Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(1849,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.c (of order \(2\), degree \(1\), not 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: | \(14.7723243739\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.3 | ||
Root | \(1.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.1849 |
Dual form | 1850.2.c.g.1849.2 |
$q$-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 \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.79129i | 1.03420i | 0.855925 | + | 0.517100i | \(0.172989\pi\) | ||||
−0.855925 | + | 0.517100i | \(0.827011\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.79129i | − | 0.731290i | ||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.208712 | −0.0695707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.791288 | −0.238582 | −0.119291 | − | 0.992859i | \(-0.538062\pi\) | ||||
−0.119291 | + | 0.992859i | \(0.538062\pi\) | |||||||
\(12\) | 1.79129i | 0.517100i | ||||||||
\(13\) | 3.79129 | 1.05151 | 0.525757 | − | 0.850635i | \(-0.323782\pi\) | ||||
0.525757 | + | 0.850635i | \(0.323782\pi\) | |||||||
\(14\) | − | 2.00000i | − | 0.534522i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.58258 | 1.83904 | 0.919522 | − | 0.393038i | \(-0.128576\pi\) | ||||
0.919522 | + | 0.393038i | \(0.128576\pi\) | |||||||
\(18\) | 0.208712 | 0.0491939 | ||||||||
\(19\) | − | 1.58258i | − | 0.363068i | −0.983385 | − | 0.181534i | \(-0.941894\pi\) | ||
0.983385 | − | 0.181534i | \(-0.0581062\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.58258 | −0.781782 | ||||||||
\(22\) | 0.791288 | 0.168703 | ||||||||
\(23\) | 3.79129 | 0.790538 | 0.395269 | − | 0.918565i | \(-0.370651\pi\) | ||||
0.395269 | + | 0.918565i | \(0.370651\pi\) | |||||||
\(24\) | − | 1.79129i | − | 0.365645i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.79129 | −0.743533 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | − | 3.79129i | − | 0.704024i | −0.935995 | − | 0.352012i | \(-0.885498\pi\) | ||
0.935995 | − | 0.352012i | \(-0.114502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.37386i | − | 1.50399i | −0.659169 | − | 0.751995i | \(-0.729092\pi\) | ||
0.659169 | − | 0.751995i | \(-0.270908\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | − | 1.41742i | − | 0.246742i | ||||||
\(34\) | −7.58258 | −1.30040 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.208712 | −0.0347854 | ||||||||
\(37\) | −4.58258 | − | 4.00000i | −0.753371 | − | 0.657596i | ||||
\(38\) | 1.58258i | 0.256728i | ||||||||
\(39\) | 6.79129i | 1.08748i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.79129 | 1.52914 | 0.764571 | − | 0.644539i | \(-0.222951\pi\) | ||||
0.764571 | + | 0.644539i | \(0.222951\pi\) | |||||||
\(42\) | 3.58258 | 0.552803 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | −0.791288 | −0.119291 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.79129 | −0.558995 | ||||||||
\(47\) | 7.58258i | 1.10603i | 0.833171 | + | 0.553016i | \(0.186523\pi\) | ||||
−0.833171 | + | 0.553016i | \(0.813477\pi\) | |||||||
\(48\) | 1.79129i | 0.258550i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.5826i | 1.90194i | ||||||||
\(52\) | 3.79129 | 0.525757 | ||||||||
\(53\) | − | 1.58258i | − | 0.217383i | −0.994076 | − | 0.108692i | \(-0.965334\pi\) | ||
0.994076 | − | 0.108692i | \(-0.0346661\pi\) | |||||||
\(54\) | − | 5.00000i | − | 0.680414i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 2.00000i | − | 0.267261i | ||||||
\(57\) | 2.83485 | 0.375485 | ||||||||
\(58\) | 3.79129i | 0.497820i | ||||||||
\(59\) | − | 1.58258i | − | 0.206034i | −0.994680 | − | 0.103017i | \(-0.967150\pi\) | ||
0.994680 | − | 0.103017i | \(-0.0328496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7913i | 1.63776i | 0.573967 | + | 0.818878i | \(0.305404\pi\) | ||||
−0.573967 | + | 0.818878i | \(0.694596\pi\) | |||||||
\(62\) | 8.37386i | 1.06348i | ||||||||
\(63\) | − | 0.417424i | − | 0.0525905i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.41742i | 0.174473i | ||||||||
\(67\) | − | 6.37386i | − | 0.778691i | −0.921092 | − | 0.389346i | \(-0.872701\pi\) | ||
0.921092 | − | 0.389346i | \(-0.127299\pi\) | |||||||
\(68\) | 7.58258 | 0.919522 | ||||||||
\(69\) | 6.79129i | 0.817575i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.16515 | −1.08770 | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(72\) | 0.208712 | 0.0245970 | ||||||||
\(73\) | − | 4.37386i | − | 0.511922i | −0.966687 | − | 0.255961i | \(-0.917608\pi\) | ||
0.966687 | − | 0.255961i | \(-0.0823919\pi\) | |||||||
\(74\) | 4.58258 | + | 4.00000i | 0.532714 | + | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.58258i | − | 0.181534i | ||||||
\(77\) | − | 1.58258i | − | 0.180351i | ||||||
\(78\) | − | 6.79129i | − | 0.768962i | ||||||
\(79\) | − | 8.20871i | − | 0.923552i | −0.886997 | − | 0.461776i | \(-0.847212\pi\) | ||
0.886997 | − | 0.461776i | \(-0.152788\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.58258 | −1.06473 | ||||||||
\(82\) | −9.79129 | −1.08127 | ||||||||
\(83\) | 15.1652i | 1.66459i | 0.554332 | + | 0.832296i | \(0.312974\pi\) | ||||
−0.554332 | + | 0.832296i | \(0.687026\pi\) | |||||||
\(84\) | −3.58258 | −0.390891 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | 6.79129 | 0.728102 | ||||||||
\(88\) | 0.791288 | 0.0843516 | ||||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.58258i | 0.794870i | ||||||||
\(92\) | 3.79129 | 0.395269 | ||||||||
\(93\) | 15.0000 | 1.55543 | ||||||||
\(94\) | − | 7.58258i | − | 0.782083i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.79129i | − | 0.182823i | ||||||
\(97\) | −13.5826 | −1.37910 | −0.689551 | − | 0.724237i | \(-0.742192\pi\) | ||||
−0.689551 | + | 0.724237i | \(0.742192\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0.165151 | 0.0165983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.58258 | 0.754494 | 0.377247 | − | 0.926113i | \(-0.376871\pi\) | ||||
0.377247 | + | 0.926113i | \(0.376871\pi\) | |||||||
\(102\) | − | 13.5826i | − | 1.34488i | ||||||
\(103\) | −6.79129 | −0.669165 | −0.334583 | − | 0.942366i | \(-0.608595\pi\) | ||||
−0.334583 | + | 0.942366i | \(0.608595\pi\) | |||||||
\(104\) | −3.79129 | −0.371766 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.58258i | 0.153713i | ||||||||
\(107\) | 5.37386i | 0.519511i | 0.965674 | + | 0.259755i | \(0.0836420\pi\) | ||||
−0.965674 | + | 0.259755i | \(0.916358\pi\) | |||||||
\(108\) | 5.00000i | 0.481125i | ||||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.16515 | − | 8.20871i | 0.680086 | − | 0.779136i | ||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 10.4174 | 0.979989 | 0.489994 | − | 0.871726i | \(-0.336999\pi\) | ||||
0.489994 | + | 0.871726i | \(0.336999\pi\) | |||||||
\(114\) | −2.83485 | −0.265508 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.79129i | − | 0.352012i | ||||||
\(117\) | −0.791288 | −0.0731546 | ||||||||
\(118\) | 1.58258i | 0.145688i | ||||||||
\(119\) | 15.1652i | 1.39019i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3739 | −0.943079 | ||||||||
\(122\) | − | 12.7913i | − | 1.15807i | ||||||
\(123\) | 17.5390i | 1.58144i | ||||||||
\(124\) | − | 8.37386i | − | 0.751995i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.417424i | 0.0371871i | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.7477i | 0.946285i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.7477i | 1.46326i | 0.681704 | + | 0.731628i | \(0.261239\pi\) | ||||
−0.681704 | + | 0.731628i | \(0.738761\pi\) | |||||||
\(132\) | − | 1.41742i | − | 0.123371i | ||||||
\(133\) | 3.16515 | 0.274453 | ||||||||
\(134\) | 6.37386i | 0.550618i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.58258 | −0.650201 | ||||||||
\(137\) | 3.62614i | 0.309802i | 0.987930 | + | 0.154901i | \(0.0495058\pi\) | ||||
−0.987930 | + | 0.154901i | \(0.950494\pi\) | |||||||
\(138\) | − | 6.79129i | − | 0.578113i | ||||||
\(139\) | 13.3739 | 1.13436 | 0.567178 | − | 0.823595i | \(-0.308035\pi\) | ||||
0.567178 | + | 0.823595i | \(0.308035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5826 | −1.14386 | ||||||||
\(142\) | 9.16515 | 0.769122 | ||||||||
\(143\) | −3.00000 | −0.250873 | ||||||||
\(144\) | −0.208712 | −0.0173927 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.37386i | 0.361984i | ||||||||
\(147\) | 5.37386i | 0.443229i | ||||||||
\(148\) | −4.58258 | − | 4.00000i | −0.376685 | − | 0.328798i | ||||
\(149\) | 4.41742 | 0.361889 | 0.180945 | − | 0.983493i | \(-0.442084\pi\) | ||||
0.180945 | + | 0.983493i | \(0.442084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7477 | −1.20015 | −0.600077 | − | 0.799943i | \(-0.704863\pi\) | ||||
−0.600077 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(152\) | 1.58258i | 0.128364i | ||||||||
\(153\) | −1.58258 | −0.127944 | ||||||||
\(154\) | 1.58258i | 0.127528i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.79129i | 0.543738i | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 8.20871i | 0.653050i | ||||||||
\(159\) | 2.83485 | 0.224818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.58258i | 0.597591i | ||||||||
\(162\) | 9.58258 | 0.752878 | ||||||||
\(163\) | −19.5826 | −1.53383 | −0.766913 | − | 0.641751i | \(-0.778208\pi\) | ||||
−0.766913 | + | 0.641751i | \(0.778208\pi\) | |||||||
\(164\) | 9.79129 | 0.764571 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 15.1652i | − | 1.17704i | ||||||
\(167\) | −21.9564 | −1.69904 | −0.849520 | − | 0.527556i | \(-0.823108\pi\) | ||||
−0.849520 | + | 0.527556i | \(0.823108\pi\) | |||||||
\(168\) | 3.58258 | 0.276402 | ||||||||
\(169\) | 1.37386 | 0.105682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.330303i | 0.0252589i | ||||||||
\(172\) | 6.00000 | 0.457496 | ||||||||
\(173\) | 15.1652i | 1.15299i | 0.817102 | + | 0.576493i | \(0.195579\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(174\) | −6.79129 | −0.514846 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.791288 | −0.0596456 | ||||||||
\(177\) | 2.83485 | 0.213080 | ||||||||
\(178\) | 6.00000i | 0.449719i | ||||||||
\(179\) | − | 1.58258i | − | 0.118287i | −0.998249 | − | 0.0591436i | \(-0.981163\pi\) | ||
0.998249 | − | 0.0591436i | \(-0.0188370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.74773 | 0.650213 | 0.325107 | − | 0.945677i | \(-0.394600\pi\) | ||||
0.325107 | + | 0.945677i | \(0.394600\pi\) | |||||||
\(182\) | − | 7.58258i | − | 0.562058i | ||||||
\(183\) | −22.9129 | −1.69377 | ||||||||
\(184\) | −3.79129 | −0.279497 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.0000 | −1.09985 | ||||||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | 7.58258i | 0.553016i | ||||||||
\(189\) | −10.0000 | −0.727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.37386i | 0.605912i | 0.953005 | + | 0.302956i | \(0.0979734\pi\) | ||||
−0.953005 | + | 0.302956i | \(0.902027\pi\) | |||||||
\(192\) | 1.79129i | 0.129275i | ||||||||
\(193\) | 18.3303 | 1.31944 | 0.659722 | − | 0.751510i | \(-0.270674\pi\) | ||||
0.659722 | + | 0.751510i | \(0.270674\pi\) | |||||||
\(194\) | 13.5826 | 0.975172 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 19.9129i | 1.41873i | 0.704839 | + | 0.709367i | \(0.251019\pi\) | ||||
−0.704839 | + | 0.709367i | \(0.748981\pi\) | |||||||
\(198\) | −0.165151 | −0.0117368 | ||||||||
\(199\) | 15.1652i | 1.07503i | 0.843254 | + | 0.537515i | \(0.180637\pi\) | ||||
−0.843254 | + | 0.537515i | \(0.819363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4174 | 0.805323 | ||||||||
\(202\) | −7.58258 | −0.533508 | ||||||||
\(203\) | 7.58258 | 0.532192 | ||||||||
\(204\) | 13.5826i | 0.950971i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.79129 | 0.473171 | ||||||||
\(207\) | −0.791288 | −0.0549983 | ||||||||
\(208\) | 3.79129 | 0.262879 | ||||||||
\(209\) | 1.25227i | 0.0866215i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3739 | 0.714166 | 0.357083 | − | 0.934073i | \(-0.383771\pi\) | ||||
0.357083 | + | 0.934073i | \(0.383771\pi\) | |||||||
\(212\) | − | 1.58258i | − | 0.108692i | ||||||
\(213\) | − | 16.4174i | − | 1.12490i | ||||||
\(214\) | − | 5.37386i | − | 0.367350i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.00000i | − | 0.340207i | ||||||
\(217\) | 16.7477 | 1.13691 | ||||||||
\(218\) | 6.00000i | 0.406371i | ||||||||
\(219\) | 7.83485 | 0.529430 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.7477 | 1.93378 | ||||||||
\(222\) | −7.16515 | + | 8.20871i | −0.480893 | + | 0.550933i | ||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | − | 2.00000i | − | 0.133631i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4174 | −0.692957 | ||||||||
\(227\) | −25.9129 | −1.71990 | −0.859949 | − | 0.510380i | \(-0.829505\pi\) | ||||
−0.859949 | + | 0.510380i | \(0.829505\pi\) | |||||||
\(228\) | 2.83485 | 0.187742 | ||||||||
\(229\) | −6.74773 | −0.445902 | −0.222951 | − | 0.974830i | \(-0.571569\pi\) | ||||
−0.222951 | + | 0.974830i | \(0.571569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.83485 | 0.186519 | ||||||||
\(232\) | 3.79129i | 0.248910i | ||||||||
\(233\) | − | 16.1216i | − | 1.05616i | −0.849194 | − | 0.528080i | \(-0.822912\pi\) | ||
0.849194 | − | 0.528080i | \(-0.177088\pi\) | |||||||
\(234\) | 0.791288 | 0.0517281 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.58258i | − | 0.103017i | ||||||
\(237\) | 14.7042 | 0.955138 | ||||||||
\(238\) | − | 15.1652i | − | 0.983011i | ||||||
\(239\) | − | 2.04356i | − | 0.132187i | −0.997813 | − | 0.0660935i | \(-0.978946\pi\) | ||
0.997813 | − | 0.0660935i | \(-0.0210536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.41742i | 0.284551i | 0.989827 | + | 0.142276i | \(0.0454419\pi\) | ||||
−0.989827 | + | 0.142276i | \(0.954558\pi\) | |||||||
\(242\) | 10.3739 | 0.666857 | ||||||||
\(243\) | − | 2.16515i | − | 0.138895i | ||||||
\(244\) | 12.7913i | 0.818878i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 17.5390i | − | 1.11825i | ||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 8.37386i | 0.531741i | ||||||||
\(249\) | −27.1652 | −1.72152 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.41742i | 0.278825i | 0.990234 | + | 0.139413i | \(0.0445215\pi\) | ||||
−0.990234 | + | 0.139413i | \(0.955479\pi\) | |||||||
\(252\) | − | 0.417424i | − | 0.0262953i | ||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 8.00000i | 0.501965i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.74773 | −0.296155 | −0.148078 | − | 0.988976i | \(-0.547309\pi\) | ||||
−0.148078 | + | 0.988976i | \(0.547309\pi\) | |||||||
\(258\) | − | 10.7477i | − | 0.669124i | ||||||
\(259\) | 8.00000 | − | 9.16515i | 0.497096 | − | 0.569495i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.791288i | 0.0489795i | ||||||||
\(262\) | − | 16.7477i | − | 1.03468i | ||||||
\(263\) | − | 27.1652i | − | 1.67507i | −0.546380 | − | 0.837537i | \(-0.683994\pi\) | ||
0.546380 | − | 0.837537i | \(-0.316006\pi\) | |||||||
\(264\) | 1.41742i | 0.0872364i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.16515 | −0.194068 | ||||||||
\(267\) | 10.7477 | 0.657750 | ||||||||
\(268\) | − | 6.37386i | − | 0.389346i | ||||||
\(269\) | −16.7477 | −1.02113 | −0.510563 | − | 0.859840i | \(-0.670563\pi\) | ||||
−0.510563 | + | 0.859840i | \(0.670563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | 7.58258 | 0.459761 | ||||||||
\(273\) | −13.5826 | −0.822055 | ||||||||
\(274\) | − | 3.62614i | − | 0.219063i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.79129i | 0.408787i | ||||||||
\(277\) | −9.62614 | −0.578378 | −0.289189 | − | 0.957272i | \(-0.593386\pi\) | ||||
−0.289189 | + | 0.957272i | \(0.593386\pi\) | |||||||
\(278\) | −13.3739 | −0.802111 | ||||||||
\(279\) | 1.74773i | 0.104634i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 13.5826 | 0.808831 | ||||||||
\(283\) | −24.0000 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(284\) | −9.16515 | −0.543852 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 19.5826i | 1.15592i | ||||||||
\(288\) | 0.208712 | 0.0122985 | ||||||||
\(289\) | 40.4955 | 2.38209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 24.3303i | − | 1.42627i | ||||||
\(292\) | − | 4.37386i | − | 0.255961i | ||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | − | 5.37386i | − | 0.313410i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.58258 | + | 4.00000i | 0.266357 | + | 0.232495i | ||||
\(297\) | − | 3.95644i | − | 0.229576i | ||||||
\(298\) | −4.41742 | −0.255895 | ||||||||
\(299\) | 14.3739 | 0.831262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000i | 0.691669i | ||||||||
\(302\) | 14.7477 | 0.848636 | ||||||||
\(303\) | 13.5826i | 0.780299i | ||||||||
\(304\) | − | 1.58258i | − | 0.0907669i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.58258 | 0.0904698 | ||||||||
\(307\) | − | 1.37386i | − | 0.0784105i | −0.999231 | − | 0.0392053i | \(-0.987517\pi\) | ||
0.999231 | − | 0.0392053i | \(-0.0124826\pi\) | |||||||
\(308\) | − | 1.58258i | − | 0.0901756i | ||||||
\(309\) | − | 12.1652i | − | 0.692051i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.3739i | − | 1.32541i | −0.748880 | − | 0.662705i | \(-0.769408\pi\) | ||
0.748880 | − | 0.662705i | \(-0.230592\pi\) | |||||||
\(312\) | − | 6.79129i | − | 0.384481i | ||||||
\(313\) | 14.8348 | 0.838515 | 0.419258 | − | 0.907867i | \(-0.362290\pi\) | ||||
0.419258 | + | 0.907867i | \(0.362290\pi\) | |||||||
\(314\) | − | 2.00000i | − | 0.112867i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.20871i | − | 0.461776i | ||||||
\(317\) | 28.7477i | 1.61463i | 0.590119 | + | 0.807317i | \(0.299081\pi\) | ||||
−0.590119 | + | 0.807317i | \(0.700919\pi\) | |||||||
\(318\) | −2.83485 | −0.158970 | ||||||||
\(319\) | 3.00000i | 0.167968i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.62614 | −0.537279 | ||||||||
\(322\) | − | 7.58258i | − | 0.422560i | ||||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | −9.58258 | −0.532365 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.5826 | 1.08458 | ||||||||
\(327\) | 10.7477 | 0.594351 | ||||||||
\(328\) | −9.79129 | −0.540633 | ||||||||
\(329\) | −15.1652 | −0.836082 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 25.5826i | − | 1.40615i | −0.711118 | − | 0.703073i | \(-0.751811\pi\) | ||
0.711118 | − | 0.703073i | \(-0.248189\pi\) | |||||||
\(332\) | 15.1652i | 0.832296i | ||||||||
\(333\) | 0.956439 | + | 0.834849i | 0.0524125 | + | 0.0457494i | ||||
\(334\) | 21.9564 | 1.20140 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.58258 | −0.195446 | ||||||||
\(337\) | − | 33.1216i | − | 1.80425i | −0.431477 | − | 0.902124i | \(-0.642007\pi\) | ||
0.431477 | − | 0.902124i | \(-0.357993\pi\) | |||||||
\(338\) | −1.37386 | −0.0747283 | ||||||||
\(339\) | 18.6606i | 1.01350i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.62614i | 0.358825i | ||||||||
\(342\) | − | 0.330303i | − | 0.0178607i | ||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.1652i | − | 0.815284i | ||||||
\(347\) | 7.58258 | 0.407054 | 0.203527 | − | 0.979069i | \(-0.434760\pi\) | ||||
0.203527 | + | 0.979069i | \(0.434760\pi\) | |||||||
\(348\) | 6.79129 | 0.364051 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9564i | 1.01182i | ||||||||
\(352\) | 0.791288 | 0.0421758 | ||||||||
\(353\) | 1.58258 | 0.0842320 | 0.0421160 | − | 0.999113i | \(-0.486590\pi\) | ||||
0.0421160 | + | 0.999113i | \(0.486590\pi\) | |||||||
\(354\) | −2.83485 | −0.150671 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.00000i | − | 0.317999i | ||||||
\(357\) | −27.1652 | −1.43773 | ||||||||
\(358\) | 1.58258i | 0.0836417i | ||||||||
\(359\) | 8.83485 | 0.466285 | 0.233143 | − | 0.972443i | \(-0.425099\pi\) | ||||
0.233143 | + | 0.972443i | \(0.425099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4955 | 0.868182 | ||||||||
\(362\) | −8.74773 | −0.459770 | ||||||||
\(363\) | − | 18.5826i | − | 0.975332i | ||||||
\(364\) | 7.58258i | 0.397435i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 22.9129 | 1.19768 | ||||||||
\(367\) | 5.25227i | 0.274166i | 0.990560 | + | 0.137083i | \(0.0437728\pi\) | ||||
−0.990560 | + | 0.137083i | \(0.956227\pi\) | |||||||
\(368\) | 3.79129 | 0.197635 | ||||||||
\(369\) | −2.04356 | −0.106384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16515 | 0.164326 | ||||||||
\(372\) | 15.0000 | 0.777714 | ||||||||
\(373\) | − | 12.7477i | − | 0.660052i | −0.943972 | − | 0.330026i | \(-0.892942\pi\) | ||
0.943972 | − | 0.330026i | \(-0.107058\pi\) | |||||||
\(374\) | 6.00000 | 0.310253 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.58258i | − | 0.391041i | ||||||
\(377\) | − | 14.3739i | − | 0.740292i | ||||||
\(378\) | 10.0000 | 0.514344 | ||||||||
\(379\) | −20.1216 | −1.03358 | −0.516788 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516788 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3303 | 0.734164 | ||||||||
\(382\) | − | 8.37386i | − | 0.428444i | ||||||
\(383\) | 18.3303 | 0.936635 | 0.468317 | − | 0.883560i | \(-0.344860\pi\) | ||||
0.468317 | + | 0.883560i | \(0.344860\pi\) | |||||||
\(384\) | − | 1.79129i | − | 0.0914113i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.3303 | −0.932988 | ||||||||
\(387\) | −1.25227 | −0.0636566 | ||||||||
\(388\) | −13.5826 | −0.689551 | ||||||||
\(389\) | − | 32.8693i | − | 1.66654i | −0.552866 | − | 0.833270i | \(-0.686466\pi\) | ||
0.552866 | − | 0.833270i | \(-0.313534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.7477 | 1.45384 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | −30.0000 | −1.51330 | ||||||||
\(394\) | − | 19.9129i | − | 1.00320i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.165151 | 0.00829917 | ||||||||
\(397\) | − | 14.7477i | − | 0.740167i | −0.928998 | − | 0.370084i | \(-0.879329\pi\) | ||
0.928998 | − | 0.370084i | \(-0.120671\pi\) | |||||||
\(398\) | − | 15.1652i | − | 0.760160i | ||||||
\(399\) | 5.66970i | 0.283840i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.7477i | − | 0.836342i | −0.908368 | − | 0.418171i | \(-0.862671\pi\) | ||
0.908368 | − | 0.418171i | \(-0.137329\pi\) | |||||||
\(402\) | −11.4174 | −0.569449 | ||||||||
\(403\) | − | 31.7477i | − | 1.58147i | ||||||
\(404\) | 7.58258 | 0.377247 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.58258 | −0.376317 | ||||||||
\(407\) | 3.62614 | + | 3.16515i | 0.179741 | + | 0.156891i | ||||
\(408\) | − | 13.5826i | − | 0.672438i | ||||||
\(409\) | − | 27.1652i | − | 1.34323i | −0.740900 | − | 0.671615i | \(-0.765601\pi\) | ||
0.740900 | − | 0.671615i | \(-0.234399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.49545 | −0.320397 | ||||||||
\(412\) | −6.79129 | −0.334583 | ||||||||
\(413\) | 3.16515 | 0.155747 | ||||||||
\(414\) | 0.791288 | 0.0388897 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.79129 | −0.185883 | ||||||||
\(417\) | 23.9564i | 1.17315i | ||||||||
\(418\) | − | 1.25227i | − | 0.0612507i | ||||||
\(419\) | −2.20871 | −0.107903 | −0.0539513 | − | 0.998544i | \(-0.517182\pi\) | ||||
−0.0539513 | + | 0.998544i | \(0.517182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.9564i | − | 0.923880i | −0.886911 | − | 0.461940i | \(-0.847153\pi\) | ||
0.886911 | − | 0.461940i | \(-0.152847\pi\) | |||||||
\(422\) | −10.3739 | −0.504992 | ||||||||
\(423\) | − | 1.58258i | − | 0.0769475i | ||||||
\(424\) | 1.58258i | 0.0768567i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.4174i | 0.795427i | ||||||||
\(427\) | −25.5826 | −1.23803 | ||||||||
\(428\) | 5.37386i | 0.259755i | ||||||||
\(429\) | − | 5.37386i | − | 0.259453i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.83485i | − | 0.425560i | −0.977100 | − | 0.212780i | \(-0.931748\pi\) | ||
0.977100 | − | 0.212780i | \(-0.0682517\pi\) | |||||||
\(432\) | 5.00000i | 0.240563i | ||||||||
\(433\) | 10.6261i | 0.510660i | 0.966854 | + | 0.255330i | \(0.0821840\pi\) | ||||
−0.966854 | + | 0.255330i | \(0.917816\pi\) | |||||||
\(434\) | −16.7477 | −0.803917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 6.00000i | − | 0.287348i | ||||||
\(437\) | − | 6.00000i | − | 0.287019i | ||||||
\(438\) | −7.83485 | −0.374364 | ||||||||
\(439\) | − | 12.6261i | − | 0.602613i | −0.953527 | − | 0.301306i | \(-0.902577\pi\) | ||
0.953527 | − | 0.301306i | \(-0.0974227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.626136 | −0.0298160 | ||||||||
\(442\) | −28.7477 | −1.36739 | ||||||||
\(443\) | 27.9564i | 1.32825i | 0.747621 | + | 0.664125i | \(0.231196\pi\) | ||||
−0.747621 | + | 0.664125i | \(0.768804\pi\) | |||||||
\(444\) | 7.16515 | − | 8.20871i | 0.340043 | − | 0.389568i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 14.0000i | − | 0.662919i | ||||||
\(447\) | 7.91288i | 0.374266i | ||||||||
\(448\) | 2.00000i | 0.0944911i | ||||||||
\(449\) | 2.83485i | 0.133785i | 0.997760 | + | 0.0668924i | \(0.0213084\pi\) | ||||
−0.997760 | + | 0.0668924i | \(0.978692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.74773 | −0.364826 | ||||||||
\(452\) | 10.4174 | 0.489994 | ||||||||
\(453\) | − | 26.4174i | − | 1.24120i | ||||||
\(454\) | 25.9129 | 1.21615 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.83485 | −0.132754 | ||||||||
\(457\) | −21.4955 | −1.00551 | −0.502757 | − | 0.864428i | \(-0.667681\pi\) | ||||
−0.502757 | + | 0.864428i | \(0.667681\pi\) | |||||||
\(458\) | 6.74773 | 0.315301 | ||||||||
\(459\) | 37.9129i | 1.76962i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3303i | 0.574279i | 0.957889 | + | 0.287140i | \(0.0927044\pi\) | ||||
−0.957889 | + | 0.287140i | \(0.907296\pi\) | |||||||
\(462\) | −2.83485 | −0.131889 | ||||||||
\(463\) | −29.7042 | −1.38047 | −0.690235 | − | 0.723585i | \(-0.742493\pi\) | ||||
−0.690235 | + | 0.723585i | \(0.742493\pi\) | |||||||
\(464\) | − | 3.79129i | − | 0.176006i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.1216i | 0.746818i | ||||||||
\(467\) | 16.4174 | 0.759708 | 0.379854 | − | 0.925046i | \(-0.375974\pi\) | ||||
0.379854 | + | 0.925046i | \(0.375974\pi\) | |||||||
\(468\) | −0.791288 | −0.0365773 | ||||||||
\(469\) | 12.7477 | 0.588635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.58258 | −0.165076 | ||||||||
\(472\) | 1.58258i | 0.0728440i | ||||||||
\(473\) | −4.74773 | −0.218301 | ||||||||
\(474\) | −14.7042 | −0.675385 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.1652i | 0.695094i | ||||||||
\(477\) | 0.330303i | 0.0151235i | ||||||||
\(478\) | 2.04356i | 0.0934703i | ||||||||
\(479\) | − | 3.79129i | − | 0.173228i | −0.996242 | − | 0.0866142i | \(-0.972395\pi\) | ||
0.996242 | − | 0.0866142i | \(-0.0276047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3739 | − | 15.1652i | −0.792180 | − | 0.691471i | ||||
\(482\) | − | 4.41742i | − | 0.201208i | ||||||
\(483\) | −13.5826 | −0.618029 | ||||||||
\(484\) | −10.3739 | −0.471539 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.16515i | 0.0982133i | ||||||||
\(487\) | 36.6606 | 1.66125 | 0.830625 | − | 0.556832i | \(-0.187983\pi\) | ||||
0.830625 | + | 0.556832i | \(0.187983\pi\) | |||||||
\(488\) | − | 12.7913i | − | 0.579034i | ||||||
\(489\) | − | 35.0780i | − | 1.58628i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.37386 | 0.242519 | 0.121260 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121260 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(492\) | 17.5390i | 0.790720i | ||||||||
\(493\) | − | 28.7477i | − | 1.29473i | ||||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.37386i | − | 0.375998i | ||||||
\(497\) | − | 18.3303i | − | 0.822226i | ||||||
\(498\) | 27.1652 | 1.21730 | ||||||||
\(499\) | 10.7477i | 0.481134i | 0.970632 | + | 0.240567i | \(0.0773334\pi\) | ||||
−0.970632 | + | 0.240567i | \(0.922667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 39.3303i | − | 1.75715i | ||||||
\(502\) | − | 4.41742i | − | 0.197159i | ||||||
\(503\) | −15.6261 | −0.696735 | −0.348367 | − | 0.937358i | \(-0.613264\pi\) | ||||
−0.348367 | + | 0.937358i | \(0.613264\pi\) | |||||||
\(504\) | 0.417424i | 0.0185936i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | 0.133366 | ||||||||
\(507\) | 2.46099i | 0.109296i | ||||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | −4.41742 | −0.195799 | −0.0978994 | − | 0.995196i | \(-0.531212\pi\) | ||||
−0.0978994 | + | 0.995196i | \(0.531212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.74773 | 0.386977 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.91288 | 0.349362 | ||||||||
\(514\) | 4.74773 | 0.209413 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.7477i | 0.473142i | ||||||||
\(517\) | − | 6.00000i | − | 0.263880i | ||||||
\(518\) | −8.00000 | + | 9.16515i | −0.351500 | + | 0.402694i | ||||
\(519\) | −27.1652 | −1.19242 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.16515 | −0.401533 | −0.200766 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200766 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(522\) | − | 0.791288i | − | 0.0346337i | ||||||
\(523\) | −15.1652 | −0.663126 | −0.331563 | − | 0.943433i | \(-0.607576\pi\) | ||||
−0.331563 | + | 0.943433i | \(0.607576\pi\) | |||||||
\(524\) | 16.7477i | 0.731628i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.1652i | 1.18446i | ||||||||
\(527\) | − | 63.4955i | − | 2.76591i | ||||||
\(528\) | − | 1.41742i | − | 0.0616855i | ||||||
\(529\) | −8.62614 | −0.375049 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.330303i | 0.0143339i | ||||||||
\(532\) | 3.16515 | 0.137227 | ||||||||
\(533\) | 37.1216 | 1.60791 | ||||||||
\(534\) | −10.7477 | −0.465100 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.37386i | 0.275309i | ||||||||
\(537\) | 2.83485 | 0.122333 | ||||||||
\(538\) | 16.7477 | 0.722046 | ||||||||
\(539\) | −2.37386 | −0.102250 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.7913i | − | 0.549940i | −0.961453 | − | 0.274970i | \(-0.911332\pi\) | ||
0.961453 | − | 0.274970i | \(-0.0886680\pi\) | |||||||
\(542\) | −22.0000 | −0.944981 | ||||||||
\(543\) | 15.6697i | 0.672451i | ||||||||
\(544\) | −7.58258 | −0.325100 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.5826 | 0.581281 | ||||||||
\(547\) | −25.9129 | −1.10795 | −0.553977 | − | 0.832532i | \(-0.686891\pi\) | ||||
−0.553977 | + | 0.832532i | \(0.686891\pi\) | |||||||
\(548\) | 3.62614i | 0.154901i | ||||||||
\(549\) | − | 2.66970i | − | 0.113940i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | − | 6.79129i | − | 0.289056i | ||||||
\(553\) | 16.4174 | 0.698140 | ||||||||
\(554\) | 9.62614 | 0.408975 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.3739 | 0.567178 | ||||||||
\(557\) | −8.70417 | −0.368807 | −0.184404 | − | 0.982851i | \(-0.559035\pi\) | ||||
−0.184404 | + | 0.982851i | \(0.559035\pi\) | |||||||
\(558\) | − | 1.74773i | − | 0.0739872i | ||||||
\(559\) | 22.7477 | 0.962126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 10.7477i | − | 0.453769i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.7477 | −0.452963 | −0.226481 | − | 0.974016i | \(-0.572722\pi\) | ||||
−0.226481 | + | 0.974016i | \(0.572722\pi\) | |||||||
\(564\) | −13.5826 | −0.571930 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | − | 19.1652i | − | 0.804861i | ||||||
\(568\) | 9.16515 | 0.384561 | ||||||||
\(569\) | 45.1652i | 1.89342i | 0.322085 | + | 0.946711i | \(0.395616\pi\) | ||||
−0.322085 | + | 0.946711i | \(0.604384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6261 | −0.612085 | −0.306042 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306042 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(572\) | −3.00000 | −0.125436 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | − | 19.5826i | − | 0.817361i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.208712 | −0.00869634 | ||||||||
\(577\) | −13.5826 | −0.565450 | −0.282725 | − | 0.959201i | \(-0.591238\pi\) | ||||
−0.282725 | + | 0.959201i | \(0.591238\pi\) | |||||||
\(578\) | −40.4955 | −1.68439 | ||||||||
\(579\) | 32.8348i | 1.36457i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.3303 | −1.25831 | ||||||||
\(582\) | 24.3303i | 1.00852i | ||||||||
\(583\) | 1.25227i | 0.0518638i | ||||||||
\(584\) | 4.37386i | 0.180992i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000i | 0.247858i | ||||||||
\(587\) | 19.9129 | 0.821892 | 0.410946 | − | 0.911660i | \(-0.365198\pi\) | ||||
0.410946 | + | 0.911660i | \(0.365198\pi\) | |||||||
\(588\) | 5.37386i | 0.221614i | ||||||||
\(589\) | −13.2523 | −0.546050 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.6697 | −1.46726 | ||||||||
\(592\) | −4.58258 | − | 4.00000i | −0.188343 | − | 0.164399i | ||||
\(593\) | − | 18.7913i | − | 0.771666i | −0.922569 | − | 0.385833i | \(-0.873914\pi\) | ||
0.922569 | − | 0.385833i | \(-0.126086\pi\) | |||||||
\(594\) | 3.95644i | 0.162335i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.41742 | 0.180945 | ||||||||
\(597\) | −27.1652 | −1.11180 | ||||||||
\(598\) | −14.3739 | −0.587791 | ||||||||
\(599\) | −8.83485 | −0.360982 | −0.180491 | − | 0.983577i | \(-0.557769\pi\) | ||||
−0.180491 | + | 0.983577i | \(0.557769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.1216 | −1.35106 | −0.675529 | − | 0.737333i | \(-0.736085\pi\) | ||||
−0.675529 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(602\) | − | 12.0000i | − | 0.489083i | ||||||
\(603\) | 1.33030i | 0.0541741i | ||||||||
\(604\) | −14.7477 | −0.600077 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 13.5826i | − | 0.551754i | ||||||
\(607\) | 26.5390 | 1.07719 | 0.538593 | − | 0.842566i | \(-0.318956\pi\) | ||||
0.538593 | + | 0.842566i | \(0.318956\pi\) | |||||||
\(608\) | 1.58258i | 0.0641819i | ||||||||
\(609\) | 13.5826i | 0.550394i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.7477i | 1.16301i | ||||||||
\(612\) | −1.58258 | −0.0639718 | ||||||||
\(613\) | − | 49.4955i | − | 1.99910i | −0.0299539 | − | 0.999551i | \(-0.509536\pi\) | ||
0.0299539 | − | 0.999551i | \(-0.490464\pi\) | |||||||
\(614\) | 1.37386i | 0.0554446i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.58258i | 0.0637638i | ||||||||
\(617\) | 23.0436i | 0.927699i | 0.885914 | + | 0.463849i | \(0.153532\pi\) | ||||
−0.885914 | + | 0.463849i | \(0.846468\pi\) | |||||||
\(618\) | 12.1652i | 0.489354i | ||||||||
\(619\) | 35.1216 | 1.41166 | 0.705828 | − | 0.708383i | \(-0.250575\pi\) | ||||
0.705828 | + | 0.708383i | \(0.250575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9564i | 0.760696i | ||||||||
\(622\) | 23.3739i | 0.937207i | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 6.79129i | 0.271869i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.8348 | −0.592920 | ||||||||
\(627\) | −2.24318 | −0.0895840 | ||||||||
\(628\) | 2.00000i | 0.0798087i | ||||||||
\(629\) | −34.7477 | − | 30.3303i | −1.38548 | − | 1.20935i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9564i | 0.754644i | 0.926082 | + | 0.377322i | \(0.123155\pi\) | ||||
−0.926082 | + | 0.377322i | \(0.876845\pi\) | |||||||
\(632\) | 8.20871i | 0.326525i | ||||||||
\(633\) | 18.5826i | 0.738591i | ||||||||
\(634\) | − | 28.7477i | − | 1.14172i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.83485 | 0.112409 | ||||||||
\(637\) | 11.3739 | 0.450649 | ||||||||
\(638\) | − | 3.00000i | − | 0.118771i | ||||||
\(639\) | 1.91288 | 0.0756723 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.46099 | −0.136701 | −0.0683503 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683503 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(642\) | 9.62614 | 0.379913 | ||||||||
\(643\) | 39.4955 | 1.55755 | 0.778774 | − | 0.627304i | \(-0.215842\pi\) | ||||
0.778774 | + | 0.627304i | \(0.215842\pi\) | |||||||
\(644\) | 7.58258i | 0.298795i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000i | 0.472134i | ||||||||
\(647\) | 17.7042 | 0.696023 | 0.348011 | − | 0.937490i | \(-0.386857\pi\) | ||||
0.348011 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(648\) | 9.58258 | 0.376439 | ||||||||
\(649\) | 1.25227i | 0.0491560i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.0000i | 1.17579i | ||||||||
\(652\) | −19.5826 | −0.766913 | ||||||||
\(653\) | −0.626136 | −0.0245026 | −0.0122513 | − | 0.999925i | \(-0.503900\pi\) | ||||
−0.0122513 | + | 0.999925i | \(0.503900\pi\) | |||||||
\(654\) | −10.7477 | −0.420269 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.79129 | 0.382286 | ||||||||
\(657\) | 0.912878i | 0.0356148i | ||||||||
\(658\) | 15.1652 | 0.591199 | ||||||||
\(659\) | −11.0436 | −0.430196 | −0.215098 | − | 0.976592i | \(-0.569007\pi\) | ||||
−0.215098 | + | 0.976592i | \(0.569007\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2087i | 1.25277i | 0.779512 | + | 0.626387i | \(0.215467\pi\) | ||||
−0.779512 | + | 0.626387i | \(0.784533\pi\) | |||||||
\(662\) | 25.5826i | 0.994295i | ||||||||
\(663\) | 51.4955i | 1.99992i | ||||||||
\(664\) | − | 15.1652i | − | 0.588522i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.956439 | − | 0.834849i | −0.0370613 | − | 0.0323497i | ||||
\(667\) | − | 14.3739i | − | 0.556558i | ||||||
\(668\) | −21.9564 | −0.849520 | ||||||||
\(669\) | −25.0780 | −0.969573 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.1216i | − | 0.390740i | ||||||
\(672\) | 3.58258 | 0.138201 | ||||||||
\(673\) | − | 36.1216i | − | 1.39238i | −0.717855 | − | 0.696192i | \(-0.754876\pi\) | ||
0.717855 | − | 0.696192i | \(-0.245124\pi\) | |||||||
\(674\) | 33.1216i | 1.27580i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.37386 | 0.0528409 | ||||||||
\(677\) | − | 9.16515i | − | 0.352245i | −0.984368 | − | 0.176123i | \(-0.943644\pi\) | ||
0.984368 | − | 0.176123i | \(-0.0563555\pi\) | |||||||
\(678\) | − | 18.6606i | − | 0.716656i | ||||||
\(679\) | − | 27.1652i | − | 1.04250i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 46.4174i | − | 1.77872i | ||||||
\(682\) | − | 6.62614i | − | 0.253728i | ||||||
\(683\) | 31.5826 | 1.20847 | 0.604237 | − | 0.796805i | \(-0.293478\pi\) | ||||
0.604237 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(684\) | 0.330303i | 0.0126294i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 20.0000i | − | 0.763604i | ||||||
\(687\) | − | 12.0871i | − | 0.461152i | ||||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | − | 6.00000i | − | 0.228582i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4955 | 0.969893 | 0.484946 | − | 0.874544i | \(-0.338839\pi\) | ||||
0.484946 | + | 0.874544i | \(0.338839\pi\) | |||||||
\(692\) | 15.1652i | 0.576493i | ||||||||
\(693\) | 0.330303i | 0.0125472i | ||||||||
\(694\) | −7.58258 | −0.287831 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.79129 | −0.257423 | ||||||||
\(697\) | 74.2432 | 2.81216 | ||||||||
\(698\) | 10.0000 | 0.378506 | ||||||||
\(699\) | 28.8784 | 1.09228 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.95644i | 0.149433i | 0.997205 | + | 0.0747163i | \(0.0238051\pi\) | ||||
−0.997205 | + | 0.0747163i | \(0.976195\pi\) | |||||||
\(702\) | − | 18.9564i | − | 0.715465i | ||||||
\(703\) | −6.33030 | + | 7.25227i | −0.238752 | + | 0.273525i | ||||
\(704\) | −0.791288 | −0.0298228 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.58258 | −0.0595610 | ||||||||
\(707\) | 15.1652i | 0.570344i | ||||||||
\(708\) | 2.83485 | 0.106540 | ||||||||
\(709\) | − | 23.2087i | − | 0.871621i | −0.900038 | − | 0.435811i | \(-0.856462\pi\) | ||
0.900038 | − | 0.435811i | \(-0.143538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.71326i | 0.0642522i | ||||||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | − | 31.7477i | − | 1.18896i | ||||||
\(714\) | 27.1652 | 1.01663 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.58258i | − | 0.0591436i | ||||||
\(717\) | 3.66061 | 0.136708 | ||||||||
\(718\) | −8.83485 | −0.329714 | ||||||||
\(719\) | 21.1652 | 0.789327 | 0.394663 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394663 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.5826i | − | 0.505842i | ||||||
\(722\) | −16.4955 | −0.613897 | ||||||||
\(723\) | −7.91288 | −0.294283 | ||||||||
\(724\) | 8.74773 | 0.325107 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18.5826i | 0.689664i | ||||||||
\(727\) | −13.1216 | −0.486653 | −0.243326 | − | 0.969944i | \(-0.578239\pi\) | ||||
−0.243326 | + | 0.969944i | \(0.578239\pi\) | |||||||
\(728\) | − | 7.58258i | − | 0.281029i | ||||||
\(729\) | −24.8693 | −0.921086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.4955 | 1.68271 | ||||||||
\(732\) | −22.9129 | −0.846884 | ||||||||
\(733\) | 47.4955i | 1.75428i | 0.480231 | + | 0.877142i | \(0.340553\pi\) | ||||
−0.480231 | + | 0.877142i | \(0.659447\pi\) | |||||||
\(734\) | − | 5.25227i | − | 0.193865i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.79129 | −0.139749 | ||||||||
\(737\) | 5.04356i | 0.185782i | ||||||||
\(738\) | 2.04356 | 0.0752245 | ||||||||
\(739\) | 35.1216 | 1.29197 | 0.645984 | − | 0.763351i | \(-0.276447\pi\) | ||||
0.645984 | + | 0.763351i | \(0.276447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.7477 | 0.394828 | ||||||||
\(742\) | −3.16515 | −0.116196 | ||||||||
\(743\) | 15.1652i | 0.556355i | 0.960530 | + | 0.278178i | \(0.0897304\pi\) | ||||
−0.960530 | + | 0.278178i | \(0.910270\pi\) | |||||||
\(744\) | −15.0000 | −0.549927 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.7477i | 0.466727i | ||||||||
\(747\) | − | 3.16515i | − | 0.115807i | ||||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | −10.7477 | −0.392713 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4955 | −1.51419 | −0.757095 | − | 0.653304i | \(-0.773382\pi\) | ||||
−0.757095 | + | 0.653304i | \(0.773382\pi\) | |||||||
\(752\) | 7.58258i | 0.276508i | ||||||||
\(753\) | −7.91288 | −0.288361 | ||||||||
\(754\) | 14.3739i | 0.523465i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.0000 | −0.363696 | ||||||||
\(757\) | −35.2087 | −1.27968 | −0.639841 | − | 0.768507i | \(-0.721000\pi\) | ||||
−0.639841 | + | 0.768507i | \(0.721000\pi\) | |||||||
\(758\) | 20.1216 | 0.730849 | ||||||||
\(759\) | − | 5.37386i | − | 0.195059i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2087 | 0.515065 | 0.257533 | − | 0.966270i | \(-0.417090\pi\) | ||||
0.257533 | + | 0.966270i | \(0.417090\pi\) | |||||||
\(762\) | −14.3303 | −0.519132 | ||||||||
\(763\) | 12.0000 | 0.434429 | ||||||||
\(764\) | 8.37386i | 0.302956i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.3303 | −0.662301 | ||||||||
\(767\) | − | 6.00000i | − | 0.216647i | ||||||
\(768\) | 1.79129i | 0.0646375i | ||||||||
\(769\) | 11.6697i | 0.420820i | 0.977613 | + | 0.210410i | \(0.0674799\pi\) | ||||
−0.977613 | + | 0.210410i | \(0.932520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 8.50455i | − | 0.306284i | ||||||
\(772\) | 18.3303 | 0.659722 | ||||||||
\(773\) | 31.9129i | 1.14783i | 0.818916 | + | 0.573913i | \(0.194575\pi\) | ||||
−0.818916 | + | 0.573913i | \(0.805425\pi\) | |||||||
\(774\) | 1.25227 | 0.0450120 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.5826 | 0.487586 | ||||||||
\(777\) | 16.4174 | + | 14.3303i | 0.588972 | + | 0.514097i | ||||
\(778\) | 32.8693i | 1.17842i | ||||||||
\(779\) | − | 15.4955i | − | 0.555182i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.25227 | 0.259507 | ||||||||
\(782\) | −28.7477 | −1.02802 | ||||||||
\(783\) | 18.9564 | 0.677448 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 30.0000 | 1.07006 | ||||||||
\(787\) | − | 8.00000i | − | 0.285169i | −0.989783 | − | 0.142585i | \(-0.954459\pi\) | ||
0.989783 | − | 0.142585i | \(-0.0455413\pi\) | |||||||
\(788\) | 19.9129i | 0.709367i | ||||||||
\(789\) | 48.6606 | 1.73236 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.8348i | 0.740802i | ||||||||
\(792\) | −0.165151 | −0.00586840 | ||||||||
\(793\) | 48.4955i | 1.72212i | ||||||||
\(794\) | 14.7477i | 0.523377i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.1652i | 0.537515i | ||||||||
\(797\) | 35.3739 | 1.25301 | 0.626503 | − | 0.779419i | \(-0.284486\pi\) | ||||
0.626503 | + | 0.779419i | \(0.284486\pi\) | |||||||
\(798\) | − | 5.66970i | − | 0.200705i | ||||||
\(799\) | 57.4955i | 2.03404i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.25227i | 0.0442469i | ||||||||
\(802\) | 16.7477i | 0.591383i | ||||||||
\(803\) | 3.46099i | 0.122136i | ||||||||
\(804\) | 11.4174 | 0.402662 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.7477i | 1.11827i | ||||||||
\(807\) | − | 30.0000i | − | 1.05605i | ||||||
\(808\) | −7.58258 | −0.266754 | ||||||||
\(809\) | 53.0780i | 1.86612i | 0.359715 | + | 0.933062i | \(0.382874\pi\) | ||||
−0.359715 | + | 0.933062i | \(0.617126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.8693 | −0.697706 | −0.348853 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348853 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(812\) | 7.58258 | 0.266096 | ||||||||
\(813\) | 39.4083i | 1.38211i | ||||||||
\(814\) | −3.62614 | − | 3.16515i | −0.127096 | − | 0.110938i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.5826i | 0.475485i | ||||||||
\(817\) | − | 9.49545i | − | 0.332204i | ||||||
\(818\) | 27.1652i | 0.949807i | ||||||||
\(819\) | − | 1.58258i | − | 0.0552997i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.16515 | 0.110465 | 0.0552323 | − | 0.998474i | \(-0.482410\pi\) | ||||
0.0552323 | + | 0.998474i | \(0.482410\pi\) | |||||||
\(822\) | 6.49545 | 0.226555 | ||||||||
\(823\) | − | 16.0000i | − | 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | 6.79129 | 0.236586 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.16515 | −0.110130 | ||||||||
\(827\) | 33.1652 | 1.15327 | 0.576633 | − | 0.817004i | \(-0.304366\pi\) | ||||
0.576633 | + | 0.817004i | \(0.304366\pi\) | |||||||
\(828\) | −0.791288 | −0.0274992 | ||||||||
\(829\) | − | 17.0436i | − | 0.591947i | −0.955196 | − | 0.295974i | \(-0.904356\pi\) | ||
0.955196 | − | 0.295974i | \(-0.0956441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 17.2432i | − | 0.598159i | ||||||
\(832\) | 3.79129 | 0.131439 | ||||||||
\(833\) | 22.7477 | 0.788162 | ||||||||
\(834\) | − | 23.9564i | − | 0.829544i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.25227i | 0.0433108i | ||||||||
\(837\) | 41.8693 | 1.44722 | ||||||||
\(838\) | 2.20871 | 0.0762987 | ||||||||
\(839\) | −3.49545 | −0.120676 | −0.0603382 | − | 0.998178i | \(-0.519218\pi\) | ||||
−0.0603382 | + | 0.998178i | \(0.519218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.6261 | 0.504350 | ||||||||
\(842\) | 18.9564i | 0.653282i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3739 | 0.357083 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.58258i | 0.0544101i | ||||||||
\(847\) | − | 20.7477i | − | 0.712900i | ||||||
\(848\) | − | 1.58258i | − | 0.0543459i | ||||||
\(849\) | − | 42.9909i | − | 1.47544i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.3739 | − | 15.1652i | −0.595568 | − | 0.519855i | ||||
\(852\) | − | 16.4174i | − | 0.562452i | ||||||
\(853\) | −44.7042 | −1.53064 | −0.765321 | − | 0.643649i | \(-0.777420\pi\) | ||||
−0.765321 | + | 0.643649i | \(0.777420\pi\) | |||||||
\(854\) | 25.5826 | 0.875418 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 5.37386i | − | 0.183675i | ||||||
\(857\) | 33.1652 | 1.13290 | 0.566450 | − | 0.824096i | \(-0.308316\pi\) | ||||
0.566450 | + | 0.824096i | \(0.308316\pi\) | |||||||
\(858\) | 5.37386i | 0.183461i | ||||||||
\(859\) | 18.6606i | 0.636692i | 0.947975 | + | 0.318346i | \(0.103127\pi\) | ||||
−0.947975 | + | 0.318346i | \(0.896873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.0780 | −1.19546 | ||||||||
\(862\) | 8.83485i | 0.300916i | ||||||||
\(863\) | − | 19.2523i | − | 0.655355i | −0.944790 | − | 0.327677i | \(-0.893734\pi\) | ||
0.944790 | − | 0.327677i | \(-0.106266\pi\) | |||||||
\(864\) | − | 5.00000i | − | 0.170103i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10.6261i | − | 0.361091i | ||||||
\(867\) | 72.5390i | 2.46355i | ||||||||
\(868\) | 16.7477 | 0.568455 | ||||||||
\(869\) | 6.49545i | 0.220343i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.1652i | − | 0.818805i | ||||||
\(872\) | 6.00000i | 0.203186i | ||||||||
\(873\) | 2.83485 | 0.0959451 | ||||||||
\(874\) | 6.00000i | 0.202953i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.83485 | 0.264715 | ||||||||
\(877\) | − | 11.2523i | − | 0.379962i | −0.981788 | − | 0.189981i | \(-0.939157\pi\) | ||
0.981788 | − | 0.189981i | \(-0.0608427\pi\) | |||||||
\(878\) | 12.6261i | 0.426111i | ||||||||
\(879\) | 10.7477 | 0.362512 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.1216 | −0.442078 | −0.221039 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221039 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(882\) | 0.626136 | 0.0210831 | ||||||||
\(883\) | −31.9129 | −1.07395 | −0.536977 | − | 0.843597i | \(-0.680434\pi\) | ||||
−0.536977 | + | 0.843597i | \(0.680434\pi\) | |||||||
\(884\) | 28.7477 | 0.966891 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 27.9564i | − | 0.939215i | ||||||
\(887\) | 57.8258i | 1.94160i | 0.239893 | + | 0.970799i | \(0.422888\pi\) | ||||
−0.239893 | + | 0.970799i | \(0.577112\pi\) | |||||||
\(888\) | −7.16515 | + | 8.20871i | −0.240447 | + | 0.275466i | ||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.58258 | 0.254026 | ||||||||
\(892\) | 14.0000i | 0.468755i | ||||||||
\(893\) | 12.0000 | 0.401565 | ||||||||
\(894\) | − | 7.91288i | − | 0.264646i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.00000i | − | 0.0668153i | ||||||
\(897\) | 25.7477i | 0.859692i | ||||||||
\(898\) | − | 2.83485i | − | 0.0946001i | ||||||
\(899\) | −31.7477 | −1.05885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 12.0000i | − | 0.399778i | ||||||
\(902\) | 7.74773 | 0.257971 | ||||||||
\(903\) | −21.4955 | −0.715324 | ||||||||
\(904\) | −10.4174 | −0.346478 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 26.4174i | 0.877660i | ||||||||
\(907\) | −30.3303 | −1.00710 | −0.503551 | − | 0.863966i | \(-0.667973\pi\) | ||||
−0.503551 | + | 0.863966i | \(0.667973\pi\) | |||||||
\(908\) | −25.9129 | −0.859949 | ||||||||
\(909\) | −1.58258 | −0.0524907 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.6697i | 0.585423i | 0.956201 | + | 0.292712i | \(0.0945576\pi\) | ||||
−0.956201 | + | 0.292712i | \(0.905442\pi\) | |||||||
\(912\) | 2.83485 | 0.0938712 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | 21.4955 | 0.711006 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.74773 | −0.222951 | ||||||||
\(917\) | −33.4955 | −1.10612 | ||||||||
\(918\) | − | 37.9129i | − | 1.25131i | ||||||
\(919\) | − | 36.0000i | − | 1.18753i | −0.804638 | − | 0.593765i | \(-0.797641\pi\) | ||
0.804638 | − | 0.593765i | \(-0.202359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.46099 | 0.0810922 | ||||||||
\(922\) | − | 12.3303i | − | 0.406077i | ||||||
\(923\) | −34.7477 | −1.14374 | ||||||||
\(924\) | 2.83485 | 0.0932597 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 29.7042 | 0.976139 | ||||||||
\(927\) | 1.41742 | 0.0465543 | ||||||||
\(928\) | 3.79129i | 0.124455i | ||||||||
\(929\) | −8.37386 | −0.274738 | −0.137369 | − | 0.990520i | \(-0.543865\pi\) | ||||
−0.137369 | + | 0.990520i | \(0.543865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.74773i | − | 0.155600i | ||||||
\(932\) | − | 16.1216i | − | 0.528080i | ||||||
\(933\) | 41.8693 | 1.37074 | ||||||||
\(934\) | −16.4174 | −0.537195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.791288 | 0.0258641 | ||||||||
\(937\) | − | 34.8693i | − | 1.13913i | −0.821946 | − | 0.569565i | \(-0.807111\pi\) | ||
0.821946 | − | 0.569565i | \(-0.192889\pi\) | |||||||
\(938\) | −12.7477 | −0.416228 | ||||||||
\(939\) | 26.5735i | 0.867193i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.4955 | −0.700732 | −0.350366 | − | 0.936613i | \(-0.613943\pi\) | ||||
−0.350366 | + | 0.936613i | \(0.613943\pi\) | |||||||
\(942\) | 3.58258 | 0.116727 | ||||||||
\(943\) | 37.1216 | 1.20885 | ||||||||
\(944\) | − | 1.58258i | − | 0.0515085i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.74773 | 0.154362 | ||||||||
\(947\) | −1.25227 | −0.0406934 | −0.0203467 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203467 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(948\) | 14.7042 | 0.477569 | ||||||||
\(949\) | − | 16.5826i | − | 0.538293i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.4955 | −1.66985 | ||||||||
\(952\) | − | 15.1652i | − | 0.491505i | ||||||
\(953\) | 31.4519i | 1.01883i | 0.860522 | + | 0.509413i | \(0.170138\pi\) | ||||
−0.860522 | + | 0.509413i | \(0.829862\pi\) | |||||||
\(954\) | − | 0.330303i | − | 0.0106939i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.04356i | − | 0.0660935i | ||||||
\(957\) | −5.37386 | −0.173712 | ||||||||
\(958\) | 3.79129i | 0.122491i | ||||||||
\(959\) | −7.25227 | −0.234188 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.1216 | −1.26199 | ||||||||
\(962\) | 17.3739 | + | 15.1652i | 0.560156 | + | 0.488944i | ||||
\(963\) | − | 1.12159i | − | 0.0361428i | ||||||
\(964\) | 4.41742i | 0.142276i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.5826 | 0.437012 | ||||||||
\(967\) | −21.9564 | −0.706071 | −0.353036 | − | 0.935610i | \(-0.614851\pi\) | ||||
−0.353036 | + | 0.935610i | \(0.614851\pi\) | |||||||
\(968\) | 10.3739 | 0.333429 | ||||||||
\(969\) | 21.4955 | 0.690533 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.3739 | 1.61657 | 0.808287 | − | 0.588789i | \(-0.200395\pi\) | ||||
0.808287 | + | 0.588789i | \(0.200395\pi\) | |||||||
\(972\) | − | 2.16515i | − | 0.0694473i | ||||||
\(973\) | 26.7477i | 0.857493i | ||||||||
\(974\) | −36.6606 | −1.17468 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7913i | 0.409439i | ||||||||
\(977\) | 41.0780 | 1.31420 | 0.657101 | − | 0.753802i | \(-0.271782\pi\) | ||||
0.657101 | + | 0.753802i | \(0.271782\pi\) | |||||||
\(978\) | 35.0780i | 1.12167i | ||||||||
\(979\) | 4.74773i | 0.151738i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.25227i | 0.0399820i | ||||||||
\(982\) | −5.37386 | −0.171487 | ||||||||
\(983\) | − | 18.3303i | − | 0.584646i | −0.956320 | − | 0.292323i | \(-0.905572\pi\) | ||
0.956320 | − | 0.292323i | \(-0.0944282\pi\) | |||||||
\(984\) | − | 17.5390i | − | 0.559123i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28.7477i | 0.915514i | ||||||||
\(987\) | − | 27.1652i | − | 0.864676i | ||||||
\(988\) | − | 6.00000i | − | 0.190885i | ||||||
\(989\) | 22.7477 | 0.723336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9564i | 0.602171i | 0.953597 | + | 0.301086i | \(0.0973490\pi\) | ||||
−0.953597 | + | 0.301086i | \(0.902651\pi\) | |||||||
\(992\) | 8.37386i | 0.265870i | ||||||||
\(993\) | 45.8258 | 1.45424 | ||||||||
\(994\) | 18.3303i | 0.581402i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −27.1652 | −0.860761 | ||||||||
\(997\) | −18.0000 | −0.570066 | −0.285033 | − | 0.958518i | \(-0.592005\pi\) | ||||
−0.285033 | + | 0.958518i | \(0.592005\pi\) | |||||||
\(998\) | − | 10.7477i | − | 0.340213i | ||||||
\(999\) | 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 | 1850.2.c.g.1849.3 | 4 | ||
5.2 | odd | 4 | 74.2.b.a.73.2 | ✓ | 4 | ||
5.3 | odd | 4 | 1850.2.d.e.1701.3 | 4 | |||
5.4 | even | 2 | 1850.2.c.h.1849.2 | 4 | |||
15.2 | even | 4 | 666.2.c.b.73.3 | 4 | |||
20.7 | even | 4 | 592.2.g.c.369.2 | 4 | |||
37.36 | even | 2 | 1850.2.c.h.1849.3 | 4 | |||
40.27 | even | 4 | 2368.2.g.h.961.3 | 4 | |||
40.37 | odd | 4 | 2368.2.g.j.961.1 | 4 | |||
60.47 | odd | 4 | 5328.2.h.m.2737.2 | 4 | |||
185.73 | odd | 4 | 1850.2.d.e.1701.1 | 4 | |||
185.117 | even | 4 | 2738.2.a.h.1.1 | 2 | |||
185.142 | even | 4 | 2738.2.a.k.1.1 | 2 | |||
185.147 | odd | 4 | 74.2.b.a.73.4 | yes | 4 | ||
185.184 | even | 2 | inner | 1850.2.c.g.1849.2 | 4 | ||
555.332 | even | 4 | 666.2.c.b.73.2 | 4 | |||
740.147 | even | 4 | 592.2.g.c.369.1 | 4 | |||
1480.147 | even | 4 | 2368.2.g.h.961.4 | 4 | |||
1480.517 | odd | 4 | 2368.2.g.j.961.2 | 4 | |||
2220.887 | odd | 4 | 5328.2.h.m.2737.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.b.a.73.2 | ✓ | 4 | 5.2 | odd | 4 | ||
74.2.b.a.73.4 | yes | 4 | 185.147 | odd | 4 | ||
592.2.g.c.369.1 | 4 | 740.147 | even | 4 | |||
592.2.g.c.369.2 | 4 | 20.7 | even | 4 | |||
666.2.c.b.73.2 | 4 | 555.332 | even | 4 | |||
666.2.c.b.73.3 | 4 | 15.2 | even | 4 | |||
1850.2.c.g.1849.2 | 4 | 185.184 | even | 2 | inner | ||
1850.2.c.g.1849.3 | 4 | 1.1 | even | 1 | trivial | ||
1850.2.c.h.1849.2 | 4 | 5.4 | even | 2 | |||
1850.2.c.h.1849.3 | 4 | 37.36 | even | 2 | |||
1850.2.d.e.1701.1 | 4 | 185.73 | odd | 4 | |||
1850.2.d.e.1701.3 | 4 | 5.3 | odd | 4 | |||
2368.2.g.h.961.3 | 4 | 40.27 | even | 4 | |||
2368.2.g.h.961.4 | 4 | 1480.147 | even | 4 | |||
2368.2.g.j.961.1 | 4 | 40.37 | odd | 4 | |||
2368.2.g.j.961.2 | 4 | 1480.517 | odd | 4 | |||
2738.2.a.h.1.1 | 2 | 185.117 | even | 4 | |||
2738.2.a.k.1.1 | 2 | 185.142 | even | 4 | |||
5328.2.h.m.2737.2 | 4 | 60.47 | odd | 4 | |||
5328.2.h.m.2737.3 | 4 | 2220.887 | odd | 4 |