Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,4,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(47.2015280046\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.4.c.h.449.4 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 7.21110i | − 1.38778i | −0.720082 | − | 0.693889i | \(-0.755896\pi\) | ||||
0.720082 | − | 0.693889i | \(-0.244104\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.21110i | 0.389363i | 0.980867 | + | 0.194681i | \(0.0623673\pi\) | ||||
−0.980867 | + | 0.194681i | \(0.937633\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.0000 | −0.925926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.2666 | 1.18594 | 0.592972 | − | 0.805223i | \(-0.297955\pi\) | ||||
0.592972 | + | 0.805223i | \(0.297955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 34.0000i | − 0.725377i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) | ||||
0.931910 | − | 0.362689i | \(-0.118141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 114.000i | 1.62642i | 0.581974 | + | 0.813208i | \(0.302281\pi\) | ||||
−0.581974 | + | 0.813208i | \(0.697719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 52.0000 | 0.540349 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 209.122i | 1.89587i | 0.318468 | + | 0.947934i | \(0.396832\pi\) | ||||
−0.318468 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 14.4222i | − 0.102798i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.0000 | 0.166485 | 0.0832427 | − | 0.996529i | \(-0.473472\pi\) | ||||
0.0832427 | + | 0.996529i | \(0.473472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 100.955 | 0.584907 | 0.292454 | − | 0.956280i | \(-0.405528\pi\) | ||||
0.292454 | + | 0.956280i | \(0.405528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 312.000i | − 1.64583i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 150.000i | − 0.666482i | −0.942842 | − | 0.333241i | \(-0.891858\pi\) | ||||
0.942842 | − | 0.333241i | \(-0.108142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −245.177 | −1.00666 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 342.000 | 1.30272 | 0.651359 | − | 0.758770i | \(-0.274199\pi\) | ||||
0.651359 | + | 0.758770i | \(0.274199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 454.299i | 1.61116i | 0.592485 | + | 0.805582i | \(0.298147\pi\) | ||||
−0.592485 | + | 0.805582i | \(0.701853\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 584.099i | 1.81276i | 0.422465 | + | 0.906379i | \(0.361165\pi\) | ||||
−0.422465 | + | 0.906379i | \(0.638835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 291.000 | 0.848397 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 822.066 | 2.25710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 262.000i | 0.679028i | 0.940601 | + | 0.339514i | \(0.110263\pi\) | ||||
−0.940601 | + | 0.339514i | \(0.889737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 490.355 | 1.08201 | 0.541007 | − | 0.841018i | \(-0.318043\pi\) | ||||
0.541007 | + | 0.841018i | \(0.318043\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −262.000 | −0.549929 | −0.274964 | − | 0.961454i | \(-0.588666\pi\) | ||||
−0.274964 | + | 0.961454i | \(0.588666\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 180.278i | − 0.360521i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 497.566i | − 0.907274i | −0.891187 | − | 0.453637i | \(-0.850126\pi\) | ||||
0.891187 | − | 0.453637i | \(-0.149874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1508.00 | 2.63104 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1052.82 | −1.75981 | −0.879907 | − | 0.475145i | \(-0.842396\pi\) | ||||
−0.879907 | + | 0.475145i | \(0.842396\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 682.000i | − 1.09345i | −0.837311 | − | 0.546726i | \(-0.815874\pi\) | ||||
0.837311 | − | 0.546726i | \(-0.184126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 312.000i | 0.461762i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 201.911 | 0.287554 | 0.143777 | − | 0.989610i | \(-0.454075\pi\) | ||||
0.143777 | + | 0.989610i | \(0.454075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −779.000 | −1.06859 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 151.433i | − 0.200264i | −0.994974 | − | 0.100132i | \(-0.968073\pi\) | ||||
0.994974 | − | 0.100132i | \(-0.0319266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 187.489i | − 0.231045i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 630.000 | 0.750336 | 0.375168 | − | 0.926957i | \(-0.377585\pi\) | ||||
0.375168 | + | 0.926957i | \(0.377585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 245.177 | 0.282435 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 728.000i | − 0.811721i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 966.000i | − 1.01116i | −0.862780 | − | 0.505580i | \(-0.831279\pi\) | ||||
0.862780 | − | 0.505580i | \(-0.168721\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1081.67 | −1.09810 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1638.00 | 1.61373 | 0.806867 | − | 0.590733i | \(-0.201162\pi\) | ||||
0.806867 | + | 0.590733i | \(0.201162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 685.055i | − 0.655344i | −0.944792 | − | 0.327672i | \(-0.893736\pi\) | ||||
0.944792 | − | 0.327672i | \(-0.106264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 612.944i | − 0.553790i | −0.960900 | − | 0.276895i | \(-0.910695\pi\) | ||||
0.960900 | − | 0.276895i | \(-0.0893054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 342.000 | 0.300529 | 0.150264 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150264 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1081.67 | −0.924929 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2106.00i | − 1.75324i | −0.481186 | − | 0.876619i | \(-0.659794\pi\) | ||||
0.481186 | − | 0.876619i | \(-0.340206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 850.000i | 0.671646i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −822.066 | −0.633266 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 541.000 | 0.406461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2466.20i | − 1.80788i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 439.877i | 0.307345i | 0.988122 | + | 0.153672i | \(0.0491101\pi\) | ||||
−0.988122 | + | 0.153672i | \(0.950890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3276.00 | 2.23594 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1773.93 | −1.18312 | −0.591561 | − | 0.806260i | \(-0.701488\pi\) | ||||
−0.591561 | + | 0.806260i | \(0.701488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1618.00i | 1.00902i | 0.863407 | + | 0.504508i | \(0.168326\pi\) | ||||
−0.863407 | + | 0.504508i | \(0.831674\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2509.46 | 1.53129 | 0.765647 | − | 0.643261i | \(-0.222419\pi\) | ||||
0.765647 | + | 0.643261i | \(0.222419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4212.00 | 2.51570 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1471.06i | − 0.860256i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2098.43i | − 1.17739i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1010.00 | −0.555318 | −0.277659 | − | 0.960680i | \(-0.589559\pi\) | ||||
−0.277659 | + | 0.960680i | \(0.589559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4222 | −0.00777260 | −0.00388630 | − | 0.999992i | \(-0.501237\pi\) | ||||
−0.00388630 | + | 0.999992i | \(0.501237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2850.00i | − 1.50594i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1794.00i | 0.911954i | 0.889992 | + | 0.455977i | \(0.150710\pi\) | ||||
−0.889992 | + | 0.455977i | \(0.849290\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1889.31 | 0.942339 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1508.00 | −0.738180 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1983.05i | 0.952912i | 0.879198 | + | 0.476456i | \(0.158079\pi\) | ||||
−0.879198 | + | 0.476456i | \(0.841921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 757.166i | 0.350846i | 0.984493 | + | 0.175423i | \(0.0561293\pi\) | ||||
−0.984493 | + | 0.175423i | \(0.943871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1041.00 | 0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2834.00i | − 1.24546i | −0.782436 | − | 0.622731i | \(-0.786023\pi\) | ||||
0.782436 | − | 0.622731i | \(-0.213977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 3536.00i | − 1.50159i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −951.866 | −0.397462 | −0.198731 | − | 0.980054i | \(-0.563682\pi\) | ||||
−0.198731 | + | 0.980054i | \(0.563682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1466.00 | −0.602027 | −0.301014 | − | 0.953620i | \(-0.597325\pi\) | ||||
−0.301014 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1889.31i | 0.763179i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4932.39i | 1.92884i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 104.000 | 0.0400259 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3475.75 | 1.31674 | 0.658368 | − | 0.752696i | \(-0.271247\pi\) | ||||
0.658368 | + | 0.752696i | \(0.271247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 46.0000i | 0.0171562i | 0.999963 | + | 0.00857812i | \(0.00273053\pi\) | ||||
−0.999963 | + | 0.00857812i | \(0.997269\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1122.00i | 0.405783i | 0.979201 | + | 0.202891i | \(0.0650338\pi\) | ||||
−0.979201 | + | 0.202891i | \(0.934966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2999.82 | −1.06860 | −0.534300 | − | 0.845295i | \(-0.679425\pi\) | ||||
−0.534300 | + | 0.845295i | \(0.679425\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3588.00 | −1.25909 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 187.489i | 0.0648233i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 5228.05i | − 1.75543i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 418.244 | 0.136460 | 0.0682301 | − | 0.997670i | \(-0.478265\pi\) | ||||
0.0682301 | + | 0.997670i | \(0.478265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7592.00i | 2.44223i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 728.000i | 0.227741i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4917.97 | −1.51747 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3876.00 | 1.17976 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2545.52i | 0.764397i | 0.924080 | + | 0.382199i | \(0.124833\pi\) | ||||
−0.924080 | + | 0.382199i | \(0.875167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5069.41i | 1.48224i | 0.671373 | + | 0.741119i | \(0.265705\pi\) | ||||
−0.671373 | + | 0.741119i | \(0.734295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6194.00 | 1.78738 | 0.893692 | − | 0.448681i | \(-0.148106\pi\) | ||||
0.893692 | + | 0.448681i | \(0.148106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2249.86 | 0.640823 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4290.00i | − 1.20621i | −0.797661 | − | 0.603106i | \(-0.793930\pi\) | ||||
0.797661 | − | 0.603106i | \(-0.206070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1456.00i | − 0.399061i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5278.53 | 1.42862 | 0.714309 | − | 0.699831i | \(-0.246741\pi\) | ||||
0.714309 | + | 0.699831i | \(0.246741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3074.00 | −0.821634 | −0.410817 | − | 0.911718i | \(-0.634756\pi\) | ||||
−0.410817 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5228.05i | 1.38016i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1092.00 | −0.277922 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2062.38 | 0.518629 | 0.259315 | − | 0.965793i | \(-0.416503\pi\) | ||||
0.259315 | + | 0.965793i | \(0.416503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9048.00i | 2.24839i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3718.00i | − 0.902422i | −0.892417 | − | 0.451211i | \(-0.850992\pi\) | ||||
0.892417 | − | 0.451211i | \(-0.149008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1081.67 | 0.259504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −650.000 | −0.154153 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7045.25i | 1.65182i | 0.563802 | + | 0.825910i | \(0.309338\pi\) | ||||
−0.563802 | + | 0.825910i | \(0.690662\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4542.99i | − 1.04130i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6058.00 | −1.37310 | −0.686548 | − | 0.727085i | \(-0.740875\pi\) | ||||
−0.686548 | + | 0.727085i | \(0.740875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5206.42 | 1.16704 | 0.583519 | − | 0.812100i | \(-0.301675\pi\) | ||||
0.583519 | + | 0.812100i | \(0.301675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1768.00i | − 0.391957i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2990.00i | − 0.648562i | −0.945961 | − | 0.324281i | \(-0.894878\pi\) | ||||
0.945961 | − | 0.324281i | \(-0.105122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2523.89 | −0.541581 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2710.00 | 0.575320 | 0.287660 | − | 0.957733i | \(-0.407123\pi\) | ||||
0.287660 | + | 0.957733i | \(0.407123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4593.47i | − 0.964854i | −0.875936 | − | 0.482427i | \(-0.839755\pi\) | ||||
0.875936 | − | 0.482427i | \(-0.160245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2466.20i | 0.507230i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8083.00 | −1.64523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6965.93 | −1.40326 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3750.00i | 0.747704i | 0.927488 | + | 0.373852i | \(0.121963\pi\) | ||||
−0.927488 | + | 0.373852i | \(0.878037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 624.000i | − 0.121913i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7110.15 | 1.37522 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3276.00 | −0.627327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 11811.8i | − 2.23950i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4405.98i | 0.819097i | 0.912288 | + | 0.409548i | \(0.134314\pi\) | ||||
−0.912288 | + | 0.409548i | \(0.865686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4940.00 | −0.909472 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2956.55 | 0.539070 | 0.269535 | − | 0.962991i | \(-0.413130\pi\) | ||||
0.269535 | + | 0.962991i | \(0.413130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5642.00i | − 1.01886i | −0.860511 | − | 0.509432i | \(-0.829855\pi\) | ||||
0.860511 | − | 0.509432i | \(-0.170145\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4650.00i | 0.823880i | 0.911211 | + | 0.411940i | \(0.135149\pi\) | ||||
−0.911211 | + | 0.411940i | \(0.864851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1124.93 | 0.197442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4420.00 | −0.768537 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2466.20i | − 0.417067i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4212.00 | −0.705821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5523.70 | −0.917252 | −0.458626 | − | 0.888630i | \(-0.651658\pi\) | ||||
−0.458626 | + | 0.888630i | \(0.651658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3750.00i | 0.617113i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9266.00i | 1.49778i | 0.662695 | + | 0.748889i | \(0.269412\pi\) | ||||
−0.662695 | + | 0.748889i | \(0.730588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15186.6 | −2.43310 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4368.00 | 0.693667 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4571.84i | 0.719697i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 814.855i | − 0.126062i | −0.998012 | − | 0.0630312i | \(-0.979923\pi\) | ||||
0.998012 | − | 0.0630312i | \(-0.0200768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7494.00 | −1.14941 | −0.574706 | − | 0.818360i | \(-0.694883\pi\) | ||||
−0.574706 | + | 0.818360i | \(0.694883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −490.355 | −0.0745676 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6270.00i | 0.945378i | 0.881229 | + | 0.472689i | \(0.156717\pi\) | ||||
−0.881229 | + | 0.472689i | \(0.843283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5928.00i | 0.878832i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 692.266 | 0.101773 | 0.0508863 | − | 0.998704i | \(-0.483795\pi\) | ||||
0.0508863 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6859.00 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3901.21i | − 0.564078i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2141.70i | 0.304620i | 0.988333 | + | 0.152310i | \(0.0486713\pi\) | ||||
−0.988333 | + | 0.152310i | \(0.951329\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8550.00 | −1.20622 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1889.31 | −0.264388 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2574.00i | 0.357310i | 0.983912 | + | 0.178655i | \(0.0571746\pi\) | ||||
−0.983912 | + | 0.178655i | \(0.942825\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 884.000i | − 0.120765i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13729.9 | 1.86084 | 0.930422 | − | 0.366491i | \(-0.119441\pi\) | ||||
0.930422 | + | 0.366491i | \(0.119441\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3172.00 | 0.426526 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 4204.07i | − 0.560883i | −0.959871 | − | 0.280441i | \(-0.909519\pi\) | ||||
0.959871 | − | 0.280441i | \(-0.0904808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 11357.5i | − 1.49182i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5314.00 | −0.692623 | −0.346312 | − | 0.938120i | \(-0.612566\pi\) | ||||
−0.346312 | + | 0.938120i | \(0.612566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23839.9 | −3.08347 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12792.0i | 1.64191i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8638.00i | − 1.09201i | −0.837781 | − | 0.546006i | \(-0.816148\pi\) | ||||
0.837781 | − | 0.546006i | \(-0.183852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2802.00 | 0.348941 | 0.174470 | − | 0.984662i | \(-0.444179\pi\) | ||||
0.174470 | + | 0.984662i | \(0.444179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3432.48i | − 0.424279i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6489.99i | − 0.790410i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 82.0000 | 0.00991354 | 0.00495677 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495677 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11667.6 | 1.40029 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3536.00i | 0.421296i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 18096.0i | − 2.12510i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1067.24 | −0.124435 | −0.0622175 | − | 0.998063i | \(-0.519817\pi\) | ||||
−0.0622175 | + | 0.998063i | \(0.519817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5742.00 | −0.664722 | −0.332361 | − | 0.943152i | \(-0.607845\pi\) | ||||
−0.332361 | + | 0.943152i | \(0.607845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 14602.5i | − 1.67848i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1889.31i | − 0.214122i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10608.0 | −1.19384 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14234.7 | −1.59086 | −0.795432 | − | 0.606043i | \(-0.792756\pi\) | ||||
−0.795432 | + | 0.606043i | \(0.792756\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7098.00i | − 0.787779i | −0.919158 | − | 0.393889i | \(-0.871129\pi\) | ||||
0.919158 | − | 0.393889i | \(-0.128871\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −461.511 | −0.0501747 | −0.0250874 | − | 0.999685i | \(-0.507986\pi\) | ||||
−0.0250874 | + | 0.999685i | \(0.507986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7275.00 | −0.785552 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6064.54i | − 0.650417i | −0.945642 | − | 0.325209i | \(-0.894565\pi\) | ||||
0.945642 | − | 0.325209i | \(-0.105435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7283.21i | 0.770658i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11706.0 | 1.23038 | 0.615190 | − | 0.788379i | \(-0.289079\pi\) | ||||
0.615190 | + | 0.788379i | \(0.289079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14797.2 | 1.54495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 104.000i | 0.0107866i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5066.00i | 0.518550i | 0.965803 | + | 0.259275i | \(0.0834836\pi\) | ||||
−0.965803 | + | 0.259275i | \(0.916516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1644.13 | 0.167193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −594.000 | −0.0600116 | −0.0300058 | − | 0.999550i | \(-0.509553\pi\) | ||||
−0.0300058 | + | 0.999550i | \(0.509553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 483.144i | − 0.0484959i | −0.999706 | − | 0.0242479i | \(-0.992281\pi\) | ||||
0.999706 | − | 0.0242479i | \(-0.00771912\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2271.50i | 0.225080i | 0.993647 | + | 0.112540i | \(0.0358986\pi\) | ||||
−0.993647 | + | 0.112540i | \(0.964101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3588.00 | 0.353259 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12936.7 | 1.26559 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19656.0i | 1.91075i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6550.00i | − 0.628729i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4067.06 | −0.387952 | −0.193976 | − | 0.981006i | \(-0.562138\pi\) | ||||
−0.193976 | + | 0.981006i | \(0.562138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5100.00 | −0.483451 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10874.3i | 1.02443i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11170.0i | 1.03934i | 0.854366 | + | 0.519672i | \(0.173946\pi\) | ||||
−0.854366 | + | 0.519672i | \(0.826054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14300.0 | 1.32243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4600.68 | 0.422863 | 0.211432 | − | 0.977393i | \(-0.432187\pi\) | ||||
0.211432 | + | 0.977393i | \(0.432187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2964.00i | 0.270775i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 7592.00i | − 0.685207i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −288.444 | −0.0258768 | −0.0129384 | − | 0.999916i | \(-0.504119\pi\) | ||||
−0.0129384 | + | 0.999916i | \(0.504119\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5460.00 | 0.486896 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18409.9i | 1.63193i | 0.578104 | + | 0.815963i | \(0.303793\pi\) | ||||
−0.578104 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7506.76i | − 0.657568i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8714.00 | 0.758824 | 0.379412 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379412 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4917.97 | 0.425750 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25272.0i | 2.14983i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20436.3 | −1.72842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11830.0 | −0.994783 | −0.497391 | − | 0.867526i | \(-0.665709\pi\) | ||||
−0.497391 | + | 0.867526i | \(0.665709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8963.40i | 0.749411i | 0.927144 | + | 0.374706i | \(0.122256\pi\) | ||||
−0.927144 | + | 0.374706i | \(0.877744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11508.9i | 0.951302i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31565.0 | −2.59431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12258.9 | −1.00186 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11628.0i | − 0.944962i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6864.00i | 0.551589i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12590.6 | 1.00615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15490.0 | −1.23099 | −0.615496 | − | 0.788140i | \(-0.711044\pi\) | ||||
−0.615496 | + | 0.788140i | \(0.711044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10571.5i | 0.835480i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 11429.6i | − 0.893408i | −0.894682 | − | 0.446704i | \(-0.852598\pi\) | ||||
0.894682 | − | 0.446704i | \(-0.147402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6550.00 | 0.509193 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1456.00i | 0.111963i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 23862.0i | − 1.81520i | −0.419838 | − | 0.907599i | \(-0.637913\pi\) | ||||
0.419838 | − | 0.907599i | \(-0.362087\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15446.2 | 1.16870 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35568.0 | 2.67680 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7261.58i | 0.543586i | 0.962356 | + | 0.271793i | \(0.0876167\pi\) | ||||
−0.962356 | + | 0.271793i | \(0.912383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 5617.45i | − 0.416068i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9074.00 | 0.668545 | 0.334272 | − | 0.942477i | \(-0.391509\pi\) | ||||
0.334272 | + | 0.942477i | \(0.391509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7860.10 | 0.576068 | 0.288034 | − | 0.957620i | \(-0.406998\pi\) | ||||
0.288034 | + | 0.957620i | \(0.406998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 25064.0i | − 1.82734i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4762.00i | 0.343578i | 0.985134 | + | 0.171789i | \(0.0549548\pi\) | ||||
−0.985134 | + | 0.171789i | \(0.945045\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 331.711 | 0.0238090 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1092.00 | 0.0779755 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11335.9i | 0.805288i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21481.9i | 1.51048i | 0.655448 | + | 0.755240i | \(0.272480\pi\) | ||||
−0.655448 | + | 0.755240i | \(0.727520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8090.86 | 0.563136 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 11954.0i | − 0.827811i | −0.910320 | − | 0.413906i | \(-0.864164\pi\) | ||||
0.910320 | − | 0.413906i | \(-0.135836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21632.0i | 1.48298i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10759.0 | −0.733889 | −0.366944 | − | 0.930243i | \(-0.619596\pi\) | ||||
−0.366944 | + | 0.930243i | \(0.619596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17862.0 | 1.21232 | 0.606162 | − | 0.795342i | \(-0.292708\pi\) | ||||
0.606162 | + | 0.795342i | \(0.292708\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12439.2i | 0.840069i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7506.76i | 0.501960i | 0.967992 | + | 0.250980i | \(0.0807529\pi\) | ||||
−0.967992 | + | 0.250980i | \(0.919247\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1352.00 | 0.0899603 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19859.4 | 1.31493 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 11522.0i | − 0.759167i | −0.925158 | − | 0.379583i | \(-0.876067\pi\) | ||||
0.925158 | − | 0.379583i | \(-0.123933\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8290.00i | 0.540912i | 0.962732 | + | 0.270456i | \(0.0871745\pi\) | ||||
−0.962732 | + | 0.270456i | \(0.912826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24171.6 | −1.56953 | −0.784765 | − | 0.619793i | \(-0.787216\pi\) | ||||
−0.784765 | + | 0.619793i | \(0.787216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3016.00 | 0.194892 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4542.99i | 0.292153i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17100.0 | 1.08398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12388.7 | 0.781593 | 0.390797 | − | 0.920477i | \(-0.372200\pi\) | ||||
0.390797 | + | 0.920477i | \(0.372200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3016.00i | − 0.189376i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9894.00i | − 0.615407i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26320.5 | 1.62946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6750.00 | 0.415927 | 0.207963 | − | 0.978137i | \(-0.433317\pi\) | ||||
0.207963 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23428.9i | − 1.43693i | −0.695564 | − | 0.718464i | \(-0.744846\pi\) | ||||
0.695564 | − | 0.718464i | \(-0.255154\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8689.38i | 0.527998i | 0.964523 | + | 0.263999i | \(0.0850416\pi\) | ||||
−0.964523 | + | 0.263999i | \(0.914958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21216.0 | 1.28321 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5249.68 | 0.316054 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 22282.0i | − 1.33532i | −0.744468 | − | 0.667659i | \(-0.767297\pi\) | ||||
0.744468 | − | 0.667659i | \(-0.232703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17050.0i | 1.01246i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15835.6 | 0.936065 | 0.468032 | − | 0.883711i | \(-0.344963\pi\) | ||||
0.468032 | + | 0.883711i | \(0.344963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11758.0 | −0.691881 | −0.345940 | − | 0.938256i | \(-0.612440\pi\) | ||||
−0.345940 | + | 0.938256i | \(0.612440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 27950.2i | − 1.63725i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5437.17i | 0.315634i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18356.0 | 1.06081 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11335.9 | −0.652184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 11866.0i | − 0.679644i | −0.940490 | − | 0.339822i | \(-0.889633\pi\) | ||||
0.940490 | − | 0.339822i | \(-0.110367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 26574.0i | − 1.50860i | −0.656530 | − | 0.754300i | \(-0.727977\pi\) | ||||
0.656530 | − | 0.754300i | \(-0.272023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6965.93 | 0.393708 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36556.0 | 2.05702 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13737.2i | − 0.769601i | −0.923000 | − | 0.384800i | \(-0.874270\pi\) | ||||
0.923000 | − | 0.384800i | \(-0.125730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 44665.6i | − 2.48049i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8908.00 | 0.492551 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22570.8 | −1.24259 | −0.621297 | − | 0.783576i | \(-0.713394\pi\) | ||||
−0.621297 | + | 0.783576i | \(0.713394\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7800.00i | − 0.427558i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38988.0i | 2.11876i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30935.6 | −1.67395 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7062.00 | −0.380497 | −0.190248 | − | 0.981736i | \(-0.560929\pi\) | ||||
−0.190248 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11811.8i | 0.628328i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1554.00 | 0.0823155 | 0.0411578 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411578 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5047.77 | −0.266253 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21112.0i | 1.10891i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 38064.0i | − 1.98260i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31065.4 | −1.61133 | −0.805664 | − | 0.592373i | \(-0.798191\pi\) | ||||
−0.805664 | + | 0.592373i | \(0.798191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4940.00 | 0.255167 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22166.9i | 1.14024i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 24452.8i | − 1.24746i | −0.781638 | − | 0.623732i | \(-0.785616\pi\) | ||||
0.781638 | − | 0.623732i | \(-0.214384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16667.0 | 0.846771 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51790.1 | −2.62042 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15058.0i | − 0.758772i | −0.925238 | − | 0.379386i | \(-0.876135\pi\) | ||||
0.925238 | − | 0.379386i | \(-0.123865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 21528.0i | − 1.07598i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11912.7 | 0.592987 | 0.296493 | − | 0.955035i | \(-0.404183\pi\) | ||||
0.296493 | + | 0.955035i | \(0.404183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 17270.6i | − 0.852754i | −0.904545 | − | 0.426377i | \(-0.859790\pi\) | ||||
0.904545 | − | 0.426377i | \(-0.140210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3785.83i | 0.185430i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4420.00 | 0.215625 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17869.1 | 0.868247 | 0.434123 | − | 0.900853i | \(-0.357058\pi\) | ||||
0.434123 | + | 0.900853i | \(0.357058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 14872.0i | − 0.719742i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35410.0i | 1.70013i | 0.526678 | + | 0.850065i | \(0.323437\pi\) | ||||
−0.526678 | + | 0.850065i | \(0.676563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65246.1 | 3.12027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3386.00 | 0.161291 | 0.0806455 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806455 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2466.20i | 0.117015i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 16672.1i | − 0.784868i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11522.0 | −0.540304 | −0.270152 | − | 0.962818i | \(-0.587074\pi\) | ||||
−0.270152 | + | 0.962818i | \(0.587074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26810.9 | −1.25236 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14382.0i | 0.669191i | 0.942362 | + | 0.334595i | \(0.108600\pi\) | ||||
−0.942362 | + | 0.334595i | \(0.891400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 7800.00i | − 0.360133i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45552.0 | −2.08704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 374.977i | − 0.0171144i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 814.855i | − 0.0369078i | −0.999830 | − | 0.0184539i | \(-0.994126\pi\) | ||||
0.999830 | − | 0.0184539i | \(-0.00587439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50804.0 | 2.29236 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15186.6 | 0.682646 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8908.00i | 0.398906i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14550.0i | − 0.646659i | −0.946286 | − | 0.323330i | \(-0.895198\pi\) | ||||
0.946286 | − | 0.323330i | \(-0.104802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66587.3 | −2.94830 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15750.0 | −0.694755 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 29507.8i | − 1.29677i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43684.9i | 1.90555i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37622.0 | 1.63501 | 0.817503 | − | 0.575925i | \(-0.195358\pi\) | ||||
0.817503 | + | 0.575925i | \(0.195358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 331.711 | 0.0143624 | 0.00718122 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718122 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 37544.0i | − 1.61959i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6129.44 | −0.261514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18690.0 | 0.794501 | 0.397251 | − | 0.917710i | \(-0.369964\pi\) | ||||
0.397251 | + | 0.917710i | \(0.369964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 16866.8i | − 0.714385i | −0.934031 | − | 0.357192i | \(-0.883734\pi\) | ||||
0.934031 | − | 0.357192i | \(-0.116266\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 39235.6i | − 1.64977i | −0.565304 | − | 0.824883i | \(-0.691241\pi\) | ||||
0.565304 | − | 0.824883i | \(-0.308759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3718.00 | 0.155768 | 0.0778839 | − | 0.996962i | \(-0.475184\pi\) | ||||
0.0778839 | + | 0.996962i | \(0.475184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21561.2 | −0.900060 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33174.0i | 1.37985i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1456.00i | − 0.0601275i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14335.7 | 0.589896 | 0.294948 | − | 0.955513i | \(-0.404698\pi\) | ||||
0.294948 | + | 0.955513i | \(0.404698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23713.0 | −0.972283 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 19542.1i | − 0.798417i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3901.21i | 0.158261i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33124.0 | −1.33900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31368.3 | 1.26356 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 26786.0i | − 1.07519i | −0.843204 | − | 0.537594i | \(-0.819333\pi\) | ||||
0.843204 | − | 0.537594i | \(-0.180667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19682.0i | 0.784509i | 0.919857 | + | 0.392255i | \(0.128305\pi\) | ||||
−0.919857 | + | 0.392255i | \(0.871695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33199.9 | 1.31870 | 0.659352 | − | 0.751834i | \(-0.270831\pi\) | ||||
0.659352 | + | 0.751834i | \(0.270831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17784.0 | 0.703922 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 10203.7i | − 0.402478i | −0.979542 | − | 0.201239i | \(-0.935503\pi\) | ||||
0.979542 | − | 0.201239i | \(-0.0644968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 58287.3i | 2.28321i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8736.00 | 0.341022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16917.2 | −0.658116 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24150.0i | 0.936258i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41986.0i | 1.61661i | 0.588764 | + | 0.808305i | \(0.299615\pi\) | ||||
−0.588764 | + | 0.808305i | \(0.700385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27041.6 | 1.03765 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38142.0 | 1.45861 | 0.729306 | − | 0.684188i | \(-0.239843\pi\) | ||||
0.729306 | + | 0.684188i | \(0.239843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 39235.6i | − 1.49534i | −0.664072 | − | 0.747669i | \(-0.731173\pi\) | ||||
0.664072 | − | 0.747669i | \(-0.268827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 41528.7i | − 1.57204i | −0.618202 | − | 0.786020i | \(-0.712139\pi\) | ||||
0.618202 | − | 0.786020i | \(-0.287861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3172.00 | −0.119669 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33704.7 | −1.26728 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 51272.0i | − 1.90850i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2624.84 | 0.0973786 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29868.0 | −1.10438 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23623.6i | 0.870591i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4319.45i | 0.158131i | 0.996869 | + | 0.0790656i | \(0.0251937\pi\) | ||||
−0.996869 | + | 0.0790656i | \(0.974806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40950.0 | −1.49420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49713.3 | 1.80799 | 0.903994 | − | 0.427546i | \(-0.140622\pi\) | ||||
0.903994 | + | 0.427546i | \(0.140622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6552.00i | − 0.237502i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12792.0i | − 0.460664i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5220.84 | 0.187399 | 0.0936994 | − | 0.995601i | \(-0.470131\pi\) | ||||
0.0936994 | + | 0.995601i | \(0.470131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31772.0 | 1.13672 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35795.9i | 1.27653i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17126.4i | 0.606800i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17546.0 | 0.619662 | 0.309831 | − | 0.950792i | \(-0.399728\pi\) | ||||
0.309831 | + | 0.950792i | \(0.399728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 21320.0i | − 0.748109i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 11390.0i | − 0.397113i | −0.980089 | − | 0.198557i | \(-0.936375\pi\) | ||||
0.980089 | − | 0.198557i | \(-0.0636254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40685.0 | −1.41396 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41838.0 | 1.44939 | 0.724697 | − | 0.689068i | \(-0.241980\pi\) | ||||
0.724697 | + | 0.689068i | \(0.241980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71519.7i | 2.46978i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 35226.2i | − 1.20876i | −0.796695 | − | 0.604382i | \(-0.793420\pi\) | ||||
0.796695 | − | 0.604382i | \(-0.206580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23188.0 | −0.793166 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33531.6 | 1.14336 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 28522.0i | − 0.969484i | −0.874657 | − | 0.484742i | \(-0.838914\pi\) | ||||
0.874657 | − | 0.484742i | \(-0.161086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 8112.00i | − 0.274006i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11667.6 | −0.392873 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19599.0 | −0.657883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15323.6i | 0.512768i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4579.05i | − 0.152277i | −0.997097 | − | 0.0761387i | \(-0.975741\pi\) | ||||
0.997097 | − | 0.0761387i | \(-0.0242592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22282.3 | 0.736430 | 0.368215 | − | 0.929741i | \(-0.379969\pi\) | ||||
0.368215 | + | 0.929741i | \(0.379969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18096.0i | 0.596229i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 2214.00i | − 0.0724996i | −0.999343 | − | 0.0362498i | \(-0.988459\pi\) | ||||
0.999343 | − | 0.0362498i | \(-0.0115412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27258.0 | 0.889855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8550.00 | −0.278268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24871.1i | 0.806983i | 0.914983 | + | 0.403492i | \(0.132204\pi\) | ||||
−0.914983 | + | 0.403492i | \(0.867796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30373.2i | 0.979522i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −95004.0 | −3.05455 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46453.9 | −1.48906 | −0.744530 | − | 0.667590i | \(-0.767326\pi\) | ||||
−0.744530 | + | 0.667590i | \(0.767326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39832.0i | 1.27294i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57930.0i | 1.84018i | 0.391705 | + | 0.920091i | \(0.371886\pi\) | ||||
−0.391705 | + | 0.920091i | \(0.628114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2163.33 | −0.0685133 |
(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 | 800.4.c.h.449.2 | 4 | ||
4.3 | odd | 2 | inner | 800.4.c.h.449.3 | 4 | ||
5.2 | odd | 4 | 800.4.a.q.1.1 | 2 | |||
5.3 | odd | 4 | 160.4.a.e.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 800.4.c.h.449.4 | 4 | ||
15.8 | even | 4 | 1440.4.a.bd.1.2 | 2 | |||
20.3 | even | 4 | 160.4.a.e.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 800.4.a.q.1.2 | 2 | |||
20.19 | odd | 2 | inner | 800.4.c.h.449.1 | 4 | ||
40.3 | even | 4 | 320.4.a.r.1.2 | 2 | |||
40.13 | odd | 4 | 320.4.a.r.1.1 | 2 | |||
40.27 | even | 4 | 1600.4.a.ci.1.1 | 2 | |||
40.37 | odd | 4 | 1600.4.a.ci.1.2 | 2 | |||
60.23 | odd | 4 | 1440.4.a.bd.1.1 | 2 | |||
80.3 | even | 4 | 1280.4.d.t.641.2 | 4 | |||
80.13 | odd | 4 | 1280.4.d.t.641.4 | 4 | |||
80.43 | even | 4 | 1280.4.d.t.641.3 | 4 | |||
80.53 | odd | 4 | 1280.4.d.t.641.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.e.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
160.4.a.e.1.2 | yes | 2 | 5.3 | odd | 4 | ||
320.4.a.r.1.1 | 2 | 40.13 | odd | 4 | |||
320.4.a.r.1.2 | 2 | 40.3 | even | 4 | |||
800.4.a.q.1.1 | 2 | 5.2 | odd | 4 | |||
800.4.a.q.1.2 | 2 | 20.7 | even | 4 | |||
800.4.c.h.449.1 | 4 | 20.19 | odd | 2 | inner | ||
800.4.c.h.449.2 | 4 | 1.1 | even | 1 | trivial | ||
800.4.c.h.449.3 | 4 | 4.3 | odd | 2 | inner | ||
800.4.c.h.449.4 | 4 | 5.4 | even | 2 | inner | ||
1280.4.d.t.641.1 | 4 | 80.53 | odd | 4 | |||
1280.4.d.t.641.2 | 4 | 80.3 | even | 4 | |||
1280.4.d.t.641.3 | 4 | 80.43 | even | 4 | |||
1280.4.d.t.641.4 | 4 | 80.13 | odd | 4 | |||
1440.4.a.bd.1.1 | 2 | 60.23 | odd | 4 | |||
1440.4.a.bd.1.2 | 2 | 15.8 | even | 4 | |||
1600.4.a.ci.1.1 | 2 | 40.27 | even | 4 | |||
1600.4.a.ci.1.2 | 2 | 40.37 | odd | 4 |