Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,4,Mod(749,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.749");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1100.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.9021010063\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 749.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1100.749 |
Dual form | 1100.4.b.c.749.1 |
$q$-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 \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(551\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.00000i | 0.962250i | 0.876652 | + | 0.481125i | \(0.159772\pi\) | ||||
−0.876652 | + | 0.481125i | \(0.840228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 26.0000i | − 1.40387i | −0.712242 | − | 0.701934i | \(-0.752320\pi\) | ||||
0.712242 | − | 0.701934i | \(-0.247680\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 52.0000i | − 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 46.0000i | 0.656273i | 0.944630 | + | 0.328136i | \(0.106421\pi\) | ||||
−0.944630 | + | 0.328136i | \(0.893579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 96.0000 | 1.15915 | 0.579577 | − | 0.814918i | \(-0.303218\pi\) | ||||
0.579577 | + | 0.814918i | \(0.303218\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 130.000 | 1.35087 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 27.0000i | − 0.244778i | −0.992482 | − | 0.122389i | \(-0.960944\pi\) | ||||
0.992482 | − | 0.122389i | \(-0.0390555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 145.000i | 1.03353i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −16.0000 | −0.102453 | −0.0512263 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512263 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −293.000 | −1.69756 | −0.848780 | − | 0.528746i | \(-0.822662\pi\) | ||||
−0.848780 | + | 0.528746i | \(0.822662\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 55.0000i | − 0.290129i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 29.0000i | − 0.128853i | −0.997922 | − | 0.0644266i | \(-0.979478\pi\) | ||||
0.997922 | − | 0.0644266i | \(-0.0205218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 260.000 | 1.06752 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −472.000 | −1.79790 | −0.898951 | − | 0.438048i | \(-0.855670\pi\) | ||||
−0.898951 | + | 0.438048i | \(0.855670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 110.000i | 0.390113i | 0.980792 | + | 0.195056i | \(0.0624890\pi\) | ||||
−0.980792 | + | 0.195056i | \(0.937511\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 224.000i | − 0.695186i | −0.937645 | − | 0.347593i | \(-0.886999\pi\) | ||||
0.937645 | − | 0.347593i | \(-0.113001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −333.000 | −0.970845 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −230.000 | −0.631499 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 754.000i | − 1.95415i | −0.212899 | − | 0.977074i | \(-0.568291\pi\) | ||||
0.212899 | − | 0.977074i | \(-0.431709\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 480.000i | 1.11540i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −825.000 | −1.82044 | −0.910219 | − | 0.414127i | \(-0.864087\pi\) | ||||
−0.910219 | + | 0.414127i | \(0.864087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −548.000 | −1.15023 | −0.575116 | − | 0.818072i | \(-0.695043\pi\) | ||||
−0.575116 | + | 0.818072i | \(0.695043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 52.0000i | − 0.103990i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 123.000i | − 0.224281i | −0.993692 | − | 0.112141i | \(-0.964229\pi\) | ||||
0.993692 | − | 0.112141i | \(-0.0357707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 135.000 | 0.235538 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1001.00 | 1.67319 | 0.836597 | − | 0.547818i | \(-0.184541\pi\) | ||||
0.836597 | + | 0.547818i | \(0.184541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1020.00i | 1.63537i | 0.575666 | + | 0.817685i | \(0.304743\pi\) | ||||
−0.575666 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 286.000i | 0.423282i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −526.000 | −0.749109 | −0.374555 | − | 0.927205i | \(-0.622204\pi\) | ||||
−0.374555 | + | 0.927205i | \(0.622204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 158.000i | 0.208949i | 0.994528 | + | 0.104474i | \(0.0333160\pi\) | ||||
−0.994528 | + | 0.104474i | \(0.966684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 80.0000i | − 0.0985851i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1217.00 | 1.44946 | 0.724729 | − | 0.689034i | \(-0.241965\pi\) | ||||
0.724729 | + | 0.689034i | \(0.241965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1352.00 | −1.55745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1465.00i | − 1.63348i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 263.000i | − 0.275295i | −0.990481 | − | 0.137647i | \(-0.956046\pi\) | ||||
0.990481 | − | 0.137647i | \(-0.0439541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.0000 | −0.0223342 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −814.000 | −0.801941 | −0.400970 | − | 0.916091i | \(-0.631327\pi\) | ||||
−0.400970 | + | 0.916091i | \(0.631327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 376.000i | − 0.359693i | −0.983695 | − | 0.179847i | \(-0.942440\pi\) | ||||
0.983695 | − | 0.179847i | \(-0.0575601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1494.00i | − 1.34982i | −0.737901 | − | 0.674909i | \(-0.764183\pi\) | ||||
0.737901 | − | 0.674909i | \(-0.235817\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −842.000 | −0.739899 | −0.369949 | − | 0.929052i | \(-0.620625\pi\) | ||||
−0.369949 | + | 0.929052i | \(0.620625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 145.000 | 0.123989 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1281.00i | − 1.06643i | −0.845980 | − | 0.533214i | \(-0.820984\pi\) | ||||
0.845980 | − | 0.533214i | \(-0.179016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 104.000i | − 0.0821778i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1196.00 | 0.921321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2360.00i | − 1.73003i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1736.00i | 1.21295i | 0.795101 | + | 0.606477i | \(0.207418\pi\) | ||||
−0.795101 | + | 0.606477i | \(0.792582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −550.000 | −0.375386 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.00400170 | 0.00200085 | − | 0.999998i | \(-0.499363\pi\) | ||||
0.00200085 | + | 0.999998i | \(0.499363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2496.00i | − 1.62730i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1439.00i | − 0.897387i | −0.893686 | − | 0.448694i | \(-0.851889\pi\) | ||||
0.893686 | − | 0.448694i | \(-0.148111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 318.000 | 0.194046 | 0.0970231 | − | 0.995282i | \(-0.469068\pi\) | ||||
0.0970231 | + | 0.995282i | \(0.469068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1120.00 | 0.668943 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 572.000i | 0.334497i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1665.00i | − 0.934196i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 922.000 | 0.506934 | 0.253467 | − | 0.967344i | \(-0.418429\pi\) | ||||
0.253467 | + | 0.967344i | \(0.418429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1030.00 | −0.555101 | −0.277550 | − | 0.960711i | \(-0.589523\pi\) | ||||
−0.277550 | + | 0.960711i | \(0.589523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 92.0000i | 0.0486128i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1017.00i | 0.516977i | 0.966014 | + | 0.258489i | \(0.0832245\pi\) | ||||
−0.966014 | + | 0.258489i | \(0.916776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3770.00 | 1.88038 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −702.000 | −0.343636 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2444.00i | 1.17441i | 0.809438 | + | 0.587205i | \(0.199772\pi\) | ||||
−0.809438 | + | 0.587205i | \(0.800228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1452.00i | − 0.672809i | −0.941718 | − | 0.336405i | \(-0.890789\pi\) | ||||
0.941718 | − | 0.336405i | \(-0.109211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −507.000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 192.000 | 0.0858632 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1914.00i | − 0.841149i | −0.907258 | − | 0.420574i | \(-0.861829\pi\) | ||||
0.907258 | − | 0.420574i | \(-0.138171\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 4125.00i | − 1.75172i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1293.00 | −0.539907 | −0.269954 | − | 0.962873i | \(-0.587008\pi\) | ||||
−0.269954 | + | 0.962873i | \(0.587008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 455.000 | 0.186850 | 0.0934251 | − | 0.995626i | \(-0.470218\pi\) | ||||
0.0934251 | + | 0.995626i | \(0.470218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2740.00i | − 1.10681i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 506.000i | − 0.197874i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3770.00 | 1.45094 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1115.00 | −0.422401 | −0.211200 | − | 0.977443i | \(-0.567737\pi\) | ||||
−0.211200 | + | 0.977443i | \(0.567737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 5012.00i | − 1.86928i | −0.355591 | − | 0.934642i | \(-0.615720\pi\) | ||||
0.355591 | − | 0.934642i | \(-0.384280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4146.00i | − 1.49944i | −0.661753 | − | 0.749721i | \(-0.730187\pi\) | ||||
0.661753 | − | 0.749721i | \(-0.269813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1240.00 | 0.441715 | 0.220857 | − | 0.975306i | \(-0.429114\pi\) | ||||
0.220857 | + | 0.975306i | \(0.429114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 615.000 | 0.215815 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 416.000i | 0.143830i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 54.0000i | − 0.0181317i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1056.00 | −0.349498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2820.00 | −0.920080 | −0.460040 | − | 0.887898i | \(-0.652165\pi\) | ||||
−0.460040 | + | 0.887898i | \(0.652165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5005.00i | 1.61003i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7618.00i | 2.38315i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5100.00 | −1.57363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2392.00 | 0.728069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3695.00i | − 1.10958i | −0.831992 | − | 0.554788i | \(-0.812799\pi\) | ||||
0.831992 | − | 0.554788i | \(-0.187201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 486.000i | − 0.142101i | −0.997473 | − | 0.0710506i | \(-0.977365\pi\) | ||||
0.997473 | − | 0.0710506i | \(-0.0226352\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4231.00 | −1.22093 | −0.610464 | − | 0.792044i | \(-0.709017\pi\) | ||||
−0.610464 | + | 0.792044i | \(0.709017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1430.00 | −0.407303 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3336.00i | 0.937977i | 0.883204 | + | 0.468988i | \(0.155381\pi\) | ||||
−0.883204 | + | 0.468988i | \(0.844619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2630.00i | − 0.720831i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3610.00 | −0.977036 | −0.488518 | − | 0.872554i | \(-0.662462\pi\) | ||||
−0.488518 | + | 0.872554i | \(0.662462\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6408.00 | −1.71276 | −0.856381 | − | 0.516345i | \(-0.827292\pi\) | ||||
−0.856381 | + | 0.516345i | \(0.827292\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 560.000i | 0.147835i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4992.00i | − 1.28596i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −790.000 | −0.201061 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1787.00 | −0.449380 | −0.224690 | − | 0.974430i | \(-0.572137\pi\) | ||||
−0.224690 | + | 0.974430i | \(0.572137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 297.000i | 0.0738033i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 354.000i | − 0.0859218i | −0.999077 | − | 0.0429609i | \(-0.986321\pi\) | ||||
0.999077 | − | 0.0429609i | \(-0.0136791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −754.000 | −0.180893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.0000 | −0.00758908 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2026.00i | 0.475013i | 0.971386 | + | 0.237507i | \(0.0763302\pi\) | ||||
−0.971386 | + | 0.237507i | \(0.923670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6085.00i | 1.39474i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8750.00 | 1.98326 | 0.991630 | − | 0.129112i | \(-0.0412128\pi\) | ||||
0.991630 | + | 0.129112i | \(0.0412128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5036.00 | −1.12884 | −0.564419 | − | 0.825488i | \(-0.690900\pi\) | ||||
−0.564419 | + | 0.825488i | \(0.690900\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 6760.00i | − 1.49866i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4306.00i | − 0.934016i | −0.884253 | − | 0.467008i | \(-0.845332\pi\) | ||||
0.884253 | − | 0.467008i | \(-0.154668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −586.000 | −0.125745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1202.00 | −0.255179 | −0.127590 | − | 0.991827i | \(-0.540724\pi\) | ||||
−0.127590 | + | 0.991827i | \(0.540724\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6620.00i | 1.39052i | 0.718757 | + | 0.695262i | \(0.244712\pi\) | ||||
−0.718757 | + | 0.695262i | \(0.755288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12272.0i | 2.52402i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2797.00 | 0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1315.00 | 0.264903 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6968.00i | − 1.38933i | −0.719331 | − | 0.694667i | \(-0.755552\pi\) | ||||
0.719331 | − | 0.694667i | \(-0.244448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1595.00i | − 0.311620i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1404.00 | −0.271557 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2860.00 | 0.547667 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4070.00i | − 0.771668i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7640.00i | 1.42032i | 0.704041 | + | 0.710159i | \(0.251377\pi\) | ||||
−0.704041 | + | 0.710159i | \(0.748623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1880.00 | 0.346115 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −652.000 | −0.118880 | −0.0594398 | − | 0.998232i | \(-0.518931\pi\) | ||||
−0.0594398 | + | 0.998232i | \(0.518931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8055.00i | − 1.45462i | −0.686310 | − | 0.727309i | \(-0.740771\pi\) | ||||
0.686310 | − | 0.727309i | \(-0.259229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5675.00i | − 1.00549i | −0.864435 | − | 0.502744i | \(-0.832324\pi\) | ||||
0.864435 | − | 0.502744i | \(-0.167676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 176.000 | 0.0308906 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7470.00 | 1.29886 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4416.00i | 0.760721i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4210.00i | − 0.711968i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5824.00 | −0.975950 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2245.00 | −0.372799 | −0.186399 | − | 0.982474i | \(-0.559682\pi\) | ||||
−0.186399 | + | 0.982474i | \(0.559682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 58.0000i | − 0.00954469i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 694.000i | − 0.112180i | −0.998426 | − | 0.0560899i | \(-0.982137\pi\) | ||||
0.998426 | − | 0.0560899i | \(-0.0178633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6405.00 | 1.02617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3223.00 | 0.511834 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 260.000i | − 0.0409291i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4092.00i | 0.633055i | 0.948583 | + | 0.316527i | \(0.102517\pi\) | ||||
−0.948583 | + | 0.316527i | \(0.897483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −334.000 | −0.0512281 | −0.0256141 | − | 0.999672i | \(-0.508154\pi\) | ||||
−0.0256141 | + | 0.999672i | \(0.508154\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7540.00 | 1.14660 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 891.000i | − 0.134343i | −0.997741 | − | 0.0671716i | \(-0.978603\pi\) | ||||
0.997741 | − | 0.0671716i | \(-0.0213975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5980.00i | 0.886541i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2476.00 | −0.364006 | −0.182003 | − | 0.983298i | \(-0.558258\pi\) | ||||
−0.182003 | + | 0.983298i | \(0.558258\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2357.00 | 0.343636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 605.000i | 0.0874773i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1379.00i | 0.196140i | 0.995180 | + | 0.0980698i | \(0.0312668\pi\) | ||||
−0.995180 | + | 0.0980698i | \(0.968733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −944.000 | −0.133178 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19604.0 | −2.74337 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6266.00i | 0.869816i | 0.900475 | + | 0.434908i | \(0.143219\pi\) | ||||
−0.900475 | + | 0.434908i | \(0.856781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 832.000i | 0.113661i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −151.000 | −0.0204653 | −0.0102327 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102327 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8680.00 | −1.16717 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1989.00i | 0.265361i | 0.991159 | + | 0.132680i | \(0.0423584\pi\) | ||||
−0.991159 | + | 0.132680i | \(0.957642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 220.000i | 0.0288972i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6817.00 | −0.888523 | −0.444262 | − | 0.895897i | \(-0.646534\pi\) | ||||
−0.444262 | + | 0.895897i | \(0.646534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1242.00 | 0.160641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.0000i | 0.00385064i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4170.00i | − 0.527170i | −0.964636 | − | 0.263585i | \(-0.915095\pi\) | ||||
0.964636 | − | 0.263585i | \(-0.0849049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12480.0 | 1.56587 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10914.0 | 1.35915 | 0.679575 | − | 0.733606i | \(-0.262164\pi\) | ||||
0.679575 | + | 0.733606i | \(0.262164\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15236.0i | 1.88327i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 319.000i | 0.0388507i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1102.00 | 0.133228 | 0.0666142 | − | 0.997779i | \(-0.478780\pi\) | ||||
0.0666142 | + | 0.997779i | \(0.478780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7195.00 | 0.863511 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21450.0i | 2.55565i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1590.00i | 0.186721i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11028.0 | −1.28581 | −0.642903 | − | 0.765947i | \(-0.722270\pi\) | ||||
−0.642903 | + | 0.765947i | \(0.722270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2622.00 | 0.303536 | 0.151768 | − | 0.988416i | \(-0.451503\pi\) | ||||
0.151768 | + | 0.988416i | \(0.451503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 448.000i | − 0.0514953i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14248.0i | 1.61478i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2860.00 | −0.321870 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16598.0 | 1.85498 | 0.927491 | − | 0.373845i | \(-0.121961\pi\) | ||||
0.927491 | + | 0.373845i | \(0.121961\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5763.00i | 0.639612i | 0.947483 | + | 0.319806i | \(0.103618\pi\) | ||||
−0.947483 | + | 0.319806i | \(0.896382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2592.00i | − 0.283735i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3128.00 | 0.340071 | 0.170036 | − | 0.985438i | \(-0.445612\pi\) | ||||
0.170036 | + | 0.985438i | \(0.445612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −666.000 | −0.0719145 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6369.00i | − 0.683071i | −0.939869 | − | 0.341535i | \(-0.889053\pi\) | ||||
0.939869 | − | 0.341535i | \(-0.110947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4610.00i | 0.487798i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8691.00 | −0.913483 | −0.456741 | − | 0.889600i | \(-0.650983\pi\) | ||||
−0.456741 | + | 0.889600i | \(0.650983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5192.00 | 0.542088 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5150.00i | − 0.534146i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2260.00i | 0.231331i | 0.993288 | + | 0.115666i | \(0.0369001\pi\) | ||||
−0.993288 | + | 0.115666i | \(0.963100\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6670.00 | −0.678277 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12756.0 | −1.28873 | −0.644367 | − | 0.764717i | \(-0.722879\pi\) | ||||
−0.644367 | + | 0.764717i | \(0.722879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6887.00i | 0.691287i | 0.938366 | + | 0.345644i | \(0.112339\pi\) | ||||
−0.938366 | + | 0.345644i | \(0.887661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1535.00i | − 0.152101i | −0.997104 | − | 0.0760507i | \(-0.975769\pi\) | ||||
0.997104 | − | 0.0760507i | \(-0.0242311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3198.00 | −0.314861 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5085.00 | −0.497462 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1210.00i | − 0.117623i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1508.00i | − 0.144752i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17564.0 | 1.67541 | 0.837703 | − | 0.546126i | \(-0.183898\pi\) | ||||
0.837703 | + | 0.546126i | \(0.183898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1508.00 | −0.142950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3510.00i | − 0.330664i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7541.00i | − 0.701674i | −0.936437 | − | 0.350837i | \(-0.885897\pi\) | ||||
0.936437 | − | 0.350837i | \(-0.114103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12220.0 | −1.13008 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12552.0 | 1.15369 | 0.576847 | − | 0.816852i | \(-0.304283\pi\) | ||||
0.576847 | + | 0.816852i | \(0.304283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 736.000i | − 0.0672369i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 26026.0i | − 2.34894i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8396.00 | 0.753220 | 0.376610 | − | 0.926372i | \(-0.377090\pi\) | ||||
0.376610 | + | 0.926372i | \(0.377090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7260.00 | 0.647411 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12194.0i | 1.08092i | 0.841369 | + | 0.540461i | \(0.181750\pi\) | ||||
−0.841369 | + | 0.540461i | \(0.818250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2535.00i | − 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18295.0 | −1.59315 | −0.796573 | − | 0.604542i | \(-0.793356\pi\) | ||||
−0.796573 | + | 0.604542i | \(0.793356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26520.0 | 2.29584 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13920.0i | 1.19802i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2464.00i | 0.209607i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9570.00 | 0.809396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7101.00 | 0.597122 | 0.298561 | − | 0.954391i | \(-0.403493\pi\) | ||||
0.298561 | + | 0.954391i | \(0.403493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4912.00i | 0.410682i | 0.978690 | + | 0.205341i | \(0.0658304\pi\) | ||||
−0.978690 | + | 0.205341i | \(0.934170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 13478.0i | − 1.11406i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11438.0 | 0.940084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1650.00 | −0.134847 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24544.0i | 1.99459i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 6465.00i | − 0.519526i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3663.00 | 0.292721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11496.0 | 0.913589 | 0.456794 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456794 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2275.00i | 0.179797i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19048.0i | 1.48891i | 0.667673 | + | 0.744455i | \(0.267291\pi\) | ||||
−0.667673 | + | 0.744455i | \(0.732709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1096.00 | −0.0852024 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1536.00 | −0.118758 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13676.0i | 1.05165i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10718.0i | 0.815325i | 0.913133 | + | 0.407663i | \(0.133656\pi\) | ||||
−0.913133 | + | 0.407663i | \(0.866344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5720.00 | 0.432791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2530.00 | 0.190404 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 6660.00i | − 0.498553i | −0.968432 | − | 0.249277i | \(-0.919807\pi\) | ||||
0.968432 | − | 0.249277i | \(-0.0801929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17446.0i | 1.29217i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10960.0 | 0.807499 | 0.403750 | − | 0.914870i | \(-0.367707\pi\) | ||||
0.403750 | + | 0.914870i | \(0.367707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18596.0 | 1.36290 | 0.681452 | − | 0.731863i | \(-0.261349\pi\) | ||||
0.681452 | + | 0.731863i | \(0.261349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5575.00i | − 0.406455i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 21119.0i | − 1.52374i | −0.647733 | − | 0.761868i | \(-0.724283\pi\) | ||||
0.647733 | − | 0.761868i | \(-0.275717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25060.0 | 1.79872 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4108.00 | 0.293337 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8294.00i | 0.589198i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2836.00i | − 0.199411i | −0.995017 | − | 0.0997055i | \(-0.968210\pi\) | ||||
0.995017 | − | 0.0997055i | \(-0.0317901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28128.0 | −1.96773 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20730.0 | 1.44284 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 18044.0i | − 1.24954i | −0.780808 | − | 0.624771i | \(-0.785192\pi\) | ||||
0.780808 | − | 0.624771i | \(-0.214808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6200.00i | 0.425040i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9264.00 | 0.631914 | 0.315957 | − | 0.948773i | \(-0.397674\pi\) | ||||
0.315957 | + | 0.948773i | \(0.397674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19326.0 | −1.31169 | −0.655844 | − | 0.754897i | \(-0.727687\pi\) | ||||
−0.655844 | + | 0.754897i | \(0.727687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 246.000i | − 0.0166134i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10082.0i | 0.674161i | 0.941476 | + | 0.337081i | \(0.109439\pi\) | ||||
−0.941476 | + | 0.337081i | \(0.890561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2080.00 | −0.138400 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11648.0 | −0.771240 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13088.0i | − 0.862348i | −0.902269 | − | 0.431174i | \(-0.858100\pi\) | ||||
0.902269 | − | 0.431174i | \(-0.141900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23426.0i | 1.52852i | 0.644910 | + | 0.764259i | \(0.276895\pi\) | ||||
−0.644910 | + | 0.764259i | \(0.723105\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23587.0 | −1.53157 | −0.765785 | − | 0.643097i | \(-0.777649\pi\) | ||||
−0.765785 | + | 0.643097i | \(0.777649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3915.00 | 0.252985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 31642.0i | − 2.03485i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5280.00i | − 0.336304i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1334.00 | 0.0845629 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19683.0 | 1.24179 | 0.620894 | − | 0.783895i | \(-0.286770\pi\) | ||||
0.620894 | + | 0.783895i | \(0.286770\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 14100.0i | − 0.885347i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17316.0i | 1.07706i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2002.00 | 0.123940 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 375.000 | 0.0231070 | 0.0115535 | − | 0.999933i | \(-0.496322\pi\) | ||||
0.0115535 | + | 0.999933i | \(0.496322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21055.0i | 1.29133i | 0.763619 | + | 0.645667i | \(0.223421\pi\) | ||||
−0.763619 | + | 0.645667i | \(0.776579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 6427.00i | − 0.390528i | −0.980751 | − | 0.195264i | \(-0.937444\pi\) | ||||
0.980751 | − | 0.195264i | \(-0.0625563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9075.00 | 0.548883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38090.0 | −2.29319 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7617.00i | 0.456472i | 0.973606 | + | 0.228236i | \(0.0732958\pi\) | ||||
−0.973606 | + | 0.228236i | \(0.926704\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2040.00i | 0.121138i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17630.0 | 1.04214 | 0.521068 | − | 0.853515i | \(-0.325534\pi\) | ||||
0.521068 | + | 0.853515i | \(0.325534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4605.00 | 0.270974 | 0.135487 | − | 0.990779i | \(-0.456740\pi\) | ||||
0.135487 | + | 0.990779i | \(0.456740\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11960.0i | 0.700585i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 432.000i | 0.0250781i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18475.0 | 1.06769 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6028.00 | 0.346808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2818.00i | 0.161406i | 0.996738 | + | 0.0807028i | \(0.0257165\pi\) | ||||
−0.996738 | + | 0.0807028i | \(0.974284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8438.00i | 0.479023i | 0.970894 | + | 0.239512i | \(0.0769873\pi\) | ||||
−0.970894 | + | 0.239512i | \(0.923013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6838.00 | −0.386478 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2430.00 | 0.136737 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17344.0i | 0.971669i | 0.874051 | + | 0.485834i | \(0.161484\pi\) | ||||
−0.874051 | + | 0.485834i | \(0.838516\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 21155.0i | − 1.17484i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39208.0 | −2.16793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3947.00 | −0.217295 | −0.108648 | − | 0.994080i | \(-0.534652\pi\) | ||||
−0.108648 | + | 0.994080i | \(0.534652\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 572.000i | 0.0313542i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 21712.0i | − 1.17991i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16680.0 | −0.902569 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7998.00 | −0.430928 | −0.215464 | − | 0.976512i | \(-0.569126\pi\) | ||||
−0.215464 | + | 0.976512i | \(0.569126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2784.00i | − 0.149361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21164.0i | 1.12582i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 881.000 | 0.0466666 | 0.0233333 | − | 0.999728i | \(-0.492572\pi\) | ||||
0.0233333 | + | 0.999728i | \(0.492572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1052.00 | −0.0554896 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7911.00i | 0.415525i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 18050.0i | − 0.940153i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26093.0 | 1.35341 | 0.676707 | − | 0.736252i | \(-0.263406\pi\) | ||||
0.676707 | + | 0.736252i | \(0.263406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9776.00 | −0.504962 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 32040.0i | − 1.64811i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7481.00i | − 0.381644i | −0.981625 | − | 0.190822i | \(-0.938885\pi\) | ||||
0.981625 | − | 0.190822i | \(-0.0611153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20917.0 | −1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5060.00 | −0.256020 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 17788.0i | − 0.896337i | −0.893949 | − | 0.448168i | \(-0.852077\pi\) | ||||
0.893949 | − | 0.448168i | \(-0.147923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1353.00i | 0.0676233i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32182.0 | 1.60194 | 0.800970 | − | 0.598704i | \(-0.204317\pi\) | ||||
0.800970 | + | 0.598704i | \(0.204317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24960.0 | 1.23742 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32044.0i | 1.58221i | 0.611682 | + | 0.791104i | \(0.290493\pi\) | ||||
−0.611682 | + | 0.791104i | \(0.709507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 316.000i | 0.0154777i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38844.0 | −1.89497 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33779.0 | −1.64130 | −0.820648 | − | 0.571434i | \(-0.806387\pi\) | ||||
−0.820648 | + | 0.571434i | \(0.806387\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 8935.00i | − 0.432416i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 15630.0i | − 0.750439i | −0.926936 | − | 0.375219i | \(-0.877567\pi\) | ||||
0.926936 | − | 0.375219i | \(-0.122433\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1485.00 | −0.0710172 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1948.00 | 0.0927923 | 0.0463962 | − | 0.998923i | \(-0.485226\pi\) | ||||
0.0463962 | + | 0.998923i | \(0.485226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21892.0i | 1.03872i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42900.0i | 2.01959i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17420.0 | 0.816881 | 0.408440 | − | 0.912785i | \(-0.366073\pi\) | ||||
0.408440 | + | 0.912785i | \(0.366073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1770.00 | 0.0826783 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11122.0i | − 0.517504i | −0.965944 | − | 0.258752i | \(-0.916689\pi\) | ||||
0.965944 | − | 0.258752i | \(-0.0833112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3770.00i | − 0.174064i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45312.0 | −2.08404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11011.0 | −0.504487 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2320.00i | − 0.105888i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29648.0i | 1.34287i | 0.741064 | + | 0.671434i | \(0.234321\pi\) | ||||
−0.741064 | + | 0.671434i | \(0.765679\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10130.0 | −0.457082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33306.0 | −1.49712 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28496.0i | 1.27607i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23219.0i | − 1.03194i | −0.856606 | − | 0.515972i | \(-0.827431\pi\) | ||||
0.856606 | − | 0.515972i | \(-0.172569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10304.0 | 0.456232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2434.00 | 0.107367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11220.0i | − 0.493082i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43750.0i | 1.90839i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9232.00 | −0.401211 | −0.200606 | − | 0.979672i | \(-0.564291\pi\) | ||||
−0.200606 | + | 0.979672i | \(0.564291\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32286.0 | −1.39792 | −0.698961 | − | 0.715160i | \(-0.746354\pi\) | ||||
−0.698961 | + | 0.715160i | \(0.746354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 25180.0i | − 1.08623i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10560.0i | 0.452200i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2704.00 | −0.115367 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31706.0 | −1.34780 | −0.673902 | − | 0.738821i | \(-0.735383\pi\) | ||||
−0.673902 | + | 0.738821i | \(0.735383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 41139.0i | − 1.74242i | −0.490906 | − | 0.871212i | \(-0.663334\pi\) | ||||
0.490906 | − | 0.871212i | \(-0.336666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 15252.0i | − 0.641311i | −0.947196 | − | 0.320655i | \(-0.896097\pi\) | ||||
0.947196 | − | 0.320655i | \(-0.103903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −369.000 | −0.0154595 | −0.00772973 | − | 0.999970i | \(-0.502460\pi\) | ||||
−0.00772973 | + | 0.999970i | \(0.502460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21530.0 | 0.898757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 15318.0i | − 0.637140i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 42485.0i | − 1.75448i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10257.0 | 0.422063 | 0.211032 | − | 0.977479i | \(-0.432318\pi\) | ||||
0.211032 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24133.0 | −0.989503 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 6010.00i | − 0.245546i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3146.00i | − 0.127624i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33100.0 | −1.33803 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −783.000 | −0.0315404 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34386.0i | 1.38025i | 0.723690 | + | 0.690126i | \(0.242445\pi\) | ||||
−0.723690 | + | 0.690126i | \(0.757555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 23464.0i | − 0.935257i | −0.883925 | − | 0.467628i | \(-0.845109\pi\) | ||||
0.883925 | − | 0.467628i | \(-0.154891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22475.0 | 0.892709 | 0.446355 | − | 0.894856i | \(-0.352722\pi\) | ||||
0.446355 | + | 0.894856i | \(0.352722\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −61360.0 | −2.42874 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 2880.00i | − 0.113599i | −0.998386 | − | 0.0567997i | \(-0.981910\pi\) | ||||
0.998386 | − | 0.0567997i | \(-0.0180897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13985.0i | 0.547815i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5786.00 | 0.225865 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6396.00 | −0.248818 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 526.000i | − 0.0203922i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 11084.0i | − 0.426773i | −0.976968 | − | 0.213387i | \(-0.931551\pi\) | ||||
0.976968 | − | 0.213387i | \(-0.0684494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34840.0 | 1.33689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41797.0 | 1.59838 | 0.799192 | − | 0.601076i | \(-0.205261\pi\) | ||||
0.799192 | + | 0.601076i | \(0.205261\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 23780.0i | − 0.906298i | −0.891435 | − | 0.453149i | \(-0.850301\pi\) | ||||
0.891435 | − | 0.453149i | \(-0.149699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 14334.0i | − 0.542603i | −0.962494 | − | 0.271301i | \(-0.912546\pi\) | ||||
0.962494 | − | 0.271301i | \(-0.0874540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45136.0 | 1.70283 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7381.00 | 0.277523 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 21504.0i | − 0.805827i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7020.00i | − 0.261305i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4688.00 | 0.173919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34684.0 | 1.28245 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14300.0i | 0.526992i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25716.0i | 0.941440i | 0.882283 | + | 0.470720i | \(0.156006\pi\) | ||||
−0.882283 | + | 0.470720i | \(0.843994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1628.00 | −0.0594030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28300.0 | −1.02922 | −0.514611 | − | 0.857424i | \(-0.672064\pi\) | ||||
−0.514611 | + | 0.857424i | \(0.672064\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1738.00i | − 0.0630004i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 156.000i | − 0.00561786i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21410.0 | −0.768499 | −0.384250 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384250 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38200.0 | −1.36670 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 52052.0i | − 1.85624i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 752.000i | − 0.0266439i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19938.0 | −0.704138 | −0.352069 | − | 0.935974i | \(-0.614522\pi\) | ||||
−0.352069 | + | 0.935974i | \(0.614522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31968.0 | −1.12536 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3260.00i | − 0.114392i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26728.0i | 0.931874i | 0.884818 | + | 0.465937i | \(0.154283\pi\) | ||||
−0.884818 | + | 0.465937i | \(0.845717\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40275.0 | 1.39971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8634.00 | 0.299108 | 0.149554 | − | 0.988754i | \(-0.452216\pi\) | ||||
0.149554 | + | 0.988754i | \(0.452216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12744.0i | 0.440087i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24841.0i | 0.852401i | 0.904629 | + | 0.426201i | \(0.140148\pi\) | ||||
−0.904629 | + | 0.426201i | \(0.859852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53040.0 | 1.81428 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28375.0 | 0.967531 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 51234.0i | − 1.74148i | −0.491742 | − | 0.870741i | \(-0.663640\pi\) | ||||
0.491742 | − | 0.870741i | \(-0.336360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 880.000i | 0.0297245i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37414.0 | −1.25981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56058.0 | 1.88171 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2988.00i | − 0.0999865i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 26752.0i | − 0.889645i | −0.895619 | − | 0.444822i | \(-0.853267\pi\) | ||||
0.895619 | − | 0.444822i | \(-0.146733\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22080.0 | −0.732004 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21155.0 | 0.699172 | 0.349586 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349586 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8268.00i | − 0.272415i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 56323.0i | − 1.84435i | −0.386770 | − | 0.922176i | \(-0.626409\pi\) | ||||
0.386770 | − | 0.922176i | \(-0.373591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13387.0 | −0.437028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1684.00 | −0.0548073 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 24683.0i | − 0.800880i | −0.916323 | − | 0.400440i | \(-0.868857\pi\) | ||||
0.916323 | − | 0.400440i | \(-0.131143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 29120.0i | − 0.939108i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2970.00 | 0.0954909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26816.0 | −0.859574 | −0.429787 | − | 0.902930i | \(-0.641411\pi\) | ||||
−0.429787 | + | 0.902930i | \(0.641411\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 11225.0i | − 0.358726i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18614.0i | 0.591285i | 0.955299 | + | 0.295643i | \(0.0955337\pi\) | ||||
−0.955299 | + | 0.295643i | \(0.904466\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4205.00 | 0.133173 |
(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 | 1100.4.b.c.749.2 | 2 | ||
5.2 | odd | 4 | 1100.4.a.d.1.1 | 1 | |||
5.3 | odd | 4 | 44.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 1100.4.b.c.749.1 | 2 | ||
15.8 | even | 4 | 396.4.a.e.1.1 | 1 | |||
20.3 | even | 4 | 176.4.a.e.1.1 | 1 | |||
35.13 | even | 4 | 2156.4.a.b.1.1 | 1 | |||
40.3 | even | 4 | 704.4.a.c.1.1 | 1 | |||
40.13 | odd | 4 | 704.4.a.j.1.1 | 1 | |||
55.43 | even | 4 | 484.4.a.a.1.1 | 1 | |||
60.23 | odd | 4 | 1584.4.a.p.1.1 | 1 | |||
220.43 | odd | 4 | 1936.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
44.4.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
176.4.a.e.1.1 | 1 | 20.3 | even | 4 | |||
396.4.a.e.1.1 | 1 | 15.8 | even | 4 | |||
484.4.a.a.1.1 | 1 | 55.43 | even | 4 | |||
704.4.a.c.1.1 | 1 | 40.3 | even | 4 | |||
704.4.a.j.1.1 | 1 | 40.13 | odd | 4 | |||
1100.4.a.d.1.1 | 1 | 5.2 | odd | 4 | |||
1100.4.b.c.749.1 | 2 | 5.4 | even | 2 | inner | ||
1100.4.b.c.749.2 | 2 | 1.1 | even | 1 | trivial | ||
1584.4.a.p.1.1 | 1 | 60.23 | odd | 4 | |||
1936.4.a.m.1.1 | 1 | 220.43 | odd | 4 | |||
2156.4.a.b.1.1 | 1 | 35.13 | even | 4 |