Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [520,2,Mod(1,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(4.15222090511\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 520.1 |
$q$-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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.73205 | −1.54444 | −0.772219 | − | 0.635356i | \(-0.780853\pi\) | ||||
−0.772219 | + | 0.635356i | \(0.780853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.53590 | −0.553378 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.19615 | 0.457929 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.46410 | 0.271877 | 0.135938 | − | 0.990717i | \(-0.456595\pi\) | ||||
0.135938 | + | 0.990717i | \(0.456595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26795 | −0.227730 | −0.113865 | − | 0.993496i | \(-0.536323\pi\) | ||||
−0.113865 | + | 0.993496i | \(0.536323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.928203 | −0.161579 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | 0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9282 | 1.79659 | 0.898293 | − | 0.439397i | \(-0.144808\pi\) | ||||
0.898293 | + | 0.439397i | \(0.144808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.732051 | 0.117222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.53590 | −0.708388 | −0.354194 | − | 0.935172i | \(-0.615245\pi\) | ||||
−0.354194 | + | 0.935172i | \(0.615245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.732051 | 0.111637 | 0.0558184 | − | 0.998441i | \(-0.482223\pi\) | ||||
0.0558184 | + | 0.998441i | \(0.482223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46410 | 0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.53590 | −0.661629 | −0.330814 | − | 0.943696i | \(-0.607323\pi\) | ||||
−0.330814 | + | 0.943696i | \(0.607323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.53590 | 0.623054 | 0.311527 | − | 0.950237i | \(-0.399160\pi\) | ||||
0.311527 | + | 0.950237i | \(0.399160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26795 | 0.170970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.92820 | −0.652756 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.1962 | −1.58780 | −0.793902 | − | 0.608046i | \(-0.791954\pi\) | ||||
−0.793902 | + | 0.608046i | \(0.791954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46410 | 0.187459 | 0.0937295 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937295 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.53590 | 1.07542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8564 | −1.44849 | −0.724245 | − | 0.689542i | \(-0.757812\pi\) | ||||
−0.724245 | + | 0.689542i | \(0.757812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.60770 | 0.193544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.66025 | −0.671749 | −0.335874 | − | 0.941907i | \(-0.609032\pi\) | ||||
−0.335874 | + | 0.941907i | \(0.609032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.39230 | 0.500550 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.46410 | 1.06479 | 0.532397 | − | 0.846495i | \(-0.321291\pi\) | ||||
0.532397 | + | 0.846495i | \(0.321291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.53590 | 0.497880 | 0.248940 | − | 0.968519i | \(-0.419918\pi\) | ||||
0.248940 | + | 0.968519i | \(0.419918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.07180 | 0.114909 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.92820 | 0.946388 | 0.473194 | − | 0.880958i | \(-0.343101\pi\) | ||||
0.473194 | + | 0.880958i | \(0.343101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.46410 | −0.363137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.928203 | −0.0962502 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.73205 | 0.690694 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8564 | 1.60997 | 0.804987 | − | 0.593292i | \(-0.202172\pi\) | ||||
0.804987 | + | 0.593292i | \(0.202172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.12436 | 0.314010 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9282 | −1.68442 | −0.842210 | − | 0.539150i | \(-0.818745\pi\) | ||||
−0.842210 | + | 0.539150i | \(0.818745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.26795 | −0.322001 | −0.161000 | − | 0.986954i | \(-0.551472\pi\) | ||||
−0.161000 | + | 0.986954i | \(0.551472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.53590 | 0.247478 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.1962 | −1.37239 | −0.686197 | − | 0.727416i | \(-0.740721\pi\) | ||||
−0.686197 | + | 0.727416i | \(0.740721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3923 | 1.35391 | 0.676957 | − | 0.736022i | \(-0.263298\pi\) | ||||
0.676957 | + | 0.736022i | \(0.263298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.19615 | −0.204792 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.46410 | −0.227806 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | 1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.32051 | −0.299400 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1244 | 1.51954 | 0.759770 | − | 0.650191i | \(-0.225311\pi\) | ||||
0.759770 | + | 0.650191i | \(0.225311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9282 | 0.954802 | 0.477401 | − | 0.878686i | \(-0.341579\pi\) | ||||
0.477401 | + | 0.878686i | \(0.341579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.3205 | 2.02214 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9282 | −1.10453 | −0.552265 | − | 0.833668i | \(-0.686237\pi\) | ||||
−0.552265 | + | 0.833668i | \(0.686237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.39230 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.32051 | −0.279637 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26795 | −0.106031 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.46410 | −0.121587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.66025 | 0.301893 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.8564 | −1.95439 | −0.977196 | − | 0.212337i | \(-0.931893\pi\) | ||||
−0.977196 | + | 0.212337i | \(0.931893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.26795 | −0.428700 | −0.214350 | − | 0.976757i | \(-0.568763\pi\) | ||||
−0.214350 | + | 0.976757i | \(0.568763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.53590 | 0.690086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.26795 | 0.101844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.32051 | 0.263333 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.60770 | −0.599570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8564 | 0.928665 | 0.464333 | − | 0.885661i | \(-0.346294\pi\) | ||||
0.464333 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.928203 | 0.0722605 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.39230 | −0.494651 | −0.247326 | − | 0.968932i | \(-0.579552\pi\) | ||||
−0.247326 | + | 0.968932i | \(0.579552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.5885 | 1.26855 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.60770 | −0.122231 | −0.0611154 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611154 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | −0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.92820 | −0.671085 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8564 | −1.03568 | −0.517838 | − | 0.855479i | \(-0.673263\pi\) | ||||
−0.517838 | + | 0.855479i | \(0.673263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3205 | −1.73340 | −0.866700 | − | 0.498830i | \(-0.833763\pi\) | ||||
−0.866700 | + | 0.498830i | \(0.833763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.07180 | 0.0792295 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.9282 | −0.803457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.39230 | 0.321197 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8564 | 1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9282 | 1.36960 | 0.684798 | − | 0.728733i | \(-0.259890\pi\) | ||||
0.684798 | + | 0.728733i | \(0.259890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.732051 | −0.0524232 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.9282 | −0.921096 | −0.460548 | − | 0.887635i | \(-0.652347\pi\) | ||||
−0.460548 | + | 0.887635i | \(0.652347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.07180 | 0.0759777 | 0.0379888 | − | 0.999278i | \(-0.487905\pi\) | ||||
0.0379888 | + | 0.999278i | \(0.487905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.67949 | −0.612204 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.07180 | −0.355970 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.53590 | 0.316801 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.41154 | −0.376128 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.53590 | 0.590440 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7846 | −1.15550 | −0.577750 | − | 0.816214i | \(-0.696069\pi\) | ||||
−0.577750 | + | 0.816214i | \(0.696069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.14359 | −0.283914 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.732051 | −0.0499255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.39230 | 0.298169 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | −0.233021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3923 | 1.23164 | 0.615820 | − | 0.787887i | \(-0.288825\pi\) | ||||
0.615820 | + | 0.787887i | \(0.288825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0718 | −1.00035 | −0.500175 | − | 0.865924i | \(-0.666731\pi\) | ||||
−0.500175 | + | 0.865924i | \(0.666731\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.46410 | −0.493242 | −0.246621 | − | 0.969112i | \(-0.579320\pi\) | ||||
−0.246621 | + | 0.969112i | \(0.579320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.21539 | 0.211557 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8564 | −1.30084 | −0.650418 | − | 0.759576i | \(-0.725406\pi\) | ||||
−0.650418 | + | 0.759576i | \(0.725406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.53590 | 0.295889 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.92820 | 0.450035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5167 | −1.26243 | −0.631214 | − | 0.775609i | \(-0.717443\pi\) | ||||
−0.631214 | + | 0.775609i | \(0.717443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3923 | −1.18475 | −0.592376 | − | 0.805661i | \(-0.701810\pi\) | ||||
−0.592376 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.73205 | −0.428350 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.32051 | 0.210429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.53590 | −0.412542 | −0.206271 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206271 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.78461 | −0.175067 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.53590 | 0.158804 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.8564 | 0.739582 | 0.369791 | − | 0.929115i | \(-0.379429\pi\) | ||||
0.369791 | + | 0.929115i | \(0.379429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −37.8564 | −2.35228 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.60770 | −0.223311 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.58846 | −0.406262 | −0.203131 | − | 0.979152i | \(-0.565112\pi\) | ||||
−0.203131 | + | 0.979152i | \(0.565112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.53590 | −0.278638 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.53590 | 0.399990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.8564 | −0.722898 | −0.361449 | − | 0.932392i | \(-0.617718\pi\) | ||||
−0.361449 | + | 0.932392i | \(0.617718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.80385 | 0.474050 | 0.237025 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237025 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.53590 | −0.153480 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.26795 | −0.0764602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.60770 | 0.336934 | 0.168467 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168467 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.12436 | 0.187050 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.60770 | −0.573147 | −0.286574 | − | 0.958058i | \(-0.592516\pi\) | ||||
−0.286574 | + | 0.958058i | \(0.592516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1962 | −1.55720 | −0.778600 | − | 0.627521i | \(-0.784070\pi\) | ||||
−0.778600 | + | 0.627521i | \(0.784070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.92820 | 0.291922 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.7128 | 0.927498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6077 | 0.680455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.85641 | 0.108452 | 0.0542262 | − | 0.998529i | \(-0.482731\pi\) | ||||
0.0542262 | + | 0.998529i | \(0.482731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1962 | 0.710087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.07180 | 0.294295 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.19615 | 0.127007 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.53590 | −0.146167 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3923 | −0.711919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.46410 | −0.0838342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4641 | −0.882583 | −0.441291 | − | 0.897364i | \(-0.645479\pi\) | ||||
−0.441291 | + | 0.897364i | \(0.645479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.39230 | −0.136093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.53590 | −0.370617 | −0.185308 | − | 0.982680i | \(-0.559328\pi\) | ||||
−0.185308 | + | 0.982680i | \(0.559328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2487 | −1.59671 | −0.798356 | − | 0.602186i | \(-0.794297\pi\) | ||||
−0.798356 | + | 0.602186i | \(0.794297\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.53590 | −0.480943 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.7846 | −1.61670 | −0.808352 | − | 0.588699i | \(-0.799640\pi\) | ||||
−0.808352 | + | 0.588699i | \(0.799640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.85641 | −0.103939 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3923 | −0.580042 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.3205 | 1.29759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.39230 | −0.242895 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.7128 | 0.866275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.9808 | 1.59293 | 0.796463 | − | 0.604687i | \(-0.206702\pi\) | ||||
0.796463 | + | 0.604687i | \(0.206702\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.9282 | −1.47566 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8564 | 0.647785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.60770 | 0.305471 | 0.152735 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.5359 | 0.572231 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.60770 | 0.0870616 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.60770 | −0.0865554 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.3397 | 0.662432 | 0.331216 | − | 0.943555i | \(-0.392541\pi\) | ||||
0.331216 | + | 0.943555i | \(0.392541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3205 | 1.56949 | 0.784745 | − | 0.619818i | \(-0.212794\pi\) | ||||
0.784745 | + | 0.619818i | \(0.212794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8564 | −1.37620 | −0.688099 | − | 0.725617i | \(-0.741554\pi\) | ||||
−0.688099 | + | 0.725617i | \(0.741554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.66025 | 0.300415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.78461 | 0.464931 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.1962 | 1.91036 | 0.955180 | − | 0.296026i | \(-0.0956615\pi\) | ||||
0.955180 | + | 0.296026i | \(0.0956615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3205 | 1.38529 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.87564 | −0.360878 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.05256 | −0.420340 | −0.210170 | − | 0.977665i | \(-0.567402\pi\) | ||||
−0.210170 | + | 0.977665i | \(0.567402\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1769 | 0.581847 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.7128 | −0.815769 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0000 | −0.932005 | −0.466002 | − | 0.884783i | \(-0.654306\pi\) | ||||
−0.466002 | + | 0.884783i | \(0.654306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.732051 | −0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.46410 | 0.0754051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3397 | −0.531117 | −0.265559 | − | 0.964095i | \(-0.585556\pi\) | ||||
−0.265559 | + | 0.964095i | \(0.585556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5359 | 0.642234 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.3923 | −1.55297 | −0.776487 | − | 0.630133i | \(-0.783000\pi\) | ||||
−0.776487 | + | 0.630133i | \(0.783000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.39230 | −0.223853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.80385 | −0.0916947 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7128 | 1.30369 | 0.651846 | − | 0.758352i | \(-0.273995\pi\) | ||||
0.651846 | + | 0.758352i | \(0.273995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.60770 | −0.384738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.46410 | −0.476191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0000 | 0.803017 | 0.401508 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401508 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.0718 | 0.854659 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.7846 | 1.93681 | 0.968405 | − | 0.249381i | \(-0.0802271\pi\) | ||||
0.968405 | + | 0.249381i | \(0.0802271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.26795 | −0.0631610 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.46410 | −0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8564 | −0.686837 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.3205 | −1.84538 | −0.922690 | − | 0.385542i | \(-0.874014\pi\) | ||||
−0.922690 | + | 0.385542i | \(0.874014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.46410 | −0.466830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 42.2487 | 2.07892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.53590 | −0.222658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.14359 | 0.300853 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.3205 | −1.13928 | −0.569641 | − | 0.821894i | \(-0.692918\pi\) | ||||
−0.569641 | + | 0.821894i | \(0.692918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7846 | 0.915506 | 0.457753 | − | 0.889079i | \(-0.348654\pi\) | ||||
0.457753 | + | 0.889079i | \(0.348654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.1769 | 0.543440 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.07180 | −0.245441 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.928203 | −0.0448141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.4449 | 1.27380 | 0.636902 | − | 0.770945i | \(-0.280216\pi\) | ||||
0.636902 | + | 0.770945i | \(0.280216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.7846 | 1.28719 | 0.643593 | − | 0.765368i | \(-0.277443\pi\) | ||||
0.643593 | + | 0.765368i | \(0.277443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.07180 | −0.0513887 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.7846 | −0.707244 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3205 | −0.586691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.12436 | −0.243465 | −0.121733 | − | 0.992563i | \(-0.538845\pi\) | ||||
−0.121733 | + | 0.992563i | \(0.538845\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.92820 | −0.423237 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.4641 | −0.826024 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.32051 | −0.439862 | −0.219931 | − | 0.975515i | \(-0.570583\pi\) | ||||
−0.219931 | + | 0.975515i | \(0.570583\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.75129 | 0.270818 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.85641 | −0.181190 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.46410 | 0.162400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7846 | 0.878707 | 0.439353 | − | 0.898314i | \(-0.355208\pi\) | ||||
0.439353 | + | 0.898314i | \(0.355208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.53590 | 0.211258 | 0.105629 | − | 0.994406i | \(-0.466314\pi\) | ||||
0.105629 | + | 0.994406i | \(0.466314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.7846 | −1.43068 | −0.715341 | − | 0.698775i | \(-0.753729\pi\) | ||||
−0.715341 | + | 0.698775i | \(0.753729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.928203 | 0.0430444 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.12436 | −0.0520290 | −0.0260145 | − | 0.999662i | \(-0.508282\pi\) | ||||
−0.0260145 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.0718 | 1.89652 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.2487 | 0.472236 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.928203 | −0.0426788 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.73205 | −0.308888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.1769 | −0.511756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.8038 | −0.539332 | −0.269666 | − | 0.962954i | \(-0.586913\pi\) | ||||
−0.269666 | + | 0.962954i | \(0.586913\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9282 | 0.498283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.56922 | −0.253408 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8564 | −0.720002 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.9282 | 1.67338 | 0.836688 | − | 0.547679i | \(-0.184489\pi\) | ||||
0.836688 | + | 0.547679i | \(0.184489\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.67949 | 0.392500 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.53590 | 0.294961 | 0.147480 | − | 0.989065i | \(-0.452884\pi\) | ||||
0.147480 | + | 0.989065i | \(0.452884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.07180 | −0.228422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.12436 | −0.140429 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.6077 | 0.879525 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.6603 | −1.50684 | −0.753420 | − | 0.657540i | \(-0.771597\pi\) | ||||
−0.753420 | + | 0.657540i | \(0.771597\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.67949 | −0.209064 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.33975 | −0.371851 | −0.185925 | − | 0.982564i | \(-0.559528\pi\) | ||||
−0.185925 | + | 0.982564i | \(0.559528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.9282 | 0.753295 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.732051 | 0.0325115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.3923 | −0.637928 | −0.318964 | − | 0.947767i | \(-0.603335\pi\) | ||||
−0.318964 | + | 0.947767i | \(0.603335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 26.9282 | 1.18891 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.26795 | 0.144003 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.75129 | 0.252941 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.17691 | −0.0516608 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.2487 | 1.32522 | 0.662610 | − | 0.748965i | \(-0.269449\pi\) | ||||
0.662610 | + | 0.748965i | \(0.269449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.6603 | 1.20950 | 0.604749 | − | 0.796416i | \(-0.293273\pi\) | ||||
0.604749 | + | 0.796416i | \(0.293273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.53590 | −0.110676 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.39230 | 0.191332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.0526 | 1.30417 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.53590 | −0.196472 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1962 | 0.613753 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.1436 | −0.437728 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.33975 | −0.273072 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4641 | 0.492880 | 0.246440 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246440 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.0718 | −0.732621 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.6603 | 1.01164 | 0.505820 | − | 0.862639i | \(-0.331190\pi\) | ||||
0.505820 | + | 0.862639i | \(0.331190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.60770 | −0.153973 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.85641 | −0.419897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.7846 | −1.39414 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | −0.339581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0718 | 0.892841 | 0.446420 | − | 0.894823i | \(-0.352699\pi\) | ||||
0.446420 | + | 0.894823i | \(0.352699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.732051 | 0.0309625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.21539 | 0.135754 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2679 | −0.643467 | −0.321734 | − | 0.946830i | \(-0.604266\pi\) | ||||
−0.321734 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3923 | −0.605489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.4641 | −0.649431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.39230 | 0.184135 | 0.0920675 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920675 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2487 | 0.931080 | 0.465540 | − | 0.885027i | \(-0.345860\pi\) | ||||
0.465540 | + | 0.885027i | \(0.345860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.19615 | 0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.0000 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2487 | 0.425922 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.7128 | −0.651877 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.75129 | −0.238194 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46410 | 0.101878 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.7128 | 0.731086 | 0.365543 | − | 0.930794i | \(-0.380883\pi\) | ||||
0.365543 | + | 0.930794i | \(0.380883\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.53590 | 0.351716 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.46410 | −0.389301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.92820 | −0.366637 | −0.183319 | − | 0.983054i | \(-0.558684\pi\) | ||||
−0.183319 | + | 0.983054i | \(0.558684\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.784610 | 0.0321119 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.3923 | 0.833207 | 0.416603 | − | 0.909088i | \(-0.363220\pi\) | ||||
0.416603 | + | 0.909088i | \(0.363220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8564 | 1.62578 | 0.812888 | − | 0.582420i | \(-0.197894\pi\) | ||||
0.812888 | + | 0.582420i | \(0.197894\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.2154 | 1.18974 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.39230 | 0.381851 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.26795 | 0.132642 | 0.0663210 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663210 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.71281 | −0.150451 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.53590 | −0.183503 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1436 | −0.652034 | −0.326017 | − | 0.945364i | \(-0.605707\pi\) | ||||
−0.326017 | + | 0.945364i | \(0.605707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.32051 | 0.133896 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.1962 | −1.45485 | −0.727423 | − | 0.686189i | \(-0.759282\pi\) | ||||
−0.727423 | + | 0.686189i | \(0.759282\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.78461 | −0.352514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.9282 | −1.23911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.24871 | 0.249549 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.8564 | −1.50943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1244 | 1.23904 | 0.619521 | − | 0.784980i | \(-0.287327\pi\) | ||||
0.619521 | + | 0.784980i | \(0.287327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.2872 | −0.488372 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.1244 | −0.679559 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | 0.198107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.9474 | 0.551752 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0718 | −0.437310 | −0.218655 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218655 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5359 | −0.652112 | −0.326056 | − | 0.945350i | \(-0.605720\pi\) | ||||
−0.326056 | + | 0.945350i | \(0.605720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.535898 | −0.0211010 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.5885 | −0.730788 | −0.365394 | − | 0.930853i | \(-0.619066\pi\) | ||||
−0.365394 | + | 0.930853i | \(0.619066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4641 | 0.607019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.21539 | 0.126021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.14359 | 0.162151 | 0.0810757 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810757 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9282 | −0.427000 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.4641 | 1.61521 | 0.807606 | − | 0.589722i | \(-0.200763\pi\) | ||||
0.807606 | + | 0.589722i | \(0.200763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7846 | 0.419473 | 0.209736 | − | 0.977758i | \(-0.432739\pi\) | ||||
0.209736 | + | 0.977758i | \(0.432739\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.53590 | −0.0984861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.3205 | −0.904331 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.21539 | 0.124500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4641 | 0.520552 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.85641 | −0.0716658 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.53590 | −0.329035 | −0.164517 | − | 0.986374i | \(-0.552607\pi\) | ||||
−0.164517 | + | 0.986374i | \(0.552607\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6077 | −0.830451 | −0.415226 | − | 0.909718i | \(-0.636297\pi\) | ||||
−0.415226 | + | 0.909718i | \(0.636297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.9282 | −2.10795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0333 | −0.422798 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7128 | 0.830818 | 0.415409 | − | 0.909635i | \(-0.363639\pi\) | ||||
0.415409 | + | 0.909635i | \(0.363639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9282 | 0.493961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.46410 | −0.208468 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.53590 | 0.172804 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6603 | −1.28050 | −0.640248 | − | 0.768168i | \(-0.721169\pi\) | ||||
−0.640248 | + | 0.768168i | \(0.721169\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.8231 | −0.411135 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.39230 | −0.318338 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128 | 0.595165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.5359 | −0.549798 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −73.5692 | −2.77472 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.32051 | 0.125058 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 58.6410 | 2.20542 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.6077 | −0.961717 | −0.480859 | − | 0.876798i | \(-0.659675\pi\) | ||||
−0.480859 | + | 0.876798i | \(0.659675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.3205 | −0.874587 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.78461 | −0.104284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.26795 | 0.0474186 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.2872 | −0.533565 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.9282 | 1.45178 | 0.725889 | − | 0.687812i | \(-0.241429\pi\) | ||||
0.725889 | + | 0.687812i | \(0.241429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3205 | 0.421598 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4641 | −0.500735 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.46410 | 0.0543754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9090 | −1.40597 | −0.702983 | − | 0.711207i | \(-0.748149\pi\) | ||||
−0.702983 | + | 0.711207i | \(0.748149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.53590 | −0.0937936 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.143594 | 0.00530375 | 0.00265187 | − | 0.999996i | \(-0.499156\pi\) | ||||
0.00265187 | + | 0.999996i | \(0.499156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.66025 | −0.135011 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0333 | 0.553759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5885 | −0.904501 | −0.452251 | − | 0.891891i | \(-0.649379\pi\) | ||||
−0.452251 | + | 0.891891i | \(0.649379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.92820 | −0.181042 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.46410 | −0.127086 | −0.0635428 | − | 0.997979i | \(-0.520240\pi\) | ||||
−0.0635428 | + | 0.997979i | \(0.520240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8564 | 0.874031 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1769 | −0.408942 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.1769 | 1.79689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5359 | −0.384460 | −0.192230 | − | 0.981350i | \(-0.561572\pi\) | ||||
−0.192230 | + | 0.981350i | \(0.561572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.78461 | −0.174361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.26795 | 0.191720 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4641 | 0.707435 | 0.353717 | − | 0.935352i | \(-0.384917\pi\) | ||||
0.353717 | + | 0.935352i | \(0.384917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.03848 | −0.0739920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.71281 | −0.352089 | −0.176045 | − | 0.984382i | \(-0.556330\pi\) | ||||
−0.176045 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.7846 | 0.752453 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.53590 | −0.308616 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1962 | −0.440378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7846 | 0.965878 | 0.482939 | − | 0.875654i | \(-0.339569\pi\) | ||||
0.482939 | + | 0.875654i | \(0.339569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.67949 | 0.312584 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.8564 | 1.36160 | 0.680800 | − | 0.732469i | \(-0.261632\pi\) | ||||
0.680800 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.26795 | −0.0455461 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27.7128 | −0.994192 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.5359 | 1.09406 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.17691 | 0.256810 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.85641 | −0.209291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5359 | −0.446857 | −0.223428 | − | 0.974720i | \(-0.571725\pi\) | ||||
−0.223428 | + | 0.974720i | \(0.571725\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.82309 | −0.171706 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.8564 | −1.77269 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.46410 | 0.0519918 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.32051 | −0.117766 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.92820 | 0.316253 | 0.158127 | − | 0.987419i | \(-0.449455\pi\) | ||||
0.158127 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7128 | 0.555879 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0000 | −0.777332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.60770 | 0.268136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.67949 | −0.305533 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.0333 | −1.79424 | −0.897118 | − | 0.441791i | \(-0.854343\pi\) | ||||
−0.897118 | + | 0.441791i | \(0.854343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.1962 | 0.990101 | 0.495050 | − | 0.868864i | \(-0.335150\pi\) | ||||
0.495050 | + | 0.868864i | \(0.335150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.71281 | 0.200357 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8564 | −0.415312 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.92820 | −0.172416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.53590 | 0.298268 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.9282 | −0.451197 | −0.225599 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225599 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.3397 | −0.848430 | −0.424215 | − | 0.905561i | \(-0.639450\pi\) | ||||
−0.424215 | + | 0.905561i | \(0.639450\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.928203 | −0.0323159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.3923 | 1.75231 | 0.876156 | − | 0.482028i | \(-0.160099\pi\) | ||||
0.876156 | + | 0.482028i | \(0.160099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.6077 | −0.403152 | −0.201576 | − | 0.979473i | \(-0.564606\pi\) | ||||
−0.201576 | + | 0.979473i | \(0.564606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.10512 | 0.142405 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.3205 | −0.600120 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.39230 | 0.221215 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.07180 | 0.175307 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6603 | 1.02399 | 0.511993 | − | 0.858990i | \(-0.328907\pi\) | ||||
0.511993 | + | 0.858990i | \(0.328907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8564 | −0.926083 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.03332 | −0.242240 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.5359 | 1.11795 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.1769 | −0.658150 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.6410 | −1.73392 | −0.866958 | − | 0.498382i | \(-0.833928\pi\) | ||||
−0.866958 | + | 0.498382i | \(0.833928\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.5885 | −0.567313 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0000 | −0.888143 | −0.444072 | − | 0.895991i | \(-0.646466\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.32051 | 0.249773 | 0.124886 | − | 0.992171i | \(-0.460143\pi\) | ||||
0.124886 | + | 0.992171i | \(0.460143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5026 | 0.392007 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.1769 | 0.652790 | 0.326395 | − | 0.945234i | \(-0.394166\pi\) | ||||
0.326395 | + | 0.945234i | \(0.394166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60770 | 0.0546633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.66025 | −0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.8564 | −0.401739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.0718 | −1.32238 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.46410 | 0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.7128 | −1.40854 | −0.704271 | − | 0.709931i | \(-0.748726\pi\) | ||||
−0.704271 | + | 0.709931i | \(0.748726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.35898 | 0.0458374 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.392305 | −0.0132171 | −0.00660854 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00660854 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.41154 | −0.0475022 | −0.0237511 | − | 0.999718i | \(-0.507561\pi\) | ||||
−0.0237511 | + | 0.999718i | \(0.507561\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.92820 | 0.300118 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0526 | −0.538992 | −0.269496 | − | 0.963001i | \(-0.586857\pi\) | ||||
−0.269496 | + | 0.963001i | \(0.586857\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.3205 | −1.98955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.66025 | −0.189626 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.5359 | 1.02184 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8564 | 0.463169 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.60770 | 0.0536794 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.85641 | −0.0619146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.7128 | −0.523470 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.85641 | −0.0617773 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.3205 | 0.775200 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1244 | −0.568605 | −0.284302 | − | 0.958735i | \(-0.591762\pi\) | ||||
−0.284302 | + | 0.958735i | \(0.591762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.7128 | 1.38353 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.7846 | −0.953677 | −0.476838 | − | 0.878991i | \(-0.658217\pi\) | ||||
−0.476838 | + | 0.878991i | \(0.658217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.75129 | −0.190340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.07180 | −0.0354325 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.8564 | −1.25013 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1769 | 0.962458 | 0.481229 | − | 0.876595i | \(-0.340191\pi\) | ||||
0.481229 | + | 0.876595i | \(0.340191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.3205 | −0.373023 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.66025 | −0.186310 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9282 | 0.359317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.05256 | 0.264481 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.248711 | 0.00815995 | 0.00407998 | − | 0.999992i | \(-0.498701\pi\) | ||||
0.00407998 | + | 0.999992i | \(0.498701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.6603 | −1.10317 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.78461 | −0.156641 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.39230 | −0.143644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7846 | −0.744341 | −0.372170 | − | 0.928164i | \(-0.621386\pi\) | ||||
−0.372170 | + | 0.928164i | \(0.621386\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.6795 | −0.674850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3205 | 0.564632 | 0.282316 | − | 0.959321i | \(-0.408897\pi\) | ||||
0.282316 | + | 0.959321i | \(0.408897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.96152 | −0.324392 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.8564 | −0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.32051 | 0.172893 | 0.0864466 | − | 0.996256i | \(-0.472449\pi\) | ||||
0.0864466 | + | 0.996256i | \(0.472449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0718 | −0.683300 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.6410 | −0.798201 | −0.399100 | − | 0.916907i | \(-0.630678\pi\) | ||||
−0.399100 | + | 0.916907i | \(0.630678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.9282 | −0.612502 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.35898 | −0.0439297 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.7846 | 1.44617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3923 | −0.948139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.9808 | 1.12724 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6410 | 1.56419 | 0.782095 | − | 0.623159i | \(-0.214151\pi\) | ||||
0.782095 | + | 0.623159i | \(0.214151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.0718 | 0.548425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0000 | 1.28366 | 0.641831 | − | 0.766846i | \(-0.278175\pi\) | ||||
0.641831 | + | 0.766846i | \(0.278175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.0718 | −0.931999 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.732051 | 0.0234444 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.4256 | 1.77322 | 0.886611 | − | 0.462515i | \(-0.153053\pi\) | ||||
0.886611 | + | 0.462515i | \(0.153053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3205 | −0.361805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.7846 | 0.472036 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.6410 | 1.80657 | 0.903284 | − | 0.429043i | \(-0.141149\pi\) | ||||
0.903284 | + | 0.429043i | \(0.141149\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.9282 | 0.411927 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.5026 | 0.366131 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.60770 | 0.0511217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7128 | 0.372070 | 0.186035 | − | 0.982543i | \(-0.440436\pi\) | ||||
0.186035 | + | 0.982543i | \(0.440436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.2154 | 0.673250 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.07180 | −0.0339782 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.3923 | −0.962534 | −0.481267 | − | 0.876574i | \(-0.659823\pi\) | ||||
−0.481267 | + | 0.876574i | \(0.659823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.7128 | −1.38301 |
(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 | 520.2.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4680.2.a.be.1.1 | 2 | |||
4.3 | odd | 2 | 1040.2.a.m.1.1 | 2 | |||
5.2 | odd | 4 | 2600.2.d.l.1249.2 | 4 | |||
5.3 | odd | 4 | 2600.2.d.l.1249.3 | 4 | |||
5.4 | even | 2 | 2600.2.a.u.1.1 | 2 | |||
8.3 | odd | 2 | 4160.2.a.v.1.2 | 2 | |||
8.5 | even | 2 | 4160.2.a.bl.1.1 | 2 | |||
12.11 | even | 2 | 9360.2.a.cq.1.2 | 2 | |||
13.12 | even | 2 | 6760.2.a.p.1.2 | 2 | |||
20.19 | odd | 2 | 5200.2.a.bo.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1040.2.a.m.1.1 | 2 | 4.3 | odd | 2 | |||
2600.2.a.u.1.1 | 2 | 5.4 | even | 2 | |||
2600.2.d.l.1249.2 | 4 | 5.2 | odd | 4 | |||
2600.2.d.l.1249.3 | 4 | 5.3 | odd | 4 | |||
4160.2.a.v.1.2 | 2 | 8.3 | odd | 2 | |||
4160.2.a.bl.1.1 | 2 | 8.5 | even | 2 | |||
4680.2.a.be.1.1 | 2 | 3.2 | odd | 2 | |||
5200.2.a.bo.1.2 | 2 | 20.19 | odd | 2 | |||
6760.2.a.p.1.2 | 2 | 13.12 | even | 2 | |||
9360.2.a.cq.1.2 | 2 | 12.11 | even | 2 |