Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [592,3,Mod(401,592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(592, 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("592.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.k (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: | \(16.1308316501\) |
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 74) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 592.401 |
Dual form | 592.3.k.c.561.1 |
$q$-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 \(\left(\mathbb{Z}/592\mathbb{Z}\right)^\times\).
\(n\) | \(113\) | \(149\) | \(223\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 4.00000i | − | 1.33333i | −0.745356 | − | 0.666667i | \(-0.767720\pi\) | ||
0.745356 | − | 0.666667i | \(-0.232280\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 3.00000i | 0.600000 | − | 0.600000i | −0.340312 | − | 0.940312i | \(-0.610533\pi\) |
0.940312 | + | 0.340312i | \(0.110533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.571429 | 0.285714 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285714 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.00000 | −0.777778 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.00000i | − | 0.363636i | −0.983332 | − | 0.181818i | \(-0.941802\pi\) | ||
0.983332 | − | 0.181818i | \(-0.0581982\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −12.0000 | − | 12.0000i | −0.800000 | − | 0.800000i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.0000 | − | 23.0000i | 1.35294 | − | 1.35294i | 0.470588 | − | 0.882353i | \(-0.344042\pi\) |
0.882353 | − | 0.470588i | \(-0.155958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0000 | + | 10.0000i | −0.526316 | + | 0.526316i | −0.919472 | − | 0.393156i | \(-0.871383\pi\) |
0.393156 | + | 0.919472i | \(0.371383\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 16.0000i | − | 0.761905i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.0000 | − | 10.0000i | 0.434783 | − | 0.434783i | −0.455469 | − | 0.890252i | \(-0.650528\pi\) |
0.890252 | + | 0.455469i | \(0.150528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000i | 0.280000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 8.00000i | − | 0.296296i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19.0000 | − | 19.0000i | −0.655172 | − | 0.655172i | 0.299061 | − | 0.954234i | \(-0.403326\pi\) |
−0.954234 | + | 0.299061i | \(0.903326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | + | 18.0000i | 0.580645 | + | 0.580645i | 0.935081 | − | 0.354435i | \(-0.115327\pi\) |
−0.354435 | + | 0.935081i | \(0.615327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.0000 | −0.484848 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0000 | − | 12.0000i | 0.342857 | − | 0.342857i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 37.0000i | − | 1.00000i | ||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.0000 | − | 12.0000i | −0.307692 | − | 0.307692i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 74.0000i | 1.80488i | 0.430818 | + | 0.902439i | \(0.358225\pi\) | ||||
−0.430818 | + | 0.902439i | \(0.641775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −42.0000 | + | 42.0000i | −0.976744 | + | 0.976744i | −0.999736 | − | 0.0229915i | \(-0.992681\pi\) |
0.0229915 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21.0000 | + | 21.0000i | −0.466667 | + | 0.466667i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 44.0000 | 0.936170 | 0.468085 | − | 0.883683i | \(-0.344944\pi\) | ||||
0.468085 | + | 0.883683i | \(0.344944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.0000 | −0.673469 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −92.0000 | − | 92.0000i | −1.80392 | − | 1.80392i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −80.0000 | −1.50943 | −0.754717 | − | 0.656051i | \(-0.772226\pi\) | ||||
−0.754717 | + | 0.656051i | \(0.772226\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | − | 12.0000i | −0.218182 | − | 0.218182i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.0000 | + | 40.0000i | 0.701754 | + | 0.701754i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.0000 | − | 54.0000i | 0.915254 | − | 0.915254i | −0.0814252 | − | 0.996679i | \(-0.525947\pi\) |
0.996679 | + | 0.0814252i | \(0.0259472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 3.00000i | −0.0491803 | − | 0.0491803i | 0.682089 | − | 0.731269i | \(-0.261072\pi\) |
−0.731269 | + | 0.682089i | \(0.761072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28.0000 | −0.444444 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 18.0000i | − | 0.276923i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000i | 0.179104i | 0.995982 | + | 0.0895522i | \(0.0285436\pi\) | ||||
−0.995982 | + | 0.0895522i | \(0.971456\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −40.0000 | − | 40.0000i | −0.579710 | − | 0.579710i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −124.000 | −1.74648 | −0.873239 | − | 0.487291i | \(-0.837985\pi\) | ||||
−0.873239 | + | 0.487291i | \(0.837985\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.0000i | − | 0.136986i | −0.997652 | − | 0.0684932i | \(-0.978181\pi\) | ||
0.997652 | − | 0.0684932i | \(-0.0218191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.0000 | 0.373333 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 16.0000i | − | 0.207792i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0000 | + | 14.0000i | −0.177215 | + | 0.177215i | −0.790141 | − | 0.612926i | \(-0.789993\pi\) |
0.612926 | + | 0.790141i | \(0.289993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −95.0000 | −1.17284 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64.0000 | 0.771084 | 0.385542 | − | 0.922690i | \(-0.374014\pi\) | ||||
0.385542 | + | 0.922690i | \(0.374014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 138.000i | − | 1.62353i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −76.0000 | + | 76.0000i | −0.873563 | + | 0.873563i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.0000 | + | 17.0000i | 0.191011 | + | 0.191011i | 0.796133 | − | 0.605122i | \(-0.206876\pi\) |
−0.605122 | + | 0.796133i | \(0.706876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | − | 12.0000i | 0.131868 | − | 0.131868i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 72.0000 | − | 72.0000i | 0.774194 | − | 0.774194i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 60.0000i | 0.631579i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 129.000 | − | 129.000i | 1.32990 | − | 1.32990i | 0.424442 | − | 0.905455i | \(-0.360470\pi\) |
0.905455 | − | 0.424442i | \(-0.139530\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 28.0000i | 0.282828i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 118.000i | 1.16832i | 0.811640 | + | 0.584158i | \(0.198575\pi\) | ||||
−0.811640 | + | 0.584158i | \(0.801425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42.0000 | + | 42.0000i | 0.407767 | + | 0.407767i | 0.880959 | − | 0.473192i | \(-0.156898\pi\) |
−0.473192 | + | 0.880959i | \(0.656898\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −48.0000 | − | 48.0000i | −0.457143 | − | 0.457143i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 24.0000 | 0.224299 | 0.112150 | − | 0.993691i | \(-0.464226\pi\) | ||||
0.112150 | + | 0.993691i | \(0.464226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −91.0000 | + | 91.0000i | −0.834862 | + | 0.834862i | −0.988177 | − | 0.153315i | \(-0.951005\pi\) |
0.153315 | + | 0.988177i | \(0.451005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −148.000 | −1.33333 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.00000 | + | 7.00000i | 0.0619469 | + | 0.0619469i | 0.737402 | − | 0.675455i | \(-0.236053\pi\) |
−0.675455 | + | 0.737402i | \(0.736053\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 60.0000i | − | 0.521739i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −21.0000 | + | 21.0000i | −0.179487 | + | 0.179487i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 92.0000 | − | 92.0000i | 0.773109 | − | 0.773109i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 105.000 | 0.867769 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 296.000 | 2.40650 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 96.0000 | + | 96.0000i | 0.768000 | + | 0.768000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −76.0000 | −0.598425 | −0.299213 | − | 0.954186i | \(-0.596724\pi\) | ||||
−0.299213 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 168.000 | + | 168.000i | 1.30233 | + | 1.30233i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −70.0000 | − | 70.0000i | −0.534351 | − | 0.534351i | 0.387513 | − | 0.921864i | \(-0.373334\pi\) |
−0.921864 | + | 0.387513i | \(0.873334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −40.0000 | + | 40.0000i | −0.300752 | + | 0.300752i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.0000 | − | 24.0000i | −0.177778 | − | 0.177778i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 216.000 | 1.57664 | 0.788321 | − | 0.615264i | \(-0.210951\pi\) | ||||
0.788321 | + | 0.615264i | \(0.210951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 180.000i | − | 1.29496i | −0.762081 | − | 0.647482i | \(-0.775822\pi\) | ||
0.762081 | − | 0.647482i | \(-0.224178\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 176.000i | − | 1.24823i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | − | 12.0000i | −0.0839161 | − | 0.0839161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −114.000 | −0.786207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 132.000i | 0.897959i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −34.0000 | −0.228188 | −0.114094 | − | 0.993470i | \(-0.536396\pi\) | ||||
−0.114094 | + | 0.993470i | \(0.536396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 72.0000i | 0.476821i | 0.971164 | + | 0.238411i | \(0.0766264\pi\) | ||||
−0.971164 | + | 0.238411i | \(0.923374\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −161.000 | + | 161.000i | −1.05229 | + | 1.05229i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 108.000 | 0.696774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −0.0891720 | −0.0445860 | − | 0.999006i | \(-0.514197\pi\) | ||||
−0.0445860 | + | 0.999006i | \(0.514197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 320.000i | 2.01258i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 40.0000 | − | 40.0000i | 0.248447 | − | 0.248447i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66.0000 | + | 66.0000i | 0.404908 | + | 0.404908i | 0.879959 | − | 0.475051i | \(-0.157570\pi\) |
−0.475051 | + | 0.879959i | \(0.657570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48.0000 | + | 48.0000i | −0.290909 | + | 0.290909i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 230.000 | − | 230.000i | 1.37725 | − | 1.37725i | 0.528003 | − | 0.849242i | \(-0.322941\pi\) |
0.849242 | − | 0.528003i | \(-0.177059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 151.000i | 0.893491i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 70.0000 | − | 70.0000i | 0.409357 | − | 0.409357i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 88.0000i | − | 0.508671i | −0.967116 | − | 0.254335i | \(-0.918143\pi\) | ||
0.967116 | − | 0.254335i | \(-0.0818567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.0000i | 0.160000i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −216.000 | − | 216.000i | −1.22034 | − | 1.22034i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 166.000 | + | 166.000i | 0.927374 | + | 0.927374i | 0.997536 | − | 0.0701614i | \(-0.0223514\pi\) |
−0.0701614 | + | 0.997536i | \(0.522351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 304.000 | 1.67956 | 0.839779 | − | 0.542928i | \(-0.182684\pi\) | ||||
0.839779 | + | 0.542928i | \(0.182684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | + | 12.0000i | −0.0655738 | + | 0.0655738i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −111.000 | − | 111.000i | −0.600000 | − | 0.600000i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −92.0000 | − | 92.0000i | −0.491979 | − | 0.491979i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 32.0000i | − | 0.169312i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −186.000 | + | 186.000i | −0.973822 | + | 0.973822i | −0.999666 | − | 0.0258440i | \(-0.991773\pi\) |
0.0258440 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.00000 | + | 9.00000i | −0.0466321 | + | 0.0466321i | −0.730038 | − | 0.683406i | \(-0.760498\pi\) |
0.683406 | + | 0.730038i | \(0.260498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −72.0000 | −0.369231 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 34.0000 | 0.172589 | 0.0862944 | − | 0.996270i | \(-0.472497\pi\) | ||||
0.0862944 | + | 0.996270i | \(0.472497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −46.0000 | − | 46.0000i | −0.231156 | − | 0.231156i | 0.582019 | − | 0.813175i | \(-0.302263\pi\) |
−0.813175 | + | 0.582019i | \(0.802263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 48.0000 | 0.238806 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −76.0000 | − | 76.0000i | −0.374384 | − | 0.374384i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 222.000 | + | 222.000i | 1.08293 | + | 1.08293i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −70.0000 | + | 70.0000i | −0.338164 | + | 0.338164i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40.0000 | + | 40.0000i | 0.191388 | + | 0.191388i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 208.000 | 0.985782 | 0.492891 | − | 0.870091i | \(-0.335940\pi\) | ||||
0.492891 | + | 0.870091i | \(0.335940\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 496.000i | 2.32864i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 252.000i | 1.17209i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 72.0000 | + | 72.0000i | 0.331797 | + | 0.331797i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −40.0000 | −0.182648 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 138.000i | − | 0.624434i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 124.000 | 0.556054 | 0.278027 | − | 0.960573i | \(-0.410320\pi\) | ||||
0.278027 | + | 0.960573i | \(0.410320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 49.0000i | − | 0.217778i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 90.0000 | − | 90.0000i | 0.396476 | − | 0.396476i | −0.480512 | − | 0.876988i | \(-0.659549\pi\) |
0.876988 | + | 0.480512i | \(0.159549\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.00873362 | −0.00436681 | − | 0.999990i | \(-0.501390\pi\) | ||||
−0.00436681 | + | 0.999990i | \(0.501390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −64.0000 | −0.277056 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 42.0000i | 0.180258i | 0.995930 | + | 0.0901288i | \(0.0287279\pi\) | ||||
−0.995930 | + | 0.0901288i | \(0.971272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 132.000 | − | 132.000i | 0.561702 | − | 0.561702i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 56.0000 | + | 56.0000i | 0.236287 | + | 0.236287i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.0000 | + | 22.0000i | −0.0920502 | + | 0.0920502i | −0.751632 | − | 0.659582i | \(-0.770733\pi\) |
0.659582 | + | 0.751632i | \(0.270733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −175.000 | + | 175.000i | −0.726141 | + | 0.726141i | −0.969849 | − | 0.243708i | \(-0.921636\pi\) |
0.243708 | + | 0.969849i | \(0.421636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 308.000i | 1.26749i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −99.0000 | + | 99.0000i | −0.404082 | + | 0.404082i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 60.0000i | 0.242915i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 256.000i | − | 1.02811i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 198.000 | + | 198.000i | 0.788845 | + | 0.788845i | 0.981305 | − | 0.192460i | \(-0.0616466\pi\) |
−0.192460 | + | 0.981305i | \(0.561647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.0000 | − | 40.0000i | −0.158103 | − | 0.158103i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −552.000 | −2.16471 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −159.000 | + | 159.000i | −0.618677 | + | 0.618677i | −0.945192 | − | 0.326515i | \(-0.894126\pi\) |
0.326515 | + | 0.945192i | \(0.394126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 148.000i | − | 0.571429i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 133.000 | + | 133.000i | 0.509579 | + | 0.509579i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 88.0000i | 0.334601i | 0.985906 | + | 0.167300i | \(0.0535050\pi\) | ||||
−0.985906 | + | 0.167300i | \(0.946495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −240.000 | + | 240.000i | −0.905660 | + | 0.905660i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 68.0000 | − | 68.0000i | 0.254682 | − | 0.254682i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 178.000 | 0.661710 | 0.330855 | − | 0.943682i | \(-0.392663\pi\) | ||||
0.330855 | + | 0.943682i | \(0.392663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −404.000 | −1.49077 | −0.745387 | − | 0.666631i | \(-0.767735\pi\) | ||||
−0.745387 | + | 0.666631i | \(0.767735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −48.0000 | − | 48.0000i | −0.175824 | − | 0.175824i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.0000 | 0.101818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −147.000 | − | 147.000i | −0.530686 | − | 0.530686i | 0.390091 | − | 0.920776i | \(-0.372444\pi\) |
−0.920776 | + | 0.390091i | \(0.872444\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −126.000 | − | 126.000i | −0.451613 | − | 0.451613i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 135.000 | − | 135.000i | 0.480427 | − | 0.480427i | −0.424841 | − | 0.905268i | \(-0.639670\pi\) |
0.905268 | + | 0.424841i | \(0.139670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 258.000 | + | 258.000i | 0.911661 | + | 0.911661i | 0.996403 | − | 0.0847421i | \(-0.0270066\pi\) |
−0.0847421 | + | 0.996403i | \(0.527007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 240.000 | 0.842105 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 296.000i | 1.03136i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 769.000i | − | 2.66090i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −516.000 | − | 516.000i | −1.77320 | − | 1.77320i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 324.000i | − | 1.09831i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −32.0000 | −0.107744 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 60.0000i | − | 0.200669i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −168.000 | + | 168.000i | −0.558140 | + | 0.558140i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 472.000 | 1.55776 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.0000 | −0.0590164 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 364.000i | − | 1.18567i | −0.805325 | − | 0.592834i | \(-0.798009\pi\) | ||
0.805325 | − | 0.592834i | \(-0.201991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 168.000 | − | 168.000i | 0.543689 | − | 0.543689i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 238.000 | + | 238.000i | 0.765273 | + | 0.765273i | 0.977270 | − | 0.211997i | \(-0.0679967\pi\) |
−0.211997 | + | 0.977270i | \(0.567997\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 87.0000 | − | 87.0000i | 0.277955 | − | 0.277955i | −0.554337 | − | 0.832292i | \(-0.687028\pi\) |
0.832292 | + | 0.554337i | \(0.187028\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −84.0000 | + | 84.0000i | −0.266667 | + | 0.266667i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 264.000i | 0.832808i | 0.909180 | + | 0.416404i | \(0.136710\pi\) | ||||
−0.909180 | + | 0.416404i | \(0.863290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −76.0000 | + | 76.0000i | −0.238245 | + | 0.238245i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 96.0000i | − | 0.299065i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 460.000i | 1.42415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0000 | + | 21.0000i | 0.0646154 | + | 0.0646154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 364.000 | + | 364.000i | 1.11315 | + | 1.11315i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 176.000 | 0.534954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 326.000 | − | 326.000i | 0.984894 | − | 0.984894i | −0.0149933 | − | 0.999888i | \(-0.504773\pi\) |
0.999888 | + | 0.0149933i | \(0.00477271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 259.000i | 0.777778i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.0000 | + | 36.0000i | 0.107463 | + | 0.107463i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 230.000i | − | 0.682493i | −0.939974 | − | 0.341246i | \(-0.889151\pi\) | ||
0.939974 | − | 0.341246i | \(-0.110849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.0000 | − | 28.0000i | 0.0825959 | − | 0.0825959i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 72.0000 | − | 72.0000i | 0.211144 | − | 0.211144i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −328.000 | −0.956268 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −240.000 | −0.695652 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −362.000 | − | 362.000i | −1.04323 | − | 1.04323i | −0.999022 | − | 0.0442052i | \(-0.985924\pi\) |
−0.0442052 | − | 0.999022i | \(-0.514076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −48.0000 | −0.137536 | −0.0687679 | − | 0.997633i | \(-0.521907\pi\) | ||||
−0.0687679 | + | 0.997633i | \(0.521907\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.0000 | − | 24.0000i | −0.0683761 | − | 0.0683761i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 343.000 | + | 343.000i | 0.971671 | + | 0.971671i | 0.999610 | − | 0.0279383i | \(-0.00889418\pi\) |
−0.0279383 | + | 0.999610i | \(0.508894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −372.000 | + | 372.000i | −1.04789 | + | 1.04789i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −368.000 | − | 368.000i | −1.03081 | − | 1.03081i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 404.000 | 1.12535 | 0.562674 | − | 0.826679i | \(-0.309773\pi\) | ||||
0.562674 | + | 0.826679i | \(0.309773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 161.000i | 0.445983i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 420.000i | − | 1.15702i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.0000 | − | 30.0000i | −0.0821918 | − | 0.0821918i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −492.000 | −1.34060 | −0.670300 | − | 0.742090i | \(-0.733834\pi\) | ||||
−0.670300 | + | 0.742090i | \(0.733834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 518.000i | − | 1.40379i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −320.000 | −0.862534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 488.000i | − | 1.30831i | −0.756360 | − | 0.654155i | \(-0.773024\pi\) | ||
0.756360 | − | 0.654155i | \(-0.226976\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 384.000 | − | 384.000i | 1.02400 | − | 1.02400i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −114.000 | −0.302387 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 440.000 | 1.16095 | 0.580475 | − | 0.814278i | \(-0.302867\pi\) | ||||
0.580475 | + | 0.814278i | \(0.302867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 304.000i | 0.797900i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 450.000 | − | 450.000i | 1.17493 | − | 1.17493i | 0.193917 | − | 0.981018i | \(-0.437881\pi\) |
0.981018 | − | 0.193917i | \(-0.0621192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.0000 | − | 48.0000i | −0.124675 | − | 0.124675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 294.000 | − | 294.000i | 0.759690 | − | 0.759690i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0000 | − | 21.0000i | 0.0539846 | − | 0.0539846i | −0.679599 | − | 0.733584i | \(-0.737846\pi\) |
0.733584 | + | 0.679599i | \(0.237846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 460.000i | − | 1.17647i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −280.000 | + | 280.000i | −0.712468 | + | 0.712468i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 84.0000i | 0.212658i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 646.000i | − | 1.62720i | −0.581422 | − | 0.813602i | \(-0.697504\pi\) | ||
0.581422 | − | 0.813602i | \(-0.302496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 160.000 | + | 160.000i | 0.401003 | + | 0.401003i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 273.000 | + | 273.000i | 0.680798 | + | 0.680798i | 0.960180 | − | 0.279382i | \(-0.0901296\pi\) |
−0.279382 | + | 0.960180i | \(0.590130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 108.000 | 0.267990 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −285.000 | + | 285.000i | −0.703704 | + | 0.703704i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −148.000 | −0.363636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.0000 | + | 39.0000i | 0.0953545 | + | 0.0953545i | 0.753175 | − | 0.657820i | \(-0.228521\pi\) |
−0.657820 | + | 0.753175i | \(0.728521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 864.000i | − | 2.10219i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 216.000 | − | 216.000i | 0.523002 | − | 0.523002i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 192.000 | − | 192.000i | 0.462651 | − | 0.462651i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −720.000 | −1.72662 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −464.000 | −1.10740 | −0.553699 | − | 0.832717i | \(-0.686784\pi\) | ||||
−0.553699 | + | 0.832717i | \(0.686784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −469.000 | − | 469.000i | −1.11401 | − | 1.11401i | −0.992602 | − | 0.121412i | \(-0.961258\pi\) |
−0.121412 | − | 0.992602i | \(-0.538742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −308.000 | −0.728132 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 161.000 | + | 161.000i | 0.378824 | + | 0.378824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | − | 12.0000i | −0.0281030 | − | 0.0281030i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.0000 | + | 48.0000i | −0.111888 | + | 0.111888i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −450.000 | − | 450.000i | −1.04408 | − | 1.04408i | −0.998982 | − | 0.0451011i | \(-0.985639\pi\) |
−0.0451011 | − | 0.998982i | \(-0.514361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 200.000 | 0.461894 | 0.230947 | − | 0.972966i | \(-0.425818\pi\) | ||||
0.230947 | + | 0.972966i | \(0.425818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 456.000i | 1.04828i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 200.000i | 0.457666i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −246.000 | − | 246.000i | −0.560364 | − | 0.560364i | 0.369046 | − | 0.929411i | \(-0.379684\pi\) |
−0.929411 | + | 0.369046i | \(0.879684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 231.000 | 0.523810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 668.000i | 1.50790i | 0.656931 | + | 0.753950i | \(0.271854\pi\) | ||||
−0.656931 | + | 0.753950i | \(0.728146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 102.000 | 0.229213 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 136.000i | 0.304251i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 199.000 | − | 199.000i | 0.443207 | − | 0.443207i | −0.449881 | − | 0.893088i | \(-0.648534\pi\) |
0.893088 | + | 0.449881i | \(0.148534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 296.000 | 0.656319 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 288.000 | 0.635762 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 72.0000i | − | 0.158242i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −255.000 | + | 255.000i | −0.557987 | + | 0.557987i | −0.928734 | − | 0.370747i | \(-0.879102\pi\) |
0.370747 | + | 0.928734i | \(0.379102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −184.000 | − | 184.000i | −0.400871 | − | 0.400871i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −555.000 | + | 555.000i | −1.20390 | + | 1.20390i | −0.230935 | + | 0.972969i | \(0.574179\pi\) |
−0.972969 | + | 0.230935i | \(0.925821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −554.000 | + | 554.000i | −1.19654 | + | 1.19654i | −0.221350 | + | 0.975194i | \(0.571046\pi\) |
−0.975194 | + | 0.221350i | \(0.928954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 432.000i | − | 0.929032i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −158.000 | + | 158.000i | −0.338330 | + | 0.338330i | −0.855738 | − | 0.517409i | \(-0.826897\pi\) |
0.517409 | + | 0.855738i | \(0.326897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.0000i | 0.102345i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 56.0000i | 0.118896i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 168.000 | + | 168.000i | 0.355180 | + | 0.355180i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −70.0000 | − | 70.0000i | −0.147368 | − | 0.147368i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 560.000 | 1.17400 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −290.000 | + | 290.000i | −0.605428 | + | 0.605428i | −0.941748 | − | 0.336320i | \(-0.890818\pi\) |
0.336320 | + | 0.941748i | \(0.390818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −111.000 | − | 111.000i | −0.230769 | − | 0.230769i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −160.000 | − | 160.000i | −0.331263 | − | 0.331263i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 774.000i | − | 1.59588i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −266.000 | + | 266.000i | −0.546201 | + | 0.546201i | −0.925340 | − | 0.379139i | \(-0.876220\pi\) |
0.379139 | + | 0.925340i | \(0.376220\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 264.000 | − | 264.000i | 0.539877 | − | 0.539877i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −312.000 | −0.635438 | −0.317719 | − | 0.948185i | \(-0.602917\pi\) | ||||
−0.317719 | + | 0.948185i | \(0.602917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −874.000 | −1.77282 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 84.0000 | + | 84.0000i | 0.169697 | + | 0.169697i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −496.000 | −0.997988 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 210.000 | + | 210.000i | 0.420842 | + | 0.420842i | 0.885493 | − | 0.464652i | \(-0.153820\pi\) |
−0.464652 | + | 0.885493i | \(0.653820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −920.000 | − | 920.000i | −1.83633 | − | 1.83633i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −298.000 | + | 298.000i | −0.592445 | + | 0.592445i | −0.938291 | − | 0.345846i | \(-0.887592\pi\) |
0.345846 | + | 0.938291i | \(0.387592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 354.000 | + | 354.000i | 0.700990 | + | 0.700990i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 604.000 | 1.19132 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 808.000i | 1.58743i | 0.608292 | + | 0.793713i | \(0.291855\pi\) | ||||
−0.608292 | + | 0.793713i | \(0.708145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 40.0000i | − | 0.0782779i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 80.0000 | + | 80.0000i | 0.155945 | + | 0.155945i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 252.000 | 0.489320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 176.000i | − | 0.340426i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −352.000 | −0.678227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 170.000i | − | 0.326296i | −0.986602 | − | 0.163148i | \(-0.947835\pi\) | ||
0.986602 | − | 0.163148i | \(-0.0521647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −654.000 | + | 654.000i | −1.25048 | + | 1.25048i | −0.294972 | + | 0.955506i | \(0.595310\pi\) |
−0.955506 | + | 0.294972i | \(0.904690\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 112.000 | 0.213333 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 828.000 | 1.57116 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 329.000i | 0.621928i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −378.000 | + | 378.000i | −0.711864 | + | 0.711864i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 222.000 | + | 222.000i | 0.416510 | + | 0.416510i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 72.0000 | − | 72.0000i | 0.134579 | − | 0.134579i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 664.000 | − | 664.000i | 1.23650 | − | 1.23650i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 132.000i | 0.244898i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 147.000 | − | 147.000i | 0.271719 | − | 0.271719i | −0.558073 | − | 0.829792i | \(-0.688459\pi\) |
0.829792 | + | 0.558073i | \(0.188459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1216.00i | − | 2.23941i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 546.000i | 1.00183i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 294.000 | + | 294.000i | 0.537477 | + | 0.537477i | 0.922787 | − | 0.385310i | \(-0.125905\pi\) |
−0.385310 | + | 0.922787i | \(0.625905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.0000 | + | 21.0000i | 0.0382514 | + | 0.0382514i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 380.000 | 0.689655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.0000 | + | 56.0000i | −0.101266 | + | 0.101266i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −444.000 | + | 444.000i | −0.800000 | + | 0.800000i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −179.000 | − | 179.000i | −0.321364 | − | 0.321364i | 0.527926 | − | 0.849290i | \(-0.322970\pi\) |
−0.849290 | + | 0.527926i | \(0.822970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 252.000i | 0.450805i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −368.000 | + | 368.000i | −0.655971 | + | 0.655971i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −282.000 | + | 282.000i | −0.500888 | + | 0.500888i | −0.911714 | − | 0.410826i | \(-0.865240\pi\) |
0.410826 | + | 0.911714i | \(0.365240\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.0000 | 0.0743363 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −380.000 | −0.670194 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 375.000 | + | 375.000i | 0.659051 | + | 0.659051i | 0.955156 | − | 0.296105i | \(-0.0956877\pi\) |
−0.296105 | + | 0.955156i | \(0.595688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 184.000 | 0.322242 | 0.161121 | − | 0.986935i | \(-0.448489\pi\) | ||||
0.161121 | + | 0.986935i | \(0.448489\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 744.000 | + | 744.000i | 1.29843 | + | 1.29843i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 70.0000 | + | 70.0000i | 0.121739 | + | 0.121739i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −623.000 | + | 623.000i | −1.07972 | + | 1.07972i | −0.0831889 | + | 0.996534i | \(0.526510\pi\) |
−0.996534 | + | 0.0831889i | \(0.973490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.0000 | + | 36.0000i | 0.0621762 | + | 0.0621762i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 256.000 | 0.440620 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 320.000i | 0.548885i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 126.000i | 0.215385i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 382.000 | + | 382.000i | 0.650767 | + | 0.650767i | 0.953178 | − | 0.302411i | \(-0.0977915\pi\) |
−0.302411 | + | 0.953178i | \(0.597792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −360.000 | −0.611205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 136.000i | − | 0.230118i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 734.000 | 1.23777 | 0.618887 | − | 0.785480i | \(-0.287584\pi\) | ||||
0.618887 | + | 0.785480i | \(0.287584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 552.000i | − | 0.927731i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −184.000 | + | 184.000i | −0.308208 | + | 0.308208i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1004.00 | 1.67613 | 0.838063 | − | 0.545573i | \(-0.183688\pi\) | ||||
0.838063 | + | 0.545573i | \(0.183688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 306.000 | 0.509151 | 0.254576 | − | 0.967053i | \(-0.418064\pi\) | ||||
0.254576 | + | 0.967053i | \(0.418064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 84.0000i | − | 0.139303i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 315.000 | − | 315.000i | 0.520661 | − | 0.520661i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −298.000 | − | 298.000i | −0.490939 | − | 0.490939i | 0.417663 | − | 0.908602i | \(-0.362849\pi\) |
−0.908602 | + | 0.417663i | \(0.862849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −304.000 | + | 304.000i | −0.499179 | + | 0.499179i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 132.000 | − | 132.000i | 0.216039 | − | 0.216039i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 470.000i | 0.766721i | 0.923599 | + | 0.383361i | \(0.125233\pi\) | ||||
−0.923599 | + | 0.383361i | \(0.874767\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 888.000 | − | 888.000i | 1.44390 | − | 1.44390i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 304.000i | 0.492707i | 0.969180 | + | 0.246353i | \(0.0792324\pi\) | ||||
−0.969180 | + | 0.246353i | \(0.920768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 956.000i | − | 1.54443i | −0.635363 | − | 0.772213i | \(-0.719150\pi\) | ||
0.635363 | − | 0.772213i | \(-0.280850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −80.0000 | − | 80.0000i | −0.128824 | − | 0.128824i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 68.0000 | + | 68.0000i | 0.109149 | + | 0.109149i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 401.000 | 0.641600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 160.000 | − | 160.000i | 0.255183 | − | 0.255183i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −851.000 | − | 851.000i | −1.35294 | − | 1.35294i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 362.000 | + | 362.000i | 0.573693 | + | 0.573693i | 0.933158 | − | 0.359466i | \(-0.117041\pi\) |
−0.359466 | + | 0.933158i | \(0.617041\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 832.000i | − | 1.31438i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −228.000 | + | 228.000i | −0.359055 | + | 0.359055i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −99.0000 | + | 99.0000i | −0.155416 | + | 0.155416i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 868.000 | 1.35837 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −398.000 | −0.620905 | −0.310452 | − | 0.950589i | \(-0.600481\pi\) | ||||
−0.310452 | + | 0.950589i | \(0.600481\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −218.000 | − | 218.000i | −0.339036 | − | 0.339036i | 0.516969 | − | 0.856004i | \(-0.327060\pi\) |
−0.856004 | + | 0.516969i | \(0.827060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1008.00 | 1.56279 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 358.000 | + | 358.000i | 0.553323 | + | 0.553323i | 0.927398 | − | 0.374075i | \(-0.122040\pi\) |
−0.374075 | + | 0.927398i | \(0.622040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −216.000 | − | 216.000i | −0.332820 | − | 0.332820i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 288.000 | − | 288.000i | 0.442396 | − | 0.442396i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 555.000 | + | 555.000i | 0.849923 | + | 0.849923i | 0.990123 | − | 0.140200i | \(-0.0447745\pi\) |
−0.140200 | + | 0.990123i | \(0.544774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −420.000 | −0.641221 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70.0000i | 0.106545i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 788.000i | − | 1.19575i | −0.801589 | − | 0.597876i | \(-0.796012\pi\) | ||
0.801589 | − | 0.597876i | \(-0.203988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −661.000 | − | 661.000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −552.000 | −0.832579 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 240.000i | 0.360902i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −380.000 | −0.569715 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 496.000i | − | 0.741405i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | + | 12.0000i | −0.0178838 | + | 0.0178838i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.0000 | 0.0742942 | 0.0371471 | − | 0.999310i | \(-0.488173\pi\) | ||||
0.0371471 | + | 0.999310i | \(0.488173\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 56.0000 | 0.0829630 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 296.000i | − | 0.437223i | −0.975812 | − | 0.218612i | \(-0.929847\pi\) | ||
0.975812 | − | 0.218612i | \(-0.0701527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 516.000 | − | 516.000i | 0.759941 | − | 0.759941i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −360.000 | − | 360.000i | −0.528634 | − | 0.528634i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | + | 6.00000i | −0.00878477 | + | 0.00878477i | −0.711486 | − | 0.702701i | \(-0.751977\pi\) |
0.702701 | + | 0.711486i | \(0.251977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 648.000 | − | 648.000i | 0.945985 | − | 0.945985i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.00000i | 0.0116448i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −240.000 | + | 240.000i | −0.348331 | + | 0.348331i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 708.000i | 1.02460i | 0.858806 | + | 0.512301i | \(0.171207\pi\) | ||||
−0.858806 | + | 0.512301i | \(0.828793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 112.000i | 0.161616i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −540.000 | − | 540.000i | −0.776978 | − | 0.776978i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1702.00 | + | 1702.00i | 2.44189 | + | 2.44189i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 168.000 | 0.240343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 291.000 | − | 291.000i | 0.415121 | − | 0.415121i | −0.468397 | − | 0.883518i | \(-0.655168\pi\) |
0.883518 | + | 0.468397i | \(0.155168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 370.000 | + | 370.000i | 0.526316 | + | 0.526316i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −528.000 | − | 528.000i | −0.748936 | − | 0.748936i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 472.000i | 0.667610i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −77.0000 | + | 77.0000i | −0.108604 | + | 0.108604i | −0.759320 | − | 0.650717i | \(-0.774469\pi\) |
0.650717 | + | 0.759320i | \(0.274469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 98.0000 | − | 98.0000i | 0.137834 | − | 0.137834i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 360.000 | 0.504909 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −72.0000 | −0.100699 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 88.0000 | + | 88.0000i | 0.122734 | + | 0.122734i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 412.000 | 0.573018 | 0.286509 | − | 0.958078i | \(-0.407505\pi\) | ||||
0.286509 | + | 0.958078i | \(0.407505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 168.000 | + | 168.000i | 0.233010 | + | 0.233010i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 700.000 | + | 700.000i | 0.968188 | + | 0.968188i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 133.000 | − | 133.000i | 0.183448 | − | 0.183448i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 262.000 | + | 262.000i | 0.360385 | + | 0.360385i | 0.863955 | − | 0.503570i | \(-0.167980\pi\) |
−0.503570 | + | 0.863955i | \(0.667980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 377.000 | 0.517147 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1932.00i | 2.64295i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 682.000i | 0.930423i | 0.885200 | + | 0.465211i | \(0.154022\pi\) | ||||
−0.885200 | + | 0.465211i | \(0.845978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 396.000 | + | 396.000i | 0.538776 | + | 0.538776i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.0000 | 0.0651289 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 100.000i | − | 0.135318i | −0.997709 | − | 0.0676590i | \(-0.978447\pi\) | ||
0.997709 | − | 0.0676590i | \(-0.0215530\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 240.000 | 0.323887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 800.000i | 1.07672i | 0.842716 | + | 0.538358i | \(0.180955\pi\) | ||||
−0.842716 | + | 0.538358i | \(0.819045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −102.000 | + | 102.000i | −0.136913 | + | 0.136913i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −448.000 | −0.599732 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 96.0000 | 0.128171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 536.000i | − | 0.713715i | −0.934159 | − | 0.356858i | \(-0.883848\pi\) | ||
0.934159 | − | 0.356858i | \(-0.116152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 792.000 | − | 792.000i | 1.05179 | − | 1.05179i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 216.000 | + | 216.000i | 0.286093 | + | 0.286093i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −157.000 | + | 157.000i | −0.207398 | + | 0.207398i | −0.803160 | − | 0.595763i | \(-0.796850\pi\) |
0.595763 | + | 0.803160i | \(0.296850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −160.000 | + | 160.000i | −0.210804 | + | 0.210804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 272.000i | 0.357424i | 0.983901 | + | 0.178712i | \(0.0571931\pi\) | ||||
−0.983901 | + | 0.178712i | \(0.942807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −364.000 | + | 364.000i | −0.477064 | + | 0.477064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 966.000i | 1.26275i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 324.000i | − | 0.422425i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −761.000 | − | 761.000i | −0.989597 | − | 0.989597i | 0.0103496 | − | 0.999946i | \(-0.496706\pi\) |
−0.999946 | + | 0.0103496i | \(0.996706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 636.000 | + | 636.000i | 0.824903 | + | 0.824903i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1282.00 | −1.65847 | −0.829237 | − | 0.558898i | \(-0.811225\pi\) | ||||
−0.829237 | + | 0.558898i | \(0.811225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −126.000 | + | 126.000i | −0.162581 | + | 0.162581i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −592.000 | −0.761905 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −740.000 | − | 740.000i | −0.949936 | − | 0.949936i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 496.000i | 0.635083i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −152.000 | + | 152.000i | −0.194125 | + | 0.194125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.0000 | + | 42.0000i | −0.0535032 | + | 0.0535032i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 376.000 | 0.477764 | 0.238882 | − | 0.971049i | \(-0.423219\pi\) | ||||
0.238882 | + | 0.971049i | \(0.423219\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 352.000 | 0.446134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0000 | + | 28.0000i | 0.0353982 | + | 0.0353982i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | −0.0226986 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 960.000 | + | 960.000i | 1.20755 | + | 1.20755i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −69.0000 | − | 69.0000i | −0.0865747 | − | 0.0865747i | 0.662493 | − | 0.749068i | \(-0.269498\pi\) |
−0.749068 | + | 0.662493i | \(0.769498\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1012.00 | − | 1012.00i | 1.26658 | − | 1.26658i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −119.000 | − | 119.000i | −0.148564 | − | 0.148564i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.0000 | −0.0498132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 240.000i | − | 0.298137i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 712.000i | − | 0.882280i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 631.000 | + | 631.000i | 0.779975 | + | 0.779975i | 0.979826 | − | 0.199851i | \(-0.0640458\pi\) |
−0.199851 | + | 0.979826i | \(0.564046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1184.00 | −1.45993 | −0.729963 | − | 0.683487i | \(-0.760463\pi\) | ||||
−0.729963 | + | 0.683487i | \(0.760463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1616.00i | 1.98770i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 396.000 | 0.485890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 840.000i | − | 1.02815i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −84.0000 | + | 84.0000i | −0.102564 | + | 0.102564i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 784.000 | 0.954933 | 0.477467 | − | 0.878650i | \(-0.341555\pi\) | ||||
0.477467 | + | 0.878650i | \(0.341555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1116.00 | −1.35601 | −0.678007 | − | 0.735055i | \(-0.737156\pi\) | ||||
−0.678007 | + | 0.735055i | \(0.737156\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 112.000i | − | 0.135758i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −382.000 | + | 382.000i | −0.461911 | + | 0.461911i | −0.899281 | − | 0.437371i | \(-0.855910\pi\) |
0.437371 | + | 0.899281i | \(0.355910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 603.000 | + | 603.000i | 0.727382 | + | 0.727382i | 0.970098 | − | 0.242715i | \(-0.0780381\pi\) |
−0.242715 | + | 0.970098i | \(0.578038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −588.000 | + | 588.000i | −0.707581 | + | 0.707581i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −759.000 | + | 759.000i | −0.911164 | + | 0.911164i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1380.00i | − | 1.65269i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 144.000 | − | 144.000i | 0.172043 | − | 0.172043i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000i | 0.0572110i | 0.999591 | + | 0.0286055i | \(0.00910665\pi\) | ||||
−0.999591 | + | 0.0286055i | \(0.990893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 119.000i | − | 0.141498i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −540.000 | − | 540.000i | −0.640569 | − | 0.640569i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 453.000 | + | 453.000i | 0.536095 | + | 0.536095i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 420.000 | 0.495868 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1032.00 | − | 1032.00i | 1.21555 | − | 1.21555i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −370.000 | − | 370.000i | −0.434783 | − | 0.434783i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −163.000 | − | 163.000i | −0.191090 | − | 0.191090i | 0.605077 | − | 0.796167i | \(-0.293142\pi\) |
−0.796167 | + | 0.605077i | \(0.793142\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 420.000i | − | 0.491228i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −815.000 | + | 815.000i | −0.950992 | + | 0.950992i | −0.998854 | − | 0.0478621i | \(-0.984759\pi\) |
0.0478621 | + | 0.998854i | \(0.484759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −962.000 | + | 962.000i | −1.11991 | + | 1.11991i | −0.128152 | + | 0.991754i | \(0.540905\pi\) |
−0.991754 | + | 0.128152i | \(0.959095\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1184.00 | 1.37515 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −156.000 | −0.180765 | −0.0903824 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903824 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −264.000 | − | 264.000i | −0.305202 | − | 0.305202i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3076.00 | −3.54787 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.0000 | + | 56.0000i | 0.0644419 | + | 0.0644419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000 | + | 36.0000i | 0.0413318 | + | 0.0413318i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −903.000 | + | 903.000i | −1.03436 | + | 1.03436i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 384.000 | + | 384.000i | 0.438857 | + | 0.438857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 210.000 | 0.239453 | 0.119726 | − | 0.992807i | \(-0.461798\pi\) | ||||
0.119726 | + | 0.992807i | \(0.461798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 720.000i | − | 0.817253i | −0.912702 | − | 0.408627i | \(-0.866008\pi\) | ||
0.912702 | − | 0.408627i | \(-0.133992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 294.000 | + | 294.000i | 0.332956 | + | 0.332956i | 0.853708 | − | 0.520752i | \(-0.174348\pi\) |
−0.520752 | + | 0.853708i | \(0.674348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1296.00 | −1.46441 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 904.000i | − | 1.01917i | −0.860422 | − | 0.509583i | \(-0.829800\pi\) | ||
0.860422 | − | 0.509583i | \(-0.170200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −304.000 | −0.341957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 380.000i | 0.426487i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −440.000 | + | 440.000i | −0.492721 | + | 0.492721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 996.000 | 1.11285 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −240.000 | −0.267559 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 684.000i | − | 0.760845i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1840.00 | + | 1840.00i | −2.04218 | + | 2.04218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 672.000 | + | 672.000i | 0.744186 | + | 0.744186i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 912.000 | − | 912.000i | 1.00773 | − | 1.00773i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −618.000 | + | 618.000i | −0.681367 | + | 0.681367i | −0.960308 | − | 0.278941i | \(-0.910017\pi\) |
0.278941 | + | 0.960308i | \(0.410017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 826.000i | − | 0.908691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 882.000 | − | 882.000i | 0.968167 | − | 0.968167i | −0.0313419 | − | 0.999509i | \(-0.509978\pi\) |
0.999509 | + | 0.0313419i | \(0.00997806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 256.000i | − | 0.280394i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 72.0000i | 0.0786885i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −280.000 | − | 280.000i | −0.305344 | − | 0.305344i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1218.00 | + | 1218.00i | 1.32535 | + | 1.32535i | 0.909374 | + | 0.415980i | \(0.136561\pi\) |
0.415980 | + | 0.909374i | \(0.363439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1456.00 | −1.58089 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −372.000 | + | 372.000i | −0.403034 | + | 0.403034i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 259.000 | 0.280000 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −294.000 | − | 294.000i | −0.317152 | − | 0.317152i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 666.000i | − | 0.716900i | −0.933549 | − | 0.358450i | \(-0.883305\pi\) | ||
0.933549 | − | 0.358450i | \(-0.116695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 330.000 | − | 330.000i | 0.354458 | − | 0.354458i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 952.000 | − | 952.000i | 1.02036 | − | 1.02036i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −552.000 | −0.590374 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −424.000 | −0.452508 | −0.226254 | − | 0.974068i | \(-0.572648\pi\) | ||||
−0.226254 | + | 0.974068i | \(0.572648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −348.000 | − | 348.000i | −0.370607 | − | 0.370607i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −912.000 | −0.969182 | −0.484591 | − | 0.874741i | \(-0.661032\pi\) | ||||
−0.484591 | + | 0.874741i | \(0.661032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 740.000 | + | 740.000i | 0.784730 | + | 0.784730i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −96.0000 | − | 96.0000i | −0.101587 | − | 0.101587i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 134.000 | − | 134.000i | 0.141499 | − | 0.141499i | −0.632809 | − | 0.774308i | \(-0.718098\pi\) |
0.774308 | + | 0.632809i | \(0.218098\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0000 | − | 30.0000i | −0.0316122 | − | 0.0316122i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1056.00 | 1.11041 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1264.00i | − | 1.32634i | −0.748470 | − | 0.663169i | \(-0.769211\pi\) | ||
0.748470 | − | 0.663169i | \(-0.230789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1116.00i | 1.16859i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 304.000 | + | 304.000i | 0.317659 | + | 0.317659i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 864.000 | 0.900938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 313.000i | − | 0.325702i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −168.000 | −0.174455 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.0000i | 0.0559585i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1006.00 | + | 1006.00i | −1.04033 | + | 1.04033i | −0.0411791 | + | 0.999152i | \(0.513111\pi\) |
−0.999152 | + | 0.0411791i | \(0.986889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1840.00 | 1.89886 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 720.000i | − | 0.739979i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 84.0000 | − | 84.0000i | 0.0861538 | − | 0.0861538i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −921.000 | − | 921.000i | −0.942682 | − | 0.942682i | 0.0557624 | − | 0.998444i | \(-0.482241\pi\) |
−0.998444 | + | 0.0557624i | \(0.982241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.0000 | − | 68.0000i | 0.0694586 | − | 0.0694586i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 637.000 | − | 637.000i | 0.649337 | − | 0.649337i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1480.00i | − | 1.50560i | −0.658252 | − | 0.752798i | \(-0.728704\pi\) | ||
0.658252 | − | 0.752798i | \(-0.271296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 102.000 | − | 102.000i | 0.103553 | − | 0.103553i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 704.000i | − | 0.713273i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 840.000i | 0.849343i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1038.00 | − | 1038.00i | −1.04743 | − | 1.04743i | −0.998818 | − | 0.0486090i | \(-0.984521\pi\) |
−0.0486090 | − | 0.998818i | \(-0.515479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1304.00 | − | 1304.00i | −1.31319 | − | 1.31319i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −276.000 | −0.277387 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 355.000 | − | 355.000i | 0.356068 | − | 0.356068i | −0.506293 | − | 0.862361i | \(-0.668985\pi\) |
0.862361 | + | 0.506293i | \(0.168985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −296.000 | −0.296296 |
(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 | 592.3.k.c.401.1 | 2 | ||
4.3 | odd | 2 | 74.3.d.b.31.1 | ✓ | 2 | ||
12.11 | even | 2 | 666.3.i.a.253.1 | 2 | |||
37.6 | odd | 4 | inner | 592.3.k.c.561.1 | 2 | ||
148.43 | even | 4 | 74.3.d.b.43.1 | yes | 2 | ||
444.191 | odd | 4 | 666.3.i.a.487.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.3.d.b.31.1 | ✓ | 2 | 4.3 | odd | 2 | ||
74.3.d.b.43.1 | yes | 2 | 148.43 | even | 4 | ||
592.3.k.c.401.1 | 2 | 1.1 | even | 1 | trivial | ||
592.3.k.c.561.1 | 2 | 37.6 | odd | 4 | inner | ||
666.3.i.a.253.1 | 2 | 12.11 | even | 2 | |||
666.3.i.a.487.1 | 2 | 444.191 | odd | 4 |