Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.a (trivial) |
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: | yes |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.0000 | −1.43108 | −0.715542 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.0000 | 0.493382 | 0.246691 | − | 0.969094i | \(-0.420657\pi\) | ||||
0.246691 | + | 0.969094i | \(0.420657\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.0000 | −1.15207 | −0.576035 | − | 0.817425i | \(-0.695401\pi\) | ||||
−0.576035 | + | 0.817425i | \(0.695401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 48.0000 | 0.826236 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −128.000 | −1.82615 | −0.913075 | − | 0.407791i | \(-0.866299\pi\) | ||||
−0.913075 | + | 0.407791i | \(0.866299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.0000 | −0.627875 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 202.000 | 1.83130 | 0.915650 | − | 0.401976i | \(-0.131676\pi\) | ||||
0.915650 | + | 0.401976i | \(0.131676\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 131.000 | 1.04800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 302.000 | 1.93379 | 0.966896 | − | 0.255169i | \(-0.0821312\pi\) | ||||
0.966896 | + | 0.255169i | \(0.0821312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 200.000 | 1.15874 | 0.579372 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579372 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −54.0000 | −0.284854 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 112.000 | 0.540899 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −150.000 | −0.666482 | −0.333241 | − | 0.942842i | \(-0.608142\pi\) | ||||
−0.333241 | + | 0.942842i | \(0.608142\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 162.000 | 0.665148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 172.000 | 0.655168 | 0.327584 | − | 0.944822i | \(-0.393766\pi\) | ||||
0.327584 | + | 0.944822i | \(0.393766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −144.000 | −0.477028 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 460.000 | 1.42761 | 0.713807 | − | 0.700342i | \(-0.246969\pi\) | ||||
0.713807 | + | 0.700342i | \(0.246969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 384.000 | 1.05433 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −190.000 | −0.492425 | −0.246212 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246212 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −288.000 | −0.706071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 156.000 | 0.362504 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −96.0000 | −0.211833 | −0.105916 | − | 0.994375i | \(-0.533778\pi\) | ||||
−0.105916 | + | 0.994375i | \(0.533778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 622.000 | 1.30556 | 0.652778 | − | 0.757549i | \(-0.273603\pi\) | ||||
0.652778 | + | 0.757549i | \(0.273603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 864.000 | 1.64871 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −744.000 | −1.35663 | −0.678314 | − | 0.734772i | \(-0.737289\pi\) | ||||
−0.678314 | + | 0.734772i | \(0.737289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −606.000 | −1.05730 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 54.0000 | 0.0902623 | 0.0451311 | − | 0.998981i | \(-0.485629\pi\) | ||||
0.0451311 | + | 0.998981i | \(0.485629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 742.000 | 1.18965 | 0.594826 | − | 0.803855i | \(-0.297221\pi\) | ||||
0.594826 | + | 0.803855i | \(0.297221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −393.000 | −0.605063 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −126.000 | −0.186481 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 92.0000 | 0.131023 | 0.0655114 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655114 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 228.000 | 0.301521 | 0.150761 | − | 0.988570i | \(-0.451828\pi\) | ||||
0.150761 | + | 0.988570i | \(0.451828\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2048.00 | 2.61337 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −906.000 | −1.11648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −116.000 | −0.138157 | −0.0690785 | − | 0.997611i | \(-0.522006\pi\) | ||||
−0.0690785 | + | 0.997611i | \(0.522006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 378.000 | 0.435441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −600.000 | −0.669001 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 832.000 | 0.898541 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −554.000 | −0.579899 | −0.289949 | − | 0.957042i | \(-0.593638\pi\) | ||||
−0.289949 | + | 0.957042i | \(0.593638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 162.000 | 0.164461 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −780.000 | −0.768445 | −0.384222 | − | 0.923241i | \(-0.625530\pi\) | ||||
−0.384222 | + | 0.923241i | \(0.625530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −24.0000 | −0.0229591 | −0.0114796 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114796 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −336.000 | −0.312288 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −78.0000 | −0.0704724 | −0.0352362 | − | 0.999379i | \(-0.511218\pi\) | ||||
−0.0352362 | + | 0.999379i | \(0.511218\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1034.00 | −0.908617 | −0.454308 | − | 0.890844i | \(-0.650114\pi\) | ||||
−0.454308 | + | 0.890844i | \(0.650114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 450.000 | 0.384794 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186.000 | 0.154844 | 0.0774222 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774222 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3232.00 | −2.62074 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −486.000 | −0.384023 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 896.000 | 0.690220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1007.00 | −0.756574 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −516.000 | −0.378261 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −96.0000 | −0.0686920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 316.000 | 0.220791 | 0.110396 | − | 0.993888i | \(-0.464788\pi\) | ||||
0.110396 | + | 0.993888i | \(0.464788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 492.000 | 0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 988.000 | 0.658946 | 0.329473 | − | 0.944165i | \(-0.393129\pi\) | ||||
0.329473 | + | 0.944165i | \(0.393129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 364.000 | 0.237314 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 432.000 | 0.275412 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 950.000 | 0.592438 | 0.296219 | − | 0.955120i | \(-0.404274\pi\) | ||||
0.296219 | + | 0.955120i | \(0.404274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2124.00 | 1.29608 | 0.648041 | − | 0.761606i | \(-0.275589\pi\) | ||||
0.648041 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1380.00 | −0.824234 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −972.000 | −0.568411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4832.00 | −2.76742 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2242.00 | 1.23270 | 0.616348 | − | 0.787474i | \(-0.288611\pi\) | ||||
0.616348 | + | 0.787474i | \(0.288611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2776.00 | −1.49608 | −0.748039 | − | 0.663655i | \(-0.769004\pi\) | ||||
−0.748039 | + | 0.663655i | \(0.769004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1152.00 | −0.608717 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3200.00 | −1.65826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3258.00 | −1.65616 | −0.828079 | − | 0.560612i | \(-0.810566\pi\) | ||||
−0.828079 | + | 0.560612i | \(0.810566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 570.000 | 0.284302 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1414.00 | −0.692167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2432.00 | 1.16864 | 0.584322 | − | 0.811522i | \(-0.301361\pi\) | ||||
0.584322 | + | 0.811522i | \(0.301361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 864.000 | 0.407650 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3156.00 | 1.46239 | 0.731193 | − | 0.682170i | \(-0.238964\pi\) | ||||
0.731193 | + | 0.682170i | \(0.238964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −468.000 | −0.209292 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3724.00 | −1.63659 | −0.818296 | − | 0.574797i | \(-0.805081\pi\) | ||||
−0.818296 | + | 0.574797i | \(0.805081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −917.000 | −0.396107 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 288.000 | 0.122302 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2398.00 | 1.00131 | 0.500656 | − | 0.865646i | \(-0.333092\pi\) | ||||
0.500656 | + | 0.865646i | \(0.333092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2906.00 | 1.19338 | 0.596689 | − | 0.802473i | \(-0.296483\pi\) | ||||
0.596689 | + | 0.802473i | \(0.296483\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1866.00 | −0.753763 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2400.00 | 0.953792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2304.00 | −0.900990 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1478.00 | 0.559918 | 0.279959 | − | 0.960012i | \(-0.409679\pi\) | ||||
0.279959 | + | 0.960012i | \(0.409679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1098.00 | −0.409512 | −0.204756 | − | 0.978813i | \(-0.565640\pi\) | ||||
−0.204756 | + | 0.978813i | \(0.565640\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2592.00 | −0.951882 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5058.00 | 1.82928 | 0.914639 | − | 0.404273i | \(-0.132475\pi\) | ||||
0.914639 | + | 0.404273i | \(0.132475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4432.00 | 1.57877 | 0.789387 | − | 0.613895i | \(-0.210398\pi\) | ||||
0.789387 | + | 0.613895i | \(0.210398\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2232.00 | 0.783249 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2114.00 | −0.730905 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2752.00 | −0.937600 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1818.00 | 0.610434 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −936.000 | −0.309782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5444.00 | −1.77621 | −0.888105 | − | 0.459640i | \(-0.847978\pi\) | ||||
−0.888105 | + | 0.459640i | \(0.847978\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −162.000 | −0.0521129 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2624.00 | 0.832350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1400.00 | −0.437964 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2226.00 | −0.686845 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6912.00 | 2.10385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5352.00 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1179.00 | 0.349333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3752.00 | −1.09704 | −0.548522 | − | 0.836136i | \(-0.684809\pi\) | ||||
−0.548522 | + | 0.836136i | \(0.684809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5446.00 | −1.57154 | −0.785768 | − | 0.618521i | \(-0.787732\pi\) | ||||
−0.785768 | + | 0.618521i | \(0.787732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 378.000 | 0.107665 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2602.00 | −0.731600 | −0.365800 | − | 0.930694i | \(-0.619204\pi\) | ||||
−0.365800 | + | 0.930694i | \(0.619204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7360.00 | −2.04304 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −276.000 | −0.0756461 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1810.00 | 0.489871 | 0.244935 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244935 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 310.000 | 0.0828583 | 0.0414292 | − | 0.999141i | \(-0.486809\pi\) | ||||
0.0414292 | + | 0.999141i | \(0.486809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −784.000 | −0.204441 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2808.00 | 0.723355 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −684.000 | −0.174083 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 32.0000 | 0.00804710 | 0.00402355 | − | 0.999992i | \(-0.498719\pi\) | ||||
0.00402355 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3636.00 | 0.903531 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6144.00 | −1.50883 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3348.00 | 0.812617 | 0.406308 | − | 0.913736i | \(-0.366816\pi\) | ||||
0.406308 | + | 0.913736i | \(0.366816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1050.00 | 0.251907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2718.00 | 0.644598 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4086.00 | −0.957998 | −0.478999 | − | 0.877815i | \(-0.659000\pi\) | ||||
−0.478999 | + | 0.877815i | \(0.659000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3040.00 | 0.704701 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 348.000 | 0.0797650 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1416.00 | 0.320948 | 0.160474 | − | 0.987040i | \(-0.448698\pi\) | ||||
0.160474 | + | 0.987040i | \(0.448698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3856.00 | 0.864337 | 0.432168 | − | 0.901793i | \(-0.357749\pi\) | ||||
0.432168 | + | 0.901793i | \(0.357749\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1134.00 | −0.251402 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2358.00 | 0.517065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1358.00 | −0.294564 | −0.147282 | − | 0.989095i | \(-0.547053\pi\) | ||||
−0.147282 | + | 0.989095i | \(0.547053\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1800.00 | 0.386248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1698.00 | −0.360478 | −0.180239 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180239 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6340.00 | 1.33171 | 0.665855 | − | 0.746081i | \(-0.268067\pi\) | ||||
0.665855 | + | 0.746081i | \(0.268067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2496.00 | −0.518773 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1204.00 | −0.247630 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11471.0 | 2.33483 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1662.00 | 0.334805 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9204.00 | 1.83517 | 0.917583 | − | 0.397545i | \(-0.130138\pi\) | ||||
0.917583 | + | 0.397545i | \(0.130138\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1536.00 | 0.303150 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −486.000 | −0.0949514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10908.0 | −2.10979 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1148.00 | 0.219833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2340.00 | 0.443662 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9952.00 | −1.86836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2180.00 | 0.405274 | 0.202637 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202637 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 72.0000 | 0.0132555 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7212.00 | −1.31497 | −0.657484 | − | 0.753469i | \(-0.728379\pi\) | ||||
−0.657484 | + | 0.753469i | \(0.728379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1322.00 | 0.238734 | 0.119367 | − | 0.992850i | \(-0.461913\pi\) | ||||
0.119367 | + | 0.992850i | \(0.461913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1008.00 | 0.180300 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 474.000 | 0.0839826 | 0.0419913 | − | 0.999118i | \(-0.486630\pi\) | ||||
0.0419913 | + | 0.999118i | \(0.486630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5436.00 | 0.954099 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 234.000 | 0.0406872 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6656.00 | 1.14659 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7074.00 | −1.20737 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3102.00 | 0.524590 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3220.00 | −0.539588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11284.0 | 1.87379 | 0.936895 | − | 0.349610i | \(-0.113686\pi\) | ||||
0.936895 | + | 0.349610i | \(0.113686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1350.00 | −0.222161 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11904.0 | 1.94145 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6986.00 | 1.12923 | 0.564617 | − | 0.825353i | \(-0.309024\pi\) | ||||
0.564617 | + | 0.825353i | \(0.309024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −558.000 | −0.0893994 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3600.00 | 0.571704 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9696.00 | 1.51309 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7926.00 | 1.22620 | 0.613098 | − | 0.790007i | \(-0.289923\pi\) | ||||
0.613098 | + | 0.790007i | \(0.289923\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3058.00 | −0.469029 | −0.234514 | − | 0.972113i | \(-0.575350\pi\) | ||||
−0.234514 | + | 0.972113i | \(0.575350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1458.00 | 0.221716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7008.00 | 1.05665 | 0.528326 | − | 0.849042i | \(-0.322820\pi\) | ||||
0.528326 | + | 0.849042i | \(0.322820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −864.000 | −0.129173 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2688.00 | −0.398499 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11286.0 | 1.65920 | 0.829599 | − | 0.558359i | \(-0.188569\pi\) | ||||
0.829599 | + | 0.558359i | \(0.188569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4155.00 | −0.605773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3021.00 | 0.436808 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11872.0 | −1.70249 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2752.00 | 0.391426 | 0.195713 | − | 0.980661i | \(-0.437298\pi\) | ||||
0.195713 | + | 0.980661i | \(0.437298\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1548.00 | 0.218389 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1330.00 | 0.186119 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 206.000 | 0.0285959 | 0.0142980 | − | 0.999898i | \(-0.495449\pi\) | ||||
0.0142980 | + | 0.999898i | \(0.495449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 288.000 | 0.0396593 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16308.0 | −2.22786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −684.000 | −0.0927037 | −0.0463519 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463519 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −948.000 | −0.127474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9048.00 | −1.20713 | −0.603566 | − | 0.797313i | \(-0.706254\pi\) | ||||
−0.603566 | + | 0.797313i | \(0.706254\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2016.00 | 0.266870 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1476.00 | −0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3242.00 | −0.422560 | −0.211280 | − | 0.977426i | \(-0.567763\pi\) | ||||
−0.211280 | + | 0.977426i | \(0.567763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25856.0 | −3.34423 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2964.00 | −0.380443 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1472.00 | −0.187505 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1702.00 | 0.215166 | 0.107583 | − | 0.994196i | \(-0.465689\pi\) | ||||
0.107583 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1092.00 | −0.137013 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8742.00 | 1.08866 | 0.544332 | − | 0.838870i | \(-0.316783\pi\) | ||||
0.544332 | + | 0.838870i | \(0.316783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10800.0 | −1.33495 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1296.00 | −0.159009 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2700.00 | −0.328831 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 510.000 | 0.0616574 | 0.0308287 | − | 0.999525i | \(-0.490185\pi\) | ||||
0.0308287 | + | 0.999525i | \(0.490185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2850.00 | −0.342044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 672.000 | 0.0800653 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3648.00 | −0.431502 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6372.00 | −0.748293 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5144.00 | −0.599763 | −0.299882 | − | 0.953976i | \(-0.596947\pi\) | ||||
−0.299882 | + | 0.953976i | \(0.596947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 514.000 | 0.0595032 | 0.0297516 | − | 0.999557i | \(-0.490528\pi\) | ||||
0.0297516 | + | 0.999557i | \(0.490528\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4140.00 | 0.475872 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16768.0 | −1.91381 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4354.00 | −0.493454 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2916.00 | 0.328172 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13626.0 | −1.52283 | −0.761417 | − | 0.648263i | \(-0.775496\pi\) | ||||
−0.761417 | + | 0.648263i | \(0.775496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8794.00 | 0.976011 | 0.488005 | − | 0.872841i | \(-0.337725\pi\) | ||||
0.488005 | + | 0.872841i | \(0.337725\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14496.0 | 1.59777 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10504.0 | −1.14983 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2616.00 | −0.284407 | −0.142204 | − | 0.989837i | \(-0.545419\pi\) | ||||
−0.142204 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 838.000 | 0.0898749 | 0.0449375 | − | 0.998990i | \(-0.485691\pi\) | ||||
0.0449375 | + | 0.998990i | \(0.485691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1856.00 | 0.197714 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6726.00 | −0.711698 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9662.00 | −1.01554 | −0.507771 | − | 0.861492i | \(-0.669530\pi\) | ||||
−0.507771 | + | 0.861492i | \(0.669530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3096.00 | 0.323248 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8328.00 | 0.863761 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6048.00 | −0.623153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3590.00 | −0.367469 | −0.183734 | − | 0.982976i | \(-0.558819\pi\) | ||||
−0.183734 | + | 0.982976i | \(0.558819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3456.00 | 0.351443 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11628.0 | 1.17477 | 0.587386 | − | 0.809307i | \(-0.300157\pi\) | ||||
0.587386 | + | 0.809307i | \(0.300157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2116.00 | 0.212395 | 0.106197 | − | 0.994345i | \(-0.466132\pi\) | ||||
0.106197 | + | 0.994345i | \(0.466132\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9600.00 | 0.957396 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5088.00 | 0.504164 | 0.252082 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252082 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5208.00 | 0.512757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9774.00 | 0.956183 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2952.00 | −0.286962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6812.00 | −0.658013 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1710.00 | −0.164142 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5068.00 | −0.483430 | −0.241715 | − | 0.970347i | \(-0.577710\pi\) | ||||
−0.241715 | + | 0.970347i | \(0.577710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8100.00 | 0.767834 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4242.00 | 0.399623 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8864.00 | 0.829884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11008.0 | −1.02427 | −0.512136 | − | 0.858905i | \(-0.671145\pi\) | ||||
−0.512136 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7296.00 | −0.674717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11466.0 | −1.05388 | −0.526938 | − | 0.849904i | \(-0.676660\pi\) | ||||
−0.526938 | + | 0.849904i | \(0.676660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38656.0 | −3.53140 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2592.00 | −0.235357 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −378.000 | −0.0341159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11900.0 | 1.06757 | 0.533785 | − | 0.845620i | \(-0.320769\pi\) | ||||
0.533785 | + | 0.845620i | \(0.320769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9468.00 | −0.844309 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1832.00 | 0.162395 | 0.0811977 | − | 0.996698i | \(-0.474125\pi\) | ||||
0.0811977 | + | 0.996698i | \(0.474125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12480.0 | 1.09971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2157.00 | −0.188946 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16968.0 | 1.47759 | 0.738795 | − | 0.673930i | \(-0.235395\pi\) | ||||
0.738795 | + | 0.673930i | \(0.235395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5194.00 | −0.449646 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1404.00 | 0.120835 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 384.000 | 0.0328564 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8280.00 | 0.704360 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11172.0 | 0.944887 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14976.0 | −1.25933 | −0.629665 | − | 0.776867i | \(-0.716808\pi\) | ||||
−0.629665 | + | 0.776867i | \(0.716808\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9812.00 | −0.820361 | −0.410181 | − | 0.912004i | \(-0.634534\pi\) | ||||
−0.410181 | + | 0.912004i | \(0.634534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2751.00 | 0.228692 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25600.0 | −2.11604 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28637.0 | 2.35366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −864.000 | −0.0706109 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9288.00 | −0.754799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1248.00 | 0.100852 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7194.00 | −0.578108 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 882.000 | 0.0704832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21370.0 | 1.69828 | 0.849139 | − | 0.528170i | \(-0.177122\pi\) | ||||
0.849139 | + | 0.528170i | \(0.177122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8718.00 | −0.688997 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16544.0 | 1.30031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8120.00 | 0.634710 | 0.317355 | − | 0.948307i | \(-0.397205\pi\) | ||||
0.317355 | + | 0.948307i | \(0.397205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5598.00 | 0.435185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15704.0 | −1.21418 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −644.000 | −0.0495220 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7200.00 | −0.550672 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19934.0 | −1.51639 | −0.758196 | − | 0.652026i | \(-0.773919\pi\) | ||||
−0.758196 | + | 0.652026i | \(0.773919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8856.00 | 0.670070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6912.00 | 0.520187 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −352.000 | −0.0263500 | −0.0131750 | − | 0.999913i | \(-0.504194\pi\) | ||||
−0.0131750 | + | 0.999913i | \(0.504194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2976.00 | −0.221595 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10698.0 | −0.788196 | −0.394098 | − | 0.919068i | \(-0.628943\pi\) | ||||
−0.394098 | + | 0.919068i | \(0.628943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14824.0 | 1.08645 | 0.543227 | − | 0.839586i | \(-0.317202\pi\) | ||||
0.543227 | + | 0.839586i | \(0.317202\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4434.00 | −0.323269 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26462.0 | 1.91920 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15318.0 | −1.10519 | −0.552597 | − | 0.833449i | \(-0.686363\pi\) | ||||
−0.552597 | + | 0.833449i | \(0.686363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3294.00 | 0.236432 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1596.00 | −0.113964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3420.00 | −0.242954 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7776.00 | 0.549569 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5672.00 | 0.398822 | 0.199411 | − | 0.979916i | \(-0.436097\pi\) | ||||
0.199411 | + | 0.979916i | \(0.436097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10400.0 | −0.727546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15174.0 | −1.05613 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25968.0 | −1.79828 | −0.899138 | − | 0.437665i | \(-0.855806\pi\) | ||||
−0.899138 | + | 0.437665i | \(0.855806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14336.0 | −0.987763 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13296.0 | −0.911506 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20846.0 | 1.42194 | 0.710972 | − | 0.703220i | \(-0.248255\pi\) | ||||
0.710972 | + | 0.703220i | \(0.248255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4430.00 | −0.300671 | −0.150336 | − | 0.988635i | \(-0.548035\pi\) | ||||
−0.150336 | + | 0.988635i | \(0.548035\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6696.00 | −0.452209 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16112.0 | 1.08272 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23744.0 | 1.58771 | 0.793854 | − | 0.608108i | \(-0.208071\pi\) | ||||
0.793854 | + | 0.608108i | \(0.208071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6342.00 | 0.421988 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24840.0 | −1.64471 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9982.00 | 0.657699 | 0.328849 | − | 0.944382i | \(-0.393339\pi\) | ||||
0.328849 | + | 0.944382i | \(0.393339\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8256.00 | 0.541324 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21090.0 | −1.37610 | −0.688048 | − | 0.725665i | \(-0.741532\pi\) | ||||
−0.688048 | + | 0.725665i | \(0.741532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12900.0 | 0.837633 | 0.418816 | − | 0.908071i | \(-0.362445\pi\) | ||||
0.418816 | + | 0.908071i | \(0.362445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5454.00 | −0.352434 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 812.000 | 0.0522184 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14839.0 | −0.949696 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2808.00 | 0.178853 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19200.0 | 1.21710 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −140.000 | −0.00883251 | −0.00441625 | − | 0.999990i | \(-0.501406\pi\) | ||||
−0.00441625 | + | 0.999990i | \(0.501406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16332.0 | 1.02550 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5056.00 | −0.315970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2646.00 | −0.164581 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 486.000 | 0.0300874 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2642.00 | −0.162797 | −0.0813984 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0813984 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1388.00 | 0.0851281 | 0.0425641 | − | 0.999094i | \(-0.486447\pi\) | ||||
0.0425641 | + | 0.999094i | \(0.486447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7872.00 | −0.480558 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11196.0 | 0.680309 | 0.340155 | − | 0.940369i | \(-0.389521\pi\) | ||||
0.340155 | + | 0.940369i | \(0.389521\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1728.00 | −0.104515 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4200.00 | 0.252859 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9398.00 | 0.563204 | 0.281602 | − | 0.959531i | \(-0.409134\pi\) | ||||
0.281602 | + | 0.959531i | \(0.409134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15808.0 | −0.943007 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6678.00 | 0.396550 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14050.0 | 0.830516 | 0.415258 | − | 0.909704i | \(-0.363691\pi\) | ||||
0.415258 | + | 0.909704i | \(0.363691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22382.0 | 1.31703 | 0.658517 | − | 0.752566i | \(-0.271184\pi\) | ||||
0.658517 | + | 0.752566i | \(0.271184\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20736.0 | −1.21466 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5824.00 | −0.339617 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 61004.0 | 3.54136 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16056.0 | −0.927894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11196.0 | 0.644138 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6050.00 | −0.346524 | −0.173262 | − | 0.984876i | \(-0.555431\pi\) | ||||
−0.173262 | + | 0.984876i | \(0.555431\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3537.00 | −0.201688 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7500.00 | 0.425773 | 0.212887 | − | 0.977077i | \(-0.431714\pi\) | ||||
0.212887 | + | 0.977077i | \(0.431714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3878.00 | 0.219181 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11256.0 | 0.633379 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26430.0 | 1.48070 | 0.740348 | − | 0.672223i | \(-0.234661\pi\) | ||||
0.740348 | + | 0.672223i | \(0.234661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15200.0 | −0.847828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16338.0 | 0.907327 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10260.0 | 0.567308 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14228.0 | −0.783298 | −0.391649 | − | 0.920115i | \(-0.628095\pi\) | ||||
−0.391649 | + | 0.920115i | \(0.628095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1134.00 | −0.0621603 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33984.0 | −1.85480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22016.0 | −1.19644 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7806.00 | 0.422389 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12338.0 | −0.664764 | −0.332382 | − | 0.943145i | \(-0.607852\pi\) | ||||
−0.332382 | + | 0.943145i | \(0.607852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7800.00 | 0.418467 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22080.0 | 1.17955 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5460.00 | 0.290445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7054.00 | 0.373651 | 0.186825 | − | 0.982393i | \(-0.440180\pi\) | ||||
0.186825 | + | 0.982393i | \(0.440180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 828.000 | 0.0436743 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40400.0 | 2.12201 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15552.0 | 0.813443 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5430.00 | −0.282827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8640.00 | −0.448147 | −0.224073 | − | 0.974572i | \(-0.571936\pi\) | ||||
−0.224073 | + | 0.974572i | \(0.571936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 168.000 | 0.00867774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −930.000 | −0.0478383 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39562.0 | 2.02661 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20120.0 | −1.02642 | −0.513211 | − | 0.858262i | \(-0.671544\pi\) | ||||
−0.513211 | + | 0.858262i | \(0.671544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20992.0 | 1.06213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14554.0 | 0.733376 | 0.366688 | − | 0.930344i | \(-0.380492\pi\) | ||||
0.366688 | + | 0.930344i | \(0.380492\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2352.00 | 0.118034 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13392.0 | −0.669336 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23600.0 | 1.17475 | 0.587375 | − | 0.809315i | \(-0.300161\pi\) | ||||
0.587375 | + | 0.809315i | \(0.300161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8424.00 | −0.417629 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28970.0 | −1.43043 | −0.715213 | − | 0.698907i | \(-0.753670\pi\) | ||||
−0.715213 | + | 0.698907i | \(0.753670\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35872.0 | −1.76409 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2052.00 | 0.100507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 546.000 | 0.0266361 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18848.0 | −0.915810 | −0.457905 | − | 0.889001i | \(-0.651400\pi\) | ||||
−0.457905 | + | 0.889001i | \(0.651400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −96.0000 | −0.00464600 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44416.0 | 2.14101 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26594.0 | −1.27685 | −0.638425 | − | 0.769684i | \(-0.720414\pi\) | ||||
−0.638425 | + | 0.769684i | \(0.720414\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10908.0 | −0.521654 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3012.00 | −0.143476 | −0.0717378 | − | 0.997424i | \(-0.522854\pi\) | ||||
−0.0717378 | + | 0.997424i | \(0.522854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7238.00 | 0.343425 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18432.0 | 0.871125 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5184.00 | 0.244046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12614.0 | −0.591512 | −0.295756 | − | 0.955264i | \(-0.595571\pi\) | ||||
−0.295756 | + | 0.955264i | \(0.595571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10044.0 | −0.469164 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40684.0 | 1.89302 | 0.946508 | − | 0.322680i | \(-0.104584\pi\) | ||||
0.946508 | + | 0.322680i | \(0.104584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26200.0 | 1.21436 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3150.00 | −0.145438 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8944.00 | −0.411363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 972.000 | 0.0445338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8154.00 | −0.372159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52128.0 | 2.37010 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28564.0 | −1.29377 | −0.646885 | − | 0.762588i | \(-0.723929\pi\) | ||||
−0.646885 | + | 0.762588i | \(0.723929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12258.0 | 0.553101 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1302.00 | −0.0585257 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33588.0 | −1.50409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9120.00 | −0.406859 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7140.00 | 0.317330 | 0.158665 | − | 0.987332i | \(-0.449281\pi\) | ||||
0.158665 | + | 0.987332i | \(0.449281\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58880.0 | −2.60704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1044.00 | −0.0460523 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13356.0 | 0.586953 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22624.0 | 0.990548 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4248.00 | −0.185299 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26682.0 | 1.15957 | 0.579783 | − | 0.814771i | \(-0.303137\pi\) | ||||
0.579783 | + | 0.814771i | \(0.303137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18012.0 | −0.779885 | −0.389943 | − | 0.920839i | \(-0.627505\pi\) | ||||
−0.389943 | + | 0.920839i | \(0.627505\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11568.0 | −0.499025 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38912.0 | −1.67243 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8528.00 | 0.365186 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3402.00 | 0.145147 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3270.00 | −0.139006 | −0.0695029 | − | 0.997582i | \(-0.522141\pi\) | ||||
−0.0695029 | + | 0.997582i | \(0.522141\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41692.0 | 1.76585 | 0.882923 | − | 0.469517i | \(-0.155572\pi\) | ||||
0.882923 | + | 0.469517i | \(0.155572\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7074.00 | −0.298527 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12078.0 | −0.507852 | −0.253926 | − | 0.967224i | \(-0.581722\pi\) | ||||
−0.253926 | + | 0.967224i | \(0.581722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24046.0 | −1.00742 | −0.503711 | − | 0.863872i | \(-0.668032\pi\) | ||||
−0.503711 | + | 0.863872i | \(0.668032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4074.00 | 0.170067 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6272.00 | −0.260879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50496.0 | −2.09280 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5400.00 | −0.223000 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12204.0 | 0.502180 | 0.251090 | − | 0.967964i | \(-0.419211\pi\) | ||||
0.251090 | + | 0.967964i | \(0.419211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66815.0 | 2.73955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5094.00 | 0.208122 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11504.0 | −0.468343 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7049.00 | 0.285958 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19020.0 | −0.768863 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30300.0 | −1.22053 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5930.00 | −0.238030 | −0.119015 | − | 0.992892i | \(-0.537974\pi\) | ||||
−0.119015 | + | 0.992892i | \(0.537974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7488.00 | 0.299514 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5268.00 | −0.209978 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10028.0 | 0.398313 | 0.199157 | − | 0.979968i | \(-0.436180\pi\) | ||||
0.199157 | + | 0.979968i | \(0.436180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3612.00 | 0.142969 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37306.0 | 1.47151 | 0.735754 | − | 0.677249i | \(-0.236828\pi\) | ||||
0.735754 | + | 0.677249i | \(0.236828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 59584.0 | 2.34210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34413.0 | −1.34801 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1656.00 | 0.0646444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40176.0 | 1.56293 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4986.00 | −0.193300 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 672.000 | 0.0259631 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39178.0 | −1.50849 | −0.754246 | − | 0.656592i | \(-0.771997\pi\) | ||||
−0.754246 | + | 0.656592i | \(0.771997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27612.0 | −1.05953 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36872.0 | −1.41004 | −0.705022 | − | 0.709185i | \(-0.749063\pi\) | ||||
−0.705022 | + | 0.709185i | \(0.749063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19964.0 | 0.760863 | 0.380432 | − | 0.924809i | \(-0.375775\pi\) | ||||
0.380432 | + | 0.924809i | \(0.375775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4608.00 | −0.175024 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12924.0 | −0.489228 | −0.244614 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244614 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2212.00 | −0.0834512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1458.00 | 0.0548202 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23920.0 | −0.896363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38368.0 | −1.43296 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32724.0 | 1.21809 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 60400.0 | 2.24077 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24320.0 | 0.899242 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3444.00 | −0.126920 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46496.0 | −1.70782 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44804.0 | −1.64023 | −0.820117 | − | 0.572196i | \(-0.806092\pi\) | ||||
−0.820117 | + | 0.572196i | \(0.806092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7020.00 | −0.256148 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26102.0 | 0.949284 | 0.474642 | − | 0.880179i | \(-0.342578\pi\) | ||||
0.474642 | + | 0.880179i | \(0.342578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4104.00 | 0.148765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29856.0 | 1.07870 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6916.00 | −0.249058 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 176.000 | 0.00631741 | 0.00315871 | − | 0.999995i | \(-0.498995\pi\) | ||||
0.00315871 | + | 0.999995i | \(0.498995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6540.00 | −0.233985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2916.00 | −0.103988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19650.0 | −0.698474 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −216.000 | −0.00765304 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23116.0 | 0.816374 | 0.408187 | − | 0.912898i | \(-0.366161\pi\) | ||||
0.408187 | + | 0.912898i | \(0.366161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2548.00 | −0.0896964 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21636.0 | 0.759197 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36864.0 | 1.28939 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20142.0 | −0.702252 | −0.351126 | − | 0.936328i | \(-0.614201\pi\) | ||||
−0.351126 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3966.00 | −0.137833 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19896.0 | 0.689257 | 0.344629 | − | 0.938739i | \(-0.388005\pi\) | ||||
0.344629 | + | 0.938739i | \(0.388005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34744.0 | 1.19981 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3024.00 | −0.104096 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7658.00 | 0.262779 | 0.131389 | − | 0.991331i | \(-0.458056\pi\) | ||||
0.131389 | + | 0.991331i | \(0.458056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40068.0 | −1.37056 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1422.00 | −0.0484874 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12826.0 | 0.435965 | 0.217983 | − | 0.975953i | \(-0.430052\pi\) | ||||
0.217983 | + | 0.975953i | \(0.430052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23648.0 | −0.801289 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16308.0 | −0.550849 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6650.00 | −0.223920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10209.0 | 0.342687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −702.000 | −0.0234908 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17568.0 | 0.586046 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53148.0 | −1.76745 | −0.883725 | − | 0.468006i | \(-0.844972\pi\) | ||||
−0.883725 | + | 0.468006i | \(0.844972\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19968.0 | −0.661986 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30340.0 | −1.00274 | −0.501368 | − | 0.865234i | \(-0.667170\pi\) | ||||
−0.501368 | + | 0.865234i | \(0.667170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14868.0 | −0.489873 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21222.0 | 0.697075 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6714.00 | −0.219857 | −0.109928 | − | 0.993940i | \(-0.535062\pi\) | ||||
−0.109928 | + | 0.993940i | \(0.535062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2088.00 | −0.0681642 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9306.00 | −0.302872 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22128.0 | −0.717979 | −0.358990 | − | 0.933342i | \(-0.616879\pi\) | ||||
−0.358990 | + | 0.933342i | \(0.616879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −80928.0 | −2.61785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9660.00 | 0.311531 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33128.0 | −1.06513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41928.0 | −1.34398 | −0.671991 | − | 0.740559i | \(-0.734561\pi\) | ||||
−0.671991 | + | 0.740559i | \(0.734561\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33852.0 | −1.08183 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −70912.0 | −2.25936 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28894.0 | 0.917836 | 0.458918 | − | 0.888479i | \(-0.348237\pi\) | ||||
0.458918 | + | 0.888479i | \(0.348237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4050.00 | 0.128265 |
(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 | 336.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1008.4.a.t.1.1 | 1 | |||
4.3 | odd | 2 | 168.4.a.d.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 2352.4.a.bj.1.1 | 1 | |||
8.3 | odd | 2 | 1344.4.a.l.1.1 | 1 | |||
8.5 | even | 2 | 1344.4.a.z.1.1 | 1 | |||
12.11 | even | 2 | 504.4.a.h.1.1 | 1 | |||
28.27 | even | 2 | 1176.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
336.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
504.4.a.h.1.1 | 1 | 12.11 | even | 2 | |||
1008.4.a.t.1.1 | 1 | 3.2 | odd | 2 | |||
1176.4.a.h.1.1 | 1 | 28.27 | even | 2 | |||
1344.4.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
1344.4.a.z.1.1 | 1 | 8.5 | even | 2 | |||
2352.4.a.bj.1.1 | 1 | 7.6 | odd | 2 |