Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,3,Mod(17,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("80.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.p (of order \(4\), degree \(2\), 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: | \(2.17984211488\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.17 |
Dual form | 80.3.p.c.33.1 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.00000 | − | 2.00000i | 0.666667 | − | 0.666667i | −0.290276 | − | 0.956943i | \(-0.593747\pi\) |
0.956943 | + | 0.290276i | \(0.0937472\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.00000i | − | 1.00000i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 2.00000i | −0.285714 | − | 0.285714i | 0.549669 | − | 0.835383i | \(-0.314754\pi\) |
−0.835383 | + | 0.549669i | \(0.814754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.111111i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | \(0.197825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0000 | − | 10.0000i | −0.666667 | − | 0.666667i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.00000 | + | 7.00000i | 0.411765 | + | 0.411765i | 0.882353 | − | 0.470588i | \(-0.155958\pi\) |
−0.470588 | + | 0.882353i | \(0.655958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000i | 1.05263i | 0.850289 | + | 0.526316i | \(0.176427\pi\) | ||||
−0.850289 | + | 0.526316i | \(0.823573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.00000 | −0.380952 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 20.0000 | + | 20.0000i | 0.740741 | + | 0.740741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.0000i | 1.37931i | 0.724138 | + | 0.689655i | \(0.242238\pi\) | ||||
−0.724138 | + | 0.689655i | \(0.757762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −52.0000 | −1.67742 | −0.838710 | − | 0.544579i | \(-0.816690\pi\) | ||||
−0.838710 | + | 0.544579i | \(0.816690\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.0000 | − | 16.0000i | 0.484848 | − | 0.484848i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −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 | \(0.768260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 12.0000i | − | 0.307692i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −0.195122 | −0.0975610 | − | 0.995230i | \(-0.531104\pi\) | ||||
−0.0975610 | + | 0.995230i | \(0.531104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.0000 | − | 42.0000i | 0.976744 | − | 0.976744i | −0.0229915 | − | 0.999736i | \(-0.507319\pi\) |
0.999736 | + | 0.0229915i | \(0.00731906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00000 | 0.111111 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.0000 | 0.549020 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 53.0000 | − | 53.0000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 40.0000i | − | 0.727273i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.0000 | + | 40.0000i | 0.701754 | + | 0.701754i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.628716\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 2.00000i | 0.0317460 | − | 0.0317460i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.0000 | − | 15.0000i | −0.230769 | − | 0.230769i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.0000 | − | 62.0000i | −0.925373 | − | 0.925373i | 0.0720294 | − | 0.997403i | \(-0.477052\pi\) |
−0.997403 | + | 0.0720294i | \(0.977052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.00000i | − | 0.115942i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(0.400454\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −50.0000 | + | 50.0000i | −0.666667 | + | 0.666667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0000 | − | 16.0000i | −0.207792 | − | 0.207792i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 71.0000 | 0.876543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −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 | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 80.0000 | + | 80.0000i | 0.919540 | + | 0.919540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 80.0000i | 0.898876i | 0.893311 | + | 0.449438i | \(0.148376\pi\) | ||||
−0.893311 | + | 0.449438i | \(0.851624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −0.131868 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −104.000 | + | 104.000i | −1.11828 | + | 1.11828i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 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 | \(0.901884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.00000i | 0.0808081i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62.0000 | 0.613861 | 0.306931 | − | 0.951732i | \(-0.400698\pi\) | ||||
0.306931 | + | 0.951732i | \(0.400698\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −118.000 | + | 118.000i | −1.14563 | + | 1.14563i | −0.158229 | + | 0.987403i | \(0.550578\pi\) |
−0.987403 | + | 0.158229i | \(0.949422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 40.0000i | 0.380952i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −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 | \(-0.0146065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −0.108108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 23.0000 | − | 23.0000i | 0.203540 | − | 0.203540i | −0.597975 | − | 0.801515i | \(-0.704028\pi\) |
0.801515 | + | 0.597975i | \(0.204028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0000 | − | 10.0000i | −0.0869565 | − | 0.0869565i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 3.00000i | 0.0256410 | + | 0.0256410i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 28.0000i | − | 0.235294i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −57.0000 | −0.471074 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.0000 | + | 16.0000i | −0.130081 | + | 0.130081i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.000 | + | 118.000i | 0.929134 | + | 0.929134i | 0.997650 | − | 0.0685161i | \(-0.0218265\pi\) |
−0.0685161 | + | 0.997650i | \(0.521826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 168.000i | − | 1.30233i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 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 | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 100.000 | − | 100.000i | 0.740741 | − | 0.740741i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −63.0000 | − | 63.0000i | −0.459854 | − | 0.459854i | 0.438753 | − | 0.898607i | \(-0.355420\pi\) |
−0.898607 | + | 0.438753i | \(0.855420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 140.000i | − | 1.00719i | −0.863939 | − | 0.503597i | \(-0.832010\pi\) | ||
0.863939 | − | 0.503597i | \(-0.167990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 72.0000 | 0.510638 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0000 | − | 24.0000i | 0.167832 | − | 0.167832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 200.000 | 1.37931 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −82.0000 | − | 82.0000i | −0.557823 | − | 0.557823i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 150.000i | − | 1.00671i | −0.864079 | − | 0.503356i | \(-0.832099\pi\) | ||
0.864079 | − | 0.503356i | \(-0.167901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −52.0000 | −0.344371 | −0.172185 | − | 0.985065i | \(-0.555083\pi\) | ||||
−0.172185 | + | 0.985065i | \(0.555083\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.00000 | + | 7.00000i | −0.0457516 | + | 0.0457516i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 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 | ||||||||
\(159\) | − | 212.000i | − | 1.33333i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.0496894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82.0000 | − | 82.0000i | 0.503067 | − | 0.503067i | −0.409322 | − | 0.912390i | \(-0.634235\pi\) |
0.912390 | + | 0.409322i | \(0.134235\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −80.0000 | − | 80.0000i | −0.484848 | − | 0.484848i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.0000 | −0.116959 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −107.000 | + | 107.000i | −0.618497 | + | 0.618497i | −0.945146 | − | 0.326649i | \(-0.894081\pi\) |
0.326649 | + | 0.945146i | \(0.394081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.0000 | + | 50.0000i | 0.285714 | + | 0.285714i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.0000 | + | 40.0000i | 0.225989 | + | 0.225989i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.498241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −96.0000 | + | 96.0000i | −0.524590 | + | 0.524590i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0000 | + | 15.0000i | −0.0810811 | + | 0.0810811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 56.0000 | + | 56.0000i | 0.299465 | + | 0.299465i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 80.0000i | − | 0.423280i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −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 | \(0.316967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −60.0000 | −0.307692 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | − | 3.00000i | −0.0152284 | − | 0.0152284i | 0.699452 | − | 0.714680i | \(-0.253428\pi\) |
−0.714680 | + | 0.699452i | \(0.753428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 120.000i | 0.603015i | 0.953464 | + | 0.301508i | \(0.0974898\pi\) | ||||
−0.953464 | + | 0.301508i | \(0.902510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −248.000 | −1.23383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 80.0000 | − | 80.0000i | 0.394089 | − | 0.394089i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.0000i | 0.195122i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | + | 2.00000i | 0.00966184 | + | 0.00966184i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160.000i | 0.765550i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 328.000 | 1.55450 | 0.777251 | − | 0.629190i | \(-0.216613\pi\) | ||||
0.777251 | + | 0.629190i | \(0.216613\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 56.0000 | − | 56.0000i | 0.262911 | − | 0.262911i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −210.000 | − | 210.000i | −0.976744 | − | 0.976744i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 104.000 | + | 104.000i | 0.479263 | + | 0.479263i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 188.000i | 0.858447i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.0000 | 0.190045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −138.000 | + | 138.000i | −0.618834 | + | 0.618834i | −0.945232 | − | 0.326398i | \(-0.894165\pi\) |
0.326398 | + | 0.945232i | \(0.394165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 25.0000i | − | 0.111111i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −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 | \(0.915615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −64.0000 | −0.277056 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 183.000 | − | 183.000i | 0.785408 | − | 0.785408i | −0.195330 | − | 0.980738i | \(-0.562578\pi\) |
0.980738 | + | 0.195330i | \(0.0625777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 90.0000 | − | 90.0000i | 0.382979 | − | 0.382979i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 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 | \(0.340155\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −38.0000 | + | 38.0000i | −0.156379 | + | 0.156379i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −205.000 | −0.836735 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 60.0000 | + | 60.0000i | 0.242915 | + | 0.242915i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 72.0000i | 0.289157i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 140.000i | − | 0.549020i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −313.000 | − | 313.000i | −1.21790 | − | 1.21790i | −0.968366 | − | 0.249532i | \(-0.919723\pi\) |
−0.249532 | − | 0.968366i | \(-0.580277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000i | 0.0463320i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.0000 | −0.153257 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 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 | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 160.000 | + | 160.000i | 0.599251 | + | 0.599251i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000i | 0.0371747i | 0.999827 | + | 0.0185874i | \(0.00591688\pi\) | ||||
−0.999827 | + | 0.0185874i | \(0.994083\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −252.000 | −0.929889 | −0.464945 | − | 0.885340i | \(-0.653926\pi\) | ||||
−0.464945 | + | 0.885340i | \(0.653926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.0000 | + | 24.0000i | −0.0879121 | + | 0.0879121i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −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 | \(0.511293\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 52.0000i | − | 0.186380i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 312.000 | 1.11032 | 0.555160 | − | 0.831743i | \(-0.312657\pi\) | ||||
0.555160 | + | 0.831743i | \(0.312657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 262.000 | − | 262.000i | 0.925795 | − | 0.925795i | −0.0716358 | − | 0.997431i | \(-0.522822\pi\) |
0.997431 | + | 0.0716358i | \(0.0228219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 200.000 | − | 200.000i | 0.701754 | − | 0.701754i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0000 | + | 16.0000i | 0.0557491 | + | 0.0557491i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 191.000i | − | 0.660900i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −252.000 | −0.865979 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 243.000 | − | 243.000i | 0.829352 | − | 0.829352i | −0.158075 | − | 0.987427i | \(-0.550529\pi\) |
0.987427 | + | 0.158075i | \(0.0505289\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 100.000 | 0.338983 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 160.000 | + | 160.000i | 0.538721 | + | 0.538721i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 12.0000i | − | 0.0401338i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −168.000 | −0.558140 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 124.000 | − | 124.000i | 0.409241 | − | 0.409241i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 240.000i | 0.786885i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | + | 18.0000i | 0.0586319 | + | 0.0586319i | 0.735815 | − | 0.677183i | \(-0.236799\pi\) |
−0.677183 | + | 0.735815i | \(0.736799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 472.000i | 1.52751i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(0.114334\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.0000 | − | 10.0000i | −0.0317460 | − | 0.0317460i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −213.000 | − | 213.000i | −0.671924 | − | 0.671924i | 0.286235 | − | 0.958159i | \(-0.407596\pi\) |
−0.958159 | + | 0.286235i | \(0.907596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 320.000i | 1.00313i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −568.000 | −1.76947 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −140.000 | + | 140.000i | −0.433437 | + | 0.433437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −75.0000 | + | 75.0000i | −0.230769 | + | 0.230769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0000 | − | 20.0000i | −0.0611621 | − | 0.0611621i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 72.0000i | − | 0.218845i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −232.000 | −0.700906 | −0.350453 | − | 0.936580i | \(-0.613972\pi\) | ||||
−0.350453 | + | 0.936580i | \(0.613972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | − | 3.00000i | 0.00900901 | − | 0.00900901i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −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 | \(0.410884\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 92.0000i | − | 0.271386i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −416.000 | −1.21994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −180.000 | + | 180.000i | −0.524781 | + | 0.524781i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −40.0000 | −0.115942 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −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 | \(-0.217098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 120.000 | 0.341880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −447.000 | + | 447.000i | −1.26629 | + | 1.26629i | −0.318298 | + | 0.947991i | \(0.603111\pi\) |
−0.947991 | + | 0.318298i | \(0.896889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 140.000i | − | 0.394366i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −56.0000 | − | 56.0000i | −0.156863 | − | 0.156863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −114.000 | + | 114.000i | −0.314050 | + | 0.314050i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 235.000 | + | 235.000i | 0.643836 | + | 0.643836i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 118.000 | + | 118.000i | 0.321526 | + | 0.321526i | 0.849352 | − | 0.527826i | \(-0.176993\pi\) |
−0.527826 | + | 0.849352i | \(0.676993\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.00000i | − | 0.0216802i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −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 | \(0.315018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 250.000 | + | 250.000i | 0.666667 | + | 0.666667i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 120.000 | + | 120.000i | 0.318302 | + | 0.318302i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 340.000i | − | 0.897098i | −0.893758 | − | 0.448549i | \(-0.851941\pi\) | ||
0.893758 | − | 0.448549i | \(-0.148059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 472.000 | 1.23885 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 42.0000 | + | 42.0000i | 0.108527 | + | 0.108527i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 390.000i | 1.00257i | 0.865282 | + | 0.501285i | \(0.167139\pi\) | ||||
−0.865282 | + | 0.501285i | \(0.832861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0000 | 0.0716113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 256.000 | − | 256.000i | 0.651399 | − | 0.651399i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 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 | \(0.945116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 160.000i | − | 0.401003i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 642.000 | 1.60100 | 0.800499 | − | 0.599334i | \(-0.204568\pi\) | ||||
0.800499 | + | 0.599334i | \(0.204568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −156.000 | + | 156.000i | −0.387097 | + | 0.387097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 355.000i | − | 0.876543i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −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 | \(-0.0587020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −252.000 | −0.613139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.0000 | − | 40.0000i | 0.0968523 | − | 0.0968523i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 90.0000 | + | 90.0000i | 0.216867 | + | 0.216867i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −280.000 | − | 280.000i | −0.671463 | − | 0.671463i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 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 | \(0.579455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.0000 | + | 18.0000i | −0.0425532 | + | 0.0425532i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −175.000 | − | 175.000i | −0.411765 | − | 0.411765i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 96.0000 | + | 96.0000i | 0.224824 | + | 0.224824i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 96.0000i | − | 0.223776i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(0.454565\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 400.000 | − | 400.000i | 0.919540 | − | 0.919540i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.0000 | + | 40.0000i | 0.0915332 | + | 0.0915332i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 560.000i | − | 1.27563i | −0.770191 | − | 0.637813i | \(-0.779839\pi\) | ||
0.770191 | − | 0.637813i | \(-0.220161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41.0000 | 0.0929705 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −300.000 | − | 300.000i | −0.671141 | − | 0.671141i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 410.000i | − | 0.913140i | −0.889687 | − | 0.456570i | \(-0.849078\pi\) | ||
0.889687 | − | 0.456570i | \(-0.150922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −64.0000 | −0.141907 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −104.000 | + | 104.000i | −0.229581 | + | 0.229581i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 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 | \(0.958060\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 280.000i | 0.610022i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 622.000 | 1.34924 | 0.674620 | − | 0.738165i | \(-0.264307\pi\) | ||||
0.674620 | + | 0.738165i | \(0.264307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −278.000 | + | 278.000i | −0.600432 | + | 0.600432i | −0.940427 | − | 0.339995i | \(-0.889575\pi\) |
0.339995 | + | 0.940427i | \(0.389575\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 520.000 | + | 520.000i | 1.11828 | + | 1.11828i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 108.000 | 0.229299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 336.000 | − | 336.000i | 0.710359 | − | 0.710359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 500.000i | − | 1.05263i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53.0000 | + | 53.0000i | 0.111111 | + | 0.111111i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | + | 16.0000i | −0.0331263 | + | 0.0331263i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −315.000 | + | 315.000i | −0.649485 | + | 0.649485i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −522.000 | − | 522.000i | −1.07187 | − | 1.07187i | −0.997209 | − | 0.0746595i | \(-0.976213\pi\) |
−0.0746595 | − | 0.997209i | \(-0.523787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 328.000i | − | 0.670757i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 40.0000 | 0.0808081 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −56.0000 | − | 56.0000i | −0.112676 | − | 0.112676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 380.000i | − | 0.761523i | −0.924673 | − | 0.380762i | \(-0.875662\pi\) | ||
0.924673 | − | 0.380762i | \(-0.124338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −248.000 | −0.495010 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 302.000 | + | 302.000i | 0.595661 | + | 0.595661i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 440.000i | − | 0.864440i | −0.901768 | − | 0.432220i | \(-0.857730\pi\) | ||
0.901768 | − | 0.432220i | \(-0.142270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 188.000 | 0.367906 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −400.000 | + | 400.000i | −0.779727 | + | 0.779727i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 590.000 | + | 590.000i | 1.14563 | + | 1.14563i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 144.000 | + | 144.000i | 0.278530 | + | 0.278530i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 428.000i | 0.824663i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −258.000 | −0.495202 | −0.247601 | − | 0.968862i | \(-0.579642\pi\) | ||||
−0.247601 | + | 0.968862i | \(0.579642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −258.000 | + | 258.000i | −0.493308 | + | 0.493308i | −0.909347 | − | 0.416039i | \(-0.863418\pi\) |
0.416039 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 200.000 | 0.380952 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −364.000 | − | 364.000i | −0.690702 | − | 0.690702i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 521.000i | 0.984877i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0000 | −0.0376648 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | + | 24.0000i | −0.0450281 | + | 0.0450281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −710.000 | + | 710.000i | −1.32710 | + | 1.32710i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 440.000 | + | 440.000i | 0.819367 | + | 0.819367i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 328.000i | − | 0.608534i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −338.000 | −0.624769 | −0.312384 | − | 0.949956i | \(-0.601128\pi\) | ||||
−0.312384 | + | 0.949956i | \(0.601128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | − | 4.00000i | 0.00736648 | − | 0.00736648i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.0000 | −0.0917431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 558.000 | + | 558.000i | 1.02011 | + | 1.02011i | 0.999794 | + | 0.0203161i | \(0.00646725\pi\) |
0.0203161 | + | 0.999794i | \(0.493533\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 48.0000i | − | 0.0874317i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −800.000 | −1.45191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 60.0000i | 0.108108i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | − | 3.00000i | −0.00538600 | − | 0.00538600i | 0.704409 | − | 0.709795i | \(-0.251212\pi\) |
−0.709795 | + | 0.704409i | \(0.751212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 252.000i | − | 0.450805i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 224.000 | 0.399287 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −142.000 | − | 142.000i | −0.250441 | − | 0.250441i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 950.000i | 1.66960i | 0.550557 | + | 0.834798i | \(0.314416\pi\) | ||||
−0.550557 | + | 0.834798i | \(0.685584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −392.000 | −0.686515 | −0.343257 | − | 0.939241i | \(-0.611530\pi\) | ||||
−0.343257 | + | 0.939241i | \(0.611530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −424.000 | + | 424.000i | −0.739965 | + | 0.739965i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −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 | \(0.946813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 228.000i | 0.393782i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 72.0000 | 0.123924 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 424.000 | − | 424.000i | 0.727273 | − | 0.727273i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0000 | − | 15.0000i | 0.0256410 | − | 0.0256410i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 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 | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | −0.0203046 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.0000 | + | 47.0000i | −0.0792580 | + | 0.0792580i | −0.745624 | − | 0.666366i | \(-0.767849\pi\) |
0.666366 | + | 0.745624i | \(0.267849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −140.000 | −0.235294 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 240.000 | + | 240.000i | 0.402010 | + | 0.402010i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 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 | \(0.587976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62.0000 | − | 62.0000i | 0.102819 | − | 0.102819i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 285.000i | 0.471074i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −462.000 | − | 462.000i | −0.761120 | − | 0.761120i | 0.215405 | − | 0.976525i | \(-0.430893\pi\) |
−0.976525 | + | 0.215405i | \(0.930893\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 320.000i | − | 0.525452i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 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 | \(-0.0639512\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 80.0000 | + | 80.0000i | 0.130081 | + | 0.130081i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 327.000 | + | 327.000i | 0.529984 | + | 0.529984i | 0.920567 | − | 0.390584i | \(-0.127727\pi\) |
−0.390584 | + | 0.920567i | \(0.627727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 660.000i | 1.06624i | 0.846041 | + | 0.533118i | \(0.178980\pi\) | ||||
−0.846041 | + | 0.533118i | \(0.821020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 80.0000 | 0.128824 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 160.000 | − | 160.000i | 0.256822 | − | 0.256822i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 320.000 | + | 320.000i | 0.510367 | + | 0.510367i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 42.0000i | − | 0.0667727i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 548.000 | 0.868463 | 0.434231 | − | 0.900801i | \(-0.357020\pi\) | ||||
0.434231 | + | 0.900801i | \(0.357020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 656.000 | − | 656.000i | 1.03633 | − | 1.03633i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 590.000 | − | 590.000i | 0.929134 | − | 0.929134i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −123.000 | − | 123.000i | −0.193093 | − | 0.193093i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.0000i | 0.0438185i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −568.000 | −0.886115 | −0.443058 | − | 0.896493i | \(-0.646106\pi\) | ||||
−0.443058 | + | 0.896493i | \(0.646106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 342.000 | − | 342.000i | 0.531882 | − | 0.531882i | −0.389250 | − | 0.921132i | \(-0.627266\pi\) |
0.921132 | + | 0.389250i | \(0.127266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −840.000 | −1.30233 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 416.000 | 0.639017 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 453.000 | − | 453.000i | 0.693721 | − | 0.693721i | −0.269327 | − | 0.963049i | \(-0.586801\pi\) |
0.963049 | + | 0.269327i | \(0.0868014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 640.000i | − | 0.977099i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −47.0000 | − | 47.0000i | −0.0715373 | − | 0.0715373i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 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 | \(0.373411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 84.0000 | − | 84.0000i | 0.126697 | − | 0.126697i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −200.000 | − | 200.000i | −0.300752 | − | 0.300752i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 80.0000 | + | 80.0000i | 0.119940 | + | 0.119940i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 552.000i | 0.825112i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −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 | \(0.185002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −500.000 | − | 500.000i | −0.740741 | − | 0.740741i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 157.000 | + | 157.000i | 0.231905 | + | 0.231905i | 0.813488 | − | 0.581582i | \(-0.197566\pi\) |
−0.581582 | + | 0.813488i | \(0.697566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 252.000i | 0.371134i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00000 | −0.0117474 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 240.000 | + | 240.000i | 0.349345 | + | 0.349345i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 318.000i | − | 0.461538i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1032.00 | −1.49349 | −0.746744 | − | 0.665112i | \(-0.768384\pi\) | ||||
−0.746744 | + | 0.665112i | \(0.768384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.0000 | − | 16.0000i | 0.0230880 | − | 0.0230880i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −700.000 | −1.00719 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.0000 | − | 56.0000i | −0.0803443 | − | 0.0803443i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 732.000i | − | 1.04721i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −128.000 | −0.182596 | −0.0912981 | − | 0.995824i | \(-0.529102\pi\) | ||||
−0.0912981 | + | 0.995824i | \(0.529102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.0000 | − | 60.0000i | 0.0853485 | − | 0.0853485i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 360.000i | − | 0.510638i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −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 | \(0.819947\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −104.000 | + | 104.000i | −0.145863 | + | 0.145863i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −120.000 | − | 120.000i | −0.167832 | − | 0.167832i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −240.000 | − | 240.000i | −0.334728 | − | 0.334728i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 464.000 | − | 464.000i | 0.641770 | − | 0.641770i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1000.00i | − | 1.37931i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 558.000 | + | 558.000i | 0.767538 | + | 0.767538i | 0.977672 | − | 0.210135i | \(-0.0673902\pi\) |
−0.210135 | + | 0.977672i | \(0.567390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 791.000i | 1.08505i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 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 | \(0.956004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −410.000 | + | 410.000i | −0.557823 | + | 0.557823i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −496.000 | − | 496.000i | −0.672999 | − | 0.672999i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 700.000i | 0.947226i | 0.880733 | + | 0.473613i | \(0.157050\pi\) | ||||
−0.880733 | + | 0.473613i | \(0.842950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 240.000 | 0.323887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.0000 | − | 18.0000i | −0.0240964 | − | 0.0240964i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 568.000i | 0.758344i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 588.000 | 0.782956 | 0.391478 | − | 0.920187i | \(-0.371964\pi\) | ||||
0.391478 | + | 0.920187i | \(0.371964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 96.0000 | − | 96.0000i | 0.127490 | − | 0.127490i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 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 | \(0.376597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 64.0000i | − | 0.0843215i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −158.000 | −0.207622 | −0.103811 | − | 0.994597i | \(-0.533104\pi\) | ||||
−0.103811 | + | 0.994597i | \(0.533104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | + | 20.0000i | −0.0262123 | + | 0.0262123i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35.0000 | + | 35.0000i | 0.0457516 | + | 0.0457516i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 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 | \(0.983435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1252.00 | −1.62387 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 243.000 | − | 243.000i | 0.314360 | − | 0.314360i | −0.532236 | − | 0.846596i | \(-0.678648\pi\) |
0.846596 | + | 0.532236i | \(0.178648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1300.00 | 1.67742 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000 | + | 24.0000i | 0.0308880 | + | 0.0308880i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 160.000i | − | 0.205392i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 224.000 | 0.286812 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −800.000 | + | 800.000i | −1.02171 | + | 1.02171i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 135.000 | − | 135.000i | 0.171975 | − | 0.171975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −262.000 | − | 262.000i | −0.332910 | − | 0.332910i | 0.520781 | − | 0.853690i | \(-0.325641\pi\) |
−0.853690 | + | 0.520781i | \(0.825641\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1048.00i | − | 1.32826i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.0000 | −0.116308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −144.000 | + | 144.000i | −0.181589 | + | 0.181589i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1060.00 | −1.33333 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 267.000 | + | 267.000i | 0.335006 | + | 0.335006i | 0.854484 | − | 0.519478i | \(-0.173873\pi\) |
−0.519478 | + | 0.854484i | \(0.673873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 252.000i | 0.315394i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −80.0000 | −0.0998752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −376.000 | + | 376.000i | −0.468244 | + | 0.468244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.0000i | 0.0496894i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0000 | + | 20.0000i | 0.0247831 | + | 0.0247831i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 560.000i | 0.692213i | 0.938195 | + | 0.346106i | \(0.112496\pi\) | ||||
−0.938195 | + | 0.346106i | \(0.887504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 208.000 | 0.256473 | 0.128237 | − | 0.991744i | \(-0.459068\pi\) | ||||
0.128237 | + | 0.991744i | \(0.459068\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −504.000 | + | 504.000i | −0.619926 | + | 0.619926i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −410.000 | − | 410.000i | −0.503067 | − | 0.503067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 840.000 | + | 840.000i | 1.02815 | + | 1.02815i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 12.0000i | − | 0.0146520i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1568.00 | −1.90987 | −0.954933 | − | 0.296821i | \(-0.904073\pi\) | ||||
−0.954933 | + | 0.296821i | \(0.904073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 562.000 | − | 562.000i | 0.682868 | − | 0.682868i | −0.277778 | − | 0.960645i | \(-0.589598\pi\) |
0.960645 | + | 0.277778i | \(0.0895979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −400.000 | + | 400.000i | −0.484848 | + | 0.484848i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | \(0.967305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1068.00 | 1.28520 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 287.000 | − | 287.000i | 0.344538 | − | 0.344538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −310.000 | + | 310.000i | −0.371257 | + | 0.371257i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1040.00 | − | 1040.00i | −1.24253 | − | 1.24253i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 624.000 | − | 624.000i | 0.740214 | − | 0.740214i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 755.000 | 0.893491 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 114.000 | + | 114.000i | 0.134593 | + | 0.134593i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1048.00i | − | 1.23439i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −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 | \(-0.130999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 100.000i | 0.116959i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 417.000 | + | 417.000i | 0.486581 | + | 0.486581i | 0.907226 | − | 0.420644i | \(-0.138196\pi\) |
−0.420644 | + | 0.907226i | \(0.638196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1300.00i | 1.51339i | 0.653769 | + | 0.756694i | \(0.273187\pi\) | ||||
−0.653769 | + | 0.756694i | \(0.726813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 64.0000 | 0.0743322 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −382.000 | − | 382.000i | −0.440600 | − | 0.440600i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −372.000 | −0.427095 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 63.0000 | − | 63.0000i | 0.0721649 | − | 0.0721649i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 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 | \(0.869015\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 972.000i | − | 1.10580i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 712.000 | 0.808173 | 0.404086 | − | 0.914721i | \(-0.367590\pi\) | ||||
0.404086 | + | 0.914721i | \(0.367590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −118.000 | + | 118.000i | −0.133635 | + | 0.133635i | −0.770760 | − | 0.637125i | \(-0.780123\pi\) |
0.637125 | + | 0.770760i | \(0.280123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 200.000 | − | 200.000i | 0.225989 | − | 0.225989i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 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 | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 568.000 | 0.637486 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −360.000 | + | 360.000i | −0.403135 | + | 0.403135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1100.00 | 1.22905 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | − | 24.0000i | −0.0267559 | − | 0.0267559i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2080.00i | − | 2.31368i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 742.000 | 0.823529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −336.000 | + | 336.000i | −0.372093 | + | 0.372093i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 10.0000i | − | 0.0110497i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −142.000 | − | 142.000i | −0.156560 | − | 0.156560i | 0.624480 | − | 0.781040i | \(-0.285311\pi\) |
−0.781040 | + | 0.624480i | \(0.785311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 62.0000i | 0.0682068i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 480.000 | + | 480.000i | 0.524590 | + | 0.524590i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −256.000 | − | 256.000i | −0.279171 | − | 0.279171i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 920.000i | − | 1.00109i | −0.865711 | − | 0.500544i | \(-0.833133\pi\) | ||
0.865711 | − | 0.500544i | \(-0.166867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72.0000 | 0.0781759 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 84.0000 | − | 84.0000i | 0.0910076 | − | 0.0910076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75.0000 | + | 75.0000i | 0.0810811 | + | 0.0810811i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −118.000 | − | 118.000i | −0.127292 | − | 0.127292i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1190.00i | − | 1.28095i | −0.767980 | − | 0.640474i | \(-0.778738\pi\) | ||
0.767980 | − | 0.640474i | \(-0.221262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 820.000 | 0.880773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 776.000 | − | 776.000i | 0.831726 | − | 0.831726i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | \(0.806262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 732.000i | − | 0.779553i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −78.0000 | −0.0828905 | −0.0414453 | − | 0.999141i | \(-0.513196\pi\) | ||||
−0.0414453 | + | 0.999141i | \(0.513196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | + | 16.0000i | −0.0169671 | + | 0.0169671i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −400.000 | −0.423280 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −852.000 | −0.895899 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1017.00 | + | 1017.00i | −1.06716 | + | 1.06716i | −0.0695800 | + | 0.997576i | \(0.522166\pi\) |
−0.997576 | + | 0.0695800i | \(0.977834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1060.00i | 1.10995i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 640.000 | + | 640.000i | 0.668757 | + | 0.668757i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 252.000i | 0.262774i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1743.00 | 1.81374 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 142.000 | − | 142.000i | 0.147456 | − | 0.147456i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 285.000 | + | 285.000i | 0.295337 | + | 0.295337i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −502.000 | − | 502.000i | −0.519131 | − | 0.519131i | 0.398177 | − | 0.917309i | \(-0.369643\pi\) |
−0.917309 | + | 0.398177i | \(0.869643\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 560.000i | 0.577915i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −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 | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 300.000i | 0.307692i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −783.000 | − | 783.000i | −0.801433 | − | 0.801433i | 0.181887 | − | 0.983320i | \(-0.441780\pi\) |
−0.983320 | + | 0.181887i | \(0.941780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 640.000i | 0.653728i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.0101937 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −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 | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −144.000 | − | 144.000i | −0.145897 | − | 0.145897i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 168.000i | − | 0.169869i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 68.0000 | 0.0686176 | 0.0343088 | − | 0.999411i | \(-0.489077\pi\) | ||||
0.0343088 | + | 0.999411i | \(0.489077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −464.000 | + | 464.000i | −0.467271 | + | 0.467271i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 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 | \(0.934701\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 120.000i | − | 0.120120i |
(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 | 80.3.p.c.17.1 | 2 | ||
3.2 | odd | 2 | 720.3.bh.c.577.1 | 2 | |||
4.3 | odd | 2 | 10.3.c.a.7.1 | yes | 2 | ||
5.2 | odd | 4 | 400.3.p.b.193.1 | 2 | |||
5.3 | odd | 4 | inner | 80.3.p.c.33.1 | 2 | ||
5.4 | even | 2 | 400.3.p.b.257.1 | 2 | |||
8.3 | odd | 2 | 320.3.p.h.257.1 | 2 | |||
8.5 | even | 2 | 320.3.p.a.257.1 | 2 | |||
12.11 | even | 2 | 90.3.g.b.37.1 | 2 | |||
15.8 | even | 4 | 720.3.bh.c.433.1 | 2 | |||
20.3 | even | 4 | 10.3.c.a.3.1 | ✓ | 2 | ||
20.7 | even | 4 | 50.3.c.c.43.1 | 2 | |||
20.19 | odd | 2 | 50.3.c.c.7.1 | 2 | |||
28.27 | even | 2 | 490.3.f.b.197.1 | 2 | |||
40.3 | even | 4 | 320.3.p.h.193.1 | 2 | |||
40.13 | odd | 4 | 320.3.p.a.193.1 | 2 | |||
60.23 | odd | 4 | 90.3.g.b.73.1 | 2 | |||
60.47 | odd | 4 | 450.3.g.b.343.1 | 2 | |||
60.59 | even | 2 | 450.3.g.b.307.1 | 2 | |||
140.83 | odd | 4 | 490.3.f.b.393.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.3.c.a.3.1 | ✓ | 2 | 20.3 | even | 4 | ||
10.3.c.a.7.1 | yes | 2 | 4.3 | odd | 2 | ||
50.3.c.c.7.1 | 2 | 20.19 | odd | 2 | |||
50.3.c.c.43.1 | 2 | 20.7 | even | 4 | |||
80.3.p.c.17.1 | 2 | 1.1 | even | 1 | trivial | ||
80.3.p.c.33.1 | 2 | 5.3 | odd | 4 | inner | ||
90.3.g.b.37.1 | 2 | 12.11 | even | 2 | |||
90.3.g.b.73.1 | 2 | 60.23 | odd | 4 | |||
320.3.p.a.193.1 | 2 | 40.13 | odd | 4 | |||
320.3.p.a.257.1 | 2 | 8.5 | even | 2 | |||
320.3.p.h.193.1 | 2 | 40.3 | even | 4 | |||
320.3.p.h.257.1 | 2 | 8.3 | odd | 2 | |||
400.3.p.b.193.1 | 2 | 5.2 | odd | 4 | |||
400.3.p.b.257.1 | 2 | 5.4 | even | 2 | |||
450.3.g.b.307.1 | 2 | 60.59 | even | 2 | |||
450.3.g.b.343.1 | 2 | 60.47 | odd | 4 | |||
490.3.f.b.197.1 | 2 | 28.27 | even | 2 | |||
490.3.f.b.393.1 | 2 | 140.83 | odd | 4 | |||
720.3.bh.c.433.1 | 2 | 15.8 | even | 4 | |||
720.3.bh.c.577.1 | 2 | 3.2 | odd | 2 |