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 | 73.4 | ||
Root | \(1.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.73 |
Dual form | 74.2.b.a.73.2 |
$q$-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 | ||||||||
\(3\) | 1.79129 | 1.03420 | 0.517100 | − | 0.855925i | \(-0.327011\pi\) | ||||
0.517100 | + | 0.855925i | \(0.327011\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.791288i | − | 0.353875i | −0.984222 | − | 0.176937i | \(-0.943381\pi\) | ||
0.984222 | − | 0.176937i | \(-0.0566190\pi\) | |||||||
\(6\) | 1.79129i | 0.731290i | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.208712 | 0.0695707 | ||||||||
\(10\) | 0.791288 | 0.250227 | ||||||||
\(11\) | −0.791288 | −0.238582 | −0.119291 | − | 0.992859i | \(-0.538062\pi\) | ||||
−0.119291 | + | 0.992859i | \(0.538062\pi\) | |||||||
\(12\) | −1.79129 | −0.517100 | ||||||||
\(13\) | 3.79129i | 1.05151i | 0.850635 | + | 0.525757i | \(0.176218\pi\) | ||||
−0.850635 | + | 0.525757i | \(0.823782\pi\) | |||||||
\(14\) | − | 2.00000i | − | 0.534522i | ||||||
\(15\) | − | 1.41742i | − | 0.365977i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 7.58258i | − | 1.83904i | −0.393038 | − | 0.919522i | \(-0.628576\pi\) | ||
0.393038 | − | 0.919522i | \(-0.371424\pi\) | |||||||
\(18\) | 0.208712i | 0.0491939i | ||||||||
\(19\) | − | 1.58258i | − | 0.363068i | −0.983385 | − | 0.181534i | \(-0.941894\pi\) | ||
0.983385 | − | 0.181534i | \(-0.0581062\pi\) | |||||||
\(20\) | 0.791288i | 0.176937i | ||||||||
\(21\) | −3.58258 | −0.781782 | ||||||||
\(22\) | − | 0.791288i | − | 0.168703i | ||||||
\(23\) | 3.79129i | 0.790538i | 0.918565 | + | 0.395269i | \(0.129349\pi\) | ||||
−0.918565 | + | 0.395269i | \(0.870651\pi\) | |||||||
\(24\) | − | 1.79129i | − | 0.365645i | ||||||
\(25\) | 4.37386 | 0.874773 | ||||||||
\(26\) | −3.79129 | −0.743533 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | − | 3.79129i | − | 0.704024i | −0.935995 | − | 0.352012i | \(-0.885498\pi\) | ||
0.935995 | − | 0.352012i | \(-0.114502\pi\) | |||||||
\(30\) | 1.41742 | 0.258785 | ||||||||
\(31\) | 8.37386i | 1.50399i | 0.659169 | + | 0.751995i | \(0.270908\pi\) | ||||
−0.659169 | + | 0.751995i | \(0.729092\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.41742 | −0.246742 | ||||||||
\(34\) | 7.58258 | 1.30040 | ||||||||
\(35\) | 1.58258i | 0.267504i | ||||||||
\(36\) | −0.208712 | −0.0347854 | ||||||||
\(37\) | 4.00000 | + | 4.58258i | 0.657596 | + | 0.753371i | ||||
\(38\) | 1.58258 | 0.256728 | ||||||||
\(39\) | 6.79129i | 1.08748i | ||||||||
\(40\) | −0.791288 | −0.125114 | ||||||||
\(41\) | 9.79129 | 1.52914 | 0.764571 | − | 0.644539i | \(-0.222951\pi\) | ||||
0.764571 | + | 0.644539i | \(0.222951\pi\) | |||||||
\(42\) | − | 3.58258i | − | 0.552803i | ||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 0.791288 | 0.119291 | ||||||||
\(45\) | − | 0.165151i | − | 0.0246193i | ||||||
\(46\) | −3.79129 | −0.558995 | ||||||||
\(47\) | −7.58258 | −1.10603 | −0.553016 | − | 0.833171i | \(-0.686523\pi\) | ||||
−0.553016 | + | 0.833171i | \(0.686523\pi\) | |||||||
\(48\) | 1.79129 | 0.258550 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 4.37386i | 0.618558i | ||||||||
\(51\) | − | 13.5826i | − | 1.90194i | ||||||
\(52\) | − | 3.79129i | − | 0.525757i | ||||||
\(53\) | −1.58258 | −0.217383 | −0.108692 | − | 0.994076i | \(-0.534666\pi\) | ||||
−0.108692 | + | 0.994076i | \(0.534666\pi\) | |||||||
\(54\) | − | 5.00000i | − | 0.680414i | ||||||
\(55\) | 0.626136i | 0.0844282i | ||||||||
\(56\) | 2.00000i | 0.267261i | ||||||||
\(57\) | − | 2.83485i | − | 0.375485i | ||||||
\(58\) | 3.79129 | 0.497820 | ||||||||
\(59\) | − | 1.58258i | − | 0.206034i | −0.994680 | − | 0.103017i | \(-0.967150\pi\) | ||
0.994680 | − | 0.103017i | \(-0.0328496\pi\) | |||||||
\(60\) | 1.41742i | 0.182989i | ||||||||
\(61\) | − | 12.7913i | − | 1.63776i | −0.573967 | − | 0.818878i | \(-0.694596\pi\) | ||
0.573967 | − | 0.818878i | \(-0.305404\pi\) | |||||||
\(62\) | −8.37386 | −1.06348 | ||||||||
\(63\) | −0.417424 | −0.0525905 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | − | 1.41742i | − | 0.174473i | ||||||
\(67\) | 6.37386 | 0.778691 | 0.389346 | − | 0.921092i | \(-0.372701\pi\) | ||||
0.389346 | + | 0.921092i | \(0.372701\pi\) | |||||||
\(68\) | 7.58258i | 0.919522i | ||||||||
\(69\) | 6.79129i | 0.817575i | ||||||||
\(70\) | −1.58258 | −0.189154 | ||||||||
\(71\) | −9.16515 | −1.08770 | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(72\) | − | 0.208712i | − | 0.0245970i | ||||||
\(73\) | −4.37386 | −0.511922 | −0.255961 | − | 0.966687i | \(-0.582392\pi\) | ||||
−0.255961 | + | 0.966687i | \(0.582392\pi\) | |||||||
\(74\) | −4.58258 | + | 4.00000i | −0.532714 | + | 0.464991i | ||||
\(75\) | 7.83485 | 0.904690 | ||||||||
\(76\) | 1.58258i | 0.181534i | ||||||||
\(77\) | 1.58258 | 0.180351 | ||||||||
\(78\) | −6.79129 | −0.768962 | ||||||||
\(79\) | − | 8.20871i | − | 0.923552i | −0.886997 | − | 0.461776i | \(-0.847212\pi\) | ||
0.886997 | − | 0.461776i | \(-0.152788\pi\) | |||||||
\(80\) | − | 0.791288i | − | 0.0884687i | ||||||
\(81\) | −9.58258 | −1.06473 | ||||||||
\(82\) | 9.79129i | 1.08127i | ||||||||
\(83\) | 15.1652 | 1.66459 | 0.832296 | − | 0.554332i | \(-0.187026\pi\) | ||||
0.832296 | + | 0.554332i | \(0.187026\pi\) | |||||||
\(84\) | 3.58258 | 0.390891 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | − | 6.79129i | − | 0.728102i | ||||||
\(88\) | 0.791288i | 0.0843516i | ||||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0.165151 | 0.0174085 | ||||||||
\(91\) | − | 7.58258i | − | 0.794870i | ||||||
\(92\) | − | 3.79129i | − | 0.395269i | ||||||
\(93\) | 15.0000i | 1.55543i | ||||||||
\(94\) | − | 7.58258i | − | 0.782083i | ||||||
\(95\) | −1.25227 | −0.128480 | ||||||||
\(96\) | 1.79129i | 0.182823i | ||||||||
\(97\) | 13.5826i | 1.37910i | 0.724237 | + | 0.689551i | \(0.242192\pi\) | ||||
−0.724237 | + | 0.689551i | \(0.757808\pi\) | |||||||
\(98\) | − | 3.00000i | − | 0.303046i | ||||||
\(99\) | −0.165151 | −0.0165983 | ||||||||
\(100\) | −4.37386 | −0.437386 | ||||||||
\(101\) | 7.58258 | 0.754494 | 0.377247 | − | 0.926113i | \(-0.376871\pi\) | ||||
0.377247 | + | 0.926113i | \(0.376871\pi\) | |||||||
\(102\) | 13.5826 | 1.34488 | ||||||||
\(103\) | − | 6.79129i | − | 0.669165i | −0.942366 | − | 0.334583i | \(-0.891405\pi\) | ||
0.942366 | − | 0.334583i | \(-0.108595\pi\) | |||||||
\(104\) | 3.79129 | 0.371766 | ||||||||
\(105\) | 2.83485i | 0.276653i | ||||||||
\(106\) | − | 1.58258i | − | 0.153713i | ||||||
\(107\) | −5.37386 | −0.519511 | −0.259755 | − | 0.965674i | \(-0.583642\pi\) | ||||
−0.259755 | + | 0.965674i | \(0.583642\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | −0.626136 | −0.0596998 | ||||||||
\(111\) | 7.16515 | + | 8.20871i | 0.680086 | + | 0.779136i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 10.4174i | 0.979989i | 0.871726 | + | 0.489994i | \(0.163001\pi\) | ||||
−0.871726 | + | 0.489994i | \(0.836999\pi\) | |||||||
\(114\) | 2.83485 | 0.265508 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | 3.79129i | 0.352012i | ||||||||
\(117\) | 0.791288i | 0.0731546i | ||||||||
\(118\) | 1.58258 | 0.145688 | ||||||||
\(119\) | 15.1652i | 1.39019i | ||||||||
\(120\) | −1.41742 | −0.129393 | ||||||||
\(121\) | −10.3739 | −0.943079 | ||||||||
\(122\) | 12.7913 | 1.15807 | ||||||||
\(123\) | 17.5390 | 1.58144 | ||||||||
\(124\) | − | 8.37386i | − | 0.751995i | ||||||
\(125\) | − | 7.41742i | − | 0.663435i | ||||||
\(126\) | − | 0.417424i | − | 0.0371871i | ||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 10.7477i | 0.946285i | ||||||||
\(130\) | 3.00000i | 0.263117i | ||||||||
\(131\) | − | 16.7477i | − | 1.46326i | −0.681704 | − | 0.731628i | \(-0.738761\pi\) | ||
0.681704 | − | 0.731628i | \(-0.261239\pi\) | |||||||
\(132\) | 1.41742 | 0.123371 | ||||||||
\(133\) | 3.16515i | 0.274453i | ||||||||
\(134\) | 6.37386i | 0.550618i | ||||||||
\(135\) | 3.95644i | 0.340516i | ||||||||
\(136\) | −7.58258 | −0.650201 | ||||||||
\(137\) | −3.62614 | −0.309802 | −0.154901 | − | 0.987930i | \(-0.549506\pi\) | ||||
−0.154901 | + | 0.987930i | \(0.549506\pi\) | |||||||
\(138\) | −6.79129 | −0.578113 | ||||||||
\(139\) | −13.3739 | −1.13436 | −0.567178 | − | 0.823595i | \(-0.691965\pi\) | ||||
−0.567178 | + | 0.823595i | \(0.691965\pi\) | |||||||
\(140\) | − | 1.58258i | − | 0.133752i | ||||||
\(141\) | −13.5826 | −1.14386 | ||||||||
\(142\) | − | 9.16515i | − | 0.769122i | ||||||
\(143\) | − | 3.00000i | − | 0.250873i | ||||||
\(144\) | 0.208712 | 0.0173927 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | − | 4.37386i | − | 0.361984i | ||||||
\(147\) | −5.37386 | −0.443229 | ||||||||
\(148\) | −4.00000 | − | 4.58258i | −0.328798 | − | 0.376685i | ||||
\(149\) | −4.41742 | −0.361889 | −0.180945 | − | 0.983493i | \(-0.557916\pi\) | ||||
−0.180945 | + | 0.983493i | \(0.557916\pi\) | |||||||
\(150\) | 7.83485i | 0.639713i | ||||||||
\(151\) | −14.7477 | −1.20015 | −0.600077 | − | 0.799943i | \(-0.704863\pi\) | ||||
−0.600077 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(152\) | −1.58258 | −0.128364 | ||||||||
\(153\) | − | 1.58258i | − | 0.127944i | ||||||
\(154\) | 1.58258i | 0.127528i | ||||||||
\(155\) | 6.62614 | 0.532224 | ||||||||
\(156\) | − | 6.79129i | − | 0.543738i | ||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 8.20871 | 0.653050 | ||||||||
\(159\) | −2.83485 | −0.224818 | ||||||||
\(160\) | 0.791288 | 0.0625568 | ||||||||
\(161\) | − | 7.58258i | − | 0.597591i | ||||||
\(162\) | − | 9.58258i | − | 0.752878i | ||||||
\(163\) | − | 19.5826i | − | 1.53383i | −0.641751 | − | 0.766913i | \(-0.721792\pi\) | ||
0.641751 | − | 0.766913i | \(-0.278208\pi\) | |||||||
\(164\) | −9.79129 | −0.764571 | ||||||||
\(165\) | 1.12159i | 0.0873157i | ||||||||
\(166\) | 15.1652i | 1.17704i | ||||||||
\(167\) | 21.9564i | 1.69904i | 0.527556 | + | 0.849520i | \(0.323108\pi\) | ||||
−0.527556 | + | 0.849520i | \(0.676892\pi\) | |||||||
\(168\) | 3.58258i | 0.276402i | ||||||||
\(169\) | −1.37386 | −0.105682 | ||||||||
\(170\) | − | 6.00000i | − | 0.460179i | ||||||
\(171\) | − | 0.330303i | − | 0.0252589i | ||||||
\(172\) | − | 6.00000i | − | 0.457496i | ||||||
\(173\) | 15.1652 | 1.15299 | 0.576493 | − | 0.817102i | \(-0.304421\pi\) | ||||
0.576493 | + | 0.817102i | \(0.304421\pi\) | |||||||
\(174\) | 6.79129 | 0.514846 | ||||||||
\(175\) | −8.74773 | −0.661266 | ||||||||
\(176\) | −0.791288 | −0.0596456 | ||||||||
\(177\) | − | 2.83485i | − | 0.213080i | ||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | − | 1.58258i | − | 0.118287i | −0.998249 | − | 0.0591436i | \(-0.981163\pi\) | ||
0.998249 | − | 0.0591436i | \(-0.0188370\pi\) | |||||||
\(180\) | 0.165151i | 0.0123097i | ||||||||
\(181\) | 8.74773 | 0.650213 | 0.325107 | − | 0.945677i | \(-0.394600\pi\) | ||||
0.325107 | + | 0.945677i | \(0.394600\pi\) | |||||||
\(182\) | 7.58258 | 0.562058 | ||||||||
\(183\) | − | 22.9129i | − | 1.69377i | ||||||
\(184\) | 3.79129 | 0.279497 | ||||||||
\(185\) | 3.62614 | − | 3.16515i | 0.266599 | − | 0.232707i | ||||
\(186\) | −15.0000 | −1.09985 | ||||||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | 7.58258 | 0.553016 | ||||||||
\(189\) | 10.0000 | 0.727393 | ||||||||
\(190\) | − | 1.25227i | − | 0.0908494i | ||||||
\(191\) | − | 8.37386i | − | 0.605912i | −0.953005 | − | 0.302956i | \(-0.902027\pi\) | ||
0.953005 | − | 0.302956i | \(-0.0979734\pi\) | |||||||
\(192\) | −1.79129 | −0.129275 | ||||||||
\(193\) | 18.3303i | 1.31944i | 0.751510 | + | 0.659722i | \(0.229326\pi\) | ||||
−0.751510 | + | 0.659722i | \(0.770674\pi\) | |||||||
\(194\) | −13.5826 | −0.975172 | ||||||||
\(195\) | 5.37386 | 0.384830 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −19.9129 | −1.41873 | −0.709367 | − | 0.704839i | \(-0.751019\pi\) | ||||
−0.709367 | + | 0.704839i | \(0.751019\pi\) | |||||||
\(198\) | − | 0.165151i | − | 0.0117368i | ||||||
\(199\) | 15.1652i | 1.07503i | 0.843254 | + | 0.537515i | \(0.180637\pi\) | ||||
−0.843254 | + | 0.537515i | \(0.819363\pi\) | |||||||
\(200\) | − | 4.37386i | − | 0.309279i | ||||||
\(201\) | 11.4174 | 0.805323 | ||||||||
\(202\) | 7.58258i | 0.533508i | ||||||||
\(203\) | 7.58258i | 0.532192i | ||||||||
\(204\) | 13.5826i | 0.950971i | ||||||||
\(205\) | − | 7.74773i | − | 0.541125i | ||||||
\(206\) | 6.79129 | 0.473171 | ||||||||
\(207\) | 0.791288i | 0.0549983i | ||||||||
\(208\) | 3.79129i | 0.262879i | ||||||||
\(209\) | 1.25227i | 0.0866215i | ||||||||
\(210\) | −2.83485 | −0.195623 | ||||||||
\(211\) | 10.3739 | 0.714166 | 0.357083 | − | 0.934073i | \(-0.383771\pi\) | ||||
0.357083 | + | 0.934073i | \(0.383771\pi\) | |||||||
\(212\) | 1.58258 | 0.108692 | ||||||||
\(213\) | −16.4174 | −1.12490 | ||||||||
\(214\) | − | 5.37386i | − | 0.367350i | ||||||
\(215\) | 4.74773 | 0.323792 | ||||||||
\(216\) | 5.00000i | 0.340207i | ||||||||
\(217\) | − | 16.7477i | − | 1.13691i | ||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | −7.83485 | −0.529430 | ||||||||
\(220\) | − | 0.626136i | − | 0.0422141i | ||||||
\(221\) | 28.7477 | 1.93378 | ||||||||
\(222\) | −8.20871 | + | 7.16515i | −0.550933 | + | 0.480893i | ||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | − | 2.00000i | − | 0.133631i | ||||||
\(225\) | 0.912878 | 0.0608586 | ||||||||
\(226\) | −10.4174 | −0.692957 | ||||||||
\(227\) | 25.9129i | 1.71990i | 0.510380 | + | 0.859949i | \(0.329505\pi\) | ||||
−0.510380 | + | 0.859949i | \(0.670495\pi\) | |||||||
\(228\) | 2.83485i | 0.187742i | ||||||||
\(229\) | 6.74773 | 0.445902 | 0.222951 | − | 0.974830i | \(-0.428431\pi\) | ||||
0.222951 | + | 0.974830i | \(0.428431\pi\) | |||||||
\(230\) | 3.00000i | 0.197814i | ||||||||
\(231\) | 2.83485 | 0.186519 | ||||||||
\(232\) | −3.79129 | −0.248910 | ||||||||
\(233\) | −16.1216 | −1.05616 | −0.528080 | − | 0.849194i | \(-0.677088\pi\) | ||||
−0.528080 | + | 0.849194i | \(0.677088\pi\) | |||||||
\(234\) | −0.791288 | −0.0517281 | ||||||||
\(235\) | 6.00000i | 0.391397i | ||||||||
\(236\) | 1.58258i | 0.103017i | ||||||||
\(237\) | − | 14.7042i | − | 0.955138i | ||||||
\(238\) | −15.1652 | −0.983011 | ||||||||
\(239\) | − | 2.04356i | − | 0.132187i | −0.997813 | − | 0.0660935i | \(-0.978946\pi\) | ||
0.997813 | − | 0.0660935i | \(-0.0210536\pi\) | |||||||
\(240\) | − | 1.41742i | − | 0.0914943i | ||||||
\(241\) | − | 4.41742i | − | 0.284551i | −0.989827 | − | 0.142276i | \(-0.954558\pi\) | ||
0.989827 | − | 0.142276i | \(-0.0454419\pi\) | |||||||
\(242\) | − | 10.3739i | − | 0.666857i | ||||||
\(243\) | −2.16515 | −0.138895 | ||||||||
\(244\) | 12.7913i | 0.818878i | ||||||||
\(245\) | 2.37386i | 0.151661i | ||||||||
\(246\) | 17.5390i | 1.11825i | ||||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | 8.37386 | 0.531741 | ||||||||
\(249\) | 27.1652 | 1.72152 | ||||||||
\(250\) | 7.41742 | 0.469119 | ||||||||
\(251\) | − | 4.41742i | − | 0.278825i | −0.990234 | − | 0.139413i | \(-0.955479\pi\) | ||
0.990234 | − | 0.139413i | \(-0.0445215\pi\) | |||||||
\(252\) | 0.417424 | 0.0262953 | ||||||||
\(253\) | − | 3.00000i | − | 0.188608i | ||||||
\(254\) | 8.00000i | 0.501965i | ||||||||
\(255\) | −10.7477 | −0.673049 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.74773i | 0.296155i | 0.988976 | + | 0.148078i | \(0.0473085\pi\) | ||||
−0.988976 | + | 0.148078i | \(0.952691\pi\) | |||||||
\(258\) | −10.7477 | −0.669124 | ||||||||
\(259\) | −8.00000 | − | 9.16515i | −0.497096 | − | 0.569495i | ||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | − | 0.791288i | − | 0.0489795i | ||||||
\(262\) | 16.7477 | 1.03468 | ||||||||
\(263\) | −27.1652 | −1.67507 | −0.837537 | − | 0.546380i | \(-0.816006\pi\) | ||||
−0.837537 | + | 0.546380i | \(0.816006\pi\) | |||||||
\(264\) | 1.41742i | 0.0872364i | ||||||||
\(265\) | 1.25227i | 0.0769265i | ||||||||
\(266\) | −3.16515 | −0.194068 | ||||||||
\(267\) | − | 10.7477i | − | 0.657750i | ||||||
\(268\) | −6.37386 | −0.389346 | ||||||||
\(269\) | 16.7477 | 1.02113 | 0.510563 | − | 0.859840i | \(-0.329437\pi\) | ||||
0.510563 | + | 0.859840i | \(0.329437\pi\) | |||||||
\(270\) | −3.95644 | −0.240781 | ||||||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | − | 7.58258i | − | 0.459761i | ||||||
\(273\) | − | 13.5826i | − | 0.822055i | ||||||
\(274\) | − | 3.62614i | − | 0.219063i | ||||||
\(275\) | −3.46099 | −0.208705 | ||||||||
\(276\) | − | 6.79129i | − | 0.408787i | ||||||
\(277\) | 9.62614i | 0.578378i | 0.957272 | + | 0.289189i | \(0.0933857\pi\) | ||||
−0.957272 | + | 0.289189i | \(0.906614\pi\) | |||||||
\(278\) | − | 13.3739i | − | 0.802111i | ||||||
\(279\) | 1.74773i | 0.104634i | ||||||||
\(280\) | 1.58258 | 0.0945770 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | − | 13.5826i | − | 0.808831i | ||||||
\(283\) | − | 24.0000i | − | 1.42665i | −0.700832 | − | 0.713326i | \(-0.747188\pi\) | ||
0.700832 | − | 0.713326i | \(-0.252812\pi\) | |||||||
\(284\) | 9.16515 | 0.543852 | ||||||||
\(285\) | −2.24318 | −0.132875 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | −19.5826 | −1.15592 | ||||||||
\(288\) | 0.208712i | 0.0122985i | ||||||||
\(289\) | −40.4955 | −2.38209 | ||||||||
\(290\) | − | 3.00000i | − | 0.176166i | ||||||
\(291\) | 24.3303i | 1.42627i | ||||||||
\(292\) | 4.37386 | 0.255961 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | − | 5.37386i | − | 0.313410i | ||||||
\(295\) | −1.25227 | −0.0729101 | ||||||||
\(296\) | 4.58258 | − | 4.00000i | 0.266357 | − | 0.232495i | ||||
\(297\) | 3.95644 | 0.229576 | ||||||||
\(298\) | − | 4.41742i | − | 0.255895i | ||||||
\(299\) | −14.3739 | −0.831262 | ||||||||
\(300\) | −7.83485 | −0.452345 | ||||||||
\(301\) | − | 12.0000i | − | 0.691669i | ||||||
\(302\) | − | 14.7477i | − | 0.848636i | ||||||
\(303\) | 13.5826 | 0.780299 | ||||||||
\(304\) | − | 1.58258i | − | 0.0907669i | ||||||
\(305\) | −10.1216 | −0.579561 | ||||||||
\(306\) | 1.58258 | 0.0904698 | ||||||||
\(307\) | 1.37386 | 0.0784105 | 0.0392053 | − | 0.999231i | \(-0.487517\pi\) | ||||
0.0392053 | + | 0.999231i | \(0.487517\pi\) | |||||||
\(308\) | −1.58258 | −0.0901756 | ||||||||
\(309\) | − | 12.1652i | − | 0.692051i | ||||||
\(310\) | 6.62614i | 0.376339i | ||||||||
\(311\) | 23.3739i | 1.32541i | 0.748880 | + | 0.662705i | \(0.230592\pi\) | ||||
−0.748880 | + | 0.662705i | \(0.769408\pi\) | |||||||
\(312\) | 6.79129 | 0.384481 | ||||||||
\(313\) | 14.8348i | 0.838515i | 0.907867 | + | 0.419258i | \(0.137710\pi\) | ||||
−0.907867 | + | 0.419258i | \(0.862290\pi\) | |||||||
\(314\) | − | 2.00000i | − | 0.112867i | ||||||
\(315\) | 0.330303i | 0.0186105i | ||||||||
\(316\) | 8.20871i | 0.461776i | ||||||||
\(317\) | −28.7477 | −1.61463 | −0.807317 | − | 0.590119i | \(-0.799081\pi\) | ||||
−0.807317 | + | 0.590119i | \(0.799081\pi\) | |||||||
\(318\) | − | 2.83485i | − | 0.158970i | ||||||
\(319\) | 3.00000i | 0.167968i | ||||||||
\(320\) | 0.791288i | 0.0442343i | ||||||||
\(321\) | −9.62614 | −0.537279 | ||||||||
\(322\) | 7.58258 | 0.422560 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 9.58258 | 0.532365 | ||||||||
\(325\) | 16.5826i | 0.919836i | ||||||||
\(326\) | 19.5826 | 1.08458 | ||||||||
\(327\) | − | 10.7477i | − | 0.594351i | ||||||
\(328\) | − | 9.79129i | − | 0.540633i | ||||||
\(329\) | 15.1652 | 0.836082 | ||||||||
\(330\) | −1.12159 | −0.0617415 | ||||||||
\(331\) | 25.5826i | 1.40615i | 0.711118 | + | 0.703073i | \(0.248189\pi\) | ||||
−0.711118 | + | 0.703073i | \(0.751811\pi\) | |||||||
\(332\) | −15.1652 | −0.832296 | ||||||||
\(333\) | 0.834849 | + | 0.956439i | 0.0457494 | + | 0.0524125i | ||||
\(334\) | −21.9564 | −1.20140 | ||||||||
\(335\) | − | 5.04356i | − | 0.275559i | ||||||
\(336\) | −3.58258 | −0.195446 | ||||||||
\(337\) | 33.1216 | 1.80425 | 0.902124 | − | 0.431477i | \(-0.142007\pi\) | ||||
0.902124 | + | 0.431477i | \(0.142007\pi\) | |||||||
\(338\) | − | 1.37386i | − | 0.0747283i | ||||||
\(339\) | 18.6606i | 1.01350i | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | − | 6.62614i | − | 0.358825i | ||||||
\(342\) | 0.330303 | 0.0178607 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | 5.37386 | 0.289319 | ||||||||
\(346\) | 15.1652i | 0.815284i | ||||||||
\(347\) | − | 7.58258i | − | 0.407054i | −0.979069 | − | 0.203527i | \(-0.934760\pi\) | ||
0.979069 | − | 0.203527i | \(-0.0652405\pi\) | |||||||
\(348\) | 6.79129i | 0.364051i | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | − | 8.74773i | − | 0.467586i | ||||||
\(351\) | − | 18.9564i | − | 1.01182i | ||||||
\(352\) | − | 0.791288i | − | 0.0421758i | ||||||
\(353\) | 1.58258i | 0.0842320i | 0.999113 | + | 0.0421160i | \(0.0134099\pi\) | ||||
−0.999113 | + | 0.0421160i | \(0.986590\pi\) | |||||||
\(354\) | 2.83485 | 0.150671 | ||||||||
\(355\) | 7.25227i | 0.384911i | ||||||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | 27.1652i | 1.43773i | ||||||||
\(358\) | 1.58258 | 0.0836417 | ||||||||
\(359\) | −8.83485 | −0.466285 | −0.233143 | − | 0.972443i | \(-0.574901\pi\) | ||||
−0.233143 | + | 0.972443i | \(0.574901\pi\) | |||||||
\(360\) | −0.165151 | −0.00870424 | ||||||||
\(361\) | 16.4955 | 0.868182 | ||||||||
\(362\) | 8.74773i | 0.459770i | ||||||||
\(363\) | −18.5826 | −0.975332 | ||||||||
\(364\) | 7.58258i | 0.397435i | ||||||||
\(365\) | 3.46099i | 0.181156i | ||||||||
\(366\) | 22.9129 | 1.19768 | ||||||||
\(367\) | −5.25227 | −0.274166 | −0.137083 | − | 0.990560i | \(-0.543773\pi\) | ||||
−0.137083 | + | 0.990560i | \(0.543773\pi\) | |||||||
\(368\) | 3.79129i | 0.197635i | ||||||||
\(369\) | 2.04356 | 0.106384 | ||||||||
\(370\) | 3.16515 | + | 3.62614i | 0.164548 | + | 0.188514i | ||||
\(371\) | 3.16515 | 0.164326 | ||||||||
\(372\) | − | 15.0000i | − | 0.777714i | ||||||
\(373\) | −12.7477 | −0.660052 | −0.330026 | − | 0.943972i | \(-0.607058\pi\) | ||||
−0.330026 | + | 0.943972i | \(0.607058\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | − | 13.2867i | − | 0.686124i | ||||||
\(376\) | 7.58258i | 0.391041i | ||||||||
\(377\) | 14.3739 | 0.740292 | ||||||||
\(378\) | 10.0000i | 0.514344i | ||||||||
\(379\) | 20.1216 | 1.03358 | 0.516788 | − | 0.856113i | \(-0.327127\pi\) | ||||
0.516788 | + | 0.856113i | \(0.327127\pi\) | |||||||
\(380\) | 1.25227 | 0.0642402 | ||||||||
\(381\) | 14.3303 | 0.734164 | ||||||||
\(382\) | 8.37386 | 0.428444 | ||||||||
\(383\) | 18.3303i | 0.936635i | 0.883560 | + | 0.468317i | \(0.155140\pi\) | ||||
−0.883560 | + | 0.468317i | \(0.844860\pi\) | |||||||
\(384\) | − | 1.79129i | − | 0.0914113i | ||||||
\(385\) | − | 1.25227i | − | 0.0638217i | ||||||
\(386\) | −18.3303 | −0.932988 | ||||||||
\(387\) | 1.25227i | 0.0636566i | ||||||||
\(388\) | − | 13.5826i | − | 0.689551i | ||||||
\(389\) | − | 32.8693i | − | 1.66654i | −0.552866 | − | 0.833270i | \(-0.686466\pi\) | ||
0.552866 | − | 0.833270i | \(-0.313534\pi\) | |||||||
\(390\) | 5.37386i | 0.272116i | ||||||||
\(391\) | 28.7477 | 1.45384 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | − | 30.0000i | − | 1.51330i | ||||||
\(394\) | − | 19.9129i | − | 1.00320i | ||||||
\(395\) | −6.49545 | −0.326822 | ||||||||
\(396\) | 0.165151 | 0.00829917 | ||||||||
\(397\) | 14.7477 | 0.740167 | 0.370084 | − | 0.928998i | \(-0.379329\pi\) | ||||
0.370084 | + | 0.928998i | \(0.379329\pi\) | |||||||
\(398\) | −15.1652 | −0.760160 | ||||||||
\(399\) | 5.66970i | 0.283840i | ||||||||
\(400\) | 4.37386 | 0.218693 | ||||||||
\(401\) | 16.7477i | 0.836342i | 0.908368 | + | 0.418171i | \(0.137329\pi\) | ||||
−0.908368 | + | 0.418171i | \(0.862671\pi\) | |||||||
\(402\) | 11.4174i | 0.569449i | ||||||||
\(403\) | −31.7477 | −1.58147 | ||||||||
\(404\) | −7.58258 | −0.377247 | ||||||||
\(405\) | 7.58258i | 0.376781i | ||||||||
\(406\) | −7.58258 | −0.376317 | ||||||||
\(407\) | −3.16515 | − | 3.62614i | −0.156891 | − | 0.179741i | ||||
\(408\) | −13.5826 | −0.672438 | ||||||||
\(409\) | − | 27.1652i | − | 1.34323i | −0.740900 | − | 0.671615i | \(-0.765601\pi\) | ||
0.740900 | − | 0.671615i | \(-0.234399\pi\) | |||||||
\(410\) | 7.74773 | 0.382633 | ||||||||
\(411\) | −6.49545 | −0.320397 | ||||||||
\(412\) | 6.79129i | 0.334583i | ||||||||
\(413\) | 3.16515i | 0.155747i | ||||||||
\(414\) | −0.791288 | −0.0388897 | ||||||||
\(415\) | − | 12.0000i | − | 0.589057i | ||||||
\(416\) | −3.79129 | −0.185883 | ||||||||
\(417\) | −23.9564 | −1.17315 | ||||||||
\(418\) | −1.25227 | −0.0612507 | ||||||||
\(419\) | 2.20871 | 0.107903 | 0.0539513 | − | 0.998544i | \(-0.482818\pi\) | ||||
0.0539513 | + | 0.998544i | \(0.482818\pi\) | |||||||
\(420\) | − | 2.83485i | − | 0.138326i | ||||||
\(421\) | 18.9564i | 0.923880i | 0.886911 | + | 0.461940i | \(0.152847\pi\) | ||||
−0.886911 | + | 0.461940i | \(0.847153\pi\) | |||||||
\(422\) | 10.3739i | 0.504992i | ||||||||
\(423\) | −1.58258 | −0.0769475 | ||||||||
\(424\) | 1.58258i | 0.0768567i | ||||||||
\(425\) | − | 33.1652i | − | 1.60875i | ||||||
\(426\) | − | 16.4174i | − | 0.795427i | ||||||
\(427\) | 25.5826i | 1.23803i | ||||||||
\(428\) | 5.37386 | 0.259755 | ||||||||
\(429\) | − | 5.37386i | − | 0.259453i | ||||||
\(430\) | 4.74773i | 0.228956i | ||||||||
\(431\) | 8.83485i | 0.425560i | 0.977100 | + | 0.212780i | \(0.0682517\pi\) | ||||
−0.977100 | + | 0.212780i | \(0.931748\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | 10.6261 | 0.510660 | 0.255330 | − | 0.966854i | \(-0.417816\pi\) | ||||
0.255330 | + | 0.966854i | \(0.417816\pi\) | |||||||
\(434\) | 16.7477 | 0.803917 | ||||||||
\(435\) | −5.37386 | −0.257657 | ||||||||
\(436\) | 6.00000i | 0.287348i | ||||||||
\(437\) | 6.00000 | 0.287019 | ||||||||
\(438\) | − | 7.83485i | − | 0.374364i | ||||||
\(439\) | − | 12.6261i | − | 0.602613i | −0.953527 | − | 0.301306i | \(-0.902577\pi\) | ||
0.953527 | − | 0.301306i | \(-0.0974227\pi\) | |||||||
\(440\) | 0.626136 | 0.0298499 | ||||||||
\(441\) | −0.626136 | −0.0298160 | ||||||||
\(442\) | 28.7477i | 1.36739i | ||||||||
\(443\) | 27.9564 | 1.32825 | 0.664125 | − | 0.747621i | \(-0.268804\pi\) | ||||
0.664125 | + | 0.747621i | \(0.268804\pi\) | |||||||
\(444\) | −7.16515 | − | 8.20871i | −0.340043 | − | 0.389568i | ||||
\(445\) | −4.74773 | −0.225064 | ||||||||
\(446\) | 14.0000i | 0.662919i | ||||||||
\(447\) | −7.91288 | −0.374266 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | 2.83485i | 0.133785i | 0.997760 | + | 0.0668924i | \(0.0213084\pi\) | ||||
−0.997760 | + | 0.0668924i | \(0.978692\pi\) | |||||||
\(450\) | 0.912878i | 0.0430335i | ||||||||
\(451\) | −7.74773 | −0.364826 | ||||||||
\(452\) | − | 10.4174i | − | 0.489994i | ||||||
\(453\) | −26.4174 | −1.24120 | ||||||||
\(454\) | −25.9129 | −1.21615 | ||||||||
\(455\) | −6.00000 | −0.281284 | ||||||||
\(456\) | −2.83485 | −0.132754 | ||||||||
\(457\) | 21.4955i | 1.00551i | 0.864428 | + | 0.502757i | \(0.167681\pi\) | ||||
−0.864428 | + | 0.502757i | \(0.832319\pi\) | |||||||
\(458\) | 6.74773i | 0.315301i | ||||||||
\(459\) | 37.9129i | 1.76962i | ||||||||
\(460\) | −3.00000 | −0.139876 | ||||||||
\(461\) | − | 12.3303i | − | 0.574279i | −0.957889 | − | 0.287140i | \(-0.907296\pi\) | ||
0.957889 | − | 0.287140i | \(-0.0927044\pi\) | |||||||
\(462\) | 2.83485i | 0.131889i | ||||||||
\(463\) | − | 29.7042i | − | 1.38047i | −0.723585 | − | 0.690235i | \(-0.757507\pi\) | ||
0.723585 | − | 0.690235i | \(-0.242493\pi\) | |||||||
\(464\) | − | 3.79129i | − | 0.176006i | ||||||
\(465\) | 11.8693 | 0.550426 | ||||||||
\(466\) | − | 16.1216i | − | 0.746818i | ||||||
\(467\) | − | 16.4174i | − | 0.759708i | −0.925046 | − | 0.379854i | \(-0.875974\pi\) | ||
0.925046 | − | 0.379854i | \(-0.124026\pi\) | |||||||
\(468\) | − | 0.791288i | − | 0.0365773i | ||||||
\(469\) | −12.7477 | −0.588635 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | −3.58258 | −0.165076 | ||||||||
\(472\) | −1.58258 | −0.0728440 | ||||||||
\(473\) | − | 4.74773i | − | 0.218301i | ||||||
\(474\) | 14.7042 | 0.675385 | ||||||||
\(475\) | − | 6.92197i | − | 0.317602i | ||||||
\(476\) | − | 15.1652i | − | 0.695094i | ||||||
\(477\) | −0.330303 | −0.0151235 | ||||||||
\(478\) | 2.04356 | 0.0934703 | ||||||||
\(479\) | − | 3.79129i | − | 0.173228i | −0.996242 | − | 0.0866142i | \(-0.972395\pi\) | ||
0.996242 | − | 0.0866142i | \(-0.0276047\pi\) | |||||||
\(480\) | 1.41742 | 0.0646963 | ||||||||
\(481\) | −17.3739 | + | 15.1652i | −0.792180 | + | 0.691471i | ||||
\(482\) | 4.41742 | 0.201208 | ||||||||
\(483\) | − | 13.5826i | − | 0.618029i | ||||||
\(484\) | 10.3739 | 0.471539 | ||||||||
\(485\) | 10.7477 | 0.488029 | ||||||||
\(486\) | − | 2.16515i | − | 0.0982133i | ||||||
\(487\) | − | 36.6606i | − | 1.66125i | −0.556832 | − | 0.830625i | \(-0.687983\pi\) | ||
0.556832 | − | 0.830625i | \(-0.312017\pi\) | |||||||
\(488\) | −12.7913 | −0.579034 | ||||||||
\(489\) | − | 35.0780i | − | 1.58628i | ||||||
\(490\) | −2.37386 | −0.107240 | ||||||||
\(491\) | 5.37386 | 0.242519 | 0.121260 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121260 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(492\) | −17.5390 | −0.790720 | ||||||||
\(493\) | −28.7477 | −1.29473 | ||||||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 0.130682i | 0.00587373i | ||||||||
\(496\) | 8.37386i | 0.375998i | ||||||||
\(497\) | 18.3303 | 0.822226 | ||||||||
\(498\) | 27.1652i | 1.21730i | ||||||||
\(499\) | 10.7477i | 0.481134i | 0.970632 | + | 0.240567i | \(0.0773334\pi\) | ||||
−0.970632 | + | 0.240567i | \(0.922667\pi\) | |||||||
\(500\) | 7.41742i | 0.331717i | ||||||||
\(501\) | 39.3303i | 1.75715i | ||||||||
\(502\) | 4.41742 | 0.197159 | ||||||||
\(503\) | − | 15.6261i | − | 0.696735i | −0.937358 | − | 0.348367i | \(-0.886736\pi\) | ||
0.937358 | − | 0.348367i | \(-0.113264\pi\) | |||||||
\(504\) | 0.417424i | 0.0185936i | ||||||||
\(505\) | − | 6.00000i | − | 0.266996i | ||||||
\(506\) | 3.00000 | 0.133366 | ||||||||
\(507\) | −2.46099 | −0.109296 | ||||||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 4.41742 | 0.195799 | 0.0978994 | − | 0.995196i | \(-0.468788\pi\) | ||||
0.0978994 | + | 0.995196i | \(0.468788\pi\) | |||||||
\(510\) | − | 10.7477i | − | 0.475917i | ||||||
\(511\) | 8.74773 | 0.386977 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 7.91288i | 0.349362i | ||||||||
\(514\) | −4.74773 | −0.209413 | ||||||||
\(515\) | −5.37386 | −0.236801 | ||||||||
\(516\) | − | 10.7477i | − | 0.473142i | ||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 9.16515 | − | 8.00000i | 0.402694 | − | 0.351500i | ||||
\(519\) | 27.1652 | 1.19242 | ||||||||
\(520\) | − | 3.00000i | − | 0.131559i | ||||||
\(521\) | −9.16515 | −0.401533 | −0.200766 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200766 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(522\) | 0.791288 | 0.0346337 | ||||||||
\(523\) | − | 15.1652i | − | 0.663126i | −0.943433 | − | 0.331563i | \(-0.892424\pi\) | ||
0.943433 | − | 0.331563i | \(-0.107576\pi\) | |||||||
\(524\) | 16.7477i | 0.731628i | ||||||||
\(525\) | −15.6697 | −0.683882 | ||||||||
\(526\) | − | 27.1652i | − | 1.18446i | ||||||
\(527\) | 63.4955 | 2.76591 | ||||||||
\(528\) | −1.41742 | −0.0616855 | ||||||||
\(529\) | 8.62614 | 0.375049 | ||||||||
\(530\) | −1.25227 | −0.0543953 | ||||||||
\(531\) | − | 0.330303i | − | 0.0143339i | ||||||
\(532\) | − | 3.16515i | − | 0.137227i | ||||||
\(533\) | 37.1216i | 1.60791i | ||||||||
\(534\) | 10.7477 | 0.465100 | ||||||||
\(535\) | 4.25227i | 0.183842i | ||||||||
\(536\) | − | 6.37386i | − | 0.275309i | ||||||
\(537\) | − | 2.83485i | − | 0.122333i | ||||||
\(538\) | 16.7477i | 0.722046i | ||||||||
\(539\) | 2.37386 | 0.102250 | ||||||||
\(540\) | − | 3.95644i | − | 0.170258i | ||||||
\(541\) | 12.7913i | 0.549940i | 0.961453 | + | 0.274970i | \(0.0886680\pi\) | ||||
−0.961453 | + | 0.274970i | \(0.911332\pi\) | |||||||
\(542\) | 22.0000i | 0.944981i | ||||||||
\(543\) | 15.6697 | 0.672451 | ||||||||
\(544\) | 7.58258 | 0.325100 | ||||||||
\(545\) | −4.74773 | −0.203370 | ||||||||
\(546\) | 13.5826 | 0.581281 | ||||||||
\(547\) | 25.9129i | 1.10795i | 0.832532 | + | 0.553977i | \(0.186891\pi\) | ||||
−0.832532 | + | 0.553977i | \(0.813109\pi\) | |||||||
\(548\) | 3.62614 | 0.154901 | ||||||||
\(549\) | − | 2.66970i | − | 0.113940i | ||||||
\(550\) | − | 3.46099i | − | 0.147577i | ||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 6.79129 | 0.289056 | ||||||||
\(553\) | 16.4174i | 0.698140i | ||||||||
\(554\) | −9.62614 | −0.408975 | ||||||||
\(555\) | 6.49545 | − | 5.66970i | 0.275717 | − | 0.240665i | ||||
\(556\) | 13.3739 | 0.567178 | ||||||||
\(557\) | 8.70417i | 0.368807i | 0.982851 | + | 0.184404i | \(0.0590354\pi\) | ||||
−0.982851 | + | 0.184404i | \(0.940965\pi\) | |||||||
\(558\) | −1.74773 | −0.0739872 | ||||||||
\(559\) | −22.7477 | −0.962126 | ||||||||
\(560\) | 1.58258i | 0.0668760i | ||||||||
\(561\) | 10.7477i | 0.453769i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10.7477i | − | 0.452963i | −0.974016 | − | 0.226481i | \(-0.927278\pi\) | ||
0.974016 | − | 0.226481i | \(-0.0727222\pi\) | |||||||
\(564\) | 13.5826 | 0.571930 | ||||||||
\(565\) | 8.24318 | 0.346793 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | 19.1652 | 0.804861 | ||||||||
\(568\) | 9.16515i | 0.384561i | ||||||||
\(569\) | 45.1652i | 1.89342i | 0.322085 | + | 0.946711i | \(0.395616\pi\) | ||||
−0.322085 | + | 0.946711i | \(0.604384\pi\) | |||||||
\(570\) | − | 2.24318i | − | 0.0939565i | ||||||
\(571\) | −14.6261 | −0.612085 | −0.306042 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306042 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(572\) | 3.00000i | 0.125436i | ||||||||
\(573\) | − | 15.0000i | − | 0.626634i | ||||||
\(574\) | − | 19.5826i | − | 0.817361i | ||||||
\(575\) | 16.5826i | 0.691541i | ||||||||
\(576\) | −0.208712 | −0.00869634 | ||||||||
\(577\) | 13.5826i | 0.565450i | 0.959201 | + | 0.282725i | \(0.0912384\pi\) | ||||
−0.959201 | + | 0.282725i | \(0.908762\pi\) | |||||||
\(578\) | − | 40.4955i | − | 1.68439i | ||||||
\(579\) | 32.8348i | 1.36457i | ||||||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | −30.3303 | −1.25831 | ||||||||
\(582\) | −24.3303 | −1.00852 | ||||||||
\(583\) | 1.25227 | 0.0518638 | ||||||||
\(584\) | 4.37386i | 0.180992i | ||||||||
\(585\) | 0.626136 | 0.0258876 | ||||||||
\(586\) | − | 6.00000i | − | 0.247858i | ||||||
\(587\) | − | 19.9129i | − | 0.821892i | −0.911660 | − | 0.410946i | \(-0.865198\pi\) | ||
0.911660 | − | 0.410946i | \(-0.134802\pi\) | |||||||
\(588\) | 5.37386 | 0.221614 | ||||||||
\(589\) | 13.2523 | 0.546050 | ||||||||
\(590\) | − | 1.25227i | − | 0.0515553i | ||||||
\(591\) | −35.6697 | −1.46726 | ||||||||
\(592\) | 4.00000 | + | 4.58258i | 0.164399 | + | 0.188343i | ||||
\(593\) | −18.7913 | −0.771666 | −0.385833 | − | 0.922569i | \(-0.626086\pi\) | ||||
−0.385833 | + | 0.922569i | \(0.626086\pi\) | |||||||
\(594\) | 3.95644i | 0.162335i | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 4.41742 | 0.180945 | ||||||||
\(597\) | 27.1652i | 1.11180i | ||||||||
\(598\) | − | 14.3739i | − | 0.587791i | ||||||
\(599\) | 8.83485 | 0.360982 | 0.180491 | − | 0.983577i | \(-0.442231\pi\) | ||||
0.180491 | + | 0.983577i | \(0.442231\pi\) | |||||||
\(600\) | − | 7.83485i | − | 0.319856i | ||||||
\(601\) | −33.1216 | −1.35106 | −0.675529 | − | 0.737333i | \(-0.736085\pi\) | ||||
−0.675529 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(602\) | 12.0000 | 0.489083 | ||||||||
\(603\) | 1.33030 | 0.0541741 | ||||||||
\(604\) | 14.7477 | 0.600077 | ||||||||
\(605\) | 8.20871i | 0.333732i | ||||||||
\(606\) | 13.5826i | 0.551754i | ||||||||
\(607\) | − | 26.5390i | − | 1.07719i | −0.842566 | − | 0.538593i | \(-0.818956\pi\) | ||
0.842566 | − | 0.538593i | \(-0.181044\pi\) | |||||||
\(608\) | 1.58258 | 0.0641819 | ||||||||
\(609\) | 13.5826i | 0.550394i | ||||||||
\(610\) | − | 10.1216i | − | 0.409811i | ||||||
\(611\) | − | 28.7477i | − | 1.16301i | ||||||
\(612\) | 1.58258i | 0.0639718i | ||||||||
\(613\) | −49.4955 | −1.99910 | −0.999551 | − | 0.0299539i | \(-0.990464\pi\) | ||||
−0.999551 | + | 0.0299539i | \(0.990464\pi\) | |||||||
\(614\) | 1.37386i | 0.0554446i | ||||||||
\(615\) | − | 13.8784i | − | 0.559631i | ||||||
\(616\) | − | 1.58258i | − | 0.0637638i | ||||||
\(617\) | −23.0436 | −0.927699 | −0.463849 | − | 0.885914i | \(-0.653532\pi\) | ||||
−0.463849 | + | 0.885914i | \(0.653532\pi\) | |||||||
\(618\) | 12.1652 | 0.489354 | ||||||||
\(619\) | −35.1216 | −1.41166 | −0.705828 | − | 0.708383i | \(-0.749425\pi\) | ||||
−0.705828 | + | 0.708383i | \(0.749425\pi\) | |||||||
\(620\) | −6.62614 | −0.266112 | ||||||||
\(621\) | − | 18.9564i | − | 0.760696i | ||||||
\(622\) | −23.3739 | −0.937207 | ||||||||
\(623\) | 12.0000i | 0.480770i | ||||||||
\(624\) | 6.79129i | 0.271869i | ||||||||
\(625\) | 16.0000 | 0.640000 | ||||||||
\(626\) | −14.8348 | −0.592920 | ||||||||
\(627\) | 2.24318i | 0.0895840i | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | 34.7477 | − | 30.3303i | 1.38548 | − | 1.20935i | ||||
\(630\) | −0.330303 | −0.0131596 | ||||||||
\(631\) | − | 18.9564i | − | 0.754644i | −0.926082 | − | 0.377322i | \(-0.876845\pi\) | ||
0.926082 | − | 0.377322i | \(-0.123155\pi\) | |||||||
\(632\) | −8.20871 | −0.326525 | ||||||||
\(633\) | 18.5826 | 0.738591 | ||||||||
\(634\) | − | 28.7477i | − | 1.14172i | ||||||
\(635\) | − | 6.33030i | − | 0.251210i | ||||||
\(636\) | 2.83485 | 0.112409 | ||||||||
\(637\) | − | 11.3739i | − | 0.450649i | ||||||
\(638\) | −3.00000 | −0.118771 | ||||||||
\(639\) | −1.91288 | −0.0756723 | ||||||||
\(640\) | −0.791288 | −0.0312784 | ||||||||
\(641\) | −3.46099 | −0.136701 | −0.0683503 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683503 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(642\) | − | 9.62614i | − | 0.379913i | ||||||
\(643\) | 39.4955i | 1.55755i | 0.627304 | + | 0.778774i | \(0.284158\pi\) | ||||
−0.627304 | + | 0.778774i | \(0.715842\pi\) | |||||||
\(644\) | 7.58258i | 0.298795i | ||||||||
\(645\) | 8.50455 | 0.334866 | ||||||||
\(646\) | − | 12.0000i | − | 0.472134i | ||||||
\(647\) | − | 17.7042i | − | 0.696023i | −0.937490 | − | 0.348011i | \(-0.886857\pi\) | ||
0.937490 | − | 0.348011i | \(-0.113143\pi\) | |||||||
\(648\) | 9.58258i | 0.376439i | ||||||||
\(649\) | 1.25227i | 0.0491560i | ||||||||
\(650\) | −16.5826 | −0.650422 | ||||||||
\(651\) | − | 30.0000i | − | 1.17579i | ||||||
\(652\) | 19.5826i | 0.766913i | ||||||||
\(653\) | − | 0.626136i | − | 0.0245026i | −0.999925 | − | 0.0122513i | \(-0.996100\pi\) | ||
0.999925 | − | 0.0122513i | \(-0.00389981\pi\) | |||||||
\(654\) | 10.7477 | 0.420269 | ||||||||
\(655\) | −13.2523 | −0.517809 | ||||||||
\(656\) | 9.79129 | 0.382286 | ||||||||
\(657\) | −0.912878 | −0.0356148 | ||||||||
\(658\) | 15.1652i | 0.591199i | ||||||||
\(659\) | 11.0436 | 0.430196 | 0.215098 | − | 0.976592i | \(-0.430993\pi\) | ||||
0.215098 | + | 0.976592i | \(0.430993\pi\) | |||||||
\(660\) | − | 1.12159i | − | 0.0436579i | ||||||
\(661\) | − | 32.2087i | − | 1.25277i | −0.779512 | − | 0.626387i | \(-0.784533\pi\) | ||
0.779512 | − | 0.626387i | \(-0.215467\pi\) | |||||||
\(662\) | −25.5826 | −0.994295 | ||||||||
\(663\) | 51.4955 | 1.99992 | ||||||||
\(664\) | − | 15.1652i | − | 0.588522i | ||||||
\(665\) | 2.50455 | 0.0971221 | ||||||||
\(666\) | −0.956439 | + | 0.834849i | −0.0370613 | + | 0.0323497i | ||||
\(667\) | 14.3739 | 0.556558 | ||||||||
\(668\) | − | 21.9564i | − | 0.849520i | ||||||
\(669\) | 25.0780 | 0.969573 | ||||||||
\(670\) | 5.04356 | 0.194850 | ||||||||
\(671\) | 10.1216i | 0.390740i | ||||||||
\(672\) | − | 3.58258i | − | 0.138201i | ||||||
\(673\) | −36.1216 | −1.39238 | −0.696192 | − | 0.717855i | \(-0.745124\pi\) | ||||
−0.696192 | + | 0.717855i | \(0.745124\pi\) | |||||||
\(674\) | 33.1216i | 1.27580i | ||||||||
\(675\) | −21.8693 | −0.841750 | ||||||||
\(676\) | 1.37386 | 0.0528409 | ||||||||
\(677\) | 9.16515 | 0.352245 | 0.176123 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176123 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(678\) | −18.6606 | −0.716656 | ||||||||
\(679\) | − | 27.1652i | − | 1.04250i | ||||||
\(680\) | 6.00000i | 0.230089i | ||||||||
\(681\) | 46.4174i | 1.77872i | ||||||||
\(682\) | 6.62614 | 0.253728 | ||||||||
\(683\) | 31.5826i | 1.20847i | 0.796805 | + | 0.604237i | \(0.206522\pi\) | ||||
−0.796805 | + | 0.604237i | \(0.793478\pi\) | |||||||
\(684\) | 0.330303i | 0.0126294i | ||||||||
\(685\) | 2.86932i | 0.109631i | ||||||||
\(686\) | 20.0000i | 0.763604i | ||||||||
\(687\) | 12.0871 | 0.461152 | ||||||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | − | 6.00000i | − | 0.228582i | ||||||
\(690\) | 5.37386i | 0.204579i | ||||||||
\(691\) | 25.4955 | 0.969893 | 0.484946 | − | 0.874544i | \(-0.338839\pi\) | ||||
0.484946 | + | 0.874544i | \(0.338839\pi\) | |||||||
\(692\) | −15.1652 | −0.576493 | ||||||||
\(693\) | 0.330303 | 0.0125472 | ||||||||
\(694\) | 7.58258 | 0.287831 | ||||||||
\(695\) | 10.5826i | 0.401420i | ||||||||
\(696\) | −6.79129 | −0.257423 | ||||||||
\(697\) | − | 74.2432i | − | 2.81216i | ||||||
\(698\) | 10.0000i | 0.378506i | ||||||||
\(699\) | −28.8784 | −1.09228 | ||||||||
\(700\) | 8.74773 | 0.330633 | ||||||||
\(701\) | − | 3.95644i | − | 0.149433i | −0.997205 | − | 0.0747163i | \(-0.976195\pi\) | ||
0.997205 | − | 0.0747163i | \(-0.0238051\pi\) | |||||||
\(702\) | 18.9564 | 0.715465 | ||||||||
\(703\) | 7.25227 | − | 6.33030i | 0.273525 | − | 0.238752i | ||||
\(704\) | 0.791288 | 0.0298228 | ||||||||
\(705\) | 10.7477i | 0.404783i | ||||||||
\(706\) | −1.58258 | −0.0595610 | ||||||||
\(707\) | −15.1652 | −0.570344 | ||||||||
\(708\) | 2.83485i | 0.106540i | ||||||||
\(709\) | − | 23.2087i | − | 0.871621i | −0.900038 | − | 0.435811i | \(-0.856462\pi\) | ||
0.900038 | − | 0.435811i | \(-0.143538\pi\) | |||||||
\(710\) | −7.25227 | −0.272173 | ||||||||
\(711\) | − | 1.71326i | − | 0.0642522i | ||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | −31.7477 | −1.18896 | ||||||||
\(714\) | −27.1652 | −1.01663 | ||||||||
\(715\) | −2.37386 | −0.0887775 | ||||||||
\(716\) | 1.58258i | 0.0591436i | ||||||||
\(717\) | − | 3.66061i | − | 0.136708i | ||||||
\(718\) | − | 8.83485i | − | 0.329714i | ||||||
\(719\) | −21.1652 | −0.789327 | −0.394663 | − | 0.918826i | \(-0.629139\pi\) | ||||
−0.394663 | + | 0.918826i | \(0.629139\pi\) | |||||||
\(720\) | − | 0.165151i | − | 0.00615483i | ||||||
\(721\) | 13.5826i | 0.505842i | ||||||||
\(722\) | 16.4955i | 0.613897i | ||||||||
\(723\) | − | 7.91288i | − | 0.294283i | ||||||
\(724\) | −8.74773 | −0.325107 | ||||||||
\(725\) | − | 16.5826i | − | 0.615861i | ||||||
\(726\) | − | 18.5826i | − | 0.689664i | ||||||
\(727\) | 13.1216i | 0.486653i | 0.969944 | + | 0.243326i | \(0.0782386\pi\) | ||||
−0.969944 | + | 0.243326i | \(0.921761\pi\) | |||||||
\(728\) | −7.58258 | −0.281029 | ||||||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | −3.46099 | −0.128097 | ||||||||
\(731\) | 45.4955 | 1.68271 | ||||||||
\(732\) | 22.9129i | 0.846884i | ||||||||
\(733\) | 47.4955 | 1.75428 | 0.877142 | − | 0.480231i | \(-0.159447\pi\) | ||||
0.877142 | + | 0.480231i | \(0.159447\pi\) | |||||||
\(734\) | − | 5.25227i | − | 0.193865i | ||||||
\(735\) | 4.25227i | 0.156847i | ||||||||
\(736\) | −3.79129 | −0.139749 | ||||||||
\(737\) | −5.04356 | −0.185782 | ||||||||
\(738\) | 2.04356i | 0.0752245i | ||||||||
\(739\) | −35.1216 | −1.29197 | −0.645984 | − | 0.763351i | \(-0.723553\pi\) | ||||
−0.645984 | + | 0.763351i | \(0.723553\pi\) | |||||||
\(740\) | −3.62614 | + | 3.16515i | −0.133299 | + | 0.116353i | ||||
\(741\) | 10.7477 | 0.394828 | ||||||||
\(742\) | 3.16515i | 0.116196i | ||||||||
\(743\) | 15.1652 | 0.556355 | 0.278178 | − | 0.960530i | \(-0.410270\pi\) | ||||
0.278178 | + | 0.960530i | \(0.410270\pi\) | |||||||
\(744\) | 15.0000 | 0.549927 | ||||||||
\(745\) | 3.49545i | 0.128064i | ||||||||
\(746\) | − | 12.7477i | − | 0.466727i | ||||||
\(747\) | 3.16515 | 0.115807 | ||||||||
\(748\) | − | 6.00000i | − | 0.219382i | ||||||
\(749\) | 10.7477 | 0.392713 | ||||||||
\(750\) | 13.2867 | 0.485163 | ||||||||
\(751\) | −41.4955 | −1.51419 | −0.757095 | − | 0.653304i | \(-0.773382\pi\) | ||||
−0.757095 | + | 0.653304i | \(0.773382\pi\) | |||||||
\(752\) | −7.58258 | −0.276508 | ||||||||
\(753\) | − | 7.91288i | − | 0.288361i | ||||||
\(754\) | 14.3739i | 0.523465i | ||||||||
\(755\) | 11.6697i | 0.424704i | ||||||||
\(756\) | −10.0000 | −0.363696 | ||||||||
\(757\) | 35.2087i | 1.27968i | 0.768507 | + | 0.639841i | \(0.221000\pi\) | ||||
−0.768507 | + | 0.639841i | \(0.779000\pi\) | |||||||
\(758\) | 20.1216i | 0.730849i | ||||||||
\(759\) | − | 5.37386i | − | 0.195059i | ||||||
\(760\) | 1.25227i | 0.0454247i | ||||||||
\(761\) | 14.2087 | 0.515065 | 0.257533 | − | 0.966270i | \(-0.417090\pi\) | ||||
0.257533 | + | 0.966270i | \(0.417090\pi\) | |||||||
\(762\) | 14.3303i | 0.519132i | ||||||||
\(763\) | 12.0000i | 0.434429i | ||||||||
\(764\) | 8.37386i | 0.302956i | ||||||||
\(765\) | −1.25227 | −0.0452760 | ||||||||
\(766\) | −18.3303 | −0.662301 | ||||||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | 1.79129 | 0.0646375 | ||||||||
\(769\) | 11.6697i | 0.420820i | 0.977613 | + | 0.210410i | \(0.0674799\pi\) | ||||
−0.977613 | + | 0.210410i | \(0.932520\pi\) | |||||||
\(770\) | 1.25227 | 0.0451288 | ||||||||
\(771\) | 8.50455i | 0.306284i | ||||||||
\(772\) | − | 18.3303i | − | 0.659722i | ||||||
\(773\) | 31.9129 | 1.14783 | 0.573913 | − | 0.818916i | \(-0.305425\pi\) | ||||
0.573913 | + | 0.818916i | \(0.305425\pi\) | |||||||
\(774\) | −1.25227 | −0.0450120 | ||||||||
\(775\) | 36.6261i | 1.31565i | ||||||||
\(776\) | 13.5826 | 0.487586 | ||||||||
\(777\) | −14.3303 | − | 16.4174i | −0.514097 | − | 0.588972i | ||||
\(778\) | 32.8693 | 1.17842 | ||||||||
\(779\) | − | 15.4955i | − | 0.555182i | ||||||
\(780\) | −5.37386 | −0.192415 | ||||||||
\(781\) | 7.25227 | 0.259507 | ||||||||
\(782\) | 28.7477i | 1.02802i | ||||||||
\(783\) | 18.9564i | 0.677448i | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 1.58258i | 0.0564845i | ||||||||
\(786\) | 30.0000 | 1.07006 | ||||||||
\(787\) | 8.00000 | 0.285169 | 0.142585 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142585 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(788\) | 19.9129 | 0.709367 | ||||||||
\(789\) | −48.6606 | −1.73236 | ||||||||
\(790\) | − | 6.49545i | − | 0.231098i | ||||||
\(791\) | − | 20.8348i | − | 0.740802i | ||||||
\(792\) | 0.165151i | 0.00586840i | ||||||||
\(793\) | 48.4955 | 1.72212 | ||||||||
\(794\) | 14.7477i | 0.523377i | ||||||||
\(795\) | 2.24318i | 0.0795574i | ||||||||
\(796\) | − | 15.1652i | − | 0.537515i | ||||||
\(797\) | − | 35.3739i | − | 1.25301i | −0.779419 | − | 0.626503i | \(-0.784486\pi\) | ||
0.779419 | − | 0.626503i | \(-0.215514\pi\) | |||||||
\(798\) | −5.66970 | −0.200705 | ||||||||
\(799\) | 57.4955i | 2.03404i | ||||||||
\(800\) | 4.37386i | 0.154639i | ||||||||
\(801\) | − | 1.25227i | − | 0.0442469i | ||||||
\(802\) | −16.7477 | −0.591383 | ||||||||
\(803\) | 3.46099 | 0.122136 | ||||||||
\(804\) | −11.4174 | −0.402662 | ||||||||
\(805\) | −6.00000 | −0.211472 | ||||||||
\(806\) | − | 31.7477i | − | 1.11827i | ||||||
\(807\) | 30.0000 | 1.05605 | ||||||||
\(808\) | − | 7.58258i | − | 0.266754i | ||||||
\(809\) | 53.0780i | 1.86612i | 0.359715 | + | 0.933062i | \(0.382874\pi\) | ||||
−0.359715 | + | 0.933062i | \(0.617126\pi\) | |||||||
\(810\) | −7.58258 | −0.266425 | ||||||||
\(811\) | −19.8693 | −0.697706 | −0.348853 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348853 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(812\) | − | 7.58258i | − | 0.266096i | ||||||
\(813\) | 39.4083 | 1.38211 | ||||||||
\(814\) | 3.62614 | − | 3.16515i | 0.127096 | − | 0.110938i | ||||
\(815\) | −15.4955 | −0.542782 | ||||||||
\(816\) | − | 13.5826i | − | 0.475485i | ||||||
\(817\) | 9.49545 | 0.332204 | ||||||||
\(818\) | 27.1652 | 0.949807 | ||||||||
\(819\) | − | 1.58258i | − | 0.0552997i | ||||||
\(820\) | 7.74773i | 0.270562i | ||||||||
\(821\) | 3.16515 | 0.110465 | 0.0552323 | − | 0.998474i | \(-0.482410\pi\) | ||||
0.0552323 | + | 0.998474i | \(0.482410\pi\) | |||||||
\(822\) | − | 6.49545i | − | 0.226555i | ||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −6.79129 | −0.236586 | ||||||||
\(825\) | −6.19962 | −0.215843 | ||||||||
\(826\) | −3.16515 | −0.110130 | ||||||||
\(827\) | − | 33.1652i | − | 1.15327i | −0.817004 | − | 0.576633i | \(-0.804366\pi\) | ||
0.817004 | − | 0.576633i | \(-0.195634\pi\) | |||||||
\(828\) | − | 0.791288i | − | 0.0274992i | ||||||
\(829\) | − | 17.0436i | − | 0.591947i | −0.955196 | − | 0.295974i | \(-0.904356\pi\) | ||
0.955196 | − | 0.295974i | \(-0.0956441\pi\) | |||||||
\(830\) | 12.0000 | 0.416526 | ||||||||
\(831\) | 17.2432i | 0.598159i | ||||||||
\(832\) | − | 3.79129i | − | 0.131439i | ||||||
\(833\) | 22.7477i | 0.788162i | ||||||||
\(834\) | − | 23.9564i | − | 0.829544i | ||||||
\(835\) | 17.3739 | 0.601247 | ||||||||
\(836\) | − | 1.25227i | − | 0.0433108i | ||||||
\(837\) | − | 41.8693i | − | 1.44722i | ||||||
\(838\) | 2.20871i | 0.0762987i | ||||||||
\(839\) | 3.49545 | 0.120676 | 0.0603382 | − | 0.998178i | \(-0.480782\pi\) | ||||
0.0603382 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(840\) | 2.83485 | 0.0978116 | ||||||||
\(841\) | 14.6261 | 0.504350 | ||||||||
\(842\) | −18.9564 | −0.653282 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.3739 | −0.357083 | ||||||||
\(845\) | 1.08712i | 0.0373981i | ||||||||
\(846\) | − | 1.58258i | − | 0.0544101i | ||||||
\(847\) | 20.7477 | 0.712900 | ||||||||
\(848\) | −1.58258 | −0.0543459 | ||||||||
\(849\) | − | 42.9909i | − | 1.47544i | ||||||
\(850\) | 33.1652 | 1.13756 | ||||||||
\(851\) | −17.3739 | + | 15.1652i | −0.595568 | + | 0.519855i | ||||
\(852\) | 16.4174 | 0.562452 | ||||||||
\(853\) | − | 44.7042i | − | 1.53064i | −0.643649 | − | 0.765321i | \(-0.722580\pi\) | ||
0.643649 | − | 0.765321i | \(-0.277420\pi\) | |||||||
\(854\) | −25.5826 | −0.875418 | ||||||||
\(855\) | −0.261365 | −0.00893848 | ||||||||
\(856\) | 5.37386i | 0.183675i | ||||||||
\(857\) | − | 33.1652i | − | 1.13290i | −0.824096 | − | 0.566450i | \(-0.808316\pi\) | ||
0.824096 | − | 0.566450i | \(-0.191684\pi\) | |||||||
\(858\) | 5.37386 | 0.183461 | ||||||||
\(859\) | 18.6606i | 0.636692i | 0.947975 | + | 0.318346i | \(0.103127\pi\) | ||||
−0.947975 | + | 0.318346i | \(0.896873\pi\) | |||||||
\(860\) | −4.74773 | −0.161896 | ||||||||
\(861\) | −35.0780 | −1.19546 | ||||||||
\(862\) | −8.83485 | −0.300916 | ||||||||
\(863\) | −19.2523 | −0.655355 | −0.327677 | − | 0.944790i | \(-0.606266\pi\) | ||||
−0.327677 | + | 0.944790i | \(0.606266\pi\) | |||||||
\(864\) | − | 5.00000i | − | 0.170103i | ||||||
\(865\) | − | 12.0000i | − | 0.408012i | ||||||
\(866\) | 10.6261i | 0.361091i | ||||||||
\(867\) | −72.5390 | −2.46355 | ||||||||
\(868\) | 16.7477i | 0.568455i | ||||||||
\(869\) | 6.49545i | 0.220343i | ||||||||
\(870\) | − | 5.37386i | − | 0.182191i | ||||||
\(871\) | 24.1652i | 0.818805i | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 2.83485i | 0.0959451i | ||||||||
\(874\) | 6.00000i | 0.202953i | ||||||||
\(875\) | 14.8348i | 0.501509i | ||||||||
\(876\) | 7.83485 | 0.264715 | ||||||||
\(877\) | 11.2523 | 0.379962 | 0.189981 | − | 0.981788i | \(-0.439157\pi\) | ||||
0.189981 | + | 0.981788i | \(0.439157\pi\) | |||||||
\(878\) | 12.6261 | 0.426111 | ||||||||
\(879\) | −10.7477 | −0.362512 | ||||||||
\(880\) | 0.626136i | 0.0211071i | ||||||||
\(881\) | −13.1216 | −0.442078 | −0.221039 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221039 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(882\) | − | 0.626136i | − | 0.0210831i | ||||||
\(883\) | − | 31.9129i | − | 1.07395i | −0.843597 | − | 0.536977i | \(-0.819566\pi\) | ||
0.843597 | − | 0.536977i | \(-0.180434\pi\) | |||||||
\(884\) | −28.7477 | −0.966891 | ||||||||
\(885\) | −2.24318 | −0.0754037 | ||||||||
\(886\) | 27.9564i | 0.939215i | ||||||||
\(887\) | −57.8258 | −1.94160 | −0.970799 | − | 0.239893i | \(-0.922888\pi\) | ||||
−0.970799 | + | 0.239893i | \(0.922888\pi\) | |||||||
\(888\) | 8.20871 | − | 7.16515i | 0.275466 | − | 0.240447i | ||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | − | 4.74773i | − | 0.159144i | ||||||
\(891\) | 7.58258 | 0.254026 | ||||||||
\(892\) | −14.0000 | −0.468755 | ||||||||
\(893\) | 12.0000i | 0.401565i | ||||||||
\(894\) | − | 7.91288i | − | 0.264646i | ||||||
\(895\) | −1.25227 | −0.0418589 | ||||||||
\(896\) | 2.00000i | 0.0668153i | ||||||||
\(897\) | −25.7477 | −0.859692 | ||||||||
\(898\) | −2.83485 | −0.0946001 | ||||||||
\(899\) | 31.7477 | 1.05885 | ||||||||
\(900\) | −0.912878 | −0.0304293 | ||||||||
\(901\) | 12.0000i | 0.399778i | ||||||||
\(902\) | − | 7.74773i | − | 0.257971i | ||||||
\(903\) | − | 21.4955i | − | 0.715324i | ||||||
\(904\) | 10.4174 | 0.346478 | ||||||||
\(905\) | − | 6.92197i | − | 0.230094i | ||||||
\(906\) | − | 26.4174i | − | 0.877660i | ||||||
\(907\) | 30.3303i | 1.00710i | 0.863966 | + | 0.503551i | \(0.167973\pi\) | ||||
−0.863966 | + | 0.503551i | \(0.832027\pi\) | |||||||
\(908\) | − | 25.9129i | − | 0.859949i | ||||||
\(909\) | 1.58258 | 0.0524907 | ||||||||
\(910\) | − | 6.00000i | − | 0.198898i | ||||||
\(911\) | − | 17.6697i | − | 0.585423i | −0.956201 | − | 0.292712i | \(-0.905442\pi\) | ||
0.956201 | − | 0.292712i | \(-0.0945576\pi\) | |||||||
\(912\) | − | 2.83485i | − | 0.0938712i | ||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | −21.4955 | −0.711006 | ||||||||
\(915\) | −18.1307 | −0.599382 | ||||||||
\(916\) | −6.74773 | −0.222951 | ||||||||
\(917\) | 33.4955i | 1.10612i | ||||||||
\(918\) | −37.9129 | −1.25131 | ||||||||
\(919\) | − | 36.0000i | − | 1.18753i | −0.804638 | − | 0.593765i | \(-0.797641\pi\) | ||
0.804638 | − | 0.593765i | \(-0.202359\pi\) | |||||||
\(920\) | − | 3.00000i | − | 0.0989071i | ||||||
\(921\) | 2.46099 | 0.0810922 | ||||||||
\(922\) | 12.3303 | 0.406077 | ||||||||
\(923\) | − | 34.7477i | − | 1.14374i | ||||||
\(924\) | −2.83485 | −0.0932597 | ||||||||
\(925\) | 17.4955 | + | 20.0436i | 0.575247 | + | 0.659028i | ||||
\(926\) | 29.7042 | 0.976139 | ||||||||
\(927\) | − | 1.41742i | − | 0.0465543i | ||||||
\(928\) | 3.79129 | 0.124455 | ||||||||
\(929\) | 8.37386 | 0.274738 | 0.137369 | − | 0.990520i | \(-0.456135\pi\) | ||||
0.137369 | + | 0.990520i | \(0.456135\pi\) | |||||||
\(930\) | 11.8693i | 0.389210i | ||||||||
\(931\) | 4.74773i | 0.155600i | ||||||||
\(932\) | 16.1216 | 0.528080 | ||||||||
\(933\) | 41.8693i | 1.37074i | ||||||||
\(934\) | 16.4174 | 0.537195 | ||||||||
\(935\) | 4.74773 | 0.155267 | ||||||||
\(936\) | 0.791288 | 0.0258641 | ||||||||
\(937\) | 34.8693 | 1.13913 | 0.569565 | − | 0.821946i | \(-0.307111\pi\) | ||||
0.569565 | + | 0.821946i | \(0.307111\pi\) | |||||||
\(938\) | − | 12.7477i | − | 0.416228i | ||||||
\(939\) | 26.5735i | 0.867193i | ||||||||
\(940\) | − | 6.00000i | − | 0.195698i | ||||||
\(941\) | −21.4955 | −0.700732 | −0.350366 | − | 0.936613i | \(-0.613943\pi\) | ||||
−0.350366 | + | 0.936613i | \(0.613943\pi\) | |||||||
\(942\) | − | 3.58258i | − | 0.116727i | ||||||
\(943\) | 37.1216i | 1.20885i | ||||||||
\(944\) | − | 1.58258i | − | 0.0515085i | ||||||
\(945\) | − | 7.91288i | − | 0.257406i | ||||||
\(946\) | 4.74773 | 0.154362 | ||||||||
\(947\) | 1.25227i | 0.0406934i | 0.999793 | + | 0.0203467i | \(0.00647700\pi\) | ||||
−0.999793 | + | 0.0203467i | \(0.993523\pi\) | |||||||
\(948\) | 14.7042i | 0.477569i | ||||||||
\(949\) | − | 16.5826i | − | 0.538293i | ||||||
\(950\) | 6.92197 | 0.224578 | ||||||||
\(951\) | −51.4955 | −1.66985 | ||||||||
\(952\) | 15.1652 | 0.491505 | ||||||||
\(953\) | 31.4519 | 1.01883 | 0.509413 | − | 0.860522i | \(-0.329862\pi\) | ||||
0.509413 | + | 0.860522i | \(0.329862\pi\) | |||||||
\(954\) | − | 0.330303i | − | 0.0106939i | ||||||
\(955\) | −6.62614 | −0.214417 | ||||||||
\(956\) | 2.04356i | 0.0660935i | ||||||||
\(957\) | 5.37386i | 0.173712i | ||||||||
\(958\) | 3.79129 | 0.122491 | ||||||||
\(959\) | 7.25227 | 0.234188 | ||||||||
\(960\) | 1.41742i | 0.0457472i | ||||||||
\(961\) | −39.1216 | −1.26199 | ||||||||
\(962\) | −15.1652 | − | 17.3739i | −0.488944 | − | 0.560156i | ||||
\(963\) | −1.12159 | −0.0361428 | ||||||||
\(964\) | 4.41742i | 0.142276i | ||||||||
\(965\) | 14.5045 | 0.466918 | ||||||||
\(966\) | 13.5826 | 0.437012 | ||||||||
\(967\) | 21.9564i | 0.706071i | 0.935610 | + | 0.353036i | \(0.114851\pi\) | ||||
−0.935610 | + | 0.353036i | \(0.885149\pi\) | |||||||
\(968\) | 10.3739i | 0.333429i | ||||||||
\(969\) | −21.4955 | −0.690533 | ||||||||
\(970\) | 10.7477i | 0.345089i | ||||||||
\(971\) | 50.3739 | 1.61657 | 0.808287 | − | 0.588789i | \(-0.200395\pi\) | ||||
0.808287 | + | 0.588789i | \(0.200395\pi\) | |||||||
\(972\) | 2.16515 | 0.0694473 | ||||||||
\(973\) | 26.7477 | 0.857493 | ||||||||
\(974\) | 36.6606 | 1.17468 | ||||||||
\(975\) | 29.7042i | 0.951295i | ||||||||
\(976\) | − | 12.7913i | − | 0.409439i | ||||||
\(977\) | − | 41.0780i | − | 1.31420i | −0.753802 | − | 0.657101i | \(-0.771782\pi\) | ||
0.753802 | − | 0.657101i | \(-0.228218\pi\) | |||||||
\(978\) | 35.0780 | 1.12167 | ||||||||
\(979\) | 4.74773i | 0.151738i | ||||||||
\(980\) | − | 2.37386i | − | 0.0758303i | ||||||
\(981\) | − | 1.25227i | − | 0.0399820i | ||||||
\(982\) | 5.37386i | 0.171487i | ||||||||
\(983\) | −18.3303 | −0.584646 | −0.292323 | − | 0.956320i | \(-0.594428\pi\) | ||||
−0.292323 | + | 0.956320i | \(0.594428\pi\) | |||||||
\(984\) | − | 17.5390i | − | 0.559123i | ||||||
\(985\) | 15.7568i | 0.502054i | ||||||||
\(986\) | − | 28.7477i | − | 0.915514i | ||||||
\(987\) | 27.1652 | 0.864676 | ||||||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | −22.7477 | −0.723336 | ||||||||
\(990\) | −0.130682 | −0.00415336 | ||||||||
\(991\) | − | 18.9564i | − | 0.602171i | −0.953597 | − | 0.301086i | \(-0.902651\pi\) | ||
0.953597 | − | 0.301086i | \(-0.0973490\pi\) | |||||||
\(992\) | −8.37386 | −0.265870 | ||||||||
\(993\) | 45.8258i | 1.45424i | ||||||||
\(994\) | 18.3303i | 0.581402i | ||||||||
\(995\) | 12.0000 | 0.380426 | ||||||||
\(996\) | −27.1652 | −0.860761 | ||||||||
\(997\) | 18.0000i | 0.570066i | 0.958518 | + | 0.285033i | \(0.0920045\pi\) | ||||
−0.958518 | + | 0.285033i | \(0.907995\pi\) | |||||||
\(998\) | −10.7477 | −0.340213 | ||||||||
\(999\) | −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.73.4 | yes | 4 | |
3.2 | odd | 2 | 666.2.c.b.73.2 | 4 | |||
4.3 | odd | 2 | 592.2.g.c.369.1 | 4 | |||
5.2 | odd | 4 | 1850.2.c.g.1849.2 | 4 | |||
5.3 | odd | 4 | 1850.2.c.h.1849.3 | 4 | |||
5.4 | even | 2 | 1850.2.d.e.1701.1 | 4 | |||
8.3 | odd | 2 | 2368.2.g.h.961.4 | 4 | |||
8.5 | even | 2 | 2368.2.g.j.961.2 | 4 | |||
12.11 | even | 2 | 5328.2.h.m.2737.3 | 4 | |||
37.6 | odd | 4 | 2738.2.a.k.1.1 | 2 | |||
37.31 | odd | 4 | 2738.2.a.h.1.1 | 2 | |||
37.36 | even | 2 | inner | 74.2.b.a.73.2 | ✓ | 4 | |
111.110 | odd | 2 | 666.2.c.b.73.3 | 4 | |||
148.147 | odd | 2 | 592.2.g.c.369.2 | 4 | |||
185.73 | odd | 4 | 1850.2.c.g.1849.3 | 4 | |||
185.147 | odd | 4 | 1850.2.c.h.1849.2 | 4 | |||
185.184 | even | 2 | 1850.2.d.e.1701.3 | 4 | |||
296.147 | odd | 2 | 2368.2.g.h.961.3 | 4 | |||
296.221 | even | 2 | 2368.2.g.j.961.1 | 4 | |||
444.443 | even | 2 | 5328.2.h.m.2737.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.b.a.73.2 | ✓ | 4 | 37.36 | even | 2 | inner | |
74.2.b.a.73.4 | yes | 4 | 1.1 | even | 1 | trivial | |
592.2.g.c.369.1 | 4 | 4.3 | odd | 2 | |||
592.2.g.c.369.2 | 4 | 148.147 | odd | 2 | |||
666.2.c.b.73.2 | 4 | 3.2 | odd | 2 | |||
666.2.c.b.73.3 | 4 | 111.110 | odd | 2 | |||
1850.2.c.g.1849.2 | 4 | 5.2 | odd | 4 | |||
1850.2.c.g.1849.3 | 4 | 185.73 | odd | 4 | |||
1850.2.c.h.1849.2 | 4 | 185.147 | odd | 4 | |||
1850.2.c.h.1849.3 | 4 | 5.3 | odd | 4 | |||
1850.2.d.e.1701.1 | 4 | 5.4 | even | 2 | |||
1850.2.d.e.1701.3 | 4 | 185.184 | even | 2 | |||
2368.2.g.h.961.3 | 4 | 296.147 | odd | 2 | |||
2368.2.g.h.961.4 | 4 | 8.3 | odd | 2 | |||
2368.2.g.j.961.1 | 4 | 296.221 | even | 2 | |||
2368.2.g.j.961.2 | 4 | 8.5 | even | 2 | |||
2738.2.a.h.1.1 | 2 | 37.31 | odd | 4 | |||
2738.2.a.k.1.1 | 2 | 37.6 | odd | 4 | |||
5328.2.h.m.2737.2 | 4 | 444.443 | even | 2 | |||
5328.2.h.m.2737.3 | 4 | 12.11 | even | 2 |