Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(1,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, 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("1568.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1 |
$q$-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 | ||||||||
\(3\) | −2.64575 | −1.52753 | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||||
−0.763763 | + | 0.645497i | \(0.776650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.00000 | 1.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.64575 | −0.797724 | −0.398862 | − | 0.917011i | \(-0.630595\pi\) | ||||
−0.398862 | + | 0.917011i | \(0.630595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.93725 | −2.04939 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.93725 | 1.82093 | 0.910465 | − | 0.413585i | \(-0.135724\pi\) | ||||
0.910465 | + | 0.413585i | \(0.135724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.64575 | −0.551677 | −0.275839 | − | 0.961204i | \(-0.588956\pi\) | ||||
−0.275839 | + | 0.961204i | \(0.588956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | −0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64575 | 0.475191 | 0.237595 | − | 0.971364i | \(-0.423641\pi\) | ||||
0.237595 | + | 0.971364i | \(0.423641\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.00000 | 1.21854 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.5830 | −1.69464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5830 | 1.61389 | 0.806947 | − | 0.590624i | \(-0.201119\pi\) | ||||
0.806947 | + | 0.590624i | \(0.201119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.0000 | 1.78885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.64575 | −0.385922 | −0.192961 | − | 0.981206i | \(-0.561809\pi\) | ||||
−0.192961 | + | 0.981206i | \(0.561809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.64575 | 0.370479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | 0.961524 | 0.480762 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480762 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.93725 | −1.07026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.0000 | −2.78152 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.64575 | −0.344447 | −0.172224 | − | 0.985058i | \(-0.555095\pi\) | ||||
−0.172224 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.64575 | 0.323230 | 0.161615 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161615 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.00000 | 0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5830 | −1.22202 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64575 | −0.297670 | −0.148835 | − | 0.988862i | \(-0.547552\pi\) | ||||
−0.148835 | + | 0.988862i | \(0.547552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5830 | 1.16164 | 0.580818 | − | 0.814034i | \(-0.302733\pi\) | ||||
0.580818 | + | 0.814034i | \(0.302733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.5830 | 1.13462 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.00000 | −0.725866 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.8118 | 2.44304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.5830 | −1.06363 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0000 | 1.49256 | 0.746278 | − | 0.665635i | \(-0.231839\pi\) | ||||
0.746278 | + | 0.665635i | \(0.231839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.64575 | 0.260694 | 0.130347 | − | 0.991468i | \(-0.458391\pi\) | ||||
0.130347 | + | 0.991468i | \(0.458391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2288 | 1.27887 | 0.639436 | − | 0.768844i | \(-0.279168\pi\) | ||||
0.639436 | + | 0.768844i | \(0.279168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | 0.0957826 | 0.0478913 | − | 0.998853i | \(-0.484750\pi\) | ||||
0.0478913 | + | 0.998853i | \(0.484750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.2288 | 1.25562 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.93725 | −0.740153 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.0000 | 1.47920 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | −0.363636 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.1660 | 1.90847 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.1660 | 1.87818 | 0.939090 | − | 0.343672i | \(-0.111671\pi\) | ||||
0.939090 | + | 0.343672i | \(0.111671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.0000 | −2.46526 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.93725 | −0.693481 | −0.346741 | − | 0.937961i | \(-0.612712\pi\) | ||||
−0.346741 | + | 0.937961i | \(0.612712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.93725 | −0.683130 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | 0.0854358 | 0.0427179 | − | 0.999087i | \(-0.486398\pi\) | ||||
0.0427179 | + | 0.999087i | \(0.486398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5830 | 0.897639 | 0.448819 | − | 0.893622i | \(-0.351845\pi\) | ||||
0.448819 | + | 0.893622i | \(0.351845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5830 | −0.884995 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.0000 | 1.72039 | 0.860194 | − | 0.509968i | \(-0.170343\pi\) | ||||
0.860194 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.64575 | −0.215308 | −0.107654 | − | 0.994188i | \(-0.534334\pi\) | ||||
−0.107654 | + | 0.994188i | \(0.534334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.93725 | 0.637536 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | 0.718278 | 0.359139 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359139 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.5203 | −1.46875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2288 | −1.03616 | −0.518078 | − | 0.855333i | \(-0.673352\pi\) | ||||
−0.518078 | + | 0.855333i | \(0.673352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.0000 | 1.63485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.29150 | −0.409469 | −0.204734 | − | 0.978818i | \(-0.565633\pi\) | ||||
−0.204734 | + | 0.978818i | \(0.565633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.7490 | 2.42791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | −0.228086 | −0.114043 | − | 0.993476i | \(-0.536380\pi\) | ||||
−0.114043 | + | 0.993476i | \(0.536380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.00000 | 0.526152 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.8118 | −1.77977 | −0.889887 | − | 0.456180i | \(-0.849217\pi\) | ||||
−0.889887 | + | 0.456180i | \(0.849217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.2288 | −0.977898 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0000 | −1.10282 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.64575 | 0.193476 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.8118 | 1.72296 | 0.861479 | − | 0.507793i | \(-0.169538\pi\) | ||||
0.861479 | + | 0.507793i | \(0.169538\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −31.7490 | −2.27359 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.5203 | −1.31287 | −0.656433 | − | 0.754384i | \(-0.727936\pi\) | ||||
−0.656433 | + | 0.754384i | \(0.727936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.00000 | −0.493742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.0000 | −1.67623 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.5830 | −0.735570 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0000 | −1.45260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5830 | −0.728564 | −0.364282 | − | 0.931289i | \(-0.618686\pi\) | ||||
−0.364282 | + | 0.931289i | \(0.618686\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.7490 | 2.16526 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.8118 | −1.60905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.0000 | 1.06667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.64575 | 0.175605 | 0.0878023 | − | 0.996138i | \(-0.472016\pi\) | ||||
0.0878023 | + | 0.996138i | \(0.472016\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0000 | 0.726900 | 0.363450 | − | 0.931614i | \(-0.381599\pi\) | ||||
0.363450 | + | 0.931614i | \(0.381599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.93725 | −0.517769 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.00000 | 0.454699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.8745 | 1.02684 | 0.513418 | − | 0.858138i | \(-0.328379\pi\) | ||||
0.513418 | + | 0.858138i | \(0.328379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | 0.0322078 | − | 0.999481i | \(-0.489746\pi\) | ||||
0.0322078 | + | 0.999481i | \(0.489746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.1660 | 1.35780 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.7490 | 2.02014 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.0000 | −1.77443 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.29150 | −0.333997 | −0.166998 | − | 0.985957i | \(-0.553407\pi\) | ||||
−0.166998 | + | 0.985957i | \(0.553407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.00000 | 0.440086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.93725 | 0.497050 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.0000 | −1.06043 | −0.530215 | − | 0.847863i | \(-0.677889\pi\) | ||||
−0.530215 | + | 0.847863i | \(0.677889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0000 | −0.990375 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5203 | −1.14201 | −0.571004 | − | 0.820947i | \(-0.693446\pi\) | ||||
−0.571004 | + | 0.820947i | \(0.693446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0000 | 1.29002 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.8118 | −1.45726 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | −0.914566 | −0.457283 | − | 0.889321i | \(-0.651177\pi\) | ||||
−0.457283 | + | 0.889321i | \(0.651177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.64575 | 0.160718 | 0.0803590 | − | 0.996766i | \(-0.474393\pi\) | ||||
0.0803590 | + | 0.996766i | \(0.474393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.5830 | −0.638179 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.0000 | −1.50210 | −0.751052 | − | 0.660243i | \(-0.770453\pi\) | ||||
−0.751052 | + | 0.660243i | \(0.770453\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.5830 | 0.633588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.5203 | −1.10092 | −0.550458 | − | 0.834863i | \(-0.685547\pi\) | ||||
−0.550458 | + | 0.834863i | \(0.685547\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −63.0000 | −3.73180 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.1660 | −1.24077 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.93725 | −0.462125 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.00000 | 0.406181 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5830 | −0.612031 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −39.6863 | −2.27992 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0000 | 0.858898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5830 | −0.604004 | −0.302002 | − | 0.953307i | \(-0.597655\pi\) | ||||
−0.302002 | + | 0.953307i | \(0.597655\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.8118 | −1.35024 | −0.675121 | − | 0.737707i | \(-0.735908\pi\) | ||||
−0.675121 | + | 0.737707i | \(0.735908\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0000 | 0.960897 | 0.480448 | − | 0.877023i | \(-0.340474\pi\) | ||||
0.480448 | + | 0.877023i | \(0.340474\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0000 | −0.730153 | −0.365076 | − | 0.930978i | \(-0.618957\pi\) | ||||
−0.365076 | + | 0.930978i | \(0.618957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.5830 | 0.592535 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.0000 | −1.95351 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.93725 | −0.441641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0000 | 0.887520 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.64575 | −0.146310 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.93725 | 0.436271 | 0.218135 | − | 0.975918i | \(-0.430003\pi\) | ||||
0.218135 | + | 0.975918i | \(0.430003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.0000 | −1.09599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.93725 | 0.433659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.0000 | 1.30736 | 0.653682 | − | 0.756770i | \(-0.273224\pi\) | ||||
0.653682 | + | 0.756770i | \(0.273224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.00000 | −0.379071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.0000 | 1.13060 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.8118 | 1.27828 | 0.639141 | − | 0.769089i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769089i | \(0.279290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.5830 | −0.564879 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | −0.479022 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.5203 | −0.977462 | −0.488731 | − | 0.872435i | \(-0.662540\pi\) | ||||
−0.488731 | + | 0.872435i | \(0.662540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.0000 | 2.31579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5830 | 0.555464 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.0000 | 1.41324 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.5203 | 0.966750 | 0.483375 | − | 0.875413i | \(-0.339411\pi\) | ||||
0.483375 | + | 0.875413i | \(0.339411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −32.0000 | −1.66585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | −1.08734 | −0.543669 | − | 0.839299i | \(-0.682965\pi\) | ||||
−0.543669 | + | 0.839299i | \(0.682965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.93725 | 0.409878 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.0000 | −0.824042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.29150 | −0.271806 | −0.135903 | − | 0.990722i | \(-0.543394\pi\) | ||||
−0.135903 | + | 0.990722i | \(0.543394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −56.0000 | −2.86897 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.5203 | 0.946341 | 0.473171 | − | 0.880971i | \(-0.343109\pi\) | ||||
0.473171 | + | 0.880971i | \(0.343109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.3320 | 2.15186 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | −0.760530 | −0.380265 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380265 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.64575 | 0.133801 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0000 | 1.05931 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.93725 | −0.399367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.00000 | −0.250943 | −0.125471 | − | 0.992097i | \(-0.540044\pi\) | ||||
−0.125471 | + | 0.992097i | \(0.540044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0000 | −1.14857 | −0.574283 | − | 0.818657i | \(-0.694719\pi\) | ||||
−0.574283 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5830 | 0.527177 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.0000 | −0.745356 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.2288 | 0.655725 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0000 | 1.13728 | 0.568638 | − | 0.822588i | \(-0.307470\pi\) | ||||
0.568638 | + | 0.822588i | \(0.307470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.64575 | −0.130505 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.7490 | 1.55850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.0000 | −1.37117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7490 | 1.55104 | 0.775520 | − | 0.631322i | \(-0.217488\pi\) | ||||
0.775520 | + | 0.631322i | \(0.217488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.5830 | −0.514563 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.0000 | 1.35185 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.64575 | −0.127441 | −0.0637207 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637207 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000 | 1.53782 | 0.768911 | − | 0.639356i | \(-0.220799\pi\) | ||||
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.7490 | 1.52225 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.0000 | −1.00457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8118 | −1.13647 | −0.568237 | − | 0.822865i | \(-0.692374\pi\) | ||||
−0.568237 | + | 0.822865i | \(0.692374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.93725 | −0.377110 | −0.188555 | − | 0.982063i | \(-0.560380\pi\) | ||||
−0.188555 | + | 0.982063i | \(0.560380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.0000 | 1.27992 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −55.5608 | −2.62793 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.1660 | 0.996669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.00000 | 0.328889 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.00000 | 0.327446 | 0.163723 | − | 0.986506i | \(-0.447650\pi\) | ||||
0.163723 | + | 0.986506i | \(0.447650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.64575 | 0.123493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0000 | 0.931493 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.0000 | −0.973852 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.93725 | −0.367292 | −0.183646 | − | 0.982992i | \(-0.558790\pi\) | ||||
−0.183646 | + | 0.982992i | \(0.558790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.8118 | −1.09719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.0000 | −1.28744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7490 | 1.45674 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.0000 | 1.28203 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.6863 | 1.81331 | 0.906656 | − | 0.421871i | \(-0.138626\pi\) | ||||
0.906656 | + | 0.421871i | \(0.138626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.0000 | 1.08978 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.8118 | 1.07901 | 0.539507 | − | 0.841981i | \(-0.318611\pi\) | ||||
0.539507 | + | 0.841981i | \(0.318611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.0000 | 1.58275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.0405 | 1.67162 | 0.835808 | − | 0.549022i | \(-0.185000\pi\) | ||||
0.835808 | + | 0.549022i | \(0.185000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.7490 | −1.42701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2288 | −0.592200 | −0.296100 | − | 0.955157i | \(-0.595686\pi\) | ||||
−0.296100 | + | 0.955157i | \(0.595686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.0000 | 0.625474 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1660 | −0.943746 | −0.471873 | − | 0.881667i | \(-0.656422\pi\) | ||||
−0.471873 | + | 0.881667i | \(0.656422\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.0000 | 2.00247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.93725 | −0.352506 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0000 | 0.842160 | 0.421080 | − | 0.907023i | \(-0.361651\pi\) | ||||
0.421080 | + | 0.907023i | \(0.361651\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.0000 | −0.927173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.93725 | 0.349757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.00000 | 0.307860 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.93725 | 0.348407 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0000 | −1.00765 | −0.503824 | − | 0.863806i | \(-0.668074\pi\) | ||||
−0.503824 | + | 0.863806i | \(0.668074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.3948 | −1.50398 | −0.751989 | − | 0.659176i | \(-0.770905\pi\) | ||||
−0.751989 | + | 0.659176i | \(0.770905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.64575 | −0.115251 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.0000 | −0.695652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5830 | −0.459263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.0000 | −1.38607 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.6863 | 1.71579 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 63.0000 | 2.71865 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.0000 | 0.902861 | 0.451430 | − | 0.892306i | \(-0.350914\pi\) | ||||
0.451430 | + | 0.892306i | \(0.350914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.8745 | −0.681240 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4575 | 1.13124 | 0.565621 | − | 0.824665i | \(-0.308637\pi\) | ||||
0.565621 | + | 0.824665i | \(0.308637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.0000 | 0.853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.7490 | −1.35255 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 39.6863 | 1.68459 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.0000 | −1.65248 | −0.826242 | − | 0.563316i | \(-0.809525\pi\) | ||||
−0.826242 | + | 0.563316i | \(0.809525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.3320 | 1.79045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.00000 | −0.295540 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.64575 | −0.111505 | −0.0557526 | − | 0.998445i | \(-0.517756\pi\) | ||||
−0.0557526 | + | 0.998445i | \(0.517756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.0000 | −1.38343 | −0.691716 | − | 0.722170i | \(-0.743145\pi\) | ||||
−0.691716 | + | 0.722170i | \(0.743145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.64575 | −0.110721 | −0.0553606 | − | 0.998466i | \(-0.517631\pi\) | ||||
−0.0553606 | + | 0.998466i | \(0.517631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −63.0000 | −2.63186 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.5830 | −0.441342 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.0000 | 1.70685 | 0.853426 | − | 0.521214i | \(-0.174521\pi\) | ||||
0.853426 | + | 0.521214i | \(0.174521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.5203 | 0.769676 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5203 | −0.767031 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 48.0000 | 1.98456 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.7490 | −1.31042 | −0.655211 | − | 0.755446i | \(-0.727420\pi\) | ||||
−0.655211 | + | 0.755446i | \(0.727420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.0000 | 0.865290 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.7490 | −1.30598 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 49.0000 | 2.00544 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.8118 | 0.972922 | 0.486461 | − | 0.873702i | \(-0.338288\pi\) | ||||
0.486461 | + | 0.873702i | \(0.338288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5830 | 0.430973 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.0000 | −0.487869 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.6863 | 1.61082 | 0.805408 | − | 0.592721i | \(-0.201946\pi\) | ||||
0.805408 | + | 0.592721i | \(0.201946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.5830 | −0.428143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.0000 | 1.65597 | 0.827987 | − | 0.560747i | \(-0.189486\pi\) | ||||
0.827987 | + | 0.560747i | \(0.189486\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.4980 | 2.56049 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.0000 | −1.28827 | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.9778 | −1.80781 | −0.903905 | − | 0.427734i | \(-0.859312\pi\) | ||||
−0.903905 | + | 0.427734i | \(0.859312\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.00000 | 0.280900 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.5608 | 2.21888 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.00000 | 0.199363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3320 | −1.68521 | −0.842606 | − | 0.538531i | \(-0.818979\pi\) | ||||
−0.842606 | + | 0.538531i | \(0.818979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.0000 | 1.11290 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.4980 | 2.51984 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | −0.0394976 | −0.0197488 | − | 0.999805i | \(-0.506287\pi\) | ||||
−0.0197488 | + | 0.999805i | \(0.506287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5830 | 0.417353 | 0.208676 | − | 0.977985i | \(-0.433084\pi\) | ||||
0.208676 | + | 0.977985i | \(0.433084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −84.0000 | −3.30750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.6863 | 1.56023 | 0.780114 | − | 0.625637i | \(-0.215161\pi\) | ||||
0.780114 | + | 0.625637i | \(0.215161\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | 0.743527 | 0.371764 | − | 0.928327i | \(-0.378753\pi\) | ||||
0.371764 | + | 0.928327i | \(0.378753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.8118 | −0.930403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.0000 | 1.40449 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.7490 | −1.23677 | −0.618383 | − | 0.785877i | \(-0.712212\pi\) | ||||
−0.618383 | + | 0.785877i | \(0.712212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0000 | 1.28355 | 0.641776 | − | 0.766892i | \(-0.278198\pi\) | ||||
0.641776 | + | 0.766892i | \(0.278198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.5830 | 0.411010 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5830 | 0.409776 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.2288 | −0.510690 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | −0.925132 | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||||
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.5830 | −0.407340 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.00000 | 0.115299 | 0.0576497 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576497 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | −0.268241 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.8118 | −0.911132 | −0.455566 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455566 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.00000 | 0.114624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.1033 | −1.11036 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.0000 | 1.06672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1033 | −1.10714 | −0.553570 | − | 0.832803i | \(-0.686735\pi\) | ||||
−0.553570 | + | 0.832803i | \(0.686735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.7490 | 1.20431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.8118 | −0.900644 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6863 | −1.49680 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.0000 | 0.790906 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0000 | −1.38956 | −0.694782 | − | 0.719220i | \(-0.744499\pi\) | ||||
−0.694782 | + | 0.719220i | \(0.744499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5830 | −0.396894 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.00000 | −0.262152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7490 | −1.18735 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −42.0000 | −1.56852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.6863 | −1.48005 | −0.740024 | − | 0.672580i | \(-0.765186\pi\) | ||||
−0.740024 | + | 0.672580i | \(0.765186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.64575 | −0.0983965 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.0000 | −0.594225 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.3320 | −1.57001 | −0.785004 | − | 0.619491i | \(-0.787339\pi\) | ||||
−0.785004 | + | 0.619491i | \(0.787339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5830 | −0.391427 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | −0.406294 | −0.203147 | − | 0.979148i | \(-0.565117\pi\) | ||||
−0.203147 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.00000 | −0.257848 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.9778 | −1.65453 | −0.827267 | − | 0.561809i | \(-0.810106\pi\) | ||||
−0.827267 | + | 0.561809i | \(0.810106\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −84.0000 | −3.08582 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.1660 | −0.776506 | −0.388253 | − | 0.921553i | \(-0.626921\pi\) | ||||
−0.388253 | + | 0.921553i | \(0.626921\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.0000 | 2.30814 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.3320 | 1.54885 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.6863 | −1.44817 | −0.724086 | − | 0.689709i | \(-0.757738\pi\) | ||||
−0.724086 | + | 0.689709i | \(0.757738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.0000 | 0.510188 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.93725 | −0.288866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.00000 | 0.145382 | 0.0726912 | − | 0.997354i | \(-0.476841\pi\) | ||||
0.0726912 | + | 0.997354i | \(0.476841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.5203 | −0.672243 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | −0.326250 | −0.163125 | − | 0.986605i | \(-0.552157\pi\) | ||||
−0.163125 | + | 0.986605i | \(0.552157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0000 | −0.433861 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.5830 | −0.382130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0000 | 0.865462 | 0.432731 | − | 0.901523i | \(-0.357550\pi\) | ||||
0.432731 | + | 0.901523i | \(0.357550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.9778 | 1.61983 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.0000 | −1.18693 | −0.593464 | − | 0.804861i | \(-0.702240\pi\) | ||||
−0.593464 | + | 0.804861i | \(0.702240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.5830 | 0.380153 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.4980 | −2.27505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5830 | 0.378206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.0000 | 0.963671 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5203 | 0.660176 | 0.330088 | − | 0.943950i | \(-0.392922\pi\) | ||||
0.330088 | + | 0.943950i | \(0.392922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.0000 | 1.74445 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | 0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55.5608 | −1.97054 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.0000 | 1.84193 | 0.920967 | − | 0.389640i | \(-0.127401\pi\) | ||||
0.920967 | + | 0.389640i | \(0.127401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.64575 | 0.0936000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | 1.27200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.8118 | −0.840299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.6863 | 1.39702 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.0000 | 1.08990 | 0.544951 | − | 0.838468i | \(-0.316548\pi\) | ||||
0.544951 | + | 0.838468i | \(0.316548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.5830 | −0.371620 | −0.185810 | − | 0.982586i | \(-0.559491\pi\) | ||||
−0.185810 | + | 0.982586i | \(0.559491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.00000 | −0.245501 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.6863 | −1.39015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 84.0000 | 2.93879 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0000 | 0.453703 | 0.226852 | − | 0.973929i | \(-0.427157\pi\) | ||||
0.226852 | + | 0.973929i | \(0.427157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5203 | −0.645576 | −0.322788 | − | 0.946471i | \(-0.604620\pi\) | ||||
−0.322788 | + | 0.946471i | \(0.604620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.0000 | 0.974835 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.7490 | −1.10402 | −0.552011 | − | 0.833837i | \(-0.686139\pi\) | ||||
−0.552011 | + | 0.833837i | \(0.686139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0000 | 0.520972 | 0.260486 | − | 0.965478i | \(-0.416117\pi\) | ||||
0.260486 | + | 0.965478i | \(0.416117\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 66.1438 | 2.29450 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.8745 | −0.549360 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.00000 | −0.241955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.1660 | −0.730732 | −0.365366 | − | 0.930864i | \(-0.619056\pi\) | ||||
−0.365366 | + | 0.930864i | \(0.619056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 63.4980 | 2.18699 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.0000 | 1.68168 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2288 | 0.453476 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0000 | 1.23262 | 0.616308 | − | 0.787505i | \(-0.288628\pi\) | ||||
0.616308 | + | 0.787505i | \(0.288628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 95.2470 | 3.25738 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | −0.512390 | −0.256195 | − | 0.966625i | \(-0.582469\pi\) | ||||
−0.256195 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.1033 | 0.992991 | 0.496495 | − | 0.868039i | \(-0.334620\pi\) | ||||
0.496495 | + | 0.868039i | \(0.334620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.6863 | 1.35094 | 0.675468 | − | 0.737389i | \(-0.263942\pi\) | ||||
0.675468 | + | 0.737389i | \(0.263942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.00000 | −0.306009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.3320 | 1.43767 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.00000 | 0.237459 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5830 | 0.358591 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.0000 | 1.08304 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0000 | 1.24940 | 0.624701 | − | 0.780864i | \(-0.285221\pi\) | ||||
0.624701 | + | 0.780864i | \(0.285221\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.4575 | −0.892390 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0000 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5830 | −0.356146 | −0.178073 | − | 0.984017i | \(-0.556986\pi\) | ||||
−0.178073 | + | 0.984017i | \(0.556986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.0000 | 0.705907 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.64575 | −0.0888356 | −0.0444178 | − | 0.999013i | \(-0.514143\pi\) | ||||
−0.0444178 | + | 0.999013i | \(0.514143\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.2288 | 0.443180 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0000 | −0.702738 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.4353 | −2.38782 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.0000 | 0.934893 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.5830 | −0.352963 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.00000 | −0.233204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | 0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5203 | −0.614955 | −0.307478 | − | 0.951555i | \(-0.599485\pi\) | ||||
−0.307478 | + | 0.951555i | \(0.599485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 60.0000 | 1.99007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.1660 | −0.701261 | −0.350631 | − | 0.936514i | \(-0.614033\pi\) | ||||
−0.350631 | + | 0.936514i | \(0.614033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.0000 | −0.926665 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.6863 | −1.31199 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.5203 | −0.610927 | −0.305463 | − | 0.952204i | \(-0.598811\pi\) | ||||
−0.305463 | + | 0.952204i | \(0.598811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | −0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5830 | 0.347591 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | 0.295280 | 0.147640 | − | 0.989041i | \(-0.452832\pi\) | ||||
0.147640 | + | 0.989041i | \(0.452832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 63.0000 | 2.06253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.93725 | 0.259576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.9778 | −1.46779 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.00000 | 0.0325991 | 0.0162995 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0162995 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.1660 | 0.689260 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.1033 | 0.945729 | 0.472865 | − | 0.881135i | \(-0.343220\pi\) | ||||
0.472865 | + | 0.881135i | \(0.343220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000 | 1.16861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.3948 | 1.11533 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0000 | −0.518291 | −0.259145 | − | 0.965838i | \(-0.583441\pi\) | ||||
−0.259145 | + | 0.965838i | \(0.583441\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 71.4353 | 2.31159 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.0000 | −0.905111 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0000 | −0.774194 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.9150 | 1.70516 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0000 | −0.676014 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.3320 | 1.36131 | 0.680653 | − | 0.732606i | \(-0.261696\pi\) | ||||
0.680653 | + | 0.732606i | \(0.261696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0000 | 0.674617 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.93725 | −0.254719 | −0.127359 | − | 0.991857i | \(-0.540650\pi\) | ||||
−0.127359 | + | 0.991857i | \(0.540650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.3320 | −1.35571 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.0000 | 1.31171 | 0.655853 | − | 0.754889i | \(-0.272309\pi\) | ||||
0.655853 | + | 0.754889i | \(0.272309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.8118 | −0.761027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.8118 | 0.759477 | 0.379739 | − | 0.925094i | \(-0.376014\pi\) | ||||
0.379739 | + | 0.925094i | \(0.376014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | 1.14706 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9778 | 1.42877 | 0.714383 | − | 0.699755i | \(-0.246707\pi\) | ||||
0.714383 | + | 0.699755i | \(0.246707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −55.5608 | −1.76140 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0000 | −0.728417 | −0.364209 | − | 0.931317i | \(-0.618661\pi\) | ||||
−0.364209 | + | 0.931317i | \(0.618661\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.2288 | 0.418539 |
(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 | 1568.2.a.t.1.1 | 2 | ||
4.3 | odd | 2 | inner | 1568.2.a.t.1.2 | 2 | ||
7.2 | even | 3 | 1568.2.i.p.1537.2 | 4 | |||
7.3 | odd | 6 | 224.2.i.c.65.1 | ✓ | 4 | ||
7.4 | even | 3 | 1568.2.i.p.961.2 | 4 | |||
7.5 | odd | 6 | 224.2.i.c.193.1 | yes | 4 | ||
7.6 | odd | 2 | 1568.2.a.m.1.2 | 2 | |||
8.3 | odd | 2 | 3136.2.a.bg.1.1 | 2 | |||
8.5 | even | 2 | 3136.2.a.bg.1.2 | 2 | |||
21.5 | even | 6 | 2016.2.s.o.865.1 | 4 | |||
21.17 | even | 6 | 2016.2.s.o.289.1 | 4 | |||
28.3 | even | 6 | 224.2.i.c.65.2 | yes | 4 | ||
28.11 | odd | 6 | 1568.2.i.p.961.1 | 4 | |||
28.19 | even | 6 | 224.2.i.c.193.2 | yes | 4 | ||
28.23 | odd | 6 | 1568.2.i.p.1537.1 | 4 | |||
28.27 | even | 2 | 1568.2.a.m.1.1 | 2 | |||
56.3 | even | 6 | 448.2.i.h.65.1 | 4 | |||
56.5 | odd | 6 | 448.2.i.h.193.2 | 4 | |||
56.13 | odd | 2 | 3136.2.a.bv.1.1 | 2 | |||
56.19 | even | 6 | 448.2.i.h.193.1 | 4 | |||
56.27 | even | 2 | 3136.2.a.bv.1.2 | 2 | |||
56.45 | odd | 6 | 448.2.i.h.65.2 | 4 | |||
84.47 | odd | 6 | 2016.2.s.o.865.2 | 4 | |||
84.59 | odd | 6 | 2016.2.s.o.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.i.c.65.1 | ✓ | 4 | 7.3 | odd | 6 | ||
224.2.i.c.65.2 | yes | 4 | 28.3 | even | 6 | ||
224.2.i.c.193.1 | yes | 4 | 7.5 | odd | 6 | ||
224.2.i.c.193.2 | yes | 4 | 28.19 | even | 6 | ||
448.2.i.h.65.1 | 4 | 56.3 | even | 6 | |||
448.2.i.h.65.2 | 4 | 56.45 | odd | 6 | |||
448.2.i.h.193.1 | 4 | 56.19 | even | 6 | |||
448.2.i.h.193.2 | 4 | 56.5 | odd | 6 | |||
1568.2.a.m.1.1 | 2 | 28.27 | even | 2 | |||
1568.2.a.m.1.2 | 2 | 7.6 | odd | 2 | |||
1568.2.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1568.2.a.t.1.2 | 2 | 4.3 | odd | 2 | inner | ||
1568.2.i.p.961.1 | 4 | 28.11 | odd | 6 | |||
1568.2.i.p.961.2 | 4 | 7.4 | even | 3 | |||
1568.2.i.p.1537.1 | 4 | 28.23 | odd | 6 | |||
1568.2.i.p.1537.2 | 4 | 7.2 | even | 3 | |||
2016.2.s.o.289.1 | 4 | 21.17 | even | 6 | |||
2016.2.s.o.289.2 | 4 | 84.59 | odd | 6 | |||
2016.2.s.o.865.1 | 4 | 21.5 | even | 6 | |||
2016.2.s.o.865.2 | 4 | 84.47 | odd | 6 | |||
3136.2.a.bg.1.1 | 2 | 8.3 | odd | 2 | |||
3136.2.a.bg.1.2 | 2 | 8.5 | even | 2 | |||
3136.2.a.bv.1.1 | 2 | 56.13 | odd | 2 | |||
3136.2.a.bv.1.2 | 2 | 56.27 | even | 2 |