Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.79129 | 1.61155 | 0.805775 | − | 0.592221i | \(-0.201749\pi\) | ||||
0.805775 | + | 0.592221i | \(0.201749\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.79129 | −1.69552 | −0.847758 | − | 0.530384i | \(-0.822048\pi\) | ||||
−0.847758 | + | 0.530384i | \(0.822048\pi\) | |||||||
\(6\) | 2.79129 | 1.13954 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | −3.79129 | −1.19891 | ||||||||
\(11\) | −3.79129 | −1.14312 | −0.571558 | − | 0.820562i | \(-0.693661\pi\) | ||||
−0.571558 | + | 0.820562i | \(0.693661\pi\) | |||||||
\(12\) | 2.79129 | 0.805775 | ||||||||
\(13\) | 0.791288 | 0.219464 | 0.109732 | − | 0.993961i | \(-0.465001\pi\) | ||||
0.109732 | + | 0.993961i | \(0.465001\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | −10.5826 | −2.73241 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.58258 | −0.383831 | −0.191915 | − | 0.981411i | \(-0.561470\pi\) | ||||
−0.191915 | + | 0.981411i | \(0.561470\pi\) | |||||||
\(18\) | 4.79129 | 1.12932 | ||||||||
\(19\) | −7.58258 | −1.73956 | −0.869781 | − | 0.493438i | \(-0.835740\pi\) | ||||
−0.869781 | + | 0.493438i | \(0.835740\pi\) | |||||||
\(20\) | −3.79129 | −0.847758 | ||||||||
\(21\) | −5.58258 | −1.21822 | ||||||||
\(22\) | −3.79129 | −0.808305 | ||||||||
\(23\) | 0.791288 | 0.164995 | 0.0824975 | − | 0.996591i | \(-0.473710\pi\) | ||||
0.0824975 | + | 0.996591i | \(0.473710\pi\) | |||||||
\(24\) | 2.79129 | 0.569769 | ||||||||
\(25\) | 9.37386 | 1.87477 | ||||||||
\(26\) | 0.791288 | 0.155184 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 0.791288 | 0.146938 | 0.0734692 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734692 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(30\) | −10.5826 | −1.93211 | ||||||||
\(31\) | −5.37386 | −0.965174 | −0.482587 | − | 0.875848i | \(-0.660303\pi\) | ||||
−0.482587 | + | 0.875848i | \(0.660303\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.5826 | −1.84219 | ||||||||
\(34\) | −1.58258 | −0.271409 | ||||||||
\(35\) | 7.58258 | 1.28169 | ||||||||
\(36\) | 4.79129 | 0.798548 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −7.58258 | −1.23006 | ||||||||
\(39\) | 2.20871 | 0.353677 | ||||||||
\(40\) | −3.79129 | −0.599455 | ||||||||
\(41\) | −5.20871 | −0.813464 | −0.406732 | − | 0.913547i | \(-0.633332\pi\) | ||||
−0.406732 | + | 0.913547i | \(0.633332\pi\) | |||||||
\(42\) | −5.58258 | −0.861410 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −3.79129 | −0.571558 | ||||||||
\(45\) | −18.1652 | −2.70790 | ||||||||
\(46\) | 0.791288 | 0.116669 | ||||||||
\(47\) | 1.58258 | 0.230842 | 0.115421 | − | 0.993317i | \(-0.463178\pi\) | ||||
0.115421 | + | 0.993317i | \(0.463178\pi\) | |||||||
\(48\) | 2.79129 | 0.402888 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 9.37386 | 1.32566 | ||||||||
\(51\) | −4.41742 | −0.618563 | ||||||||
\(52\) | 0.791288 | 0.109732 | ||||||||
\(53\) | 7.58258 | 1.04155 | 0.520773 | − | 0.853695i | \(-0.325644\pi\) | ||||
0.520773 | + | 0.853695i | \(0.325644\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 14.3739 | 1.93817 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | −21.1652 | −2.80339 | ||||||||
\(58\) | 0.791288 | 0.103901 | ||||||||
\(59\) | −7.58258 | −0.987167 | −0.493584 | − | 0.869698i | \(-0.664313\pi\) | ||||
−0.493584 | + | 0.869698i | \(0.664313\pi\) | |||||||
\(60\) | −10.5826 | −1.36620 | ||||||||
\(61\) | −8.20871 | −1.05102 | −0.525509 | − | 0.850788i | \(-0.676125\pi\) | ||||
−0.525509 | + | 0.850788i | \(0.676125\pi\) | |||||||
\(62\) | −5.37386 | −0.682481 | ||||||||
\(63\) | −9.58258 | −1.20729 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | −10.5826 | −1.30263 | ||||||||
\(67\) | 7.37386 | 0.900861 | 0.450430 | − | 0.892812i | \(-0.351271\pi\) | ||||
0.450430 | + | 0.892812i | \(0.351271\pi\) | |||||||
\(68\) | −1.58258 | −0.191915 | ||||||||
\(69\) | 2.20871 | 0.265898 | ||||||||
\(70\) | 7.58258 | 0.906291 | ||||||||
\(71\) | 9.16515 | 1.08770 | 0.543852 | − | 0.839181i | \(-0.316965\pi\) | ||||
0.543852 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(72\) | 4.79129 | 0.564659 | ||||||||
\(73\) | −9.37386 | −1.09713 | −0.548564 | − | 0.836109i | \(-0.684825\pi\) | ||||
−0.548564 | + | 0.836109i | \(0.684825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 26.1652 | 3.02129 | ||||||||
\(76\) | −7.58258 | −0.869781 | ||||||||
\(77\) | 7.58258 | 0.864115 | ||||||||
\(78\) | 2.20871 | 0.250087 | ||||||||
\(79\) | 12.7913 | 1.43913 | 0.719566 | − | 0.694424i | \(-0.244341\pi\) | ||||
0.719566 | + | 0.694424i | \(0.244341\pi\) | |||||||
\(80\) | −3.79129 | −0.423879 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | −5.20871 | −0.575206 | ||||||||
\(83\) | −3.16515 | −0.347421 | −0.173710 | − | 0.984797i | \(-0.555576\pi\) | ||||
−0.173710 | + | 0.984797i | \(0.555576\pi\) | |||||||
\(84\) | −5.58258 | −0.609109 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | 2.20871 | 0.236799 | ||||||||
\(88\) | −3.79129 | −0.404153 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −18.1652 | −1.91478 | ||||||||
\(91\) | −1.58258 | −0.165899 | ||||||||
\(92\) | 0.791288 | 0.0824975 | ||||||||
\(93\) | −15.0000 | −1.55543 | ||||||||
\(94\) | 1.58258 | 0.163230 | ||||||||
\(95\) | 28.7477 | 2.94945 | ||||||||
\(96\) | 2.79129 | 0.284885 | ||||||||
\(97\) | −4.41742 | −0.448521 | −0.224261 | − | 0.974529i | \(-0.571997\pi\) | ||||
−0.224261 | + | 0.974529i | \(0.571997\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | −18.1652 | −1.82567 | ||||||||
\(100\) | 9.37386 | 0.937386 | ||||||||
\(101\) | 1.58258 | 0.157472 | 0.0787361 | − | 0.996895i | \(-0.474912\pi\) | ||||
0.0787361 | + | 0.996895i | \(0.474912\pi\) | |||||||
\(102\) | −4.41742 | −0.437390 | ||||||||
\(103\) | −2.20871 | −0.217631 | −0.108815 | − | 0.994062i | \(-0.534706\pi\) | ||||
−0.108815 | + | 0.994062i | \(0.534706\pi\) | |||||||
\(104\) | 0.791288 | 0.0775922 | ||||||||
\(105\) | 21.1652 | 2.06551 | ||||||||
\(106\) | 7.58258 | 0.736485 | ||||||||
\(107\) | 8.37386 | 0.809532 | 0.404766 | − | 0.914420i | \(-0.367353\pi\) | ||||
0.404766 | + | 0.914420i | \(0.367353\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 14.3739 | 1.37049 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 19.5826 | 1.84217 | 0.921087 | − | 0.389357i | \(-0.127303\pi\) | ||||
0.921087 | + | 0.389357i | \(0.127303\pi\) | |||||||
\(114\) | −21.1652 | −1.98230 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | 0.791288 | 0.0734692 | ||||||||
\(117\) | 3.79129 | 0.350505 | ||||||||
\(118\) | −7.58258 | −0.698033 | ||||||||
\(119\) | 3.16515 | 0.290149 | ||||||||
\(120\) | −10.5826 | −0.966053 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | −8.20871 | −0.743182 | ||||||||
\(123\) | −14.5390 | −1.31094 | ||||||||
\(124\) | −5.37386 | −0.482587 | ||||||||
\(125\) | −16.5826 | −1.48319 | ||||||||
\(126\) | −9.58258 | −0.853684 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.7477 | −1.47456 | ||||||||
\(130\) | −3.00000 | −0.263117 | ||||||||
\(131\) | 10.7477 | 0.939033 | 0.469517 | − | 0.882924i | \(-0.344428\pi\) | ||||
0.469517 | + | 0.882924i | \(0.344428\pi\) | |||||||
\(132\) | −10.5826 | −0.921095 | ||||||||
\(133\) | 15.1652 | 1.31499 | ||||||||
\(134\) | 7.37386 | 0.637005 | ||||||||
\(135\) | −18.9564 | −1.63151 | ||||||||
\(136\) | −1.58258 | −0.135705 | ||||||||
\(137\) | −17.3739 | −1.48435 | −0.742175 | − | 0.670207i | \(-0.766206\pi\) | ||||
−0.742175 | + | 0.670207i | \(0.766206\pi\) | |||||||
\(138\) | 2.20871 | 0.188018 | ||||||||
\(139\) | −0.373864 | −0.0317107 | −0.0158553 | − | 0.999874i | \(-0.505047\pi\) | ||||
−0.0158553 | + | 0.999874i | \(0.505047\pi\) | |||||||
\(140\) | 7.58258 | 0.640845 | ||||||||
\(141\) | 4.41742 | 0.372014 | ||||||||
\(142\) | 9.16515 | 0.769122 | ||||||||
\(143\) | −3.00000 | −0.250873 | ||||||||
\(144\) | 4.79129 | 0.399274 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | −9.37386 | −0.775786 | ||||||||
\(147\) | −8.37386 | −0.690665 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5826 | −1.11273 | −0.556364 | − | 0.830939i | \(-0.687804\pi\) | ||||
−0.556364 | + | 0.830939i | \(0.687804\pi\) | |||||||
\(150\) | 26.1652 | 2.13638 | ||||||||
\(151\) | −12.7477 | −1.03740 | −0.518698 | − | 0.854958i | \(-0.673583\pi\) | ||||
−0.518698 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(152\) | −7.58258 | −0.615028 | ||||||||
\(153\) | −7.58258 | −0.613015 | ||||||||
\(154\) | 7.58258 | 0.611021 | ||||||||
\(155\) | 20.3739 | 1.63647 | ||||||||
\(156\) | 2.20871 | 0.176838 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 12.7913 | 1.01762 | ||||||||
\(159\) | 21.1652 | 1.67851 | ||||||||
\(160\) | −3.79129 | −0.299728 | ||||||||
\(161\) | −1.58258 | −0.124724 | ||||||||
\(162\) | −0.417424 | −0.0327960 | ||||||||
\(163\) | −10.4174 | −0.815956 | −0.407978 | − | 0.912992i | \(-0.633766\pi\) | ||||
−0.407978 | + | 0.912992i | \(0.633766\pi\) | |||||||
\(164\) | −5.20871 | −0.406732 | ||||||||
\(165\) | 40.1216 | 3.12346 | ||||||||
\(166\) | −3.16515 | −0.245663 | ||||||||
\(167\) | 0.956439 | 0.0740115 | 0.0370057 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370057 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(168\) | −5.58258 | −0.430705 | ||||||||
\(169\) | −12.3739 | −0.951836 | ||||||||
\(170\) | 6.00000 | 0.460179 | ||||||||
\(171\) | −36.3303 | −2.77825 | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 3.16515 | 0.240642 | 0.120321 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120321 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(174\) | 2.20871 | 0.167442 | ||||||||
\(175\) | −18.7477 | −1.41719 | ||||||||
\(176\) | −3.79129 | −0.285779 | ||||||||
\(177\) | −21.1652 | −1.59087 | ||||||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | 7.58258 | 0.566748 | 0.283374 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283374 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(180\) | −18.1652 | −1.35395 | ||||||||
\(181\) | −18.7477 | −1.39351 | −0.696754 | − | 0.717310i | \(-0.745373\pi\) | ||||
−0.696754 | + | 0.717310i | \(0.745373\pi\) | |||||||
\(182\) | −1.58258 | −0.117308 | ||||||||
\(183\) | −22.9129 | −1.69377 | ||||||||
\(184\) | 0.791288 | 0.0583345 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.0000 | −1.09985 | ||||||||
\(187\) | 6.00000 | 0.438763 | ||||||||
\(188\) | 1.58258 | 0.115421 | ||||||||
\(189\) | −10.0000 | −0.727393 | ||||||||
\(190\) | 28.7477 | 2.08558 | ||||||||
\(191\) | −5.37386 | −0.388839 | −0.194420 | − | 0.980918i | \(-0.562282\pi\) | ||||
−0.194420 | + | 0.980918i | \(0.562282\pi\) | |||||||
\(192\) | 2.79129 | 0.201444 | ||||||||
\(193\) | 18.3303 | 1.31944 | 0.659722 | − | 0.751510i | \(-0.270674\pi\) | ||||
0.659722 | + | 0.751510i | \(0.270674\pi\) | |||||||
\(194\) | −4.41742 | −0.317153 | ||||||||
\(195\) | −8.37386 | −0.599665 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 25.9129 | 1.84622 | 0.923108 | − | 0.384541i | \(-0.125640\pi\) | ||||
0.923108 | + | 0.384541i | \(0.125640\pi\) | |||||||
\(198\) | −18.1652 | −1.29094 | ||||||||
\(199\) | −3.16515 | −0.224372 | −0.112186 | − | 0.993687i | \(-0.535785\pi\) | ||||
−0.112186 | + | 0.993687i | \(0.535785\pi\) | |||||||
\(200\) | 9.37386 | 0.662832 | ||||||||
\(201\) | 20.5826 | 1.45178 | ||||||||
\(202\) | 1.58258 | 0.111350 | ||||||||
\(203\) | −1.58258 | −0.111075 | ||||||||
\(204\) | −4.41742 | −0.309282 | ||||||||
\(205\) | 19.7477 | 1.37924 | ||||||||
\(206\) | −2.20871 | −0.153888 | ||||||||
\(207\) | 3.79129 | 0.263513 | ||||||||
\(208\) | 0.791288 | 0.0548659 | ||||||||
\(209\) | 28.7477 | 1.98852 | ||||||||
\(210\) | 21.1652 | 1.46053 | ||||||||
\(211\) | −3.37386 | −0.232266 | −0.116133 | − | 0.993234i | \(-0.537050\pi\) | ||||
−0.116133 | + | 0.993234i | \(0.537050\pi\) | |||||||
\(212\) | 7.58258 | 0.520773 | ||||||||
\(213\) | 25.5826 | 1.75289 | ||||||||
\(214\) | 8.37386 | 0.572426 | ||||||||
\(215\) | 22.7477 | 1.55138 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 10.7477 | 0.729603 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | −26.1652 | −1.76808 | ||||||||
\(220\) | 14.3739 | 0.969086 | ||||||||
\(221\) | −1.25227 | −0.0842370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 44.9129 | 2.99419 | ||||||||
\(226\) | 19.5826 | 1.30261 | ||||||||
\(227\) | 19.9129 | 1.32166 | 0.660832 | − | 0.750534i | \(-0.270204\pi\) | ||||
0.660832 | + | 0.750534i | \(0.270204\pi\) | |||||||
\(228\) | −21.1652 | −1.40170 | ||||||||
\(229\) | −20.7477 | −1.37105 | −0.685524 | − | 0.728050i | \(-0.740427\pi\) | ||||
−0.685524 | + | 0.728050i | \(0.740427\pi\) | |||||||
\(230\) | −3.00000 | −0.197814 | ||||||||
\(231\) | 21.1652 | 1.39256 | ||||||||
\(232\) | 0.791288 | 0.0519506 | ||||||||
\(233\) | −25.1216 | −1.64577 | −0.822885 | − | 0.568208i | \(-0.807637\pi\) | ||||
−0.822885 | + | 0.568208i | \(0.807637\pi\) | |||||||
\(234\) | 3.79129 | 0.247844 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | −7.58258 | −0.493584 | ||||||||
\(237\) | 35.7042 | 2.31923 | ||||||||
\(238\) | 3.16515 | 0.205166 | ||||||||
\(239\) | 24.9564 | 1.61430 | 0.807149 | − | 0.590348i | \(-0.201009\pi\) | ||||
0.807149 | + | 0.590348i | \(0.201009\pi\) | |||||||
\(240\) | −10.5826 | −0.683102 | ||||||||
\(241\) | 13.5826 | 0.874931 | 0.437465 | − | 0.899235i | \(-0.355876\pi\) | ||||
0.437465 | + | 0.899235i | \(0.355876\pi\) | |||||||
\(242\) | 3.37386 | 0.216880 | ||||||||
\(243\) | −16.1652 | −1.03699 | ||||||||
\(244\) | −8.20871 | −0.525509 | ||||||||
\(245\) | 11.3739 | 0.726649 | ||||||||
\(246\) | −14.5390 | −0.926974 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | −5.37386 | −0.341241 | ||||||||
\(249\) | −8.83485 | −0.559886 | ||||||||
\(250\) | −16.5826 | −1.04877 | ||||||||
\(251\) | −13.5826 | −0.857325 | −0.428662 | − | 0.903465i | \(-0.641015\pi\) | ||||
−0.428662 | + | 0.903465i | \(0.641015\pi\) | |||||||
\(252\) | −9.58258 | −0.603646 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 16.7477 | 1.04878 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.7477 | 1.41896 | 0.709482 | − | 0.704723i | \(-0.248929\pi\) | ||||
0.709482 | + | 0.704723i | \(0.248929\pi\) | |||||||
\(258\) | −16.7477 | −1.04267 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 3.79129 | 0.234675 | ||||||||
\(262\) | 10.7477 | 0.663997 | ||||||||
\(263\) | 8.83485 | 0.544780 | 0.272390 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272390 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(264\) | −10.5826 | −0.651313 | ||||||||
\(265\) | −28.7477 | −1.76596 | ||||||||
\(266\) | 15.1652 | 0.929835 | ||||||||
\(267\) | −16.7477 | −1.02494 | ||||||||
\(268\) | 7.37386 | 0.450430 | ||||||||
\(269\) | −10.7477 | −0.655300 | −0.327650 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327650 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(270\) | −18.9564 | −1.15365 | ||||||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | −1.58258 | −0.0959577 | ||||||||
\(273\) | −4.41742 | −0.267355 | ||||||||
\(274\) | −17.3739 | −1.04959 | ||||||||
\(275\) | −35.5390 | −2.14308 | ||||||||
\(276\) | 2.20871 | 0.132949 | ||||||||
\(277\) | 23.3739 | 1.40440 | 0.702200 | − | 0.711980i | \(-0.252201\pi\) | ||||
0.702200 | + | 0.711980i | \(0.252201\pi\) | |||||||
\(278\) | −0.373864 | −0.0224228 | ||||||||
\(279\) | −25.7477 | −1.54148 | ||||||||
\(280\) | 7.58258 | 0.453146 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 4.41742 | 0.263054 | ||||||||
\(283\) | −24.0000 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(284\) | 9.16515 | 0.543852 | ||||||||
\(285\) | 80.2432 | 4.75320 | ||||||||
\(286\) | −3.00000 | −0.177394 | ||||||||
\(287\) | 10.4174 | 0.614921 | ||||||||
\(288\) | 4.79129 | 0.282329 | ||||||||
\(289\) | −14.4955 | −0.852674 | ||||||||
\(290\) | −3.00000 | −0.176166 | ||||||||
\(291\) | −12.3303 | −0.722815 | ||||||||
\(292\) | −9.37386 | −0.548564 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | −8.37386 | −0.488374 | ||||||||
\(295\) | 28.7477 | 1.67376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.9564 | −1.09996 | ||||||||
\(298\) | −13.5826 | −0.786817 | ||||||||
\(299\) | 0.626136 | 0.0362104 | ||||||||
\(300\) | 26.1652 | 1.51065 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | −12.7477 | −0.733549 | ||||||||
\(303\) | 4.41742 | 0.253774 | ||||||||
\(304\) | −7.58258 | −0.434891 | ||||||||
\(305\) | 31.1216 | 1.78202 | ||||||||
\(306\) | −7.58258 | −0.433467 | ||||||||
\(307\) | 12.3739 | 0.706214 | 0.353107 | − | 0.935583i | \(-0.385125\pi\) | ||||
0.353107 | + | 0.935583i | \(0.385125\pi\) | |||||||
\(308\) | 7.58258 | 0.432057 | ||||||||
\(309\) | −6.16515 | −0.350723 | ||||||||
\(310\) | 20.3739 | 1.15716 | ||||||||
\(311\) | 9.62614 | 0.545848 | 0.272924 | − | 0.962036i | \(-0.412009\pi\) | ||||
0.272924 | + | 0.962036i | \(0.412009\pi\) | |||||||
\(312\) | 2.20871 | 0.125044 | ||||||||
\(313\) | −33.1652 | −1.87461 | −0.937303 | − | 0.348517i | \(-0.886685\pi\) | ||||
−0.937303 | + | 0.348517i | \(0.886685\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 36.3303 | 2.04698 | ||||||||
\(316\) | 12.7913 | 0.719566 | ||||||||
\(317\) | 1.25227 | 0.0703347 | 0.0351673 | − | 0.999381i | \(-0.488804\pi\) | ||||
0.0351673 | + | 0.999381i | \(0.488804\pi\) | |||||||
\(318\) | 21.1652 | 1.18688 | ||||||||
\(319\) | −3.00000 | −0.167968 | ||||||||
\(320\) | −3.79129 | −0.211939 | ||||||||
\(321\) | 23.3739 | 1.30460 | ||||||||
\(322\) | −1.58258 | −0.0881935 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −0.417424 | −0.0231902 | ||||||||
\(325\) | 7.41742 | 0.411445 | ||||||||
\(326\) | −10.4174 | −0.576968 | ||||||||
\(327\) | 16.7477 | 0.926151 | ||||||||
\(328\) | −5.20871 | −0.287603 | ||||||||
\(329\) | −3.16515 | −0.174500 | ||||||||
\(330\) | 40.1216 | 2.20862 | ||||||||
\(331\) | −16.4174 | −0.902383 | −0.451192 | − | 0.892427i | \(-0.649001\pi\) | ||||
−0.451192 | + | 0.892427i | \(0.649001\pi\) | |||||||
\(332\) | −3.16515 | −0.173710 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.956439 | 0.0523340 | ||||||||
\(335\) | −27.9564 | −1.52742 | ||||||||
\(336\) | −5.58258 | −0.304554 | ||||||||
\(337\) | 8.12159 | 0.442411 | 0.221206 | − | 0.975227i | \(-0.429001\pi\) | ||||
0.221206 | + | 0.975227i | \(0.429001\pi\) | |||||||
\(338\) | −12.3739 | −0.673049 | ||||||||
\(339\) | 54.6606 | 2.96876 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | 20.3739 | 1.10331 | ||||||||
\(342\) | −36.3303 | −1.96452 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | −8.37386 | −0.450834 | ||||||||
\(346\) | 3.16515 | 0.170160 | ||||||||
\(347\) | 1.58258 | 0.0849571 | 0.0424786 | − | 0.999097i | \(-0.486475\pi\) | ||||
0.0424786 | + | 0.999097i | \(0.486475\pi\) | |||||||
\(348\) | 2.20871 | 0.118399 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | −18.7477 | −1.00211 | ||||||||
\(351\) | 3.95644 | 0.211179 | ||||||||
\(352\) | −3.79129 | −0.202076 | ||||||||
\(353\) | −7.58258 | −0.403580 | −0.201790 | − | 0.979429i | \(-0.564676\pi\) | ||||
−0.201790 | + | 0.979429i | \(0.564676\pi\) | |||||||
\(354\) | −21.1652 | −1.12492 | ||||||||
\(355\) | −34.7477 | −1.84422 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 8.83485 | 0.467590 | ||||||||
\(358\) | 7.58258 | 0.400752 | ||||||||
\(359\) | −27.1652 | −1.43372 | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||||
−0.716861 | + | 0.697216i | \(0.754422\pi\) | |||||||
\(360\) | −18.1652 | −0.957388 | ||||||||
\(361\) | 38.4955 | 2.02608 | ||||||||
\(362\) | −18.7477 | −0.985359 | ||||||||
\(363\) | 9.41742 | 0.494287 | ||||||||
\(364\) | −1.58258 | −0.0829495 | ||||||||
\(365\) | 35.5390 | 1.86020 | ||||||||
\(366\) | −22.9129 | −1.19768 | ||||||||
\(367\) | −32.7477 | −1.70942 | −0.854709 | − | 0.519108i | \(-0.826264\pi\) | ||||
−0.854709 | + | 0.519108i | \(0.826264\pi\) | |||||||
\(368\) | 0.791288 | 0.0412487 | ||||||||
\(369\) | −24.9564 | −1.29918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.1652 | −0.787335 | ||||||||
\(372\) | −15.0000 | −0.777714 | ||||||||
\(373\) | −14.7477 | −0.763608 | −0.381804 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381804 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(374\) | 6.00000 | 0.310253 | ||||||||
\(375\) | −46.2867 | −2.39024 | ||||||||
\(376\) | 1.58258 | 0.0816151 | ||||||||
\(377\) | 0.626136 | 0.0322477 | ||||||||
\(378\) | −10.0000 | −0.514344 | ||||||||
\(379\) | −21.1216 | −1.08494 | −0.542472 | − | 0.840074i | \(-0.682511\pi\) | ||||
−0.542472 | + | 0.840074i | \(0.682511\pi\) | |||||||
\(380\) | 28.7477 | 1.47473 | ||||||||
\(381\) | 22.3303 | 1.14402 | ||||||||
\(382\) | −5.37386 | −0.274951 | ||||||||
\(383\) | 18.3303 | 0.936635 | 0.468317 | − | 0.883560i | \(-0.344860\pi\) | ||||
0.468317 | + | 0.883560i | \(0.344860\pi\) | |||||||
\(384\) | 2.79129 | 0.142442 | ||||||||
\(385\) | −28.7477 | −1.46512 | ||||||||
\(386\) | 18.3303 | 0.932988 | ||||||||
\(387\) | −28.7477 | −1.46133 | ||||||||
\(388\) | −4.41742 | −0.224261 | ||||||||
\(389\) | −35.8693 | −1.81865 | −0.909323 | − | 0.416090i | \(-0.863400\pi\) | ||||
−0.909323 | + | 0.416090i | \(0.863400\pi\) | |||||||
\(390\) | −8.37386 | −0.424027 | ||||||||
\(391\) | −1.25227 | −0.0633302 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 30.0000 | 1.51330 | ||||||||
\(394\) | 25.9129 | 1.30547 | ||||||||
\(395\) | −48.4955 | −2.44007 | ||||||||
\(396\) | −18.1652 | −0.912833 | ||||||||
\(397\) | 12.7477 | 0.639790 | 0.319895 | − | 0.947453i | \(-0.396352\pi\) | ||||
0.319895 | + | 0.947453i | \(0.396352\pi\) | |||||||
\(398\) | −3.16515 | −0.158655 | ||||||||
\(399\) | 42.3303 | 2.11917 | ||||||||
\(400\) | 9.37386 | 0.468693 | ||||||||
\(401\) | −10.7477 | −0.536716 | −0.268358 | − | 0.963319i | \(-0.586481\pi\) | ||||
−0.268358 | + | 0.963319i | \(0.586481\pi\) | |||||||
\(402\) | 20.5826 | 1.02657 | ||||||||
\(403\) | −4.25227 | −0.211821 | ||||||||
\(404\) | 1.58258 | 0.0787361 | ||||||||
\(405\) | 1.58258 | 0.0786388 | ||||||||
\(406\) | −1.58258 | −0.0785419 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.41742 | −0.218695 | ||||||||
\(409\) | −8.83485 | −0.436855 | −0.218428 | − | 0.975853i | \(-0.570093\pi\) | ||||
−0.218428 | + | 0.975853i | \(0.570093\pi\) | |||||||
\(410\) | 19.7477 | 0.975271 | ||||||||
\(411\) | −48.4955 | −2.39210 | ||||||||
\(412\) | −2.20871 | −0.108815 | ||||||||
\(413\) | 15.1652 | 0.746228 | ||||||||
\(414\) | 3.79129 | 0.186332 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0.791288 | 0.0387961 | ||||||||
\(417\) | −1.04356 | −0.0511034 | ||||||||
\(418\) | 28.7477 | 1.40610 | ||||||||
\(419\) | 6.79129 | 0.331776 | 0.165888 | − | 0.986145i | \(-0.446951\pi\) | ||||
0.165888 | + | 0.986145i | \(0.446951\pi\) | |||||||
\(420\) | 21.1652 | 1.03275 | ||||||||
\(421\) | −3.95644 | −0.192825 | −0.0964125 | − | 0.995341i | \(-0.530737\pi\) | ||||
−0.0964125 | + | 0.995341i | \(0.530737\pi\) | |||||||
\(422\) | −3.37386 | −0.164237 | ||||||||
\(423\) | 7.58258 | 0.368677 | ||||||||
\(424\) | 7.58258 | 0.368242 | ||||||||
\(425\) | −14.8348 | −0.719596 | ||||||||
\(426\) | 25.5826 | 1.23948 | ||||||||
\(427\) | 16.4174 | 0.794495 | ||||||||
\(428\) | 8.37386 | 0.404766 | ||||||||
\(429\) | −8.37386 | −0.404294 | ||||||||
\(430\) | 22.7477 | 1.09699 | ||||||||
\(431\) | 27.1652 | 1.30850 | 0.654250 | − | 0.756279i | \(-0.272985\pi\) | ||||
0.654250 | + | 0.756279i | \(0.272985\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | 24.3739 | 1.17133 | 0.585667 | − | 0.810552i | \(-0.300833\pi\) | ||||
0.585667 | + | 0.810552i | \(0.300833\pi\) | |||||||
\(434\) | 10.7477 | 0.515907 | ||||||||
\(435\) | −8.37386 | −0.401496 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | −26.1652 | −1.25022 | ||||||||
\(439\) | −26.3739 | −1.25876 | −0.629378 | − | 0.777099i | \(-0.716690\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(440\) | 14.3739 | 0.685247 | ||||||||
\(441\) | −14.3739 | −0.684470 | ||||||||
\(442\) | −1.25227 | −0.0595645 | ||||||||
\(443\) | −5.04356 | −0.239627 | −0.119813 | − | 0.992796i | \(-0.538230\pi\) | ||||
−0.119813 | + | 0.992796i | \(0.538230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.7477 | 1.07835 | ||||||||
\(446\) | 14.0000 | 0.662919 | ||||||||
\(447\) | −37.9129 | −1.79322 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | −21.1652 | −0.998845 | −0.499423 | − | 0.866358i | \(-0.666454\pi\) | ||||
−0.499423 | + | 0.866358i | \(0.666454\pi\) | |||||||
\(450\) | 44.9129 | 2.11721 | ||||||||
\(451\) | 19.7477 | 0.929884 | ||||||||
\(452\) | 19.5826 | 0.921087 | ||||||||
\(453\) | −35.5826 | −1.67182 | ||||||||
\(454\) | 19.9129 | 0.934558 | ||||||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | −21.1652 | −0.991149 | ||||||||
\(457\) | 33.4955 | 1.56685 | 0.783426 | − | 0.621486i | \(-0.213471\pi\) | ||||
0.783426 | + | 0.621486i | \(0.213471\pi\) | |||||||
\(458\) | −20.7477 | −0.969478 | ||||||||
\(459\) | −7.91288 | −0.369342 | ||||||||
\(460\) | −3.00000 | −0.139876 | ||||||||
\(461\) | −24.3303 | −1.13318 | −0.566588 | − | 0.824002i | \(-0.691737\pi\) | ||||
−0.566588 | + | 0.824002i | \(0.691737\pi\) | |||||||
\(462\) | 21.1652 | 0.984692 | ||||||||
\(463\) | −20.7042 | −0.962204 | −0.481102 | − | 0.876665i | \(-0.659763\pi\) | ||||
−0.481102 | + | 0.876665i | \(0.659763\pi\) | |||||||
\(464\) | 0.791288 | 0.0367346 | ||||||||
\(465\) | 56.8693 | 2.63725 | ||||||||
\(466\) | −25.1216 | −1.16374 | ||||||||
\(467\) | 25.5826 | 1.18382 | 0.591910 | − | 0.806004i | \(-0.298374\pi\) | ||||
0.591910 | + | 0.806004i | \(0.298374\pi\) | |||||||
\(468\) | 3.79129 | 0.175252 | ||||||||
\(469\) | −14.7477 | −0.680987 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | −5.58258 | −0.257232 | ||||||||
\(472\) | −7.58258 | −0.349016 | ||||||||
\(473\) | 22.7477 | 1.04594 | ||||||||
\(474\) | 35.7042 | 1.63995 | ||||||||
\(475\) | −71.0780 | −3.26128 | ||||||||
\(476\) | 3.16515 | 0.145074 | ||||||||
\(477\) | 36.3303 | 1.66345 | ||||||||
\(478\) | 24.9564 | 1.14148 | ||||||||
\(479\) | −0.791288 | −0.0361549 | −0.0180774 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180774 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(480\) | −10.5826 | −0.483026 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13.5826 | 0.618669 | ||||||||
\(483\) | −4.41742 | −0.201000 | ||||||||
\(484\) | 3.37386 | 0.153357 | ||||||||
\(485\) | 16.7477 | 0.760475 | ||||||||
\(486\) | −16.1652 | −0.733266 | ||||||||
\(487\) | −36.6606 | −1.66125 | −0.830625 | − | 0.556832i | \(-0.812017\pi\) | ||||
−0.830625 | + | 0.556832i | \(0.812017\pi\) | |||||||
\(488\) | −8.20871 | −0.371591 | ||||||||
\(489\) | −29.0780 | −1.31495 | ||||||||
\(490\) | 11.3739 | 0.513819 | ||||||||
\(491\) | −8.37386 | −0.377907 | −0.188954 | − | 0.981986i | \(-0.560510\pi\) | ||||
−0.188954 | + | 0.981986i | \(0.560510\pi\) | |||||||
\(492\) | −14.5390 | −0.655469 | ||||||||
\(493\) | −1.25227 | −0.0563995 | ||||||||
\(494\) | −6.00000 | −0.269953 | ||||||||
\(495\) | 68.8693 | 3.09545 | ||||||||
\(496\) | −5.37386 | −0.241294 | ||||||||
\(497\) | −18.3303 | −0.822226 | ||||||||
\(498\) | −8.83485 | −0.395899 | ||||||||
\(499\) | −16.7477 | −0.749731 | −0.374866 | − | 0.927079i | \(-0.622311\pi\) | ||||
−0.374866 | + | 0.927079i | \(0.622311\pi\) | |||||||
\(500\) | −16.5826 | −0.741595 | ||||||||
\(501\) | 2.66970 | 0.119273 | ||||||||
\(502\) | −13.5826 | −0.606220 | ||||||||
\(503\) | 29.3739 | 1.30972 | 0.654858 | − | 0.755752i | \(-0.272728\pi\) | ||||
0.654858 | + | 0.755752i | \(0.272728\pi\) | |||||||
\(504\) | −9.58258 | −0.426842 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −3.00000 | −0.133366 | ||||||||
\(507\) | −34.5390 | −1.53393 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | −13.5826 | −0.602037 | −0.301019 | − | 0.953618i | \(-0.597327\pi\) | ||||
−0.301019 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(510\) | 16.7477 | 0.741602 | ||||||||
\(511\) | 18.7477 | 0.829351 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −37.9129 | −1.67389 | ||||||||
\(514\) | 22.7477 | 1.00336 | ||||||||
\(515\) | 8.37386 | 0.368997 | ||||||||
\(516\) | −16.7477 | −0.737278 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.83485 | 0.387807 | ||||||||
\(520\) | −3.00000 | −0.131559 | ||||||||
\(521\) | −9.16515 | −0.401533 | −0.200766 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200766 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(522\) | 3.79129 | 0.165940 | ||||||||
\(523\) | −3.16515 | −0.138402 | −0.0692012 | − | 0.997603i | \(-0.522045\pi\) | ||||
−0.0692012 | + | 0.997603i | \(0.522045\pi\) | |||||||
\(524\) | 10.7477 | 0.469517 | ||||||||
\(525\) | −52.3303 | −2.28388 | ||||||||
\(526\) | 8.83485 | 0.385218 | ||||||||
\(527\) | 8.50455 | 0.370464 | ||||||||
\(528\) | −10.5826 | −0.460547 | ||||||||
\(529\) | −22.3739 | −0.972777 | ||||||||
\(530\) | −28.7477 | −1.24872 | ||||||||
\(531\) | −36.3303 | −1.57660 | ||||||||
\(532\) | 15.1652 | 0.657493 | ||||||||
\(533\) | −4.12159 | −0.178526 | ||||||||
\(534\) | −16.7477 | −0.724745 | ||||||||
\(535\) | −31.7477 | −1.37257 | ||||||||
\(536\) | 7.37386 | 0.318502 | ||||||||
\(537\) | 21.1652 | 0.913344 | ||||||||
\(538\) | −10.7477 | −0.463367 | ||||||||
\(539\) | 11.3739 | 0.489907 | ||||||||
\(540\) | −18.9564 | −0.815755 | ||||||||
\(541\) | −8.20871 | −0.352920 | −0.176460 | − | 0.984308i | \(-0.556465\pi\) | ||||
−0.176460 | + | 0.984308i | \(0.556465\pi\) | |||||||
\(542\) | 22.0000 | 0.944981 | ||||||||
\(543\) | −52.3303 | −2.24571 | ||||||||
\(544\) | −1.58258 | −0.0678524 | ||||||||
\(545\) | −22.7477 | −0.974406 | ||||||||
\(546\) | −4.41742 | −0.189048 | ||||||||
\(547\) | −19.9129 | −0.851413 | −0.425707 | − | 0.904861i | \(-0.639974\pi\) | ||||
−0.425707 | + | 0.904861i | \(0.639974\pi\) | |||||||
\(548\) | −17.3739 | −0.742175 | ||||||||
\(549\) | −39.3303 | −1.67858 | ||||||||
\(550\) | −35.5390 | −1.51539 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 2.20871 | 0.0940090 | ||||||||
\(553\) | −25.5826 | −1.08788 | ||||||||
\(554\) | 23.3739 | 0.993060 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.373864 | −0.0158553 | ||||||||
\(557\) | −41.7042 | −1.76706 | −0.883531 | − | 0.468372i | \(-0.844841\pi\) | ||||
−0.883531 | + | 0.468372i | \(0.844841\pi\) | |||||||
\(558\) | −25.7477 | −1.08999 | ||||||||
\(559\) | −4.74773 | −0.200807 | ||||||||
\(560\) | 7.58258 | 0.320422 | ||||||||
\(561\) | 16.7477 | 0.707090 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.7477 | −0.705833 | −0.352916 | − | 0.935655i | \(-0.614810\pi\) | ||||
−0.352916 | + | 0.935655i | \(0.614810\pi\) | |||||||
\(564\) | 4.41742 | 0.186007 | ||||||||
\(565\) | −74.2432 | −3.12343 | ||||||||
\(566\) | −24.0000 | −1.00880 | ||||||||
\(567\) | 0.834849 | 0.0350603 | ||||||||
\(568\) | 9.16515 | 0.384561 | ||||||||
\(569\) | 26.8348 | 1.12498 | 0.562488 | − | 0.826806i | \(-0.309844\pi\) | ||||
0.562488 | + | 0.826806i | \(0.309844\pi\) | |||||||
\(570\) | 80.2432 | 3.36102 | ||||||||
\(571\) | −28.3739 | −1.18741 | −0.593705 | − | 0.804683i | \(-0.702335\pi\) | ||||
−0.593705 | + | 0.804683i | \(0.702335\pi\) | |||||||
\(572\) | −3.00000 | −0.125436 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 10.4174 | 0.434815 | ||||||||
\(575\) | 7.41742 | 0.309328 | ||||||||
\(576\) | 4.79129 | 0.199637 | ||||||||
\(577\) | −4.41742 | −0.183900 | −0.0919499 | − | 0.995764i | \(-0.529310\pi\) | ||||
−0.0919499 | + | 0.995764i | \(0.529310\pi\) | |||||||
\(578\) | −14.4955 | −0.602931 | ||||||||
\(579\) | 51.1652 | 2.12635 | ||||||||
\(580\) | −3.00000 | −0.124568 | ||||||||
\(581\) | 6.33030 | 0.262625 | ||||||||
\(582\) | −12.3303 | −0.511107 | ||||||||
\(583\) | −28.7477 | −1.19061 | ||||||||
\(584\) | −9.37386 | −0.387893 | ||||||||
\(585\) | −14.3739 | −0.594286 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 25.9129 | 1.06954 | 0.534769 | − | 0.844998i | \(-0.320398\pi\) | ||||
0.534769 | + | 0.844998i | \(0.320398\pi\) | |||||||
\(588\) | −8.37386 | −0.345332 | ||||||||
\(589\) | 40.7477 | 1.67898 | ||||||||
\(590\) | 28.7477 | 1.18353 | ||||||||
\(591\) | 72.3303 | 2.97527 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.2087 | −0.583482 | −0.291741 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291741 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(594\) | −18.9564 | −0.777792 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | −13.5826 | −0.556364 | ||||||||
\(597\) | −8.83485 | −0.361586 | ||||||||
\(598\) | 0.626136 | 0.0256046 | ||||||||
\(599\) | 27.1652 | 1.10994 | 0.554969 | − | 0.831871i | \(-0.312730\pi\) | ||||
0.554969 | + | 0.831871i | \(0.312730\pi\) | |||||||
\(600\) | 26.1652 | 1.06819 | ||||||||
\(601\) | 8.12159 | 0.331287 | 0.165643 | − | 0.986186i | \(-0.447030\pi\) | ||||
0.165643 | + | 0.986186i | \(0.447030\pi\) | |||||||
\(602\) | 12.0000 | 0.489083 | ||||||||
\(603\) | 35.3303 | 1.43876 | ||||||||
\(604\) | −12.7477 | −0.518698 | ||||||||
\(605\) | −12.7913 | −0.520040 | ||||||||
\(606\) | 4.41742 | 0.179446 | ||||||||
\(607\) | 5.53901 | 0.224822 | 0.112411 | − | 0.993662i | \(-0.464143\pi\) | ||||
0.112411 | + | 0.993662i | \(0.464143\pi\) | |||||||
\(608\) | −7.58258 | −0.307514 | ||||||||
\(609\) | −4.41742 | −0.179003 | ||||||||
\(610\) | 31.1216 | 1.26008 | ||||||||
\(611\) | 1.25227 | 0.0506615 | ||||||||
\(612\) | −7.58258 | −0.306507 | ||||||||
\(613\) | −5.49545 | −0.221959 | −0.110980 | − | 0.993823i | \(-0.535399\pi\) | ||||
−0.110980 | + | 0.993823i | \(0.535399\pi\) | |||||||
\(614\) | 12.3739 | 0.499368 | ||||||||
\(615\) | 55.1216 | 2.22272 | ||||||||
\(616\) | 7.58258 | 0.305511 | ||||||||
\(617\) | 45.9564 | 1.85014 | 0.925068 | − | 0.379801i | \(-0.124007\pi\) | ||||
0.925068 | + | 0.379801i | \(0.124007\pi\) | |||||||
\(618\) | −6.16515 | −0.247999 | ||||||||
\(619\) | −6.12159 | −0.246048 | −0.123024 | − | 0.992404i | \(-0.539259\pi\) | ||||
−0.123024 | + | 0.992404i | \(0.539259\pi\) | |||||||
\(620\) | 20.3739 | 0.818234 | ||||||||
\(621\) | 3.95644 | 0.158766 | ||||||||
\(622\) | 9.62614 | 0.385973 | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 2.20871 | 0.0884192 | ||||||||
\(625\) | 16.0000 | 0.640000 | ||||||||
\(626\) | −33.1652 | −1.32555 | ||||||||
\(627\) | 80.2432 | 3.20460 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 36.3303 | 1.44743 | ||||||||
\(631\) | 3.95644 | 0.157503 | 0.0787517 | − | 0.996894i | \(-0.474907\pi\) | ||||
0.0787517 | + | 0.996894i | \(0.474907\pi\) | |||||||
\(632\) | 12.7913 | 0.508810 | ||||||||
\(633\) | −9.41742 | −0.374309 | ||||||||
\(634\) | 1.25227 | 0.0497341 | ||||||||
\(635\) | −30.3303 | −1.20362 | ||||||||
\(636\) | 21.1652 | 0.839253 | ||||||||
\(637\) | −2.37386 | −0.0940559 | ||||||||
\(638\) | −3.00000 | −0.118771 | ||||||||
\(639\) | 43.9129 | 1.73717 | ||||||||
\(640\) | −3.79129 | −0.149864 | ||||||||
\(641\) | −35.5390 | −1.40371 | −0.701853 | − | 0.712321i | \(-0.747644\pi\) | ||||
−0.701853 | + | 0.712321i | \(0.747644\pi\) | |||||||
\(642\) | 23.3739 | 0.922493 | ||||||||
\(643\) | −15.4955 | −0.611081 | −0.305541 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305541 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(644\) | −1.58258 | −0.0623622 | ||||||||
\(645\) | 63.4955 | 2.50013 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 32.7042 | 1.28573 | 0.642867 | − | 0.765978i | \(-0.277745\pi\) | ||||
0.642867 | + | 0.765978i | \(0.277745\pi\) | |||||||
\(648\) | −0.417424 | −0.0163980 | ||||||||
\(649\) | 28.7477 | 1.12845 | ||||||||
\(650\) | 7.41742 | 0.290935 | ||||||||
\(651\) | 30.0000 | 1.17579 | ||||||||
\(652\) | −10.4174 | −0.407978 | ||||||||
\(653\) | −14.3739 | −0.562493 | −0.281246 | − | 0.959636i | \(-0.590748\pi\) | ||||
−0.281246 | + | 0.959636i | \(0.590748\pi\) | |||||||
\(654\) | 16.7477 | 0.654888 | ||||||||
\(655\) | −40.7477 | −1.59215 | ||||||||
\(656\) | −5.20871 | −0.203366 | ||||||||
\(657\) | −44.9129 | −1.75222 | ||||||||
\(658\) | −3.16515 | −0.123390 | ||||||||
\(659\) | −33.9564 | −1.32276 | −0.661378 | − | 0.750053i | \(-0.730028\pi\) | ||||
−0.661378 | + | 0.750053i | \(0.730028\pi\) | |||||||
\(660\) | 40.1216 | 1.56173 | ||||||||
\(661\) | −36.7913 | −1.43102 | −0.715508 | − | 0.698605i | \(-0.753805\pi\) | ||||
−0.715508 | + | 0.698605i | \(0.753805\pi\) | |||||||
\(662\) | −16.4174 | −0.638081 | ||||||||
\(663\) | −3.49545 | −0.135752 | ||||||||
\(664\) | −3.16515 | −0.122832 | ||||||||
\(665\) | −57.4955 | −2.22958 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.626136 | 0.0242441 | ||||||||
\(668\) | 0.956439 | 0.0370057 | ||||||||
\(669\) | 39.0780 | 1.51084 | ||||||||
\(670\) | −27.9564 | −1.08005 | ||||||||
\(671\) | 31.1216 | 1.20144 | ||||||||
\(672\) | −5.58258 | −0.215353 | ||||||||
\(673\) | 5.12159 | 0.197423 | 0.0987114 | − | 0.995116i | \(-0.468528\pi\) | ||||
0.0987114 | + | 0.995116i | \(0.468528\pi\) | |||||||
\(674\) | 8.12159 | 0.312832 | ||||||||
\(675\) | 46.8693 | 1.80400 | ||||||||
\(676\) | −12.3739 | −0.475918 | ||||||||
\(677\) | 9.16515 | 0.352245 | 0.176123 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176123 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(678\) | 54.6606 | 2.09923 | ||||||||
\(679\) | 8.83485 | 0.339050 | ||||||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | 55.5826 | 2.12993 | ||||||||
\(682\) | 20.3739 | 0.780156 | ||||||||
\(683\) | −22.4174 | −0.857779 | −0.428889 | − | 0.903357i | \(-0.641095\pi\) | ||||
−0.428889 | + | 0.903357i | \(0.641095\pi\) | |||||||
\(684\) | −36.3303 | −1.38912 | ||||||||
\(685\) | 65.8693 | 2.51674 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | −57.9129 | −2.20951 | ||||||||
\(688\) | −6.00000 | −0.228748 | ||||||||
\(689\) | 6.00000 | 0.228582 | ||||||||
\(690\) | −8.37386 | −0.318788 | ||||||||
\(691\) | 29.4955 | 1.12206 | 0.561030 | − | 0.827795i | \(-0.310405\pi\) | ||||
0.561030 | + | 0.827795i | \(0.310405\pi\) | |||||||
\(692\) | 3.16515 | 0.120321 | ||||||||
\(693\) | 36.3303 | 1.38007 | ||||||||
\(694\) | 1.58258 | 0.0600738 | ||||||||
\(695\) | 1.41742 | 0.0537660 | ||||||||
\(696\) | 2.20871 | 0.0837210 | ||||||||
\(697\) | 8.24318 | 0.312233 | ||||||||
\(698\) | 10.0000 | 0.378506 | ||||||||
\(699\) | −70.1216 | −2.65224 | ||||||||
\(700\) | −18.7477 | −0.708597 | ||||||||
\(701\) | −18.9564 | −0.715975 | −0.357987 | − | 0.933726i | \(-0.616537\pi\) | ||||
−0.357987 | + | 0.933726i | \(0.616537\pi\) | |||||||
\(702\) | 3.95644 | 0.149326 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.79129 | −0.142890 | ||||||||
\(705\) | −16.7477 | −0.630756 | ||||||||
\(706\) | −7.58258 | −0.285374 | ||||||||
\(707\) | −3.16515 | −0.119038 | ||||||||
\(708\) | −21.1652 | −0.795435 | ||||||||
\(709\) | 27.7913 | 1.04372 | 0.521862 | − | 0.853030i | \(-0.325238\pi\) | ||||
0.521862 | + | 0.853030i | \(0.325238\pi\) | |||||||
\(710\) | −34.7477 | −1.30406 | ||||||||
\(711\) | 61.2867 | 2.29843 | ||||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | −4.25227 | −0.159249 | ||||||||
\(714\) | 8.83485 | 0.330636 | ||||||||
\(715\) | 11.3739 | 0.425358 | ||||||||
\(716\) | 7.58258 | 0.283374 | ||||||||
\(717\) | 69.6606 | 2.60152 | ||||||||
\(718\) | −27.1652 | −1.01379 | ||||||||
\(719\) | −2.83485 | −0.105722 | −0.0528610 | − | 0.998602i | \(-0.516834\pi\) | ||||
−0.0528610 | + | 0.998602i | \(0.516834\pi\) | |||||||
\(720\) | −18.1652 | −0.676975 | ||||||||
\(721\) | 4.41742 | 0.164513 | ||||||||
\(722\) | 38.4955 | 1.43265 | ||||||||
\(723\) | 37.9129 | 1.41000 | ||||||||
\(724\) | −18.7477 | −0.696754 | ||||||||
\(725\) | 7.41742 | 0.275476 | ||||||||
\(726\) | 9.41742 | 0.349513 | ||||||||
\(727\) | −28.1216 | −1.04297 | −0.521486 | − | 0.853260i | \(-0.674622\pi\) | ||||
−0.521486 | + | 0.853260i | \(0.674622\pi\) | |||||||
\(728\) | −1.58258 | −0.0586542 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 35.5390 | 1.31536 | ||||||||
\(731\) | 9.49545 | 0.351202 | ||||||||
\(732\) | −22.9129 | −0.846884 | ||||||||
\(733\) | 7.49545 | 0.276851 | 0.138425 | − | 0.990373i | \(-0.455796\pi\) | ||||
0.138425 | + | 0.990373i | \(0.455796\pi\) | |||||||
\(734\) | −32.7477 | −1.20874 | ||||||||
\(735\) | 31.7477 | 1.17103 | ||||||||
\(736\) | 0.791288 | 0.0291673 | ||||||||
\(737\) | −27.9564 | −1.02979 | ||||||||
\(738\) | −24.9564 | −0.918659 | ||||||||
\(739\) | −6.12159 | −0.225186 | −0.112593 | − | 0.993641i | \(-0.535916\pi\) | ||||
−0.112593 | + | 0.993641i | \(0.535916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.7477 | −0.615243 | ||||||||
\(742\) | −15.1652 | −0.556730 | ||||||||
\(743\) | 3.16515 | 0.116118 | 0.0580591 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580591 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(744\) | −15.0000 | −0.549927 | ||||||||
\(745\) | 51.4955 | 1.88665 | ||||||||
\(746\) | −14.7477 | −0.539953 | ||||||||
\(747\) | −15.1652 | −0.554864 | ||||||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | −16.7477 | −0.611949 | ||||||||
\(750\) | −46.2867 | −1.69015 | ||||||||
\(751\) | −13.4955 | −0.492456 | −0.246228 | − | 0.969212i | \(-0.579191\pi\) | ||||
−0.246228 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(752\) | 1.58258 | 0.0577106 | ||||||||
\(753\) | −37.9129 | −1.38162 | ||||||||
\(754\) | 0.626136 | 0.0228025 | ||||||||
\(755\) | 48.3303 | 1.75892 | ||||||||
\(756\) | −10.0000 | −0.363696 | ||||||||
\(757\) | −39.7913 | −1.44624 | −0.723119 | − | 0.690723i | \(-0.757292\pi\) | ||||
−0.723119 | + | 0.690723i | \(0.757292\pi\) | |||||||
\(758\) | −21.1216 | −0.767171 | ||||||||
\(759\) | −8.37386 | −0.303952 | ||||||||
\(760\) | 28.7477 | 1.04279 | ||||||||
\(761\) | −18.7913 | −0.681184 | −0.340592 | − | 0.940211i | \(-0.610627\pi\) | ||||
−0.340592 | + | 0.940211i | \(0.610627\pi\) | |||||||
\(762\) | 22.3303 | 0.808942 | ||||||||
\(763\) | −12.0000 | −0.434429 | ||||||||
\(764\) | −5.37386 | −0.194420 | ||||||||
\(765\) | 28.7477 | 1.03938 | ||||||||
\(766\) | 18.3303 | 0.662301 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 2.79129 | 0.100722 | ||||||||
\(769\) | 48.3303 | 1.74284 | 0.871418 | − | 0.490542i | \(-0.163201\pi\) | ||||
0.871418 | + | 0.490542i | \(0.163201\pi\) | |||||||
\(770\) | −28.7477 | −1.03600 | ||||||||
\(771\) | 63.4955 | 2.28673 | ||||||||
\(772\) | 18.3303 | 0.659722 | ||||||||
\(773\) | −13.9129 | −0.500411 | −0.250206 | − | 0.968193i | \(-0.580498\pi\) | ||||
−0.250206 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(774\) | −28.7477 | −1.03332 | ||||||||
\(775\) | −50.3739 | −1.80948 | ||||||||
\(776\) | −4.41742 | −0.158576 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.8693 | −1.28598 | ||||||||
\(779\) | 39.4955 | 1.41507 | ||||||||
\(780\) | −8.37386 | −0.299832 | ||||||||
\(781\) | −34.7477 | −1.24337 | ||||||||
\(782\) | −1.25227 | −0.0447812 | ||||||||
\(783\) | 3.95644 | 0.141392 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 7.58258 | 0.270634 | ||||||||
\(786\) | 30.0000 | 1.07006 | ||||||||
\(787\) | 8.00000 | 0.285169 | 0.142585 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142585 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(788\) | 25.9129 | 0.923108 | ||||||||
\(789\) | 24.6606 | 0.877941 | ||||||||
\(790\) | −48.4955 | −1.72539 | ||||||||
\(791\) | −39.1652 | −1.39255 | ||||||||
\(792\) | −18.1652 | −0.645471 | ||||||||
\(793\) | −6.49545 | −0.230660 | ||||||||
\(794\) | 12.7477 | 0.452400 | ||||||||
\(795\) | −80.2432 | −2.84593 | ||||||||
\(796\) | −3.16515 | −0.112186 | ||||||||
\(797\) | −21.6261 | −0.766037 | −0.383019 | − | 0.923741i | \(-0.625115\pi\) | ||||
−0.383019 | + | 0.923741i | \(0.625115\pi\) | |||||||
\(798\) | 42.3303 | 1.49848 | ||||||||
\(799\) | −2.50455 | −0.0886045 | ||||||||
\(800\) | 9.37386 | 0.331416 | ||||||||
\(801\) | −28.7477 | −1.01575 | ||||||||
\(802\) | −10.7477 | −0.379515 | ||||||||
\(803\) | 35.5390 | 1.25414 | ||||||||
\(804\) | 20.5826 | 0.725891 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | −4.25227 | −0.149780 | ||||||||
\(807\) | −30.0000 | −1.05605 | ||||||||
\(808\) | 1.58258 | 0.0556748 | ||||||||
\(809\) | −11.0780 | −0.389483 | −0.194741 | − | 0.980855i | \(-0.562387\pi\) | ||||
−0.194741 | + | 0.980855i | \(0.562387\pi\) | |||||||
\(810\) | 1.58258 | 0.0556060 | ||||||||
\(811\) | 48.8693 | 1.71603 | 0.858017 | − | 0.513621i | \(-0.171696\pi\) | ||||
0.858017 | + | 0.513621i | \(0.171696\pi\) | |||||||
\(812\) | −1.58258 | −0.0555375 | ||||||||
\(813\) | 61.4083 | 2.15368 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.4955 | 1.38347 | ||||||||
\(816\) | −4.41742 | −0.154641 | ||||||||
\(817\) | 45.4955 | 1.59168 | ||||||||
\(818\) | −8.83485 | −0.308903 | ||||||||
\(819\) | −7.58258 | −0.264957 | ||||||||
\(820\) | 19.7477 | 0.689621 | ||||||||
\(821\) | −15.1652 | −0.529267 | −0.264634 | − | 0.964349i | \(-0.585251\pi\) | ||||
−0.264634 | + | 0.964349i | \(0.585251\pi\) | |||||||
\(822\) | −48.4955 | −1.69147 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −2.20871 | −0.0769441 | ||||||||
\(825\) | −99.1996 | −3.45369 | ||||||||
\(826\) | 15.1652 | 0.527663 | ||||||||
\(827\) | 14.8348 | 0.515858 | 0.257929 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257929 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(828\) | 3.79129 | 0.131756 | ||||||||
\(829\) | −39.9564 | −1.38774 | −0.693872 | − | 0.720098i | \(-0.744097\pi\) | ||||
−0.693872 | + | 0.720098i | \(0.744097\pi\) | |||||||
\(830\) | 12.0000 | 0.416526 | ||||||||
\(831\) | 65.2432 | 2.26326 | ||||||||
\(832\) | 0.791288 | 0.0274330 | ||||||||
\(833\) | 4.74773 | 0.164499 | ||||||||
\(834\) | −1.04356 | −0.0361356 | ||||||||
\(835\) | −3.62614 | −0.125488 | ||||||||
\(836\) | 28.7477 | 0.994261 | ||||||||
\(837\) | −26.8693 | −0.928739 | ||||||||
\(838\) | 6.79129 | 0.234601 | ||||||||
\(839\) | 51.4955 | 1.77782 | 0.888910 | − | 0.458081i | \(-0.151463\pi\) | ||||
0.888910 | + | 0.458081i | \(0.151463\pi\) | |||||||
\(840\) | 21.1652 | 0.730267 | ||||||||
\(841\) | −28.3739 | −0.978409 | ||||||||
\(842\) | −3.95644 | −0.136348 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.37386 | −0.116133 | ||||||||
\(845\) | 46.9129 | 1.61385 | ||||||||
\(846\) | 7.58258 | 0.260694 | ||||||||
\(847\) | −6.74773 | −0.231855 | ||||||||
\(848\) | 7.58258 | 0.260387 | ||||||||
\(849\) | −66.9909 | −2.29912 | ||||||||
\(850\) | −14.8348 | −0.508831 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 25.5826 | 0.876445 | ||||||||
\(853\) | 5.70417 | 0.195307 | 0.0976535 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976535 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(854\) | 16.4174 | 0.561793 | ||||||||
\(855\) | 137.739 | 4.71056 | ||||||||
\(856\) | 8.37386 | 0.286213 | ||||||||
\(857\) | 14.8348 | 0.506749 | 0.253374 | − | 0.967368i | \(-0.418460\pi\) | ||||
0.253374 | + | 0.967368i | \(0.418460\pi\) | |||||||
\(858\) | −8.37386 | −0.285879 | ||||||||
\(859\) | 54.6606 | 1.86500 | 0.932498 | − | 0.361175i | \(-0.117624\pi\) | ||||
0.932498 | + | 0.361175i | \(0.117624\pi\) | |||||||
\(860\) | 22.7477 | 0.775691 | ||||||||
\(861\) | 29.0780 | 0.990977 | ||||||||
\(862\) | 27.1652 | 0.925249 | ||||||||
\(863\) | −46.7477 | −1.59131 | −0.795656 | − | 0.605749i | \(-0.792873\pi\) | ||||
−0.795656 | + | 0.605749i | \(0.792873\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 24.3739 | 0.828258 | ||||||||
\(867\) | −40.4610 | −1.37413 | ||||||||
\(868\) | 10.7477 | 0.364802 | ||||||||
\(869\) | −48.4955 | −1.64510 | ||||||||
\(870\) | −8.37386 | −0.283901 | ||||||||
\(871\) | 5.83485 | 0.197706 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | −21.1652 | −0.716332 | ||||||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | 33.1652 | 1.12119 | ||||||||
\(876\) | −26.1652 | −0.884039 | ||||||||
\(877\) | 38.7477 | 1.30842 | 0.654209 | − | 0.756314i | \(-0.273002\pi\) | ||||
0.654209 | + | 0.756314i | \(0.273002\pi\) | |||||||
\(878\) | −26.3739 | −0.890075 | ||||||||
\(879\) | −16.7477 | −0.564887 | ||||||||
\(880\) | 14.3739 | 0.484543 | ||||||||
\(881\) | −28.1216 | −0.947440 | −0.473720 | − | 0.880675i | \(-0.657089\pi\) | ||||
−0.473720 | + | 0.880675i | \(0.657089\pi\) | |||||||
\(882\) | −14.3739 | −0.483993 | ||||||||
\(883\) | 13.9129 | 0.468206 | 0.234103 | − | 0.972212i | \(-0.424785\pi\) | ||||
0.234103 | + | 0.972212i | \(0.424785\pi\) | |||||||
\(884\) | −1.25227 | −0.0421185 | ||||||||
\(885\) | 80.2432 | 2.69735 | ||||||||
\(886\) | −5.04356 | −0.169442 | ||||||||
\(887\) | −33.8258 | −1.13576 | −0.567879 | − | 0.823112i | \(-0.692236\pi\) | ||||
−0.567879 | + | 0.823112i | \(0.692236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 22.7477 | 0.762506 | ||||||||
\(891\) | 1.58258 | 0.0530183 | ||||||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | −12.0000 | −0.401565 | ||||||||
\(894\) | −37.9129 | −1.26800 | ||||||||
\(895\) | −28.7477 | −0.960931 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 1.74773 | 0.0583549 | ||||||||
\(898\) | −21.1652 | −0.706290 | ||||||||
\(899\) | −4.25227 | −0.141821 | ||||||||
\(900\) | 44.9129 | 1.49710 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 19.7477 | 0.657527 | ||||||||
\(903\) | 33.4955 | 1.11466 | ||||||||
\(904\) | 19.5826 | 0.651307 | ||||||||
\(905\) | 71.0780 | 2.36271 | ||||||||
\(906\) | −35.5826 | −1.18215 | ||||||||
\(907\) | 6.33030 | 0.210194 | 0.105097 | − | 0.994462i | \(-0.466485\pi\) | ||||
0.105097 | + | 0.994462i | \(0.466485\pi\) | |||||||
\(908\) | 19.9129 | 0.660832 | ||||||||
\(909\) | 7.58258 | 0.251498 | ||||||||
\(910\) | 6.00000 | 0.198898 | ||||||||
\(911\) | 54.3303 | 1.80004 | 0.900022 | − | 0.435845i | \(-0.143551\pi\) | ||||
0.900022 | + | 0.435845i | \(0.143551\pi\) | |||||||
\(912\) | −21.1652 | −0.700848 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 33.4955 | 1.10793 | ||||||||
\(915\) | 86.8693 | 2.87181 | ||||||||
\(916\) | −20.7477 | −0.685524 | ||||||||
\(917\) | −21.4955 | −0.709842 | ||||||||
\(918\) | −7.91288 | −0.261164 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | −3.00000 | −0.0989071 | ||||||||
\(921\) | 34.5390 | 1.13810 | ||||||||
\(922\) | −24.3303 | −0.801276 | ||||||||
\(923\) | 7.25227 | 0.238711 | ||||||||
\(924\) | 21.1652 | 0.696282 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.7042 | −0.680381 | ||||||||
\(927\) | −10.5826 | −0.347577 | ||||||||
\(928\) | 0.791288 | 0.0259753 | ||||||||
\(929\) | 5.37386 | 0.176311 | 0.0881554 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881554 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(930\) | 56.8693 | 1.86482 | ||||||||
\(931\) | 22.7477 | 0.745527 | ||||||||
\(932\) | −25.1216 | −0.822885 | ||||||||
\(933\) | 26.8693 | 0.879662 | ||||||||
\(934\) | 25.5826 | 0.837087 | ||||||||
\(935\) | −22.7477 | −0.743930 | ||||||||
\(936\) | 3.79129 | 0.123922 | ||||||||
\(937\) | −33.8693 | −1.10646 | −0.553231 | − | 0.833028i | \(-0.686605\pi\) | ||||
−0.553231 | + | 0.833028i | \(0.686605\pi\) | |||||||
\(938\) | −14.7477 | −0.481530 | ||||||||
\(939\) | −92.5735 | −3.02102 | ||||||||
\(940\) | −6.00000 | −0.195698 | ||||||||
\(941\) | 33.4955 | 1.09192 | 0.545960 | − | 0.837811i | \(-0.316165\pi\) | ||||
0.545960 | + | 0.837811i | \(0.316165\pi\) | |||||||
\(942\) | −5.58258 | −0.181890 | ||||||||
\(943\) | −4.12159 | −0.134217 | ||||||||
\(944\) | −7.58258 | −0.246792 | ||||||||
\(945\) | 37.9129 | 1.23331 | ||||||||
\(946\) | 22.7477 | 0.739592 | ||||||||
\(947\) | −28.7477 | −0.934176 | −0.467088 | − | 0.884211i | \(-0.654697\pi\) | ||||
−0.467088 | + | 0.884211i | \(0.654697\pi\) | |||||||
\(948\) | 35.7042 | 1.15962 | ||||||||
\(949\) | −7.41742 | −0.240780 | ||||||||
\(950\) | −71.0780 | −2.30608 | ||||||||
\(951\) | 3.49545 | 0.113348 | ||||||||
\(952\) | 3.16515 | 0.102583 | ||||||||
\(953\) | 46.4519 | 1.50472 | 0.752362 | − | 0.658750i | \(-0.228914\pi\) | ||||
0.752362 | + | 0.658750i | \(0.228914\pi\) | |||||||
\(954\) | 36.3303 | 1.17624 | ||||||||
\(955\) | 20.3739 | 0.659283 | ||||||||
\(956\) | 24.9564 | 0.807149 | ||||||||
\(957\) | −8.37386 | −0.270689 | ||||||||
\(958\) | −0.791288 | −0.0255653 | ||||||||
\(959\) | 34.7477 | 1.12206 | ||||||||
\(960\) | −10.5826 | −0.341551 | ||||||||
\(961\) | −2.12159 | −0.0684384 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.1216 | 1.29290 | ||||||||
\(964\) | 13.5826 | 0.437465 | ||||||||
\(965\) | −69.4955 | −2.23714 | ||||||||
\(966\) | −4.41742 | −0.142128 | ||||||||
\(967\) | 0.956439 | 0.0307570 | 0.0153785 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153785 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(968\) | 3.37386 | 0.108440 | ||||||||
\(969\) | 33.4955 | 1.07603 | ||||||||
\(970\) | 16.7477 | 0.537737 | ||||||||
\(971\) | 36.6261 | 1.17539 | 0.587694 | − | 0.809083i | \(-0.300036\pi\) | ||||
0.587694 | + | 0.809083i | \(0.300036\pi\) | |||||||
\(972\) | −16.1652 | −0.518497 | ||||||||
\(973\) | 0.747727 | 0.0239710 | ||||||||
\(974\) | −36.6606 | −1.17468 | ||||||||
\(975\) | 20.7042 | 0.663064 | ||||||||
\(976\) | −8.20871 | −0.262754 | ||||||||
\(977\) | 23.0780 | 0.738332 | 0.369166 | − | 0.929364i | \(-0.379643\pi\) | ||||
0.369166 | + | 0.929364i | \(0.379643\pi\) | |||||||
\(978\) | −29.0780 | −0.929813 | ||||||||
\(979\) | 22.7477 | 0.727021 | ||||||||
\(980\) | 11.3739 | 0.363325 | ||||||||
\(981\) | 28.7477 | 0.917844 | ||||||||
\(982\) | −8.37386 | −0.267221 | ||||||||
\(983\) | −18.3303 | −0.584646 | −0.292323 | − | 0.956320i | \(-0.594428\pi\) | ||||
−0.292323 | + | 0.956320i | \(0.594428\pi\) | |||||||
\(984\) | −14.5390 | −0.463487 | ||||||||
\(985\) | −98.2432 | −3.13029 | ||||||||
\(986\) | −1.25227 | −0.0398805 | ||||||||
\(987\) | −8.83485 | −0.281216 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | −4.74773 | −0.150969 | ||||||||
\(990\) | 68.8693 | 2.18881 | ||||||||
\(991\) | 3.95644 | 0.125680 | 0.0628402 | − | 0.998024i | \(-0.479984\pi\) | ||||
0.0628402 | + | 0.998024i | \(0.479984\pi\) | |||||||
\(992\) | −5.37386 | −0.170620 | ||||||||
\(993\) | −45.8258 | −1.45424 | ||||||||
\(994\) | −18.3303 | −0.581402 | ||||||||
\(995\) | 12.0000 | 0.380426 | ||||||||
\(996\) | −8.83485 | −0.279943 | ||||||||
\(997\) | −18.0000 | −0.570066 | −0.285033 | − | 0.958518i | \(-0.592005\pi\) | ||||
−0.285033 | + | 0.958518i | \(0.592005\pi\) | |||||||
\(998\) | −16.7477 | −0.530140 | ||||||||
\(999\) | 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 | 2738.2.a.k.1.2 | 2 | ||
37.6 | odd | 4 | 74.2.b.a.73.1 | ✓ | 4 | ||
37.31 | odd | 4 | 74.2.b.a.73.3 | yes | 4 | ||
37.36 | even | 2 | 2738.2.a.h.1.2 | 2 | |||
111.68 | even | 4 | 666.2.c.b.73.1 | 4 | |||
111.80 | even | 4 | 666.2.c.b.73.4 | 4 | |||
148.31 | even | 4 | 592.2.g.c.369.4 | 4 | |||
148.43 | even | 4 | 592.2.g.c.369.3 | 4 | |||
185.43 | even | 4 | 1850.2.c.g.1849.1 | 4 | |||
185.68 | even | 4 | 1850.2.c.h.1849.1 | 4 | |||
185.117 | even | 4 | 1850.2.c.h.1849.4 | 4 | |||
185.142 | even | 4 | 1850.2.c.g.1849.4 | 4 | |||
185.154 | odd | 4 | 1850.2.d.e.1701.4 | 4 | |||
185.179 | odd | 4 | 1850.2.d.e.1701.2 | 4 | |||
296.43 | even | 4 | 2368.2.g.h.961.2 | 4 | |||
296.117 | odd | 4 | 2368.2.g.j.961.4 | 4 | |||
296.179 | even | 4 | 2368.2.g.h.961.1 | 4 | |||
296.253 | odd | 4 | 2368.2.g.j.961.3 | 4 | |||
444.179 | odd | 4 | 5328.2.h.m.2737.1 | 4 | |||
444.191 | odd | 4 | 5328.2.h.m.2737.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.b.a.73.1 | ✓ | 4 | 37.6 | odd | 4 | ||
74.2.b.a.73.3 | yes | 4 | 37.31 | odd | 4 | ||
592.2.g.c.369.3 | 4 | 148.43 | even | 4 | |||
592.2.g.c.369.4 | 4 | 148.31 | even | 4 | |||
666.2.c.b.73.1 | 4 | 111.68 | even | 4 | |||
666.2.c.b.73.4 | 4 | 111.80 | even | 4 | |||
1850.2.c.g.1849.1 | 4 | 185.43 | even | 4 | |||
1850.2.c.g.1849.4 | 4 | 185.142 | even | 4 | |||
1850.2.c.h.1849.1 | 4 | 185.68 | even | 4 | |||
1850.2.c.h.1849.4 | 4 | 185.117 | even | 4 | |||
1850.2.d.e.1701.2 | 4 | 185.179 | odd | 4 | |||
1850.2.d.e.1701.4 | 4 | 185.154 | odd | 4 | |||
2368.2.g.h.961.1 | 4 | 296.179 | even | 4 | |||
2368.2.g.h.961.2 | 4 | 296.43 | even | 4 | |||
2368.2.g.j.961.3 | 4 | 296.253 | odd | 4 | |||
2368.2.g.j.961.4 | 4 | 296.117 | odd | 4 | |||
2738.2.a.h.1.2 | 2 | 37.36 | even | 2 | |||
2738.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5328.2.h.m.2737.1 | 4 | 444.179 | odd | 4 | |||
5328.2.h.m.2737.4 | 4 | 444.191 | odd | 4 |