Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 13x^{7} + 8x^{6} + 56x^{5} - 15x^{4} - 81x^{3} + 2x^{2} + 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.0812095\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | ||||||||
\(3\) | 0.0812095 | 0.0468864 | 0.0234432 | − | 0.999725i | \(-0.492537\pi\) | ||||
0.0234432 | + | 0.999725i | \(0.492537\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.29286 | 1.02540 | 0.512699 | − | 0.858568i | \(-0.328646\pi\) | ||||
0.512699 | + | 0.858568i | \(0.328646\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.862825 | 0.326117 | 0.163059 | − | 0.986616i | \(-0.447864\pi\) | ||||
0.163059 | + | 0.986616i | \(0.447864\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99341 | −0.997802 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.76111 | −0.530994 | −0.265497 | − | 0.964112i | \(-0.585536\pi\) | ||||
−0.265497 | + | 0.964112i | \(0.585536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.62247 | −1.28204 | −0.641021 | − | 0.767524i | \(-0.721489\pi\) | ||||
−0.641021 | + | 0.767524i | \(0.721489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.186202 | 0.0480772 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.59644 | −1.84241 | −0.921204 | − | 0.389080i | \(-0.872793\pi\) | ||||
−0.921204 | + | 0.389080i | \(0.872793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.30697 | −1.44692 | −0.723459 | − | 0.690368i | \(-0.757449\pi\) | ||||
−0.723459 | + | 0.690368i | \(0.757449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0700696 | 0.0152904 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92950 | −1.44490 | −0.722450 | − | 0.691423i | \(-0.756984\pi\) | ||||
−0.722450 | + | 0.691423i | \(0.756984\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.257215 | 0.0514431 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.486722 | −0.0936696 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.203942 | −0.0378710 | −0.0189355 | − | 0.999821i | \(-0.506028\pi\) | ||||
−0.0189355 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.39783 | 1.32869 | 0.664345 | − | 0.747426i | \(-0.268711\pi\) | ||||
0.664345 | + | 0.747426i | \(0.268711\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.143019 | −0.0248964 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.97834 | 0.334400 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.37224 | 0.718791 | 0.359396 | − | 0.933185i | \(-0.382983\pi\) | ||||
0.359396 | + | 0.933185i | \(0.382983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.375388 | −0.0601102 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.55508 | −0.711383 | −0.355692 | − | 0.934603i | \(-0.615755\pi\) | ||||
−0.355692 | + | 0.934603i | \(0.615755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.44082 | 0.982217 | 0.491108 | − | 0.871099i | \(-0.336592\pi\) | ||||
0.491108 | + | 0.871099i | \(0.336592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.86346 | −1.02314 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.7488 | 1.85961 | 0.929803 | − | 0.368057i | \(-0.119977\pi\) | ||||
0.929803 | + | 0.368057i | \(0.119977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.25553 | −0.893648 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.616904 | −0.0863838 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.311880 | 0.0428400 | 0.0214200 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214200 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.03798 | −0.544481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.512186 | −0.0678407 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.24784 | 0.422833 | 0.211416 | − | 0.977396i | \(-0.432192\pi\) | ||||
0.211416 | + | 0.977396i | \(0.432192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.12026 | −0.655582 | −0.327791 | − | 0.944750i | \(-0.606304\pi\) | ||||
−0.327791 | + | 0.944750i | \(0.606304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.58278 | −0.325400 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5987 | −1.31460 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.11318 | −0.135997 | −0.0679986 | − | 0.997685i | \(-0.521661\pi\) | ||||
−0.0679986 | + | 0.997685i | \(0.521661\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.562742 | −0.0677461 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.73760 | 0.918284 | 0.459142 | − | 0.888363i | \(-0.348157\pi\) | ||||
0.459142 | + | 0.888363i | \(0.348157\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.17979 | 0.489207 | 0.244604 | − | 0.969623i | \(-0.421342\pi\) | ||||
0.244604 | + | 0.969623i | \(0.421342\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0208883 | 0.00241198 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.51953 | −0.173166 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.537021 | −0.0604196 | −0.0302098 | − | 0.999544i | \(-0.509618\pi\) | ||||
−0.0302098 | + | 0.999544i | \(0.509618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94069 | 0.993410 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.11313 | −0.341711 | −0.170855 | − | 0.985296i | \(-0.554653\pi\) | ||||
−0.170855 | + | 0.985296i | \(0.554653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.4176 | −1.88920 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0165620 | −0.00177563 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.20922 | 0.340177 | 0.170088 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170088 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.98838 | −0.418096 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.600775 | 0.0622974 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.4610 | −1.48367 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.73666 | 0.277866 | 0.138933 | − | 0.990302i | \(-0.455633\pi\) | ||||
0.138933 | + | 0.990302i | \(0.455633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.27171 | 0.529827 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7368 | 1.46637 | 0.733183 | − | 0.680032i | \(-0.238034\pi\) | ||||
0.733183 | + | 0.680032i | \(0.238034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.20154 | −0.315457 | −0.157729 | − | 0.987483i | \(-0.550417\pi\) | ||||
−0.157729 | + | 0.987483i | \(0.550417\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.160660 | 0.0156788 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.82728 | 0.563344 | 0.281672 | − | 0.959511i | \(-0.409111\pi\) | ||||
0.281672 | + | 0.959511i | \(0.409111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.67970 | −0.256669 | −0.128335 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128335 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.355067 | 0.0337015 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.41423 | −0.885616 | −0.442808 | − | 0.896616i | \(-0.646018\pi\) | ||||
−0.442808 | + | 0.896616i | \(0.646018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8884 | −1.48160 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.8369 | 1.27922 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.55440 | −0.600841 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.89850 | −0.718045 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.369916 | −0.0333542 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8745 | −0.972649 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9736 | 1.06248 | 0.531241 | − | 0.847220i | \(-0.321726\pi\) | ||||
0.531241 | + | 0.847220i | \(0.321726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.523056 | 0.0460525 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.57207 | −0.224723 | −0.112361 | − | 0.993667i | \(-0.535841\pi\) | ||||
−0.112361 | + | 0.993667i | \(0.535841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.44181 | −0.471864 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.11599 | −0.0960487 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.5342 | −1.92523 | −0.962613 | − | 0.270880i | \(-0.912685\pi\) | ||||
−0.962613 | + | 0.270880i | \(0.912685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4030 | −0.967189 | −0.483594 | − | 0.875292i | \(-0.660669\pi\) | ||||
−0.483594 | + | 0.875292i | \(0.660669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03533 | 0.0871902 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.14066 | 0.680756 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.467610 | −0.0388329 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.508009 | −0.0418999 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.55792 | −0.701092 | −0.350546 | − | 0.936546i | \(-0.614004\pi\) | ||||
−0.350546 | + | 0.936546i | \(0.614004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5694 | −1.10427 | −0.552133 | − | 0.833756i | \(-0.686186\pi\) | ||||
−0.552133 | + | 0.833756i | \(0.686186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.7392 | 1.83836 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9622 | 1.36244 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3501 | 0.905840 | 0.452920 | − | 0.891551i | \(-0.350382\pi\) | ||||
0.452920 | + | 0.891551i | \(0.350382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0253276 | 0.00200861 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.97895 | −0.471207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.33221 | 0.339325 | 0.169663 | − | 0.985502i | \(-0.445732\pi\) | ||||
0.169663 | + | 0.985502i | \(0.445732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.327922 | −0.0255287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.36718 | 0.643630 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.8793 | 1.44374 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.4544 | −1.55512 | −0.777559 | − | 0.628811i | \(-0.783542\pi\) | ||||
−0.777559 | + | 0.628811i | \(0.783542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.221932 | 0.0167765 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.263756 | 0.0198251 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.241097 | −0.0180204 | −0.00901022 | − | 0.999959i | \(-0.502868\pi\) | ||||
−0.00901022 | + | 0.999959i | \(0.502868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.39871 | −0.698600 | −0.349300 | − | 0.937011i | \(-0.613581\pi\) | ||||
−0.349300 | + | 0.937011i | \(0.613581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.415814 | −0.0307379 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0249 | 0.737048 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3782 | 0.978308 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.419956 | −0.0305473 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3388 | −0.748087 | −0.374044 | − | 0.927411i | \(-0.622029\pi\) | ||||
−0.374044 | + | 0.927411i | \(0.622029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9283 | 0.930599 | 0.465300 | − | 0.885153i | \(-0.345947\pi\) | ||||
0.465300 | + | 0.885153i | \(0.345947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.860713 | −0.0616370 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8318 | −0.771735 | −0.385868 | − | 0.922554i | \(-0.626098\pi\) | ||||
−0.385868 | + | 0.922554i | \(0.626098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.55955 | 0.464994 | 0.232497 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232497 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0904012 | −0.00637641 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.175966 | −0.0123504 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.4442 | −0.729452 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.7428 | 1.44172 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1073 | 0.768305 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3104 | 1.05401 | 0.527007 | − | 0.849861i | \(-0.323314\pi\) | ||||
0.527007 | + | 0.849861i | \(0.323314\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.628367 | 0.0430550 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.7679 | 1.00716 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.38303 | 0.433309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.339439 | 0.0229371 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.1143 | 2.36204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.22753 | 0.483991 | 0.241996 | − | 0.970277i | \(-0.422198\pi\) | ||||
0.241996 | + | 0.970277i | \(0.422198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.769949 | −0.0513300 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.7927 | −1.51281 | −0.756403 | − | 0.654105i | \(-0.773045\pi\) | ||||
−0.756403 | + | 0.654105i | \(0.773045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5332 | −0.960380 | −0.480190 | − | 0.877164i | \(-0.659432\pi\) | ||||
−0.480190 | + | 0.877164i | \(0.659432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.123400 | −0.00811914 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6521 | −0.894381 | −0.447191 | − | 0.894439i | \(-0.647575\pi\) | ||||
−0.447191 | + | 0.894439i | \(0.647575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.2313 | 1.90684 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0436112 | −0.00283285 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.5820 | −1.39602 | −0.698010 | − | 0.716088i | \(-0.745931\pi\) | ||||
−0.698010 | + | 0.716088i | \(0.745931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.66976 | 0.365222 | 0.182611 | − | 0.983185i | \(-0.441545\pi\) | ||||
0.182611 | + | 0.983185i | \(0.441545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.18623 | 0.140247 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.3431 | −0.916345 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.1537 | 1.85501 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.252816 | −0.0160216 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.58019 | −0.415338 | −0.207669 | − | 0.978199i | \(-0.566588\pi\) | ||||
−0.207669 | + | 0.978199i | \(0.566588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2036 | 0.767234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.41447 | −0.0885779 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8355 | 1.73633 | 0.868165 | − | 0.496276i | \(-0.165300\pi\) | ||||
0.868165 | + | 0.496276i | \(0.165300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.77248 | 0.234410 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.610480 | 0.0377878 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.19313 | 0.505210 | 0.252605 | − | 0.967570i | \(-0.418713\pi\) | ||||
0.252605 | + | 0.967570i | \(0.418713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.715097 | 0.0439281 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.260619 | 0.0159496 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.5537 | 1.67998 | 0.839989 | − | 0.542603i | \(-0.182561\pi\) | ||||
0.839989 | + | 0.542603i | \(0.182561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.62325 | −0.0986056 | −0.0493028 | − | 0.998784i | \(-0.515700\pi\) | ||||
−0.0493028 | + | 0.998784i | \(0.515700\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.323894 | −0.0196030 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.452984 | −0.0273160 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50841 | −0.330968 | −0.165484 | − | 0.986212i | \(-0.552919\pi\) | ||||
−0.165484 | + | 0.986212i | \(0.552919\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.1447 | −1.32577 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3226 | −1.09304 | −0.546518 | − | 0.837447i | \(-0.684047\pi\) | ||||
−0.546518 | + | 0.837447i | \(0.684047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.8520 | −1.00175 | −0.500874 | − | 0.865520i | \(-0.666988\pi\) | ||||
−0.500874 | + | 0.865520i | \(0.666988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.17437 | −0.0695637 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.93023 | −0.231994 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.7060 | 2.39447 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.222243 | 0.0130281 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.5638 | −0.617142 | −0.308571 | − | 0.951201i | \(-0.599851\pi\) | ||||
−0.308571 | + | 0.951201i | \(0.599851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.44685 | 0.433572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.857170 | 0.0497380 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.0314 | 1.85242 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.55730 | 0.320318 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.19677 | 0.0687525 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7400 | −0.672233 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.9725 | −1.76769 | −0.883846 | − | 0.467777i | \(-0.845055\pi\) | ||||
−0.883846 | + | 0.467777i | \(0.845055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.259996 | −0.0147906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.64222 | −0.433350 | −0.216675 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216675 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.86882 | 0.105632 | 0.0528158 | − | 0.998604i | \(-0.483180\pi\) | ||||
0.0528158 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.92197 | −0.333665 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2502 | −1.36203 | −0.681015 | − | 0.732270i | \(-0.738461\pi\) | ||||
−0.681015 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.359163 | 0.0201093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.473231 | 0.0264132 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.9105 | 2.66581 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.18897 | −0.0659521 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.217618 | −0.0120343 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0000 | 0.606449 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4463 | 1.06886 | 0.534432 | − | 0.845212i | \(-0.320526\pi\) | ||||
0.534432 | + | 0.845212i | \(0.320526\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.0879 | −0.717211 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.55238 | −0.139451 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.55152 | −0.302411 | −0.151205 | − | 0.988502i | \(-0.548315\pi\) | ||||
−0.151205 | + | 0.988502i | \(0.548315\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.764525 | −0.0415233 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.0284 | −0.705527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4372 | −0.617551 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.29029 | −0.0694668 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.70726 | −0.306382 | −0.153191 | − | 0.988197i | \(-0.548955\pi\) | ||||
−0.153191 | + | 0.988197i | \(0.548955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.24638 | 0.334361 | 0.167181 | − | 0.985926i | \(-0.446534\pi\) | ||||
0.167181 | + | 0.985926i | \(0.446534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.24985 | 0.120088 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.51596 | −0.346810 | −0.173405 | − | 0.984851i | \(-0.555477\pi\) | ||||
−0.173405 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7412 | 0.941607 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.532280 | −0.0281712 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.8370 | 0.677510 | 0.338755 | − | 0.940875i | \(-0.389994\pi\) | ||||
0.338755 | + | 0.940875i | \(0.389994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7778 | 1.09357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.641433 | −0.0336665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.58368 | 0.501633 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.2602 | 1.05758 | 0.528788 | − | 0.848754i | \(-0.322647\pi\) | ||||
0.528788 | + | 0.848754i | \(0.322647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.6352 | 0.709820 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.269098 | 0.0139709 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.9950 | −1.76020 | −0.880098 | − | 0.474792i | \(-0.842523\pi\) | ||||
−0.880098 | + | 0.474792i | \(0.842523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.883117 | −0.0456040 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.942713 | 0.0485522 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.8625 | −0.557971 | −0.278986 | − | 0.960295i | \(-0.589998\pi\) | ||||
−0.278986 | + | 0.960295i | \(0.589998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.972368 | 0.0498159 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5261 | 1.09993 | 0.549966 | − | 0.835187i | \(-0.314641\pi\) | ||||
0.549966 | + | 0.835187i | \(0.314641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.48407 | −0.177565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.2800 | −0.980057 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.4022 | −1.33864 | −0.669322 | − | 0.742972i | \(-0.733416\pi\) | ||||
−0.669322 | + | 0.742972i | \(0.733416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.6396 | 2.66210 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.208877 | −0.0105364 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.23132 | −0.0619542 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9273 | −1.50201 | −0.751003 | − | 0.660298i | \(-0.770430\pi\) | ||||
−0.751003 | + | 0.660298i | \(0.770430\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.441927 | −0.0221240 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1862 | 1.50743 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.1962 | −1.70344 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.4998 | 1.01864 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.69998 | −0.381674 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.8008 | 1.37466 | 0.687330 | − | 0.726346i | \(-0.258783\pi\) | ||||
0.687330 | + | 0.726346i | \(0.258783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.82999 | −0.0902668 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.80232 | 0.137893 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.13798 | −0.350390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.926031 | −0.0453479 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.3619 | −1.82525 | −0.912624 | − | 0.408799i | \(-0.865948\pi\) | ||||
−0.912624 | + | 0.408799i | \(0.865948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.20756 | −0.0588530 | −0.0294265 | − | 0.999567i | \(-0.509368\pi\) | ||||
−0.0294265 | + | 0.999567i | \(0.509368\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38.1624 | −1.85552 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.95392 | −0.0947791 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.41789 | −0.213797 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.661099 | 0.0319182 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.1609 | −1.54914 | −0.774568 | − | 0.632490i | \(-0.782033\pi\) | ||||
−0.774568 | + | 0.632490i | \(0.782033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3933 | 0.739756 | 0.369878 | − | 0.929080i | \(-0.379399\pi\) | ||||
0.369878 | + | 0.929080i | \(0.379399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0379744 | −0.00182073 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.7041 | 2.09065 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1790 | −1.01082 | −0.505409 | − | 0.862880i | \(-0.668658\pi\) | ||||
−0.505409 | + | 0.862880i | \(0.668658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.7253 | 0.891683 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.9637 | 0.900993 | 0.450497 | − | 0.892778i | \(-0.351247\pi\) | ||||
0.450497 | + | 0.892778i | \(0.351247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.35829 | 0.348817 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.694985 | −0.0328716 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.60577 | −0.0757809 | −0.0378905 | − | 0.999282i | \(-0.512064\pi\) | ||||
−0.0378905 | + | 0.999282i | \(0.512064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.02198 | 0.377740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.10197 | −0.0517750 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.14480 | −0.428715 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.9837 | 1.96391 | 0.981957 | − | 0.189104i | \(-0.0605585\pi\) | ||||
0.981957 | + | 0.189104i | \(0.0605585\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.69735 | 0.172578 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8844 | −0.786383 | −0.393191 | − | 0.919457i | \(-0.628629\pi\) | ||||
−0.393191 | + | 0.919457i | \(0.628629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50068 | 0.116216 | 0.0581081 | − | 0.998310i | \(-0.481493\pi\) | ||||
0.0581081 | + | 0.998310i | \(0.481493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.37749 | 0.0638797 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.3886 | −1.86896 | −0.934481 | − | 0.356014i | \(-0.884136\pi\) | ||||
−0.934481 | + | 0.356014i | \(0.884136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.960483 | −0.0443510 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.921740 | 0.0424715 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.3430 | −0.521551 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.62225 | −0.0744338 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.933583 | −0.0427458 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.8312 | −1.31733 | −0.658665 | − | 0.752436i | \(-0.728879\pi\) | ||||
−0.658665 | + | 0.752436i | \(0.728879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.2105 | −0.921520 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.485547 | −0.0220932 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.27478 | 0.284923 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.6060 | 1.52284 | 0.761418 | − | 0.648262i | \(-0.224504\pi\) | ||||
0.761418 | + | 0.648262i | \(0.224504\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.351817 | 0.0159097 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.6015 | 0.478438 | 0.239219 | − | 0.970966i | \(-0.423109\pi\) | ||||
0.239219 | + | 0.970966i | \(0.423109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.54923 | 0.0697739 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0873 | 0.543284 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.67619 | 0.299468 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.8999 | −1.69663 | −0.848317 | − | 0.529489i | \(-0.822384\pi\) | ||||
−0.848317 | + | 0.529489i | \(0.822384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0812095 | 0.00362817 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6201 | −0.696466 | −0.348233 | − | 0.937408i | \(-0.613218\pi\) | ||||
−0.348233 | + | 0.937408i | \(0.613218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.7894 | 1.50361 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.679495 | 0.0301774 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.7163 | −0.652286 | −0.326143 | − | 0.945320i | \(-0.605749\pi\) | ||||
−0.326143 | + | 0.945320i | \(0.605749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.60643 | 0.159539 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.06974 | 0.135532 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.34069 | −0.323469 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.4521 | −0.987440 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.66109 | −0.0729138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.4380 | −1.33351 | −0.666757 | − | 0.745275i | \(-0.732318\pi\) | ||||
−0.666757 | + | 0.745275i | \(0.732318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1487 | 1.14340 | 0.571701 | − | 0.820462i | \(-0.306284\pi\) | ||||
0.571701 | + | 0.820462i | \(0.306284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0180230 | 0.000786587 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56.1972 | −2.44799 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0180 | 1.08774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.72210 | −0.421903 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.0557 | 0.912023 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.3611 | 0.577653 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0195794 | −0.000844913 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0167 | 0.474522 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.81820 | −0.121164 | −0.0605818 | − | 0.998163i | \(-0.519296\pi\) | ||||
−0.0605818 | + | 0.998163i | \(0.519296\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.763265 | −0.0327548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.14419 | −0.263188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.7573 | 1.91368 | 0.956842 | − | 0.290610i | \(-0.0938581\pi\) | ||||
0.956842 | + | 0.290610i | \(0.0938581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3270 | 0.654141 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.28625 | 0.0547962 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.463355 | −0.0197039 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.814121 | 0.0345575 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.9026 | 1.35176 | 0.675878 | − | 0.737013i | \(-0.263765\pi\) | ||||
0.675878 | + | 0.737013i | \(0.263765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.7725 | −1.25924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.08643 | 0.0458693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6342 | −0.911772 | −0.455886 | − | 0.890038i | \(-0.650678\pi\) | ||||
−0.455886 | + | 0.890038i | \(0.650678\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.5855 | −0.908110 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.71425 | 0.323968 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2958 | 1.31199 | 0.655994 | − | 0.754766i | \(-0.272250\pi\) | ||||
0.655994 | + | 0.754766i | \(0.272250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9511 | −0.500140 | −0.250070 | − | 0.968228i | \(-0.580454\pi\) | ||||
−0.250070 | + | 0.968228i | \(0.580454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.839607 | −0.0350751 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.78237 | −0.0743301 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9566 | 0.789176 | 0.394588 | − | 0.918858i | \(-0.370887\pi\) | ||||
0.394588 | + | 0.918858i | \(0.370887\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.04990 | 0.0436324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.68609 | −0.111438 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.549254 | −0.0227478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.7261 | 1.31171 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.9488 | −1.02975 | −0.514874 | − | 0.857266i | \(-0.672161\pi\) | ||||
−0.514874 | + | 0.857266i | \(0.672161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.6579 | −1.92250 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.879647 | −0.0361838 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.9540 | 1.31219 | 0.656096 | − | 0.754677i | \(-0.272207\pi\) | ||||
0.656096 | + | 0.754677i | \(0.272207\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0283 | −0.616102 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.532698 | 0.0218019 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.64258 | −0.0671139 | −0.0335570 | − | 0.999437i | \(-0.510684\pi\) | ||||
−0.0335570 | + | 0.999437i | \(0.510684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6343 | 0.719317 | 0.359658 | − | 0.933084i | \(-0.382893\pi\) | ||||
0.359658 | + | 0.933084i | \(0.382893\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.33221 | 0.135698 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.1102 | −0.736283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0275 | 0.772302 | 0.386151 | − | 0.922436i | \(-0.373804\pi\) | ||||
0.386151 | + | 0.922436i | \(0.373804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0142901 | −0.000579064 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.9310 | −2.38409 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.4081 | −1.71285 | −0.856423 | − | 0.516275i | \(-0.827318\pi\) | ||||
−0.856423 | + | 0.516275i | \(0.827318\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.848165 | −0.0342013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.09479 | −0.164850 | −0.0824250 | − | 0.996597i | \(-0.526266\pi\) | ||||
−0.0824250 | + | 0.996597i | \(0.526266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0351 | 0.805280 | 0.402640 | − | 0.915358i | \(-0.368093\pi\) | ||||
0.402640 | + | 0.915358i | \(0.368093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.37274 | 0.135343 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.76899 | 0.110937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.2199 | −1.04880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.902015 | 0.0360230 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.2135 | −1.32431 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6642 | −0.782819 | −0.391410 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391410 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.24335 | 0.0494189 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.4538 | 1.08947 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.9160 | 1.14569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.1618 | −0.916265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9574 | −0.788269 | −0.394134 | − | 0.919053i | \(-0.628956\pi\) | ||||
−0.394134 | + | 0.919053i | \(0.628956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.498013 | −0.0196397 | −0.00981985 | − | 0.999952i | \(-0.503126\pi\) | ||||
−0.00981985 | + | 0.999952i | \(0.503126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.19930 | 0.0472222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.57148 | 0.219037 | 0.109519 | − | 0.993985i | \(-0.465069\pi\) | ||||
0.109519 | + | 0.993985i | \(0.465069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.71980 | −0.224522 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.518363 | 0.0203163 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.49594 | 0.293339 | 0.146669 | − | 0.989186i | \(-0.453145\pi\) | ||||
0.146669 | + | 0.989186i | \(0.453145\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.89741 | −0.230431 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.5118 | −0.488132 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.1158 | −1.83537 | −0.917686 | − | 0.397307i | \(-0.869945\pi\) | ||||
−0.917686 | + | 0.397307i | \(0.869945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.9953 | −1.01110 | −0.505550 | − | 0.862797i | \(-0.668711\pi\) | ||||
−0.505550 | + | 0.862797i | \(0.668711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.85162 | 0.110748 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4773 | −0.483849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.41321 | 0.0547199 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.586944 | 0.0226926 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.01733 | 0.348110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.98702 | 0.269330 | 0.134665 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134665 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.125192 | −0.00481865 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.3439 | 1.66584 | 0.832922 | − | 0.553391i | \(-0.186666\pi\) | ||||
0.832922 | + | 0.553391i | \(0.186666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.36126 | 0.0906167 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.85099 | −0.0709300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.8893 | −1.29674 | −0.648368 | − | 0.761327i | \(-0.724548\pi\) | ||||
−0.648368 | + | 0.761327i | \(0.724548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.6678 | −1.97413 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.18023 | −0.0450287 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.44165 | −0.0549226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2872 | 1.57064 | 0.785320 | − | 0.619090i | \(-0.212499\pi\) | ||||
0.785320 | + | 0.619090i | \(0.212499\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.54856 | 0.172786 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.1455 | −0.991754 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6024 | 1.31066 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.10868 | −0.0419343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.8124 | −0.446149 | −0.223074 | − | 0.974801i | \(-0.571609\pi\) | ||||
−0.223074 | + | 0.974801i | \(0.571609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.5756 | −1.04003 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.37386 | 0.0894047 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.7153 | 0.478207 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4545 | 0.655519 | 0.327760 | − | 0.944761i | \(-0.393706\pi\) | ||||
0.327760 | + | 0.944761i | \(0.393706\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.60752 | 0.0602868 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −51.2633 | −1.91983 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.6654 | 0.698047 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.75266 | −0.0654543 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.2491 | 1.42645 | 0.713225 | − | 0.700935i | \(-0.247234\pi\) | ||||
0.713225 | + | 0.700935i | \(0.247234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.76237 | −0.102876 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.460439 | 0.0171239 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0524569 | −0.00194820 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.9911 | 0.778517 | 0.389259 | − | 0.921129i | \(-0.372731\pi\) | ||||
0.389259 | + | 0.921129i | \(0.372731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6445 | −0.986834 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.9274 | −1.80964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.9796 | −0.885708 | −0.442854 | − | 0.896594i | \(-0.646034\pi\) | ||||
−0.442854 | + | 0.896594i | \(0.646034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.16479 | −0.0429641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.96044 | 0.0722137 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3841 | 1.08091 | 0.540455 | − | 0.841373i | \(-0.318252\pi\) | ||||
0.540455 | + | 0.841373i | \(0.318252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.36756 | 0.0869745 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.8340 | 1.42468 | 0.712340 | − | 0.701834i | \(-0.247635\pi\) | ||||
0.712340 | + | 0.701834i | \(0.247635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6221 | −0.718899 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.31887 | 0.340960 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.02792 | 0.183716 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4911 | −0.455805 | −0.227903 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227903 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.534374 | −0.0194737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.1128 | −1.13231 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4743 | 0.671461 | 0.335731 | − | 0.941958i | \(-0.391017\pi\) | ||||
0.335731 | + | 0.941958i | \(0.391017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.991049 | 0.0359728 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.60628 | −0.166977 | −0.0834887 | − | 0.996509i | \(-0.526606\pi\) | ||||
−0.0834887 | + | 0.996509i | \(0.526606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.31212 | −0.0837042 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 52.1379 | 1.88505 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.0130 | −0.542089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.1301 | −1.48319 | −0.741595 | − | 0.670848i | \(-0.765930\pi\) | ||||
−0.741595 | + | 0.670848i | \(0.765930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.26051 | 0.0814101 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.9381 | −1.29260 | −0.646301 | − | 0.763082i | \(-0.723685\pi\) | ||||
−0.646301 | + | 0.763082i | \(0.723685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.90284 | 0.0683519 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.306361 | 0.0109906 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.7287 | 1.02931 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6267 | −0.487603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0992628 | 0.00354736 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0243 | 0.928847 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.3172 | 1.15198 | 0.575991 | − | 0.817456i | \(-0.304616\pi\) | ||||
0.575991 | + | 0.817456i | \(0.304616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.665360 | 0.0236874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.12283 | −0.288815 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.6682 | 0.840483 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0580727 | 0.00205963 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.1044 | 1.34973 | 0.674863 | − | 0.737943i | \(-0.264203\pi\) | ||||
0.674863 | + | 0.737943i | \(0.264203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −96.8457 | −3.42615 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.60649 | −0.339429 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.36106 | −0.259766 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7089 | −0.483175 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.23762 | 0.0787681 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.51704 | −0.123652 | −0.0618262 | − | 0.998087i | \(-0.519692\pi\) | ||||
−0.0618262 | + | 0.998087i | \(0.519692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.5661 | 0.511484 | 0.255742 | − | 0.966745i | \(-0.417680\pi\) | ||||
0.255742 | + | 0.966745i | \(0.417680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.131824 | −0.00462325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.93317 | 0.347944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.6221 | −1.42119 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.9388 | 0.417176 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.19351 | 0.251055 | 0.125528 | − | 0.992090i | \(-0.459938\pi\) | ||||
0.125528 | + | 0.992090i | \(0.459938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.0141 | 1.88281 | 0.941407 | − | 0.337272i | \(-0.109504\pi\) | ||||
0.941407 | + | 0.337272i | \(0.109504\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0367866 | −0.00128075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.2108 | −0.807117 | −0.403559 | − | 0.914954i | \(-0.632227\pi\) | ||||
−0.403559 | + | 0.914954i | \(0.632227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3315 | 0.845067 | 0.422533 | − | 0.906347i | \(-0.361141\pi\) | ||||
0.422533 | + | 0.906347i | \(0.361141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.447335 | −0.0155179 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.5198 | 1.64646 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29286 | 0.0793478 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.60069 | −0.124458 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.5082 | −1.43302 | −0.716511 | − | 0.697576i | \(-0.754262\pi\) | ||||
−0.716511 | + | 0.697576i | \(0.754262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9584 | −0.998566 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.48797 | −0.0512485 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.1848 | 0.659977 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.81502 | −0.234167 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.36854 | −0.0469683 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2974 | −1.03858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.3947 | 1.21189 | 0.605946 | − | 0.795506i | \(-0.292795\pi\) | ||||
0.605946 | + | 0.795506i | \(0.292795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.2876 | 1.48041 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7570 | −0.401613 | −0.200806 | − | 0.979631i | \(-0.564356\pi\) | ||||
−0.200806 | + | 0.979631i | \(0.564356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.7215 | −1.52588 | −0.762939 | − | 0.646471i | \(-0.776244\pi\) | ||||
−0.762939 | + | 0.646471i | \(0.776244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.319172 | −0.0108774 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.0891 | −1.16041 | −0.580204 | − | 0.814471i | \(-0.697027\pi\) | ||||
−0.580204 | + | 0.814471i | \(0.697027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.8990 | −1.59462 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.30571 | 0.112268 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.945752 | 0.0320824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.14566 | 0.174354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.19193 | −0.277255 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.38283 | −0.317198 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.8745 | 1.11009 | 0.555046 | − | 0.831820i | \(-0.312701\pi\) | ||||
0.555046 | + | 0.831820i | \(0.312701\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.857879 | −0.0289355 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0350 | −1.55096 | −0.775480 | − | 0.631373i | \(-0.782492\pi\) | ||||
−0.775480 | + | 0.631373i | \(0.782492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6701 | 1.67153 | 0.835765 | − | 0.549087i | \(-0.185024\pi\) | ||||
0.835765 | + | 0.549087i | \(0.185024\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.604755 | 0.0203286 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.3697 | −0.650370 | −0.325185 | − | 0.945650i | \(-0.605427\pi\) | ||||
−0.325185 | + | 0.945650i | \(0.605427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3311 | 0.346494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.7455 | −0.527495 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −80.4064 | −2.69070 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.552802 | −0.0184781 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.60125 | 0.0868533 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.50873 | −0.0503188 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.36918 | −0.0789287 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.451306 | 0.0150185 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.5499 | −0.716344 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.28749 | 0.142364 | 0.0711819 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711819 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44.1132 | −1.46314 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.67992 | 0.221315 | 0.110658 | − | 0.993859i | \(-0.464704\pi\) | ||||
0.110658 | + | 0.993859i | \(0.464704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.48256 | 0.181446 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.953404 | −0.0315186 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.21925 | −0.0732860 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.93378 | −0.228724 | −0.114362 | − | 0.993439i | \(-0.536482\pi\) | ||||
−0.114362 | + | 0.993439i | \(0.536482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.51526 | −0.0828807 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.7668 | −1.17728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12461 | 0.0369768 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.58350 | 0.314764 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.7537 | 1.20585 | 0.602924 | − | 0.797798i | \(-0.294002\pi\) | ||||
0.602924 | + | 0.797798i | \(0.294002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.4534 | 1.29303 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.620621 | −0.0203182 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.6743 | 1.00316 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9060 | 0.486957 | 0.243479 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243479 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.151766 | 0.00495268 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.0487 | 1.07736 | 0.538679 | − | 0.842511i | \(-0.318924\pi\) | ||||
0.538679 | + | 0.842511i | \(0.318924\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.5644 | 1.02788 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.962900 | −0.0313231 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.7285 | −0.673585 | −0.336792 | − | 0.941579i | \(-0.609342\pi\) | ||||
−0.336792 | + | 0.941579i | \(0.609342\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3209 | −0.627184 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.96935 | −0.0638606 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.46024 | −0.144481 | −0.0722407 | − | 0.997387i | \(-0.523015\pi\) | ||||
−0.0722407 | + | 0.997387i | \(0.523015\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.7054 | −0.767088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0291675 | 0.000942851 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.4431 | −0.627849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.7279 | 0.765417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.4434 | −0.562106 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.6428 | 0.954235 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.6707 | −0.986302 | −0.493151 | − | 0.869944i | \(-0.664155\pi\) | ||||
−0.493151 | + | 0.869944i | \(0.664155\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.89079 | 0.124990 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0650 | −0.483458 | −0.241729 | − | 0.970344i | \(-0.577714\pi\) | ||||
−0.241729 | + | 0.970344i | \(0.577714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.83878 | −0.315417 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0965556 | −0.00309225 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.6234 | −0.883752 | −0.441876 | − | 0.897076i | \(-0.645687\pi\) | ||||
−0.441876 | + | 0.897076i | \(0.645687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.65178 | −0.180632 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.02144 | 0.256105 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8238 | 0.823650 | 0.411825 | − | 0.911263i | \(-0.364892\pi\) | ||||
0.411825 | + | 0.911263i | \(0.364892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.8359 | −0.791337 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.893305 | 0.0284342 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.6317 | −1.41921 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.6481 | 0.687675 | 0.343838 | − | 0.939029i | \(-0.388273\pi\) | ||||
0.343838 | + | 0.939029i | \(0.388273\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.57922 | 0.0501151 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0401 | 0.476805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0483 | 0.349902 | 0.174951 | − | 0.984577i | \(-0.444023\pi\) | ||||
0.174951 | + | 0.984577i | \(0.444023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.12806 | −0.0673289 |
(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 | 1336.2.a.c.1.5 | ✓ | 9 | |
4.3 | odd | 2 | 2672.2.a.m.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.c.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial | |
2672.2.a.m.1.5 | 9 | 4.3 | odd | 2 |