Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,3,Mod(37,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("90.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.g (of order \(4\), degree \(2\), 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: | \(2.45232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.37 |
Dual form | 90.3.g.b.73.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 5.00000i | 1.00000i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 2.00000i | 0.285714 | + | 0.285714i | 0.835383 | − | 0.549669i | \(-0.185246\pi\) |
−0.549669 | + | 0.835383i | \(0.685246\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.00000 | + | 5.00000i | −0.500000 | + | 0.500000i | ||||
\(11\) | 8.00000 | 0.727273 | 0.363636 | − | 0.931541i | \(-0.381535\pi\) | ||||
0.363636 | + | 0.931541i | \(0.381535\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 3.00000i | 0.230769 | − | 0.230769i | −0.582245 | − | 0.813014i | \(-0.697825\pi\) |
0.813014 | + | 0.582245i | \(0.197825\pi\) | |||||||
\(14\) | 4.00000i | 0.285714i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −7.00000 | − | 7.00000i | −0.411765 | − | 0.411765i | 0.470588 | − | 0.882353i | \(-0.344042\pi\) |
−0.882353 | + | 0.470588i | \(0.844042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.0000i | − | 1.05263i | −0.850289 | − | 0.526316i | \(-0.823573\pi\) | ||
0.850289 | − | 0.526316i | \(-0.176427\pi\) | |||||||
\(20\) | −10.0000 | −0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.00000 | + | 8.00000i | 0.363636 | + | 0.363636i | ||||
\(23\) | 2.00000 | − | 2.00000i | 0.0869565 | − | 0.0869565i | −0.662291 | − | 0.749247i | \(-0.730416\pi\) |
0.749247 | + | 0.662291i | \(0.230416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −1.00000 | ||||||||
\(26\) | 6.00000 | 0.230769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.00000 | + | 4.00000i | −0.142857 | + | 0.142857i | ||||
\(29\) | − | 40.0000i | − | 1.37931i | −0.724138 | − | 0.689655i | \(-0.757762\pi\) | ||
0.724138 | − | 0.689655i | \(-0.242238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 52.0000 | 1.67742 | 0.838710 | − | 0.544579i | \(-0.183310\pi\) | ||||
0.838710 | + | 0.544579i | \(0.183310\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 14.0000i | − | 0.411765i | ||||||
\(35\) | −10.0000 | + | 10.0000i | −0.285714 | + | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.0810811 | − | 0.0810811i | 0.665403 | − | 0.746484i | \(-0.268260\pi\) |
−0.746484 | + | 0.665403i | \(0.768260\pi\) | |||||||
\(38\) | 20.0000 | − | 20.0000i | 0.526316 | − | 0.526316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.0000 | − | 10.0000i | −0.250000 | − | 0.250000i | ||||
\(41\) | 8.00000 | 0.195122 | 0.0975610 | − | 0.995230i | \(-0.468896\pi\) | ||||
0.0975610 | + | 0.995230i | \(0.468896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −42.0000 | + | 42.0000i | −0.976744 | + | 0.976744i | −0.999736 | − | 0.0229915i | \(-0.992681\pi\) |
0.0229915 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(44\) | 16.0000i | 0.363636i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.0869565 | ||||||||
\(47\) | 18.0000 | + | 18.0000i | 0.382979 | + | 0.382979i | 0.872174 | − | 0.489195i | \(-0.162710\pi\) |
−0.489195 | + | 0.872174i | \(0.662710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 41.0000i | − | 0.836735i | ||||||
\(50\) | −25.0000 | − | 25.0000i | −0.500000 | − | 0.500000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | + | 6.00000i | 0.115385 | + | 0.115385i | ||||
\(53\) | −53.0000 | + | 53.0000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.0000i | 0.727273i | ||||||||
\(56\) | −8.00000 | −0.142857 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 40.0000 | − | 40.0000i | 0.689655 | − | 0.689655i | ||||
\(59\) | 20.0000i | 0.338983i | 0.985532 | + | 0.169492i | \(0.0542125\pi\) | ||||
−0.985532 | + | 0.169492i | \(0.945787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.0000 | −0.786885 | −0.393443 | − | 0.919349i | \(-0.628716\pi\) | ||||
−0.393443 | + | 0.919349i | \(0.628716\pi\) | |||||||
\(62\) | 52.0000 | + | 52.0000i | 0.838710 | + | 0.838710i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 15.0000 | + | 15.0000i | 0.230769 | + | 0.230769i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62.0000 | + | 62.0000i | 0.925373 | + | 0.925373i | 0.997403 | − | 0.0720294i | \(-0.0229475\pi\) |
−0.0720294 | + | 0.997403i | \(0.522948\pi\) | |||||||
\(68\) | 14.0000 | − | 14.0000i | 0.205882 | − | 0.205882i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20.0000 | −0.285714 | ||||||||
\(71\) | 28.0000 | 0.394366 | 0.197183 | − | 0.980367i | \(-0.436821\pi\) | ||||
0.197183 | + | 0.980367i | \(0.436821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −47.0000 | + | 47.0000i | −0.643836 | + | 0.643836i | −0.951496 | − | 0.307661i | \(-0.900454\pi\) |
0.307661 | + | 0.951496i | \(0.400454\pi\) | |||||||
\(74\) | − | 6.00000i | − | 0.0810811i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.0000 | 0.526316 | ||||||||
\(77\) | 16.0000 | + | 16.0000i | 0.207792 | + | 0.207792i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | − | 20.0000i | − | 0.250000i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.00000 | + | 8.00000i | 0.0975610 | + | 0.0975610i | ||||
\(83\) | −18.0000 | + | 18.0000i | −0.216867 | + | 0.216867i | −0.807177 | − | 0.590310i | \(-0.799006\pi\) |
0.590310 | + | 0.807177i | \(0.299006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.0000 | − | 35.0000i | 0.411765 | − | 0.411765i | ||||
\(86\) | −84.0000 | −0.976744 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.0000 | + | 16.0000i | −0.181818 | + | 0.181818i | ||||
\(89\) | − | 80.0000i | − | 0.898876i | −0.893311 | − | 0.449438i | \(-0.851624\pi\) | ||
0.893311 | − | 0.449438i | \(-0.148376\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 0.131868 | ||||||||
\(92\) | 4.00000 | + | 4.00000i | 0.0434783 | + | 0.0434783i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 36.0000i | 0.382979i | ||||||||
\(95\) | 100.000 | 1.05263 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −63.0000 | − | 63.0000i | −0.649485 | − | 0.649485i | 0.303384 | − | 0.952868i | \(-0.401884\pi\) |
−0.952868 | + | 0.303384i | \(0.901884\pi\) | |||||||
\(98\) | 41.0000 | − | 41.0000i | 0.418367 | − | 0.418367i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 50.0000i | − | 0.500000i | ||||||
\(101\) | −62.0000 | −0.613861 | −0.306931 | − | 0.951732i | \(-0.599302\pi\) | ||||
−0.306931 | + | 0.951732i | \(0.599302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 118.000 | − | 118.000i | 1.14563 | − | 1.14563i | 0.158229 | − | 0.987403i | \(-0.449422\pi\) |
0.987403 | − | 0.158229i | \(-0.0505783\pi\) | |||||||
\(104\) | 12.0000i | 0.115385i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −106.000 | −1.00000 | ||||||||
\(107\) | −142.000 | − | 142.000i | −1.32710 | − | 1.32710i | −0.907886 | − | 0.419217i | \(-0.862305\pi\) |
−0.419217 | − | 0.907886i | \(-0.637695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.0917431i | −0.998947 | − | 0.0458716i | \(-0.985394\pi\) | ||
0.998947 | − | 0.0458716i | \(-0.0146065\pi\) | |||||||
\(110\) | −40.0000 | + | 40.0000i | −0.363636 | + | 0.363636i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00000 | − | 8.00000i | −0.0714286 | − | 0.0714286i | ||||
\(113\) | −23.0000 | + | 23.0000i | −0.203540 | + | 0.203540i | −0.801515 | − | 0.597975i | \(-0.795972\pi\) |
0.597975 | + | 0.801515i | \(0.295972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | + | 10.0000i | 0.0869565 | + | 0.0869565i | ||||
\(116\) | 80.0000 | 0.689655 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.0000 | + | 20.0000i | −0.169492 | + | 0.169492i | ||||
\(119\) | − | 28.0000i | − | 0.235294i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −57.0000 | −0.471074 | ||||||||
\(122\) | −48.0000 | − | 48.0000i | −0.393443 | − | 0.393443i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 104.000i | 0.838710i | ||||||||
\(125\) | − | 125.000i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −118.000 | − | 118.000i | −0.929134 | − | 0.929134i | 0.0685161 | − | 0.997650i | \(-0.478174\pi\) |
−0.997650 | + | 0.0685161i | \(0.978174\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.0000i | 0.230769i | ||||||||
\(131\) | 128.000 | 0.977099 | 0.488550 | − | 0.872536i | \(-0.337526\pi\) | ||||
0.488550 | + | 0.872536i | \(0.337526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.0000 | − | 40.0000i | 0.300752 | − | 0.300752i | ||||
\(134\) | 124.000i | 0.925373i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.0000 | 0.205882 | ||||||||
\(137\) | 63.0000 | + | 63.0000i | 0.459854 | + | 0.459854i | 0.898607 | − | 0.438753i | \(-0.144580\pi\) |
−0.438753 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 140.000i | 1.00719i | 0.863939 | + | 0.503597i | \(0.167990\pi\) | ||||
−0.863939 | + | 0.503597i | \(0.832010\pi\) | |||||||
\(140\) | −20.0000 | − | 20.0000i | −0.142857 | − | 0.142857i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28.0000 | + | 28.0000i | 0.197183 | + | 0.197183i | ||||
\(143\) | 24.0000 | − | 24.0000i | 0.167832 | − | 0.167832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 200.000 | 1.37931 | ||||||||
\(146\) | −94.0000 | −0.643836 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | − | 6.00000i | 0.0405405 | − | 0.0405405i | ||||
\(149\) | 150.000i | 1.00671i | 0.864079 | + | 0.503356i | \(0.167901\pi\) | ||||
−0.864079 | + | 0.503356i | \(0.832099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 52.0000 | 0.344371 | 0.172185 | − | 0.985065i | \(-0.444917\pi\) | ||||
0.172185 | + | 0.985065i | \(0.444917\pi\) | |||||||
\(152\) | 40.0000 | + | 40.0000i | 0.263158 | + | 0.263158i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 32.0000i | 0.207792i | ||||||||
\(155\) | 260.000i | 1.67742i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27.0000 | + | 27.0000i | 0.171975 | + | 0.171975i | 0.787846 | − | 0.615872i | \(-0.211196\pi\) |
−0.615872 | + | 0.787846i | \(0.711196\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.0000 | − | 20.0000i | 0.125000 | − | 0.125000i | ||||
\(161\) | 8.00000 | 0.0496894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −82.0000 | + | 82.0000i | −0.503067 | + | 0.503067i | −0.912390 | − | 0.409322i | \(-0.865765\pi\) |
0.409322 | + | 0.912390i | \(0.365765\pi\) | |||||||
\(164\) | 16.0000i | 0.0975610i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.0000 | −0.216867 | ||||||||
\(167\) | −62.0000 | − | 62.0000i | −0.371257 | − | 0.371257i | 0.496678 | − | 0.867935i | \(-0.334553\pi\) |
−0.867935 | + | 0.496678i | \(0.834553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 151.000i | 0.893491i | ||||||||
\(170\) | 70.0000 | 0.411765 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −84.0000 | − | 84.0000i | −0.488372 | − | 0.488372i | ||||
\(173\) | 107.000 | − | 107.000i | 0.618497 | − | 0.618497i | −0.326649 | − | 0.945146i | \(-0.605919\pi\) |
0.945146 | + | 0.326649i | \(0.105919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −50.0000 | − | 50.0000i | −0.285714 | − | 0.285714i | ||||
\(176\) | −32.0000 | −0.181818 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 80.0000 | − | 80.0000i | 0.449438 | − | 0.449438i | ||||
\(179\) | 220.000i | 1.22905i | 0.788897 | + | 0.614525i | \(0.210652\pi\) | ||||
−0.788897 | + | 0.614525i | \(0.789348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.0110497 | 0.00552486 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552486 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(182\) | 12.0000 | + | 12.0000i | 0.0659341 | + | 0.0659341i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000i | 0.0434783i | ||||||||
\(185\) | 15.0000 | − | 15.0000i | 0.0810811 | − | 0.0810811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −56.0000 | − | 56.0000i | −0.299465 | − | 0.299465i | ||||
\(188\) | −36.0000 | + | 36.0000i | −0.191489 | + | 0.191489i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 100.000 | + | 100.000i | 0.526316 | + | 0.526316i | ||||
\(191\) | −212.000 | −1.10995 | −0.554974 | − | 0.831868i | \(-0.687272\pi\) | ||||
−0.554974 | + | 0.831868i | \(0.687272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −57.0000 | + | 57.0000i | −0.295337 | + | 0.295337i | −0.839184 | − | 0.543847i | \(-0.816967\pi\) |
0.543847 | + | 0.839184i | \(0.316967\pi\) | |||||||
\(194\) | − | 126.000i | − | 0.649485i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 82.0000 | 0.418367 | ||||||||
\(197\) | 3.00000 | + | 3.00000i | 0.0152284 | + | 0.0152284i | 0.714680 | − | 0.699452i | \(-0.246572\pi\) |
−0.699452 | + | 0.714680i | \(0.746572\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 120.000i | − | 0.603015i | −0.953464 | − | 0.301508i | \(-0.902510\pi\) | ||
0.953464 | − | 0.301508i | \(-0.0974898\pi\) | |||||||
\(200\) | 50.0000 | − | 50.0000i | 0.250000 | − | 0.250000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −62.0000 | − | 62.0000i | −0.306931 | − | 0.306931i | ||||
\(203\) | 80.0000 | − | 80.0000i | 0.394089 | − | 0.394089i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.0000i | 0.195122i | ||||||||
\(206\) | 236.000 | 1.14563 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0000 | + | 12.0000i | −0.0576923 | + | 0.0576923i | ||||
\(209\) | − | 160.000i | − | 0.765550i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −328.000 | −1.55450 | −0.777251 | − | 0.629190i | \(-0.783387\pi\) | ||||
−0.777251 | + | 0.629190i | \(0.783387\pi\) | |||||||
\(212\) | −106.000 | − | 106.000i | −0.500000 | − | 0.500000i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 284.000i | − | 1.32710i | ||||||
\(215\) | −210.000 | − | 210.000i | −0.976744 | − | 0.976744i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 104.000 | + | 104.000i | 0.479263 | + | 0.479263i | ||||
\(218\) | 10.0000 | − | 10.0000i | 0.0458716 | − | 0.0458716i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −80.0000 | −0.363636 | ||||||||
\(221\) | −42.0000 | −0.190045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 138.000 | − | 138.000i | 0.618834 | − | 0.618834i | −0.326398 | − | 0.945232i | \(-0.605835\pi\) |
0.945232 | + | 0.326398i | \(0.105835\pi\) | |||||||
\(224\) | − | 16.0000i | − | 0.0714286i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −46.0000 | −0.203540 | ||||||||
\(227\) | −2.00000 | − | 2.00000i | −0.00881057 | − | 0.00881057i | 0.702688 | − | 0.711498i | \(-0.251983\pi\) |
−0.711498 | + | 0.702688i | \(0.751983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 120.000i | 0.524017i | 0.965066 | + | 0.262009i | \(0.0843849\pi\) | ||||
−0.965066 | + | 0.262009i | \(0.915615\pi\) | |||||||
\(230\) | 20.0000i | 0.0869565i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 80.0000 | + | 80.0000i | 0.344828 | + | 0.344828i | ||||
\(233\) | −183.000 | + | 183.000i | −0.785408 | + | 0.785408i | −0.980738 | − | 0.195330i | \(-0.937422\pi\) |
0.195330 | + | 0.980738i | \(0.437422\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −90.0000 | + | 90.0000i | −0.382979 | + | 0.382979i | ||||
\(236\) | −40.0000 | −0.169492 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.0000 | − | 28.0000i | 0.117647 | − | 0.117647i | ||||
\(239\) | − | 120.000i | − | 0.502092i | −0.967975 | − | 0.251046i | \(-0.919225\pi\) | ||
0.967975 | − | 0.251046i | \(-0.0807746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 232.000 | 0.962656 | 0.481328 | − | 0.876541i | \(-0.340155\pi\) | ||||
0.481328 | + | 0.876541i | \(0.340155\pi\) | |||||||
\(242\) | −57.0000 | − | 57.0000i | −0.235537 | − | 0.235537i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 96.0000i | − | 0.393443i | ||||||
\(245\) | 205.000 | 0.836735 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −60.0000 | − | 60.0000i | −0.242915 | − | 0.242915i | ||||
\(248\) | −104.000 | + | 104.000i | −0.419355 | + | 0.419355i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 125.000 | − | 125.000i | 0.500000 | − | 0.500000i | ||||
\(251\) | 48.0000 | 0.191235 | 0.0956175 | − | 0.995418i | \(-0.469517\pi\) | ||||
0.0956175 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | − | 16.0000i | 0.0632411 | − | 0.0632411i | ||||
\(254\) | − | 236.000i | − | 0.929134i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 313.000 | + | 313.000i | 1.21790 | + | 1.21790i | 0.968366 | + | 0.249532i | \(0.0802769\pi\) |
0.249532 | + | 0.968366i | \(0.419723\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.0463320i | ||||||
\(260\) | −30.0000 | + | 30.0000i | −0.115385 | + | 0.115385i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 128.000 | + | 128.000i | 0.488550 | + | 0.488550i | ||||
\(263\) | 262.000 | − | 262.000i | 0.996198 | − | 0.996198i | −0.00379508 | − | 0.999993i | \(-0.501208\pi\) |
0.999993 | + | 0.00379508i | \(0.00120801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −265.000 | − | 265.000i | −1.00000 | − | 1.00000i | ||||
\(266\) | 80.0000 | 0.300752 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −124.000 | + | 124.000i | −0.462687 | + | 0.462687i | ||||
\(269\) | − | 10.0000i | − | 0.0371747i | −0.999827 | − | 0.0185874i | \(-0.994083\pi\) | ||
0.999827 | − | 0.0185874i | \(-0.00591688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 252.000 | 0.929889 | 0.464945 | − | 0.885340i | \(-0.346074\pi\) | ||||
0.464945 | + | 0.885340i | \(0.346074\pi\) | |||||||
\(272\) | 28.0000 | + | 28.0000i | 0.102941 | + | 0.102941i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 126.000i | 0.459854i | ||||||||
\(275\) | −200.000 | −0.727273 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 267.000 | + | 267.000i | 0.963899 | + | 0.963899i | 0.999371 | − | 0.0354718i | \(-0.0112934\pi\) |
−0.0354718 | + | 0.999371i | \(0.511293\pi\) | |||||||
\(278\) | −140.000 | + | 140.000i | −0.503597 | + | 0.503597i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 40.0000i | − | 0.142857i | ||||||
\(281\) | −312.000 | −1.11032 | −0.555160 | − | 0.831743i | \(-0.687343\pi\) | ||||
−0.555160 | + | 0.831743i | \(0.687343\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −262.000 | + | 262.000i | −0.925795 | + | 0.925795i | −0.997431 | − | 0.0716358i | \(-0.977178\pi\) |
0.0716358 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(284\) | 56.0000i | 0.197183i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 48.0000 | 0.167832 | ||||||||
\(287\) | 16.0000 | + | 16.0000i | 0.0557491 | + | 0.0557491i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 191.000i | − | 0.660900i | ||||||
\(290\) | 200.000 | + | 200.000i | 0.689655 | + | 0.689655i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −94.0000 | − | 94.0000i | −0.321918 | − | 0.321918i | ||||
\(293\) | −243.000 | + | 243.000i | −0.829352 | + | 0.829352i | −0.987427 | − | 0.158075i | \(-0.949471\pi\) |
0.158075 | + | 0.987427i | \(0.449471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −100.000 | −0.338983 | ||||||||
\(296\) | 12.0000 | 0.0405405 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −150.000 | + | 150.000i | −0.503356 | + | 0.503356i | ||||
\(299\) | − | 12.0000i | − | 0.0401338i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −168.000 | −0.558140 | ||||||||
\(302\) | 52.0000 | + | 52.0000i | 0.172185 | + | 0.172185i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 80.0000i | 0.263158i | ||||||||
\(305\) | − | 240.000i | − | 0.786885i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0000 | − | 18.0000i | −0.0586319 | − | 0.0586319i | 0.677183 | − | 0.735815i | \(-0.263201\pi\) |
−0.735815 | + | 0.677183i | \(0.763201\pi\) | |||||||
\(308\) | −32.0000 | + | 32.0000i | −0.103896 | + | 0.103896i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −260.000 | + | 260.000i | −0.838710 | + | 0.838710i | ||||
\(311\) | 388.000 | 1.24759 | 0.623794 | − | 0.781589i | \(-0.285590\pi\) | ||||
0.623794 | + | 0.781589i | \(0.285590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 183.000 | − | 183.000i | 0.584665 | − | 0.584665i | −0.351517 | − | 0.936182i | \(-0.614334\pi\) |
0.936182 | + | 0.351517i | \(0.114334\pi\) | |||||||
\(314\) | 54.0000i | 0.171975i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 213.000 | + | 213.000i | 0.671924 | + | 0.671924i | 0.958159 | − | 0.286235i | \(-0.0924038\pi\) |
−0.286235 | + | 0.958159i | \(0.592404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 320.000i | − | 1.00313i | ||||||
\(320\) | 40.0000 | 0.125000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.00000 | + | 8.00000i | 0.0248447 | + | 0.0248447i | ||||
\(323\) | −140.000 | + | 140.000i | −0.433437 | + | 0.433437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −75.0000 | + | 75.0000i | −0.230769 | + | 0.230769i | ||||
\(326\) | −164.000 | −0.503067 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.0000 | + | 16.0000i | −0.0487805 | + | 0.0487805i | ||||
\(329\) | 72.0000i | 0.218845i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 232.000 | 0.700906 | 0.350453 | − | 0.936580i | \(-0.386028\pi\) | ||||
0.350453 | + | 0.936580i | \(0.386028\pi\) | |||||||
\(332\) | −36.0000 | − | 36.0000i | −0.108434 | − | 0.108434i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 124.000i | − | 0.371257i | ||||||
\(335\) | −310.000 | + | 310.000i | −0.925373 | + | 0.925373i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 417.000 | + | 417.000i | 1.23739 | + | 1.23739i | 0.961064 | + | 0.276324i | \(0.0891164\pi\) |
0.276324 | + | 0.961064i | \(0.410884\pi\) | |||||||
\(338\) | −151.000 | + | 151.000i | −0.446746 | + | 0.446746i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 70.0000 | + | 70.0000i | 0.205882 | + | 0.205882i | ||||
\(341\) | 416.000 | 1.21994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 180.000 | − | 180.000i | 0.524781 | − | 0.524781i | ||||
\(344\) | − | 168.000i | − | 0.488372i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 214.000 | 0.618497 | ||||||||
\(347\) | −202.000 | − | 202.000i | −0.582133 | − | 0.582133i | 0.353356 | − | 0.935489i | \(-0.385040\pi\) |
−0.935489 | + | 0.353356i | \(0.885040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 440.000i | − | 1.26074i | −0.776293 | − | 0.630372i | \(-0.782902\pi\) | ||
0.776293 | − | 0.630372i | \(-0.217098\pi\) | |||||||
\(350\) | − | 100.000i | − | 0.285714i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −32.0000 | − | 32.0000i | −0.0909091 | − | 0.0909091i | ||||
\(353\) | 447.000 | − | 447.000i | 1.26629 | − | 1.26629i | 0.318298 | − | 0.947991i | \(-0.396889\pi\) |
0.947991 | − | 0.318298i | \(-0.103111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 140.000i | 0.394366i | ||||||||
\(356\) | 160.000 | 0.449438 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −220.000 | + | 220.000i | −0.614525 | + | 0.614525i | ||||
\(359\) | 400.000i | 1.11421i | 0.830443 | + | 0.557103i | \(0.188087\pi\) | ||||
−0.830443 | + | 0.557103i | \(0.811913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | 2.00000 | + | 2.00000i | 0.00552486 | + | 0.00552486i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 24.0000i | 0.0659341i | ||||||||
\(365\) | −235.000 | − | 235.000i | −0.643836 | − | 0.643836i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −118.000 | − | 118.000i | −0.321526 | − | 0.321526i | 0.527826 | − | 0.849352i | \(-0.323007\pi\) |
−0.849352 | + | 0.527826i | \(0.823007\pi\) | |||||||
\(368\) | −8.00000 | + | 8.00000i | −0.0217391 | + | 0.0217391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 30.0000 | 0.0810811 | ||||||||
\(371\) | −212.000 | −0.571429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −107.000 | + | 107.000i | −0.286863 | + | 0.286863i | −0.835839 | − | 0.548975i | \(-0.815018\pi\) |
0.548975 | + | 0.835839i | \(0.315018\pi\) | |||||||
\(374\) | − | 112.000i | − | 0.299465i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −72.0000 | −0.191489 | ||||||||
\(377\) | −120.000 | − | 120.000i | −0.318302 | − | 0.318302i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 340.000i | 0.897098i | 0.893758 | + | 0.448549i | \(0.148059\pi\) | ||||
−0.893758 | + | 0.448549i | \(0.851941\pi\) | |||||||
\(380\) | 200.000i | 0.526316i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −212.000 | − | 212.000i | −0.554974 | − | 0.554974i | ||||
\(383\) | 342.000 | − | 342.000i | 0.892950 | − | 0.892950i | −0.101849 | − | 0.994800i | \(-0.532476\pi\) |
0.994800 | + | 0.101849i | \(0.0324760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −80.0000 | + | 80.0000i | −0.207792 | + | 0.207792i | ||||
\(386\) | −114.000 | −0.295337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 126.000 | − | 126.000i | 0.324742 | − | 0.324742i | ||||
\(389\) | − | 390.000i | − | 1.00257i | −0.865282 | − | 0.501285i | \(-0.832861\pi\) | ||
0.865282 | − | 0.501285i | \(-0.167139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0000 | −0.0716113 | ||||||||
\(392\) | 82.0000 | + | 82.0000i | 0.209184 | + | 0.209184i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000i | 0.0152284i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −323.000 | − | 323.000i | −0.813602 | − | 0.813602i | 0.171570 | − | 0.985172i | \(-0.445116\pi\) |
−0.985172 | + | 0.171570i | \(0.945116\pi\) | |||||||
\(398\) | 120.000 | − | 120.000i | 0.301508 | − | 0.301508i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 100.000 | 0.250000 | ||||||||
\(401\) | −642.000 | −1.60100 | −0.800499 | − | 0.599334i | \(-0.795432\pi\) | ||||
−0.800499 | + | 0.599334i | \(0.795432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 156.000 | − | 156.000i | 0.387097 | − | 0.387097i | ||||
\(404\) | − | 124.000i | − | 0.306931i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 160.000 | 0.394089 | ||||||||
\(407\) | −24.0000 | − | 24.0000i | −0.0589681 | − | 0.0589681i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 150.000i | − | 0.366748i | −0.983043 | − | 0.183374i | \(-0.941298\pi\) | ||
0.983043 | − | 0.183374i | \(-0.0587020\pi\) | |||||||
\(410\) | −40.0000 | + | 40.0000i | −0.0975610 | + | 0.0975610i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 236.000 | + | 236.000i | 0.572816 | + | 0.572816i | ||||
\(413\) | −40.0000 | + | 40.0000i | −0.0968523 | + | 0.0968523i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −90.0000 | − | 90.0000i | −0.216867 | − | 0.216867i | ||||
\(416\) | −24.0000 | −0.0576923 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 160.000 | − | 160.000i | 0.382775 | − | 0.382775i | ||||
\(419\) | − | 300.000i | − | 0.715990i | −0.933723 | − | 0.357995i | \(-0.883460\pi\) | ||
0.933723 | − | 0.357995i | \(-0.116540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −208.000 | −0.494062 | −0.247031 | − | 0.969008i | \(-0.579455\pi\) | ||||
−0.247031 | + | 0.969008i | \(0.579455\pi\) | |||||||
\(422\) | −328.000 | − | 328.000i | −0.777251 | − | 0.777251i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 212.000i | − | 0.500000i | ||||||
\(425\) | 175.000 | + | 175.000i | 0.411765 | + | 0.411765i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −96.0000 | − | 96.0000i | −0.224824 | − | 0.224824i | ||||
\(428\) | 284.000 | − | 284.000i | 0.663551 | − | 0.663551i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 420.000i | − | 0.976744i | ||||||
\(431\) | 788.000 | 1.82831 | 0.914153 | − | 0.405369i | \(-0.132857\pi\) | ||||
0.914153 | + | 0.405369i | \(0.132857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −367.000 | + | 367.000i | −0.847575 | + | 0.847575i | −0.989830 | − | 0.142255i | \(-0.954565\pi\) |
0.142255 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(434\) | 208.000i | 0.479263i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.0000 | 0.0458716 | ||||||||
\(437\) | −40.0000 | − | 40.0000i | −0.0915332 | − | 0.0915332i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 560.000i | 1.27563i | 0.770191 | + | 0.637813i | \(0.220161\pi\) | ||||
−0.770191 | + | 0.637813i | \(0.779839\pi\) | |||||||
\(440\) | −80.0000 | − | 80.0000i | −0.181818 | − | 0.181818i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42.0000 | − | 42.0000i | −0.0950226 | − | 0.0950226i | ||||
\(443\) | −378.000 | + | 378.000i | −0.853273 | + | 0.853273i | −0.990535 | − | 0.137262i | \(-0.956170\pi\) |
0.137262 | + | 0.990535i | \(0.456170\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 400.000 | 0.898876 | ||||||||
\(446\) | 276.000 | 0.618834 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000 | − | 16.0000i | 0.0357143 | − | 0.0357143i | ||||
\(449\) | 410.000i | 0.913140i | 0.889687 | + | 0.456570i | \(0.150922\pi\) | ||||
−0.889687 | + | 0.456570i | \(0.849078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 64.0000 | 0.141907 | ||||||||
\(452\) | −46.0000 | − | 46.0000i | −0.101770 | − | 0.101770i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.00000i | − | 0.00881057i | ||||||
\(455\) | 60.0000i | 0.131868i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −393.000 | − | 393.000i | −0.859956 | − | 0.859956i | 0.131376 | − | 0.991333i | \(-0.458060\pi\) |
−0.991333 | + | 0.131376i | \(0.958060\pi\) | |||||||
\(458\) | −120.000 | + | 120.000i | −0.262009 | + | 0.262009i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.0000 | + | 20.0000i | −0.0434783 | + | 0.0434783i | ||||
\(461\) | −622.000 | −1.34924 | −0.674620 | − | 0.738165i | \(-0.735693\pi\) | ||||
−0.674620 | + | 0.738165i | \(0.735693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 278.000 | − | 278.000i | 0.600432 | − | 0.600432i | −0.339995 | − | 0.940427i | \(-0.610425\pi\) |
0.940427 | + | 0.339995i | \(0.110425\pi\) | |||||||
\(464\) | 160.000i | 0.344828i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −366.000 | −0.785408 | ||||||||
\(467\) | 38.0000 | + | 38.0000i | 0.0813704 | + | 0.0813704i | 0.746621 | − | 0.665250i | \(-0.231675\pi\) |
−0.665250 | + | 0.746621i | \(0.731675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 248.000i | 0.528785i | ||||||||
\(470\) | −180.000 | −0.382979 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.0000 | − | 40.0000i | −0.0847458 | − | 0.0847458i | ||||
\(473\) | −336.000 | + | 336.000i | −0.710359 | + | 0.710359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 500.000i | 1.05263i | ||||||||
\(476\) | 56.0000 | 0.117647 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 120.000 | − | 120.000i | 0.251046 | − | 0.251046i | ||||
\(479\) | 440.000i | 0.918580i | 0.888286 | + | 0.459290i | \(0.151896\pi\) | ||||
−0.888286 | + | 0.459290i | \(0.848104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | −0.0374220 | ||||||||
\(482\) | 232.000 | + | 232.000i | 0.481328 | + | 0.481328i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 114.000i | − | 0.235537i | ||||||
\(485\) | 315.000 | − | 315.000i | 0.649485 | − | 0.649485i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 522.000 | + | 522.000i | 1.07187 | + | 1.07187i | 0.997209 | + | 0.0746595i | \(0.0237870\pi\) |
0.0746595 | + | 0.997209i | \(0.476213\pi\) | |||||||
\(488\) | 96.0000 | − | 96.0000i | 0.196721 | − | 0.196721i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 205.000 | + | 205.000i | 0.418367 | + | 0.418367i | ||||
\(491\) | 328.000 | 0.668024 | 0.334012 | − | 0.942569i | \(-0.391597\pi\) | ||||
0.334012 | + | 0.942569i | \(0.391597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −280.000 | + | 280.000i | −0.567951 | + | 0.567951i | ||||
\(494\) | − | 120.000i | − | 0.242915i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −208.000 | −0.419355 | ||||||||
\(497\) | 56.0000 | + | 56.0000i | 0.112676 | + | 0.112676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 380.000i | 0.761523i | 0.924673 | + | 0.380762i | \(0.124338\pi\) | ||||
−0.924673 | + | 0.380762i | \(0.875662\pi\) | |||||||
\(500\) | 250.000 | 0.500000 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 48.0000 | + | 48.0000i | 0.0956175 | + | 0.0956175i | ||||
\(503\) | 42.0000 | − | 42.0000i | 0.0834990 | − | 0.0834990i | −0.664124 | − | 0.747623i | \(-0.731195\pi\) |
0.747623 | + | 0.664124i | \(0.231195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 310.000i | − | 0.613861i | ||||||
\(506\) | 32.0000 | 0.0632411 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 236.000 | − | 236.000i | 0.464567 | − | 0.464567i | ||||
\(509\) | 440.000i | 0.864440i | 0.901768 | + | 0.432220i | \(0.142270\pi\) | ||||
−0.901768 | + | 0.432220i | \(0.857730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −188.000 | −0.367906 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 626.000i | 1.21790i | ||||||||
\(515\) | 590.000 | + | 590.000i | 1.14563 | + | 1.14563i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 144.000 | + | 144.000i | 0.278530 | + | 0.278530i | ||||
\(518\) | 12.0000 | − | 12.0000i | 0.0231660 | − | 0.0231660i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −60.0000 | −0.115385 | ||||||||
\(521\) | 258.000 | 0.495202 | 0.247601 | − | 0.968862i | \(-0.420358\pi\) | ||||
0.247601 | + | 0.968862i | \(0.420358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 258.000 | − | 258.000i | 0.493308 | − | 0.493308i | −0.416039 | − | 0.909347i | \(-0.636582\pi\) |
0.909347 | + | 0.416039i | \(0.136582\pi\) | |||||||
\(524\) | 256.000i | 0.488550i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 524.000 | 0.996198 | ||||||||
\(527\) | −364.000 | − | 364.000i | −0.690702 | − | 0.690702i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 521.000i | 0.984877i | ||||||||
\(530\) | − | 530.000i | − | 1.00000i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 80.0000 | + | 80.0000i | 0.150376 | + | 0.150376i | ||||
\(533\) | 24.0000 | − | 24.0000i | 0.0450281 | − | 0.0450281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 710.000 | − | 710.000i | 1.32710 | − | 1.32710i | ||||
\(536\) | −248.000 | −0.462687 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0000 | − | 10.0000i | 0.0185874 | − | 0.0185874i | ||||
\(539\) | − | 328.000i | − | 0.608534i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −338.000 | −0.624769 | −0.312384 | − | 0.949956i | \(-0.601128\pi\) | ||||
−0.312384 | + | 0.949956i | \(0.601128\pi\) | |||||||
\(542\) | 252.000 | + | 252.000i | 0.464945 | + | 0.464945i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 56.0000i | 0.102941i | ||||||||
\(545\) | 50.0000 | 0.0917431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −558.000 | − | 558.000i | −1.02011 | − | 1.02011i | −0.999794 | − | 0.0203161i | \(-0.993533\pi\) |
−0.0203161 | − | 0.999794i | \(-0.506467\pi\) | |||||||
\(548\) | −126.000 | + | 126.000i | −0.229927 | + | 0.229927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −200.000 | − | 200.000i | −0.363636 | − | 0.363636i | ||||
\(551\) | −800.000 | −1.45191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 534.000i | 0.963899i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −280.000 | −0.503597 | ||||||||
\(557\) | 3.00000 | + | 3.00000i | 0.00538600 | + | 0.00538600i | 0.709795 | − | 0.704409i | \(-0.248788\pi\) |
−0.704409 | + | 0.709795i | \(0.748788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 252.000i | 0.450805i | ||||||||
\(560\) | 40.0000 | − | 40.0000i | 0.0714286 | − | 0.0714286i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −312.000 | − | 312.000i | −0.555160 | − | 0.555160i | ||||
\(563\) | 42.0000 | − | 42.0000i | 0.0746004 | − | 0.0746004i | −0.668822 | − | 0.743422i | \(-0.733201\pi\) |
0.743422 | + | 0.668822i | \(0.233201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −115.000 | − | 115.000i | −0.203540 | − | 0.203540i | ||||
\(566\) | −524.000 | −0.925795 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −56.0000 | + | 56.0000i | −0.0985915 | + | 0.0985915i | ||||
\(569\) | − | 950.000i | − | 1.66960i | −0.550557 | − | 0.834798i | \(-0.685584\pi\) | ||
0.550557 | − | 0.834798i | \(-0.314416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 392.000 | 0.686515 | 0.343257 | − | 0.939241i | \(-0.388470\pi\) | ||||
0.343257 | + | 0.939241i | \(0.388470\pi\) | |||||||
\(572\) | 48.0000 | + | 48.0000i | 0.0839161 | + | 0.0839161i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 32.0000i | 0.0557491i | ||||||||
\(575\) | −50.0000 | + | 50.0000i | −0.0869565 | + | 0.0869565i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −473.000 | − | 473.000i | −0.819757 | − | 0.819757i | 0.166315 | − | 0.986073i | \(-0.446813\pi\) |
−0.986073 | + | 0.166315i | \(0.946813\pi\) | |||||||
\(578\) | 191.000 | − | 191.000i | 0.330450 | − | 0.330450i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 400.000i | 0.689655i | ||||||||
\(581\) | −72.0000 | −0.123924 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −424.000 | + | 424.000i | −0.727273 | + | 0.727273i | ||||
\(584\) | − | 188.000i | − | 0.321918i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −486.000 | −0.829352 | ||||||||
\(587\) | 198.000 | + | 198.000i | 0.337308 | + | 0.337308i | 0.855353 | − | 0.518045i | \(-0.173340\pi\) |
−0.518045 | + | 0.855353i | \(0.673340\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1040.00i | − | 1.76570i | ||||||
\(590\) | −100.000 | − | 100.000i | −0.169492 | − | 0.169492i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.0000 | + | 12.0000i | 0.0202703 | + | 0.0202703i | ||||
\(593\) | 47.0000 | − | 47.0000i | 0.0792580 | − | 0.0792580i | −0.666366 | − | 0.745624i | \(-0.732151\pi\) |
0.745624 | + | 0.666366i | \(0.232151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 140.000 | 0.235294 | ||||||||
\(596\) | −300.000 | −0.503356 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | − | 12.0000i | 0.0200669 | − | 0.0200669i | ||||
\(599\) | − | 520.000i | − | 0.868114i | −0.900886 | − | 0.434057i | \(-0.857082\pi\) | ||
0.900886 | − | 0.434057i | \(-0.142918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −328.000 | −0.545757 | −0.272879 | − | 0.962048i | \(-0.587976\pi\) | ||||
−0.272879 | + | 0.962048i | \(0.587976\pi\) | |||||||
\(602\) | −168.000 | − | 168.000i | −0.279070 | − | 0.279070i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 104.000i | 0.172185i | ||||||||
\(605\) | − | 285.000i | − | 0.471074i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 462.000 | + | 462.000i | 0.761120 | + | 0.761120i | 0.976525 | − | 0.215405i | \(-0.0691070\pi\) |
−0.215405 | + | 0.976525i | \(0.569107\pi\) | |||||||
\(608\) | −80.0000 | + | 80.0000i | −0.131579 | + | 0.131579i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 240.000 | − | 240.000i | 0.393443 | − | 0.393443i | ||||
\(611\) | 108.000 | 0.176759 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 723.000 | − | 723.000i | 1.17945 | − | 1.17945i | 0.199560 | − | 0.979886i | \(-0.436049\pi\) |
0.979886 | − | 0.199560i | \(-0.0639512\pi\) | |||||||
\(614\) | − | 36.0000i | − | 0.0586319i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −64.0000 | −0.103896 | ||||||||
\(617\) | −327.000 | − | 327.000i | −0.529984 | − | 0.529984i | 0.390584 | − | 0.920567i | \(-0.372273\pi\) |
−0.920567 | + | 0.390584i | \(0.872273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 660.000i | − | 1.06624i | −0.846041 | − | 0.533118i | \(-0.821020\pi\) | ||
0.846041 | − | 0.533118i | \(-0.178980\pi\) | |||||||
\(620\) | −520.000 | −0.838710 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 388.000 | + | 388.000i | 0.623794 | + | 0.623794i | ||||
\(623\) | 160.000 | − | 160.000i | 0.256822 | − | 0.256822i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 1.00000 | ||||||||
\(626\) | 366.000 | 0.584665 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −54.0000 | + | 54.0000i | −0.0859873 | + | 0.0859873i | ||||
\(629\) | 42.0000i | 0.0667727i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −548.000 | −0.868463 | −0.434231 | − | 0.900801i | \(-0.642980\pi\) | ||||
−0.434231 | + | 0.900801i | \(0.642980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 426.000i | 0.671924i | ||||||||
\(635\) | 590.000 | − | 590.000i | 0.929134 | − | 0.929134i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −123.000 | − | 123.000i | −0.193093 | − | 0.193093i | ||||
\(638\) | 320.000 | − | 320.000i | 0.501567 | − | 0.501567i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.0000 | + | 40.0000i | 0.0625000 | + | 0.0625000i | ||||
\(641\) | 568.000 | 0.886115 | 0.443058 | − | 0.896493i | \(-0.353894\pi\) | ||||
0.443058 | + | 0.896493i | \(0.353894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −342.000 | + | 342.000i | −0.531882 | + | 0.531882i | −0.921132 | − | 0.389250i | \(-0.872734\pi\) |
0.389250 | + | 0.921132i | \(0.372734\pi\) | |||||||
\(644\) | 16.0000i | 0.0248447i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −280.000 | −0.433437 | ||||||||
\(647\) | 118.000 | + | 118.000i | 0.182380 | + | 0.182380i | 0.792392 | − | 0.610012i | \(-0.208835\pi\) |
−0.610012 | + | 0.792392i | \(0.708835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 160.000i | 0.246533i | ||||||||
\(650\) | −150.000 | −0.230769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −164.000 | − | 164.000i | −0.251534 | − | 0.251534i | ||||
\(653\) | −453.000 | + | 453.000i | −0.693721 | + | 0.693721i | −0.963049 | − | 0.269327i | \(-0.913199\pi\) |
0.269327 | + | 0.963049i | \(0.413199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 640.000i | 0.977099i | ||||||||
\(656\) | −32.0000 | −0.0487805 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −72.0000 | + | 72.0000i | −0.109422 | + | 0.109422i | ||||
\(659\) | − | 140.000i | − | 0.212443i | −0.994342 | − | 0.106222i | \(-0.966125\pi\) | ||
0.994342 | − | 0.106222i | \(-0.0338753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 512.000 | 0.774584 | 0.387292 | − | 0.921957i | \(-0.373411\pi\) | ||||
0.387292 | + | 0.921957i | \(0.373411\pi\) | |||||||
\(662\) | 232.000 | + | 232.000i | 0.350453 | + | 0.350453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 72.0000i | − | 0.108434i | ||||||
\(665\) | 200.000 | + | 200.000i | 0.300752 | + | 0.300752i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −80.0000 | − | 80.0000i | −0.119940 | − | 0.119940i | ||||
\(668\) | 124.000 | − | 124.000i | 0.185629 | − | 0.185629i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −620.000 | −0.925373 | ||||||||
\(671\) | −384.000 | −0.572280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 193.000 | − | 193.000i | 0.286776 | − | 0.286776i | −0.549028 | − | 0.835804i | \(-0.685002\pi\) |
0.835804 | + | 0.549028i | \(0.185002\pi\) | |||||||
\(674\) | 834.000i | 1.23739i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −302.000 | −0.446746 | ||||||||
\(677\) | −157.000 | − | 157.000i | −0.231905 | − | 0.231905i | 0.581582 | − | 0.813488i | \(-0.302434\pi\) |
−0.813488 | + | 0.581582i | \(0.802434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 252.000i | − | 0.371134i | ||||||
\(680\) | 140.000i | 0.205882i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 416.000 | + | 416.000i | 0.609971 | + | 0.609971i | ||||
\(683\) | −438.000 | + | 438.000i | −0.641288 | + | 0.641288i | −0.950872 | − | 0.309584i | \(-0.899810\pi\) |
0.309584 | + | 0.950872i | \(0.399810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −315.000 | + | 315.000i | −0.459854 | + | 0.459854i | ||||
\(686\) | 360.000 | 0.524781 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 168.000 | − | 168.000i | 0.244186 | − | 0.244186i | ||||
\(689\) | 318.000i | 0.461538i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1032.00 | 1.49349 | 0.746744 | − | 0.665112i | \(-0.231616\pi\) | ||||
0.746744 | + | 0.665112i | \(0.231616\pi\) | |||||||
\(692\) | 214.000 | + | 214.000i | 0.309249 | + | 0.309249i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 404.000i | − | 0.582133i | ||||||
\(695\) | −700.000 | −1.00719 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.0000 | − | 56.0000i | −0.0803443 | − | 0.0803443i | ||||
\(698\) | 440.000 | − | 440.000i | 0.630372 | − | 0.630372i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 100.000 | − | 100.000i | 0.142857 | − | 0.142857i | ||||
\(701\) | 128.000 | 0.182596 | 0.0912981 | − | 0.995824i | \(-0.470898\pi\) | ||||
0.0912981 | + | 0.995824i | \(0.470898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.0000 | + | 60.0000i | −0.0853485 | + | 0.0853485i | ||||
\(704\) | − | 64.0000i | − | 0.0909091i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 894.000 | 1.26629 | ||||||||
\(707\) | −124.000 | − | 124.000i | −0.175389 | − | 0.175389i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 760.000i | 1.07193i | 0.844239 | + | 0.535966i | \(0.180053\pi\) | ||||
−0.844239 | + | 0.535966i | \(0.819947\pi\) | |||||||
\(710\) | −140.000 | + | 140.000i | −0.197183 | + | 0.197183i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 160.000 | + | 160.000i | 0.224719 | + | 0.224719i | ||||
\(713\) | 104.000 | − | 104.000i | 0.145863 | − | 0.145863i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 120.000 | + | 120.000i | 0.167832 | + | 0.167832i | ||||
\(716\) | −440.000 | −0.614525 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −400.000 | + | 400.000i | −0.557103 | + | 0.557103i | ||||
\(719\) | 1160.00i | 1.61335i | 0.590994 | + | 0.806676i | \(0.298736\pi\) | ||||
−0.590994 | + | 0.806676i | \(0.701264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 472.000 | 0.654646 | ||||||||
\(722\) | −39.0000 | − | 39.0000i | −0.0540166 | − | 0.0540166i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.00000i | 0.00552486i | ||||||||
\(725\) | 1000.00i | 1.37931i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −558.000 | − | 558.000i | −0.767538 | − | 0.767538i | 0.210135 | − | 0.977672i | \(-0.432610\pi\) |
−0.977672 | + | 0.210135i | \(0.932610\pi\) | |||||||
\(728\) | −24.0000 | + | 24.0000i | −0.0329670 | + | 0.0329670i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 470.000i | − | 0.643836i | ||||||
\(731\) | 588.000 | 0.804378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −827.000 | + | 827.000i | −1.12824 | + | 1.12824i | −0.137777 | + | 0.990463i | \(0.543996\pi\) |
−0.990463 | + | 0.137777i | \(0.956004\pi\) | |||||||
\(734\) | − | 236.000i | − | 0.321526i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.0000 | −0.0217391 | ||||||||
\(737\) | 496.000 | + | 496.000i | 0.672999 | + | 0.672999i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 700.000i | − | 0.947226i | −0.880733 | − | 0.473613i | \(-0.842950\pi\) | ||
0.880733 | − | 0.473613i | \(-0.157050\pi\) | |||||||
\(740\) | 30.0000 | + | 30.0000i | 0.0405405 | + | 0.0405405i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −212.000 | − | 212.000i | −0.285714 | − | 0.285714i | ||||
\(743\) | 382.000 | − | 382.000i | 0.514132 | − | 0.514132i | −0.401658 | − | 0.915790i | \(-0.631566\pi\) |
0.915790 | + | 0.401658i | \(0.131566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −750.000 | −1.00671 | ||||||||
\(746\) | −214.000 | −0.286863 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 112.000 | − | 112.000i | 0.149733 | − | 0.149733i | ||||
\(749\) | − | 568.000i | − | 0.758344i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −588.000 | −0.782956 | −0.391478 | − | 0.920187i | \(-0.628036\pi\) | ||||
−0.391478 | + | 0.920187i | \(0.628036\pi\) | |||||||
\(752\) | −72.0000 | − | 72.0000i | −0.0957447 | − | 0.0957447i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 240.000i | − | 0.318302i | ||||||
\(755\) | 260.000i | 0.344371i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 987.000 | + | 987.000i | 1.30383 | + | 1.30383i | 0.925788 | + | 0.378043i | \(0.123403\pi\) |
0.378043 | + | 0.925788i | \(0.376597\pi\) | |||||||
\(758\) | −340.000 | + | 340.000i | −0.448549 | + | 0.448549i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −200.000 | + | 200.000i | −0.263158 | + | 0.263158i | ||||
\(761\) | 158.000 | 0.207622 | 0.103811 | − | 0.994597i | \(-0.466896\pi\) | ||||
0.103811 | + | 0.994597i | \(0.466896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | − | 20.0000i | 0.0262123 | − | 0.0262123i | ||||
\(764\) | − | 424.000i | − | 0.554974i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 684.000 | 0.892950 | ||||||||
\(767\) | 60.0000 | + | 60.0000i | 0.0782269 | + | 0.0782269i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 80.0000i | 0.104031i | 0.998646 | + | 0.0520156i | \(0.0165646\pi\) | ||||
−0.998646 | + | 0.0520156i | \(0.983435\pi\) | |||||||
\(770\) | −160.000 | −0.207792 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −114.000 | − | 114.000i | −0.147668 | − | 0.147668i | ||||
\(773\) | −243.000 | + | 243.000i | −0.314360 | + | 0.314360i | −0.846596 | − | 0.532236i | \(-0.821352\pi\) |
0.532236 | + | 0.846596i | \(0.321352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1300.00 | −1.67742 | ||||||||
\(776\) | 252.000 | 0.324742 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 390.000 | − | 390.000i | 0.501285 | − | 0.501285i | ||||
\(779\) | − | 160.000i | − | 0.205392i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 224.000 | 0.286812 | ||||||||
\(782\) | −28.0000 | − | 28.0000i | −0.0358056 | − | 0.0358056i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 164.000i | 0.209184i | ||||||||
\(785\) | −135.000 | + | 135.000i | −0.171975 | + | 0.171975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 262.000 | + | 262.000i | 0.332910 | + | 0.332910i | 0.853690 | − | 0.520781i | \(-0.174359\pi\) |
−0.520781 | + | 0.853690i | \(0.674359\pi\) | |||||||
\(788\) | −6.00000 | + | 6.00000i | −0.00761421 | + | 0.00761421i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.0000 | −0.116308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −144.000 | + | 144.000i | −0.181589 | + | 0.181589i | ||||
\(794\) | − | 646.000i | − | 0.813602i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 240.000 | 0.301508 | ||||||||
\(797\) | −267.000 | − | 267.000i | −0.335006 | − | 0.335006i | 0.519478 | − | 0.854484i | \(-0.326127\pi\) |
−0.854484 | + | 0.519478i | \(0.826127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 252.000i | − | 0.315394i | ||||||
\(800\) | 100.000 | + | 100.000i | 0.125000 | + | 0.125000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −642.000 | − | 642.000i | −0.800499 | − | 0.800499i | ||||
\(803\) | −376.000 | + | 376.000i | −0.468244 | + | 0.468244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.0000i | 0.0496894i | ||||||||
\(806\) | 312.000 | 0.387097 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 124.000 | − | 124.000i | 0.153465 | − | 0.153465i | ||||
\(809\) | − | 560.000i | − | 0.692213i | −0.938195 | − | 0.346106i | \(-0.887504\pi\) | ||
0.938195 | − | 0.346106i | \(-0.112496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −208.000 | −0.256473 | −0.128237 | − | 0.991744i | \(-0.540932\pi\) | ||||
−0.128237 | + | 0.991744i | \(0.540932\pi\) | |||||||
\(812\) | 160.000 | + | 160.000i | 0.197044 | + | 0.197044i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 48.0000i | − | 0.0589681i | ||||||
\(815\) | −410.000 | − | 410.000i | −0.503067 | − | 0.503067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 840.000 | + | 840.000i | 1.02815 | + | 1.02815i | ||||
\(818\) | 150.000 | − | 150.000i | 0.183374 | − | 0.183374i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −80.0000 | −0.0975610 | ||||||||
\(821\) | 1568.00 | 1.90987 | 0.954933 | − | 0.296821i | \(-0.0959266\pi\) | ||||
0.954933 | + | 0.296821i | \(0.0959266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −562.000 | + | 562.000i | −0.682868 | + | 0.682868i | −0.960645 | − | 0.277778i | \(-0.910402\pi\) |
0.277778 | + | 0.960645i | \(0.410402\pi\) | |||||||
\(824\) | 472.000i | 0.572816i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −80.0000 | −0.0968523 | ||||||||
\(827\) | −762.000 | − | 762.000i | −0.921403 | − | 0.921403i | 0.0757260 | − | 0.997129i | \(-0.475873\pi\) |
−0.997129 | + | 0.0757260i | \(0.975873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 170.000i | 0.205066i | 0.994730 | + | 0.102533i | \(0.0326948\pi\) | ||||
−0.994730 | + | 0.102533i | \(0.967305\pi\) | |||||||
\(830\) | − | 180.000i | − | 0.216867i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.0000 | − | 24.0000i | −0.0288462 | − | 0.0288462i | ||||
\(833\) | −287.000 | + | 287.000i | −0.344538 | + | 0.344538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 310.000 | − | 310.000i | 0.371257 | − | 0.371257i | ||||
\(836\) | 320.000 | 0.382775 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 300.000 | − | 300.000i | 0.357995 | − | 0.357995i | ||||
\(839\) | 280.000i | 0.333731i | 0.985980 | + | 0.166865i | \(0.0533645\pi\) | ||||
−0.985980 | + | 0.166865i | \(0.946635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −759.000 | −0.902497 | ||||||||
\(842\) | −208.000 | − | 208.000i | −0.247031 | − | 0.247031i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 656.000i | − | 0.777251i | ||||||
\(845\) | −755.000 | −0.893491 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −114.000 | − | 114.000i | −0.134593 | − | 0.134593i | ||||
\(848\) | 212.000 | − | 212.000i | 0.250000 | − | 0.250000i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 350.000i | 0.411765i | ||||||||
\(851\) | −12.0000 | −0.0141011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1123.00 | − | 1123.00i | 1.31653 | − | 1.31653i | 0.400026 | − | 0.916504i | \(-0.369001\pi\) |
0.916504 | − | 0.400026i | \(-0.130999\pi\) | |||||||
\(854\) | − | 192.000i | − | 0.224824i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 568.000 | 0.663551 | ||||||||
\(857\) | −417.000 | − | 417.000i | −0.486581 | − | 0.486581i | 0.420644 | − | 0.907226i | \(-0.361804\pi\) |
−0.907226 | + | 0.420644i | \(0.861804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1300.00i | − | 1.51339i | −0.653769 | − | 0.756694i | \(-0.726813\pi\) | ||
0.653769 | − | 0.756694i | \(-0.273187\pi\) | |||||||
\(860\) | 420.000 | − | 420.000i | 0.488372 | − | 0.488372i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 788.000 | + | 788.000i | 0.914153 | + | 0.914153i | ||||
\(863\) | 242.000 | − | 242.000i | 0.280417 | − | 0.280417i | −0.552858 | − | 0.833275i | \(-0.686463\pi\) |
0.833275 | + | 0.552858i | \(0.186463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 535.000 | + | 535.000i | 0.618497 | + | 0.618497i | ||||
\(866\) | −734.000 | −0.847575 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −208.000 | + | 208.000i | −0.239631 | + | 0.239631i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 372.000 | 0.427095 | ||||||||
\(872\) | 20.0000 | + | 20.0000i | 0.0229358 | + | 0.0229358i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 80.0000i | − | 0.0915332i | ||||||
\(875\) | 250.000 | − | 250.000i | 0.285714 | − | 0.285714i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −453.000 | − | 453.000i | −0.516534 | − | 0.516534i | 0.399987 | − | 0.916521i | \(-0.369015\pi\) |
−0.916521 | + | 0.399987i | \(0.869015\pi\) | |||||||
\(878\) | −560.000 | + | 560.000i | −0.637813 | + | 0.637813i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 160.000i | − | 0.181818i | ||||||
\(881\) | −712.000 | −0.808173 | −0.404086 | − | 0.914721i | \(-0.632410\pi\) | ||||
−0.404086 | + | 0.914721i | \(0.632410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 118.000 | − | 118.000i | 0.133635 | − | 0.133635i | −0.637125 | − | 0.770760i | \(-0.719877\pi\) |
0.770760 | + | 0.637125i | \(0.219877\pi\) | |||||||
\(884\) | − | 84.0000i | − | 0.0950226i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −756.000 | −0.853273 | ||||||||
\(887\) | 1158.00 | + | 1158.00i | 1.30552 | + | 1.30552i | 0.924611 | + | 0.380914i | \(0.124390\pi\) |
0.380914 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 472.000i | − | 0.530934i | ||||||
\(890\) | 400.000 | + | 400.000i | 0.449438 | + | 0.449438i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 276.000 | + | 276.000i | 0.309417 | + | 0.309417i | ||||
\(893\) | 360.000 | − | 360.000i | 0.403135 | − | 0.403135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1100.00 | −1.22905 | ||||||||
\(896\) | 32.0000 | 0.0357143 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −410.000 | + | 410.000i | −0.456570 | + | 0.456570i | ||||
\(899\) | − | 2080.00i | − | 2.31368i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 742.000 | 0.823529 | ||||||||
\(902\) | 64.0000 | + | 64.0000i | 0.0709534 | + | 0.0709534i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 92.0000i | − | 0.101770i | ||||||
\(905\) | 10.0000i | 0.0110497i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 142.000 | + | 142.000i | 0.156560 | + | 0.156560i | 0.781040 | − | 0.624480i | \(-0.214689\pi\) |
−0.624480 | + | 0.781040i | \(0.714689\pi\) | |||||||
\(908\) | 4.00000 | − | 4.00000i | 0.00440529 | − | 0.00440529i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −60.0000 | + | 60.0000i | −0.0659341 | + | 0.0659341i | ||||
\(911\) | −1172.00 | −1.28650 | −0.643249 | − | 0.765657i | \(-0.722414\pi\) | ||||
−0.643249 | + | 0.765657i | \(0.722414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −144.000 | + | 144.000i | −0.157722 | + | 0.157722i | ||||
\(914\) | − | 786.000i | − | 0.859956i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −240.000 | −0.262009 | ||||||||
\(917\) | 256.000 | + | 256.000i | 0.279171 | + | 0.279171i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 920.000i | 1.00109i | 0.865711 | + | 0.500544i | \(0.166867\pi\) | ||||
−0.865711 | + | 0.500544i | \(0.833133\pi\) | |||||||
\(920\) | −40.0000 | −0.0434783 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −622.000 | − | 622.000i | −0.674620 | − | 0.674620i | ||||
\(923\) | 84.0000 | − | 84.0000i | 0.0910076 | − | 0.0910076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75.0000 | + | 75.0000i | 0.0810811 | + | 0.0810811i | ||||
\(926\) | 556.000 | 0.600432 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −160.000 | + | 160.000i | −0.172414 | + | 0.172414i | ||||
\(929\) | 1190.00i | 1.28095i | 0.767980 | + | 0.640474i | \(0.221262\pi\) | ||||
−0.767980 | + | 0.640474i | \(0.778738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −820.000 | −0.880773 | ||||||||
\(932\) | −366.000 | − | 366.000i | −0.392704 | − | 0.392704i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 76.0000i | 0.0813704i | ||||||||
\(935\) | 280.000 | − | 280.000i | 0.299465 | − | 0.299465i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −233.000 | − | 233.000i | −0.248666 | − | 0.248666i | 0.571757 | − | 0.820423i | \(-0.306262\pi\) |
−0.820423 | + | 0.571757i | \(0.806262\pi\) | |||||||
\(938\) | −248.000 | + | 248.000i | −0.264392 | + | 0.264392i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −180.000 | − | 180.000i | −0.191489 | − | 0.191489i | ||||
\(941\) | 78.0000 | 0.0828905 | 0.0414453 | − | 0.999141i | \(-0.486804\pi\) | ||||
0.0414453 | + | 0.999141i | \(0.486804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | − | 16.0000i | 0.0169671 | − | 0.0169671i | ||||
\(944\) | − | 80.0000i | − | 0.0847458i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −672.000 | −0.710359 | ||||||||
\(947\) | −62.0000 | − | 62.0000i | −0.0654699 | − | 0.0654699i | 0.673614 | − | 0.739084i | \(-0.264741\pi\) |
−0.739084 | + | 0.673614i | \(0.764741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 282.000i | 0.297155i | ||||||||
\(950\) | −500.000 | + | 500.000i | −0.526316 | + | 0.526316i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 56.0000 | + | 56.0000i | 0.0588235 | + | 0.0588235i | ||||
\(953\) | 1017.00 | − | 1017.00i | 1.06716 | − | 1.06716i | 0.0695800 | − | 0.997576i | \(-0.477834\pi\) |
0.997576 | − | 0.0695800i | \(-0.0221659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1060.00i | − | 1.10995i | ||||||
\(956\) | 240.000 | 0.251046 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −440.000 | + | 440.000i | −0.459290 | + | 0.459290i | ||||
\(959\) | 252.000i | 0.262774i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1743.00 | 1.81374 | ||||||||
\(962\) | −18.0000 | − | 18.0000i | −0.0187110 | − | 0.0187110i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 464.000i | 0.481328i | ||||||||
\(965\) | −285.000 | − | 285.000i | −0.295337 | − | 0.295337i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 502.000 | + | 502.000i | 0.519131 | + | 0.519131i | 0.917309 | − | 0.398177i | \(-0.130357\pi\) |
−0.398177 | + | 0.917309i | \(0.630357\pi\) | |||||||
\(968\) | 114.000 | − | 114.000i | 0.117769 | − | 0.117769i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 630.000 | 0.649485 | ||||||||
\(971\) | −992.000 | −1.02163 | −0.510814 | − | 0.859691i | \(-0.670656\pi\) | ||||
−0.510814 | + | 0.859691i | \(0.670656\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −280.000 | + | 280.000i | −0.287770 | + | 0.287770i | ||||
\(974\) | 1044.00i | 1.07187i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 192.000 | 0.196721 | ||||||||
\(977\) | 783.000 | + | 783.000i | 0.801433 | + | 0.801433i | 0.983320 | − | 0.181887i | \(-0.0582204\pi\) |
−0.181887 | + | 0.983320i | \(0.558220\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 640.000i | − | 0.653728i | ||||||
\(980\) | 410.000i | 0.418367i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 328.000 | + | 328.000i | 0.334012 | + | 0.334012i | ||||
\(983\) | −1058.00 | + | 1058.00i | −1.07630 | + | 1.07630i | −0.0794589 | + | 0.996838i | \(0.525319\pi\) |
−0.996838 | + | 0.0794589i | \(0.974681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0000 | + | 15.0000i | −0.0152284 | + | 0.0152284i | ||||
\(986\) | −560.000 | −0.567951 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 120.000 | − | 120.000i | 0.121457 | − | 0.121457i | ||||
\(989\) | 168.000i | 0.169869i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −68.0000 | −0.0686176 | −0.0343088 | − | 0.999411i | \(-0.510923\pi\) | ||||
−0.0343088 | + | 0.999411i | \(0.510923\pi\) | |||||||
\(992\) | −208.000 | − | 208.000i | −0.209677 | − | 0.209677i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 112.000i | 0.112676i | ||||||||
\(995\) | 600.000 | 0.603015 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −773.000 | − | 773.000i | −0.775326 | − | 0.775326i | 0.203706 | − | 0.979032i | \(-0.434701\pi\) |
−0.979032 | + | 0.203706i | \(0.934701\pi\) | |||||||
\(998\) | −380.000 | + | 380.000i | −0.380762 | + | 0.380762i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 90.3.g.b.37.1 | 2 | ||
3.2 | odd | 2 | 10.3.c.a.7.1 | yes | 2 | ||
4.3 | odd | 2 | 720.3.bh.c.577.1 | 2 | |||
5.2 | odd | 4 | 450.3.g.b.343.1 | 2 | |||
5.3 | odd | 4 | inner | 90.3.g.b.73.1 | 2 | ||
5.4 | even | 2 | 450.3.g.b.307.1 | 2 | |||
12.11 | even | 2 | 80.3.p.c.17.1 | 2 | |||
15.2 | even | 4 | 50.3.c.c.43.1 | 2 | |||
15.8 | even | 4 | 10.3.c.a.3.1 | ✓ | 2 | ||
15.14 | odd | 2 | 50.3.c.c.7.1 | 2 | |||
20.3 | even | 4 | 720.3.bh.c.433.1 | 2 | |||
21.20 | even | 2 | 490.3.f.b.197.1 | 2 | |||
24.5 | odd | 2 | 320.3.p.h.257.1 | 2 | |||
24.11 | even | 2 | 320.3.p.a.257.1 | 2 | |||
60.23 | odd | 4 | 80.3.p.c.33.1 | 2 | |||
60.47 | odd | 4 | 400.3.p.b.193.1 | 2 | |||
60.59 | even | 2 | 400.3.p.b.257.1 | 2 | |||
105.83 | odd | 4 | 490.3.f.b.393.1 | 2 | |||
120.53 | even | 4 | 320.3.p.h.193.1 | 2 | |||
120.83 | odd | 4 | 320.3.p.a.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.3.c.a.3.1 | ✓ | 2 | 15.8 | even | 4 | ||
10.3.c.a.7.1 | yes | 2 | 3.2 | odd | 2 | ||
50.3.c.c.7.1 | 2 | 15.14 | odd | 2 | |||
50.3.c.c.43.1 | 2 | 15.2 | even | 4 | |||
80.3.p.c.17.1 | 2 | 12.11 | even | 2 | |||
80.3.p.c.33.1 | 2 | 60.23 | odd | 4 | |||
90.3.g.b.37.1 | 2 | 1.1 | even | 1 | trivial | ||
90.3.g.b.73.1 | 2 | 5.3 | odd | 4 | inner | ||
320.3.p.a.193.1 | 2 | 120.83 | odd | 4 | |||
320.3.p.a.257.1 | 2 | 24.11 | even | 2 | |||
320.3.p.h.193.1 | 2 | 120.53 | even | 4 | |||
320.3.p.h.257.1 | 2 | 24.5 | odd | 2 | |||
400.3.p.b.193.1 | 2 | 60.47 | odd | 4 | |||
400.3.p.b.257.1 | 2 | 60.59 | even | 2 | |||
450.3.g.b.307.1 | 2 | 5.4 | even | 2 | |||
450.3.g.b.343.1 | 2 | 5.2 | odd | 4 | |||
490.3.f.b.197.1 | 2 | 21.20 | even | 2 | |||
490.3.f.b.393.1 | 2 | 105.83 | odd | 4 | |||
720.3.bh.c.433.1 | 2 | 20.3 | even | 4 | |||
720.3.bh.c.577.1 | 2 | 4.3 | odd | 2 |