Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(73,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Root | \(-2.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.73 |
Dual form | 74.2.b.a.73.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −2.79129 | −1.61155 | −0.805775 | − | 0.592221i | \(-0.798251\pi\) | ||||
−0.805775 | + | 0.592221i | \(0.798251\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.79129i | 1.69552i | 0.530384 | + | 0.847758i | \(0.322048\pi\) | ||||
−0.530384 | + | 0.847758i | \(0.677952\pi\) | |||||||
\(6\) | − | 2.79129i | − | 1.13954i | ||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | −3.79129 | −1.19891 | ||||||||
\(11\) | 3.79129 | 1.14312 | 0.571558 | − | 0.820562i | \(-0.306339\pi\) | ||||
0.571558 | + | 0.820562i | \(0.306339\pi\) | |||||||
\(12\) | 2.79129 | 0.805775 | ||||||||
\(13\) | − | 0.791288i | − | 0.219464i | −0.993961 | − | 0.109732i | \(-0.965001\pi\) | ||
0.993961 | − | 0.109732i | \(-0.0349992\pi\) | |||||||
\(14\) | − | 2.00000i | − | 0.534522i | ||||||
\(15\) | − | 10.5826i | − | 2.73241i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.58258i | 0.383831i | 0.981411 | + | 0.191915i | \(0.0614700\pi\) | ||||
−0.981411 | + | 0.191915i | \(0.938530\pi\) | |||||||
\(18\) | 4.79129i | 1.12932i | ||||||||
\(19\) | 7.58258i | 1.73956i | 0.493438 | + | 0.869781i | \(0.335740\pi\) | ||||
−0.493438 | + | 0.869781i | \(0.664260\pi\) | |||||||
\(20\) | − | 3.79129i | − | 0.847758i | ||||||
\(21\) | 5.58258 | 1.21822 | ||||||||
\(22\) | 3.79129i | 0.808305i | ||||||||
\(23\) | − | 0.791288i | − | 0.164995i | −0.996591 | − | 0.0824975i | \(-0.973710\pi\) | ||
0.996591 | − | 0.0824975i | \(-0.0262896\pi\) | |||||||
\(24\) | 2.79129i | 0.569769i | ||||||||
\(25\) | −9.37386 | −1.87477 | ||||||||
\(26\) | 0.791288 | 0.155184 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | 0.791288i | 0.146938i | 0.997297 | + | 0.0734692i | \(0.0234071\pi\) | ||||
−0.997297 | + | 0.0734692i | \(0.976593\pi\) | |||||||
\(30\) | 10.5826 | 1.93211 | ||||||||
\(31\) | − | 5.37386i | − | 0.965174i | −0.875848 | − | 0.482587i | \(-0.839697\pi\) | ||
0.875848 | − | 0.482587i | \(-0.160303\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −10.5826 | −1.84219 | ||||||||
\(34\) | −1.58258 | −0.271409 | ||||||||
\(35\) | − | 7.58258i | − | 1.28169i | ||||||
\(36\) | −4.79129 | −0.798548 | ||||||||
\(37\) | 4.00000 | − | 4.58258i | 0.657596 | − | 0.753371i | ||||
\(38\) | −7.58258 | −1.23006 | ||||||||
\(39\) | 2.20871i | 0.353677i | ||||||||
\(40\) | 3.79129 | 0.599455 | ||||||||
\(41\) | 5.20871 | 0.813464 | 0.406732 | − | 0.913547i | \(-0.366668\pi\) | ||||
0.406732 | + | 0.913547i | \(0.366668\pi\) | |||||||
\(42\) | 5.58258i | 0.861410i | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | −3.79129 | −0.571558 | ||||||||
\(45\) | 18.1652i | 2.70790i | ||||||||
\(46\) | 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 | ||||||||
\(50\) | − | 9.37386i | − | 1.32566i | ||||||
\(51\) | − | 4.41742i | − | 0.618563i | ||||||
\(52\) | 0.791288i | 0.109732i | ||||||||
\(53\) | 7.58258 | 1.04155 | 0.520773 | − | 0.853695i | \(-0.325644\pi\) | ||||
0.520773 | + | 0.853695i | \(0.325644\pi\) | |||||||
\(54\) | − | 5.00000i | − | 0.680414i | ||||||
\(55\) | 14.3739i | 1.93817i | ||||||||
\(56\) | 2.00000i | 0.267261i | ||||||||
\(57\) | − | 21.1652i | − | 2.80339i | ||||||
\(58\) | −0.791288 | −0.103901 | ||||||||
\(59\) | 7.58258i | 0.987167i | 0.869698 | + | 0.493584i | \(0.164313\pi\) | ||||
−0.869698 | + | 0.493584i | \(0.835687\pi\) | |||||||
\(60\) | 10.5826i | 1.36620i | ||||||||
\(61\) | − | 8.20871i | − | 1.05102i | −0.850788 | − | 0.525509i | \(-0.823875\pi\) | ||
0.850788 | − | 0.525509i | \(-0.176125\pi\) | |||||||
\(62\) | 5.37386 | 0.682481 | ||||||||
\(63\) | −9.58258 | −1.20729 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | − | 10.5826i | − | 1.30263i | ||||||
\(67\) | −7.37386 | −0.900861 | −0.450430 | − | 0.892812i | \(-0.648729\pi\) | ||||
−0.450430 | + | 0.892812i | \(0.648729\pi\) | |||||||
\(68\) | − | 1.58258i | − | 0.191915i | ||||||
\(69\) | 2.20871i | 0.265898i | ||||||||
\(70\) | 7.58258 | 0.906291 | ||||||||
\(71\) | 9.16515 | 1.08770 | 0.543852 | − | 0.839181i | \(-0.316965\pi\) | ||||
0.543852 | + | 0.839181i | \(0.316965\pi\) | |||||||
\(72\) | − | 4.79129i | − | 0.564659i | ||||||
\(73\) | 9.37386 | 1.09713 | 0.548564 | − | 0.836109i | \(-0.315175\pi\) | ||||
0.548564 | + | 0.836109i | \(0.315175\pi\) | |||||||
\(74\) | 4.58258 | + | 4.00000i | 0.532714 | + | 0.464991i | ||||
\(75\) | 26.1652 | 3.02129 | ||||||||
\(76\) | − | 7.58258i | − | 0.869781i | ||||||
\(77\) | −7.58258 | −0.864115 | ||||||||
\(78\) | −2.20871 | −0.250087 | ||||||||
\(79\) | − | 12.7913i | − | 1.43913i | −0.694424 | − | 0.719566i | \(-0.744341\pi\) | ||
0.694424 | − | 0.719566i | \(-0.255659\pi\) | |||||||
\(80\) | 3.79129i | 0.423879i | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 5.20871i | 0.575206i | ||||||||
\(83\) | −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 | ||||||||
\(87\) | − | 2.20871i | − | 0.236799i | ||||||
\(88\) | − | 3.79129i | − | 0.404153i | ||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | −18.1652 | −1.91478 | ||||||||
\(91\) | 1.58258i | 0.165899i | ||||||||
\(92\) | 0.791288i | 0.0824975i | ||||||||
\(93\) | 15.0000i | 1.55543i | ||||||||
\(94\) | 1.58258i | 0.163230i | ||||||||
\(95\) | −28.7477 | −2.94945 | ||||||||
\(96\) | − | 2.79129i | − | 0.284885i | ||||||
\(97\) | 4.41742i | 0.448521i | 0.974529 | + | 0.224261i | \(0.0719967\pi\) | ||||
−0.974529 | + | 0.224261i | \(0.928003\pi\) | |||||||
\(98\) | − | 3.00000i | − | 0.303046i | ||||||
\(99\) | 18.1652 | 1.82567 | ||||||||
\(100\) | 9.37386 | 0.937386 | ||||||||
\(101\) | −1.58258 | −0.157472 | −0.0787361 | − | 0.996895i | \(-0.525088\pi\) | ||||
−0.0787361 | + | 0.996895i | \(0.525088\pi\) | |||||||
\(102\) | 4.41742 | 0.437390 | ||||||||
\(103\) | − | 2.20871i | − | 0.217631i | −0.994062 | − | 0.108815i | \(-0.965294\pi\) | ||
0.994062 | − | 0.108815i | \(-0.0347058\pi\) | |||||||
\(104\) | −0.791288 | −0.0775922 | ||||||||
\(105\) | 21.1652i | 2.06551i | ||||||||
\(106\) | 7.58258i | 0.736485i | ||||||||
\(107\) | 8.37386 | 0.809532 | 0.404766 | − | 0.914420i | \(-0.367353\pi\) | ||||
0.404766 | + | 0.914420i | \(0.367353\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | −14.3739 | −1.37049 | ||||||||
\(111\) | −11.1652 | + | 12.7913i | −1.05975 | + | 1.21410i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 19.5826i | 1.84217i | 0.389357 | + | 0.921087i | \(0.372697\pi\) | ||||
−0.389357 | + | 0.921087i | \(0.627303\pi\) | |||||||
\(114\) | 21.1652 | 1.98230 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | − | 0.791288i | − | 0.0734692i | ||||||
\(117\) | − | 3.79129i | − | 0.350505i | ||||||
\(118\) | −7.58258 | −0.698033 | ||||||||
\(119\) | − | 3.16515i | − | 0.290149i | ||||||
\(120\) | −10.5826 | −0.966053 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | 8.20871 | 0.743182 | ||||||||
\(123\) | −14.5390 | −1.31094 | ||||||||
\(124\) | 5.37386i | 0.482587i | ||||||||
\(125\) | − | 16.5826i | − | 1.48319i | ||||||
\(126\) | − | 9.58258i | − | 0.853684i | ||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | − | 16.7477i | − | 1.47456i | ||||||
\(130\) | 3.00000i | 0.263117i | ||||||||
\(131\) | 10.7477i | 0.939033i | 0.882924 | + | 0.469517i | \(0.155572\pi\) | ||||
−0.882924 | + | 0.469517i | \(0.844428\pi\) | |||||||
\(132\) | 10.5826 | 0.921095 | ||||||||
\(133\) | − | 15.1652i | − | 1.31499i | ||||||
\(134\) | − | 7.37386i | − | 0.637005i | ||||||
\(135\) | − | 18.9564i | − | 1.63151i | ||||||
\(136\) | 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 | \(-0.494953\pi\) | ||||
0.0158553 | + | 0.999874i | \(0.494953\pi\) | |||||||
\(140\) | 7.58258i | 0.640845i | ||||||||
\(141\) | −4.41742 | −0.372014 | ||||||||
\(142\) | 9.16515i | 0.769122i | ||||||||
\(143\) | − | 3.00000i | − | 0.250873i | ||||||
\(144\) | 4.79129 | 0.399274 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | 9.37386i | 0.775786i | ||||||||
\(147\) | 8.37386 | 0.690665 | ||||||||
\(148\) | −4.00000 | + | 4.58258i | −0.328798 | + | 0.376685i | ||||
\(149\) | −13.5826 | −1.11273 | −0.556364 | − | 0.830939i | \(-0.687804\pi\) | ||||
−0.556364 | + | 0.830939i | \(0.687804\pi\) | |||||||
\(150\) | 26.1652i | 2.13638i | ||||||||
\(151\) | 12.7477 | 1.03740 | 0.518698 | − | 0.854958i | \(-0.326417\pi\) | ||||
0.518698 | + | 0.854958i | \(0.326417\pi\) | |||||||
\(152\) | 7.58258 | 0.615028 | ||||||||
\(153\) | 7.58258i | 0.613015i | ||||||||
\(154\) | − | 7.58258i | − | 0.611021i | ||||||
\(155\) | 20.3739 | 1.63647 | ||||||||
\(156\) | − | 2.20871i | − | 0.176838i | ||||||
\(157\) | −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 | ||||||||
\(161\) | 1.58258i | 0.124724i | ||||||||
\(162\) | − | 0.417424i | − | 0.0327960i | ||||||
\(163\) | − | 10.4174i | − | 0.815956i | −0.912992 | − | 0.407978i | \(-0.866234\pi\) | ||
0.912992 | − | 0.407978i | \(-0.133766\pi\) | |||||||
\(164\) | −5.20871 | −0.406732 | ||||||||
\(165\) | − | 40.1216i | − | 3.12346i | ||||||
\(166\) | − | 3.16515i | − | 0.245663i | ||||||
\(167\) | − | 0.956439i | − | 0.0740115i | −0.999315 | − | 0.0370057i | \(-0.988218\pi\) | ||
0.999315 | − | 0.0370057i | \(-0.0117820\pi\) | |||||||
\(168\) | − | 5.58258i | − | 0.430705i | ||||||
\(169\) | 12.3739 | 0.951836 | ||||||||
\(170\) | − | 6.00000i | − | 0.460179i | ||||||
\(171\) | 36.3303i | 2.77825i | ||||||||
\(172\) | − | 6.00000i | − | 0.457496i | ||||||
\(173\) | −3.16515 | −0.240642 | −0.120321 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120321 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(174\) | 2.20871 | 0.167442 | ||||||||
\(175\) | 18.7477 | 1.41719 | ||||||||
\(176\) | 3.79129 | 0.285779 | ||||||||
\(177\) | − | 21.1652i | − | 1.59087i | ||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 7.58258i | 0.566748i | 0.959009 | + | 0.283374i | \(0.0914538\pi\) | ||||
−0.959009 | + | 0.283374i | \(0.908546\pi\) | |||||||
\(180\) | − | 18.1652i | − | 1.35395i | ||||||
\(181\) | −18.7477 | −1.39351 | −0.696754 | − | 0.717310i | \(-0.745373\pi\) | ||||
−0.696754 | + | 0.717310i | \(0.745373\pi\) | |||||||
\(182\) | −1.58258 | −0.117308 | ||||||||
\(183\) | 22.9129i | 1.69377i | ||||||||
\(184\) | −0.791288 | −0.0583345 | ||||||||
\(185\) | 17.3739 | + | 15.1652i | 1.27735 | + | 1.11496i | ||||
\(186\) | −15.0000 | −1.09985 | ||||||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | −1.58258 | −0.115421 | ||||||||
\(189\) | 10.0000 | 0.727393 | ||||||||
\(190\) | − | 28.7477i | − | 2.08558i | ||||||
\(191\) | 5.37386i | 0.388839i | 0.980918 | + | 0.194420i | \(0.0622823\pi\) | ||||
−0.980918 | + | 0.194420i | \(0.937718\pi\) | |||||||
\(192\) | 2.79129 | 0.201444 | ||||||||
\(193\) | − | 18.3303i | − | 1.31944i | −0.751510 | − | 0.659722i | \(-0.770674\pi\) | ||
0.751510 | − | 0.659722i | \(-0.229326\pi\) | |||||||
\(194\) | −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 | \(0.125640\pi\) | |||||||
\(198\) | 18.1652i | 1.29094i | ||||||||
\(199\) | − | 3.16515i | − | 0.224372i | −0.993687 | − | 0.112186i | \(-0.964215\pi\) | ||
0.993687 | − | 0.112186i | \(-0.0357852\pi\) | |||||||
\(200\) | 9.37386i | 0.662832i | ||||||||
\(201\) | 20.5826 | 1.45178 | ||||||||
\(202\) | − | 1.58258i | − | 0.111350i | ||||||
\(203\) | − | 1.58258i | − | 0.111075i | ||||||
\(204\) | 4.41742i | 0.309282i | ||||||||
\(205\) | 19.7477i | 1.37924i | ||||||||
\(206\) | 2.20871 | 0.153888 | ||||||||
\(207\) | − | 3.79129i | − | 0.263513i | ||||||
\(208\) | − | 0.791288i | − | 0.0548659i | ||||||
\(209\) | 28.7477i | 1.98852i | ||||||||
\(210\) | −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 | ||||||||
\(214\) | 8.37386i | 0.572426i | ||||||||
\(215\) | −22.7477 | −1.55138 | ||||||||
\(216\) | 5.00000i | 0.340207i | ||||||||
\(217\) | 10.7477i | 0.729603i | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | −26.1652 | −1.76808 | ||||||||
\(220\) | − | 14.3739i | − | 0.969086i | ||||||
\(221\) | 1.25227 | 0.0842370 | ||||||||
\(222\) | −12.7913 | − | 11.1652i | −0.858495 | − | 0.749356i | ||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | − | 2.00000i | − | 0.133631i | ||||||
\(225\) | −44.9129 | −2.99419 | ||||||||
\(226\) | −19.5826 | −1.30261 | ||||||||
\(227\) | − | 19.9129i | − | 1.32166i | −0.750534 | − | 0.660832i | \(-0.770204\pi\) | ||
0.750534 | − | 0.660832i | \(-0.229796\pi\) | |||||||
\(228\) | 21.1652i | 1.40170i | ||||||||
\(229\) | −20.7477 | −1.37105 | −0.685524 | − | 0.728050i | \(-0.740427\pi\) | ||||
−0.685524 | + | 0.728050i | \(0.740427\pi\) | |||||||
\(230\) | 3.00000i | 0.197814i | ||||||||
\(231\) | 21.1652 | 1.39256 | ||||||||
\(232\) | 0.791288 | 0.0519506 | ||||||||
\(233\) | 25.1216 | 1.64577 | 0.822885 | − | 0.568208i | \(-0.192363\pi\) | ||||
0.822885 | + | 0.568208i | \(0.192363\pi\) | |||||||
\(234\) | 3.79129 | 0.247844 | ||||||||
\(235\) | 6.00000i | 0.391397i | ||||||||
\(236\) | − | 7.58258i | − | 0.493584i | ||||||
\(237\) | 35.7042i | 2.31923i | ||||||||
\(238\) | 3.16515 | 0.205166 | ||||||||
\(239\) | − | 24.9564i | − | 1.61430i | −0.590348 | − | 0.807149i | \(-0.701009\pi\) | ||
0.590348 | − | 0.807149i | \(-0.298991\pi\) | |||||||
\(240\) | − | 10.5826i | − | 0.683102i | ||||||
\(241\) | − | 13.5826i | − | 0.874931i | −0.899235 | − | 0.437465i | \(-0.855876\pi\) | ||
0.899235 | − | 0.437465i | \(-0.144124\pi\) | |||||||
\(242\) | 3.37386i | 0.216880i | ||||||||
\(243\) | 16.1652 | 1.03699 | ||||||||
\(244\) | 8.20871i | 0.525509i | ||||||||
\(245\) | − | 11.3739i | − | 0.726649i | ||||||
\(246\) | − | 14.5390i | − | 0.926974i | ||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | −5.37386 | −0.341241 | ||||||||
\(249\) | 8.83485 | 0.559886 | ||||||||
\(250\) | 16.5826 | 1.04877 | ||||||||
\(251\) | − | 13.5826i | − | 0.857325i | −0.903465 | − | 0.428662i | \(-0.858985\pi\) | ||
0.903465 | − | 0.428662i | \(-0.141015\pi\) | |||||||
\(252\) | 9.58258 | 0.603646 | ||||||||
\(253\) | − | 3.00000i | − | 0.188608i | ||||||
\(254\) | 8.00000i | 0.501965i | ||||||||
\(255\) | 16.7477 | 1.04878 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 22.7477i | − | 1.41896i | −0.704723 | − | 0.709482i | \(-0.748929\pi\) | ||
0.704723 | − | 0.709482i | \(-0.251071\pi\) | |||||||
\(258\) | 16.7477 | 1.04267 | ||||||||
\(259\) | −8.00000 | + | 9.16515i | −0.497096 | + | 0.569495i | ||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 3.79129i | 0.234675i | ||||||||
\(262\) | −10.7477 | −0.663997 | ||||||||
\(263\) | −8.83485 | −0.544780 | −0.272390 | − | 0.962187i | \(-0.587814\pi\) | ||||
−0.272390 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(264\) | 10.5826i | 0.651313i | ||||||||
\(265\) | 28.7477i | 1.76596i | ||||||||
\(266\) | 15.1652 | 0.929835 | ||||||||
\(267\) | 16.7477i | 1.02494i | ||||||||
\(268\) | 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 | \(0.267064\pi\) | |||||||
\(272\) | 1.58258i | 0.0959577i | ||||||||
\(273\) | − | 4.41742i | − | 0.267355i | ||||||
\(274\) | − | 17.3739i | − | 1.04959i | ||||||
\(275\) | −35.5390 | −2.14308 | ||||||||
\(276\) | − | 2.20871i | − | 0.132949i | ||||||
\(277\) | 23.3739i | 1.40440i | 0.711980 | + | 0.702200i | \(0.247799\pi\) | ||||
−0.711980 | + | 0.702200i | \(0.752201\pi\) | |||||||
\(278\) | 0.373864i | 0.0224228i | ||||||||
\(279\) | − | 25.7477i | − | 1.54148i | ||||||
\(280\) | −7.58258 | −0.453146 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | − | 4.41742i | − | 0.263054i | ||||||
\(283\) | − | 24.0000i | − | 1.42665i | −0.700832 | − | 0.713326i | \(-0.747188\pi\) | ||
0.700832 | − | 0.713326i | \(-0.252812\pi\) | |||||||
\(284\) | −9.16515 | −0.543852 | ||||||||
\(285\) | 80.2432 | 4.75320 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | −10.4174 | −0.614921 | ||||||||
\(288\) | 4.79129i | 0.282329i | ||||||||
\(289\) | 14.4955 | 0.852674 | ||||||||
\(290\) | − | 3.00000i | − | 0.176166i | ||||||
\(291\) | − | 12.3303i | − | 0.722815i | ||||||
\(292\) | −9.37386 | −0.548564 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 8.37386i | 0.488374i | ||||||||
\(295\) | −28.7477 | −1.67376 | ||||||||
\(296\) | −4.58258 | − | 4.00000i | −0.266357 | − | 0.232495i | ||||
\(297\) | −18.9564 | −1.09996 | ||||||||
\(298\) | − | 13.5826i | − | 0.786817i | ||||||
\(299\) | −0.626136 | −0.0362104 | ||||||||
\(300\) | −26.1652 | −1.51065 | ||||||||
\(301\) | − | 12.0000i | − | 0.691669i | ||||||
\(302\) | 12.7477i | 0.733549i | ||||||||
\(303\) | 4.41742 | 0.253774 | ||||||||
\(304\) | 7.58258i | 0.434891i | ||||||||
\(305\) | 31.1216 | 1.78202 | ||||||||
\(306\) | −7.58258 | −0.433467 | ||||||||
\(307\) | −12.3739 | −0.706214 | −0.353107 | − | 0.935583i | \(-0.614875\pi\) | ||||
−0.353107 | + | 0.935583i | \(0.614875\pi\) | |||||||
\(308\) | 7.58258 | 0.432057 | ||||||||
\(309\) | 6.16515i | 0.350723i | ||||||||
\(310\) | 20.3739i | 1.15716i | ||||||||
\(311\) | 9.62614i | 0.545848i | 0.962036 | + | 0.272924i | \(0.0879908\pi\) | ||||
−0.962036 | + | 0.272924i | \(0.912009\pi\) | |||||||
\(312\) | 2.20871 | 0.125044 | ||||||||
\(313\) | 33.1652i | 1.87461i | 0.348517 | + | 0.937303i | \(0.386685\pi\) | ||||
−0.348517 | + | 0.937303i | \(0.613315\pi\) | |||||||
\(314\) | − | 2.00000i | − | 0.112867i | ||||||
\(315\) | − | 36.3303i | − | 2.04698i | ||||||
\(316\) | 12.7913i | 0.719566i | ||||||||
\(317\) | −1.25227 | −0.0703347 | −0.0351673 | − | 0.999381i | \(-0.511196\pi\) | ||||
−0.0351673 | + | 0.999381i | \(0.511196\pi\) | |||||||
\(318\) | − | 21.1652i | − | 1.18688i | ||||||
\(319\) | 3.00000i | 0.167968i | ||||||||
\(320\) | − | 3.79129i | − | 0.211939i | ||||||
\(321\) | −23.3739 | −1.30460 | ||||||||
\(322\) | −1.58258 | −0.0881935 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0.417424 | 0.0231902 | ||||||||
\(325\) | 7.41742i | 0.411445i | ||||||||
\(326\) | 10.4174 | 0.576968 | ||||||||
\(327\) | 16.7477i | 0.926151i | ||||||||
\(328\) | − | 5.20871i | − | 0.287603i | ||||||
\(329\) | −3.16515 | −0.174500 | ||||||||
\(330\) | 40.1216 | 2.20862 | ||||||||
\(331\) | 16.4174i | 0.902383i | 0.892427 | + | 0.451192i | \(0.149001\pi\) | ||||
−0.892427 | + | 0.451192i | \(0.850999\pi\) | |||||||
\(332\) | 3.16515 | 0.173710 | ||||||||
\(333\) | 19.1652 | − | 21.9564i | 1.05024 | − | 1.20321i | ||||
\(334\) | 0.956439 | 0.0523340 | ||||||||
\(335\) | − | 27.9564i | − | 1.52742i | ||||||
\(336\) | 5.58258 | 0.304554 | ||||||||
\(337\) | −8.12159 | −0.442411 | −0.221206 | − | 0.975227i | \(-0.570999\pi\) | ||||
−0.221206 | + | 0.975227i | \(0.570999\pi\) | |||||||
\(338\) | 12.3739i | 0.673049i | ||||||||
\(339\) | − | 54.6606i | − | 2.96876i | ||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | − | 20.3739i | − | 1.10331i | ||||||
\(342\) | −36.3303 | −1.96452 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | −8.37386 | −0.450834 | ||||||||
\(346\) | − | 3.16515i | − | 0.170160i | ||||||
\(347\) | 1.58258i | 0.0849571i | 0.999097 | + | 0.0424786i | \(0.0135254\pi\) | ||||
−0.999097 | + | 0.0424786i | \(0.986475\pi\) | |||||||
\(348\) | 2.20871i | 0.118399i | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 18.7477i | 1.00211i | ||||||||
\(351\) | 3.95644i | 0.211179i | ||||||||
\(352\) | 3.79129i | 0.202076i | ||||||||
\(353\) | − | 7.58258i | − | 0.403580i | −0.979429 | − | 0.201790i | \(-0.935324\pi\) | ||
0.979429 | − | 0.201790i | \(-0.0646758\pi\) | |||||||
\(354\) | 21.1652 | 1.12492 | ||||||||
\(355\) | 34.7477i | 1.84422i | ||||||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | 8.83485i | 0.467590i | ||||||||
\(358\) | −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 | ||||||||
\(362\) | − | 18.7477i | − | 0.985359i | ||||||
\(363\) | −9.41742 | −0.494287 | ||||||||
\(364\) | − | 1.58258i | − | 0.0829495i | ||||||
\(365\) | 35.5390i | 1.86020i | ||||||||
\(366\) | −22.9129 | −1.19768 | ||||||||
\(367\) | −32.7477 | −1.70942 | −0.854709 | − | 0.519108i | \(-0.826264\pi\) | ||||
−0.854709 | + | 0.519108i | \(0.826264\pi\) | |||||||
\(368\) | − | 0.791288i | − | 0.0412487i | ||||||
\(369\) | 24.9564 | 1.29918 | ||||||||
\(370\) | −15.1652 | + | 17.3739i | −0.788399 | + | 0.903224i | ||||
\(371\) | −15.1652 | −0.787335 | ||||||||
\(372\) | − | 15.0000i | − | 0.777714i | ||||||
\(373\) | 14.7477 | 0.763608 | 0.381804 | − | 0.924243i | \(-0.375303\pi\) | ||||
0.381804 | + | 0.924243i | \(0.375303\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | 46.2867i | 2.39024i | ||||||||
\(376\) | − | 1.58258i | − | 0.0816151i | ||||||
\(377\) | 0.626136 | 0.0322477 | ||||||||
\(378\) | 10.0000i | 0.514344i | ||||||||
\(379\) | −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 | ||||||||
\(383\) | − | 18.3303i | − | 0.936635i | −0.883560 | − | 0.468317i | \(-0.844860\pi\) | ||
0.883560 | − | 0.468317i | \(-0.155140\pi\) | |||||||
\(384\) | 2.79129i | 0.142442i | ||||||||
\(385\) | − | 28.7477i | − | 1.46512i | ||||||
\(386\) | 18.3303 | 0.932988 | ||||||||
\(387\) | 28.7477i | 1.46133i | ||||||||
\(388\) | − | 4.41742i | − | 0.224261i | ||||||
\(389\) | 35.8693i | 1.81865i | 0.416090 | + | 0.909323i | \(0.363400\pi\) | ||||
−0.416090 | + | 0.909323i | \(0.636600\pi\) | |||||||
\(390\) | − | 8.37386i | − | 0.424027i | ||||||
\(391\) | 1.25227 | 0.0633302 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | − | 30.0000i | − | 1.51330i | ||||||
\(394\) | 25.9129i | 1.30547i | ||||||||
\(395\) | 48.4955 | 2.44007 | ||||||||
\(396\) | −18.1652 | −0.912833 | ||||||||
\(397\) | −12.7477 | −0.639790 | −0.319895 | − | 0.947453i | \(-0.603648\pi\) | ||||
−0.319895 | + | 0.947453i | \(0.603648\pi\) | |||||||
\(398\) | 3.16515 | 0.158655 | ||||||||
\(399\) | 42.3303i | 2.11917i | ||||||||
\(400\) | −9.37386 | −0.468693 | ||||||||
\(401\) | − | 10.7477i | − | 0.536716i | −0.963319 | − | 0.268358i | \(-0.913519\pi\) | ||
0.963319 | − | 0.268358i | \(-0.0864810\pi\) | |||||||
\(402\) | 20.5826i | 1.02657i | ||||||||
\(403\) | −4.25227 | −0.211821 | ||||||||
\(404\) | 1.58258 | 0.0787361 | ||||||||
\(405\) | − | 1.58258i | − | 0.0786388i | ||||||
\(406\) | 1.58258 | 0.0785419 | ||||||||
\(407\) | 15.1652 | − | 17.3739i | 0.751709 | − | 0.861190i | ||||
\(408\) | −4.41742 | −0.218695 | ||||||||
\(409\) | − | 8.83485i | − | 0.436855i | −0.975853 | − | 0.218428i | \(-0.929907\pi\) | ||
0.975853 | − | 0.218428i | \(-0.0700927\pi\) | |||||||
\(410\) | −19.7477 | −0.975271 | ||||||||
\(411\) | 48.4955 | 2.39210 | ||||||||
\(412\) | 2.20871i | 0.108815i | ||||||||
\(413\) | − | 15.1652i | − | 0.746228i | ||||||
\(414\) | 3.79129 | 0.186332 | ||||||||
\(415\) | − | 12.0000i | − | 0.589057i | ||||||
\(416\) | 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 | \(0.446951\pi\) | |||||||
\(420\) | − | 21.1652i | − | 1.03275i | ||||||
\(421\) | − | 3.95644i | − | 0.192825i | −0.995341 | − | 0.0964125i | \(-0.969263\pi\) | ||
0.995341 | − | 0.0964125i | \(-0.0307368\pi\) | |||||||
\(422\) | − | 3.37386i | − | 0.164237i | ||||||
\(423\) | 7.58258 | 0.368677 | ||||||||
\(424\) | − | 7.58258i | − | 0.368242i | ||||||
\(425\) | − | 14.8348i | − | 0.719596i | ||||||
\(426\) | − | 25.5826i | − | 1.23948i | ||||||
\(427\) | 16.4174i | 0.794495i | ||||||||
\(428\) | −8.37386 | −0.404766 | ||||||||
\(429\) | 8.37386i | 0.404294i | ||||||||
\(430\) | − | 22.7477i | − | 1.09699i | ||||||
\(431\) | 27.1652i | 1.30850i | 0.756279 | + | 0.654250i | \(0.227015\pi\) | ||||
−0.756279 | + | 0.654250i | \(0.772985\pi\) | |||||||
\(432\) | −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 | ||||||||
\(436\) | 6.00000i | 0.287348i | ||||||||
\(437\) | 6.00000 | 0.287019 | ||||||||
\(438\) | − | 26.1652i | − | 1.25022i | ||||||
\(439\) | − | 26.3739i | − | 1.25876i | −0.777099 | − | 0.629378i | \(-0.783310\pi\) | ||
0.777099 | − | 0.629378i | \(-0.216690\pi\) | |||||||
\(440\) | 14.3739 | 0.685247 | ||||||||
\(441\) | −14.3739 | −0.684470 | ||||||||
\(442\) | 1.25227i | 0.0595645i | ||||||||
\(443\) | 5.04356 | 0.239627 | 0.119813 | − | 0.992796i | \(-0.461770\pi\) | ||||
0.119813 | + | 0.992796i | \(0.461770\pi\) | |||||||
\(444\) | 11.1652 | − | 12.7913i | 0.529875 | − | 0.607048i | ||||
\(445\) | 22.7477 | 1.07835 | ||||||||
\(446\) | 14.0000i | 0.662919i | ||||||||
\(447\) | 37.9129 | 1.79322 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | 21.1652i | 0.998845i | 0.866358 | + | 0.499423i | \(0.166454\pi\) | ||||
−0.866358 | + | 0.499423i | \(0.833546\pi\) | |||||||
\(450\) | − | 44.9129i | − | 2.11721i | ||||||
\(451\) | 19.7477 | 0.929884 | ||||||||
\(452\) | − | 19.5826i | − | 0.921087i | ||||||
\(453\) | −35.5826 | −1.67182 | ||||||||
\(454\) | 19.9129 | 0.934558 | ||||||||
\(455\) | −6.00000 | −0.281284 | ||||||||
\(456\) | −21.1652 | −0.991149 | ||||||||
\(457\) | − | 33.4955i | − | 1.56685i | −0.621486 | − | 0.783426i | \(-0.713471\pi\) | ||
0.621486 | − | 0.783426i | \(-0.286529\pi\) | |||||||
\(458\) | − | 20.7477i | − | 0.969478i | ||||||
\(459\) | − | 7.91288i | − | 0.369342i | ||||||
\(460\) | −3.00000 | −0.139876 | ||||||||
\(461\) | 24.3303i | 1.13318i | 0.824002 | + | 0.566588i | \(0.191737\pi\) | ||||
−0.824002 | + | 0.566588i | \(0.808263\pi\) | |||||||
\(462\) | 21.1652i | 0.984692i | ||||||||
\(463\) | 20.7042i | 0.962204i | 0.876665 | + | 0.481102i | \(0.159763\pi\) | ||||
−0.876665 | + | 0.481102i | \(0.840237\pi\) | |||||||
\(464\) | 0.791288i | 0.0367346i | ||||||||
\(465\) | −56.8693 | −2.63725 | ||||||||
\(466\) | 25.1216i | 1.16374i | ||||||||
\(467\) | − | 25.5826i | − | 1.18382i | −0.806004 | − | 0.591910i | \(-0.798374\pi\) | ||
0.806004 | − | 0.591910i | \(-0.201626\pi\) | |||||||
\(468\) | 3.79129i | 0.175252i | ||||||||
\(469\) | 14.7477 | 0.680987 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 5.58258 | 0.257232 | ||||||||
\(472\) | 7.58258 | 0.349016 | ||||||||
\(473\) | 22.7477i | 1.04594i | ||||||||
\(474\) | −35.7042 | −1.63995 | ||||||||
\(475\) | − | 71.0780i | − | 3.26128i | ||||||
\(476\) | 3.16515i | 0.145074i | ||||||||
\(477\) | 36.3303 | 1.66345 | ||||||||
\(478\) | 24.9564 | 1.14148 | ||||||||
\(479\) | 0.791288i | 0.0361549i | 0.999837 | + | 0.0180774i | \(0.00575454\pi\) | ||||
−0.999837 | + | 0.0180774i | \(0.994245\pi\) | |||||||
\(480\) | 10.5826 | 0.483026 | ||||||||
\(481\) | −3.62614 | − | 3.16515i | −0.165338 | − | 0.144318i | ||||
\(482\) | 13.5826 | 0.618669 | ||||||||
\(483\) | − | 4.41742i | − | 0.201000i | ||||||
\(484\) | −3.37386 | −0.153357 | ||||||||
\(485\) | −16.7477 | −0.760475 | ||||||||
\(486\) | 16.1652i | 0.733266i | ||||||||
\(487\) | 36.6606i | 1.66125i | 0.556832 | + | 0.830625i | \(0.312017\pi\) | ||||
−0.556832 | + | 0.830625i | \(0.687983\pi\) | |||||||
\(488\) | −8.20871 | −0.371591 | ||||||||
\(489\) | 29.0780i | 1.31495i | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 68.8693i | 3.09545i | ||||||||
\(496\) | − | 5.37386i | − | 0.241294i | ||||||
\(497\) | −18.3303 | −0.822226 | ||||||||
\(498\) | 8.83485i | 0.395899i | ||||||||
\(499\) | − | 16.7477i | − | 0.749731i | −0.927079 | − | 0.374866i | \(-0.877689\pi\) | ||
0.927079 | − | 0.374866i | \(-0.122311\pi\) | |||||||
\(500\) | 16.5826i | 0.741595i | ||||||||
\(501\) | 2.66970i | 0.119273i | ||||||||
\(502\) | 13.5826 | 0.606220 | ||||||||
\(503\) | − | 29.3739i | − | 1.30972i | −0.755752 | − | 0.654858i | \(-0.772728\pi\) | ||
0.755752 | − | 0.654858i | \(-0.227272\pi\) | |||||||
\(504\) | 9.58258i | 0.426842i | ||||||||
\(505\) | − | 6.00000i | − | 0.266996i | ||||||
\(506\) | 3.00000 | 0.133366 | ||||||||
\(507\) | −34.5390 | −1.53393 | ||||||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 13.5826 | 0.602037 | 0.301019 | − | 0.953618i | \(-0.402673\pi\) | ||||
0.301019 | + | 0.953618i | \(0.402673\pi\) | |||||||
\(510\) | 16.7477i | 0.741602i | ||||||||
\(511\) | −18.7477 | −0.829351 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 37.9129i | − | 1.67389i | ||||||
\(514\) | 22.7477 | 1.00336 | ||||||||
\(515\) | 8.37386 | 0.368997 | ||||||||
\(516\) | 16.7477i | 0.737278i | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | −9.16515 | − | 8.00000i | −0.402694 | − | 0.351500i | ||||
\(519\) | 8.83485 | 0.387807 | ||||||||
\(520\) | − | 3.00000i | − | 0.131559i | ||||||
\(521\) | 9.16515 | 0.401533 | 0.200766 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200766 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(522\) | −3.79129 | −0.165940 | ||||||||
\(523\) | 3.16515i | 0.138402i | 0.997603 | + | 0.0692012i | \(0.0220450\pi\) | ||||
−0.997603 | + | 0.0692012i | \(0.977955\pi\) | |||||||
\(524\) | − | 10.7477i | − | 0.469517i | ||||||
\(525\) | −52.3303 | −2.28388 | ||||||||
\(526\) | − | 8.83485i | − | 0.385218i | ||||||
\(527\) | 8.50455 | 0.370464 | ||||||||
\(528\) | −10.5826 | −0.460547 | ||||||||
\(529\) | 22.3739 | 0.972777 | ||||||||
\(530\) | −28.7477 | −1.24872 | ||||||||
\(531\) | 36.3303i | 1.57660i | ||||||||
\(532\) | 15.1652i | 0.657493i | ||||||||
\(533\) | − | 4.12159i | − | 0.178526i | ||||||
\(534\) | −16.7477 | −0.724745 | ||||||||
\(535\) | 31.7477i | 1.37257i | ||||||||
\(536\) | 7.37386i | 0.318502i | ||||||||
\(537\) | − | 21.1652i | − | 0.913344i | ||||||
\(538\) | − | 10.7477i | − | 0.463367i | ||||||
\(539\) | −11.3739 | −0.489907 | ||||||||
\(540\) | 18.9564i | 0.815755i | ||||||||
\(541\) | 8.20871i | 0.352920i | 0.984308 | + | 0.176460i | \(0.0564646\pi\) | ||||
−0.984308 | + | 0.176460i | \(0.943535\pi\) | |||||||
\(542\) | 22.0000i | 0.944981i | ||||||||
\(543\) | 52.3303 | 2.24571 | ||||||||
\(544\) | −1.58258 | −0.0678524 | ||||||||
\(545\) | 22.7477 | 0.974406 | ||||||||
\(546\) | 4.41742 | 0.189048 | ||||||||
\(547\) | − | 19.9129i | − | 0.851413i | −0.904861 | − | 0.425707i | \(-0.860026\pi\) | ||
0.904861 | − | 0.425707i | \(-0.139974\pi\) | |||||||
\(548\) | 17.3739 | 0.742175 | ||||||||
\(549\) | − | 39.3303i | − | 1.67858i | ||||||
\(550\) | − | 35.5390i | − | 1.51539i | ||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 2.20871 | 0.0940090 | ||||||||
\(553\) | 25.5826i | 1.08788i | ||||||||
\(554\) | −23.3739 | −0.993060 | ||||||||
\(555\) | −48.4955 | − | 42.3303i | −2.05852 | − | 1.79682i | ||||
\(556\) | −0.373864 | −0.0158553 | ||||||||
\(557\) | − | 41.7042i | − | 1.76706i | −0.468372 | − | 0.883531i | \(-0.655159\pi\) | ||
0.468372 | − | 0.883531i | \(-0.344841\pi\) | |||||||
\(558\) | 25.7477 | 1.08999 | ||||||||
\(559\) | 4.74773 | 0.200807 | ||||||||
\(560\) | − | 7.58258i | − | 0.320422i | ||||||
\(561\) | − | 16.7477i | − | 0.707090i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.7477i | 0.705833i | 0.935655 | + | 0.352916i | \(0.114810\pi\) | ||||
−0.935655 | + | 0.352916i | \(0.885190\pi\) | |||||||
\(564\) | 4.41742 | 0.186007 | ||||||||
\(565\) | −74.2432 | −3.12343 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | 0.834849 | 0.0350603 | ||||||||
\(568\) | − | 9.16515i | − | 0.384561i | ||||||
\(569\) | 26.8348i | 1.12498i | 0.826806 | + | 0.562488i | \(0.190156\pi\) | ||||
−0.826806 | + | 0.562488i | \(0.809844\pi\) | |||||||
\(570\) | 80.2432i | 3.36102i | ||||||||
\(571\) | −28.3739 | −1.18741 | −0.593705 | − | 0.804683i | \(-0.702335\pi\) | ||||
−0.593705 | + | 0.804683i | \(0.702335\pi\) | |||||||
\(572\) | 3.00000i | 0.125436i | ||||||||
\(573\) | − | 15.0000i | − | 0.626634i | ||||||
\(574\) | − | 10.4174i | − | 0.434815i | ||||||
\(575\) | 7.41742i | 0.309328i | ||||||||
\(576\) | −4.79129 | −0.199637 | ||||||||
\(577\) | 4.41742i | 0.183900i | 0.995764 | + | 0.0919499i | \(0.0293100\pi\) | ||||
−0.995764 | + | 0.0919499i | \(0.970690\pi\) | |||||||
\(578\) | 14.4955i | 0.602931i | ||||||||
\(579\) | 51.1652i | 2.12635i | ||||||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | 6.33030 | 0.262625 | ||||||||
\(582\) | 12.3303 | 0.511107 | ||||||||
\(583\) | 28.7477 | 1.19061 | ||||||||
\(584\) | − | 9.37386i | − | 0.387893i | ||||||
\(585\) | 14.3739 | 0.594286 | ||||||||
\(586\) | − | 6.00000i | − | 0.247858i | ||||||
\(587\) | 25.9129i | 1.06954i | 0.844998 | + | 0.534769i | \(0.179602\pi\) | ||||
−0.844998 | + | 0.534769i | \(0.820398\pi\) | |||||||
\(588\) | −8.37386 | −0.345332 | ||||||||
\(589\) | 40.7477 | 1.67898 | ||||||||
\(590\) | − | 28.7477i | − | 1.18353i | ||||||
\(591\) | −72.3303 | −2.97527 | ||||||||
\(592\) | 4.00000 | − | 4.58258i | 0.164399 | − | 0.188343i | ||||
\(593\) | −14.2087 | −0.583482 | −0.291741 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291741 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(594\) | − | 18.9564i | − | 0.777792i | ||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 13.5826 | 0.556364 | ||||||||
\(597\) | 8.83485i | 0.361586i | ||||||||
\(598\) | − | 0.626136i | − | 0.0256046i | ||||||
\(599\) | 27.1652 | 1.10994 | 0.554969 | − | 0.831871i | \(-0.312730\pi\) | ||||
0.554969 | + | 0.831871i | \(0.312730\pi\) | |||||||
\(600\) | − | 26.1652i | − | 1.06819i | ||||||
\(601\) | 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 | ||||||||
\(605\) | 12.7913i | 0.520040i | ||||||||
\(606\) | 4.41742i | 0.179446i | ||||||||
\(607\) | 5.53901i | 0.224822i | 0.993662 | + | 0.112411i | \(0.0358573\pi\) | ||||
−0.993662 | + | 0.112411i | \(0.964143\pi\) | |||||||
\(608\) | −7.58258 | −0.307514 | ||||||||
\(609\) | 4.41742i | 0.179003i | ||||||||
\(610\) | 31.1216i | 1.26008i | ||||||||
\(611\) | − | 1.25227i | − | 0.0506615i | ||||||
\(612\) | − | 7.58258i | − | 0.306507i | ||||||
\(613\) | 5.49545 | 0.221959 | 0.110980 | − | 0.993823i | \(-0.464601\pi\) | ||||
0.110980 | + | 0.993823i | \(0.464601\pi\) | |||||||
\(614\) | − | 12.3739i | − | 0.499368i | ||||||
\(615\) | − | 55.1216i | − | 2.22272i | ||||||
\(616\) | 7.58258i | 0.305511i | ||||||||
\(617\) | −45.9564 | −1.85014 | −0.925068 | − | 0.379801i | \(-0.875993\pi\) | ||||
−0.925068 | + | 0.379801i | \(0.875993\pi\) | |||||||
\(618\) | −6.16515 | −0.247999 | ||||||||
\(619\) | 6.12159 | 0.246048 | 0.123024 | − | 0.992404i | \(-0.460741\pi\) | ||||
0.123024 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(620\) | −20.3739 | −0.818234 | ||||||||
\(621\) | 3.95644i | 0.158766i | ||||||||
\(622\) | −9.62614 | −0.385973 | ||||||||
\(623\) | 12.0000i | 0.480770i | ||||||||
\(624\) | 2.20871i | 0.0884192i | ||||||||
\(625\) | 16.0000 | 0.640000 | ||||||||
\(626\) | −33.1652 | −1.32555 | ||||||||
\(627\) | − | 80.2432i | − | 3.20460i | ||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | 7.25227 | + | 6.33030i | 0.289167 | + | 0.252406i | ||||
\(630\) | 36.3303 | 1.44743 | ||||||||
\(631\) | 3.95644i | 0.157503i | 0.996894 | + | 0.0787517i | \(0.0250934\pi\) | ||||
−0.996894 | + | 0.0787517i | \(0.974907\pi\) | |||||||
\(632\) | −12.7913 | −0.508810 | ||||||||
\(633\) | 9.41742 | 0.374309 | ||||||||
\(634\) | − | 1.25227i | − | 0.0497341i | ||||||
\(635\) | 30.3303i | 1.20362i | ||||||||
\(636\) | 21.1652 | 0.839253 | ||||||||
\(637\) | 2.37386i | 0.0940559i | ||||||||
\(638\) | −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 | \(0.747644\pi\) | |||||||
\(642\) | − | 23.3739i | − | 0.922493i | ||||||
\(643\) | − | 15.4955i | − | 0.611081i | −0.952179 | − | 0.305541i | \(-0.901163\pi\) | ||
0.952179 | − | 0.305541i | \(-0.0988371\pi\) | |||||||
\(644\) | − | 1.58258i | − | 0.0623622i | ||||||
\(645\) | 63.4955 | 2.50013 | ||||||||
\(646\) | − | 12.0000i | − | 0.472134i | ||||||
\(647\) | 32.7042i | 1.28573i | 0.765978 | + | 0.642867i | \(0.222255\pi\) | ||||
−0.765978 | + | 0.642867i | \(0.777745\pi\) | |||||||
\(648\) | 0.417424i | 0.0163980i | ||||||||
\(649\) | 28.7477i | 1.12845i | ||||||||
\(650\) | −7.41742 | −0.290935 | ||||||||
\(651\) | − | 30.0000i | − | 1.17579i | ||||||
\(652\) | 10.4174i | 0.407978i | ||||||||
\(653\) | − | 14.3739i | − | 0.562493i | −0.959636 | − | 0.281246i | \(-0.909252\pi\) | ||
0.959636 | − | 0.281246i | \(-0.0907478\pi\) | |||||||
\(654\) | −16.7477 | −0.654888 | ||||||||
\(655\) | −40.7477 | −1.59215 | ||||||||
\(656\) | 5.20871 | 0.203366 | ||||||||
\(657\) | 44.9129 | 1.75222 | ||||||||
\(658\) | − | 3.16515i | − | 0.123390i | ||||||
\(659\) | 33.9564 | 1.32276 | 0.661378 | − | 0.750053i | \(-0.269972\pi\) | ||||
0.661378 | + | 0.750053i | \(0.269972\pi\) | |||||||
\(660\) | 40.1216i | 1.56173i | ||||||||
\(661\) | − | 36.7913i | − | 1.43102i | −0.698605 | − | 0.715508i | \(-0.746195\pi\) | ||
0.698605 | − | 0.715508i | \(-0.253805\pi\) | |||||||
\(662\) | −16.4174 | −0.638081 | ||||||||
\(663\) | −3.49545 | −0.135752 | ||||||||
\(664\) | 3.16515i | 0.122832i | ||||||||
\(665\) | 57.4955 | 2.22958 | ||||||||
\(666\) | 21.9564 | + | 19.1652i | 0.850795 | + | 0.742635i | ||||
\(667\) | 0.626136 | 0.0242441 | ||||||||
\(668\) | 0.956439i | 0.0370057i | ||||||||
\(669\) | −39.0780 | −1.51084 | ||||||||
\(670\) | 27.9564 | 1.08005 | ||||||||
\(671\) | − | 31.1216i | − | 1.20144i | ||||||
\(672\) | 5.58258i | 0.215353i | ||||||||
\(673\) | 5.12159 | 0.197423 | 0.0987114 | − | 0.995116i | \(-0.468528\pi\) | ||||
0.0987114 | + | 0.995116i | \(0.468528\pi\) | |||||||
\(674\) | − | 8.12159i | − | 0.312832i | ||||||
\(675\) | 46.8693 | 1.80400 | ||||||||
\(676\) | −12.3739 | −0.475918 | ||||||||
\(677\) | −9.16515 | −0.352245 | −0.176123 | − | 0.984368i | \(-0.556356\pi\) | ||||
−0.176123 | + | 0.984368i | \(0.556356\pi\) | |||||||
\(678\) | 54.6606 | 2.09923 | ||||||||
\(679\) | − | 8.83485i | − | 0.339050i | ||||||
\(680\) | 6.00000i | 0.230089i | ||||||||
\(681\) | 55.5826i | 2.12993i | ||||||||
\(682\) | 20.3739 | 0.780156 | ||||||||
\(683\) | 22.4174i | 0.857779i | 0.903357 | + | 0.428889i | \(0.141095\pi\) | ||||
−0.903357 | + | 0.428889i | \(0.858905\pi\) | |||||||
\(684\) | − | 36.3303i | − | 1.38912i | ||||||
\(685\) | − | 65.8693i | − | 2.51674i | ||||||
\(686\) | 20.0000i | 0.763604i | ||||||||
\(687\) | 57.9129 | 2.20951 | ||||||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | − | 6.00000i | − | 0.228582i | ||||||
\(690\) | − | 8.37386i | − | 0.318788i | ||||||
\(691\) | −29.4955 | −1.12206 | −0.561030 | − | 0.827795i | \(-0.689595\pi\) | ||||
−0.561030 | + | 0.827795i | \(0.689595\pi\) | |||||||
\(692\) | 3.16515 | 0.120321 | ||||||||
\(693\) | −36.3303 | −1.38007 | ||||||||
\(694\) | −1.58258 | −0.0600738 | ||||||||
\(695\) | 1.41742i | 0.0537660i | ||||||||
\(696\) | −2.20871 | −0.0837210 | ||||||||
\(697\) | 8.24318i | 0.312233i | ||||||||
\(698\) | 10.0000i | 0.378506i | ||||||||
\(699\) | −70.1216 | −2.65224 | ||||||||
\(700\) | −18.7477 | −0.708597 | ||||||||
\(701\) | 18.9564i | 0.715975i | 0.933726 | + | 0.357987i | \(0.116537\pi\) | ||||
−0.933726 | + | 0.357987i | \(0.883463\pi\) | |||||||
\(702\) | −3.95644 | −0.149326 | ||||||||
\(703\) | 34.7477 | + | 30.3303i | 1.31054 | + | 1.14393i | ||||
\(704\) | −3.79129 | −0.142890 | ||||||||
\(705\) | − | 16.7477i | − | 0.630756i | ||||||
\(706\) | 7.58258 | 0.285374 | ||||||||
\(707\) | 3.16515 | 0.119038 | ||||||||
\(708\) | 21.1652i | 0.795435i | ||||||||
\(709\) | − | 27.7913i | − | 1.04372i | −0.853030 | − | 0.521862i | \(-0.825238\pi\) | ||
0.853030 | − | 0.521862i | \(-0.174762\pi\) | |||||||
\(710\) | −34.7477 | −1.30406 | ||||||||
\(711\) | − | 61.2867i | − | 2.29843i | ||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | −4.25227 | −0.159249 | ||||||||
\(714\) | −8.83485 | −0.330636 | ||||||||
\(715\) | 11.3739 | 0.425358 | ||||||||
\(716\) | − | 7.58258i | − | 0.283374i | ||||||
\(717\) | 69.6606i | 2.60152i | ||||||||
\(718\) | − | 27.1652i | − | 1.01379i | ||||||
\(719\) | −2.83485 | −0.105722 | −0.0528610 | − | 0.998602i | \(-0.516834\pi\) | ||||
−0.0528610 | + | 0.998602i | \(0.516834\pi\) | |||||||
\(720\) | 18.1652i | 0.676975i | ||||||||
\(721\) | 4.41742i | 0.164513i | ||||||||
\(722\) | − | 38.4955i | − | 1.43265i | ||||||
\(723\) | 37.9129i | 1.41000i | ||||||||
\(724\) | 18.7477 | 0.696754 | ||||||||
\(725\) | − | 7.41742i | − | 0.275476i | ||||||
\(726\) | − | 9.41742i | − | 0.349513i | ||||||
\(727\) | − | 28.1216i | − | 1.04297i | −0.853260 | − | 0.521486i | \(-0.825378\pi\) | ||
0.853260 | − | 0.521486i | \(-0.174622\pi\) | |||||||
\(728\) | 1.58258 | 0.0586542 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | −35.5390 | −1.31536 | ||||||||
\(731\) | −9.49545 | −0.351202 | ||||||||
\(732\) | − | 22.9129i | − | 0.846884i | ||||||
\(733\) | −7.49545 | −0.276851 | −0.138425 | − | 0.990373i | \(-0.544204\pi\) | ||||
−0.138425 | + | 0.990373i | \(0.544204\pi\) | |||||||
\(734\) | − | 32.7477i | − | 1.20874i | ||||||
\(735\) | 31.7477i | 1.17103i | ||||||||
\(736\) | 0.791288 | 0.0291673 | ||||||||
\(737\) | −27.9564 | −1.02979 | ||||||||
\(738\) | 24.9564i | 0.918659i | ||||||||
\(739\) | 6.12159 | 0.225186 | 0.112593 | − | 0.993641i | \(-0.464084\pi\) | ||||
0.112593 | + | 0.993641i | \(0.464084\pi\) | |||||||
\(740\) | −17.3739 | − | 15.1652i | −0.638676 | − | 0.557482i | ||||
\(741\) | −16.7477 | −0.615243 | ||||||||
\(742\) | − | 15.1652i | − | 0.556730i | ||||||
\(743\) | −3.16515 | −0.116118 | −0.0580591 | − | 0.998313i | \(-0.518491\pi\) | ||||
−0.0580591 | + | 0.998313i | \(0.518491\pi\) | |||||||
\(744\) | 15.0000 | 0.549927 | ||||||||
\(745\) | − | 51.4955i | − | 1.88665i | ||||||
\(746\) | 14.7477i | 0.539953i | ||||||||
\(747\) | −15.1652 | −0.554864 | ||||||||
\(748\) | − | 6.00000i | − | 0.219382i | ||||||
\(749\) | −16.7477 | −0.611949 | ||||||||
\(750\) | −46.2867 | −1.69015 | ||||||||
\(751\) | 13.4955 | 0.492456 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(752\) | 1.58258 | 0.0577106 | ||||||||
\(753\) | 37.9129i | 1.38162i | ||||||||
\(754\) | 0.626136i | 0.0228025i | ||||||||
\(755\) | 48.3303i | 1.75892i | ||||||||
\(756\) | −10.0000 | −0.363696 | ||||||||
\(757\) | 39.7913i | 1.44624i | 0.690723 | + | 0.723119i | \(0.257292\pi\) | ||||
−0.690723 | + | 0.723119i | \(0.742708\pi\) | |||||||
\(758\) | − | 21.1216i | − | 0.767171i | ||||||
\(759\) | 8.37386i | 0.303952i | ||||||||
\(760\) | 28.7477i | 1.04279i | ||||||||
\(761\) | 18.7913 | 0.681184 | 0.340592 | − | 0.940211i | \(-0.389373\pi\) | ||||
0.340592 | + | 0.940211i | \(0.389373\pi\) | |||||||
\(762\) | − | 22.3303i | − | 0.808942i | ||||||
\(763\) | 12.0000i | 0.434429i | ||||||||
\(764\) | − | 5.37386i | − | 0.194420i | ||||||
\(765\) | −28.7477 | −1.03938 | ||||||||
\(766\) | 18.3303 | 0.662301 | ||||||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | −2.79129 | −0.100722 | ||||||||
\(769\) | 48.3303i | 1.74284i | 0.490542 | + | 0.871418i | \(0.336799\pi\) | ||||
−0.490542 | + | 0.871418i | \(0.663201\pi\) | |||||||
\(770\) | 28.7477 | 1.03600 | ||||||||
\(771\) | 63.4955i | 2.28673i | ||||||||
\(772\) | 18.3303i | 0.659722i | ||||||||
\(773\) | −13.9129 | −0.500411 | −0.250206 | − | 0.968193i | \(-0.580498\pi\) | ||||
−0.250206 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(774\) | −28.7477 | −1.03332 | ||||||||
\(775\) | 50.3739i | 1.80948i | ||||||||
\(776\) | 4.41742 | 0.158576 | ||||||||
\(777\) | 22.3303 | − | 25.5826i | 0.801095 | − | 0.917770i | ||||
\(778\) | −35.8693 | −1.28598 | ||||||||
\(779\) | 39.4955i | 1.41507i | ||||||||
\(780\) | 8.37386 | 0.299832 | ||||||||
\(781\) | 34.7477 | 1.24337 | ||||||||
\(782\) | 1.25227i | 0.0447812i | ||||||||
\(783\) | − | 3.95644i | − | 0.141392i | ||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | − | 7.58258i | − | 0.270634i | ||||||
\(786\) | 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 | ||||||||
\(790\) | 48.4955i | 1.72539i | ||||||||
\(791\) | − | 39.1652i | − | 1.39255i | ||||||
\(792\) | − | 18.1652i | − | 0.645471i | ||||||
\(793\) | −6.49545 | −0.230660 | ||||||||
\(794\) | − | 12.7477i | − | 0.452400i | ||||||
\(795\) | − | 80.2432i | − | 2.84593i | ||||||
\(796\) | 3.16515i | 0.112186i | ||||||||
\(797\) | − | 21.6261i | − | 0.766037i | −0.923741 | − | 0.383019i | \(-0.874885\pi\) | ||
0.923741 | − | 0.383019i | \(-0.125115\pi\) | |||||||
\(798\) | −42.3303 | −1.49848 | ||||||||
\(799\) | 2.50455i | 0.0886045i | ||||||||
\(800\) | − | 9.37386i | − | 0.331416i | ||||||
\(801\) | − | 28.7477i | − | 1.01575i | ||||||
\(802\) | 10.7477 | 0.379515 | ||||||||
\(803\) | 35.5390 | 1.25414 | ||||||||
\(804\) | −20.5826 | −0.725891 | ||||||||
\(805\) | −6.00000 | −0.211472 | ||||||||
\(806\) | − | 4.25227i | − | 0.149780i | ||||||
\(807\) | 30.0000 | 1.05605 | ||||||||
\(808\) | 1.58258i | 0.0556748i | ||||||||
\(809\) | − | 11.0780i | − | 0.389483i | −0.980855 | − | 0.194741i | \(-0.937613\pi\) | ||
0.980855 | − | 0.194741i | \(-0.0623868\pi\) | |||||||
\(810\) | 1.58258 | 0.0556060 | ||||||||
\(811\) | 48.8693 | 1.71603 | 0.858017 | − | 0.513621i | \(-0.171696\pi\) | ||||
0.858017 | + | 0.513621i | \(0.171696\pi\) | |||||||
\(812\) | 1.58258i | 0.0555375i | ||||||||
\(813\) | −61.4083 | −2.15368 | ||||||||
\(814\) | 17.3739 | + | 15.1652i | 0.608954 | + | 0.531538i | ||||
\(815\) | 39.4955 | 1.38347 | ||||||||
\(816\) | − | 4.41742i | − | 0.154641i | ||||||
\(817\) | −45.4955 | −1.59168 | ||||||||
\(818\) | 8.83485 | 0.308903 | ||||||||
\(819\) | 7.58258i | 0.264957i | ||||||||
\(820\) | − | 19.7477i | − | 0.689621i | ||||||
\(821\) | −15.1652 | −0.529267 | −0.264634 | − | 0.964349i | \(-0.585251\pi\) | ||||
−0.264634 | + | 0.964349i | \(0.585251\pi\) | |||||||
\(822\) | 48.4955i | 1.69147i | ||||||||
\(823\) | −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 | ||||||||
\(827\) | − | 14.8348i | − | 0.515858i | −0.966164 | − | 0.257929i | \(-0.916960\pi\) | ||
0.966164 | − | 0.257929i | \(-0.0830401\pi\) | |||||||
\(828\) | 3.79129i | 0.131756i | ||||||||
\(829\) | − | 39.9564i | − | 1.38774i | −0.720098 | − | 0.693872i | \(-0.755903\pi\) | ||
0.720098 | − | 0.693872i | \(-0.244097\pi\) | |||||||
\(830\) | 12.0000 | 0.416526 | ||||||||
\(831\) | − | 65.2432i | − | 2.26326i | ||||||
\(832\) | 0.791288i | 0.0274330i | ||||||||
\(833\) | − | 4.74773i | − | 0.164499i | ||||||
\(834\) | − | 1.04356i | − | 0.0361356i | ||||||
\(835\) | 3.62614 | 0.125488 | ||||||||
\(836\) | − | 28.7477i | − | 0.994261i | ||||||
\(837\) | 26.8693i | 0.928739i | ||||||||
\(838\) | 6.79129i | 0.234601i | ||||||||
\(839\) | −51.4955 | −1.77782 | −0.888910 | − | 0.458081i | \(-0.848537\pi\) | ||||
−0.888910 | + | 0.458081i | \(0.848537\pi\) | |||||||
\(840\) | 21.1652 | 0.730267 | ||||||||
\(841\) | 28.3739 | 0.978409 | ||||||||
\(842\) | 3.95644 | 0.136348 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.37386 | 0.116133 | ||||||||
\(845\) | 46.9129i | 1.61385i | ||||||||
\(846\) | 7.58258i | 0.260694i | ||||||||
\(847\) | −6.74773 | −0.231855 | ||||||||
\(848\) | 7.58258 | 0.260387 | ||||||||
\(849\) | 66.9909i | 2.29912i | ||||||||
\(850\) | 14.8348 | 0.508831 | ||||||||
\(851\) | −3.62614 | − | 3.16515i | −0.124302 | − | 0.108500i | ||||
\(852\) | 25.5826 | 0.876445 | ||||||||
\(853\) | 5.70417i | 0.195307i | 0.995220 | + | 0.0976535i | \(0.0311337\pi\) | ||||
−0.995220 | + | 0.0976535i | \(0.968866\pi\) | |||||||
\(854\) | −16.4174 | −0.561793 | ||||||||
\(855\) | −137.739 | −4.71056 | ||||||||
\(856\) | − | 8.37386i | − | 0.286213i | ||||||
\(857\) | − | 14.8348i | − | 0.506749i | −0.967368 | − | 0.253374i | \(-0.918460\pi\) | ||
0.967368 | − | 0.253374i | \(-0.0815405\pi\) | |||||||
\(858\) | −8.37386 | −0.285879 | ||||||||
\(859\) | − | 54.6606i | − | 1.86500i | −0.361175 | − | 0.932498i | \(-0.617624\pi\) | ||
0.361175 | − | 0.932498i | \(-0.382376\pi\) | |||||||
\(860\) | 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 | \(0.792873\pi\) | |||||||
\(864\) | − | 5.00000i | − | 0.170103i | ||||||
\(865\) | − | 12.0000i | − | 0.408012i | ||||||
\(866\) | 24.3739i | 0.828258i | ||||||||
\(867\) | −40.4610 | −1.37413 | ||||||||
\(868\) | − | 10.7477i | − | 0.364802i | ||||||
\(869\) | − | 48.4955i | − | 1.64510i | ||||||
\(870\) | 8.37386i | 0.283901i | ||||||||
\(871\) | 5.83485i | 0.197706i | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 21.1652i | 0.716332i | ||||||||
\(874\) | 6.00000i | 0.202953i | ||||||||
\(875\) | 33.1652i | 1.12119i | ||||||||
\(876\) | 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 | ||||||||
\(880\) | 14.3739i | 0.484543i | ||||||||
\(881\) | 28.1216 | 0.947440 | 0.473720 | − | 0.880675i | \(-0.342911\pi\) | ||||
0.473720 | + | 0.880675i | \(0.342911\pi\) | |||||||
\(882\) | − | 14.3739i | − | 0.483993i | ||||||
\(883\) | 13.9129i | 0.468206i | 0.972212 | + | 0.234103i | \(0.0752152\pi\) | ||||
−0.972212 | + | 0.234103i | \(0.924785\pi\) | |||||||
\(884\) | −1.25227 | −0.0421185 | ||||||||
\(885\) | 80.2432 | 2.69735 | ||||||||
\(886\) | 5.04356i | 0.169442i | ||||||||
\(887\) | 33.8258 | 1.13576 | 0.567879 | − | 0.823112i | \(-0.307764\pi\) | ||||
0.567879 | + | 0.823112i | \(0.307764\pi\) | |||||||
\(888\) | 12.7913 | + | 11.1652i | 0.429248 | + | 0.374678i | ||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 22.7477i | 0.762506i | ||||||||
\(891\) | −1.58258 | −0.0530183 | ||||||||
\(892\) | −14.0000 | −0.468755 | ||||||||
\(893\) | 12.0000i | 0.401565i | ||||||||
\(894\) | 37.9129i | 1.26800i | ||||||||
\(895\) | −28.7477 | −0.960931 | ||||||||
\(896\) | 2.00000i | 0.0668153i | ||||||||
\(897\) | 1.74773 | 0.0583549 | ||||||||
\(898\) | −21.1652 | −0.706290 | ||||||||
\(899\) | 4.25227 | 0.141821 | ||||||||
\(900\) | 44.9129 | 1.49710 | ||||||||
\(901\) | 12.0000i | 0.399778i | ||||||||
\(902\) | 19.7477i | 0.657527i | ||||||||
\(903\) | 33.4955i | 1.11466i | ||||||||
\(904\) | 19.5826 | 0.651307 | ||||||||
\(905\) | − | 71.0780i | − | 2.36271i | ||||||
\(906\) | − | 35.5826i | − | 1.18215i | ||||||
\(907\) | − | 6.33030i | − | 0.210194i | −0.994462 | − | 0.105097i | \(-0.966485\pi\) | ||
0.994462 | − | 0.105097i | \(-0.0335153\pi\) | |||||||
\(908\) | 19.9129i | 0.660832i | ||||||||
\(909\) | −7.58258 | −0.251498 | ||||||||
\(910\) | − | 6.00000i | − | 0.198898i | ||||||
\(911\) | − | 54.3303i | − | 1.80004i | −0.435845 | − | 0.900022i | \(-0.643551\pi\) | ||
0.435845 | − | 0.900022i | \(-0.356449\pi\) | |||||||
\(912\) | − | 21.1652i | − | 0.700848i | ||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 33.4955 | 1.10793 | ||||||||
\(915\) | −86.8693 | −2.87181 | ||||||||
\(916\) | 20.7477 | 0.685524 | ||||||||
\(917\) | − | 21.4955i | − | 0.709842i | ||||||
\(918\) | 7.91288 | 0.261164 | ||||||||
\(919\) | − | 36.0000i | − | 1.18753i | −0.804638 | − | 0.593765i | \(-0.797641\pi\) | ||
0.804638 | − | 0.593765i | \(-0.202359\pi\) | |||||||
\(920\) | − | 3.00000i | − | 0.0989071i | ||||||
\(921\) | 34.5390 | 1.13810 | ||||||||
\(922\) | −24.3303 | −0.801276 | ||||||||
\(923\) | − | 7.25227i | − | 0.238711i | ||||||
\(924\) | −21.1652 | −0.696282 | ||||||||
\(925\) | −37.4955 | + | 42.9564i | −1.23284 | + | 1.41240i | ||||
\(926\) | −20.7042 | −0.680381 | ||||||||
\(927\) | − | 10.5826i | − | 0.347577i | ||||||
\(928\) | −0.791288 | −0.0259753 | ||||||||
\(929\) | −5.37386 | −0.176311 | −0.0881554 | − | 0.996107i | \(-0.528097\pi\) | ||||
−0.0881554 | + | 0.996107i | \(0.528097\pi\) | |||||||
\(930\) | − | 56.8693i | − | 1.86482i | ||||||
\(931\) | − | 22.7477i | − | 0.745527i | ||||||
\(932\) | −25.1216 | −0.822885 | ||||||||
\(933\) | − | 26.8693i | − | 0.879662i | ||||||
\(934\) | 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 | \(0.686605\pi\) | |||||||
\(938\) | 14.7477i | 0.481530i | ||||||||
\(939\) | − | 92.5735i | − | 3.02102i | ||||||
\(940\) | − | 6.00000i | − | 0.195698i | ||||||
\(941\) | 33.4955 | 1.09192 | 0.545960 | − | 0.837811i | \(-0.316165\pi\) | ||||
0.545960 | + | 0.837811i | \(0.316165\pi\) | |||||||
\(942\) | 5.58258i | 0.181890i | ||||||||
\(943\) | − | 4.12159i | − | 0.134217i | ||||||
\(944\) | 7.58258i | 0.246792i | ||||||||
\(945\) | 37.9129i | 1.23331i | ||||||||
\(946\) | −22.7477 | −0.739592 | ||||||||
\(947\) | 28.7477i | 0.934176i | 0.884211 | + | 0.467088i | \(0.154697\pi\) | ||||
−0.884211 | + | 0.467088i | \(0.845303\pi\) | |||||||
\(948\) | − | 35.7042i | − | 1.15962i | ||||||
\(949\) | − | 7.41742i | − | 0.240780i | ||||||
\(950\) | 71.0780 | 2.30608 | ||||||||
\(951\) | 3.49545 | 0.113348 | ||||||||
\(952\) | −3.16515 | −0.102583 | ||||||||
\(953\) | −46.4519 | −1.50472 | −0.752362 | − | 0.658750i | \(-0.771086\pi\) | ||||
−0.752362 | + | 0.658750i | \(0.771086\pi\) | |||||||
\(954\) | 36.3303i | 1.17624i | ||||||||
\(955\) | −20.3739 | −0.659283 | ||||||||
\(956\) | 24.9564i | 0.807149i | ||||||||
\(957\) | − | 8.37386i | − | 0.270689i | ||||||
\(958\) | −0.791288 | −0.0255653 | ||||||||
\(959\) | 34.7477 | 1.12206 | ||||||||
\(960\) | 10.5826i | 0.341551i | ||||||||
\(961\) | 2.12159 | 0.0684384 | ||||||||
\(962\) | 3.16515 | − | 3.62614i | 0.102049 | − | 0.116911i | ||||
\(963\) | 40.1216 | 1.29290 | ||||||||
\(964\) | 13.5826i | 0.437465i | ||||||||
\(965\) | 69.4955 | 2.23714 | ||||||||
\(966\) | 4.41742 | 0.142128 | ||||||||
\(967\) | − | 0.956439i | − | 0.0307570i | −0.999882 | − | 0.0153785i | \(-0.995105\pi\) | ||
0.999882 | − | 0.0153785i | \(-0.00489532\pi\) | |||||||
\(968\) | − | 3.37386i | − | 0.108440i | ||||||
\(969\) | 33.4955 | 1.07603 | ||||||||
\(970\) | − | 16.7477i | − | 0.537737i | ||||||
\(971\) | 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 | ||||||||
\(975\) | − | 20.7042i | − | 0.663064i | ||||||
\(976\) | − | 8.20871i | − | 0.262754i | ||||||
\(977\) | 23.0780i | 0.738332i | 0.929364 | + | 0.369166i | \(0.120357\pi\) | ||||
−0.929364 | + | 0.369166i | \(0.879643\pi\) | |||||||
\(978\) | −29.0780 | −0.929813 | ||||||||
\(979\) | − | 22.7477i | − | 0.727021i | ||||||
\(980\) | 11.3739i | 0.363325i | ||||||||
\(981\) | − | 28.7477i | − | 0.917844i | ||||||
\(982\) | − | 8.37386i | − | 0.267221i | ||||||
\(983\) | 18.3303 | 0.584646 | 0.292323 | − | 0.956320i | \(-0.405572\pi\) | ||||
0.292323 | + | 0.956320i | \(0.405572\pi\) | |||||||
\(984\) | 14.5390i | 0.463487i | ||||||||
\(985\) | 98.2432i | 3.13029i | ||||||||
\(986\) | − | 1.25227i | − | 0.0398805i | ||||||
\(987\) | 8.83485 | 0.281216 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | 4.74773 | 0.150969 | ||||||||
\(990\) | −68.8693 | −2.18881 | ||||||||
\(991\) | 3.95644i | 0.125680i | 0.998024 | + | 0.0628402i | \(0.0200159\pi\) | ||||
−0.998024 | + | 0.0628402i | \(0.979984\pi\) | |||||||
\(992\) | 5.37386 | 0.170620 | ||||||||
\(993\) | − | 45.8258i | − | 1.45424i | ||||||
\(994\) | − | 18.3303i | − | 0.581402i | ||||||
\(995\) | 12.0000 | 0.380426 | ||||||||
\(996\) | −8.83485 | −0.279943 | ||||||||
\(997\) | 18.0000i | 0.570066i | 0.958518 | + | 0.285033i | \(0.0920045\pi\) | ||||
−0.958518 | + | 0.285033i | \(0.907995\pi\) | |||||||
\(998\) | 16.7477 | 0.530140 | ||||||||
\(999\) | −20.0000 | + | 22.9129i | −0.632772 | + | 0.724931i |
(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 | 74.2.b.a.73.3 | yes | 4 | |
3.2 | odd | 2 | 666.2.c.b.73.1 | 4 | |||
4.3 | odd | 2 | 592.2.g.c.369.4 | 4 | |||
5.2 | odd | 4 | 1850.2.c.g.1849.4 | 4 | |||
5.3 | odd | 4 | 1850.2.c.h.1849.1 | 4 | |||
5.4 | even | 2 | 1850.2.d.e.1701.2 | 4 | |||
8.3 | odd | 2 | 2368.2.g.h.961.1 | 4 | |||
8.5 | even | 2 | 2368.2.g.j.961.3 | 4 | |||
12.11 | even | 2 | 5328.2.h.m.2737.1 | 4 | |||
37.6 | odd | 4 | 2738.2.a.k.1.2 | 2 | |||
37.31 | odd | 4 | 2738.2.a.h.1.2 | 2 | |||
37.36 | even | 2 | inner | 74.2.b.a.73.1 | ✓ | 4 | |
111.110 | odd | 2 | 666.2.c.b.73.4 | 4 | |||
148.147 | odd | 2 | 592.2.g.c.369.3 | 4 | |||
185.73 | odd | 4 | 1850.2.c.g.1849.1 | 4 | |||
185.147 | odd | 4 | 1850.2.c.h.1849.4 | 4 | |||
185.184 | even | 2 | 1850.2.d.e.1701.4 | 4 | |||
296.147 | odd | 2 | 2368.2.g.h.961.2 | 4 | |||
296.221 | even | 2 | 2368.2.g.j.961.4 | 4 | |||
444.443 | even | 2 | 5328.2.h.m.2737.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.b.a.73.1 | ✓ | 4 | 37.36 | even | 2 | inner | |
74.2.b.a.73.3 | yes | 4 | 1.1 | even | 1 | trivial | |
592.2.g.c.369.3 | 4 | 148.147 | odd | 2 | |||
592.2.g.c.369.4 | 4 | 4.3 | odd | 2 | |||
666.2.c.b.73.1 | 4 | 3.2 | odd | 2 | |||
666.2.c.b.73.4 | 4 | 111.110 | odd | 2 | |||
1850.2.c.g.1849.1 | 4 | 185.73 | odd | 4 | |||
1850.2.c.g.1849.4 | 4 | 5.2 | odd | 4 | |||
1850.2.c.h.1849.1 | 4 | 5.3 | odd | 4 | |||
1850.2.c.h.1849.4 | 4 | 185.147 | odd | 4 | |||
1850.2.d.e.1701.2 | 4 | 5.4 | even | 2 | |||
1850.2.d.e.1701.4 | 4 | 185.184 | even | 2 | |||
2368.2.g.h.961.1 | 4 | 8.3 | odd | 2 | |||
2368.2.g.h.961.2 | 4 | 296.147 | odd | 2 | |||
2368.2.g.j.961.3 | 4 | 8.5 | even | 2 | |||
2368.2.g.j.961.4 | 4 | 296.221 | even | 2 | |||
2738.2.a.h.1.2 | 2 | 37.31 | odd | 4 | |||
2738.2.a.k.1.2 | 2 | 37.6 | odd | 4 | |||
5328.2.h.m.2737.1 | 4 | 12.11 | even | 2 | |||
5328.2.h.m.2737.4 | 4 | 444.443 | even | 2 |