Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.18890 | −0.978906 | −0.489453 | − | 0.872030i | \(-0.662804\pi\) | ||||
−0.489453 | + | 0.872030i | \(0.662804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.791288 | 0.299079 | 0.149539 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149539 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.79129 | −1.19891 | ||||||||
\(11\) | 0.456850 | 0.137746 | 0.0688728 | − | 0.997625i | \(-0.478060\pi\) | ||||
0.0688728 | + | 0.997625i | \(0.478060\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.79129 | −1.60621 | −0.803107 | − | 0.595835i | \(-0.796821\pi\) | ||||
−0.803107 | + | 0.595835i | \(0.796821\pi\) | |||||||
\(14\) | 1.37055 | 0.366295 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0.913701 | 0.221605 | 0.110802 | − | 0.993842i | \(-0.464658\pi\) | ||||
0.110802 | + | 0.993842i | \(0.464658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.58258 | −1.28073 | −0.640365 | − | 0.768070i | \(-0.721217\pi\) | ||||
−0.640365 | + | 0.768070i | \(0.721217\pi\) | |||||||
\(20\) | −2.18890 | −0.489453 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.791288 | 0.168703 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.208712 | −0.0417424 | ||||||||
\(26\) | −10.0308 | −1.96720 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.791288 | 0.149539 | ||||||||
\(29\) | 4.83465 | 0.897772 | 0.448886 | − | 0.893589i | \(-0.351821\pi\) | ||||
0.448886 | + | 0.893589i | \(0.351821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.58258 | −1.00266 | −0.501330 | − | 0.865256i | \(-0.667156\pi\) | ||||
−0.501330 | + | 0.865256i | \(0.667156\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.58258 | 0.271409 | ||||||||
\(35\) | −1.73205 | −0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.79129 | 0.294486 | 0.147243 | − | 0.989100i | \(-0.452960\pi\) | ||||
0.147243 | + | 0.989100i | \(0.452960\pi\) | |||||||
\(38\) | −9.66930 | −1.56857 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.79129 | 0.599455 | ||||||||
\(41\) | −6.20520 | −0.969090 | −0.484545 | − | 0.874766i | \(-0.661015\pi\) | ||||
−0.484545 | + | 0.874766i | \(0.661015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37386 | 0.819507 | 0.409753 | − | 0.912196i | \(-0.365615\pi\) | ||||
0.409753 | + | 0.912196i | \(0.365615\pi\) | |||||||
\(44\) | 0.456850 | 0.0688728 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.18890 | 0.319284 | 0.159642 | − | 0.987175i | \(-0.448966\pi\) | ||||
0.159642 | + | 0.987175i | \(0.448966\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.37386 | −0.910552 | ||||||||
\(50\) | −0.361500 | −0.0511238 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.79129 | −0.803107 | ||||||||
\(53\) | 4.83465 | 0.664091 | 0.332045 | − | 0.943263i | \(-0.392261\pi\) | ||||
0.332045 | + | 0.943263i | \(0.392261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.37055 | −0.183148 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.37386 | 1.09954 | ||||||||
\(59\) | −1.82740 | −0.237907 | −0.118954 | − | 0.992900i | \(-0.537954\pi\) | ||||
−0.118954 | + | 0.992900i | \(0.537954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.79129 | −0.357388 | −0.178694 | − | 0.983905i | \(-0.557187\pi\) | ||||
−0.178694 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(62\) | −9.66930 | −1.22800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.6766 | 1.57233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.79129 | −0.707518 | −0.353759 | − | 0.935337i | \(-0.615097\pi\) | ||||
−0.353759 | + | 0.935337i | \(0.615097\pi\) | |||||||
\(68\) | 0.913701 | 0.110802 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | −8.29875 | −0.984881 | −0.492440 | − | 0.870346i | \(-0.663895\pi\) | ||||
−0.492440 | + | 0.870346i | \(0.663895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.373864 | 0.0437574 | 0.0218787 | − | 0.999761i | \(-0.493035\pi\) | ||||
0.0218787 | + | 0.999761i | \(0.493035\pi\) | |||||||
\(74\) | 3.10260 | 0.360670 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.58258 | −0.640365 | ||||||||
\(77\) | 0.361500 | 0.0411968 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.58258 | −0.403071 | −0.201536 | − | 0.979481i | \(-0.564593\pi\) | ||||
−0.201536 | + | 0.979481i | \(0.564593\pi\) | |||||||
\(80\) | 10.9445 | 1.22363 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.7477 | −1.18689 | ||||||||
\(83\) | 16.5975 | 1.82181 | 0.910907 | − | 0.412613i | \(-0.135384\pi\) | ||||
0.910907 | + | 0.412613i | \(0.135384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 9.30780 | 1.00369 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.791288 | −0.0843516 | ||||||||
\(89\) | −0.361500 | −0.0383189 | −0.0191595 | − | 0.999816i | \(-0.506099\pi\) | ||||
−0.0191595 | + | 0.999816i | \(0.506099\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.58258 | −0.480384 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.79129 | 0.391041 | ||||||||
\(95\) | 12.2197 | 1.25372 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −11.0399 | −1.11519 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.208712 | −0.0208712 | ||||||||
\(101\) | −3.65480 | −0.363666 | −0.181833 | − | 0.983329i | \(-0.558203\pi\) | ||||
−0.181833 | + | 0.983329i | \(0.558203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.58258 | 0.155936 | 0.0779679 | − | 0.996956i | \(-0.475157\pi\) | ||||
0.0779679 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(104\) | 10.0308 | 0.983601 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.37386 | 0.813342 | ||||||||
\(107\) | −12.7719 | −1.23471 | −0.617353 | − | 0.786686i | \(-0.711795\pi\) | ||||
−0.617353 | + | 0.786686i | \(0.711795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.7477 | 1.98727 | 0.993636 | − | 0.112640i | \(-0.0359305\pi\) | ||||
0.993636 | + | 0.112640i | \(0.0359305\pi\) | |||||||
\(110\) | −1.73205 | −0.165145 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.95644 | −0.373848 | ||||||||
\(113\) | 14.7701 | 1.38945 | 0.694727 | − | 0.719273i | \(-0.255525\pi\) | ||||
0.694727 | + | 0.719273i | \(0.255525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.83465 | 0.448886 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.16515 | −0.291376 | ||||||||
\(119\) | 0.723000 | 0.0662773 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7913 | −0.981026 | ||||||||
\(122\) | −4.83465 | −0.437709 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.58258 | −0.501330 | ||||||||
\(125\) | 11.4014 | 1.01977 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 21.9564 | 1.92571 | ||||||||
\(131\) | −4.73930 | −0.414075 | −0.207037 | − | 0.978333i | \(-0.566382\pi\) | ||||
−0.207037 | + | 0.978333i | \(0.566382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.41742 | −0.383039 | ||||||||
\(134\) | −10.0308 | −0.866530 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.58258 | −0.135705 | ||||||||
\(137\) | 15.6838 | 1.33996 | 0.669979 | − | 0.742380i | \(-0.266303\pi\) | ||||
0.669979 | + | 0.742380i | \(0.266303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.16515 | 0.607740 | 0.303870 | − | 0.952713i | \(-0.401721\pi\) | ||||
0.303870 | + | 0.952713i | \(0.401721\pi\) | |||||||
\(140\) | −1.73205 | −0.146385 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3739 | −1.20623 | ||||||||
\(143\) | −2.64575 | −0.221249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5826 | −0.878835 | ||||||||
\(146\) | 0.647551 | 0.0535917 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.79129 | 0.147243 | ||||||||
\(149\) | 14.9608 | 1.22564 | 0.612819 | − | 0.790224i | \(-0.290036\pi\) | ||||
0.612819 | + | 0.790224i | \(0.290036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.37386 | −0.518698 | −0.259349 | − | 0.965784i | \(-0.583508\pi\) | ||||
−0.259349 | + | 0.965784i | \(0.583508\pi\) | |||||||
\(152\) | 9.66930 | 0.784284 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.626136 | 0.0504555 | ||||||||
\(155\) | 12.2197 | 0.981510 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.373864 | 0.0298376 | 0.0149188 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149188 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(158\) | −6.20520 | −0.493659 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.3739 | 0.899183 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −6.20520 | −0.484545 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.7477 | 2.23126 | ||||||||
\(167\) | −2.55040 | −0.197356 | −0.0986780 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986780 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.5390 | 1.57992 | ||||||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.37386 | 0.409753 | ||||||||
\(173\) | −5.84370 | −0.444289 | −0.222144 | − | 0.975014i | \(-0.571306\pi\) | ||||
−0.222144 | + | 0.975014i | \(0.571306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.165151 | −0.0124843 | ||||||||
\(176\) | −2.28425 | −0.172182 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.626136 | −0.0469309 | ||||||||
\(179\) | −10.2215 | −0.763991 | −0.381996 | − | 0.924164i | \(-0.624763\pi\) | ||||
−0.381996 | + | 0.924164i | \(0.624763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.834849 | −0.0620538 | −0.0310269 | − | 0.999519i | \(-0.509878\pi\) | ||||
−0.0310269 | + | 0.999519i | \(0.509878\pi\) | |||||||
\(182\) | −7.93725 | −0.588348 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.92095 | −0.288274 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.417424 | 0.0305251 | ||||||||
\(188\) | 2.18890 | 0.159642 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.1652 | 1.53548 | ||||||||
\(191\) | 22.8027 | 1.64995 | 0.824973 | − | 0.565172i | \(-0.191190\pi\) | ||||
0.824973 | + | 0.565172i | \(0.191190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | −13.8564 | −0.994832 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.37386 | −0.455276 | ||||||||
\(197\) | −19.8709 | −1.41574 | −0.707872 | − | 0.706341i | \(-0.750345\pi\) | ||||
−0.707872 | + | 0.706341i | \(0.750345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7477 | −0.903662 | −0.451831 | − | 0.892103i | \(-0.649229\pi\) | ||||
−0.451831 | + | 0.892103i | \(0.649229\pi\) | |||||||
\(200\) | 0.361500 | 0.0255619 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.33030 | −0.445399 | ||||||||
\(203\) | 3.82560 | 0.268505 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5826 | 0.948648 | ||||||||
\(206\) | 2.74110 | 0.190982 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28.9564 | 2.00777 | ||||||||
\(209\) | −2.55040 | −0.176415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 4.83465 | 0.332045 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −22.1216 | −1.51220 | ||||||||
\(215\) | −11.7629 | −0.802220 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.41742 | −0.299874 | ||||||||
\(218\) | 35.9361 | 2.43390 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −5.29150 | −0.355945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5390 | −0.839675 | −0.419837 | − | 0.907599i | \(-0.637913\pi\) | ||||
−0.419837 | + | 0.907599i | \(0.637913\pi\) | |||||||
\(224\) | −4.11165 | −0.274721 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.5826 | 1.70173 | ||||||||
\(227\) | 0.456850 | 0.0303222 | 0.0151611 | − | 0.999885i | \(-0.495174\pi\) | ||||
0.0151611 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.41742 | 0.556239 | 0.278120 | − | 0.960546i | \(-0.410289\pi\) | ||||
0.278120 | + | 0.960546i | \(0.410289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.37386 | −0.549771 | ||||||||
\(233\) | −14.5993 | −0.956432 | −0.478216 | − | 0.878242i | \(-0.658716\pi\) | ||||
−0.478216 | + | 0.878242i | \(0.658716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.79129 | −0.312549 | ||||||||
\(236\) | −1.82740 | −0.118954 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.25227 | 0.0811728 | ||||||||
\(239\) | −28.0942 | −1.81726 | −0.908632 | − | 0.417598i | \(-0.862872\pi\) | ||||
−0.908632 | + | 0.417598i | \(0.862872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.1652 | −1.10570 | −0.552852 | − | 0.833279i | \(-0.686461\pi\) | ||||
−0.552852 | + | 0.833279i | \(0.686461\pi\) | |||||||
\(242\) | −18.6911 | −1.20151 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.79129 | −0.178694 | ||||||||
\(245\) | 13.9518 | 0.891345 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.3303 | 2.05713 | ||||||||
\(248\) | 9.66930 | 0.614001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.7477 | 1.24896 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.73205 | −0.108679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −15.0363 | −0.937936 | −0.468968 | − | 0.883215i | \(-0.655374\pi\) | ||||
−0.468968 | + | 0.883215i | \(0.655374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.41742 | 0.0880745 | ||||||||
\(260\) | 12.6766 | 0.786167 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.20871 | −0.507136 | ||||||||
\(263\) | −27.6374 | −1.70419 | −0.852096 | − | 0.523385i | \(-0.824669\pi\) | ||||
−0.852096 | + | 0.523385i | \(0.824669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5826 | −0.650082 | ||||||||
\(266\) | −7.65120 | −0.469125 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.79129 | −0.353759 | ||||||||
\(269\) | 19.3386 | 1.17910 | 0.589548 | − | 0.807733i | \(-0.299306\pi\) | ||||
0.589548 | + | 0.807733i | \(0.299306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4174 | 0.754305 | 0.377152 | − | 0.926151i | \(-0.376903\pi\) | ||||
0.377152 | + | 0.926151i | \(0.376903\pi\) | |||||||
\(272\) | −4.56850 | −0.277006 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.1652 | 1.64111 | ||||||||
\(275\) | −0.0953502 | −0.00574983 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1652 | −0.791017 | −0.395509 | − | 0.918462i | \(-0.629432\pi\) | ||||
−0.395509 | + | 0.918462i | \(0.629432\pi\) | |||||||
\(278\) | 12.4104 | 0.744327 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −16.0453 | −0.957183 | −0.478591 | − | 0.878038i | \(-0.658852\pi\) | ||||
−0.478591 | + | 0.878038i | \(0.658852\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7913 | −0.760363 | −0.380182 | − | 0.924912i | \(-0.624138\pi\) | ||||
−0.380182 | + | 0.924912i | \(0.624138\pi\) | |||||||
\(284\) | −8.29875 | −0.492440 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.58258 | −0.270973 | ||||||||
\(287\) | −4.91010 | −0.289834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1652 | −0.950891 | ||||||||
\(290\) | −18.3296 | −1.07635 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.373864 | 0.0218787 | ||||||||
\(293\) | 20.5185 | 1.19870 | 0.599351 | − | 0.800487i | \(-0.295426\pi\) | ||||
0.599351 | + | 0.800487i | \(0.295426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −3.10260 | −0.180335 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.9129 | 1.50109 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.25227 | 0.245097 | ||||||||
\(302\) | −11.0399 | −0.635272 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.9129 | 1.60091 | ||||||||
\(305\) | 6.10985 | 0.349849 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1216 | 1.31962 | 0.659809 | − | 0.751433i | \(-0.270637\pi\) | ||||
0.659809 | + | 0.751433i | \(0.270637\pi\) | |||||||
\(308\) | 0.361500 | 0.0205984 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.1652 | 1.20210 | ||||||||
\(311\) | −11.3060 | −0.641105 | −0.320552 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320552 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5826 | −1.33297 | −0.666483 | − | 0.745520i | \(-0.732201\pi\) | ||||
−0.666483 | + | 0.745520i | \(0.732201\pi\) | |||||||
\(314\) | 0.647551 | 0.0365434 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.58258 | −0.201536 | ||||||||
\(317\) | −3.27340 | −0.183853 | −0.0919263 | − | 0.995766i | \(-0.529302\pi\) | ||||
−0.0919263 | + | 0.995766i | \(0.529302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.20871 | 0.123664 | ||||||||
\(320\) | −2.18890 | −0.122363 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.10080 | −0.283816 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.20871 | 0.0670473 | ||||||||
\(326\) | −6.92820 | −0.383718 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.7477 | 0.593444 | ||||||||
\(329\) | 1.73205 | 0.0954911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7042 | 1.35786 | 0.678932 | − | 0.734201i | \(-0.262443\pi\) | ||||
0.678932 | + | 0.734201i | \(0.262443\pi\) | |||||||
\(332\) | 16.5975 | 0.910907 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.41742 | −0.241711 | ||||||||
\(335\) | 12.6766 | 0.692594 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.9129 | −1.08472 | −0.542362 | − | 0.840145i | \(-0.682470\pi\) | ||||
−0.542362 | + | 0.840145i | \(0.682470\pi\) | |||||||
\(338\) | 35.5746 | 1.93500 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | −2.55040 | −0.138112 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.5826 | −0.571405 | ||||||||
\(344\) | −9.30780 | −0.501843 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.1216 | −0.544140 | ||||||||
\(347\) | −15.8745 | −0.852188 | −0.426094 | − | 0.904679i | \(-0.640111\pi\) | ||||
−0.426094 | + | 0.904679i | \(0.640111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5826 | −1.04823 | −0.524116 | − | 0.851647i | \(-0.675604\pi\) | ||||
−0.524116 | + | 0.851647i | \(0.675604\pi\) | |||||||
\(350\) | −0.286051 | −0.0152900 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.37386 | −0.126527 | ||||||||
\(353\) | −9.86001 | −0.524795 | −0.262398 | − | 0.964960i | \(-0.584513\pi\) | ||||
−0.262398 | + | 0.964960i | \(0.584513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.1652 | 0.964106 | ||||||||
\(356\) | −0.361500 | −0.0191595 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.7042 | −0.935694 | ||||||||
\(359\) | 19.3386 | 1.02065 | 0.510326 | − | 0.859981i | \(-0.329525\pi\) | ||||
0.510326 | + | 0.859981i | \(0.329525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1652 | 0.640271 | ||||||||
\(362\) | −1.44600 | −0.0760001 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.58258 | −0.240192 | ||||||||
\(365\) | −0.818350 | −0.0428344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | 0.104399 | 0.0521996 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521996 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.79129 | −0.353062 | ||||||||
\(371\) | 3.82560 | 0.198615 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0.723000 | 0.0373854 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.79129 | −0.195521 | ||||||||
\(377\) | −27.9989 | −1.44201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1216 | 0.622644 | 0.311322 | − | 0.950304i | \(-0.399228\pi\) | ||||
0.311322 | + | 0.950304i | \(0.399228\pi\) | |||||||
\(380\) | 12.2197 | 0.626858 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 39.4955 | 2.02076 | ||||||||
\(383\) | 11.9536 | 0.610798 | 0.305399 | − | 0.952224i | \(-0.401210\pi\) | ||||
0.305399 | + | 0.952224i | \(0.401210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.791288 | −0.0403278 | ||||||||
\(386\) | −27.7128 | −1.41055 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | −16.5975 | −0.841527 | −0.420764 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420764 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 11.0399 | 0.557597 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.4174 | −1.73392 | ||||||||
\(395\) | 7.84190 | 0.394569 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −22.0797 | −1.10676 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.04356 | 0.0521780 | ||||||||
\(401\) | −7.30960 | −0.365024 | −0.182512 | − | 0.983204i | \(-0.558423\pi\) | ||||
−0.182512 | + | 0.983204i | \(0.558423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.3303 | 1.61049 | ||||||||
\(404\) | −3.65480 | −0.181833 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.62614 | 0.328850 | ||||||||
\(407\) | 0.818350 | 0.0405641 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.16515 | 0.354294 | 0.177147 | − | 0.984184i | \(-0.443313\pi\) | ||||
0.177147 | + | 0.984184i | \(0.443313\pi\) | |||||||
\(410\) | 23.5257 | 1.16185 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.58258 | 0.0779679 | ||||||||
\(413\) | −1.44600 | −0.0711530 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.3303 | −1.78338 | ||||||||
\(416\) | 30.0924 | 1.47540 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.41742 | −0.216063 | ||||||||
\(419\) | 20.8045 | 1.01637 | 0.508183 | − | 0.861249i | \(-0.330317\pi\) | ||||
0.508183 | + | 0.861249i | \(0.330317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.16515 | 0.154260 | 0.0771300 | − | 0.997021i | \(-0.475424\pi\) | ||||
0.0771300 | + | 0.997021i | \(0.475424\pi\) | |||||||
\(422\) | 27.7128 | 1.34904 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.37386 | −0.406671 | ||||||||
\(425\) | −0.190700 | −0.00925033 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.20871 | −0.106887 | ||||||||
\(428\) | −12.7719 | −0.617353 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.3739 | −0.982515 | ||||||||
\(431\) | 12.0489 | 0.580375 | 0.290188 | − | 0.956970i | \(-0.406282\pi\) | ||||
0.290188 | + | 0.956970i | \(0.406282\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.7042 | −1.28332 | −0.641660 | − | 0.766989i | \(-0.721754\pi\) | ||||
−0.641660 | + | 0.766989i | \(0.721754\pi\) | |||||||
\(434\) | −7.65120 | −0.367270 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.7477 | 0.993636 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2087 | 0.869054 | 0.434527 | − | 0.900659i | \(-0.356915\pi\) | ||||
0.434527 | + | 0.900659i | \(0.356915\pi\) | |||||||
\(440\) | 1.73205 | 0.0825723 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.16515 | −0.435942 | ||||||||
\(443\) | 17.9681 | 0.853688 | 0.426844 | − | 0.904325i | \(-0.359625\pi\) | ||||
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.791288 | 0.0375106 | ||||||||
\(446\) | −21.7182 | −1.02839 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.791288 | 0.0373848 | ||||||||
\(449\) | −9.66930 | −0.456323 | −0.228161 | − | 0.973623i | \(-0.573271\pi\) | ||||
−0.228161 | + | 0.973623i | \(0.573271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.83485 | −0.133488 | ||||||||
\(452\) | 14.7701 | 0.694727 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.791288 | 0.0371370 | ||||||||
\(455\) | 10.0308 | 0.470251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.3739 | −1.14016 | −0.570081 | − | 0.821589i | \(-0.693088\pi\) | ||||
−0.570081 | + | 0.821589i | \(0.693088\pi\) | |||||||
\(458\) | 14.5794 | 0.681251 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.74835 | 0.267727 | 0.133864 | − | 0.991000i | \(-0.457262\pi\) | ||||
0.133864 | + | 0.991000i | \(0.457262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −24.1733 | −1.12222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.2867 | −1.17139 | ||||||||
\(467\) | −20.9753 | −0.970622 | −0.485311 | − | 0.874342i | \(-0.661294\pi\) | ||||
−0.485311 | + | 0.874342i | \(0.661294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.58258 | −0.211604 | ||||||||
\(470\) | −8.29875 | −0.382793 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.16515 | 0.145688 | ||||||||
\(473\) | 2.45505 | 0.112883 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.16515 | 0.0534608 | ||||||||
\(476\) | 0.723000 | 0.0331387 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −48.6606 | −2.22568 | ||||||||
\(479\) | 39.0387 | 1.78372 | 0.891862 | − | 0.452307i | \(-0.149399\pi\) | ||||
0.891862 | + | 0.452307i | \(0.149399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3739 | −0.473007 | ||||||||
\(482\) | −29.7309 | −1.35421 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7913 | −0.490513 | ||||||||
\(485\) | 17.5112 | 0.795143 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.95644 | 0.405855 | 0.202928 | − | 0.979194i | \(-0.434954\pi\) | ||||
0.202928 | + | 0.979194i | \(0.434954\pi\) | |||||||
\(488\) | 4.83465 | 0.218854 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 24.1652 | 1.09167 | ||||||||
\(491\) | −25.1624 | −1.13556 | −0.567782 | − | 0.823179i | \(-0.692198\pi\) | ||||
−0.567782 | + | 0.823179i | \(0.692198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.41742 | 0.198951 | ||||||||
\(494\) | 55.9977 | 2.51946 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.9129 | 1.25333 | ||||||||
\(497\) | −6.56670 | −0.294557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.3739 | 1.71785 | 0.858925 | − | 0.512101i | \(-0.171133\pi\) | ||||
0.858925 | + | 0.512101i | \(0.171133\pi\) | |||||||
\(500\) | 11.4014 | 0.509884 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.0000 | −1.33897 | ||||||||
\(503\) | −3.84550 | −0.171462 | −0.0857312 | − | 0.996318i | \(-0.527323\pi\) | ||||
−0.0857312 | + | 0.996318i | \(0.527323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.00000 | −0.0443678 | ||||||||
\(509\) | −4.75920 | −0.210948 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.295834 | 0.0130869 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.0436 | −1.14873 | ||||||||
\(515\) | −3.46410 | −0.152647 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000 | 0.0439799 | ||||||||
\(518\) | 2.45505 | 0.107869 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.9564 | −0.962854 | ||||||||
\(521\) | −29.5402 | −1.29418 | −0.647090 | − | 0.762414i | \(-0.724014\pi\) | ||||
−0.647090 | + | 0.762414i | \(0.724014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.1652 | −1.88748 | −0.943740 | − | 0.330688i | \(-0.892719\pi\) | ||||
−0.943740 | + | 0.330688i | \(0.892719\pi\) | |||||||
\(524\) | −4.73930 | −0.207037 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.8693 | −2.08720 | ||||||||
\(527\) | −5.10080 | −0.222194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −18.3296 | −0.796185 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.41742 | −0.191520 | ||||||||
\(533\) | 35.9361 | 1.55657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.9564 | 1.20866 | ||||||||
\(536\) | 10.0308 | 0.433265 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 33.4955 | 1.44409 | ||||||||
\(539\) | −2.91190 | −0.125424 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3303 | 1.73394 | 0.866968 | − | 0.498365i | \(-0.166066\pi\) | ||||
0.866968 | + | 0.498365i | \(0.166066\pi\) | |||||||
\(542\) | 21.5076 | 0.923831 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.74773 | −0.203557 | ||||||||
\(545\) | −45.4147 | −1.94535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.9564 | 1.36636 | 0.683179 | − | 0.730251i | \(-0.260597\pi\) | ||||
0.683179 | + | 0.730251i | \(0.260597\pi\) | |||||||
\(548\) | 15.6838 | 0.669979 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.165151 | −0.00704208 | ||||||||
\(551\) | −26.9898 | −1.14980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.83485 | −0.120550 | ||||||||
\(554\) | −22.8027 | −0.968794 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.16515 | 0.303870 | ||||||||
\(557\) | 14.0471 | 0.595195 | 0.297598 | − | 0.954691i | \(-0.403815\pi\) | ||||
0.297598 | + | 0.954691i | \(0.403815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.1216 | −1.31630 | ||||||||
\(560\) | 8.66025 | 0.365963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.7913 | −1.17230 | ||||||||
\(563\) | 14.7701 | 0.622486 | 0.311243 | − | 0.950330i | \(-0.399255\pi\) | ||||
0.311243 | + | 0.950330i | \(0.399255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.3303 | −1.36015 | ||||||||
\(566\) | −22.1552 | −0.931251 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.3739 | 0.603114 | ||||||||
\(569\) | 13.8564 | 0.580891 | 0.290445 | − | 0.956892i | \(-0.406197\pi\) | ||||
0.290445 | + | 0.956892i | \(0.406197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.8693 | −1.45924 | −0.729618 | − | 0.683855i | \(-0.760302\pi\) | ||||
−0.729618 | + | 0.683855i | \(0.760302\pi\) | |||||||
\(572\) | −2.64575 | −0.110624 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.50455 | −0.354973 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | −27.9989 | −1.16460 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.5826 | −0.439418 | ||||||||
\(581\) | 13.1334 | 0.544866 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.20871 | 0.0914755 | ||||||||
\(584\) | −0.647551 | −0.0267958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.5390 | 1.46810 | ||||||||
\(587\) | 15.2270 | 0.628484 | 0.314242 | − | 0.949343i | \(-0.398250\pi\) | ||||
0.314242 | + | 0.949343i | \(0.398250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.1652 | 1.28414 | ||||||||
\(590\) | 6.92820 | 0.285230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.95644 | −0.368107 | ||||||||
\(593\) | 7.57575 | 0.311099 | 0.155549 | − | 0.987828i | \(-0.450285\pi\) | ||||
0.155549 | + | 0.987828i | \(0.450285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.58258 | −0.0648793 | ||||||||
\(596\) | 14.9608 | 0.612819 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.84550 | −0.157123 | −0.0785615 | − | 0.996909i | \(-0.525033\pi\) | ||||
−0.0785615 | + | 0.996909i | \(0.525033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.74773 | 0.275246 | 0.137623 | − | 0.990485i | \(-0.456054\pi\) | ||||
0.137623 | + | 0.990485i | \(0.456054\pi\) | |||||||
\(602\) | 7.36515 | 0.300181 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.37386 | −0.259349 | ||||||||
\(605\) | 23.6211 | 0.960333 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.4955 | 1.35954 | 0.679769 | − | 0.733426i | \(-0.262080\pi\) | ||||
0.679769 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(608\) | 29.0079 | 1.17643 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.5826 | 0.428476 | ||||||||
\(611\) | −12.6766 | −0.512839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.74773 | 0.110980 | 0.0554898 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554898 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(614\) | 40.0478 | 1.61620 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.626136 | −0.0252278 | ||||||||
\(617\) | 44.5209 | 1.79234 | 0.896172 | − | 0.443706i | \(-0.146337\pi\) | ||||
0.896172 | + | 0.443706i | \(0.146337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.791288 | 0.0318045 | 0.0159023 | − | 0.999874i | \(-0.494938\pi\) | ||||
0.0159023 | + | 0.999874i | \(0.494938\pi\) | |||||||
\(620\) | 12.2197 | 0.490755 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.5826 | −0.785190 | ||||||||
\(623\) | −0.286051 | −0.0114604 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9129 | −0.956515 | ||||||||
\(626\) | −40.8462 | −1.63254 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.373864 | 0.0149188 | ||||||||
\(629\) | 1.63670 | 0.0652595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7042 | 0.625173 | 0.312586 | − | 0.949889i | \(-0.398805\pi\) | ||||
0.312586 | + | 0.949889i | \(0.398805\pi\) | |||||||
\(632\) | 6.20520 | 0.246830 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.66970 | −0.225172 | ||||||||
\(635\) | 2.18890 | 0.0868639 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.9129 | 1.46254 | ||||||||
\(638\) | 3.82560 | 0.151457 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.5390 | −1.04905 | ||||||||
\(641\) | −7.67110 | −0.302990 | −0.151495 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151495 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | −0.236617 | −0.118308 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118308 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.83485 | −0.347602 | ||||||||
\(647\) | 24.2487 | 0.953315 | 0.476658 | − | 0.879089i | \(-0.341848\pi\) | ||||
0.476658 | + | 0.879089i | \(0.341848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.834849 | −0.0327707 | ||||||||
\(650\) | 2.09355 | 0.0821158 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 23.3350 | 0.913170 | 0.456585 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456585 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3739 | 0.405340 | ||||||||
\(656\) | 31.0260 | 1.21136 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | −45.0333 | −1.75425 | −0.877125 | − | 0.480263i | \(-0.840541\pi\) | ||||
−0.877125 | + | 0.480263i | \(0.840541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7042 | 1.34984 | 0.674918 | − | 0.737893i | \(-0.264179\pi\) | ||||
0.674918 | + | 0.737893i | \(0.264179\pi\) | |||||||
\(662\) | 42.7889 | 1.66304 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.7477 | −1.11563 | ||||||||
\(665\) | 9.66930 | 0.374960 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −2.55040 | −0.0986780 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.9564 | 0.848251 | ||||||||
\(671\) | −1.27520 | −0.0492286 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.7042 | 0.913728 | 0.456864 | − | 0.889536i | \(-0.348973\pi\) | ||||
0.456864 | + | 0.889536i | \(0.348973\pi\) | |||||||
\(674\) | −34.4901 | −1.32851 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.5390 | 0.789962 | ||||||||
\(677\) | −36.6591 | −1.40892 | −0.704462 | − | 0.709742i | \(-0.748812\pi\) | ||||
−0.704462 | + | 0.709742i | \(0.748812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.33030 | −0.242935 | ||||||||
\(680\) | 3.46410 | 0.132842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.41742 | −0.169152 | ||||||||
\(683\) | 20.5939 | 0.788004 | 0.394002 | − | 0.919110i | \(-0.371090\pi\) | ||||
0.394002 | + | 0.919110i | \(0.371090\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.3303 | −1.31169 | ||||||||
\(686\) | −18.3296 | −0.699826 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.8693 | −1.02438 | ||||||||
\(689\) | −27.9989 | −1.06667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2087 | −0.692692 | −0.346346 | − | 0.938107i | \(-0.612578\pi\) | ||||
−0.346346 | + | 0.938107i | \(0.612578\pi\) | |||||||
\(692\) | −5.84370 | −0.222144 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.4955 | −1.04371 | ||||||||
\(695\) | −15.6838 | −0.594921 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.66970 | −0.214755 | ||||||||
\(698\) | −33.9180 | −1.28382 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.165151 | −0.00624214 | ||||||||
\(701\) | 7.57575 | 0.286132 | 0.143066 | − | 0.989713i | \(-0.454304\pi\) | ||||
0.143066 | + | 0.989713i | \(0.454304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 0.456850 | 0.0172182 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.0780 | −0.642740 | ||||||||
\(707\) | −2.89200 | −0.108765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.121591 | −0.00456643 | −0.00228322 | − | 0.999997i | \(-0.500727\pi\) | ||||
−0.00228322 | + | 0.999997i | \(0.500727\pi\) | |||||||
\(710\) | 31.4630 | 1.18078 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.626136 | 0.0234655 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.79129 | 0.216582 | ||||||||
\(716\) | −10.2215 | −0.381996 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.4955 | 1.25004 | ||||||||
\(719\) | −27.7327 | −1.03426 | −0.517128 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517128 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.25227 | 0.0466371 | ||||||||
\(722\) | 21.0707 | 0.784169 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.834849 | −0.0310269 | ||||||||
\(725\) | −1.00905 | −0.0374752 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7913 | −0.659842 | −0.329921 | − | 0.944008i | \(-0.607022\pi\) | ||||
−0.329921 | + | 0.944008i | \(0.607022\pi\) | |||||||
\(728\) | 7.93725 | 0.294174 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.41742 | −0.0524612 | ||||||||
\(731\) | 4.91010 | 0.181607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.0345 | −1.40484 | −0.702418 | − | 0.711765i | \(-0.747896\pi\) | ||||
−0.702418 | + | 0.711765i | \(0.747896\pi\) | |||||||
\(734\) | 3.46410 | 0.127862 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.64575 | −0.0974575 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.9129 | −0.511794 | −0.255897 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255897 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(740\) | −3.92095 | −0.144137 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.62614 | 0.243253 | ||||||||
\(743\) | 10.5830 | 0.388253 | 0.194126 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194126 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.7477 | −1.19978 | ||||||||
\(746\) | 6.92820 | 0.253660 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.417424 | 0.0152625 | ||||||||
\(749\) | −10.1063 | −0.369274 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3303 | 0.814844 | 0.407422 | − | 0.913240i | \(-0.366428\pi\) | ||||
0.407422 | + | 0.913240i | \(0.366428\pi\) | |||||||
\(752\) | −10.9445 | −0.399105 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −48.4955 | −1.76610 | ||||||||
\(755\) | 13.9518 | 0.507756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.20871 | 0.189314 | 0.0946569 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946569 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(758\) | 20.9952 | 0.762580 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.1652 | −0.767741 | ||||||||
\(761\) | −43.6628 | −1.58277 | −0.791387 | − | 0.611315i | \(-0.790641\pi\) | ||||
−0.791387 | + | 0.611315i | \(0.790641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.4174 | 0.594351 | ||||||||
\(764\) | 22.8027 | 0.824973 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.7042 | 0.748072 | ||||||||
\(767\) | 10.5830 | 0.382130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.58258 | 0.345557 | 0.172778 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172778 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(770\) | −1.37055 | −0.0493912 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | −41.4183 | −1.48971 | −0.744857 | − | 0.667224i | \(-0.767482\pi\) | ||||
−0.744857 | + | 0.667224i | \(0.767482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.16515 | 0.0418535 | ||||||||
\(776\) | 13.8564 | 0.497416 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.7477 | −1.03066 | ||||||||
\(779\) | 34.6410 | 1.24114 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.79129 | −0.135663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.8693 | 1.13819 | ||||||||
\(785\) | −0.818350 | −0.0292082 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.58258 | −0.198997 | −0.0994987 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994987 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(788\) | −19.8709 | −0.707872 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.5826 | 0.483246 | ||||||||
\(791\) | 11.6874 | 0.415556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1652 | 0.574041 | ||||||||
\(794\) | −58.8897 | −2.08992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.7477 | −0.451831 | ||||||||
\(797\) | −19.3386 | −0.685009 | −0.342504 | − | 0.939516i | \(-0.611275\pi\) | ||||
−0.342504 | + | 0.939516i | \(0.611275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000 | 0.0707549 | ||||||||
\(800\) | 1.08450 | 0.0383429 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.6606 | −0.447062 | ||||||||
\(803\) | 0.170800 | 0.00602739 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.9977 | 1.97244 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.33030 | 0.222699 | ||||||||
\(809\) | 35.2131 | 1.23803 | 0.619014 | − | 0.785380i | \(-0.287533\pi\) | ||||
0.619014 | + | 0.785380i | \(0.287533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 3.82560 | 0.134252 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.41742 | 0.0496807 | ||||||||
\(815\) | 8.75560 | 0.306695 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.0000 | −1.04957 | ||||||||
\(818\) | 12.4104 | 0.433920 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5826 | 0.474324 | ||||||||
\(821\) | −47.0713 | −1.64280 | −0.821400 | − | 0.570352i | \(-0.806807\pi\) | ||||
−0.821400 | + | 0.570352i | \(0.806807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.4174 | 0.432844 | 0.216422 | − | 0.976300i | \(-0.430561\pi\) | ||||
0.216422 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(824\) | −2.74110 | −0.0954908 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.50455 | −0.0871443 | ||||||||
\(827\) | −34.1087 | −1.18608 | −0.593038 | − | 0.805174i | \(-0.702072\pi\) | ||||
−0.593038 | + | 0.805174i | \(0.702072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.834849 | −0.0289955 | −0.0144977 | − | 0.999895i | \(-0.504615\pi\) | ||||
−0.0144977 | + | 0.999895i | \(0.504615\pi\) | |||||||
\(830\) | −62.9259 | −2.18419 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.79129 | −0.200777 | ||||||||
\(833\) | −5.82380 | −0.201783 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.58258 | 0.193193 | ||||||||
\(836\) | −2.55040 | −0.0882075 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.0345 | 1.24479 | ||||||||
\(839\) | 3.46410 | 0.119594 | 0.0597970 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597970 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.62614 | −0.194005 | ||||||||
\(842\) | 5.48220 | 0.188929 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.0000 | 0.550743 | ||||||||
\(845\) | −44.9579 | −1.54660 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.53901 | −0.293404 | ||||||||
\(848\) | −24.1733 | −0.830113 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.330303 | −0.0113293 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.74773 | −0.299516 | −0.149758 | − | 0.988723i | \(-0.547850\pi\) | ||||
−0.149758 | + | 0.988723i | \(0.547850\pi\) | |||||||
\(854\) | −3.82560 | −0.130909 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.1216 | 0.756100 | ||||||||
\(857\) | −27.7128 | −0.946652 | −0.473326 | − | 0.880887i | \(-0.656947\pi\) | ||||
−0.473326 | + | 0.880887i | \(0.656947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3739 | 0.626908 | 0.313454 | − | 0.949603i | \(-0.398514\pi\) | ||||
0.313454 | + | 0.949603i | \(0.398514\pi\) | |||||||
\(860\) | −11.7629 | −0.401110 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.8693 | 0.710812 | ||||||||
\(863\) | 15.1515 | 0.515763 | 0.257882 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257882 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7913 | 0.434917 | ||||||||
\(866\) | −46.2530 | −1.57174 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.41742 | −0.149937 | ||||||||
\(869\) | −1.63670 | −0.0555213 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.5390 | 1.13643 | ||||||||
\(872\) | −35.9361 | −1.21695 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.02175 | 0.304991 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.6170 | −1.57415 | −0.787073 | − | 0.616860i | \(-0.788404\pi\) | ||||
−0.787073 | + | 0.616860i | \(0.788404\pi\) | |||||||
\(878\) | 31.5384 | 1.06437 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.00000 | 0.168550 | ||||||||
\(881\) | −32.9289 | −1.10940 | −0.554701 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554701 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.58258 | −0.322479 | −0.161240 | − | 0.986915i | \(-0.551549\pi\) | ||||
−0.161240 | + | 0.986915i | \(0.551549\pi\) | |||||||
\(884\) | −5.29150 | −0.177972 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.1216 | 1.04555 | ||||||||
\(887\) | −35.7454 | −1.20021 | −0.600107 | − | 0.799920i | \(-0.704875\pi\) | ||||
−0.600107 | + | 0.799920i | \(0.704875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.791288 | −0.0265389 | ||||||||
\(890\) | 1.37055 | 0.0459410 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.5390 | −0.419837 | ||||||||
\(893\) | −12.2197 | −0.408917 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.3739 | 0.747876 | ||||||||
\(896\) | 9.59386 | 0.320508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.7477 | −0.558879 | ||||||||
\(899\) | −26.9898 | −0.900161 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.41742 | 0.147166 | ||||||||
\(902\) | −4.91010 | −0.163489 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.5826 | −0.850864 | ||||||||
\(905\) | 1.82740 | 0.0607449 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.3303 | −0.741466 | −0.370733 | − | 0.928740i | \(-0.620893\pi\) | ||||
−0.370733 | + | 0.928740i | \(0.620893\pi\) | |||||||
\(908\) | 0.456850 | 0.0151611 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.3739 | 0.575938 | ||||||||
\(911\) | −46.6899 | −1.54691 | −0.773453 | − | 0.633854i | \(-0.781472\pi\) | ||||
−0.773453 | + | 0.633854i | \(0.781472\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.58258 | 0.250947 | ||||||||
\(914\) | −42.2168 | −1.39641 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.41742 | 0.278120 | ||||||||
\(917\) | −3.75015 | −0.123841 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.25227 | 0.305204 | 0.152602 | − | 0.988288i | \(-0.451235\pi\) | ||||
0.152602 | + | 0.988288i | \(0.451235\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.95644 | 0.327898 | ||||||||
\(923\) | 48.0605 | 1.58193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.373864 | −0.0122926 | ||||||||
\(926\) | −6.92820 | −0.227675 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.1216 | −0.824657 | ||||||||
\(929\) | −50.0587 | −1.64237 | −0.821186 | − | 0.570661i | \(-0.806687\pi\) | ||||
−0.821186 | + | 0.570661i | \(0.806687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.5826 | 1.16617 | ||||||||
\(932\) | −14.5993 | −0.478216 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.3303 | −1.18876 | ||||||||
\(935\) | −0.913701 | −0.0298812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.4083 | 1.61410 | 0.807050 | − | 0.590483i | \(-0.201063\pi\) | ||||
0.807050 | + | 0.590483i | \(0.201063\pi\) | |||||||
\(938\) | −7.93725 | −0.259161 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.79129 | −0.156275 | ||||||||
\(941\) | 45.2240 | 1.47426 | 0.737130 | − | 0.675750i | \(-0.236180\pi\) | ||||
0.737130 | + | 0.675750i | \(0.236180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 9.13701 | 0.297384 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.25227 | 0.138253 | ||||||||
\(947\) | −24.2487 | −0.787977 | −0.393989 | − | 0.919115i | \(-0.628905\pi\) | ||||
−0.393989 | + | 0.919115i | \(0.628905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.16515 | −0.0702838 | ||||||||
\(950\) | 2.01810 | 0.0654759 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.25227 | −0.0405864 | ||||||||
\(953\) | 24.2487 | 0.785493 | 0.392746 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.9129 | −1.61514 | ||||||||
\(956\) | −28.0942 | −0.908632 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 67.6170 | 2.18461 | ||||||||
\(959\) | 12.4104 | 0.400753 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.165151 | 0.00532746 | ||||||||
\(962\) | −17.9681 | −0.579313 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.1652 | −0.552852 | ||||||||
\(965\) | 35.0224 | 1.12741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2087 | 1.48597 | 0.742986 | − | 0.669307i | \(-0.233409\pi\) | ||||
0.742986 | + | 0.669307i | \(0.233409\pi\) | |||||||
\(968\) | 18.6911 | 0.600753 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.3303 | 0.973847 | ||||||||
\(971\) | −0.0754495 | −0.00242129 | −0.00121064 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00121064 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.66970 | 0.181762 | ||||||||
\(974\) | 15.5130 | 0.497069 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9564 | 0.446735 | ||||||||
\(977\) | 38.2958 | 1.22519 | 0.612596 | − | 0.790396i | \(-0.290125\pi\) | ||||
0.612596 | + | 0.790396i | \(0.290125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.165151 | −0.00527826 | ||||||||
\(980\) | 13.9518 | 0.445673 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −43.5826 | −1.39078 | ||||||||
\(983\) | 54.7225 | 1.74538 | 0.872689 | − | 0.488277i | \(-0.162374\pi\) | ||||
0.872689 | + | 0.488277i | \(0.162374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.4955 | 1.38588 | ||||||||
\(986\) | 7.65120 | 0.243664 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.3303 | 1.02856 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.04356 | 0.128448 | 0.0642240 | − | 0.997936i | \(-0.479543\pi\) | ||||
0.0642240 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(992\) | 29.0079 | 0.921002 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.3739 | −0.360757 | ||||||||
\(995\) | 27.9035 | 0.884601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.41742 | −0.0765606 | −0.0382803 | − | 0.999267i | \(-0.512188\pi\) | ||||
−0.0382803 | + | 0.999267i | \(0.512188\pi\) | |||||||
\(998\) | 66.4655 | 2.10393 | ||||||||
\(999\) | 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 | 1143.2.a.f.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 1143.2.a.f.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.2.a.f.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1143.2.a.f.1.3 | yes | 4 | 1.1 | even | 1 | trivial |