Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2156,2,Mod(1,2156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, 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("2156.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2156.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: | \(17.2157466758\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 308) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2156.1 |
$q$-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 | ||||||||
\(3\) | 2.44949 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.44949 | −1.23407 | −0.617033 | − | 0.786937i | \(-0.711666\pi\) | ||||
−0.617033 | + | 0.786937i | \(0.711666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.89898 | −1.26491 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.44949 | −1.07916 | −0.539580 | − | 0.841934i | \(-0.681417\pi\) | ||||
−0.539580 | + | 0.841934i | \(0.681417\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.89898 | −1.12390 | −0.561951 | − | 0.827170i | \(-0.689949\pi\) | ||||
−0.561951 | + | 0.827170i | \(0.689949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.89898 | 1.85557 | 0.927783 | − | 0.373121i | \(-0.121712\pi\) | ||||
0.927783 | + | 0.373121i | \(0.121712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.89898 | −1.28111 | −0.640554 | − | 0.767913i | \(-0.721295\pi\) | ||||
−0.640554 | + | 0.767913i | \(0.721295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55051 | −0.278480 | −0.139240 | − | 0.990259i | \(-0.544466\pi\) | ||||
−0.139240 | + | 0.990259i | \(0.544466\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.44949 | −0.426401 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8990 | −1.74523 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.34847 | −0.835291 | −0.417645 | − | 0.908610i | \(-0.637145\pi\) | ||||
−0.417645 | + | 0.908610i | \(0.637145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.89898 | −1.05208 | −0.526042 | − | 0.850458i | \(-0.676325\pi\) | ||||
−0.526042 | + | 0.850458i | \(0.676325\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.55051 | 0.226165 | 0.113083 | − | 0.993586i | \(-0.463928\pi\) | ||||
0.113083 | + | 0.993586i | \(0.463928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8990 | −1.52616 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.79796 | −1.34585 | −0.672927 | − | 0.739709i | \(-0.734963\pi\) | ||||
−0.672927 | + | 0.739709i | \(0.734963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.34847 | 0.956689 | 0.478345 | − | 0.878172i | \(-0.341237\pi\) | ||||
0.478345 | + | 0.878172i | \(0.341237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.34847 | 1.19695 | 0.598474 | − | 0.801142i | \(-0.295774\pi\) | ||||
0.598474 | + | 0.801142i | \(0.295774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.89898 | 1.10378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.6969 | 1.79552 | 0.897758 | − | 0.440488i | \(-0.145195\pi\) | ||||
0.897758 | + | 0.440488i | \(0.145195\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.7980 | 2.62417 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.10102 | −0.368023 | −0.184012 | − | 0.982924i | \(-0.558908\pi\) | ||||
−0.184012 | + | 0.982924i | \(0.558908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.55051 | −0.883720 | −0.441860 | − | 0.897084i | \(-0.645681\pi\) | ||||
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44949 | −0.282843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.10102 | −0.123874 | −0.0619372 | − | 0.998080i | \(-0.519728\pi\) | ||||
−0.0619372 | + | 0.998080i | \(0.519728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.10102 | 0.779438 | 0.389719 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389719 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.89898 | 0.965230 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.8990 | −1.81176 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.79796 | −0.393830 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.79796 | 1.00525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8990 | −1.51276 | −0.756381 | − | 0.654131i | \(-0.773034\pi\) | ||||
−0.756381 | + | 0.654131i | \(0.773034\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.55051 | 0.353289 | 0.176644 | − | 0.984275i | \(-0.443476\pi\) | ||||
0.176644 | + | 0.984275i | \(0.443476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.55051 | −0.941040 | −0.470520 | − | 0.882389i | \(-0.655934\pi\) | ||||
−0.470520 | + | 0.882389i | \(0.655934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.10102 | 0.488589 | 0.244295 | − | 0.969701i | \(-0.421444\pi\) | ||||
0.244295 | + | 0.969701i | \(0.421444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79796 | 0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.7980 | −1.65967 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3485 | −1.23407 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.1010 | −1.18128 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7980 | 1.57931 | 0.789657 | − | 0.613549i | \(-0.210259\pi\) | ||||
0.789657 | + | 0.613549i | \(0.210259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.8990 | −1.48787 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.79796 | 0.856052 | 0.428026 | − | 0.903767i | \(-0.359209\pi\) | ||||
0.428026 | + | 0.903767i | \(0.359209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.79796 | −0.837096 | −0.418548 | − | 0.908195i | \(-0.637461\pi\) | ||||
−0.418548 | + | 0.908195i | \(0.637461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.69694 | 0.568027 | 0.284013 | − | 0.958820i | \(-0.408334\pi\) | ||||
0.284013 | + | 0.958820i | \(0.408334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.79796 | 0.319846 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.44949 | 0.372085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.7980 | 1.14586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.79796 | −0.638834 | −0.319417 | − | 0.947614i | \(-0.603487\pi\) | ||||
−0.319417 | + | 0.947614i | \(0.603487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.6969 | −1.68429 | −0.842146 | − | 0.539249i | \(-0.818708\pi\) | ||||
−0.842146 | + | 0.539249i | \(0.818708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.3485 | −1.07916 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.10102 | 0.249080 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.0000 | −1.90332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.898979 | −0.0704135 | −0.0352068 | − | 0.999380i | \(-0.511209\pi\) | ||||
−0.0352068 | + | 0.999380i | \(0.511209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.89898 | 0.381385 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79796 | 0.448660 | 0.224330 | − | 0.974513i | \(-0.427981\pi\) | ||||
0.224330 | + | 0.974513i | \(0.427981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6969 | −1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2474 | 1.08321 | 0.541607 | − | 0.840632i | \(-0.317816\pi\) | ||||
0.541607 | + | 0.840632i | \(0.317816\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.0000 | 1.35296 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.5959 | 1.76364 | 0.881821 | − | 0.471585i | \(-0.156318\pi\) | ||||
0.881821 | + | 0.471585i | \(0.156318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8990 | −1.40475 | −0.702375 | − | 0.711807i | \(-0.747877\pi\) | ||||
−0.702375 | + | 0.711807i | \(0.747877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.8990 | 1.69274 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44949 | 0.325379 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7980 | 1.28782 | 0.643908 | − | 0.765103i | \(-0.277312\pi\) | ||||
0.643908 | + | 0.765103i | \(0.277312\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.5959 | −1.26658 | −0.633291 | − | 0.773914i | \(-0.718296\pi\) | ||||
−0.633291 | + | 0.773914i | \(0.718296\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.7980 | 1.56098 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5959 | 0.968669 | 0.484335 | − | 0.874883i | \(-0.339062\pi\) | ||||
0.484335 | + | 0.874883i | \(0.339062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0454 | 1.27921 | 0.639603 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639603 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.0000 | 2.53924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6969 | 0.747107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.6969 | 1.85557 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.89898 | 0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.59592 | −0.520464 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.7980 | 0.941013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.4949 | −1.24977 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.7980 | 1.33175 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.1464 | −1.41607 | −0.708035 | − | 0.706178i | \(-0.750418\pi\) | ||||
−0.708035 | + | 0.706178i | \(0.750418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7980 | 1.18129 | 0.590646 | − | 0.806931i | \(-0.298873\pi\) | ||||
0.590646 | + | 0.806931i | \(0.298873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8990 | 0.984552 | 0.492276 | − | 0.870439i | \(-0.336165\pi\) | ||||
0.492276 | + | 0.870439i | \(0.336165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8990 | −0.714016 | −0.357008 | − | 0.934101i | \(-0.616203\pi\) | ||||
−0.357008 | + | 0.934101i | \(0.616203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.10102 | −0.202288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.69694 | −0.175185 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3485 | −0.859850 | −0.429925 | − | 0.902864i | \(-0.641460\pi\) | ||||
−0.429925 | + | 0.902864i | \(0.641460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.0454 | −1.41421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.7980 | 1.38697 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3939 | 1.10229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.44949 | 0.154610 | 0.0773052 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773052 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.89898 | −0.559474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.7980 | 1.36504 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.7980 | −0.985450 | −0.492725 | − | 0.870185i | \(-0.663999\pi\) | ||||
−0.492725 | + | 0.870185i | \(0.663999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.6969 | −1.28111 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.5959 | −1.20834 | −0.604168 | − | 0.796857i | \(-0.706494\pi\) | ||||
−0.604168 | + | 0.796857i | \(0.706494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.5959 | 1.20377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6969 | −0.899438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.8990 | 1.39618 | 0.698088 | − | 0.716012i | \(-0.254035\pi\) | ||||
0.698088 | + | 0.716012i | \(0.254035\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6969 | −1.86471 | −0.932353 | − | 0.361549i | \(-0.882248\pi\) | ||||
−0.932353 | + | 0.361549i | \(0.882248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.79796 | −0.228197 | −0.114099 | − | 0.993469i | \(-0.536398\pi\) | ||||
−0.114099 | + | 0.993469i | \(0.536398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.65153 | −0.278480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8990 | −0.888799 | −0.444399 | − | 0.895829i | \(-0.646583\pi\) | ||||
−0.444399 | + | 0.895829i | \(0.646583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0000 | 1.42665 | 0.713326 | − | 0.700832i | \(-0.247188\pi\) | ||||
0.713326 | + | 0.700832i | \(0.247188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | 1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.79796 | 0.164586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −36.4949 | −2.13937 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3485 | 1.48087 | 0.740437 | − | 0.672126i | \(-0.234619\pi\) | ||||
0.740437 | + | 0.672126i | \(0.234619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6969 | −0.855689 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.5959 | −2.28989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.69694 | 0.499626 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.6969 | −1.07058 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.7980 | −1.01578 | −0.507892 | − | 0.861421i | \(-0.669575\pi\) | ||||
−0.507892 | + | 0.861421i | \(0.669575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.3939 | −1.33083 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.44949 | 0.365717 | 0.182859 | − | 0.983139i | \(-0.441465\pi\) | ||||
0.182859 | + | 0.983139i | \(0.441465\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.5959 | 1.89895 | 0.949477 | − | 0.313837i | \(-0.101615\pi\) | ||||
0.949477 | + | 0.313837i | \(0.101615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.5959 | 1.43761 | 0.718805 | − | 0.695212i | \(-0.244689\pi\) | ||||
0.718805 | + | 0.695212i | \(0.244689\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.89898 | 0.386269 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.79796 | −0.546869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.7980 | 1.21287 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.44949 | 0.246813 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.4949 | 0.690969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0000 | −1.75888 | −0.879440 | − | 0.476011i | \(-0.842082\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −29.3939 | −1.60596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.69694 | −0.473752 | −0.236876 | − | 0.971540i | \(-0.576124\pi\) | ||||
−0.236876 | + | 0.971540i | \(0.576124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.4949 | −1.33038 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.55051 | 0.0839648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −43.5959 | −2.34713 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.4949 | −1.20759 | −0.603795 | − | 0.797140i | \(-0.706345\pi\) | ||||
−0.603795 | + | 0.797140i | \(0.706345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.2474 | −1.40499 | −0.702497 | − | 0.711687i | \(-0.747932\pi\) | ||||
−0.702497 | + | 0.711687i | \(0.747932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5959 | 0.723638 | 0.361819 | − | 0.932248i | \(-0.382156\pi\) | ||||
0.361819 | + | 0.932248i | \(0.382156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.20204 | 0.329170 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.69694 | 0.247895 | 0.123947 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123947 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | 0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.44949 | 0.128565 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.1010 | 0.790424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.1464 | 0.686238 | 0.343119 | − | 0.939292i | \(-0.388517\pi\) | ||||
0.343119 | + | 0.939292i | \(0.388517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.0454 | −0.835291 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7980 | 1.23221 | 0.616106 | − | 0.787663i | \(-0.288709\pi\) | ||||
0.616106 | + | 0.787663i | \(0.288709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.3939 | 1.51789 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.6969 | 1.58097 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8990 | −0.662576 | −0.331288 | − | 0.943530i | \(-0.607483\pi\) | ||||
−0.331288 | + | 0.943530i | \(0.607483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 43.5959 | 2.23349 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.6515 | −0.646463 | −0.323232 | − | 0.946320i | \(-0.604769\pi\) | ||||
−0.323232 | + | 0.946320i | \(0.604769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.6969 | −1.05208 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.5959 | 1.29776 | 0.648882 | − | 0.760889i | \(-0.275237\pi\) | ||||
0.648882 | + | 0.760889i | \(0.275237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.5959 | −2.00245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.20204 | 0.110797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.5959 | −0.682360 | −0.341180 | − | 0.939998i | \(-0.610826\pi\) | ||||
−0.341180 | + | 0.939998i | \(0.610826\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.20204 | −0.409590 | −0.204795 | − | 0.978805i | \(-0.565653\pi\) | ||||
−0.204795 | + | 0.978805i | \(0.565653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.89898 | 0.343663 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4495 | 0.813375 | 0.406687 | − | 0.913567i | \(-0.366684\pi\) | ||||
0.406687 | + | 0.913567i | \(0.366684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.0000 | −1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2020 | −0.697151 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.4041 | 0.803311 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.5505 | −0.661986 | −0.330993 | − | 0.943633i | \(-0.607384\pi\) | ||||
−0.330993 | + | 0.943633i | \(0.607384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7980 | 0.672471 | 0.336236 | − | 0.941778i | \(-0.390846\pi\) | ||||
0.336236 | + | 0.941778i | \(0.390846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.65153 | 0.226165 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.44949 | 0.215832 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.8990 | 0.526208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.8990 | −0.910332 | −0.455166 | − | 0.890407i | \(-0.650420\pi\) | ||||
−0.455166 | + | 0.890407i | \(0.650420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.8990 | −1.48491 | −0.742455 | − | 0.669896i | \(-0.766339\pi\) | ||||
−0.742455 | + | 0.669896i | \(0.766339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.7980 | 1.62049 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −43.5959 | −2.08548 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.1010 | 0.720732 | 0.360366 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360366 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.1010 | −0.903447 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5959 | −0.924789 | −0.462394 | − | 0.886674i | \(-0.653010\pi\) | ||||
−0.462394 | + | 0.886674i | \(0.653010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.34847 | 0.251850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −50.6969 | −2.38195 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.3939 | −1.84277 | −0.921384 | − | 0.388654i | \(-0.872940\pi\) | ||||
−0.921384 | + | 0.388654i | \(0.872940\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.6515 | 1.05499 | 0.527493 | − | 0.849559i | \(-0.323132\pi\) | ||||
0.527493 | + | 0.849559i | \(0.323132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.1010 | −0.701804 | −0.350902 | − | 0.936412i | \(-0.614125\pi\) | ||||
−0.350902 | + | 0.936412i | \(0.614125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.59592 | 0.352252 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.34847 | 0.340047 | 0.170023 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170023 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.4949 | −1.12867 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.89898 | 0.317215 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898 | 0.224781 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.3939 | −1.34585 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.89898 | 0.406605 | 0.203302 | − | 0.979116i | \(-0.434833\pi\) | ||||
0.203302 | + | 0.979116i | \(0.434833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.7980 | −0.811517 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.7980 | 1.35306 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.1010 | 1.22806 | 0.614032 | − | 0.789281i | \(-0.289546\pi\) | ||||
0.614032 | + | 0.789281i | \(0.289546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.20204 | −0.0995797 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.30306 | 0.149065 | 0.0745325 | − | 0.997219i | \(-0.476254\pi\) | ||||
0.0745325 | + | 0.997219i | \(0.476254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.6969 | 1.38252 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000 | 0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.3031 | −0.595527 | −0.297763 | − | 0.954640i | \(-0.596241\pi\) | ||||
−0.297763 | + | 0.954640i | \(0.596241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.2020 | 0.634500 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4949 | −1.09217 | −0.546087 | − | 0.837729i | \(-0.683883\pi\) | ||||
−0.546087 | + | 0.837729i | \(0.683883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.10102 | −0.315991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.6515 | 0.739520 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.69694 | −0.208188 | −0.104094 | − | 0.994567i | \(-0.533194\pi\) | ||||
−0.104094 | + | 0.994567i | \(0.533194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.1010 | 0.841692 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.55051 | −0.0681914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.8990 | 1.53190 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.8990 | 0.827979 | 0.413990 | − | 0.910282i | \(-0.364135\pi\) | ||||
0.413990 | + | 0.910282i | \(0.364135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.3939 | 1.46021 | 0.730106 | − | 0.683334i | \(-0.239471\pi\) | ||||
0.730106 | + | 0.683334i | \(0.239471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.89898 | 0.300524 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.1918 | 2.44312 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.0454 | 0.956689 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.7980 | 1.03080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57.7980 | 2.49417 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5959 | 0.928481 | 0.464241 | − | 0.885709i | \(-0.346327\pi\) | ||||
0.464241 | + | 0.885709i | \(0.346327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.2929 | −1.98662 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2020 | −0.437007 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 28.0454 | 1.19695 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.7980 | 1.43984 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.5959 | −0.831800 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2020 | −1.02547 | −0.512737 | − | 0.858546i | \(-0.671368\pi\) | ||||
−0.512737 | + | 0.858546i | \(0.671368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.6969 | 1.29834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8990 | 0.460155 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.2929 | −1.78243 | −0.891216 | − | 0.453580i | \(-0.850147\pi\) | ||||
−0.891216 | + | 0.453580i | \(0.850147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.0000 | 0.841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6969 | 0.867661 | 0.433830 | − | 0.900995i | \(-0.357162\pi\) | ||||
0.433830 | + | 0.900995i | \(0.357162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7980 | −1.24701 | −0.623503 | − | 0.781821i | \(-0.714291\pi\) | ||||
−0.623503 | + | 0.781821i | \(0.714291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.5959 | 1.82125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.89898 | −0.371113 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.4949 | −1.10300 | −0.551499 | − | 0.834176i | \(-0.685944\pi\) | ||||
−0.551499 | + | 0.834176i | \(0.685944\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.1010 | −1.79122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.79796 | 0.405790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.6969 | 1.10378 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.4495 | −1.09169 | −0.545844 | − | 0.837887i | \(-0.683791\pi\) | ||||
−0.545844 | + | 0.837887i | \(0.683791\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.59592 | 0.312984 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.3031 | 1.36990 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.1464 | 1.44329 | 0.721645 | − | 0.692263i | \(-0.243386\pi\) | ||||
0.721645 | + | 0.692263i | \(0.243386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.2020 | 1.80907 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8990 | −0.690474 | −0.345237 | − | 0.938516i | \(-0.612201\pi\) | ||||
−0.345237 | + | 0.938516i | \(0.612201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3485 | −0.870822 | −0.435411 | − | 0.900232i | \(-0.643397\pi\) | ||||
−0.435411 | + | 0.900232i | \(0.643397\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.0908 | 1.79552 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5959 | 0.957729 | 0.478864 | − | 0.877889i | \(-0.341049\pi\) | ||||
0.478864 | + | 0.877889i | \(0.341049\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.89898 | −0.279103 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.6969 | 0.512825 | 0.256412 | − | 0.966568i | \(-0.417460\pi\) | ||||
0.256412 | + | 0.966568i | \(0.417460\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.2020 | 1.05657 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.3939 | 1.18335 | 0.591676 | − | 0.806176i | \(-0.298466\pi\) | ||||
0.591676 | + | 0.806176i | \(0.298466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4495 | −0.420000 | −0.210000 | − | 0.977701i | \(-0.567346\pi\) | ||||
−0.210000 | + | 0.977701i | \(0.567346\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000 | 0.479234 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7980 | −0.709651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7980 | −0.867763 | −0.433882 | − | 0.900970i | \(-0.642856\pi\) | ||||
−0.433882 | + | 0.900970i | \(0.642856\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −48.9898 | −1.94717 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.5959 | −1.41258 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.30306 | −0.368023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.5959 | 1.24796 | 0.623982 | − | 0.781439i | \(-0.285514\pi\) | ||||
0.623982 | + | 0.781439i | \(0.285514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.2474 | 0.798481 | 0.399241 | − | 0.916846i | \(-0.369274\pi\) | ||||
0.399241 | + | 0.916846i | \(0.369274\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.7980 | 1.33079 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.2474 | 0.953266 | 0.476633 | − | 0.879102i | \(-0.341857\pi\) | ||||
0.476633 | + | 0.879102i | \(0.341857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.34847 | −0.288453 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.3939 | −1.69813 | −0.849067 | − | 0.528285i | \(-0.822835\pi\) | ||||
−0.849067 | + | 0.528285i | \(0.822835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5959 | −0.765676 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.6515 | −0.883720 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.8990 | 0.580382 | 0.290191 | − | 0.956969i | \(-0.406281\pi\) | ||||
0.290191 | + | 0.956969i | \(0.406281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.59592 | −0.373238 | −0.186619 | − | 0.982432i | \(-0.559753\pi\) | ||||
−0.186619 | + | 0.982432i | \(0.559753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.4949 | 1.88339 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.3939 | −2.37718 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −51.7980 | −2.00262 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.34847 | −0.360894 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6969 | 1.41456 | 0.707282 | − | 0.706932i | \(-0.249921\pi\) | ||||
0.707282 | + | 0.706932i | \(0.249921\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.9444 | 0.958691 | 0.479345 | − | 0.877626i | \(-0.340874\pi\) | ||||
0.479345 | + | 0.877626i | \(0.340874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.5959 | 1.67060 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.7980 | −1.75241 | −0.876205 | − | 0.481938i | \(-0.839933\pi\) | ||||
−0.876205 | + | 0.481938i | \(0.839933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.5959 | 0.748722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.4949 | 1.39237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.5959 | 1.66087 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.85357 | 0.260722 | 0.130361 | − | 0.991467i | \(-0.458386\pi\) | ||||
0.130361 | + | 0.991467i | \(0.458386\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.3939 | −0.508059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7980 | 0.901412 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.6969 | −1.00977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.69694 | 0.328479 | 0.164239 | − | 0.986421i | \(-0.447483\pi\) | ||||
0.164239 | + | 0.986421i | \(0.447483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5959 | −0.739074 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.59592 | −0.286079 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7980 | −0.593305 | −0.296652 | − | 0.954986i | \(-0.595870\pi\) | ||||
−0.296652 | + | 0.954986i | \(0.595870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.30306 | −0.123874 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.7980 | −0.516738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.89898 | −0.332803 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.1918 | 1.46365 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.8536 | −0.404770 | −0.202385 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202385 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.6969 | −1.21601 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.89898 | 0.256222 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.44949 | 0.239198 | 0.119599 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119599 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.6969 | 1.13537 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6515 | −1.13214 | −0.566070 | − | 0.824357i | \(-0.691537\pi\) | ||||
−0.566070 | + | 0.824357i | \(0.691537\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6969 | −0.541369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.3939 | 0.639844 | 0.319922 | − | 0.947444i | \(-0.396343\pi\) | ||||
0.319922 | + | 0.947444i | \(0.396343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.3939 | 1.96147 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.5959 | 0.718905 | 0.359452 | − | 0.933163i | \(-0.382964\pi\) | ||||
0.359452 | + | 0.933163i | \(0.382964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.5959 | 0.571390 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.3031 | 0.779438 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.10102 | −0.113158 | −0.0565789 | − | 0.998398i | \(-0.518019\pi\) | ||||
−0.0565789 | + | 0.998398i | \(0.518019\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00000 | 0.218652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.3939 | 1.50648 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.7980 | −0.791216 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8434 | 0.501822 | 0.250911 | − | 0.968010i | \(-0.419270\pi\) | ||||
0.250911 | + | 0.968010i | \(0.419270\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.6969 | 0.965230 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.6969 | −1.18062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.85357 | −0.175024 | −0.0875121 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875121 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.6969 | −1.39364 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.6969 | −1.17603 | −0.588014 | − | 0.808851i | \(-0.700090\pi\) | ||||
−0.588014 | + | 0.808851i | \(0.700090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.55051 | 0.0556960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.2020 | 0.938786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.10102 | 0.110963 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.6969 | 0.666474 | 0.333237 | − | 0.942843i | \(-0.391859\pi\) | ||||
0.333237 | + | 0.942843i | \(0.391859\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.0000 | −1.70885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.5959 | −1.47711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 48.0000 | 1.70238 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.2020 | 0.432218 | 0.216109 | − | 0.976369i | \(-0.430663\pi\) | ||||
0.216109 | + | 0.976369i | \(0.430663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.89898 | −0.244068 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.55051 | 0.266452 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 56.0908 | 1.97449 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5959 | 0.478007 | 0.239004 | − | 0.971019i | \(-0.423179\pi\) | ||||
0.239004 | + | 0.971019i | \(0.423179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5959 | −0.547647 | −0.273823 | − | 0.961780i | \(-0.588288\pi\) | ||||
−0.273823 | + | 0.961780i | \(0.588288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −75.1918 | −2.63709 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.79796 | 0.0629798 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.7980 | 1.18244 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.79796 | 0.132550 | 0.0662748 | − | 0.997801i | \(-0.478889\pi\) | ||||
0.0662748 | + | 0.997801i | \(0.478889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.1918 | −1.50557 | −0.752786 | − | 0.658265i | \(-0.771291\pi\) | ||||
−0.752786 | + | 0.658265i | \(0.771291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.44949 | 0.0852803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.3031 | 0.810327 | 0.405163 | − | 0.914244i | \(-0.367215\pi\) | ||||
0.405163 | + | 0.914244i | \(0.367215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.30306 | −0.322720 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5959 | −0.401293 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4495 | −0.498852 | −0.249426 | − | 0.968394i | \(-0.580242\pi\) | ||||
−0.249426 | + | 0.968394i | \(0.580242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5959 | 0.641239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.4949 | −1.25695 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.5959 | −0.467714 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.7878 | 2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5959 | 1.22021 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.85357 | −0.303141 | −0.151570 | − | 0.988446i | \(-0.548433\pi\) | ||||
−0.151570 | + | 0.988446i | \(0.548433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.3939 | 1.00525 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.1464 | −1.47385 | −0.736927 | − | 0.675972i | \(-0.763724\pi\) | ||||
−0.736927 | + | 0.675972i | \(0.763724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.8434 | 1.35944 | 0.679719 | − | 0.733473i | \(-0.262102\pi\) | ||||
0.679719 | + | 0.733473i | \(0.262102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0000 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.4949 | −0.968856 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.85357 | 0.232760 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.10102 | 0.0373496 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.3939 | −2.21579 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44.6969 | −1.51276 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.30306 | 0.246607 | 0.123303 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123303 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 62.0908 | 2.09427 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.69694 | −0.293007 | −0.146504 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146504 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2020 | −0.343326 | −0.171663 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171663 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.0000 | −1.21013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.2929 | −1.28575 | −0.642874 | − | 0.765972i | \(-0.722258\pi\) | ||||
−0.642874 | + | 0.765972i | \(0.722258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | 0.301511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.59592 | −0.254188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.1918 | −1.57745 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −96.9898 | −3.23839 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6969 | 0.356763 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.5959 | 1.45239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.7980 | 1.25645 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8990 | 0.428304 | 0.214152 | − | 0.976800i | \(-0.431301\pi\) | ||||
0.214152 | + | 0.976800i | \(0.431301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6515 | 0.353289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.4949 | −0.413974 | −0.206987 | − | 0.978344i | \(-0.566366\pi\) | ||||
−0.206987 | + | 0.978344i | \(0.566366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.10102 | −0.235009 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45.7980 | −1.51403 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.5959 | 1.43810 | 0.719048 | − | 0.694960i | \(-0.244578\pi\) | ||||
0.719048 | + | 0.694960i | \(0.244578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.5959 | −1.43653 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7980 | 0.454165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.6515 | −0.941040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.2929 | −0.534551 | −0.267276 | − | 0.963620i | \(-0.586123\pi\) | ||||
−0.267276 | + | 0.963620i | \(0.586123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.7980 | 0.517202 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.89898 | −0.291028 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9444 | 0.684223 | 0.342112 | − | 0.939659i | \(-0.388858\pi\) | ||||
0.342112 | + | 0.939659i | \(0.388858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 82.2929 | 2.68553 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.4495 | −1.57941 | −0.789704 | − | 0.613488i | \(-0.789766\pi\) | ||||
−0.789704 | + | 0.613488i | \(0.789766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.5959 | −1.54994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.5959 | 1.28669 | 0.643347 | − | 0.765575i | \(-0.277545\pi\) | ||||
0.643347 | + | 0.765575i | \(0.277545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.5959 | 1.09057 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62.6969 | 2.03309 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.2020 | −0.783981 | −0.391991 | − | 0.919969i | \(-0.628213\pi\) | ||||
−0.391991 | + | 0.919969i | \(0.628213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.5959 | −1.15186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.8990 | 0.546266 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5959 | −0.922449 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.1918 | 1.13287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.1010 | −0.935826 | −0.467913 | − | 0.883775i | \(-0.654994\pi\) | ||||
−0.467913 | + | 0.883775i | \(0.654994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.3939 | 1.71526 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.04541 | −0.194006 | −0.0970032 | − | 0.995284i | \(-0.530926\pi\) | ||||
−0.0970032 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.8990 | 0.349047 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7980 | 0.761364 | 0.380682 | − | 0.924706i | \(-0.375689\pi\) | ||||
0.380682 | + | 0.924706i | \(0.375689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.3031 | 0.488589 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.65153 | −0.148361 | −0.0741804 | − | 0.997245i | \(-0.523634\pi\) | ||||
−0.0741804 | + | 0.997245i | \(0.523634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.1918 | −0.866404 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61.3939 | −1.95221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0908 | −0.892334 | −0.446167 | − | 0.894950i | \(-0.647211\pi\) | ||||
−0.446167 | + | 0.894950i | \(0.647211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −78.3837 | −2.48743 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.0908 | −1.14416 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.9444 | −1.04336 | −0.521680 | − | 0.853141i | \(-0.674694\pi\) | ||||
−0.521680 | + | 0.853141i | \(0.674694\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2156.2.a.c.1.2 | 2 | ||
4.3 | odd | 2 | 8624.2.a.bj.1.1 | 2 | |||
7.2 | even | 3 | 2156.2.i.i.1145.1 | 4 | |||
7.3 | odd | 6 | 2156.2.i.e.177.2 | 4 | |||
7.4 | even | 3 | 2156.2.i.i.177.1 | 4 | |||
7.5 | odd | 6 | 2156.2.i.e.1145.2 | 4 | |||
7.6 | odd | 2 | 308.2.a.b.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 2772.2.a.n.1.2 | 2 | |||
28.27 | even | 2 | 1232.2.a.n.1.2 | 2 | |||
35.13 | even | 4 | 7700.2.e.j.1849.2 | 4 | |||
35.27 | even | 4 | 7700.2.e.j.1849.3 | 4 | |||
35.34 | odd | 2 | 7700.2.a.s.1.2 | 2 | |||
56.13 | odd | 2 | 4928.2.a.bp.1.2 | 2 | |||
56.27 | even | 2 | 4928.2.a.bq.1.1 | 2 | |||
77.76 | even | 2 | 3388.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.a.b.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1232.2.a.n.1.2 | 2 | 28.27 | even | 2 | |||
2156.2.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2156.2.i.e.177.2 | 4 | 7.3 | odd | 6 | |||
2156.2.i.e.1145.2 | 4 | 7.5 | odd | 6 | |||
2156.2.i.i.177.1 | 4 | 7.4 | even | 3 | |||
2156.2.i.i.1145.1 | 4 | 7.2 | even | 3 | |||
2772.2.a.n.1.2 | 2 | 21.20 | even | 2 | |||
3388.2.a.h.1.1 | 2 | 77.76 | even | 2 | |||
4928.2.a.bp.1.2 | 2 | 56.13 | odd | 2 | |||
4928.2.a.bq.1.1 | 2 | 56.27 | even | 2 | |||
7700.2.a.s.1.2 | 2 | 35.34 | odd | 2 | |||
7700.2.e.j.1849.2 | 4 | 35.13 | even | 4 | |||
7700.2.e.j.1849.3 | 4 | 35.27 | even | 4 | |||
8624.2.a.bj.1.1 | 2 | 4.3 | odd | 2 |