0.374190\pi\) | |||||||
\(524\) | −16.8523 | −0.736196 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.56399 | −0.373408 | ||||||||
\(527\) | −1.63554 | −0.0712450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.3178 | 1.14425 | ||||||||
\(530\) | −11.9498 | −0.519066 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.13927 | 0.136105 | ||||||||
\(533\) | 21.6603 | 0.938210 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.54930 | 0.283151 | ||||||||
\(536\) | 5.76054 | 0.248817 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.8674 | −0.511638 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5537 | 0.883675 | 0.441837 | − | 0.897095i | \(-0.354327\pi\) | ||||
0.441837 | + | 0.897095i | \(0.354327\pi\) | |||||||
\(542\) | −13.3809 | −0.574757 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.3550 | −0.786964 | ||||||||
\(545\) | 2.93597 | 0.125763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0069 | 0.684407 | 0.342204 | − | 0.939626i | \(-0.388827\pi\) | ||||
0.342204 | + | 0.939626i | \(0.388827\pi\) | |||||||
\(548\) | −27.9236 | −1.19284 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.04926 | 0.172504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.981115 | −0.0417213 | ||||||||
\(554\) | 19.3052 | 0.820200 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.6006 | 1.34016 | ||||||||
\(557\) | 12.2300 | 0.518202 | 0.259101 | − | 0.965850i | \(-0.416574\pi\) | ||||
0.259101 | + | 0.965850i | \(0.416574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.7851 | 2.78241 | ||||||||
\(560\) | −11.9192 | −0.503676 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.39577 | 0.227607 | ||||||||
\(563\) | 31.6605 | 1.33433 | 0.667165 | − | 0.744910i | \(-0.267507\pi\) | ||||
0.667165 | + | 0.744910i | \(0.267507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.7208 | 1.41865 | ||||||||
\(566\) | −18.0229 | −0.757559 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.10058 | 0.297934 | ||||||||
\(569\) | 28.6418 | 1.20073 | 0.600364 | − | 0.799727i | \(-0.295022\pi\) | ||||
0.600364 | + | 0.799727i | \(0.295022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.7649 | −0.576044 | −0.288022 | − | 0.957624i | \(-0.592998\pi\) | ||||
−0.288022 | + | 0.957624i | \(0.592998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.51380 | 0.397098 | ||||||||
\(575\) | 1.71402 | 0.0714794 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.9997 | 0.541184 | 0.270592 | − | 0.962694i | \(-0.412781\pi\) | ||||
0.270592 | + | 0.962694i | \(0.412781\pi\) | |||||||
\(578\) | −4.76322 | −0.198124 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.5027 | −1.05894 | ||||||||
\(581\) | −26.2999 | −1.09110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 27.6796 | 1.14539 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.1323 | −0.418561 | ||||||||
\(587\) | −22.4701 | −0.927439 | −0.463720 | − | 0.885982i | \(-0.653486\pi\) | ||||
−0.463720 | + | 0.885982i | \(0.653486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.274191 | 0.0112979 | ||||||||
\(590\) | 15.8634 | 0.653086 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.11670 | −0.333594 | ||||||||
\(593\) | 8.07538 | 0.331616 | 0.165808 | − | 0.986158i | \(-0.446977\pi\) | ||||
0.165808 | + | 0.986158i | \(0.446977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.6350 | 1.09193 | ||||||||
\(596\) | −6.56799 | −0.269035 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.7846 | 1.17709 | ||||||||
\(599\) | 34.7973 | 1.42178 | 0.710889 | − | 0.703304i | \(-0.248293\pi\) | ||||
0.710889 | + | 0.703304i | \(0.248293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.58485 | 0.268602 | 0.134301 | − | 0.990941i | \(-0.457121\pi\) | ||||
0.134301 | + | 0.990941i | \(0.457121\pi\) | |||||||
\(602\) | 28.8947 | 1.17766 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.1648 | −0.698425 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.62390 | −0.0659119 | −0.0329560 | − | 0.999457i | \(-0.510492\pi\) | ||||
−0.0329560 | + | 0.999457i | \(0.510492\pi\) | |||||||
\(608\) | 3.07715 | 0.124795 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.81483 | −0.275925 | ||||||||
\(611\) | −76.9549 | −3.11326 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.80435 | 0.395994 | 0.197997 | − | 0.980203i | \(-0.436556\pi\) | ||||
0.197997 | + | 0.980203i | \(0.436556\pi\) | |||||||
\(614\) | −3.32224 | −0.134075 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.7948 | −1.03846 | −0.519230 | − | 0.854635i | \(-0.673781\pi\) | ||||
−0.519230 | + | 0.854635i | \(0.673781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9268 | 1.12247 | 0.561237 | − | 0.827655i | \(-0.310326\pi\) | ||||
0.561237 | + | 0.827655i | \(0.310326\pi\) | |||||||
\(620\) | −1.72688 | −0.0693534 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.4365 | 0.418464 | ||||||||
\(623\) | −59.9993 | −2.40382 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7201 | −0.948803 | ||||||||
\(626\) | 22.3570 | 0.893566 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.2085 | −0.447266 | ||||||||
\(629\) | 18.1379 | 0.723205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0594 | −1.03741 | −0.518705 | − | 0.854954i | \(-0.673586\pi\) | ||||
−0.518705 | + | 0.854954i | \(0.673586\pi\) | |||||||
\(632\) | −0.614089 | −0.0244272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.10692 | −0.0836763 | ||||||||
\(635\) | −12.5165 | −0.496701 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −47.2406 | −1.87174 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.6032 | −0.932997 | ||||||||
\(641\) | −22.9474 | −0.906367 | −0.453184 | − | 0.891417i | \(-0.649712\pi\) | ||||
−0.453184 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.2843 | −1.23373 | −0.616866 | − | 0.787068i | \(-0.711598\pi\) | ||||
−0.616866 | + | 0.787068i | \(0.711598\pi\) | |||||||
\(644\) | −41.5262 | −1.63636 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.14865 | −0.0451929 | ||||||||
\(647\) | −14.9853 | −0.589131 | −0.294566 | − | 0.955631i | \(-0.595175\pi\) | ||||
−0.294566 | + | 0.955631i | \(0.595175\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00039 | 0.0392387 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.5964 | 1.31574 | ||||||||
\(653\) | −4.90689 | −0.192021 | −0.0960107 | − | 0.995380i | \(-0.530608\pi\) | ||||
−0.0960107 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.9705 | 0.936604 | ||||||||
\(656\) | −5.11654 | −0.199768 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.8008 | −1.31769 | ||||||||
\(659\) | −3.66895 | −0.142922 | −0.0714610 | − | 0.997443i | \(-0.522766\pi\) | ||||
−0.0714610 | + | 0.997443i | \(0.522766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1469 | 0.861413 | 0.430707 | − | 0.902492i | \(-0.358264\pi\) | ||||
0.430707 | + | 0.902492i | \(0.358264\pi\) | |||||||
\(662\) | 18.5666 | 0.721612 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.4613 | −0.638824 | ||||||||
\(665\) | −4.46526 | −0.173155 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.5636 | −2.07399 | ||||||||
\(668\) | −11.0713 | −0.428362 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.55559 | −0.137365 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0420 | −0.849657 | −0.424828 | − | 0.905274i | \(-0.639666\pi\) | ||||
−0.424828 | + | 0.905274i | \(0.639666\pi\) | |||||||
\(674\) | −24.9107 | −0.959526 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.2492 | −1.35574 | ||||||||
\(677\) | −28.7363 | −1.10443 | −0.552214 | − | 0.833703i | \(-0.686217\pi\) | ||||
−0.552214 | + | 0.833703i | \(0.686217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.8866 | 0.955059 | ||||||||
\(680\) | 16.6711 | 0.639308 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.4334 | 1.77672 | 0.888362 | − | 0.459143i | \(-0.151843\pi\) | ||||
0.888362 | + | 0.459143i | \(0.151843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.7182 | 1.51755 | ||||||||
\(686\) | −2.30425 | −0.0879767 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.5396 | −0.592442 | ||||||||
\(689\) | 48.1142 | 1.83301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.83156 | −0.297926 | −0.148963 | − | 0.988843i | \(-0.547594\pi\) | ||||
−0.148963 | + | 0.988843i | \(0.547594\pi\) | |||||||
\(692\) | 3.69146 | 0.140328 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.7230 | 0.482958 | ||||||||
\(695\) | −44.9482 | −1.70498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4336 | 0.433079 | ||||||||
\(698\) | −18.2033 | −0.689006 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.44322 | −0.0545487 | ||||||||
\(701\) | −27.6808 | −1.04549 | −0.522746 | − | 0.852489i | \(-0.675092\pi\) | ||||
−0.522746 | + | 0.852489i | \(0.675092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.04075 | −0.114684 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.9360 | −0.486853 | ||||||||
\(707\) | 3.75962 | 0.141395 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.4153 | −1.14227 | −0.571135 | − | 0.820856i | \(-0.693497\pi\) | ||||
−0.571135 | + | 0.820856i | \(0.693497\pi\) | |||||||
\(710\) | −4.38271 | −0.164480 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −37.5541 | −1.40740 | ||||||||
\(713\) | −3.62700 | −0.135832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.4155 | 0.837705 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7892 | 0.402649 | ||||||||
\(719\) | −37.3869 | −1.39430 | −0.697148 | − | 0.716927i | \(-0.745548\pi\) | ||||
−0.697148 | + | 0.716927i | \(0.745548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.15515 | −0.191988 | ||||||||
\(722\) | −12.7887 | −0.475946 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.38088 | −0.0513201 | ||||||||
\(725\) | −1.86158 | −0.0691373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3288 | 0.605603 | 0.302802 | − | 0.953054i | \(-0.402078\pi\) | ||||
0.302802 | + | 0.953054i | \(0.402078\pi\) | |||||||
\(728\) | −55.8531 | −2.07005 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.0848 | −0.632336 | ||||||||
\(731\) | 34.7254 | 1.28437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.5505 | 0.832921 | 0.416461 | − | 0.909154i | \(-0.363270\pi\) | ||||
0.416461 | + | 0.909154i | \(0.363270\pi\) | |||||||
\(734\) | 3.16508 | 0.116825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −40.7044 | −1.50039 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.7185 | 0.504641 | 0.252321 | − | 0.967644i | \(-0.418806\pi\) | ||||
0.252321 | + | 0.967644i | \(0.418806\pi\) | |||||||
\(740\) | 19.1509 | 0.704003 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.1331 | 0.775821 | ||||||||
\(743\) | 41.0233 | 1.50500 | 0.752499 | − | 0.658594i | \(-0.228848\pi\) | ||||
0.752499 | + | 0.658594i | \(0.228848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.34223 | 0.342273 | ||||||||
\(746\) | −23.6527 | −0.865987 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.5824 | −0.423211 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.9309 | 1.38412 | 0.692059 | − | 0.721841i | \(-0.256704\pi\) | ||||
0.692059 | + | 0.721841i | \(0.256704\pi\) | |||||||
\(752\) | 18.1781 | 0.662888 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.2627 | −1.13852 | ||||||||
\(755\) | 24.4150 | 0.888551 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.7700 | −0.827589 | −0.413794 | − | 0.910370i | \(-0.635797\pi\) | ||||
−0.413794 | + | 0.910370i | \(0.635797\pi\) | |||||||
\(758\) | −3.02251 | −0.109782 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.79485 | −0.101380 | ||||||||
\(761\) | 4.64031 | 0.168211 | 0.0841056 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841056 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.19224 | −0.187972 | ||||||||
\(764\) | −12.3492 | −0.446780 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.8369 | 0.680604 | ||||||||
\(767\) | −63.8718 | −2.30628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.74051 | −0.0988253 | −0.0494127 | − | 0.998778i | \(-0.515735\pi\) | ||||
−0.0494127 | + | 0.998778i | \(0.515735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.84162 | 0.0662813 | ||||||||
\(773\) | 11.0421 | 0.397158 | 0.198579 | − | 0.980085i | \(-0.436367\pi\) | ||||
0.198579 | + | 0.980085i | \(0.436367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.126055 | −0.00452802 | ||||||||
\(776\) | 15.5767 | 0.559172 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.6929 | 0.490914 | ||||||||
\(779\) | −1.91680 | −0.0686766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.1943 | 0.543346 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.1591 | 0.398539 | ||||||||
\(785\) | 15.9428 | 0.569021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.3886 | −1.04759 | −0.523795 | − | 0.851844i | \(-0.675484\pi\) | ||||
−0.523795 | + | 0.851844i | \(0.675484\pi\) | |||||||
\(788\) | −39.7808 | −1.41713 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.379036 | 0.0134855 | ||||||||
\(791\) | −59.6350 | −2.12038 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.4390 | 0.974387 | ||||||||
\(794\) | −16.7244 | −0.593529 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.33376 | 0.330826 | ||||||||
\(797\) | −1.11623 | −0.0395390 | −0.0197695 | − | 0.999805i | \(-0.506293\pi\) | ||||
−0.0197695 | + | 0.999805i | \(0.506293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.6216 | −1.43709 | ||||||||
\(800\) | −1.41466 | −0.0500159 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.5409 | −0.372210 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 59.0664 | 2.08182 | ||||||||
\(806\) | −2.11692 | −0.0745652 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.35318 | 0.0827846 | ||||||||
\(809\) | 43.3724 | 1.52489 | 0.762445 | − | 0.647053i | \(-0.223999\pi\) | ||||
0.762445 | + | 0.647053i | \(0.223999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.0062 | 1.15900 | 0.579502 | − | 0.814971i | \(-0.303247\pi\) | ||||
0.579502 | + | 0.814971i | \(0.303247\pi\) | |||||||
\(812\) | 45.1013 | 1.58274 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.7871 | −1.67391 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82158 | −0.203671 | ||||||||
\(818\) | 5.81106 | 0.203179 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0722 | 0.421580 | ||||||||
\(821\) | −27.0131 | −0.942762 | −0.471381 | − | 0.881930i | \(-0.656244\pi\) | ||||
−0.471381 | + | 0.881930i | \(0.656244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.23678 | 0.0779694 | 0.0389847 | − | 0.999240i | \(-0.487588\pi\) | ||||
0.0389847 | + | 0.999240i | \(0.487588\pi\) | |||||||
\(824\) | −3.22665 | −0.112406 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0543 | −0.976133 | ||||||||
\(827\) | −24.0696 | −0.836980 | −0.418490 | − | 0.908221i | \(-0.637441\pi\) | ||||
−0.418490 | + | 0.908221i | \(0.637441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.42634 | −0.257927 | −0.128964 | − | 0.991649i | \(-0.541165\pi\) | ||||
−0.128964 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(830\) | 10.1605 | 0.352675 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.75413 | −0.234157 | ||||||||
\(833\) | −24.9365 | −0.863999 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.7477 | 0.544972 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.67591 | −0.265160 | ||||||||
\(839\) | 11.3704 | 0.392550 | 0.196275 | − | 0.980549i | \(-0.437115\pi\) | ||||
0.196275 | + | 0.980549i | \(0.437115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.1750 | 1.00603 | ||||||||
\(842\) | −16.1367 | −0.556109 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.6935 | −0.471350 | ||||||||
\(845\) | 50.1380 | 1.72480 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.3654 | −0.390291 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.528070 | 0.0181126 | ||||||||
\(851\) | 40.2230 | 1.37883 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.35595 | −0.114905 | −0.0574527 | − | 0.998348i | \(-0.518298\pi\) | ||||
−0.0574527 | + | 0.998348i | \(0.518298\pi\) | |||||||
\(854\) | 12.0520 | 0.412410 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.24952 | −0.247783 | ||||||||
\(857\) | −18.5664 | −0.634215 | −0.317107 | − | 0.948390i | \(-0.602712\pi\) | ||||
−0.317107 | + | 0.948390i | \(0.602712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1518 | 0.482853 | 0.241426 | − | 0.970419i | \(-0.422385\pi\) | ||||
0.241426 | + | 0.970419i | \(0.422385\pi\) | |||||||
\(860\) | 36.6649 | 1.25026 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.79863 | −0.129382 | ||||||||
\(863\) | 52.4715 | 1.78615 | 0.893076 | − | 0.449906i | \(-0.148542\pi\) | ||||
0.893076 | + | 0.449906i | \(0.148542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.25068 | −0.178528 | ||||||||
\(866\) | 14.7670 | 0.501803 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.05398 | 0.103659 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3161 | 0.485083 | ||||||||
\(872\) | −3.24987 | −0.110055 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.54726 | −0.0861624 | ||||||||
\(875\) | 44.1069 | 1.49109 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8136 | −1.07427 | −0.537135 | − | 0.843496i | \(-0.680494\pi\) | ||||
−0.537135 | + | 0.843496i | \(0.680494\pi\) | |||||||
\(878\) | 5.23513 | 0.176677 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3806 | −0.989858 | −0.494929 | − | 0.868933i | \(-0.664806\pi\) | ||||
−0.494929 | + | 0.868933i | \(0.664806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.606382 | −0.0204064 | −0.0102032 | − | 0.999948i | \(-0.503248\pi\) | ||||
−0.0102032 | + | 0.999948i | \(0.503248\pi\) | |||||||
\(884\) | −29.1279 | −0.979676 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.3298 | 0.548611 | ||||||||
\(887\) | −7.56882 | −0.254136 | −0.127068 | − | 0.991894i | \(-0.540557\pi\) | ||||
−0.127068 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.1353 | 0.742393 | ||||||||
\(890\) | 23.1796 | 0.776984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.6630 | −1.36150 | ||||||||
\(893\) | 6.81005 | 0.227890 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.8835 | −1.06575 | ||||||||
\(896\) | 41.7420 | 1.39450 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.0805 | 0.770206 | ||||||||
\(899\) | 3.93925 | 0.131381 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.3977 | 0.846119 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −37.3261 | −1.24145 | ||||||||
\(905\) | 1.96415 | 0.0652905 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.7730 | −1.02180 | −0.510900 | − | 0.859640i | \(-0.670688\pi\) | ||||
−0.510900 | + | 0.859640i | \(0.670688\pi\) | |||||||
\(908\) | 3.91923 | 0.130064 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 34.4744 | 1.14281 | ||||||||
\(911\) | −11.6236 | −0.385106 | −0.192553 | − | 0.981287i | \(-0.561677\pi\) | ||||
−0.192553 | + | 0.981287i | \(0.561677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.78420 | 0.224401 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.1879 | −1.12960 | ||||||||
\(917\) | −42.3916 | −1.39989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0118 | 1.05597 | 0.527986 | − | 0.849253i | \(-0.322947\pi\) | ||||
0.527986 | + | 0.849253i | \(0.322947\pi\) | |||||||
\(920\) | 36.9702 | 1.21887 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.57076 | −0.0846636 | ||||||||
\(923\) | 17.6464 | 0.580838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.39793 | 0.0459637 | ||||||||
\(926\) | 20.1474 | 0.662084 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 44.2088 | 1.45122 | ||||||||
\(929\) | −16.0439 | −0.526384 | −0.263192 | − | 0.964744i | \(-0.584775\pi\) | ||||
−0.263192 | + | 0.964744i | \(0.584775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.18051 | 0.137011 | ||||||||
\(932\) | −28.3108 | −0.927350 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.35395 | −0.273350 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.7829 | −0.940296 | −0.470148 | − | 0.882588i | \(-0.655799\pi\) | ||||
−0.470148 | + | 0.882588i | \(0.655799\pi\) | |||||||
\(938\) | 6.28804 | 0.205312 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.8904 | −1.39893 | ||||||||
\(941\) | 32.0887 | 1.04606 | 0.523032 | − | 0.852313i | \(-0.324801\pi\) | ||||
0.523032 | + | 0.852313i | \(0.324801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3554 | 0.825687 | ||||||||
\(944\) | 15.0877 | 0.491062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8805 | 1.03598 | 0.517989 | − | 0.855387i | \(-0.326681\pi\) | ||||
0.517989 | + | 0.855387i | \(0.326681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.7895 | 2.23300 | ||||||||
\(950\) | −0.0885288 | −0.00287225 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.4827 | −0.955540 | ||||||||
\(953\) | −33.5509 | −1.08682 | −0.543410 | − | 0.839468i | \(-0.682867\pi\) | ||||
−0.543410 | + | 0.839468i | \(0.682867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.5654 | 0.568403 | ||||||||
\(956\) | 10.0881 | 0.326271 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.1974 | 0.684856 | ||||||||
\(959\) | −70.2412 | −2.26821 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7333 | −0.991395 | ||||||||
\(962\) | 23.4763 | 0.756908 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.6685 | −0.343609 | ||||||||
\(965\) | −2.61949 | −0.0843245 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3428 | 0.557708 | 0.278854 | − | 0.960333i | \(-0.410045\pi\) | ||||
0.278854 | + | 0.960333i | \(0.410045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.61447 | −0.308702 | ||||||||
\(971\) | 42.3522 | 1.35915 | 0.679573 | − | 0.733608i | \(-0.262165\pi\) | ||||
0.679573 | + | 0.733608i | \(0.262165\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 79.4906 | 2.54835 | ||||||||
\(974\) | 9.38051 | 0.300571 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.48158 | −0.207470 | ||||||||
\(977\) | 0.820225 | 0.0262413 | 0.0131207 | − | 0.999914i | \(-0.495823\pi\) | ||||
0.0131207 | + | 0.999914i | \(0.495823\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −26.3293 | −0.841058 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.76054 | 0.183826 | ||||||||
\(983\) | 31.2508 | 0.996747 | 0.498374 | − | 0.866962i | \(-0.333931\pi\) | ||||
0.498374 | + | 0.866962i | \(0.333931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.5837 | 1.80291 | ||||||||
\(986\) | −16.5024 | −0.525542 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.88317 | 0.155354 | ||||||||
\(989\) | 77.0078 | 2.44871 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.89850 | 0.155606 | 0.0778030 | − | 0.996969i | \(-0.475209\pi\) | ||||
0.0778030 | + | 0.996969i | \(0.475209\pi\) | |||||||
\(992\) | 2.99355 | 0.0950452 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.75079 | 0.245840 | ||||||||
\(995\) | −13.2762 | −0.420885 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6834 | −0.686721 | −0.343360 | − | 0.939204i | \(-0.611565\pi\) | ||||
−0.343360 | + | 0.939204i | \(0.611565\pi\) | |||||||
\(998\) | −16.9026 | −0.535044 | ||||||||
\(999\) | 0 | 0 |
(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 | 9801.2.a.bx.1.6 | yes | 8 | |
3.2 | odd | 2 | 9801.2.a.by.1.3 | yes | 8 | ||
11.10 | odd | 2 | 9801.2.a.by.1.4 | yes | 8 | ||
33.32 | even | 2 | inner | 9801.2.a.bx.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9801.2.a.bx.1.5 | ✓ | 8 | 33.32 | even | 2 | inner | |
9801.2.a.bx.1.6 | yes | 8 | 1.1 | even | 1 | trivial | |
9801.2.a.by.1.3 | yes | 8 | 3.2 | odd | 2 | ||
9801.2.a.by.1.4 | yes | 8 | 11.10 | odd | 2 |