Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,2,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, 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("2450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.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: | \(19.5633484952\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.44949 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949 | 1.00000 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | −2.44949 | −0.707107 | ||||||||
\(13\) | 0.449490 | 0.124666 | 0.0623330 | − | 0.998055i | \(-0.480146\pi\) | ||||
0.0623330 | + | 0.998055i | \(0.480146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −6.44949 | −1.47961 | −0.739807 | − | 0.672819i | \(-0.765083\pi\) | ||||
−0.739807 | + | 0.672819i | \(0.765083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.89898 | −1.04447 | ||||||||
\(23\) | −6.89898 | −1.43854 | −0.719268 | − | 0.694732i | \(-0.755523\pi\) | ||||
−0.719268 | + | 0.694732i | \(0.755523\pi\) | |||||||
\(24\) | 2.44949 | 0.500000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.449490 | −0.0881522 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89898 | −0.538327 | −0.269163 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269163 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.898979 | 0.161461 | 0.0807307 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807307 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −12.0000 | −2.08893 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 6.44949 | 1.04625 | ||||||||
\(39\) | −1.10102 | −0.176304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8990 | 1.70213 | 0.851067 | − | 0.525057i | \(-0.175956\pi\) | ||||
0.851067 | + | 0.525057i | \(0.175956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.89898 | 1.35708 | 0.678541 | − | 0.734563i | \(-0.262613\pi\) | ||||
0.678541 | + | 0.734563i | \(0.262613\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.89898 | 1.01720 | ||||||||
\(47\) | 0.898979 | 0.131130 | 0.0655648 | − | 0.997848i | \(-0.479115\pi\) | ||||
0.0655648 | + | 0.997848i | \(0.479115\pi\) | |||||||
\(48\) | −2.44949 | −0.353553 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | 0.685994 | ||||||||
\(52\) | 0.449490 | 0.0623330 | ||||||||
\(53\) | −1.10102 | −0.151237 | −0.0756184 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756184 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.7980 | 2.09249 | ||||||||
\(58\) | 2.89898 | 0.380655 | ||||||||
\(59\) | 6.44949 | 0.839652 | 0.419826 | − | 0.907605i | \(-0.362091\pi\) | ||||
0.419826 | + | 0.907605i | \(0.362091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.44949 | −1.08185 | −0.540923 | − | 0.841072i | \(-0.681925\pi\) | ||||
−0.540923 | + | 0.841072i | \(0.681925\pi\) | |||||||
\(62\) | −0.898979 | −0.114171 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.0000 | 1.47710 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 16.8990 | 2.03440 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8990 | −1.29347 | −0.646735 | − | 0.762714i | \(-0.723866\pi\) | ||||
−0.646735 | + | 0.762714i | \(0.723866\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | 6.89898 | 0.807464 | 0.403732 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403732 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.44949 | −0.739807 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.10102 | 0.124666 | ||||||||
\(79\) | −2.89898 | −0.326161 | −0.163080 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163080 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −10.8990 | −1.20359 | ||||||||
\(83\) | −2.44949 | −0.268866 | −0.134433 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134433 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.89898 | −0.959602 | ||||||||
\(87\) | 7.10102 | 0.761309 | ||||||||
\(88\) | −4.89898 | −0.522233 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.89898 | −0.719268 | ||||||||
\(93\) | −2.20204 | −0.228341 | ||||||||
\(94\) | −0.898979 | −0.0927227 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.44949 | 0.250000 | ||||||||
\(97\) | 3.79796 | 0.385624 | 0.192812 | − | 0.981236i | \(-0.438239\pi\) | ||||
0.192812 | + | 0.981236i | \(0.438239\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.6969 | 1.47710 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | −4.89898 | −0.485071 | ||||||||
\(103\) | −3.10102 | −0.305553 | −0.152776 | − | 0.988261i | \(-0.548821\pi\) | ||||
−0.152776 | + | 0.988261i | \(0.548821\pi\) | |||||||
\(104\) | −0.449490 | −0.0440761 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.10102 | 0.106941 | ||||||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.89898 | −0.277672 | −0.138836 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138836 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.89898 | −0.464991 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.202041 | 0.0190064 | 0.00950321 | − | 0.999955i | \(-0.496975\pi\) | ||||
0.00950321 | + | 0.999955i | \(0.496975\pi\) | |||||||
\(114\) | −15.7980 | −1.47961 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.89898 | −0.269163 | ||||||||
\(117\) | 1.34847 | 0.124666 | ||||||||
\(118\) | −6.44949 | −0.593724 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 8.44949 | 0.764981 | ||||||||
\(123\) | −26.6969 | −2.40718 | ||||||||
\(124\) | 0.898979 | 0.0807307 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.10102 | −0.452642 | −0.226321 | − | 0.974053i | \(-0.572670\pi\) | ||||
−0.226321 | + | 0.974053i | \(0.572670\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −21.7980 | −1.91920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.55051 | 0.135469 | 0.0677344 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677344 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(132\) | −12.0000 | −1.04447 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | 17.7980 | 1.52058 | 0.760291 | − | 0.649582i | \(-0.225056\pi\) | ||||
0.760291 | + | 0.649582i | \(0.225056\pi\) | |||||||
\(138\) | −16.8990 | −1.43854 | ||||||||
\(139\) | −6.44949 | −0.547039 | −0.273519 | − | 0.961867i | \(-0.588188\pi\) | ||||
−0.273519 | + | 0.961867i | \(0.588188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20204 | −0.185445 | ||||||||
\(142\) | 10.8990 | 0.914622 | ||||||||
\(143\) | 2.20204 | 0.184144 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.89898 | −0.570964 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 15.7980 | 1.29422 | 0.647110 | − | 0.762397i | \(-0.275978\pi\) | ||||
0.647110 | + | 0.762397i | \(0.275978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5959 | −1.59469 | −0.797347 | − | 0.603522i | \(-0.793764\pi\) | ||||
−0.797347 | + | 0.603522i | \(0.793764\pi\) | |||||||
\(152\) | 6.44949 | 0.523123 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.10102 | −0.0881522 | ||||||||
\(157\) | −8.44949 | −0.674343 | −0.337171 | − | 0.941443i | \(-0.609470\pi\) | ||||
−0.337171 | + | 0.941443i | \(0.609470\pi\) | |||||||
\(158\) | 2.89898 | 0.230630 | ||||||||
\(159\) | 2.69694 | 0.213881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | −16.8990 | −1.32363 | −0.661815 | − | 0.749667i | \(-0.730214\pi\) | ||||
−0.661815 | + | 0.749667i | \(0.730214\pi\) | |||||||
\(164\) | 10.8990 | 0.851067 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.44949 | 0.190117 | ||||||||
\(167\) | −4.89898 | −0.379094 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.3485 | −1.47961 | ||||||||
\(172\) | 8.89898 | 0.678541 | ||||||||
\(173\) | −18.2474 | −1.38733 | −0.693664 | − | 0.720299i | \(-0.744005\pi\) | ||||
−0.693664 | + | 0.720299i | \(0.744005\pi\) | |||||||
\(174\) | −7.10102 | −0.538327 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.89898 | 0.369274 | ||||||||
\(177\) | −15.7980 | −1.18745 | ||||||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | −5.79796 | −0.433360 | −0.216680 | − | 0.976243i | \(-0.569523\pi\) | ||||
−0.216680 | + | 0.976243i | \(0.569523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2474 | −1.05900 | −0.529502 | − | 0.848309i | \(-0.677621\pi\) | ||||
−0.529502 | + | 0.848309i | \(0.677621\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.6969 | 1.52996 | ||||||||
\(184\) | 6.89898 | 0.508600 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.20204 | 0.161461 | ||||||||
\(187\) | −9.79796 | −0.716498 | ||||||||
\(188\) | 0.898979 | 0.0655648 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6969 | −1.20815 | −0.604074 | − | 0.796928i | \(-0.706457\pi\) | ||||
−0.604074 | + | 0.796928i | \(0.706457\pi\) | |||||||
\(192\) | −2.44949 | −0.176777 | ||||||||
\(193\) | 17.5959 | 1.26658 | 0.633291 | − | 0.773914i | \(-0.281704\pi\) | ||||
0.633291 | + | 0.773914i | \(0.281704\pi\) | |||||||
\(194\) | −3.79796 | −0.272678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.10102 | 0.648421 | 0.324210 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324210 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(198\) | −14.6969 | −1.04447 | ||||||||
\(199\) | −7.10102 | −0.503378 | −0.251689 | − | 0.967808i | \(-0.580986\pi\) | ||||
−0.251689 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5959 | 1.38219 | ||||||||
\(202\) | 8.44949 | 0.594504 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.89898 | 0.342997 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.10102 | 0.216058 | ||||||||
\(207\) | −20.6969 | −1.43854 | ||||||||
\(208\) | 0.449490 | 0.0311665 | ||||||||
\(209\) | −31.5959 | −2.18554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | −1.10102 | −0.0756184 | ||||||||
\(213\) | 26.6969 | 1.82924 | ||||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.89898 | 0.196344 | ||||||||
\(219\) | −16.8990 | −1.14193 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.898979 | −0.0604719 | ||||||||
\(222\) | 4.89898 | 0.328798 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.202041 | −0.0134396 | ||||||||
\(227\) | 7.34847 | 0.487735 | 0.243868 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(228\) | 15.7980 | 1.04625 | ||||||||
\(229\) | −15.1464 | −1.00090 | −0.500452 | − | 0.865764i | \(-0.666833\pi\) | ||||
−0.500452 | + | 0.865764i | \(0.666833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.89898 | 0.190327 | ||||||||
\(233\) | 10.2020 | 0.668358 | 0.334179 | − | 0.942510i | \(-0.391541\pi\) | ||||
0.334179 | + | 0.942510i | \(0.391541\pi\) | |||||||
\(234\) | −1.34847 | −0.0881522 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.44949 | 0.419826 | ||||||||
\(237\) | 7.10102 | 0.461261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.7980 | −1.66873 | −0.834366 | − | 0.551211i | \(-0.814166\pi\) | ||||
−0.834366 | + | 0.551211i | \(0.814166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6969 | −1.33321 | −0.666604 | − | 0.745412i | \(-0.732253\pi\) | ||||
−0.666604 | + | 0.745412i | \(0.732253\pi\) | |||||||
\(242\) | −13.0000 | −0.835672 | ||||||||
\(243\) | 22.0454 | 1.41421 | ||||||||
\(244\) | −8.44949 | −0.540923 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.6969 | 1.70213 | ||||||||
\(247\) | −2.89898 | −0.184458 | ||||||||
\(248\) | −0.898979 | −0.0570853 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.55051 | 0.0978673 | 0.0489337 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489337 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.7980 | −2.12486 | ||||||||
\(254\) | 5.10102 | 0.320066 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.6969 | −1.29104 | −0.645520 | − | 0.763744i | \(-0.723359\pi\) | ||||
−0.645520 | + | 0.763744i | \(0.723359\pi\) | |||||||
\(258\) | 21.7980 | 1.35708 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.69694 | −0.538327 | ||||||||
\(262\) | −1.55051 | −0.0957908 | ||||||||
\(263\) | −9.79796 | −0.604168 | −0.302084 | − | 0.953281i | \(-0.597682\pi\) | ||||
−0.302084 | + | 0.953281i | \(0.597682\pi\) | |||||||
\(264\) | 12.0000 | 0.738549 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.4949 | −1.49906 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | 15.1464 | 0.923494 | 0.461747 | − | 0.887012i | \(-0.347223\pi\) | ||||
0.461747 | + | 0.887012i | \(0.347223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.7980 | −1.07521 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 16.8990 | 1.01720 | ||||||||
\(277\) | −5.10102 | −0.306491 | −0.153245 | − | 0.988188i | \(-0.548972\pi\) | ||||
−0.153245 | + | 0.988188i | \(0.548972\pi\) | |||||||
\(278\) | 6.44949 | 0.386815 | ||||||||
\(279\) | 2.69694 | 0.161461 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 2.20204 | 0.131130 | ||||||||
\(283\) | −28.2474 | −1.67914 | −0.839568 | − | 0.543254i | \(-0.817192\pi\) | ||||
−0.839568 | + | 0.543254i | \(0.817192\pi\) | |||||||
\(284\) | −10.8990 | −0.646735 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.20204 | −0.130209 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.30306 | −0.545355 | ||||||||
\(292\) | 6.89898 | 0.403732 | ||||||||
\(293\) | 6.24745 | 0.364980 | 0.182490 | − | 0.983208i | \(-0.441584\pi\) | ||||
0.182490 | + | 0.983208i | \(0.441584\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.7980 | −0.915151 | ||||||||
\(299\) | −3.10102 | −0.179337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.5959 | 1.12762 | ||||||||
\(303\) | 20.6969 | 1.18901 | ||||||||
\(304\) | −6.44949 | −0.369904 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | 0.342997 | ||||||||
\(307\) | −4.24745 | −0.242415 | −0.121207 | − | 0.992627i | \(-0.538677\pi\) | ||||
−0.121207 | + | 0.992627i | \(0.538677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.59592 | 0.432117 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 1.10102 | 0.0623330 | ||||||||
\(313\) | −17.5959 | −0.994580 | −0.497290 | − | 0.867584i | \(-0.665672\pi\) | ||||
−0.497290 | + | 0.867584i | \(0.665672\pi\) | |||||||
\(314\) | 8.44949 | 0.476832 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.89898 | −0.163080 | ||||||||
\(317\) | 26.4949 | 1.48810 | 0.744051 | − | 0.668123i | \(-0.232902\pi\) | ||||
0.744051 | + | 0.668123i | \(0.232902\pi\) | |||||||
\(318\) | −2.69694 | −0.151237 | ||||||||
\(319\) | −14.2020 | −0.795162 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.5959 | 1.09374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8990 | 0.717718 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.8990 | 0.935948 | ||||||||
\(327\) | 7.10102 | 0.392687 | ||||||||
\(328\) | −10.8990 | −0.601795 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6969 | 0.587957 | 0.293978 | − | 0.955812i | \(-0.405021\pi\) | ||||
0.293978 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(332\) | −2.44949 | −0.134433 | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | 4.89898 | 0.268060 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.5959 | −1.61219 | −0.806096 | − | 0.591785i | \(-0.798424\pi\) | ||||
−0.806096 | + | 0.591785i | \(0.798424\pi\) | |||||||
\(338\) | 12.7980 | 0.696117 | ||||||||
\(339\) | −0.494897 | −0.0268791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.40408 | 0.238494 | ||||||||
\(342\) | 19.3485 | 1.04625 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.89898 | −0.479801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.2474 | 0.980989 | ||||||||
\(347\) | 19.1010 | 1.02540 | 0.512698 | − | 0.858569i | \(-0.328646\pi\) | ||||
0.512698 | + | 0.858569i | \(0.328646\pi\) | |||||||
\(348\) | 7.10102 | 0.380655 | ||||||||
\(349\) | 3.55051 | 0.190054 | 0.0950272 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950272 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.89898 | −0.261116 | ||||||||
\(353\) | −13.1010 | −0.697297 | −0.348648 | − | 0.937254i | \(-0.613359\pi\) | ||||
−0.348648 | + | 0.937254i | \(0.613359\pi\) | |||||||
\(354\) | 15.7980 | 0.839652 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.79796 | 0.306432 | ||||||||
\(359\) | 11.5959 | 0.612009 | 0.306005 | − | 0.952030i | \(-0.401008\pi\) | ||||
0.306005 | + | 0.952030i | \(0.401008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | 14.2474 | 0.748829 | ||||||||
\(363\) | −31.8434 | −1.67134 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.6969 | −1.08185 | ||||||||
\(367\) | −32.0000 | −1.67039 | −0.835193 | − | 0.549957i | \(-0.814644\pi\) | ||||
−0.835193 | + | 0.549957i | \(0.814644\pi\) | |||||||
\(368\) | −6.89898 | −0.359634 | ||||||||
\(369\) | 32.6969 | 1.70213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.20204 | −0.114171 | ||||||||
\(373\) | 24.6969 | 1.27876 | 0.639380 | − | 0.768891i | \(-0.279191\pi\) | ||||
0.639380 | + | 0.768891i | \(0.279191\pi\) | |||||||
\(374\) | 9.79796 | 0.506640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.898979 | −0.0463613 | ||||||||
\(377\) | −1.30306 | −0.0671111 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30306 | 0.0669338 | 0.0334669 | − | 0.999440i | \(-0.489345\pi\) | ||||
0.0334669 | + | 0.999440i | \(0.489345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4949 | 0.640133 | ||||||||
\(382\) | 16.6969 | 0.854290 | ||||||||
\(383\) | 16.8990 | 0.863498 | 0.431749 | − | 0.901994i | \(-0.357897\pi\) | ||||
0.431749 | + | 0.901994i | \(0.357897\pi\) | |||||||
\(384\) | 2.44949 | 0.125000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.5959 | −0.895609 | ||||||||
\(387\) | 26.6969 | 1.35708 | ||||||||
\(388\) | 3.79796 | 0.192812 | ||||||||
\(389\) | 22.8990 | 1.16102 | 0.580512 | − | 0.814252i | \(-0.302852\pi\) | ||||
0.580512 | + | 0.814252i | \(0.302852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7980 | 0.697793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.79796 | −0.191582 | ||||||||
\(394\) | −9.10102 | −0.458503 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.6969 | 0.738549 | ||||||||
\(397\) | 17.3485 | 0.870695 | 0.435347 | − | 0.900263i | \(-0.356626\pi\) | ||||
0.435347 | + | 0.900263i | \(0.356626\pi\) | |||||||
\(398\) | 7.10102 | 0.355942 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3939 | 1.46786 | 0.733930 | − | 0.679225i | \(-0.237684\pi\) | ||||
0.733930 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(402\) | −19.5959 | −0.977356 | ||||||||
\(403\) | 0.404082 | 0.0201288 | ||||||||
\(404\) | −8.44949 | −0.420378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.79796 | 0.485667 | ||||||||
\(408\) | −4.89898 | −0.242536 | ||||||||
\(409\) | 14.4949 | 0.716727 | 0.358363 | − | 0.933582i | \(-0.383335\pi\) | ||||
0.358363 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.5959 | −2.15043 | ||||||||
\(412\) | −3.10102 | −0.152776 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 20.6969 | 1.01720 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.449490 | −0.0220380 | ||||||||
\(417\) | 15.7980 | 0.773629 | ||||||||
\(418\) | 31.5959 | 1.54541 | ||||||||
\(419\) | 6.44949 | 0.315078 | 0.157539 | − | 0.987513i | \(-0.449644\pi\) | ||||
0.157539 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7980 | −1.15984 | −0.579921 | − | 0.814673i | \(-0.696917\pi\) | ||||
−0.579921 | + | 0.814673i | \(0.696917\pi\) | |||||||
\(422\) | −12.0000 | −0.584151 | ||||||||
\(423\) | 2.69694 | 0.131130 | ||||||||
\(424\) | 1.10102 | 0.0534703 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −26.6969 | −1.29347 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | −5.39388 | −0.260419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7980 | 0.857298 | 0.428649 | − | 0.903471i | \(-0.358990\pi\) | ||||
0.428649 | + | 0.903471i | \(0.358990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7980 | 0.951429 | 0.475715 | − | 0.879600i | \(-0.342190\pi\) | ||||
0.475715 | + | 0.879600i | \(0.342190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.89898 | −0.138836 | ||||||||
\(437\) | 44.4949 | 2.12848 | ||||||||
\(438\) | 16.8990 | 0.807464 | ||||||||
\(439\) | −37.3939 | −1.78471 | −0.892356 | − | 0.451332i | \(-0.850949\pi\) | ||||
−0.892356 | + | 0.451332i | \(0.850949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.898979 | 0.0427601 | ||||||||
\(443\) | −9.79796 | −0.465515 | −0.232758 | − | 0.972535i | \(-0.574775\pi\) | ||||
−0.232758 | + | 0.972535i | \(0.574775\pi\) | |||||||
\(444\) | −4.89898 | −0.232495 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | −38.6969 | −1.83030 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.3939 | 2.51422 | ||||||||
\(452\) | 0.202041 | 0.00950321 | ||||||||
\(453\) | 48.0000 | 2.25524 | ||||||||
\(454\) | −7.34847 | −0.344881 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.7980 | −0.739807 | ||||||||
\(457\) | −9.59592 | −0.448878 | −0.224439 | − | 0.974488i | \(-0.572055\pi\) | ||||
−0.224439 | + | 0.974488i | \(0.572055\pi\) | |||||||
\(458\) | 15.1464 | 0.707746 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.65153 | −0.123494 | −0.0617470 | − | 0.998092i | \(-0.519667\pi\) | ||||
−0.0617470 | + | 0.998092i | \(0.519667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.5959 | −1.65428 | −0.827141 | − | 0.561994i | \(-0.810034\pi\) | ||||
−0.827141 | + | 0.561994i | \(0.810034\pi\) | |||||||
\(464\) | −2.89898 | −0.134582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.2020 | −0.472600 | ||||||||
\(467\) | −5.55051 | −0.256847 | −0.128423 | − | 0.991719i | \(-0.540992\pi\) | ||||
−0.128423 | + | 0.991719i | \(0.540992\pi\) | |||||||
\(468\) | 1.34847 | 0.0623330 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.6969 | 0.953665 | ||||||||
\(472\) | −6.44949 | −0.296862 | ||||||||
\(473\) | 43.5959 | 2.00454 | ||||||||
\(474\) | −7.10102 | −0.326161 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.30306 | −0.151237 | ||||||||
\(478\) | 25.7980 | 1.17997 | ||||||||
\(479\) | −38.6969 | −1.76811 | −0.884054 | − | 0.467385i | \(-0.845196\pi\) | ||||
−0.884054 | + | 0.467385i | \(0.845196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.898979 | 0.0409899 | ||||||||
\(482\) | 20.6969 | 0.942720 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.0000 | 0.590909 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −1.00000 | ||||||||
\(487\) | −36.6969 | −1.66290 | −0.831449 | − | 0.555602i | \(-0.812488\pi\) | ||||
−0.831449 | + | 0.555602i | \(0.812488\pi\) | |||||||
\(488\) | 8.44949 | 0.382490 | ||||||||
\(489\) | 41.3939 | 1.87190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5959 | −0.884351 | −0.442176 | − | 0.896928i | \(-0.645793\pi\) | ||||
−0.442176 | + | 0.896928i | \(0.645793\pi\) | |||||||
\(492\) | −26.6969 | −1.20359 | ||||||||
\(493\) | 5.79796 | 0.261127 | ||||||||
\(494\) | 2.89898 | 0.130431 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.898979 | 0.0403654 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.00000 | −0.268866 | ||||||||
\(499\) | 25.7980 | 1.15488 | 0.577438 | − | 0.816435i | \(-0.304053\pi\) | ||||
0.577438 | + | 0.816435i | \(0.304053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | −1.55051 | −0.0692027 | ||||||||
\(503\) | 4.00000 | 0.178351 | 0.0891756 | − | 0.996016i | \(-0.471577\pi\) | ||||
0.0891756 | + | 0.996016i | \(0.471577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.7980 | 1.50250 | ||||||||
\(507\) | 31.3485 | 1.39223 | ||||||||
\(508\) | −5.10102 | −0.226321 | ||||||||
\(509\) | 36.4495 | 1.61560 | 0.807798 | − | 0.589460i | \(-0.200659\pi\) | ||||
0.807798 | + | 0.589460i | \(0.200659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.6969 | 0.912903 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.7980 | −0.959602 | ||||||||
\(517\) | 4.40408 | 0.193691 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.6969 | 1.96198 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.30306 | −0.144710 | −0.0723549 | − | 0.997379i | \(-0.523051\pi\) | ||||
−0.0723549 | + | 0.997379i | \(0.523051\pi\) | |||||||
\(522\) | 8.69694 | 0.380655 | ||||||||
\(523\) | −1.14643 | −0.0501298 | −0.0250649 | − | 0.999686i | \(-0.507979\pi\) | ||||
−0.0250649 | + | 0.999686i | \(0.507979\pi\) | |||||||
\(524\) | 1.55051 | 0.0677344 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.79796 | 0.427211 | ||||||||
\(527\) | −1.79796 | −0.0783203 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | 24.5959 | 1.06939 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.3485 | 0.839652 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.89898 | 0.212198 | ||||||||
\(534\) | 24.4949 | 1.06000 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | 14.2020 | 0.612863 | ||||||||
\(538\) | −15.1464 | −0.653009 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5959 | −1.27243 | −0.636214 | − | 0.771513i | \(-0.719500\pi\) | ||||
−0.636214 | + | 0.771513i | \(0.719500\pi\) | |||||||
\(542\) | 12.0000 | 0.515444 | ||||||||
\(543\) | 34.8990 | 1.49766 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6969 | 0.457368 | 0.228684 | − | 0.973501i | \(-0.426558\pi\) | ||||
0.228684 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(548\) | 17.7980 | 0.760291 | ||||||||
\(549\) | −25.3485 | −1.08185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.6969 | 0.796516 | ||||||||
\(552\) | −16.8990 | −0.719268 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.10102 | 0.216722 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.44949 | −0.273519 | ||||||||
\(557\) | −16.6969 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(558\) | −2.69694 | −0.114171 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | −14.0454 | −0.591943 | −0.295972 | − | 0.955197i | \(-0.595643\pi\) | ||||
−0.295972 | + | 0.955197i | \(0.595643\pi\) | |||||||
\(564\) | −2.20204 | −0.0927227 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.2474 | 1.18733 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.8990 | 0.457311 | ||||||||
\(569\) | 14.2020 | 0.595381 | 0.297690 | − | 0.954663i | \(-0.403784\pi\) | ||||
0.297690 | + | 0.954663i | \(0.403784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8990 | −0.874595 | −0.437298 | − | 0.899317i | \(-0.644064\pi\) | ||||
−0.437298 | + | 0.899317i | \(0.644064\pi\) | |||||||
\(572\) | 2.20204 | 0.0920720 | ||||||||
\(573\) | 40.8990 | 1.70858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | −46.4949 | −1.93561 | −0.967804 | − | 0.251705i | \(-0.919009\pi\) | ||||
−0.967804 | + | 0.251705i | \(0.919009\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | −43.1010 | −1.79122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.30306 | 0.385624 | ||||||||
\(583\) | −5.39388 | −0.223392 | ||||||||
\(584\) | −6.89898 | −0.285482 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.24745 | −0.258080 | ||||||||
\(587\) | 33.1464 | 1.36810 | 0.684050 | − | 0.729435i | \(-0.260217\pi\) | ||||
0.684050 | + | 0.729435i | \(0.260217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79796 | −0.238901 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.2929 | −0.917006 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 1.10102 | 0.0452135 | 0.0226067 | − | 0.999744i | \(-0.492803\pi\) | ||||
0.0226067 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.7980 | 0.647110 | ||||||||
\(597\) | 17.3939 | 0.711884 | ||||||||
\(598\) | 3.10102 | 0.126810 | ||||||||
\(599\) | −22.8990 | −0.935627 | −0.467813 | − | 0.883827i | \(-0.654958\pi\) | ||||
−0.467813 | + | 0.883827i | \(0.654958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3939 | −0.791093 | −0.395546 | − | 0.918446i | \(-0.629445\pi\) | ||||
−0.395546 | + | 0.918446i | \(0.629445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0000 | −0.977356 | ||||||||
\(604\) | −19.5959 | −0.797347 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.6969 | −0.840756 | ||||||||
\(607\) | 25.3939 | 1.03071 | 0.515353 | − | 0.856978i | \(-0.327661\pi\) | ||||
0.515353 | + | 0.856978i | \(0.327661\pi\) | |||||||
\(608\) | 6.44949 | 0.261561 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.404082 | 0.0163474 | ||||||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | −8.20204 | −0.331277 | −0.165639 | − | 0.986187i | \(-0.552969\pi\) | ||||
−0.165639 | + | 0.986187i | \(0.552969\pi\) | |||||||
\(614\) | 4.24745 | 0.171413 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.59592 | −0.386317 | −0.193159 | − | 0.981168i | \(-0.561873\pi\) | ||||
−0.193159 | + | 0.981168i | \(0.561873\pi\) | |||||||
\(618\) | −7.59592 | −0.305553 | ||||||||
\(619\) | 46.4495 | 1.86696 | 0.933481 | − | 0.358626i | \(-0.116755\pi\) | ||||
0.933481 | + | 0.358626i | \(0.116755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.10102 | −0.0440761 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.5959 | 0.703274 | ||||||||
\(627\) | 77.3939 | 3.09081 | ||||||||
\(628\) | −8.44949 | −0.337171 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.49490 | 0.258558 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(632\) | 2.89898 | 0.115315 | ||||||||
\(633\) | −29.3939 | −1.16830 | ||||||||
\(634\) | −26.4949 | −1.05225 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.69694 | 0.106941 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.2020 | 0.562264 | ||||||||
\(639\) | −32.6969 | −1.29347 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.20204 | 0.244966 | 0.122483 | − | 0.992471i | \(-0.460914\pi\) | ||||
0.122483 | + | 0.992471i | \(0.460914\pi\) | |||||||
\(642\) | −19.5959 | −0.773389 | ||||||||
\(643\) | 9.14643 | 0.360700 | 0.180350 | − | 0.983603i | \(-0.442277\pi\) | ||||
0.180350 | + | 0.983603i | \(0.442277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8990 | −0.507504 | ||||||||
\(647\) | −22.2929 | −0.876423 | −0.438211 | − | 0.898872i | \(-0.644388\pi\) | ||||
−0.438211 | + | 0.898872i | \(0.644388\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 31.5959 | 1.24025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.8990 | −0.661815 | ||||||||
\(653\) | −39.7980 | −1.55741 | −0.778707 | − | 0.627387i | \(-0.784124\pi\) | ||||
−0.778707 | + | 0.627387i | \(0.784124\pi\) | |||||||
\(654\) | −7.10102 | −0.277672 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.8990 | 0.425534 | ||||||||
\(657\) | 20.6969 | 0.807464 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.10102 | 0.276616 | 0.138308 | − | 0.990389i | \(-0.455834\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9444 | −0.503478 | −0.251739 | − | 0.967795i | \(-0.581003\pi\) | ||||
−0.251739 | + | 0.967795i | \(0.581003\pi\) | |||||||
\(662\) | −10.6969 | −0.415748 | ||||||||
\(663\) | 2.20204 | 0.0855202 | ||||||||
\(664\) | 2.44949 | 0.0950586 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | 20.0000 | 0.774403 | ||||||||
\(668\) | −4.89898 | −0.189547 | ||||||||
\(669\) | −9.79796 | −0.378811 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.3939 | −1.59799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.79796 | 0.0693062 | 0.0346531 | − | 0.999399i | \(-0.488967\pi\) | ||||
0.0346531 | + | 0.999399i | \(0.488967\pi\) | |||||||
\(674\) | 29.5959 | 1.13999 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7980 | −0.492229 | ||||||||
\(677\) | 31.5505 | 1.21258 | 0.606292 | − | 0.795242i | \(-0.292656\pi\) | ||||
0.606292 | + | 0.795242i | \(0.292656\pi\) | |||||||
\(678\) | 0.494897 | 0.0190064 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | −4.40408 | −0.168641 | ||||||||
\(683\) | −35.5959 | −1.36204 | −0.681020 | − | 0.732265i | \(-0.738463\pi\) | ||||
−0.681020 | + | 0.732265i | \(0.738463\pi\) | |||||||
\(684\) | −19.3485 | −0.739807 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.1010 | 1.41549 | ||||||||
\(688\) | 8.89898 | 0.339270 | ||||||||
\(689\) | −0.494897 | −0.0188541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1464 | 0.500114 | 0.250057 | − | 0.968231i | \(-0.419551\pi\) | ||||
0.250057 | + | 0.968231i | \(0.419551\pi\) | |||||||
\(692\) | −18.2474 | −0.693664 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1010 | −0.725065 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.10102 | −0.269163 | ||||||||
\(697\) | −21.7980 | −0.825657 | ||||||||
\(698\) | −3.55051 | −0.134389 | ||||||||
\(699\) | −24.9898 | −0.945201 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6969 | 1.53710 | 0.768551 | − | 0.639788i | \(-0.220978\pi\) | ||||
0.768551 | + | 0.639788i | \(0.220978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.8990 | −0.486494 | ||||||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.1010 | 0.493063 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.7980 | −0.593724 | ||||||||
\(709\) | 40.2929 | 1.51323 | 0.756615 | − | 0.653861i | \(-0.226852\pi\) | ||||
0.756615 | + | 0.653861i | \(0.226852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69694 | −0.326161 | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | −6.20204 | −0.232268 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.79796 | −0.216680 | ||||||||
\(717\) | 63.1918 | 2.35994 | ||||||||
\(718\) | −11.5959 | −0.432756 | ||||||||
\(719\) | −44.4949 | −1.65938 | −0.829690 | − | 0.558225i | \(-0.811483\pi\) | ||||
−0.829690 | + | 0.558225i | \(0.811483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −22.5959 | −0.840933 | ||||||||
\(723\) | 50.6969 | 1.88544 | ||||||||
\(724\) | −14.2474 | −0.529502 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.8434 | 1.18182 | ||||||||
\(727\) | 6.69694 | 0.248376 | 0.124188 | − | 0.992259i | \(-0.460367\pi\) | ||||
0.124188 | + | 0.992259i | \(0.460367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7980 | −0.658281 | ||||||||
\(732\) | 20.6969 | 0.764981 | ||||||||
\(733\) | 43.6413 | 1.61193 | 0.805965 | − | 0.591964i | \(-0.201647\pi\) | ||||
0.805965 | + | 0.591964i | \(0.201647\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.89898 | 0.254300 | ||||||||
\(737\) | −39.1918 | −1.44365 | ||||||||
\(738\) | −32.6969 | −1.20359 | ||||||||
\(739\) | −44.4949 | −1.63677 | −0.818386 | − | 0.574669i | \(-0.805131\pi\) | ||||
−0.818386 | + | 0.574669i | \(0.805131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.10102 | 0.260863 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3031 | −0.561415 | −0.280707 | − | 0.959793i | \(-0.590569\pi\) | ||||
−0.280707 | + | 0.959793i | \(0.590569\pi\) | |||||||
\(744\) | 2.20204 | 0.0807307 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.6969 | −0.904219 | ||||||||
\(747\) | −7.34847 | −0.268866 | ||||||||
\(748\) | −9.79796 | −0.358249 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2020 | −0.810164 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(752\) | 0.898979 | 0.0327824 | ||||||||
\(753\) | −3.79796 | −0.138405 | ||||||||
\(754\) | 1.30306 | 0.0474547 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2020 | −1.17040 | −0.585202 | − | 0.810888i | \(-0.698985\pi\) | ||||
−0.585202 | + | 0.810888i | \(0.698985\pi\) | |||||||
\(758\) | −1.30306 | −0.0473293 | ||||||||
\(759\) | 82.7878 | 3.00501 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.8990 | 1.12009 | 0.560044 | − | 0.828463i | \(-0.310784\pi\) | ||||
0.560044 | + | 0.828463i | \(0.310784\pi\) | |||||||
\(762\) | −12.4949 | −0.452642 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.6969 | −0.604074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.8990 | −0.610585 | ||||||||
\(767\) | 2.89898 | 0.104676 | ||||||||
\(768\) | −2.44949 | −0.0883883 | ||||||||
\(769\) | 11.3031 | 0.407599 | 0.203799 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203799 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.6969 | 1.82581 | ||||||||
\(772\) | 17.5959 | 0.633291 | ||||||||
\(773\) | 13.3485 | 0.480111 | 0.240056 | − | 0.970759i | \(-0.422834\pi\) | ||||
0.240056 | + | 0.970759i | \(0.422834\pi\) | |||||||
\(774\) | −26.6969 | −0.959602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.79796 | −0.136339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.8990 | −0.820968 | ||||||||
\(779\) | −70.2929 | −2.51850 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.3939 | −1.91058 | ||||||||
\(782\) | −13.7980 | −0.493414 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.79796 | 0.135469 | ||||||||
\(787\) | −45.5505 | −1.62370 | −0.811850 | − | 0.583866i | \(-0.801539\pi\) | ||||
−0.811850 | + | 0.583866i | \(0.801539\pi\) | |||||||
\(788\) | 9.10102 | 0.324210 | ||||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.6969 | −0.522233 | ||||||||
\(793\) | −3.79796 | −0.134869 | ||||||||
\(794\) | −17.3485 | −0.615674 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.10102 | −0.251689 | ||||||||
\(797\) | −52.9444 | −1.87539 | −0.937693 | − | 0.347464i | \(-0.887043\pi\) | ||||
−0.937693 | + | 0.347464i | \(0.887043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.79796 | −0.0636072 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.0000 | 1.06000 | ||||||||
\(802\) | −29.3939 | −1.03793 | ||||||||
\(803\) | 33.7980 | 1.19270 | ||||||||
\(804\) | 19.5959 | 0.691095 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.404082 | −0.0142332 | ||||||||
\(807\) | −37.1010 | −1.30602 | ||||||||
\(808\) | 8.44949 | 0.297252 | ||||||||
\(809\) | 8.40408 | 0.295472 | 0.147736 | − | 0.989027i | \(-0.452801\pi\) | ||||
0.147736 | + | 0.989027i | \(0.452801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.9444 | 1.36752 | 0.683761 | − | 0.729706i | \(-0.260343\pi\) | ||||
0.683761 | + | 0.729706i | \(0.260343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.3939 | 1.03089 | ||||||||
\(814\) | −9.79796 | −0.343418 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.89898 | 0.171499 | ||||||||
\(817\) | −57.3939 | −2.00796 | ||||||||
\(818\) | −14.4949 | −0.506802 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.7980 | 0.970155 | 0.485078 | − | 0.874471i | \(-0.338791\pi\) | ||||
0.485078 | + | 0.874471i | \(0.338791\pi\) | |||||||
\(822\) | 43.5959 | 1.52058 | ||||||||
\(823\) | 39.1918 | 1.36614 | 0.683071 | − | 0.730352i | \(-0.260644\pi\) | ||||
0.683071 | + | 0.730352i | \(0.260644\pi\) | |||||||
\(824\) | 3.10102 | 0.108029 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5959 | 0.820510 | 0.410255 | − | 0.911971i | \(-0.365440\pi\) | ||||
0.410255 | + | 0.911971i | \(0.365440\pi\) | |||||||
\(828\) | −20.6969 | −0.719268 | ||||||||
\(829\) | −39.6413 | −1.37680 | −0.688400 | − | 0.725331i | \(-0.741687\pi\) | ||||
−0.688400 | + | 0.725331i | \(0.741687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.4949 | 0.433443 | ||||||||
\(832\) | 0.449490 | 0.0155833 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.7980 | −0.547039 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −31.5959 | −1.09277 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.44949 | −0.222794 | ||||||||
\(839\) | −27.1010 | −0.935631 | −0.467816 | − | 0.883826i | \(-0.654959\pi\) | ||||
−0.467816 | + | 0.883826i | \(0.654959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | 23.7980 | 0.820132 | ||||||||
\(843\) | 44.0908 | 1.51857 | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.69694 | −0.0927227 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.10102 | −0.0378092 | ||||||||
\(849\) | 69.1918 | 2.37466 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.7980 | −0.472988 | ||||||||
\(852\) | 26.6969 | 0.914622 | ||||||||
\(853\) | −29.8434 | −1.02182 | −0.510909 | − | 0.859635i | \(-0.670691\pi\) | ||||
−0.510909 | + | 0.859635i | \(0.670691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | −25.1918 | −0.860537 | −0.430268 | − | 0.902701i | \(-0.641581\pi\) | ||||
−0.430268 | + | 0.902701i | \(0.641581\pi\) | |||||||
\(858\) | 5.39388 | 0.184144 | ||||||||
\(859\) | 29.6413 | 1.01135 | 0.505674 | − | 0.862724i | \(-0.331244\pi\) | ||||
0.505674 | + | 0.862724i | \(0.331244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.7980 | −0.606201 | ||||||||
\(863\) | 13.3939 | 0.455933 | 0.227966 | − | 0.973669i | \(-0.426792\pi\) | ||||
0.227966 | + | 0.973669i | \(0.426792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.7980 | −0.672762 | ||||||||
\(867\) | 31.8434 | 1.08146 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.2020 | −0.481771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.59592 | −0.121843 | ||||||||
\(872\) | 2.89898 | 0.0981718 | ||||||||
\(873\) | 11.3939 | 0.385624 | ||||||||
\(874\) | −44.4949 | −1.50506 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.8990 | −0.570964 | ||||||||
\(877\) | 19.3939 | 0.654885 | 0.327442 | − | 0.944871i | \(-0.393813\pi\) | ||||
0.327442 | + | 0.944871i | \(0.393813\pi\) | |||||||
\(878\) | 37.3939 | 1.26198 | ||||||||
\(879\) | −15.3031 | −0.516159 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.7980 | −0.936537 | −0.468269 | − | 0.883586i | \(-0.655122\pi\) | ||||
−0.468269 | + | 0.883586i | \(0.655122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.7980 | 1.40661 | 0.703307 | − | 0.710887i | \(-0.251706\pi\) | ||||
0.703307 | + | 0.710887i | \(0.251706\pi\) | |||||||
\(884\) | −0.898979 | −0.0302360 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.79796 | 0.329169 | ||||||||
\(887\) | 26.6969 | 0.896395 | 0.448198 | − | 0.893934i | \(-0.352066\pi\) | ||||
0.448198 | + | 0.893934i | \(0.352066\pi\) | |||||||
\(888\) | 4.89898 | 0.164399 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.0908 | −1.47710 | ||||||||
\(892\) | 4.00000 | 0.133930 | ||||||||
\(893\) | −5.79796 | −0.194021 | ||||||||
\(894\) | 38.6969 | 1.29422 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.59592 | 0.253620 | ||||||||
\(898\) | 10.0000 | 0.333704 | ||||||||
\(899\) | −2.60612 | −0.0869191 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20204 | 0.0733606 | ||||||||
\(902\) | −53.3939 | −1.77782 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.202041 | −0.00671978 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −48.0000 | −1.59469 | ||||||||
\(907\) | −22.2020 | −0.737207 | −0.368603 | − | 0.929587i | \(-0.620164\pi\) | ||||
−0.368603 | + | 0.929587i | \(0.620164\pi\) | |||||||
\(908\) | 7.34847 | 0.243868 | ||||||||
\(909\) | −25.3485 | −0.840756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.59592 | 0.119138 | 0.0595690 | − | 0.998224i | \(-0.481027\pi\) | ||||
0.0595690 | + | 0.998224i | \(0.481027\pi\) | |||||||
\(912\) | 15.7980 | 0.523123 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 9.59592 | 0.317405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.1464 | −0.500452 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.1010 | −0.564111 | −0.282055 | − | 0.959398i | \(-0.591016\pi\) | ||||
−0.282055 | + | 0.959398i | \(0.591016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.4041 | 0.342826 | ||||||||
\(922\) | 2.65153 | 0.0873235 | ||||||||
\(923\) | −4.89898 | −0.161252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.5959 | 1.16975 | ||||||||
\(927\) | −9.30306 | −0.305553 | ||||||||
\(928\) | 2.89898 | 0.0951637 | ||||||||
\(929\) | −40.2929 | −1.32197 | −0.660983 | − | 0.750401i | \(-0.729860\pi\) | ||||
−0.660983 | + | 0.750401i | \(0.729860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.2020 | 0.334179 | ||||||||
\(933\) | 29.3939 | 0.962312 | ||||||||
\(934\) | 5.55051 | 0.181618 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.34847 | −0.0440761 | ||||||||
\(937\) | 50.8990 | 1.66280 | 0.831399 | − | 0.555677i | \(-0.187541\pi\) | ||||
0.831399 | + | 0.555677i | \(0.187541\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.1010 | 1.40655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4495 | 0.797031 | 0.398515 | − | 0.917162i | \(-0.369526\pi\) | ||||
0.398515 | + | 0.917162i | \(0.369526\pi\) | |||||||
\(942\) | −20.6969 | −0.674343 | ||||||||
\(943\) | −75.1918 | −2.44858 | ||||||||
\(944\) | 6.44949 | 0.209913 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.5959 | −1.41743 | ||||||||
\(947\) | −44.0908 | −1.43276 | −0.716379 | − | 0.697711i | \(-0.754202\pi\) | ||||
−0.716379 | + | 0.697711i | \(0.754202\pi\) | |||||||
\(948\) | 7.10102 | 0.230630 | ||||||||
\(949\) | 3.10102 | 0.100663 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −64.8990 | −2.10449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7980 | 0.706105 | 0.353053 | − | 0.935603i | \(-0.385144\pi\) | ||||
0.353053 | + | 0.935603i | \(0.385144\pi\) | |||||||
\(954\) | 3.30306 | 0.106941 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25.7980 | −0.834366 | ||||||||
\(957\) | 34.7878 | 1.12453 | ||||||||
\(958\) | 38.6969 | 1.25024 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1918 | −0.973930 | ||||||||
\(962\) | −0.898979 | −0.0289843 | ||||||||
\(963\) | −24.0000 | −0.773389 | ||||||||
\(964\) | −20.6969 | −0.666604 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2929 | 1.03847 | 0.519234 | − | 0.854632i | \(-0.326217\pi\) | ||||
0.519234 | + | 0.854632i | \(0.326217\pi\) | |||||||
\(968\) | −13.0000 | −0.417836 | ||||||||
\(969\) | −31.5959 | −1.01501 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.4495 | 0.463706 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(972\) | 22.0454 | 0.707107 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.6969 | 1.17585 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.44949 | −0.270462 | ||||||||
\(977\) | 29.3939 | 0.940393 | 0.470197 | − | 0.882562i | \(-0.344183\pi\) | ||||
0.470197 | + | 0.882562i | \(0.344183\pi\) | |||||||
\(978\) | −41.3939 | −1.32363 | ||||||||
\(979\) | 48.9898 | 1.56572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.69694 | −0.277672 | ||||||||
\(982\) | 19.5959 | 0.625331 | ||||||||
\(983\) | 42.6969 | 1.36182 | 0.680910 | − | 0.732367i | \(-0.261584\pi\) | ||||
0.680910 | + | 0.732367i | \(0.261584\pi\) | |||||||
\(984\) | 26.6969 | 0.851067 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.79796 | −0.184645 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.89898 | −0.0922288 | ||||||||
\(989\) | −61.3939 | −1.95221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.6969 | 1.92810 | 0.964051 | − | 0.265718i | \(-0.0856089\pi\) | ||||
0.964051 | + | 0.265718i | \(0.0856089\pi\) | |||||||
\(992\) | −0.898979 | −0.0285426 | ||||||||
\(993\) | −26.2020 | −0.831497 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | −42.6515 | −1.35079 | −0.675394 | − | 0.737457i | \(-0.736026\pi\) | ||||
−0.675394 | + | 0.737457i | \(0.736026\pi\) | |||||||
\(998\) | −25.7980 | −0.816620 | ||||||||
\(999\) | 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 | 2450.2.a.bl.1.1 | 2 | ||
5.2 | odd | 4 | 490.2.c.e.99.2 | 4 | |||
5.3 | odd | 4 | 490.2.c.e.99.3 | 4 | |||
5.4 | even | 2 | 2450.2.a.bq.1.2 | 2 | |||
7.6 | odd | 2 | 350.2.a.g.1.2 | 2 | |||
21.20 | even | 2 | 3150.2.a.bt.1.1 | 2 | |||
28.27 | even | 2 | 2800.2.a.bm.1.1 | 2 | |||
35.2 | odd | 12 | 490.2.i.f.459.1 | 8 | |||
35.3 | even | 12 | 490.2.i.c.79.2 | 8 | |||
35.12 | even | 12 | 490.2.i.c.459.2 | 8 | |||
35.13 | even | 4 | 70.2.c.a.29.4 | yes | 4 | ||
35.17 | even | 12 | 490.2.i.c.79.3 | 8 | |||
35.18 | odd | 12 | 490.2.i.f.79.1 | 8 | |||
35.23 | odd | 12 | 490.2.i.f.459.4 | 8 | |||
35.27 | even | 4 | 70.2.c.a.29.1 | ✓ | 4 | ||
35.32 | odd | 12 | 490.2.i.f.79.4 | 8 | |||
35.33 | even | 12 | 490.2.i.c.459.3 | 8 | |||
35.34 | odd | 2 | 350.2.a.h.1.1 | 2 | |||
105.62 | odd | 4 | 630.2.g.g.379.4 | 4 | |||
105.83 | odd | 4 | 630.2.g.g.379.2 | 4 | |||
105.104 | even | 2 | 3150.2.a.bs.1.1 | 2 | |||
140.27 | odd | 4 | 560.2.g.e.449.3 | 4 | |||
140.83 | odd | 4 | 560.2.g.e.449.1 | 4 | |||
140.139 | even | 2 | 2800.2.a.bl.1.2 | 2 | |||
280.13 | even | 4 | 2240.2.g.j.449.2 | 4 | |||
280.27 | odd | 4 | 2240.2.g.i.449.2 | 4 | |||
280.83 | odd | 4 | 2240.2.g.i.449.4 | 4 | |||
280.237 | even | 4 | 2240.2.g.j.449.4 | 4 | |||
420.83 | even | 4 | 5040.2.t.t.1009.4 | 4 | |||
420.167 | even | 4 | 5040.2.t.t.1009.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.c.a.29.1 | ✓ | 4 | 35.27 | even | 4 | ||
70.2.c.a.29.4 | yes | 4 | 35.13 | even | 4 | ||
350.2.a.g.1.2 | 2 | 7.6 | odd | 2 | |||
350.2.a.h.1.1 | 2 | 35.34 | odd | 2 | |||
490.2.c.e.99.2 | 4 | 5.2 | odd | 4 | |||
490.2.c.e.99.3 | 4 | 5.3 | odd | 4 | |||
490.2.i.c.79.2 | 8 | 35.3 | even | 12 | |||
490.2.i.c.79.3 | 8 | 35.17 | even | 12 | |||
490.2.i.c.459.2 | 8 | 35.12 | even | 12 | |||
490.2.i.c.459.3 | 8 | 35.33 | even | 12 | |||
490.2.i.f.79.1 | 8 | 35.18 | odd | 12 | |||
490.2.i.f.79.4 | 8 | 35.32 | odd | 12 | |||
490.2.i.f.459.1 | 8 | 35.2 | odd | 12 | |||
490.2.i.f.459.4 | 8 | 35.23 | odd | 12 | |||
560.2.g.e.449.1 | 4 | 140.83 | odd | 4 | |||
560.2.g.e.449.3 | 4 | 140.27 | odd | 4 | |||
630.2.g.g.379.2 | 4 | 105.83 | odd | 4 | |||
630.2.g.g.379.4 | 4 | 105.62 | odd | 4 | |||
2240.2.g.i.449.2 | 4 | 280.27 | odd | 4 | |||
2240.2.g.i.449.4 | 4 | 280.83 | odd | 4 | |||
2240.2.g.j.449.2 | 4 | 280.13 | even | 4 | |||
2240.2.g.j.449.4 | 4 | 280.237 | even | 4 | |||
2450.2.a.bl.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2450.2.a.bq.1.2 | 2 | 5.4 | even | 2 | |||
2800.2.a.bl.1.2 | 2 | 140.139 | even | 2 | |||
2800.2.a.bm.1.1 | 2 | 28.27 | even | 2 | |||
3150.2.a.bs.1.1 | 2 | 105.104 | even | 2 | |||
3150.2.a.bt.1.1 | 2 | 21.20 | even | 2 | |||
5040.2.t.t.1009.3 | 4 | 420.167 | even | 4 | |||
5040.2.t.t.1009.4 | 4 | 420.83 | even | 4 |