Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.37228 | 1.92132 | 0.960658 | − | 0.277736i | \(-0.0895839\pi\) | ||||
0.960658 | + | 0.277736i | \(0.0895839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.37228 | 1.21265 | 0.606326 | − | 0.795216i | \(-0.292643\pi\) | ||||
0.606326 | + | 0.795216i | \(0.292643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.372281 | 0.0902915 | 0.0451457 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451457 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74456 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.74456 | −0.989310 | −0.494655 | − | 0.869090i | \(-0.664706\pi\) | ||||
−0.494655 | + | 0.869090i | \(0.664706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.37228 | 0.811912 | 0.405956 | − | 0.913893i | \(-0.366939\pi\) | ||||
0.405956 | + | 0.913893i | \(0.366939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.74456 | −1.05332 | −0.526662 | − | 0.850075i | \(-0.676557\pi\) | ||||
−0.526662 | + | 0.850075i | \(0.676557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.74456 | 1.33353 | 0.666767 | − | 0.745267i | \(-0.267678\pi\) | ||||
0.666767 | + | 0.745267i | \(0.267678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.11684 | −1.03810 | −0.519049 | − | 0.854744i | \(-0.673714\pi\) | ||||
−0.519049 | + | 0.854744i | \(0.673714\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7446 | −1.47588 | −0.737940 | − | 0.674867i | \(-0.764201\pi\) | ||||
−0.737940 | + | 0.674867i | \(0.764201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.37228 | 0.859238 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.74456 | −0.351405 | −0.175703 | − | 0.984443i | \(-0.556220\pi\) | ||||
−0.175703 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.37228 | 0.542315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.37228 | 0.726189 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1168 | −1.70078 | −0.850389 | − | 0.526155i | \(-0.823633\pi\) | ||||
−0.850389 | + | 0.526155i | \(0.823633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.48913 | −1.04157 | −0.520783 | − | 0.853689i | \(-0.674360\pi\) | ||||
−0.520783 | + | 0.853689i | \(0.674360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.372281 | 0.0403796 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7446 | −1.56292 | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623955i | \(0.785525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.37228 | 0.458340 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.74456 | 0.486782 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.86141 | −1.00127 | −0.500637 | − | 0.865657i | \(-0.666901\pi\) | ||||
−0.500637 | + | 0.865657i | \(0.666901\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.62772 | 0.554516 | 0.277258 | − | 0.960796i | \(-0.410574\pi\) | ||||
0.277258 | + | 0.960796i | \(0.410574\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.74456 | 0.845369 | 0.422684 | − | 0.906277i | \(-0.361088\pi\) | ||||
0.422684 | + | 0.906277i | \(0.361088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.372281 | 0.0356581 | 0.0178290 | − | 0.999841i | \(-0.494325\pi\) | ||||
0.0178290 | + | 0.999841i | \(0.494325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.74456 | −0.442433 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.372281 | 0.0341270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.6060 | 2.69145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.74456 | −0.414534 | −0.207267 | − | 0.978284i | \(-0.566457\pi\) | ||||
−0.207267 | + | 0.978284i | \(0.566457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.74456 | 0.411406 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.7446 | −1.25971 | −0.629857 | − | 0.776712i | \(-0.716886\pi\) | ||||
−0.629857 | + | 0.776712i | \(0.716886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.74456 | 0.402429 | 0.201214 | − | 0.979547i | \(-0.435511\pi\) | ||||
0.201214 | + | 0.979547i | \(0.435511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.8614 | 2.32989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37228 | 0.363098 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4891 | −1.26892 | −0.634459 | − | 0.772956i | \(-0.718777\pi\) | ||||
−0.634459 | + | 0.772956i | \(0.718777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1168 | −1.23019 | −0.615096 | − | 0.788452i | \(-0.710883\pi\) | ||||
−0.615096 | + | 0.788452i | \(0.710883\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4891 | −1.23617 | −0.618083 | − | 0.786113i | \(-0.712091\pi\) | ||||
−0.618083 | + | 0.786113i | \(0.712091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.74456 | −0.373924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7446 | 1.31154 | 0.655768 | − | 0.754963i | \(-0.272345\pi\) | ||||
0.655768 | + | 0.754963i | \(0.272345\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.62772 | −0.435486 | −0.217743 | − | 0.976006i | \(-0.569869\pi\) | ||||
−0.217743 | + | 0.976006i | \(0.569869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.11684 | 0.470526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.372281 | 0.0283040 | 0.0141520 | − | 0.999900i | \(-0.495495\pi\) | ||||
0.0141520 | + | 0.999900i | \(0.495495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9783 | −1.71748 | −0.858738 | − | 0.512416i | \(-0.828751\pi\) | ||||
−0.858738 | + | 0.512416i | \(0.828751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2337 | 1.20664 | 0.603320 | − | 0.797499i | \(-0.293844\pi\) | ||||
0.603320 | + | 0.797499i | \(0.293844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.37228 | 0.173478 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.86141 | 0.279402 | 0.139701 | − | 0.990194i | \(-0.455386\pi\) | ||||
0.139701 | + | 0.990194i | \(0.455386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74456 | 0.485484 | 0.242742 | − | 0.970091i | \(-0.421953\pi\) | ||||
0.242742 | + | 0.970091i | \(0.421953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.23369 | 0.586626 | 0.293313 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293313 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.37228 | 0.306874 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.74456 | −0.471061 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.2337 | 2.09131 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3723 | 0.989429 | 0.494714 | − | 0.869056i | \(-0.335273\pi\) | ||||
0.494714 | + | 0.869056i | \(0.335273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.74456 | 0.596374 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.62772 | 0.109492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.62772 | 0.376860 | 0.188430 | − | 0.982087i | \(-0.439660\pi\) | ||||
0.188430 | + | 0.982087i | \(0.439660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.8614 | 1.31825 | 0.659124 | − | 0.752034i | \(-0.270927\pi\) | ||||
0.659124 | + | 0.752034i | \(0.270927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2337 | −0.808425 | −0.404212 | − | 0.914665i | \(-0.632454\pi\) | ||||
−0.404212 | + | 0.914665i | \(0.632454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.25544 | 0.0822464 | 0.0411232 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411232 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.11684 | −0.464252 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6277 | 0.881504 | 0.440752 | − | 0.897629i | \(-0.354712\pi\) | ||||
0.440752 | + | 0.897629i | \(0.354712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.7446 | 1.31994 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.74456 | 0.299474 | 0.149737 | − | 0.988726i | \(-0.452157\pi\) | ||||
0.149737 | + | 0.988726i | \(0.452157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.2337 | −1.90078 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4891 | 1.46521 | 0.732606 | − | 0.680653i | \(-0.238304\pi\) | ||||
0.732606 | + | 0.680653i | \(0.238304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2337 | 1.37099 | 0.685494 | − | 0.728078i | \(-0.259586\pi\) | ||||
0.685494 | + | 0.728078i | \(0.259586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7446 | −0.660033 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.48913 | −0.576423 | −0.288212 | − | 0.957567i | \(-0.593061\pi\) | ||||
−0.288212 | + | 0.957567i | \(0.593061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.37228 | 0.384263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9783 | 1.50080 | 0.750399 | − | 0.660985i | \(-0.229861\pi\) | ||||
0.750399 | + | 0.660985i | \(0.229861\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.6060 | −1.10994 | −0.554970 | − | 0.831871i | \(-0.687270\pi\) | ||||
−0.554970 | + | 0.831871i | \(0.687270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.88316 | 0.528049 | 0.264024 | − | 0.964516i | \(-0.414950\pi\) | ||||
0.264024 | + | 0.964516i | \(0.414950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.74456 | −0.398119 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.1168 | −1.46734 | −0.733671 | − | 0.679505i | \(-0.762195\pi\) | ||||
−0.733671 | + | 0.679505i | \(0.762195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.7446 | −1.19969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.74456 | 0.504028 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.74456 | −0.157153 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.1168 | −1.77593 | −0.887966 | − | 0.459909i | \(-0.847882\pi\) | ||||
−0.887966 | + | 0.459909i | \(0.847882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7446 | −0.722678 | −0.361339 | − | 0.932435i | \(-0.617680\pi\) | ||||
−0.361339 | + | 0.932435i | \(0.617680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.88316 | 0.162966 | 0.0814828 | − | 0.996675i | \(-0.474034\pi\) | ||||
0.0814828 | + | 0.996675i | \(0.474034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.8614 | 1.55994 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.76631 | 0.0982802 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.37228 | 0.242531 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.11684 | −0.392364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.48913 | −0.407959 | −0.203979 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203979 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.9783 | 2.76063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.7446 | −1.32836 | −0.664179 | − | 0.747574i | \(-0.731219\pi\) | ||||
−0.664179 | + | 0.747574i | \(0.731219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4891 | 1.04323 | 0.521614 | − | 0.853181i | \(-0.325330\pi\) | ||||
0.521614 | + | 0.853181i | \(0.325330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.86141 | 0.0990727 | 0.0495363 | − | 0.998772i | \(-0.484226\pi\) | ||||
0.0495363 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.8614 | −1.03676 | −0.518378 | − | 0.855151i | \(-0.673464\pi\) | ||||
−0.518378 | + | 0.855151i | \(0.673464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7446 | −0.557830 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.7446 | −1.59189 | −0.795947 | − | 0.605367i | \(-0.793026\pi\) | ||||
−0.795947 | + | 0.605367i | \(0.793026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.1168 | 0.984568 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.4891 | −0.893653 | −0.446826 | − | 0.894621i | \(-0.647446\pi\) | ||||
−0.446826 | + | 0.894621i | \(0.647446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.37228 | 0.324762 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8614 | −0.905609 | −0.452805 | − | 0.891610i | \(-0.649576\pi\) | ||||
−0.452805 | + | 0.891610i | \(0.649576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.76631 | −0.0893262 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1168 | −0.760611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.6277 | 1.58735 | 0.793675 | − | 0.608342i | \(-0.208165\pi\) | ||||
0.793675 | + | 0.608342i | \(0.208165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.6060 | 1.92789 | 0.963945 | − | 0.266101i | \(-0.0857356\pi\) | ||||
0.963945 | + | 0.266101i | \(0.0857356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.9783 | 1.74239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7446 | −0.631725 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4891 | 0.568101 | 0.284050 | − | 0.958809i | \(-0.408322\pi\) | ||||
0.284050 | + | 0.958809i | \(0.408322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.48913 | −0.465803 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.5109 | −0.708903 | −0.354451 | − | 0.935074i | \(-0.615332\pi\) | ||||
−0.354451 | + | 0.935074i | \(0.615332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.6060 | −0.906799 | −0.453400 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453400 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.372281 | 0.0180583 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.74456 | −0.132819 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3723 | 0.884962 | 0.442481 | − | 0.896778i | \(-0.354098\pi\) | ||||
0.442481 | + | 0.896778i | \(0.354098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9783 | 1.39261 | 0.696303 | − | 0.717748i | \(-0.254827\pi\) | ||||
0.696303 | + | 0.717748i | \(0.254827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.5109 | −1.07684 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.23369 | 0.297518 | 0.148759 | − | 0.988874i | \(-0.452472\pi\) | ||||
0.148759 | + | 0.988874i | \(0.452472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7446 | −0.795558 | −0.397779 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397779 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7446 | −0.698959 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1168 | −0.807794 | −0.403897 | − | 0.914805i | \(-0.632345\pi\) | ||||
−0.403897 | + | 0.914805i | \(0.632345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.9783 | −2.02377 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.37228 | 0.204976 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.25544 | 0.245839 | 0.122919 | − | 0.992417i | \(-0.460774\pi\) | ||||
0.122919 | + | 0.992417i | \(0.460774\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.25544 | 0.0584715 | 0.0292358 | − | 0.999573i | \(-0.490693\pi\) | ||||
0.0292358 | + | 0.999573i | \(0.490693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51087 | 0.302586 | 0.151293 | − | 0.988489i | \(-0.451656\pi\) | ||||
0.151293 | + | 0.988489i | \(0.451656\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.60597 | 0.398237 | 0.199118 | − | 0.979975i | \(-0.436192\pi\) | ||||
0.199118 | + | 0.979975i | \(0.436192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 55.7228 | 2.56214 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.74456 | 0.217695 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.2337 | 1.01588 | 0.507942 | − | 0.861392i | \(-0.330407\pi\) | ||||
0.507942 | + | 0.861392i | \(0.330407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.74456 | −0.398718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.86141 | −0.447783 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2337 | −1.37002 | −0.685010 | − | 0.728534i | \(-0.740202\pi\) | ||||
−0.685010 | + | 0.728534i | \(0.740202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1168 | 1.58480 | 0.792400 | − | 0.610001i | \(-0.208831\pi\) | ||||
0.792400 | + | 0.610001i | \(0.208831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.62772 | 0.0733088 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8614 | −1.42631 | −0.713156 | − | 0.701005i | \(-0.752735\pi\) | ||||
−0.713156 | + | 0.701005i | \(0.752735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.3723 | −0.819180 | −0.409590 | − | 0.912270i | \(-0.634328\pi\) | ||||
−0.409590 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.9783 | 1.81633 | 0.908165 | − | 0.418613i | \(-0.137484\pi\) | ||||
0.908165 | + | 0.418613i | \(0.137484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.62772 | 0.247987 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.3505 | −1.99451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.4674 | 1.59461 | 0.797304 | − | 0.603579i | \(-0.206259\pi\) | ||||
0.797304 | + | 0.603579i | \(0.206259\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.97825 | 0.129735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.489125 | −0.0212663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.4891 | −1.27732 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.74456 | 0.378060 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.37228 | 0.274474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.3505 | −1.34786 | −0.673932 | − | 0.738793i | \(-0.735396\pi\) | ||||
−0.673932 | + | 0.738793i | \(0.735396\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.372281 | 0.0159468 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.9783 | 1.32453 | 0.662267 | − | 0.749268i | \(-0.269594\pi\) | ||||
0.662267 | + | 0.749268i | \(0.269594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7446 | 0.883748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1168 | −0.642834 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.76631 | 0.159584 | 0.0797919 | − | 0.996812i | \(-0.474574\pi\) | ||||
0.0797919 | + | 0.996812i | \(0.474574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.2337 | 1.61711 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4891 | 0.737079 | 0.368539 | − | 0.929612i | \(-0.379858\pi\) | ||||
0.368539 | + | 0.929612i | \(0.379858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.9783 | 1.04714 | 0.523571 | − | 0.851982i | \(-0.324599\pi\) | ||||
0.523571 | + | 0.851982i | \(0.324599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.74456 | −0.197862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.6060 | −0.941099 | −0.470549 | − | 0.882374i | \(-0.655944\pi\) | ||||
−0.470549 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.48913 | −0.393675 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −68.4674 | −2.83563 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.9783 | −1.44371 | −0.721853 | − | 0.692046i | \(-0.756710\pi\) | ||||
−0.721853 | + | 0.692046i | \(0.756710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.9565 | 1.56397 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.6277 | 0.806014 | 0.403007 | − | 0.915197i | \(-0.367965\pi\) | ||||
0.403007 | + | 0.915197i | \(0.367965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.372281 | 0.0152620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.6060 | −1.33224 | −0.666122 | − | 0.745843i | \(-0.732047\pi\) | ||||
−0.666122 | + | 0.745843i | \(0.732047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5109 | 0.673493 | 0.336746 | − | 0.941595i | \(-0.390674\pi\) | ||||
0.336746 | + | 0.941595i | \(0.390674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.6060 | 1.20365 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6060 | −0.998725 | −0.499363 | − | 0.866393i | \(-0.666432\pi\) | ||||
−0.499363 | + | 0.866393i | \(0.666432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.1168 | −1.25885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.51087 | −0.343751 | −0.171875 | − | 0.985119i | \(-0.554983\pi\) | ||||
−0.171875 | + | 0.985119i | \(0.554983\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7446 | 0.512247 | 0.256124 | − | 0.966644i | \(-0.417555\pi\) | ||||
0.256124 | + | 0.966644i | \(0.417555\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.7446 | −0.590728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.744563 | −0.0296877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.37228 | −0.0944390 | −0.0472195 | − | 0.998885i | \(-0.515036\pi\) | ||||
−0.0472195 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.37228 | 0.173236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.3723 | −0.724532 | −0.362266 | − | 0.932075i | \(-0.617997\pi\) | ||||
−0.362266 | + | 0.932075i | \(0.617997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0000 | −0.629025 | −0.314512 | − | 0.949253i | \(-0.601841\pi\) | ||||
−0.314512 | + | 0.949253i | \(0.601841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.9783 | 2.00107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.74456 | −0.185385 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1168 | −0.433051 | −0.216525 | − | 0.976277i | \(-0.569472\pi\) | ||||
−0.216525 | + | 0.976277i | \(0.569472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7446 | 0.573497 | 0.286749 | − | 0.958006i | \(-0.407426\pi\) | ||||
0.286749 | + | 0.958006i | \(0.407426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.74456 | 0.183986 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.7446 | −0.803233 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.4891 | −0.675160 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7228 | 0.991542 | 0.495771 | − | 0.868453i | \(-0.334886\pi\) | ||||
0.495771 | + | 0.868453i | \(0.334886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.3505 | −0.589969 | −0.294984 | − | 0.955502i | \(-0.595314\pi\) | ||||
−0.294984 | + | 0.955502i | \(0.595314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.86141 | −0.378446 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.7446 | −0.563361 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −46.9783 | −1.78973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.48913 | 0.360983 | 0.180492 | − | 0.983577i | \(-0.442231\pi\) | ||||
0.180492 | + | 0.983577i | \(0.442231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.74456 | 0.179972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.51087 | −0.0951062 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.13859 | −0.0807736 | −0.0403868 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403868 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.48913 | −0.357889 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.60597 | 0.248092 | 0.124046 | − | 0.992276i | \(-0.460413\pi\) | ||||
0.124046 | + | 0.992276i | \(0.460413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.9565 | −1.42148 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.8614 | 1.04196 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.25544 | 0.121407 | 0.0607037 | − | 0.998156i | \(-0.480666\pi\) | ||||
0.0607037 | + | 0.998156i | \(0.480666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.62772 | 0.209587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.37228 | 0.162382 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.25544 | 0.120407 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.1386 | −0.374477 | −0.187239 | − | 0.982314i | \(-0.559954\pi\) | ||||
−0.187239 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.4891 | 0.938904 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6060 | 0.758003 | 0.379001 | − | 0.925396i | \(-0.376268\pi\) | ||||
0.379001 | + | 0.925396i | \(0.376268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.51087 | −0.238861 | −0.119430 | − | 0.992843i | \(-0.538107\pi\) | ||||
−0.119430 | + | 0.992843i | \(0.538107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.4891 | −0.567478 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.74456 | 0.319519 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.1386 | −0.734868 | −0.367434 | − | 0.930050i | \(-0.619764\pi\) | ||||
−0.367434 | + | 0.930050i | \(0.619764\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.1168 | −0.550158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.76631 | −0.136889 | −0.0684445 | − | 0.997655i | \(-0.521804\pi\) | ||||
−0.0684445 | + | 0.997655i | \(0.521804\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.97825 | −0.180461 | −0.0902307 | − | 0.995921i | \(-0.528760\pi\) | ||||
−0.0902307 | + | 0.995921i | \(0.528760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.372281 | 0.0134775 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.9783 | 1.26299 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.48913 | 0.125821 | 0.0629105 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629105 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.37228 | −0.157260 | −0.0786300 | − | 0.996904i | \(-0.525055\pi\) | ||||
−0.0786300 | + | 0.996904i | \(0.525055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.0000 | −1.14652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.9783 | 1.82415 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4891 | −0.552831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1168 | 1.10920 | 0.554598 | − | 0.832119i | \(-0.312872\pi\) | ||||
0.554598 | + | 0.832119i | \(0.312872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.6277 | −0.553562 | −0.276781 | − | 0.960933i | \(-0.589268\pi\) | ||||
−0.276781 | + | 0.960933i | \(0.589268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.64947 | −0.0937314 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.2337 | −1.34924 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.74456 | −0.167224 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3723 | −0.716251 | −0.358126 | − | 0.933673i | \(-0.616584\pi\) | ||||
−0.358126 | + | 0.933673i | \(0.616584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.7446 | −0.447522 | −0.223761 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223761 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.7446 | 0.586536 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.4891 | 1.45152 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.1168 | 0.876584 | 0.438292 | − | 0.898833i | \(-0.355584\pi\) | ||||
0.438292 | + | 0.898833i | \(0.355584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7446 | 0.860453 | 0.430226 | − | 0.902721i | \(-0.358434\pi\) | ||||
0.430226 | + | 0.902721i | \(0.358434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.2337 | −0.424894 | −0.212447 | − | 0.977173i | \(-0.568143\pi\) | ||||
−0.212447 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.372281 | 0.0128988 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.62772 | −0.194755 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.2554 | −0.388581 | −0.194290 | − | 0.980944i | \(-0.562240\pi\) | ||||
−0.194290 | + | 0.980944i | \(0.562240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.88316 | −0.340798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.11684 | 0.210426 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6060 | 1.01727 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.48913 | 0.325283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.4891 | −1.35208 | −0.676041 | − | 0.736864i | \(-0.736306\pi\) | ||||
−0.676041 | + | 0.736864i | \(0.736306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.4674 | −1.51721 | −0.758604 | − | 0.651552i | \(-0.774118\pi\) | ||||
−0.758604 | + | 0.651552i | \(0.774118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4891 | 0.867660 | 0.433830 | − | 0.900995i | \(-0.357162\pi\) | ||||
0.433830 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.372281 | 0.0126579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −96.3288 | −3.26773 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.4891 | 0.592596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.02175 | −0.237108 | −0.118554 | − | 0.992948i | \(-0.537826\pi\) | ||||
−0.118554 | + | 0.992948i | \(0.537826\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2554 | 0.850877 | 0.425439 | − | 0.904987i | \(-0.360120\pi\) | ||||
0.425439 | + | 0.904987i | \(0.360120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5109 | 0.353719 | 0.176860 | − | 0.984236i | \(-0.443406\pi\) | ||||
0.176860 | + | 0.984236i | \(0.443406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.0217 | −0.437228 | −0.218614 | − | 0.975811i | \(-0.570153\pi\) | ||||
−0.218614 | + | 0.975811i | \(0.570153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.7663 | −1.12995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.9783 | −0.768078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.9783 | 1.16659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.2337 | 0.539626 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7228 | −0.389250 | −0.194625 | − | 0.980878i | \(-0.562349\pi\) | ||||
−0.194625 | + | 0.980878i | \(0.562349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.9565 | −1.52261 | −0.761303 | − | 0.648396i | \(-0.775440\pi\) | ||||
−0.761303 | + | 0.648396i | \(0.775440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.4674 | −2.00118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.74456 | −0.156679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6277 | −0.449537 | −0.224768 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224768 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.9783 | 1.15132 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.76631 | 0.254804 | 0.127402 | − | 0.991851i | \(-0.459336\pi\) | ||||
0.127402 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.74456 | 0.155497 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37228 | 0.0775819 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0951 | 0.917827 | 0.458913 | − | 0.888481i | \(-0.348239\pi\) | ||||
0.458913 | + | 0.888481i | \(0.348239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.2337 | −1.05079 | −0.525394 | − | 0.850859i | \(-0.676082\pi\) | ||||
−0.525394 | + | 0.850859i | \(0.676082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0000 | −0.909878 | −0.454939 | − | 0.890523i | \(-0.650339\pi\) | ||||
−0.454939 | + | 0.890523i | \(0.650339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.2337 | −0.851582 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.2554 | −1.20682 | −0.603411 | − | 0.797430i | \(-0.706192\pi\) | ||||
−0.603411 | + | 0.797430i | \(0.706192\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.86141 | 0.124952 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7446 | −0.476127 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.74456 | 0.217115 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.76631 | −0.0568008 | −0.0284004 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0284004 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.4891 | 1.07472 | 0.537359 | − | 0.843354i | \(-0.319422\pi\) | ||||
0.537359 | + | 0.843354i | \(0.319422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.74456 | 0.152104 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.9783 | −1.69492 | −0.847462 | − | 0.530856i | \(-0.821871\pi\) | ||||
−0.847462 | + | 0.530856i | \(0.821871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −93.9565 | −3.00286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.3723 | −0.330824 | −0.165412 | − | 0.986225i | \(-0.552895\pi\) | ||||
−0.165412 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.23369 | 0.262347 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.4891 | −1.31928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9565 | 1.20573 | 0.602864 | − | 0.797844i | \(-0.294026\pi\) | ||||
0.602864 | + | 0.797844i | \(0.294026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.88316 | −0.217992 | −0.108996 | − | 0.994042i | \(-0.534764\pi\) | ||||
−0.108996 | + | 0.994042i | \(0.534764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5040.2.a.by.1.2 | 2 | ||
3.2 | odd | 2 | 560.2.a.h.1.1 | 2 | |||
4.3 | odd | 2 | 2520.2.a.x.1.1 | 2 | |||
12.11 | even | 2 | 280.2.a.c.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 2800.2.g.r.449.3 | 4 | |||
15.8 | even | 4 | 2800.2.g.r.449.2 | 4 | |||
15.14 | odd | 2 | 2800.2.a.bk.1.2 | 2 | |||
21.20 | even | 2 | 3920.2.a.bt.1.2 | 2 | |||
24.5 | odd | 2 | 2240.2.a.bg.1.2 | 2 | |||
24.11 | even | 2 | 2240.2.a.bk.1.1 | 2 | |||
60.23 | odd | 4 | 1400.2.g.i.449.3 | 4 | |||
60.47 | odd | 4 | 1400.2.g.i.449.2 | 4 | |||
60.59 | even | 2 | 1400.2.a.r.1.1 | 2 | |||
84.11 | even | 6 | 1960.2.q.t.961.1 | 4 | |||
84.23 | even | 6 | 1960.2.q.t.361.1 | 4 | |||
84.47 | odd | 6 | 1960.2.q.r.361.2 | 4 | |||
84.59 | odd | 6 | 1960.2.q.r.961.2 | 4 | |||
84.83 | odd | 2 | 1960.2.a.s.1.1 | 2 | |||
420.419 | odd | 2 | 9800.2.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.c.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
560.2.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
1400.2.a.r.1.1 | 2 | 60.59 | even | 2 | |||
1400.2.g.i.449.2 | 4 | 60.47 | odd | 4 | |||
1400.2.g.i.449.3 | 4 | 60.23 | odd | 4 | |||
1960.2.a.s.1.1 | 2 | 84.83 | odd | 2 | |||
1960.2.q.r.361.2 | 4 | 84.47 | odd | 6 | |||
1960.2.q.r.961.2 | 4 | 84.59 | odd | 6 | |||
1960.2.q.t.361.1 | 4 | 84.23 | even | 6 | |||
1960.2.q.t.961.1 | 4 | 84.11 | even | 6 | |||
2240.2.a.bg.1.2 | 2 | 24.5 | odd | 2 | |||
2240.2.a.bk.1.1 | 2 | 24.11 | even | 2 | |||
2520.2.a.x.1.1 | 2 | 4.3 | odd | 2 | |||
2800.2.a.bk.1.2 | 2 | 15.14 | odd | 2 | |||
2800.2.g.r.449.2 | 4 | 15.8 | even | 4 | |||
2800.2.g.r.449.3 | 4 | 15.2 | even | 4 | |||
3920.2.a.bt.1.2 | 2 | 21.20 | even | 2 | |||
5040.2.a.by.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9800.2.a.bu.1.2 | 2 | 420.419 | odd | 2 |