Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,3,Mod(307,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, 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("450.307");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(12.2616118962\) |
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 | 343.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.343 |
Dual form | 450.3.g.b.307.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 2.00000i | −0.285714 | + | 0.285714i | −0.835383 | − | 0.549669i | \(-0.814754\pi\) |
0.549669 | + | 0.835383i | \(0.314754\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.302175\pi\) |
−0.813014 | + | 0.582245i | \(0.802175\pi\) | |||||||
\(14\) | − | 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 | \(-0.655958\pi\) |
0.882353 | + | 0.470588i | \(0.155958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000i | 1.05263i | 0.850289 | + | 0.526316i | \(0.176427\pi\) | ||||
−0.850289 | + | 0.526316i | \(0.823573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.00000 | + | 8.00000i | −0.363636 | + | 0.363636i | ||||
\(23\) | −2.00000 | − | 2.00000i | −0.0869565 | − | 0.0869565i | 0.662291 | − | 0.749247i | \(-0.269584\pi\) |
−0.749247 | + | 0.662291i | \(0.769584\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 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 | \(0.242238\pi\) | ||||
−0.724138 | + | 0.689655i | \(0.757762\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.0810811 | − | 0.0810811i | −0.665403 | − | 0.746484i | \(-0.731740\pi\) |
0.746484 | + | 0.665403i | \(0.231740\pi\) | |||||||
\(38\) | −20.0000 | − | 20.0000i | −0.526316 | − | 0.526316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.00731906\pi\) |
−0.0229915 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(44\) | − | 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 | \(-0.837290\pi\) |
0.489195 | + | 0.872174i | \(0.337290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.0000i | 0.836735i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | + | 6.00000i | −0.115385 | + | 0.115385i | ||||
\(53\) | 53.0000 | + | 53.0000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −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 | \(-0.945787\pi\) | ||
0.985532 | − | 0.169492i | \(-0.0542125\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.0000 | + | 62.0000i | −0.925373 | + | 0.925373i | −0.997403 | − | 0.0720294i | \(-0.977052\pi\) |
0.0720294 | + | 0.997403i | \(0.477052\pi\) | |||||||
\(68\) | −14.0000 | − | 14.0000i | −0.205882 | − | 0.205882i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.0995461\pi\) |
−0.307661 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(74\) | 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 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.00000 | + | 8.00000i | −0.0975610 | + | 0.0975610i | ||||
\(83\) | 18.0000 | + | 18.0000i | 0.216867 | + | 0.216867i | 0.807177 | − | 0.590310i | \(-0.200994\pi\) |
−0.590310 | + | 0.807177i | \(0.700994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −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 | \(0.148376\pi\) | ||||
−0.893311 | + | 0.449438i | \(0.851624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 0.131868 | ||||||||
\(92\) | −4.00000 | + | 4.00000i | −0.0434783 | + | 0.0434783i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 36.0000i | − | 0.382979i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 63.0000 | − | 63.0000i | 0.649485 | − | 0.649485i | −0.303384 | − | 0.952868i | \(-0.598116\pi\) |
0.952868 | + | 0.303384i | \(0.0981164\pi\) | |||||||
\(98\) | −41.0000 | − | 41.0000i | −0.418367 | − | 0.418367i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −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 | −0.987403 | − | 0.158229i | \(-0.949422\pi\) |
−0.158229 | − | 0.987403i | \(-0.550578\pi\) | |||||||
\(104\) | − | 12.0000i | − | 0.115385i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −106.000 | −1.00000 | ||||||||
\(107\) | 142.000 | − | 142.000i | 1.32710 | − | 1.32710i | 0.419217 | − | 0.907886i | \(-0.362305\pi\) |
0.907886 | − | 0.419217i | \(-0.137695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000i | 0.0917431i | 0.998947 | + | 0.0458716i | \(0.0146065\pi\) | ||||
−0.998947 | + | 0.0458716i | \(0.985394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.00000 | − | 8.00000i | 0.0714286 | − | 0.0714286i | ||||
\(113\) | 23.0000 | + | 23.0000i | 0.203540 | + | 0.203540i | 0.801515 | − | 0.597975i | \(-0.204028\pi\) |
−0.597975 | + | 0.801515i | \(0.704028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.000 | − | 118.000i | 0.929134 | − | 0.929134i | −0.0685161 | − | 0.997650i | \(-0.521826\pi\) |
0.997650 | + | 0.0685161i | \(0.0218265\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||
\(134\) | − | 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 | \(-0.855420\pi\) |
0.438753 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 140.000i | − | 1.00719i | −0.863939 | − | 0.503597i | \(-0.832010\pi\) | ||
0.863939 | − | 0.503597i | \(-0.167990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −28.0000 | + | 28.0000i | −0.197183 | + | 0.197183i | ||||
\(143\) | −24.0000 | − | 24.0000i | −0.167832 | − | 0.167832i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −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 | \(-0.832099\pi\) | ||
0.864079 | − | 0.503356i | \(-0.167901\pi\) | |||||||
\(150\) | 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 | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −27.0000 | + | 27.0000i | −0.171975 | + | 0.171975i | −0.787846 | − | 0.615872i | \(-0.788804\pi\) |
0.615872 | + | 0.787846i | \(0.288804\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.0496894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82.0000 | + | 82.0000i | 0.503067 | + | 0.503067i | 0.912390 | − | 0.409322i | \(-0.134235\pi\) |
−0.409322 | + | 0.912390i | \(0.634235\pi\) | |||||||
\(164\) | − | 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 | \(-0.665447\pi\) |
0.867935 | + | 0.496678i | \(0.165447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 151.000i | − | 0.893491i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 84.0000 | − | 84.0000i | 0.488372 | − | 0.488372i | ||||
\(173\) | −107.000 | − | 107.000i | −0.618497 | − | 0.618497i | 0.326649 | − | 0.945146i | \(-0.394081\pi\) |
−0.945146 | + | 0.326649i | \(0.894081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | \(-0.789348\pi\) | ||
0.788897 | − | 0.614525i | \(-0.210652\pi\) | |||||||
\(180\) | 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 | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 56.0000 | − | 56.0000i | 0.299465 | − | 0.299465i | ||||
\(188\) | 36.0000 | + | 36.0000i | 0.191489 | + | 0.191489i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.183033\pi\) |
−0.543847 | + | 0.839184i | \(0.683033\pi\) | |||||||
\(194\) | 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 | \(-0.753428\pi\) |
0.699452 | + | 0.714680i | \(0.253428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 120.000i | 0.603015i | 0.953464 | + | 0.301508i | \(0.0974898\pi\) | ||||
−0.953464 | + | 0.301508i | \(0.902510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 62.0000 | − | 62.0000i | 0.306931 | − | 0.306931i | ||||
\(203\) | −80.0000 | − | 80.0000i | −0.394089 | − | 0.394089i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −104.000 | + | 104.000i | −0.479263 | + | 0.479263i | ||||
\(218\) | −10.0000 | − | 10.0000i | −0.0458716 | − | 0.0458716i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −42.0000 | −0.190045 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −138.000 | − | 138.000i | −0.618834 | − | 0.618834i | 0.326398 | − | 0.945232i | \(-0.394165\pi\) |
−0.945232 | + | 0.326398i | \(0.894165\pi\) | |||||||
\(224\) | 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 | \(-0.748017\pi\) |
0.711498 | + | 0.702688i | \(0.248017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 120.000i | − | 0.524017i | −0.965066 | − | 0.262009i | \(-0.915615\pi\) | ||
0.965066 | − | 0.262009i | \(-0.0843849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −80.0000 | + | 80.0000i | −0.344828 | + | 0.344828i | ||||
\(233\) | 183.000 | + | 183.000i | 0.785408 | + | 0.785408i | 0.980738 | − | 0.195330i | \(-0.0625777\pi\) |
−0.195330 | + | 0.980738i | \(0.562578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −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 | \(0.0807746\pi\) | ||||
−0.967975 | + | 0.251046i | \(0.919225\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 60.0000 | − | 60.0000i | 0.242915 | − | 0.242915i | ||||
\(248\) | 104.000 | + | 104.000i | 0.419355 | + | 0.419355i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||
\(254\) | 236.000i | 0.929134i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −313.000 | + | 313.000i | −1.21790 | + | 1.21790i | −0.249532 | + | 0.968366i | \(0.580277\pi\) |
−0.968366 | + | 0.249532i | \(0.919723\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000i | 0.0463320i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −128.000 | + | 128.000i | −0.488550 | + | 0.488550i | ||||
\(263\) | −262.000 | − | 262.000i | −0.996198 | − | 0.996198i | 0.00379508 | − | 0.999993i | \(-0.498792\pi\) |
−0.999993 | + | 0.00379508i | \(0.998792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 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 | \(0.00591688\pi\) | ||||
−0.999827 | + | 0.0185874i | \(0.994083\pi\) | |||||||
\(270\) | 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 | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −267.000 | + | 267.000i | −0.963899 | + | 0.963899i | −0.999371 | − | 0.0354718i | \(-0.988707\pi\) |
0.0354718 | + | 0.999371i | \(0.488707\pi\) | |||||||
\(278\) | 140.000 | + | 140.000i | 0.503597 | + | 0.503597i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −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 | \(-0.0228219\pi\) |
−0.0716358 | + | 0.997431i | \(0.522822\pi\) | |||||||
\(284\) | − | 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 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 94.0000 | − | 94.0000i | 0.321918 | − | 0.321918i | ||||
\(293\) | 243.000 | + | 243.000i | 0.829352 | + | 0.829352i | 0.987427 | − | 0.158075i | \(-0.0505289\pi\) |
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | − | 18.0000i | 0.0586319 | − | 0.0586319i | −0.677183 | − | 0.735815i | \(-0.736799\pi\) |
0.735815 | + | 0.677183i | \(0.236799\pi\) | |||||||
\(308\) | 32.0000 | + | 32.0000i | 0.103896 | + | 0.103896i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.385666\pi\) |
−0.936182 | + | 0.351517i | \(0.885666\pi\) | |||||||
\(314\) | − | 54.0000i | − | 0.171975i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −213.000 | + | 213.000i | −0.671924 | + | 0.671924i | −0.958159 | − | 0.286235i | \(-0.907596\pi\) |
0.286235 | + | 0.958159i | \(0.407596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 320.000i | 1.00313i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | + | 8.00000i | −0.0248447 | + | 0.0248447i | ||||
\(323\) | 140.000 | + | 140.000i | 0.433437 | + | 0.433437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −417.000 | + | 417.000i | −1.23739 | + | 1.23739i | −0.276324 | + | 0.961064i | \(0.589116\pi\) |
−0.961064 | + | 0.276324i | \(0.910884\pi\) | |||||||
\(338\) | 151.000 | + | 151.000i | 0.446746 | + | 0.446746i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | \(-0.614960\pi\) |
0.935489 | + | 0.353356i | \(0.114960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 440.000i | 1.26074i | 0.776293 | + | 0.630372i | \(0.217098\pi\) | ||||
−0.776293 | + | 0.630372i | \(0.782902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32.0000 | − | 32.0000i | 0.0909091 | − | 0.0909091i | ||||
\(353\) | −447.000 | − | 447.000i | −1.26629 | − | 1.26629i | −0.947991 | − | 0.318298i | \(-0.896889\pi\) |
−0.318298 | − | 0.947991i | \(-0.603111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | \(-0.811913\pi\) | ||
0.830443 | − | 0.557103i | \(-0.188087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | −2.00000 | + | 2.00000i | −0.00552486 | + | 0.00552486i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 24.0000i | − | 0.0659341i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 118.000 | − | 118.000i | 0.321526 | − | 0.321526i | −0.527826 | − | 0.849352i | \(-0.676993\pi\) |
0.849352 | + | 0.527826i | \(0.176993\pi\) | |||||||
\(368\) | 8.00000 | + | 8.00000i | 0.0217391 | + | 0.0217391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −212.000 | −0.571429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 107.000 | + | 107.000i | 0.286863 | + | 0.286863i | 0.835839 | − | 0.548975i | \(-0.184982\pi\) |
−0.548975 | + | 0.835839i | \(0.684982\pi\) | |||||||
\(374\) | 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 | \(-0.851941\pi\) | ||
0.893758 | − | 0.448549i | \(-0.148059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 212.000 | − | 212.000i | 0.554974 | − | 0.554974i | ||||
\(383\) | −342.000 | − | 342.000i | −0.892950 | − | 0.892950i | 0.101849 | − | 0.994800i | \(-0.467524\pi\) |
−0.994800 | + | 0.101849i | \(0.967524\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | \(0.167139\pi\) | ||||
−0.865282 | + | 0.501285i | \(0.832861\pi\) | |||||||
\(390\) | 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 | \(-0.554884\pi\) |
0.985172 | + | 0.171570i | \(0.0548839\pi\) | |||||||
\(398\) | −120.000 | − | 120.000i | −0.301508 | − | 0.301508i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −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 | \(0.0587020\pi\) | ||||
−0.983043 | + | 0.183374i | \(0.941298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −236.000 | + | 236.000i | −0.572816 | + | 0.572816i | ||||
\(413\) | 40.0000 | + | 40.0000i | 0.0968523 | + | 0.0968523i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −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 | \(0.116540\pi\) | ||||
−0.933723 | + | 0.357995i | \(0.883460\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 96.0000 | − | 96.0000i | 0.224824 | − | 0.224824i | ||||
\(428\) | −284.000 | − | 284.000i | −0.663551 | − | 0.663551i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.0454353\pi\) |
−0.142255 | + | 0.989830i | \(0.545435\pi\) | |||||||
\(434\) | − | 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 | \(-0.779839\pi\) | ||
0.770191 | − | 0.637813i | \(-0.220161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 42.0000 | − | 42.0000i | 0.0950226 | − | 0.0950226i | ||||
\(443\) | 378.000 | + | 378.000i | 0.853273 | + | 0.853273i | 0.990535 | − | 0.137262i | \(-0.0438301\pi\) |
−0.137262 | + | 0.990535i | \(0.543830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 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 | \(-0.849078\pi\) | ||
0.889687 | − | 0.456570i | \(-0.150922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 64.0000 | 0.141907 | ||||||||
\(452\) | 46.0000 | − | 46.0000i | 0.101770 | − | 0.101770i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00000i | 0.00881057i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 393.000 | − | 393.000i | 0.859956 | − | 0.859956i | −0.131376 | − | 0.991333i | \(-0.541940\pi\) |
0.991333 | + | 0.131376i | \(0.0419396\pi\) | |||||||
\(458\) | 120.000 | + | 120.000i | 0.262009 | + | 0.262009i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −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 | \(-0.389575\pi\) |
−0.940427 | + | 0.339995i | \(0.889575\pi\) | |||||||
\(464\) | − | 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 | \(-0.768325\pi\) |
0.665250 | + | 0.746621i | \(0.268325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 248.000i | − | 0.528785i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 40.0000 | − | 40.0000i | 0.0847458 | − | 0.0847458i | ||||
\(473\) | 336.000 | + | 336.000i | 0.710359 | + | 0.710359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | \(-0.848104\pi\) | ||
0.888286 | − | 0.459290i | \(-0.151896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | −0.0374220 | ||||||||
\(482\) | −232.000 | + | 232.000i | −0.481328 | + | 0.481328i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 114.000i | 0.235537i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −522.000 | + | 522.000i | −1.07187 | + | 1.07187i | −0.0746595 | + | 0.997209i | \(0.523787\pi\) |
−0.997209 | + | 0.0746595i | \(0.976213\pi\) | |||||||
\(488\) | −96.0000 | − | 96.0000i | −0.196721 | − | 0.196721i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||
\(494\) | 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 | \(-0.875662\pi\) | ||
0.924673 | − | 0.380762i | \(-0.124338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −48.0000 | + | 48.0000i | −0.0956175 | + | 0.0956175i | ||||
\(503\) | −42.0000 | − | 42.0000i | −0.0834990 | − | 0.0834990i | 0.664124 | − | 0.747623i | \(-0.268805\pi\) |
−0.747623 | + | 0.664124i | \(0.768805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | \(-0.857730\pi\) | ||
0.901768 | − | 0.432220i | \(-0.142270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −188.000 | −0.367906 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 626.000i | − | 1.21790i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −144.000 | + | 144.000i | −0.278530 | + | 0.278530i | ||||
\(518\) | −12.0000 | − | 12.0000i | −0.0231660 | − | 0.0231660i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.363418\pi\) |
−0.909347 | + | 0.416039i | \(0.863418\pi\) | |||||||
\(524\) | − | 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 | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −80.0000 | + | 80.0000i | −0.150376 | + | 0.150376i | ||||
\(533\) | −24.0000 | − | 24.0000i | −0.0450281 | − | 0.0450281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −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 | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 558.000 | − | 558.000i | 1.02011 | − | 1.02011i | 0.0203161 | − | 0.999794i | \(-0.493533\pi\) |
0.999794 | − | 0.0203161i | \(-0.00646725\pi\) | |||||||
\(548\) | 126.000 | + | 126.000i | 0.229927 | + | 0.229927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −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 | \(-0.751212\pi\) |
0.704409 | + | 0.709795i | \(0.251212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 252.000i | − | 0.450805i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 312.000 | − | 312.000i | 0.555160 | − | 0.555160i | ||||
\(563\) | −42.0000 | − | 42.0000i | −0.0746004 | − | 0.0746004i | 0.668822 | − | 0.743422i | \(-0.266799\pi\) |
−0.743422 | + | 0.668822i | \(0.766799\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −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 | \(0.314416\pi\) | ||||
−0.550557 | + | 0.834798i | \(0.685584\pi\) | |||||||
\(570\) | 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 | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 473.000 | − | 473.000i | 0.819757 | − | 0.819757i | −0.166315 | − | 0.986073i | \(-0.553187\pi\) |
0.986073 | + | 0.166315i | \(0.0531869\pi\) | |||||||
\(578\) | −191.000 | − | 191.000i | −0.330450 | − | 0.330450i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −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 | \(-0.826660\pi\) |
0.518045 | + | 0.855353i | \(0.326660\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1040.00i | 1.76570i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | + | 12.0000i | −0.0202703 | + | 0.0202703i | ||||
\(593\) | −47.0000 | − | 47.0000i | −0.0792580 | − | 0.0792580i | 0.666366 | − | 0.745624i | \(-0.267849\pi\) |
−0.745624 | + | 0.666366i | \(0.767849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −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 | \(0.142918\pi\) | ||||
−0.900886 | + | 0.434057i | \(0.857082\pi\) | |||||||
\(600\) | 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 | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −462.000 | + | 462.000i | −0.761120 | + | 0.761120i | −0.976525 | − | 0.215405i | \(-0.930893\pi\) |
0.215405 | + | 0.976525i | \(0.430893\pi\) | |||||||
\(608\) | 80.0000 | + | 80.0000i | 0.131579 | + | 0.131579i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 108.000 | 0.176759 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −723.000 | − | 723.000i | −1.17945 | − | 1.17945i | −0.979886 | − | 0.199560i | \(-0.936049\pi\) |
−0.199560 | − | 0.979886i | \(-0.563951\pi\) | |||||||
\(614\) | 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 | \(-0.627727\pi\) |
0.920567 | + | 0.390584i | \(0.127727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 660.000i | 1.06624i | 0.846041 | + | 0.533118i | \(0.178980\pi\) | ||||
−0.846041 | + | 0.533118i | \(0.821020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −388.000 | + | 388.000i | −0.623794 | + | 0.623794i | ||||
\(623\) | −160.000 | − | 160.000i | −0.256822 | − | 0.256822i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 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 | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 123.000 | − | 123.000i | 0.193093 | − | 0.193093i | ||||
\(638\) | −320.000 | − | 320.000i | −0.501567 | − | 0.501567i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 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 | \(-0.127266\pi\) |
−0.389250 | + | 0.921132i | \(0.627266\pi\) | |||||||
\(644\) | − | 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 | \(-0.791165\pi\) |
0.610012 | + | 0.792392i | \(0.291165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 160.000i | − | 0.246533i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 164.000 | − | 164.000i | 0.251534 | − | 0.251534i | ||||
\(653\) | 453.000 | + | 453.000i | 0.693721 | + | 0.693721i | 0.963049 | − | 0.269327i | \(-0.0868014\pi\) |
−0.269327 | + | 0.963049i | \(0.586801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −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 | \(0.0338753\pi\) | ||||
−0.994342 | + | 0.106222i | \(0.966125\pi\) | |||||||
\(660\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 80.0000 | − | 80.0000i | 0.119940 | − | 0.119940i | ||||
\(668\) | −124.000 | − | 124.000i | −0.185629 | − | 0.185629i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −384.000 | −0.572280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −193.000 | − | 193.000i | −0.286776 | − | 0.286776i | 0.549028 | − | 0.835804i | \(-0.314998\pi\) |
−0.835804 | + | 0.549028i | \(0.814998\pi\) | |||||||
\(674\) | − | 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 | \(-0.697566\pi\) |
0.813488 | + | 0.581582i | \(0.197566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 252.000i | 0.371134i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −416.000 | + | 416.000i | −0.609971 | + | 0.609971i | ||||
\(683\) | 438.000 | + | 438.000i | 0.641288 | + | 0.641288i | 0.950872 | − | 0.309584i | \(-0.100190\pi\) |
−0.309584 | + | 0.950872i | \(0.600190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.0000 | − | 56.0000i | 0.0803443 | − | 0.0803443i | ||||
\(698\) | −440.000 | − | 440.000i | −0.630372 | − | 0.630372i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | \(-0.819947\pi\) | ||
0.844239 | − | 0.535966i | \(-0.180053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −160.000 | + | 160.000i | −0.224719 | + | 0.224719i | ||||
\(713\) | −104.000 | − | 104.000i | −0.145863 | − | 0.145863i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −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 | \(-0.701264\pi\) | ||
0.590994 | − | 0.806676i | \(-0.298736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 472.000 | 0.654646 | ||||||||
\(722\) | 39.0000 | − | 39.0000i | 0.0540166 | − | 0.0540166i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.00000i | − | 0.00552486i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 558.000 | − | 558.000i | 0.767538 | − | 0.767538i | −0.210135 | − | 0.977672i | \(-0.567390\pi\) |
0.977672 | + | 0.210135i | \(0.0673902\pi\) | |||||||
\(728\) | 24.0000 | + | 24.0000i | 0.0329670 | + | 0.0329670i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 588.000 | 0.804378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 827.000 | + | 827.000i | 1.12824 | + | 1.12824i | 0.990463 | + | 0.137777i | \(0.0439957\pi\) |
0.137777 | + | 0.990463i | \(0.456004\pi\) | |||||||
\(734\) | 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 | \(0.157050\pi\) | ||||
−0.880733 | + | 0.473613i | \(0.842950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 212.000 | − | 212.000i | 0.285714 | − | 0.285714i | ||||
\(743\) | −382.000 | − | 382.000i | −0.514132 | − | 0.514132i | 0.401658 | − | 0.915790i | \(-0.368434\pi\) |
−0.915790 | + | 0.401658i | \(0.868434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −987.000 | + | 987.000i | −1.30383 | + | 1.30383i | −0.378043 | + | 0.925788i | \(0.623403\pi\) |
−0.925788 | + | 0.378043i | \(0.876597\pi\) | |||||||
\(758\) | 340.000 | + | 340.000i | 0.448549 | + | 0.448549i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | \(-0.983435\pi\) | ||
0.998646 | − | 0.0520156i | \(-0.0165646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 114.000 | − | 114.000i | 0.147668 | − | 0.147668i | ||||
\(773\) | 243.000 | + | 243.000i | 0.314360 | + | 0.314360i | 0.846596 | − | 0.532236i | \(-0.178648\pi\) |
−0.532236 | + | 0.846596i | \(0.678648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −262.000 | + | 262.000i | −0.332910 | + | 0.332910i | −0.853690 | − | 0.520781i | \(-0.825641\pi\) |
0.520781 | + | 0.853690i | \(0.325641\pi\) | |||||||
\(788\) | 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 | \(-0.673873\pi\) |
0.854484 | + | 0.519478i | \(0.173873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 252.000i | 0.315394i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 642.000 | − | 642.000i | 0.800499 | − | 0.800499i | ||||
\(803\) | 376.000 | + | 376.000i | 0.468244 | + | 0.468244i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(0.112496\pi\) | ||||
−0.938195 | + | 0.346106i | \(0.887504\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −840.000 | + | 840.000i | −1.02815 | + | 1.02815i | ||||
\(818\) | −150.000 | − | 150.000i | −0.183374 | − | 0.183374i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 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 | \(-0.0895979\pi\) |
−0.277778 | + | 0.960645i | \(0.589598\pi\) | |||||||
\(824\) | − | 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 | \(-0.524127\pi\) |
0.997129 | + | 0.0757260i | \(0.0241274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 170.000i | − | 0.205066i | −0.994730 | − | 0.102533i | \(-0.967305\pi\) | ||
0.994730 | − | 0.102533i | \(-0.0326948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.0000 | − | 24.0000i | 0.0288462 | − | 0.0288462i | ||||
\(833\) | 287.000 | + | 287.000i | 0.344538 | + | 0.344538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | \(-0.946635\pi\) | ||
0.985980 | − | 0.166865i | \(-0.0533645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −759.000 | −0.902497 | ||||||||
\(842\) | 208.000 | − | 208.000i | 0.247031 | − | 0.247031i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 656.000i | 0.777251i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 114.000 | − | 114.000i | 0.134593 | − | 0.134593i | ||||
\(848\) | −212.000 | − | 212.000i | −0.250000 | − | 0.250000i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | −0.0141011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1123.00 | − | 1123.00i | −1.31653 | − | 1.31653i | −0.916504 | − | 0.400026i | \(-0.869001\pi\) |
−0.400026 | − | 0.916504i | \(-0.630999\pi\) | |||||||
\(854\) | 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 | \(-0.638196\pi\) |
0.907226 | + | 0.420644i | \(0.138196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1300.00i | 1.51339i | 0.653769 | + | 0.756694i | \(0.273187\pi\) | ||||
−0.653769 | + | 0.756694i | \(0.726813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −788.000 | + | 788.000i | −0.914153 | + | 0.914153i | ||||
\(863\) | −242.000 | − | 242.000i | −0.280417 | − | 0.280417i | 0.552858 | − | 0.833275i | \(-0.313537\pi\) |
−0.833275 | + | 0.552858i | \(0.813537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 453.000 | − | 453.000i | 0.516534 | − | 0.516534i | −0.399987 | − | 0.916521i | \(-0.630985\pi\) |
0.916521 | + | 0.399987i | \(0.130985\pi\) | |||||||
\(878\) | 560.000 | + | 560.000i | 0.637813 | + | 0.637813i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.280123\pi\) |
−0.770760 | + | 0.637125i | \(0.780123\pi\) | |||||||
\(884\) | 84.0000i | 0.0950226i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −756.000 | −0.853273 | ||||||||
\(887\) | −1158.00 | + | 1158.00i | −1.30552 | + | 1.30552i | −0.380914 | + | 0.924611i | \(0.624390\pi\) |
−0.924611 | + | 0.380914i | \(0.875610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 472.000i | 0.530934i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −276.000 | + | 276.000i | −0.309417 | + | 0.309417i | ||||
\(893\) | −360.000 | − | 360.000i | −0.403135 | − | 0.403135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −142.000 | + | 142.000i | −0.156560 | + | 0.156560i | −0.781040 | − | 0.624480i | \(-0.785311\pi\) |
0.624480 | + | 0.781040i | \(0.285311\pi\) | |||||||
\(908\) | −4.00000 | − | 4.00000i | −0.00440529 | − | 0.00440529i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||
\(914\) | 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 | \(-0.833133\pi\) | ||
0.865711 | − | 0.500544i | \(-0.166867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 622.000 | − | 622.000i | 0.674620 | − | 0.674620i | ||||
\(923\) | −84.0000 | − | 84.0000i | −0.0910076 | − | 0.0910076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | \(-0.778738\pi\) | ||
0.767980 | − | 0.640474i | \(-0.221262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −820.000 | −0.880773 | ||||||||
\(932\) | 366.000 | − | 366.000i | 0.392704 | − | 0.392704i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 76.0000i | − | 0.0813704i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 233.000 | − | 233.000i | 0.248666 | − | 0.248666i | −0.571757 | − | 0.820423i | \(-0.693738\pi\) |
0.820423 | + | 0.571757i | \(0.193738\pi\) | |||||||
\(938\) | 248.000 | + | 248.000i | 0.264392 | + | 0.264392i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | \(-0.735259\pi\) |
0.739084 | + | 0.673614i | \(0.235259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 282.000i | − | 0.297155i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −56.0000 | + | 56.0000i | −0.0588235 | + | 0.0588235i | ||||
\(953\) | −1017.00 | − | 1017.00i | −1.06716 | − | 1.06716i | −0.997576 | − | 0.0695800i | \(-0.977834\pi\) |
−0.0695800 | − | 0.997576i | \(-0.522166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −502.000 | + | 502.000i | −0.519131 | + | 0.519131i | −0.917309 | − | 0.398177i | \(-0.869643\pi\) |
0.398177 | + | 0.917309i | \(0.369643\pi\) | |||||||
\(968\) | −114.000 | − | 114.000i | −0.117769 | − | 0.117769i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||
\(974\) | − | 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 | \(-0.941780\pi\) |
0.181887 | + | 0.983320i | \(0.441780\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 640.000i | 0.653728i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −328.000 | + | 328.000i | −0.334012 | + | 0.334012i | ||||
\(983\) | 1058.00 | + | 1058.00i | 1.07630 | + | 1.07630i | 0.996838 | + | 0.0794589i | \(0.0253192\pi\) |
0.0794589 | + | 0.996838i | \(0.474681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −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 | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 773.000 | − | 773.000i | 0.775326 | − | 0.775326i | −0.203706 | − | 0.979032i | \(-0.565299\pi\) |
0.979032 | + | 0.203706i | \(0.0652987\pi\) | |||||||
\(998\) | 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 | 450.3.g.b.343.1 | 2 | ||
3.2 | odd | 2 | 50.3.c.c.43.1 | 2 | |||
5.2 | odd | 4 | inner | 450.3.g.b.307.1 | 2 | ||
5.3 | odd | 4 | 90.3.g.b.37.1 | 2 | |||
5.4 | even | 2 | 90.3.g.b.73.1 | 2 | |||
12.11 | even | 2 | 400.3.p.b.193.1 | 2 | |||
15.2 | even | 4 | 50.3.c.c.7.1 | 2 | |||
15.8 | even | 4 | 10.3.c.a.7.1 | yes | 2 | ||
15.14 | odd | 2 | 10.3.c.a.3.1 | ✓ | 2 | ||
20.3 | even | 4 | 720.3.bh.c.577.1 | 2 | |||
20.19 | odd | 2 | 720.3.bh.c.433.1 | 2 | |||
60.23 | odd | 4 | 80.3.p.c.17.1 | 2 | |||
60.47 | odd | 4 | 400.3.p.b.257.1 | 2 | |||
60.59 | even | 2 | 80.3.p.c.33.1 | 2 | |||
105.83 | odd | 4 | 490.3.f.b.197.1 | 2 | |||
105.104 | even | 2 | 490.3.f.b.393.1 | 2 | |||
120.29 | odd | 2 | 320.3.p.h.193.1 | 2 | |||
120.53 | even | 4 | 320.3.p.h.257.1 | 2 | |||
120.59 | even | 2 | 320.3.p.a.193.1 | 2 | |||
120.83 | odd | 4 | 320.3.p.a.257.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.3.c.a.3.1 | ✓ | 2 | 15.14 | odd | 2 | ||
10.3.c.a.7.1 | yes | 2 | 15.8 | even | 4 | ||
50.3.c.c.7.1 | 2 | 15.2 | even | 4 | |||
50.3.c.c.43.1 | 2 | 3.2 | odd | 2 | |||
80.3.p.c.17.1 | 2 | 60.23 | odd | 4 | |||
80.3.p.c.33.1 | 2 | 60.59 | even | 2 | |||
90.3.g.b.37.1 | 2 | 5.3 | odd | 4 | |||
90.3.g.b.73.1 | 2 | 5.4 | even | 2 | |||
320.3.p.a.193.1 | 2 | 120.59 | even | 2 | |||
320.3.p.a.257.1 | 2 | 120.83 | odd | 4 | |||
320.3.p.h.193.1 | 2 | 120.29 | odd | 2 | |||
320.3.p.h.257.1 | 2 | 120.53 | even | 4 | |||
400.3.p.b.193.1 | 2 | 12.11 | even | 2 | |||
400.3.p.b.257.1 | 2 | 60.47 | odd | 4 | |||
450.3.g.b.307.1 | 2 | 5.2 | odd | 4 | inner | ||
450.3.g.b.343.1 | 2 | 1.1 | even | 1 | trivial | ||
490.3.f.b.197.1 | 2 | 105.83 | odd | 4 | |||
490.3.f.b.393.1 | 2 | 105.104 | even | 2 | |||
720.3.bh.c.433.1 | 2 | 20.19 | odd | 2 | |||
720.3.bh.c.577.1 | 2 | 20.3 | even | 4 |