Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,7,Mod(161,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.h (of order \(2\), degree \(1\), 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: | \(132.511152165\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.22 | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.7.h.b.161.23 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 89.8672 | 0.718937 | 0.359469 | − | 0.933157i | \(-0.382958\pi\) | ||||
0.359469 | + | 0.933157i | \(0.382958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −443.362 | −1.29260 | −0.646301 | − | 0.763083i | \(-0.723685\pi\) | ||||
−0.646301 | + | 0.763083i | \(0.723685\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.6164 | −0.0320183 | −0.0160092 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160092 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1280.86i | 0.583004i | 0.956570 | + | 0.291502i | \(0.0941549\pi\) | ||||
−0.956570 | + | 0.291502i | \(0.905845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6980.95i | − 1.42091i | −0.703741 | − | 0.710457i | \(-0.748488\pi\) | ||||
0.703741 | − | 0.710457i | \(-0.251512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5878.06i | 0.856984i | 0.903545 | + | 0.428492i | \(0.140955\pi\) | ||||
−0.903545 | + | 0.428492i | \(0.859045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4676.83i | 0.384386i | 0.981357 | + | 0.192193i | \(0.0615600\pi\) | ||||
−0.981357 | + | 0.192193i | \(0.938440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7548.89 | −0.483129 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29022.5 | −1.18998 | −0.594991 | − | 0.803733i | \(-0.702844\pi\) | ||||
−0.594991 | + | 0.803733i | \(0.702844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35918.8 | 1.20569 | 0.602847 | − | 0.797857i | \(-0.294033\pi\) | ||||
0.602847 | + | 0.797857i | \(0.294033\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −39843.7 | −0.929300 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 13478.5i | − 0.266095i | −0.991110 | − | 0.133047i | \(-0.957524\pi\) | ||||
0.991110 | − | 0.133047i | \(-0.0424763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 94302.7i | − 1.36827i | −0.729354 | − | 0.684136i | \(-0.760179\pi\) | ||||
0.729354 | − | 0.684136i | \(-0.239821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 127117.i | 1.59881i | 0.600792 | + | 0.799406i | \(0.294852\pi\) | ||||
−0.600792 | + | 0.799406i | \(0.705148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23599.2i | 0.227303i | 0.993521 | + | 0.113651i | \(0.0362547\pi\) | ||||
−0.993521 | + | 0.113651i | \(0.963745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 78921.2 | 0.670819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 50787.5 | 0.341137 | 0.170569 | − | 0.985346i | \(-0.445440\pi\) | ||||
0.170569 | + | 0.985346i | \(0.445440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3829.81 | −0.0230192 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 251523. | 1.22468 | 0.612338 | − | 0.790596i | \(-0.290229\pi\) | ||||
0.612338 | + | 0.790596i | \(0.290229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 44183.6i | − 0.194658i | −0.995252 | − | 0.0973289i | \(-0.968970\pi\) | ||||
0.995252 | − | 0.0973289i | \(-0.0310299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 115107.i | 0.419143i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 275182.i | − 0.914945i | −0.889224 | − | 0.457473i | \(-0.848755\pi\) | ||||
0.889224 | − | 0.457473i | \(-0.151245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 202612.i | − 0.566096i | −0.959106 | − | 0.283048i | \(-0.908655\pi\) | ||||
0.959106 | − | 0.283048i | \(-0.0913455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 126284. | 0.324623 | 0.162311 | − | 0.986740i | \(-0.448105\pi\) | ||||
0.162311 | + | 0.986740i | \(0.448105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18894.5 | 0.0413869 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 132427. | 0.268594 | 0.134297 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134297 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 336972. | 0.589331 | 0.294666 | − | 0.955600i | \(-0.404792\pi\) | ||||
0.294666 | + | 0.955600i | \(0.404792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 627358.i | − 1.02155i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 487794.i | 0.691937i | 0.938246 | + | 0.345968i | \(0.112450\pi\) | ||||
−0.938246 | + | 0.345968i | \(0.887550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 567885.i | − 0.753591i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 528244.i | 0.616118i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −548674. | −0.601173 | −0.300586 | − | 0.953755i | \(-0.597182\pi\) | ||||
−0.300586 | + | 0.953755i | \(0.597182\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.96827e6 | 1.91039 | 0.955193 | − | 0.295985i | \(-0.0956479\pi\) | ||||
0.955193 | + | 0.295985i | \(0.0956479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −610969. | −0.559123 | −0.279562 | − | 0.960128i | \(-0.590189\pi\) | ||||
−0.279562 | + | 0.960128i | \(0.590189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −917363. | −0.748841 | −0.374421 | − | 0.927259i | \(-0.622158\pi\) | ||||
−0.374421 | + | 0.927259i | \(0.622158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.42620e6i | 1.10129i | 0.834740 | + | 0.550645i | \(0.185618\pi\) | ||||
−0.834740 | + | 0.550645i | \(0.814382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.18126e6i | − 0.818671i | −0.912384 | − | 0.409335i | \(-0.865761\pi\) | ||||
0.912384 | − | 0.409335i | \(-0.134239\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 420293.i | 0.276350i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.09509e6i | 1.83668i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.76974e6 | −0.998975 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.08257e6 | −1.06628 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.05167e6 | 1.48980 | 0.744898 | − | 0.667178i | \(-0.232498\pi\) | ||||
0.744898 | + | 0.667178i | \(0.232498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −166786. | −0.0741902 | −0.0370951 | − | 0.999312i | \(-0.511810\pi\) | ||||
−0.0370951 | + | 0.999312i | \(0.511810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.60611e6i | − 1.10774i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.87781e6i | − 1.11918i | −0.828769 | − | 0.559591i | \(-0.810958\pi\) | ||||
0.828769 | − | 0.559591i | \(-0.189042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.02839e6i | − 0.755278i | −0.925953 | − | 0.377639i | \(-0.876736\pi\) | ||||
0.925953 | − | 0.377639i | \(-0.123264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 54585.6i | − 0.0186668i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.60817e6 | −0.855522 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.22778e6 | 1.58037 | 0.790184 | − | 0.612869i | \(-0.209985\pi\) | ||||
0.790184 | + | 0.612869i | \(0.209985\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.66916e6 | 0.484805 | 0.242402 | − | 0.970176i | \(-0.422065\pi\) | ||||
0.242402 | + | 0.970176i | \(0.422065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.22792e6 | 0.866818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.48935e6i | − 0.643262i | −0.946865 | − | 0.321631i | \(-0.895769\pi\) | ||||
0.946865 | − | 0.321631i | \(-0.104231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.07353e6i | − 0.496858i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 953137.i | 0.220086i | 0.993927 | + | 0.110043i | \(0.0350988\pi\) | ||||
−0.993927 | + | 0.110043i | \(0.964901\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.85882e6i | 1.25794i | 0.777428 | + | 0.628971i | \(0.216524\pi\) | ||||
−0.777428 | + | 0.628971i | \(0.783476\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.18621e6 | 0.660107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.56280e6 | 1.07437 | 0.537187 | − | 0.843463i | \(-0.319487\pi\) | ||||
0.537187 | + | 0.843463i | \(0.319487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.34689e6 | 0.624493 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.72771e6 | 1.52174 | 0.760872 | − | 0.648902i | \(-0.224772\pi\) | ||||
0.760872 | + | 0.648902i | \(0.224772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.28035e6i | − 1.22777i | −0.789396 | − | 0.613885i | \(-0.789606\pi\) | ||||
0.789396 | − | 0.613885i | \(-0.210394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.21128e6i | − 0.191306i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 297503.i | 0.0454953i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.61648e6i | 0.519022i | 0.965740 | + | 0.259511i | \(0.0835613\pi\) | ||||
−0.965740 | + | 0.259511i | \(0.916439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.22425e6 | 1.14400 | 0.571998 | − | 0.820255i | \(-0.306169\pi\) | ||||
0.571998 | + | 0.820255i | \(0.306169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.09570e7 | 1.43315 | 0.716576 | − | 0.697509i | \(-0.245708\pi\) | ||||
0.716576 | + | 0.697509i | \(0.245708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.36810e6 | 0.554285 | 0.277143 | − | 0.960829i | \(-0.410613\pi\) | ||||
0.277143 | + | 0.960829i | \(0.410613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.28675e7 | 1.53817 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 8.47472e6i | − 0.983703i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 250501.i | − 0.0274392i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.72401e7i | − 1.83524i | −0.397456 | − | 0.917621i | \(-0.630107\pi\) | ||||
0.397456 | − | 0.917621i | \(-0.369893\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.14236e7i | 1.14945i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.59251e7 | −1.55848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.94161e6 | 0.828398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.98062e7 | 1.78602 | 0.893008 | − | 0.450040i | \(-0.148590\pi\) | ||||
0.893008 | + | 0.450040i | \(0.148590\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.89837e6 | −0.504260 | −0.252130 | − | 0.967693i | \(-0.581131\pi\) | ||||
−0.252130 | + | 0.967693i | \(0.581131\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.06812e7i | − 0.889432i | −0.895672 | − | 0.444716i | \(-0.853305\pi\) | ||||
0.895672 | − | 0.444716i | \(-0.146695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.66399e7i | − 1.31547i | −0.753248 | − | 0.657737i | \(-0.771514\pi\) | ||||
0.753248 | − | 0.657737i | \(-0.228486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.12080e6i | 0.163416i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.06411e7i | 0.779461i | 0.920929 | + | 0.389730i | \(0.127432\pi\) | ||||
−0.920929 | + | 0.389730i | \(0.872568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.33513e7 | −1.66824 | −0.834122 | − | 0.551580i | \(-0.814025\pi\) | ||||
−0.834122 | + | 0.551580i | \(0.814025\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.09243e6 | 0.482277 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.52896e6 | −0.499625 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.67640e6 | 0.106012 | 0.0530062 | − | 0.998594i | \(-0.483120\pi\) | ||||
0.0530062 | + | 0.998594i | \(0.483120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 199309.i | − 0.0123074i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2.40911e7i | − 1.41924i | −0.704582 | − | 0.709622i | \(-0.748866\pi\) | ||||
0.704582 | − | 0.709622i | \(-0.251134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.97586e6i | 0.343955i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.53990e7i | 1.94591i | 0.230985 | + | 0.972957i | \(0.425805\pi\) | ||||
−0.230985 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.56413e6 | 0.245256 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.61266e7 | 1.85597 | 0.927983 | − | 0.372622i | \(-0.121541\pi\) | ||||
0.927983 | + | 0.372622i | \(0.121541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.59271e7 | 0.800253 | 0.400127 | − | 0.916460i | \(-0.368966\pi\) | ||||
0.400127 | + | 0.916460i | \(0.368966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 321706. | 0.0154690 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87252e7i | 0.881023i | 0.897747 | + | 0.440511i | \(0.145203\pi\) | ||||
−0.897747 | + | 0.440511i | \(0.854797\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09704e7i | 0.494427i | 0.968961 | + | 0.247213i | \(0.0795149\pi\) | ||||
−0.968961 | + | 0.247213i | \(0.920485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.72731e7i | − 1.64451i | −0.569121 | − | 0.822254i | \(-0.692716\pi\) | ||||
0.569121 | − | 0.822254i | \(-0.307284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.18103e7i | 1.76863i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.45961e7 | −1.01900 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.07872e7 | −0.428852 | −0.214426 | − | 0.976740i | \(-0.568788\pi\) | ||||
−0.214426 | + | 0.976740i | \(0.568788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.26037e7 | 0.880466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.99035e6 | −0.224098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.63588e7i | − 2.06663i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 3.97066e6i | − 0.139947i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.03376e7i | 0.702886i | 0.936209 | + | 0.351443i | \(0.114309\pi\) | ||||
−0.936209 | + | 0.351443i | \(0.885691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.59570e7i | − 0.862924i | −0.902131 | − | 0.431462i | \(-0.857998\pi\) | ||||
0.902131 | − | 0.431462i | \(-0.142002\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23211e7 | −0.401807 | −0.200904 | − | 0.979611i | \(-0.564388\pi\) | ||||
−0.200904 | + | 0.979611i | \(0.564388\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.20662e7 | 1.32055 | 0.660276 | − | 0.751023i | \(-0.270439\pi\) | ||||
0.660276 | + | 0.751023i | \(0.270439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23683e6 | 0.0381012 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.10344e7 | 1.21770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9.66906e6i | − 0.281666i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 1.04630e7i | − 0.293812i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.66885e7i | − 0.735937i | −0.929838 | − | 0.367968i | \(-0.880053\pi\) | ||||
0.929838 | − | 0.367968i | \(-0.119947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 2.47298e7i | − 0.657788i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.77829e7 | 1.50977 | 0.754883 | − | 0.655860i | \(-0.227694\pi\) | ||||
0.754883 | + | 0.655860i | \(0.227694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.53073e6 | −0.0386043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.71704e7 | 0.425500 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.65007e7 | 1.59161 | 0.795807 | − | 0.605550i | \(-0.207047\pi\) | ||||
0.795807 | + | 0.605550i | \(0.207047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.59885e7i | − 0.376124i | −0.982157 | − | 0.188062i | \(-0.939779\pi\) | ||||
0.982157 | − | 0.188062i | \(-0.0602207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.58567e7i | 0.587826i | 0.955832 | + | 0.293913i | \(0.0949576\pi\) | ||||
−0.955832 | + | 0.293913i | \(0.905042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.82082e7i | − 0.406987i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 3.71990e6i | − 0.0803986i | −0.999192 | − | 0.0401993i | \(-0.987201\pi\) | ||||
0.999192 | − | 0.0401993i | \(-0.0127993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.24943e7 | 0.265578 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.13488e7 | 0.233384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.46513e7 | −1.10561 | −0.552805 | − | 0.833311i | \(-0.686443\pi\) | ||||
−0.552805 | + | 0.833311i | \(0.686443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.25173e7 | −0.440955 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.17609e6i | 0.157550i | 0.996892 | + | 0.0787752i | \(0.0251009\pi\) | ||||
−0.996892 | + | 0.0787752i | \(0.974899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.71737e7i | − 0.693763i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.26957e7i | 0.967960i | 0.875079 | + | 0.483980i | \(0.160809\pi\) | ||||
−0.875079 | + | 0.483980i | \(0.839191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.02655e7i | 0.716700i | 0.933587 | + | 0.358350i | \(0.116660\pi\) | ||||
−0.933587 | + | 0.358350i | \(0.883340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.69800e6 | 0.0297546 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.13341e7 | −0.192548 | −0.0962742 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962742 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.26487e7 | 0.546180 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.19009e7 | 0.193102 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.76000e7i | 0.920558i | 0.887774 | + | 0.460279i | \(0.152251\pi\) | ||||
−0.887774 | + | 0.460279i | \(0.847749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 1.31623e7i | − 0.204126i | −0.994778 | − | 0.102063i | \(-0.967456\pi\) | ||||
0.994778 | − | 0.102063i | \(-0.0325443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.60069e7i | 0.702924i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 574405.i | 0.00851991i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.37357e7 | 0.346922 | 0.173461 | − | 0.984841i | \(-0.444505\pi\) | ||||
0.173461 | + | 0.984841i | \(0.444505\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.11516e8 | −1.58302 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.02827e7 | 0.423692 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.19810e8 | −1.62874 | −0.814371 | − | 0.580345i | \(-0.802918\pi\) | ||||
−0.814371 | + | 0.580345i | \(0.802918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.41749e7i | − 0.457995i | −0.973427 | − | 0.228998i | \(-0.926455\pi\) | ||||
0.973427 | − | 0.228998i | \(-0.0735448\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.26984e7i | 0.686485i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.95894e7i | 0.251615i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.31163e8i | − 1.63825i | −0.573617 | − | 0.819123i | \(-0.694460\pi\) | ||||
0.573617 | − | 0.819123i | \(-0.305540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.36200e7 | −0.660485 | −0.330243 | − | 0.943896i | \(-0.607131\pi\) | ||||
−0.330243 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.74906e7 | −0.329413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 569641. | 0.00673299 | 0.00336649 | − | 0.999994i | \(-0.498928\pi\) | ||||
0.00336649 | + | 0.999994i | \(0.498928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.19062e7 | −1.05714 | −0.528571 | − | 0.848889i | \(-0.677272\pi\) | ||||
−0.528571 | + | 0.848889i | \(0.677272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.38367e7i | 0.497459i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.65056e6i | 0.106614i | 0.998578 | + | 0.0533069i | \(0.0169762\pi\) | ||||
−0.998578 | + | 0.0533069i | \(0.983024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.01884e6i | 0.0438098i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 5.10342e7i | − 0.541785i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.77393e7 | −0.814502 | −0.407251 | − | 0.913316i | \(-0.633513\pi\) | ||||
−0.407251 | + | 0.913316i | \(0.633513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.29523e7 | −0.540483 | −0.270241 | − | 0.962793i | \(-0.587104\pi\) | ||||
−0.270241 | + | 0.962793i | \(0.587104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.91760e8 | −1.93204 | −0.966019 | − | 0.258472i | \(-0.916781\pi\) | ||||
−0.966019 | + | 0.258472i | \(0.916781\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.45026e8 | −1.42396 | −0.711978 | − | 0.702202i | \(-0.752200\pi\) | ||||
−0.711978 | + | 0.702202i | \(0.752200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.22005e8i | 1.18266i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.41725e6i | − 0.0511912i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.43728e7i | − 0.414034i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.36591e8i | 1.24284i | 0.783478 | + | 0.621419i | \(0.213444\pi\) | ||||
−0.783478 | + | 0.621419i | \(0.786556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.72641e7 | 0.155134 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.93078e7 | −0.432206 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.85713e7 | −0.680263 | −0.340132 | − | 0.940378i | \(-0.610472\pi\) | ||||
−0.340132 | + | 0.940378i | \(0.610472\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.72964e8 | 1.46121 | 0.730604 | − | 0.682802i | \(-0.239239\pi\) | ||||
0.730604 | + | 0.682802i | \(0.239239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.02604e8i | 1.69086i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.98305e7i | 0.731736i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.93484e7i | 0.638611i | 0.947652 | + | 0.319306i | \(0.103450\pi\) | ||||
−0.947652 | + | 0.319306i | \(0.896550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.23058e8i | − 1.75273i | −0.481648 | − | 0.876365i | \(-0.659962\pi\) | ||||
0.481648 | − | 0.876365i | \(-0.340038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.76883e8 | 1.37345 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.75511e8 | −1.33092 | −0.665458 | − | 0.746436i | \(-0.731764\pi\) | ||||
−0.665458 | + | 0.746436i | \(0.731764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.59895e7 | −0.419608 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.49061e7 | −0.401975 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.00571e6i | − 0.00727784i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.60442e8i | 1.84161i | 0.390025 | + | 0.920804i | \(0.372466\pi\) | ||||
−0.390025 | + | 0.920804i | \(0.627534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.43273e8i | − 1.00152i | −0.865586 | − | 0.500760i | \(-0.833054\pi\) | ||||
0.865586 | − | 0.500760i | \(-0.166946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.50748e8i | − 1.71319i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.26163e8 | 0.852247 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20788e8 | 0.797708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.24408e7 | −0.538370 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.36334e6 | −0.0214785 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.45953e7i | − 0.281642i | −0.990035 | − | 0.140821i | \(-0.955026\pi\) | ||||
0.990035 | − | 0.140821i | \(-0.0449742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.28169e8i | 0.791758i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.65329e8i | 1.01016i | 0.863074 | + | 0.505078i | \(0.168536\pi\) | ||||
−0.863074 | + | 0.505078i | \(0.831464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.70596e8i | − 1.01980i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.87133e7 | −0.347185 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.28148e8 | −1.32024 | −0.660118 | − | 0.751162i | \(-0.729494\pi\) | ||||
−0.660118 | + | 0.751162i | \(0.729494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.62819e8 | −0.932113 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.27992e8 | −0.717229 | −0.358615 | − | 0.933486i | \(-0.616751\pi\) | ||||
−0.358615 | + | 0.933486i | \(0.616751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.06156e8i | − 0.588573i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.89105e7i | 0.428349i | 0.976795 | + | 0.214175i | \(0.0687062\pi\) | ||||
−0.976795 | + | 0.214175i | \(0.931294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.95304e7i | − 0.266050i | −0.991113 | − | 0.133025i | \(-0.957531\pi\) | ||||
0.991113 | − | 0.133025i | \(-0.0424691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 3.53048e7i | − 0.185708i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.02547e8 | 0.533821 | 0.266910 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266910 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.49401e8 | −0.761770 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.16438e6 | −0.0109226 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.04244e8 | −0.515389 | −0.257694 | − | 0.966226i | \(-0.582963\pi\) | ||||
−0.257694 | + | 0.966226i | \(0.582963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.11133e8i | 1.03326i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 8.76870e7i | − 0.420505i | −0.977647 | − | 0.210252i | \(-0.932571\pi\) | ||||
0.977647 | − | 0.210252i | \(-0.0674286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.78147e8i | 1.32046i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.02978e8i | − 0.479142i | −0.970879 | − | 0.239571i | \(-0.922993\pi\) | ||||
0.970879 | − | 0.239571i | \(-0.0770068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.53945e8 | 1.16981 | 0.584907 | − | 0.811100i | \(-0.301131\pi\) | ||||
0.584907 | + | 0.811100i | \(0.301131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.59042e8 | −0.718200 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.34354e8 | 1.49500 | 0.747500 | − | 0.664262i | \(-0.231254\pi\) | ||||
0.747500 | + | 0.664262i | \(0.231254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.02273e7 | −0.132518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.24904e7i | 0.141050i | 0.997510 | + | 0.0705251i | \(0.0224675\pi\) | ||||
−0.997510 | + | 0.0705251i | \(0.977533\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 2.64427e8i | − 1.12577i | −0.826535 | − | 0.562885i | \(-0.809691\pi\) | ||||
0.826535 | − | 0.562885i | \(-0.190309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.99576e7i | 0.168472i | 0.996446 | + | 0.0842359i | \(0.0268449\pi\) | ||||
−0.996446 | + | 0.0842359i | \(0.973155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.16270e8i | − 0.894399i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.92035e7 | −0.283458 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.40928e7 | −0.378098 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.60716e8 | −1.83377 | −0.916886 | − | 0.399148i | \(-0.869306\pi\) | ||||
−0.916886 | + | 0.399148i | \(0.869306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.74245e8 | 1.07107 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.01087e8i | 0.391090i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.20142e7i | 0.273429i | 0.990611 | + | 0.136714i | \(0.0436543\pi\) | ||||
−0.990611 | + | 0.136714i | \(0.956346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.30921e8i | 1.62093i | 0.585786 | + | 0.810466i | \(0.300786\pi\) | ||||
−0.585786 | + | 0.810466i | \(0.699214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.79530e8i | 1.40131i | 0.713502 | + | 0.700653i | \(0.247108\pi\) | ||||
−0.713502 | + | 0.700653i | \(0.752892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07190e7 | −0.0392121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.45700e7 | −0.160067 | −0.0800337 | − | 0.996792i | \(-0.525503\pi\) | ||||
−0.0800337 | + | 0.996792i | \(0.525503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.49886e7 | −0.0533381 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.65766e8 | −1.62746 | −0.813731 | − | 0.581241i | \(-0.802567\pi\) | ||||
−0.813731 | + | 0.581241i | \(0.802567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.06364e8i | 1.75331i | 0.481121 | + | 0.876654i | \(0.340230\pi\) | ||||
−0.481121 | + | 0.876654i | \(0.659770\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2.34204e8i | − 0.796395i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.35733e8i | − 0.457412i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.88295e6i | 0.00623262i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.72114e7 | −0.122076 | −0.0610381 | − | 0.998135i | \(-0.519441\pi\) | ||||
−0.0610381 | + | 0.998135i | \(0.519441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.38536e8 | −1.73560 | −0.867798 | − | 0.496917i | \(-0.834465\pi\) | ||||
−0.867798 | + | 0.496917i | \(0.834465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43261e8 | 0.777077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.97430e8 | 0.619656 | 0.309828 | − | 0.950793i | \(-0.399729\pi\) | ||||
0.309828 | + | 0.950793i | \(0.399729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2.58621e8i | − 0.804622i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.50516e7i | 0.198884i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 3.11370e8i | − 0.943720i | −0.881673 | − | 0.471860i | \(-0.843583\pi\) | ||||
0.881673 | − | 0.471860i | \(-0.156417\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.82286e8i | − 0.542998i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.58323e8 | −1.94420 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.34596e8 | 1.84223 | 0.921113 | − | 0.389295i | \(-0.127281\pi\) | ||||
0.921113 | + | 0.389295i | \(0.127281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.92274e7 | 0.228039 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.72658e8 | −2.46937 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 4.45746e8i | − 1.25069i | −0.780350 | − | 0.625344i | \(-0.784959\pi\) | ||||
0.780350 | − | 0.625344i | \(-0.215041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.67986e8i | 0.463452i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4.90545e6i | − 0.0134203i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.71293e8i | − 0.460842i | −0.973091 | − | 0.230421i | \(-0.925990\pi\) | ||||
0.973091 | − | 0.230421i | \(-0.0740103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.70881e8 | 0.722724 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.19087e8 | 0.574914 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.16750e7 | 0.186537 | 0.0932683 | − | 0.995641i | \(-0.470269\pi\) | ||||
0.0932683 | + | 0.995641i | \(0.470269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.87395e8 | 2.27177 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.52426e8i | − 1.14878i | −0.818583 | − | 0.574388i | \(-0.805240\pi\) | ||||
0.818583 | − | 0.574388i | \(-0.194760\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17272e7i | 0.0292950i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.11428e8i | − 0.523878i | −0.965084 | − | 0.261939i | \(-0.915638\pi\) | ||||
0.965084 | − | 0.261939i | \(-0.0843619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.92654e8i | 0.957291i | 0.878008 | + | 0.478645i | \(0.158872\pi\) | ||||
−0.878008 | + | 0.478645i | \(0.841128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.69806e8 | 1.13619 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.06724e8 | 0.967953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.33542e8 | −0.315282 | −0.157641 | − | 0.987496i | \(-0.550389\pi\) | ||||
−0.157641 | + | 0.987496i | \(0.550389\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.50003e8 | 0.348544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.62083e8i | 1.29572i | 0.761758 | + | 0.647862i | \(0.224337\pi\) | ||||
−0.761758 | + | 0.647862i | \(0.775663\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.74241e8i | 1.75680i | 0.477926 | + | 0.878400i | \(0.341389\pi\) | ||||
−0.477926 | + | 0.878400i | \(0.658611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6.32324e8i | − 1.42353i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.22165e8i | 0.713991i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.80577e8 | −0.836880 | −0.418440 | − | 0.908245i | \(-0.637423\pi\) | ||||
−0.418440 | + | 0.908245i | \(0.637423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.34339e8 | 0.290846 | 0.145423 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145423 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.71147e8 | −0.582505 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.54317e8 | 1.17259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.63458e6i | 0.0181254i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 2.23711e8i | − 0.462465i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.53435e8i | 0.725079i | 0.931968 | + | 0.362540i | \(0.118090\pi\) | ||||
−0.931968 | + | 0.362540i | \(0.881910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.23725e8i | 1.05822i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.65930e7 | 0.113486 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.95605e8 | 0.781424 | 0.390712 | − | 0.920513i | \(-0.372229\pi\) | ||||
0.390712 | + | 0.920513i | \(0.372229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.64745e8 | 0.322977 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.38176e6 | −0.0103939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.86342e8i | − 0.357210i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 3.17458e8i | − 0.599572i | −0.954007 | − | 0.299786i | \(-0.903085\pi\) | ||||
0.954007 | − | 0.299786i | \(-0.0969152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.33047e8i | − 1.74921i | −0.484839 | − | 0.874603i | \(-0.661122\pi\) | ||||
0.484839 | − | 0.874603i | \(-0.338878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.56557e7i | 0.158228i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.47199e8 | −1.37016 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.78907e8 | 1.04611 | 0.523057 | − | 0.852298i | \(-0.324791\pi\) | ||||
0.523057 | + | 0.852298i | \(0.324791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.89598e8 | 0.519512 | 0.259756 | − | 0.965674i | \(-0.416358\pi\) | ||||
0.259756 | + | 0.965674i | \(0.416358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.87138e8 | 0.330861 | 0.165431 | − | 0.986221i | \(-0.447099\pi\) | ||||
0.165431 | + | 0.986221i | \(0.447099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.96994e8i | − 0.696820i | −0.937342 | − | 0.348410i | \(-0.886722\pi\) | ||||
0.937342 | − | 0.348410i | \(-0.113278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.50945e8i | − 0.953176i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.26516e8i | 0.904382i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23895e8i | 0.209782i | 0.994484 | + | 0.104891i | \(0.0334493\pi\) | ||||
−0.994484 | + | 0.104891i | \(0.966551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.47480e8 | 0.416056 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.86336e8 | 0.474576 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.84638e8 | 1.29128 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.30366e7 | 0.102283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.14278e8i | − 1.15085i | −0.817853 | − | 0.575427i | \(-0.804836\pi\) | ||||
0.817853 | − | 0.575427i | \(-0.195164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.13028e9i | − 1.79574i | −0.440258 | − | 0.897871i | \(-0.645113\pi\) | ||||
0.440258 | − | 0.897871i | \(-0.354887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.88951e8i | − 0.771411i | −0.922622 | − | 0.385705i | \(-0.873958\pi\) | ||||
0.922622 | − | 0.385705i | \(-0.126042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.12311e8i | 0.330324i | 0.986266 | + | 0.165162i | \(0.0528147\pi\) | ||||
−0.986266 | + | 0.165162i | \(0.947185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.99914e8 | 0.772408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.64357e6 | −0.00859992 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.52469e8 | 0.533416 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.23334e8 | 1.37827 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.59326e8i | − 0.977465i | −0.872434 | − | 0.488733i | \(-0.837459\pi\) | ||||
0.872434 | − | 0.488733i | \(-0.162541\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.67349e8i | 0.390976i | 0.980706 | + | 0.195488i | \(0.0626291\pi\) | ||||
−0.980706 | + | 0.195488i | \(0.937371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.01615e9i | 1.47596i | 0.674824 | + | 0.737979i | \(0.264220\pi\) | ||||
−0.674824 | + | 0.737979i | \(0.735780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.93480e8i | 0.850423i | 0.905094 | + | 0.425212i | \(0.139800\pi\) | ||||
−0.905094 | + | 0.425212i | \(0.860200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35300e9 | −1.92571 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.38718e8 | −0.194795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.84335e8 | 1.09404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.04245e9 | −1.43475 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.54545e8i | − 0.484727i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.54265e8i | − 0.882689i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.02396e8i | − 0.539302i | −0.962958 | − | 0.269651i | \(-0.913092\pi\) | ||||
0.962958 | − | 0.269651i | \(-0.0869083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.06320e9i | 1.40624i | 0.711072 | + | 0.703119i | \(0.248210\pi\) | ||||
−0.711072 | + | 0.703119i | \(0.751790\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.43605e7 | −0.0188694 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.39468e7 | 0.0958984 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.18958e8 | 0.797471 | 0.398735 | − | 0.917066i | \(-0.369449\pi\) | ||||
0.398735 | + | 0.917066i | \(0.369449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.59517e8 | 0.330036 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.01748e8i | 0.128558i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 9.86097e8i | − 1.22991i | −0.788563 | − | 0.614954i | \(-0.789175\pi\) | ||||
0.788563 | − | 0.614954i | \(-0.210825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.63903e8i | 0.574882i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.67357e7i | 0.0327083i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.48195e7 | −0.103104 | −0.0515522 | − | 0.998670i | \(-0.516417\pi\) | ||||
−0.0515522 | + | 0.998670i | \(0.516417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.05514e9 | 1.26632 | 0.633158 | − | 0.774023i | \(-0.281758\pi\) | ||||
0.633158 | + | 0.774023i | \(0.281758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.41037e8 | 0.525945 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.06273e8 | −0.596122 | −0.298061 | − | 0.954547i | \(-0.596340\pi\) | ||||
−0.298061 | + | 0.954547i | \(0.596340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.61752e8i | 0.189256i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.12053e7i | 0.105376i | 0.998611 | + | 0.0526880i | \(0.0167789\pi\) | ||||
−0.998611 | + | 0.0526880i | \(0.983221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.25003e8i | 0.373144i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.27591e9i | 1.44666i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.02658e8 | 0.453697 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.39090e8 | 0.822461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.98020e8 | 0.218992 | 0.109496 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109496 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67278e9 | 1.82718 | 0.913592 | − | 0.406633i | \(-0.133297\pi\) | ||||
0.913592 | + | 0.406633i | \(0.133297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.99312e8i | 0.976274i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.70123e8i | − 0.182422i | −0.995832 | − | 0.0912112i | \(-0.970926\pi\) | ||||
0.995832 | − | 0.0912112i | \(-0.0290738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.07880e7i | − 0.0221547i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.02146e8i | 0.212816i | 0.994323 | + | 0.106408i | \(0.0339349\pi\) | ||||
−0.994323 | + | 0.106408i | \(0.966065\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.84674e8 | 1.03035 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.94503e8 | −0.614561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.58498e9 | −1.62856 | −0.814280 | − | 0.580473i | \(-0.802868\pi\) | ||||
−0.814280 | + | 0.580473i | \(0.802868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.92549e8 | 0.398496 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.57004e9i | − 1.58425i | −0.610358 | − | 0.792126i | \(-0.708974\pi\) | ||||
0.610358 | − | 0.792126i | \(-0.291026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 576.7.h.b.161.22 | yes | 32 | |
3.2 | odd | 2 | inner | 576.7.h.b.161.10 | yes | 32 | |
4.3 | odd | 2 | inner | 576.7.h.b.161.24 | yes | 32 | |
8.3 | odd | 2 | inner | 576.7.h.b.161.12 | yes | 32 | |
8.5 | even | 2 | inner | 576.7.h.b.161.11 | yes | 32 | |
12.11 | even | 2 | inner | 576.7.h.b.161.9 | ✓ | 32 | |
24.5 | odd | 2 | inner | 576.7.h.b.161.23 | yes | 32 | |
24.11 | even | 2 | inner | 576.7.h.b.161.21 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.7.h.b.161.9 | ✓ | 32 | 12.11 | even | 2 | inner | |
576.7.h.b.161.10 | yes | 32 | 3.2 | odd | 2 | inner | |
576.7.h.b.161.11 | yes | 32 | 8.5 | even | 2 | inner | |
576.7.h.b.161.12 | yes | 32 | 8.3 | odd | 2 | inner | |
576.7.h.b.161.21 | yes | 32 | 24.11 | even | 2 | inner | |
576.7.h.b.161.22 | yes | 32 | 1.1 | even | 1 | trivial | |
576.7.h.b.161.23 | yes | 32 | 24.5 | odd | 2 | inner | |
576.7.h.b.161.24 | yes | 32 | 4.3 | odd | 2 | inner |