Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (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: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.4 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.7.b.a.319.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 196.000i | 1.56800i | 0.620761 | + | 0.784000i | \(0.286824\pi\) | ||||
−0.620761 | + | 0.784000i | \(0.713176\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 270.200i | − 0.787755i | −0.919163 | − | 0.393877i | \(-0.871133\pi\) | ||||
0.919163 | − | 0.393877i | \(-0.128867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1725.12 | 1.29611 | 0.648055 | − | 0.761593i | \(-0.275583\pi\) | ||||
0.648055 | + | 0.761593i | \(0.275583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2880.00i | 1.31088i | 0.755248 | + | 0.655439i | \(0.227516\pi\) | ||||
−0.755248 | + | 0.655439i | \(0.772484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3055.34i | 0.905285i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2898.00 | −0.589864 | −0.294932 | − | 0.955518i | \(-0.595297\pi\) | ||||
−0.294932 | + | 0.955518i | \(0.595297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9789.55 | 1.42726 | 0.713628 | − | 0.700525i | \(-0.247051\pi\) | ||||
0.713628 | + | 0.700525i | \(0.247051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 4212.00i | − 0.454810i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1621.20i | − 0.133246i | −0.997778 | − | 0.0666228i | \(-0.978778\pi\) | ||||
0.997778 | − | 0.0666228i | \(-0.0212224\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22791.0 | −1.45862 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14596.0i | 0.598467i | 0.954180 | + | 0.299233i | \(0.0967309\pi\) | ||||
−0.954180 | + | 0.299233i | \(0.903269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6879.71i | − 0.230932i | −0.993311 | − | 0.115466i | \(-0.963164\pi\) | ||||
0.993311 | − | 0.115466i | \(-0.0368362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 26892.0 | 0.748310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52959.2 | 1.23520 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 12168.0i | − 0.240223i | −0.992760 | − | 0.120111i | \(-0.961675\pi\) | ||||
0.992760 | − | 0.120111i | \(-0.0383252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44894.8i | 0.756836i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18738.0 | 0.271876 | 0.135938 | − | 0.990717i | \(-0.456595\pi\) | ||||
0.135938 | + | 0.990717i | \(0.456595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 135245. | 1.70105 | 0.850525 | − | 0.525934i | \(-0.176284\pi\) | ||||
0.850525 | + | 0.525934i | \(0.176284\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 47628.0i | 0.522667i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 151270.i | − 1.45700i | −0.685044 | − | 0.728501i | \(-0.740217\pi\) | ||||
0.685044 | − | 0.728501i | \(-0.259783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44641.0 | 0.379442 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45175.3 | −0.340558 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 144236.i | 0.968827i | 0.874839 | + | 0.484413i | \(0.160967\pi\) | ||||
−0.874839 | + | 0.484413i | \(0.839033\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 338124.i | 2.03230i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 152604. | 0.824027 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −333655. | −1.62458 | −0.812292 | − | 0.583251i | \(-0.801780\pi\) | ||||
−0.812292 | + | 0.583251i | \(0.801780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 333432.i | 1.46899i | 0.678616 | + | 0.734493i | \(0.262580\pi\) | ||||
−0.678616 | + | 0.734493i | \(0.737420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 65658.6i | − 0.262585i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −564480. | −2.05546 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −319439. | −1.06209 | −0.531047 | − | 0.847342i | \(-0.678201\pi\) | ||||
−0.531047 | + | 0.847342i | \(0.678201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 25272.0i | − 0.0769294i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 420639.i | 1.17526i | 0.809129 | + | 0.587631i | \(0.199939\pi\) | ||||
−0.809129 | + | 0.587631i | \(0.800061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 628238. | 1.61494 | 0.807469 | − | 0.589911i | \(-0.200837\pi\) | ||||
0.807469 | + | 0.589911i | \(0.200837\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −355277. | −0.842137 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 466128.i | − 1.02102i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 291878.i | − 0.591998i | −0.955188 | − | 0.295999i | \(-0.904347\pi\) | ||||
0.955188 | − | 0.295999i | \(-0.0956526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −357017. | −0.624389 | −0.312194 | − | 0.950018i | \(-0.601064\pi\) | ||||
−0.312194 | + | 0.950018i | \(0.601064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 568008.i | − 0.924906i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 227529.i | 0.345525i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.37507e6 | −1.95055 | −0.975273 | − | 0.221005i | \(-0.929066\pi\) | ||||
−0.975273 | + | 0.221005i | \(0.929066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 778176. | 1.03265 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 107244.i | − 0.133329i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.91875e6i | 2.23794i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 489710. | 0.536567 | 0.268283 | − | 0.963340i | \(-0.413544\pi\) | ||||
0.268283 | + | 0.963340i | \(0.413544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 419205. | 0.432037 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13539e6i | 1.10200i | 0.834506 | + | 0.550998i | \(0.185753\pi\) | ||||
−0.834506 | + | 0.550998i | \(0.814247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 501262.i | 0.458726i | 0.973341 | + | 0.229363i | \(0.0736643\pi\) | ||||
−0.973341 | + | 0.229363i | \(0.926336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 825552. | 0.713143 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.27948e6 | 1.04444 | 0.522218 | − | 0.852812i | \(-0.325105\pi\) | ||||
0.522218 | + | 0.852812i | \(0.325105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 384336.i | − 0.296778i | −0.988929 | − | 0.148389i | \(-0.952591\pi\) | ||||
0.988929 | − | 0.148389i | \(-0.0474088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 189680.i | − 0.138693i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58125e6 | −1.09588 | −0.547941 | − | 0.836517i | \(-0.684588\pi\) | ||||
−0.547941 | + | 0.836517i | \(0.684588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 317755. | 0.208929 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 699840.i | 0.436959i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 783039.i | 0.464668i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.20449e6 | 0.679902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 292097. | 0.156968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.40454e6i | − 0.719122i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.02180e6i | 1.96340i | 0.190426 | + | 0.981701i | \(0.439013\pi\) | ||||
−0.190426 | + | 0.981701i | \(0.560987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.10827e6 | 0.982102 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.01277e6 | 0.450503 | 0.225251 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225251 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.64514e6i | − 1.12433i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 742447.i | 0.301762i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.29394e6 | 0.892113 | 0.446057 | − | 0.895005i | \(-0.352828\pi\) | ||||
0.446057 | + | 0.895005i | \(0.352828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15526.1 | 0.00578120 | 0.00289060 | − | 0.999996i | \(-0.499080\pi\) | ||||
0.00289060 | + | 0.999996i | \(0.499080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.35807e6i | − 0.841201i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.96835e6i | 1.69904i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.86082e6 | −0.938396 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 695884. | 0.219071 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.97326e6i | − 0.898823i | −0.893325 | − | 0.449411i | \(-0.851634\pi\) | ||||
0.893325 | − | 0.449411i | \(-0.148366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.62197e6i | 1.63289i | 0.577422 | + | 0.816446i | \(0.304059\pi\) | ||||
−0.577422 | + | 0.816446i | \(0.695941\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −704214. | −0.196621 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.34842e6 | 0.362102 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.27998e6i | 1.36437i | 0.731178 | + | 0.682186i | \(0.238971\pi\) | ||||
−0.731178 | + | 0.682186i | \(0.761029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.24842e6i | 0.559352i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −438048. | −0.104965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.90176e6 | −1.59366 | −0.796832 | − | 0.604201i | \(-0.793493\pi\) | ||||
−0.796832 | + | 0.604201i | \(0.793493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.27083e6i | 1.17335i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.72567e6i | − 1.01465i | −0.861756 | − | 0.507323i | \(-0.830635\pi\) | ||||
0.861756 | − | 0.507323i | \(-0.169365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.46759e6 | −0.718402 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.37886e6 | 0.475752 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.49729e6i | 1.06172i | 0.847459 | + | 0.530861i | \(0.178131\pi\) | ||||
−0.847459 | + | 0.530861i | \(0.821869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.15813e6i | 1.14904i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.20117e6 | −0.937954 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.14334e6 | −1.59421 | −0.797105 | − | 0.603840i | \(-0.793636\pi\) | ||||
−0.797105 | + | 0.603840i | \(0.793636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.71646e6i | − 1.46996i | −0.678090 | − | 0.734978i | \(-0.737192\pi\) | ||||
0.678090 | − | 0.734978i | \(-0.262808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.19769e6i | 0.848120i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.38493e6 | 0.376669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.99941e6 | −0.764528 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.02352e6i | − 0.151603i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.32374e6i | 1.19459i | 0.802022 | + | 0.597294i | \(0.203758\pi\) | ||||
−0.802022 | + | 0.597294i | \(0.796242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.03977e6 | 0.561934 | 0.280967 | − | 0.959717i | \(-0.409345\pi\) | ||||
0.280967 | + | 0.959717i | \(0.409345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.79937e6 | −1.18672 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.27599e7i | 1.66897i | 0.551027 | + | 0.834487i | \(0.314236\pi\) | ||||
−0.551027 | + | 0.834487i | \(0.685764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 963969.i | − 0.122322i | −0.998128 | − | 0.0611609i | \(-0.980520\pi\) | ||||
0.998128 | − | 0.0611609i | \(-0.0194803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.97956e6 | −0.613200 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.94384e6 | 0.471445 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.67265e6i | 0.426302i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 393951.i | − 0.0444152i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.68882e7 | 1.84988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.69955e6 | 0.500275 | 0.250137 | − | 0.968210i | \(-0.419524\pi\) | ||||
0.250137 | + | 0.968210i | \(0.419524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.55711e6i | 0.678537i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.65081e7i | 2.66725i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.85890e6 | −0.181918 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.79326e6 | 0.932384 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 8.34624e6i | − 0.773240i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.13047e6i | − 0.642989i | −0.946911 | − | 0.321495i | \(-0.895815\pi\) | ||||
0.946911 | − | 0.321495i | \(-0.104185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.53821e6 | −0.486208 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.69883e6 | 0.145235 | 0.0726177 | − | 0.997360i | \(-0.476865\pi\) | ||||
0.0726177 | + | 0.997360i | \(0.476865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.20413e7i | − 1.00269i | −0.865248 | − | 0.501344i | \(-0.832839\pi\) | ||||
0.865248 | − | 0.501344i | \(-0.167161\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 7.26622e6i | − 0.589484i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.57341e6 | 0.203442 | 0.101721 | − | 0.994813i | \(-0.467565\pi\) | ||||
0.101721 | + | 0.994813i | \(0.467565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.96490e7 | 2.28458 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 4.54993e6i | − 0.341790i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.72461e7i | − 1.26327i | −0.775266 | − | 0.631635i | \(-0.782384\pi\) | ||||
0.775266 | − | 0.631635i | \(-0.217616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.02288e6 | 0.144517 | 0.0722584 | − | 0.997386i | \(-0.476979\pi\) | ||||
0.0722584 | + | 0.997386i | \(0.476979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.74964e6i | 0.594965i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.81939e7i | 1.87096i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.56535e6 | −0.360491 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.60223e7 | 1.64560 | 0.822801 | − | 0.568330i | \(-0.192410\pi\) | ||||
0.822801 | + | 0.568330i | \(0.192410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.79677e6i | − 0.172701i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 8.85437e6i | − 0.533995i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.19807e7 | 0.705800 | 0.352900 | − | 0.935661i | \(-0.385196\pi\) | ||||
0.352900 | + | 0.935661i | \(0.385196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.28779e6 | −0.189237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.54683e6i | 0.199489i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3.55118e6i | − 0.195211i | −0.995225 | − | 0.0976056i | \(-0.968882\pi\) | ||||
0.995225 | − | 0.0976056i | \(-0.0311184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.82703e7 | −1.51912 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.14353e7 | −1.12615 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.35329e6i | − 0.275020i | −0.990500 | − | 0.137510i | \(-0.956090\pi\) | ||||
0.990500 | − | 0.137510i | \(-0.0439099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.58492e7i | − 0.796342i | −0.917311 | − | 0.398171i | \(-0.869645\pi\) | ||||
0.917311 | − | 0.398171i | \(-0.130355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.21306e7 | 0.596201 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.93173e7 | −1.89054 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.29206e7i | − 1.07842i | −0.842172 | − | 0.539209i | \(-0.818723\pi\) | ||||
0.842172 | − | 0.539209i | \(-0.181277\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 1.67177e6i | − 0.0769775i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.02713e7 | 0.913614 | 0.456807 | − | 0.889566i | \(-0.348993\pi\) | ||||
0.456807 | + | 0.889566i | \(0.348993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.08364e7 | 0.478108 | 0.239054 | − | 0.971006i | \(-0.423163\pi\) | ||||
0.239054 | + | 0.971006i | \(0.423163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.99104e7i | 1.29207i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 5.06301e6i | − 0.214172i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.57392e7 | −0.652061 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.63382e6 | 0.309787 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.99362e7i | 0.792572i | 0.918127 | + | 0.396286i | \(0.129701\pi\) | ||||
−0.918127 | + | 0.396286i | \(0.870299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.53964e7i | − 2.54735i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.53476e6 | 0.249437 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.66905e6 | 0.174669 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3.65433e7i | − 1.34001i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.76989e7i | 0.636238i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.53527e7 | −2.30337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.44670e7 | −1.88243 | −0.941214 | − | 0.337811i | \(-0.890314\pi\) | ||||
−0.941214 | + | 0.337811i | \(0.890314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.81391e6i | 0.264846i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.77118e7i | − 0.921262i | −0.887592 | − | 0.460631i | \(-0.847623\pi\) | ||||
0.887592 | − | 0.460631i | \(-0.152377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46046e7 | 1.12850 | 0.564250 | − | 0.825604i | \(-0.309166\pi\) | ||||
0.564250 | + | 0.825604i | \(0.309166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.28691e7 | 0.411733 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7.74888e6i | − 0.243255i | −0.992576 | − | 0.121627i | \(-0.961189\pi\) | ||||
0.992576 | − | 0.121627i | \(-0.0388113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.51799e7i | 0.775679i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.99451e7 | 0.603006 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.83701e7 | −0.841887 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.56381e7i | − 1.91208i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 5.99121e6i | − 0.171345i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.08732e7 | −1.14776 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.63895e7 | 1.00344 | 0.501721 | − | 0.865030i | \(-0.332700\pi\) | ||||
0.501721 | + | 0.865030i | \(0.332700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.95682e6i | − 0.0800742i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 6.26100e7i | − 1.66536i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.72631e7 | 0.712338 | 0.356169 | − | 0.934422i | \(-0.384083\pi\) | ||||
0.356169 | + | 0.934422i | \(0.384083\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.46492e7 | −0.632708 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.18683e7i | − 0.299314i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 4.38507e7i | − 1.08666i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.95331e6 | 0.120625 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.13891e6 | 0.170861 | 0.0854306 | − | 0.996344i | \(-0.472773\pi\) | ||||
0.0854306 | + | 0.996344i | \(0.472773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.72416e7i | − 1.11134i | −0.831402 | − | 0.555671i | \(-0.812461\pi\) | ||||
0.831402 | − | 0.555671i | \(-0.187539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.09094e7i | 0.252279i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.46933e7 | 0.334039 | 0.167019 | − | 0.985954i | \(-0.446586\pi\) | ||||
0.167019 | + | 0.985954i | \(0.446586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.24452e7 | −1.84281 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.22064e7i | 0.268276i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 7.67789e7i | − 1.65943i | −0.558189 | − | 0.829714i | \(-0.688503\pi\) | ||||
0.558189 | − | 0.829714i | \(-0.311497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.87894e7 | 1.03706 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.87761e7 | 0.392541 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.23135e8i | 2.53222i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.02395e7i | − 0.611754i | −0.952071 | − | 0.305877i | \(-0.901050\pi\) | ||||
0.952071 | − | 0.305877i | \(-0.0989496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.55333e6 | 0.0906255 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.89726e7 | 0.763198 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.98541e7i | 1.53876i | 0.638791 | + | 0.769380i | \(0.279435\pi\) | ||||
−0.638791 | + | 0.769380i | \(0.720565\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 2.18945e7i | − 0.415186i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.20365e7 | −0.784517 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.61074e7 | 0.479563 | 0.239781 | − | 0.970827i | \(-0.422924\pi\) | ||||
0.239781 | + | 0.970827i | \(0.422924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.26937e7i | 1.13357i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.22550e7i | 0.218131i | 0.994035 | + | 0.109066i | \(0.0347859\pi\) | ||||
−0.994035 | + | 0.109066i | \(0.965214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.13611e7 | 1.60095 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.28646e7 | 0.567017 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.25279e6i | 0.0382712i | 0.999817 | + | 0.0191356i | \(0.00609141\pi\) | ||||
−0.999817 | + | 0.0191356i | \(0.993909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.69824e6i | 0.0785967i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.57875e7 | 0.260098 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.72081e7 | 0.928253 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.03690e8i | − 1.65716i | −0.559873 | − | 0.828578i | \(-0.689150\pi\) | ||||
0.559873 | − | 0.828578i | \(-0.310850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 4.12336e7i | − 0.649131i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.15940e8 | −1.79805 | −0.899023 | − | 0.437901i | \(-0.855722\pi\) | ||||
−0.899023 | + | 0.437901i | \(0.855722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.98136e7 | 0.302724 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.15736e7i | 0.174222i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.09913e7i | − 0.311355i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.81538e7 | −0.557658 | −0.278829 | − | 0.960341i | \(-0.589946\pi\) | ||||
−0.278829 | + | 0.960341i | \(0.589946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.57590e7 | 0.515062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.01536e7i | 1.27977i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 6.99754e7i | − 0.979041i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 242028. | 0.00333778 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.37135e6 | −0.0730199 | −0.0365099 | − | 0.999333i | \(-0.511624\pi\) | ||||
−0.0365099 | + | 0.999333i | \(0.511624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7.40412e7i | − 0.992264i | −0.868247 | − | 0.496132i | \(-0.834753\pi\) | ||||
0.868247 | − | 0.496132i | \(-0.165247\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3.67587e7i | − 0.485668i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.60483e7 | 0.860389 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.00933e7 | 1.15720 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.74490e7i | 0.980943i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.81463e7i | − 0.226651i | −0.993558 | − | 0.113325i | \(-0.963850\pi\) | ||||
0.993558 | − | 0.113325i | \(-0.0361502\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.56953e8 | −1.93333 | −0.966665 | − | 0.256046i | \(-0.917580\pi\) | ||||
−0.966665 | + | 0.256046i | \(0.917580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.45957e7 | −0.541783 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.58708e7i | − 0.190176i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 6.59653e7i | − 0.779691i | −0.920880 | − | 0.389845i | \(-0.872528\pi\) | ||||
0.920880 | − | 0.389845i | \(-0.127472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.08478e7 | 0.126481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.07019e8 | 1.23098 | 0.615489 | − | 0.788145i | \(-0.288958\pi\) | ||||
0.615489 | + | 0.788145i | \(0.288958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.69515e8i | − 3.05846i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.63485e7i | − 0.518936i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.53200e7 | −0.500669 | −0.250335 | − | 0.968159i | \(-0.580541\pi\) | ||||
−0.250335 | + | 0.968159i | \(0.580541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.23253e7 | 0.352382 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.76378e7i | 0.942751i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.52522e8i | 1.61920i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.38273e6 | −0.0249647 | −0.0124824 | − | 0.999922i | \(-0.503973\pi\) | ||||
−0.0124824 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.09776e7 | −0.113519 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.20106e7i | 0.122591i | 0.998120 | + | 0.0612957i | \(0.0195233\pi\) | ||||
−0.998120 | + | 0.0612957i | \(0.980477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.28538e6i | 0.0935528i | 0.998905 | + | 0.0467764i | \(0.0148948\pi\) | ||||
−0.998905 | + | 0.0467764i | \(0.985105\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.10198e7 | 0.209060 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.33286e8 | −1.30868 | −0.654341 | − | 0.756199i | \(-0.727054\pi\) | ||||
−0.654341 | + | 0.756199i | \(0.727054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.63123e7i | 0.836670i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.23067e7i | 0.787721i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.33315e8 | 2.20475 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.23114e8 | −2.08183 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.50493e7i | 0.322942i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.64790e7i | 0.604892i | 0.953166 | + | 0.302446i | \(0.0978033\pi\) | ||||
−0.953166 | + | 0.302446i | \(0.902197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.50438e7 | 0.314903 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.82849e6 | −0.0606015 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.59832e7i | 0.841337i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.25653e8i | 1.08789i | 0.839121 | + | 0.543945i | \(0.183070\pi\) | ||||
−0.839121 | + | 0.543945i | \(0.816930\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.07588e8 | −0.920103 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.89229e8 | −1.59861 | −0.799304 | − | 0.600927i | \(-0.794798\pi\) | ||||
−0.799304 | + | 0.600927i | \(0.794798\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.22992e7i | − 0.353014i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.21641e7i | 0.677434i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.13657e8 | 0.925818 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.09389e7 | 0.0880385 | 0.0440193 | − | 0.999031i | \(-0.485984\pi\) | ||||
0.0440193 | + | 0.999031i | \(0.485984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 7.36659e7i | − 0.585806i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.12787e8i | − 0.886247i | −0.896460 | − | 0.443124i | \(-0.853870\pi\) | ||||
0.896460 | − | 0.443124i | \(-0.146130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.22536e8 | −1.72793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.40544e7 | −0.414770 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.40530e7i | 0.334058i | 0.985952 | + | 0.167029i | \(0.0534173\pi\) | ||||
−0.985952 | + | 0.167029i | \(0.946583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1.69750e8i | − 1.27217i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.70828e7 | 0.274676 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.82474e7 | −0.719283 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.60960e8i | − 1.88844i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.56943e7i | 0.612985i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.54449e8 | 1.09213 | 0.546063 | − | 0.837744i | \(-0.316126\pi\) | ||||
0.546063 | + | 0.837744i | \(0.316126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.91307e6 | 0.0692952 | 0.0346476 | − | 0.999400i | \(-0.488969\pi\) | ||||
0.0346476 | + | 0.999400i | \(0.488969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.59957e7i | 0.663398i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.99374e7i | 0.136219i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.45408e8 | 0.982246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.10782e7 | −0.541528 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.39654e7i | 0.356397i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.50778e8i | 1.63768i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.42531e8 | −0.920418 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.70112e7 | 0.491799 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 1.41127e8i | − 0.891287i | −0.895211 | − | 0.445644i | \(-0.852975\pi\) | ||||
0.895211 | − | 0.445644i | \(-0.147025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.35876e8i | − 0.848680i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.53299e7 | 0.465348 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.92266e8 | 1.78573 | 0.892865 | − | 0.450324i | \(-0.148692\pi\) | ||||
0.892865 | + | 0.450324i | \(0.148692\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.10240e7i | 0.489662i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.42888e8i | 0.854165i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.88655e7 | −0.466350 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.71773e7 | 0.217470 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6.89434e7i | − 0.398958i | −0.979902 | − | 0.199479i | \(-0.936075\pi\) | ||||
0.979902 | − | 0.199479i | \(-0.0639249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.89507e8i | 2.22987i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.79330e7 | −0.441401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.26589e7 | 0.407159 | 0.203579 | − | 0.979058i | \(-0.434743\pi\) | ||||
0.203579 | + | 0.979058i | \(0.434743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.09924e8i | − 1.71834i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.59550e7i | − 0.0875283i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.16272e8 | −0.631161 | −0.315581 | − | 0.948899i | \(-0.602199\pi\) | ||||
−0.315581 | + | 0.948899i | \(0.602199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.62675e7 | 0.409667 | 0.204834 | − | 0.978797i | \(-0.434335\pi\) | ||||
0.204834 | + | 0.978797i | \(0.434335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.29754e8i | 0.689696i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.69488e7i | 0.194355i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.84696e6 | −0.0200258 | −0.0100129 | − | 0.999950i | \(-0.503187\pi\) | ||||
−0.0100129 | + | 0.999950i | \(0.503187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.29738e7 | 0.324433 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.64660e7i | 0.491865i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.48825e8i | 1.25571i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.37169e8 | −0.685152 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.80286e8 | 0.891348 | 0.445674 | − | 0.895195i | \(-0.352964\pi\) | ||||
0.445674 | + | 0.895195i | \(0.352964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.73492e7i | − 0.329600i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.98908e8i | 0.963583i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.58548e7 | 0.123987 | 0.0619936 | − | 0.998077i | \(-0.480254\pi\) | ||||
0.0619936 | + | 0.998077i | \(0.480254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.53476e8 | −0.728599 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.50268e7i | − 0.0706226i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.37569e8i | − 0.640088i | −0.947403 | − | 0.320044i | \(-0.896302\pi\) | ||||
0.947403 | − | 0.320044i | \(-0.103698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.09688e8 | 1.42659 | 0.713297 | − | 0.700862i | \(-0.247201\pi\) | ||||
0.713297 | + | 0.700862i | \(0.247201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.76236e7 | −0.354031 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.36079e8i | 1.06609i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.21384e8i | 0.989875i | 0.868929 | + | 0.494937i | \(0.164809\pi\) | ||||
−0.868929 | + | 0.494937i | \(0.835191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.14784e7 | 0.272189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.35659e8 | 1.90995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.15371e8i | − 1.36912i | −0.728957 | − | 0.684559i | \(-0.759995\pi\) | ||||
0.728957 | − | 0.684559i | \(-0.240005\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.72509e7i | 0.246126i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.80709e7 | −0.119509 | −0.0597546 | − | 0.998213i | \(-0.519032\pi\) | ||||
−0.0597546 | + | 0.998213i | \(0.519032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.78560e7 | 0.0752855 | 0.0376427 | − | 0.999291i | \(-0.488015\pi\) | ||||
0.0376427 | + | 0.999291i | \(0.488015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 6.14110e6i | − 0.0256431i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.71545e8i | 1.53655i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.08203e7 | −0.331040 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.63261e8 | 1.06803 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.52629e7i | 0.141699i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 4.60375e8i | − 1.83241i | −0.400706 | − | 0.916207i | \(-0.631235\pi\) | ||||
0.400706 | − | 0.916207i | \(-0.368765\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.32587e7 | 0.288834 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.88273e8 | −3.07862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.28566e8i | 0.497403i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.02215e8i | 0.391754i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.39176e8 | −1.66750 | −0.833748 | − | 0.552145i | \(-0.813810\pi\) | ||||
−0.833748 | + | 0.552145i | \(0.813810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.13354e8 | 0.426387 | 0.213194 | − | 0.977010i | \(-0.431613\pi\) | ||||
0.213194 | + | 0.977010i | \(0.431613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.13221e8i | 1.53994i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.52127e8i | 1.30013i | 0.759879 | + | 0.650064i | \(0.225258\pi\) | ||||
−0.759879 | + | 0.650064i | \(0.774742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.75596e8 | −2.10564 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.89773e7 | −0.105030 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.37871e8i | − 1.21342i | −0.794923 | − | 0.606711i | \(-0.792489\pi\) | ||||
0.794923 | − | 0.606711i | \(-0.207511\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.98503e8i | 0.706389i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.52662e8 | 0.538312 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.27619e8 | 1.49417 | 0.747086 | − | 0.664727i | \(-0.231452\pi\) | ||||
0.747086 | + | 0.664727i | \(0.231452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.35404e8i | 1.50761i | 0.657100 | + | 0.753803i | \(0.271783\pi\) | ||||
−0.657100 | + | 0.753803i | \(0.728217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.30105e8i | − 0.446430i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.18447e8 | 1.76295 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.36630e7 | 0.0797430 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.11153e8i | − 0.371230i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.75211e8i | 1.90397i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.20237e8 | 1.70669 | 0.853347 | − | 0.521343i | \(-0.174569\pi\) | ||||
0.853347 | + | 0.521343i | \(0.174569\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.63322e7 | −0.280712 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.23676e8i | 1.68771i | 0.536574 | + | 0.843853i | \(0.319718\pi\) | ||||
−0.536574 | + | 0.843853i | \(0.680282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.32320e8i | − 0.422683i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.64821e7 | 0.0838517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.29151e7 | 0.0719216 | 0.0359608 | − | 0.999353i | \(-0.488551\pi\) | ||||
0.0359608 | + | 0.999353i | \(0.488551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.49612e8i | 1.39883i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1.87705e8i | − 0.578903i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.15400e8 | −1.27001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.31509e8 | −1.00476 | −0.502379 | − | 0.864647i | \(-0.667542\pi\) | ||||
−0.502379 | + | 0.864647i | \(0.667542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.13269e8i | − 0.340339i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.04312e6i | 0.00906492i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.43027e7 | −0.160370 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.01154e7 | 0.117457 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.52665e8i | 1.02378i | 0.859050 | + | 0.511891i | \(0.171055\pi\) | ||||
−0.859050 | + | 0.511891i | \(0.828945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.19119e8i | − 0.342859i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.62182e8 | 1.31900 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.06782e8 | 0.868103 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6.26217e8i | − 1.75706i | −0.477688 | − | 0.878530i | \(-0.658525\pi\) | ||||
0.477688 | − | 0.878530i | \(-0.341475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 7.09264e7i | − 0.197333i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.11534e7 | −0.0307707 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.73797e8 | −2.66410 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.68840e8i | − 0.729350i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.63123e8i | − 0.976937i | −0.872581 | − | 0.488469i | \(-0.837556\pi\) | ||||
0.872581 | − | 0.488469i | \(-0.162444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.35441e8 | 0.361364 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.15335e7 | 0.0834369 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.32657e8i | − 0.872938i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.63836e8i | 0.946897i | 0.880821 | + | 0.473449i | \(0.156991\pi\) | ||||
−0.880821 | + | 0.473449i | \(0.843009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.91941e8 | −1.00339 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.50829e8i | − 1.39864i | −0.714811 | − | 0.699318i | \(-0.753487\pi\) | ||||
0.714811 | − | 0.699318i | \(-0.246513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.36393e8i | 0.343503i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.51071e8 | −1.37659 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.89298e8 | 0.716823 | 0.358412 | − | 0.933564i | \(-0.383318\pi\) | ||||
0.358412 | + | 0.933564i | \(0.383318\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.39500e8i | 1.08020i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00629e7i | 0.219573i | 0.993955 | + | 0.109787i | \(0.0350167\pi\) | ||||
−0.993955 | + | 0.109787i | \(0.964983\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.82759e8 | 1.40935 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.67552e7 | −0.208130 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.45715e8i | − 0.822760i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 5.56903e8i | − 1.31480i | −0.753542 | − | 0.657400i | \(-0.771656\pi\) | ||||
0.753542 | − | 0.657400i | \(-0.228344\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.05648e8 | 0.950089 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.10191e9 | −2.56037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.67647e8i | − 0.386463i | −0.981153 | − | 0.193232i | \(-0.938103\pi\) | ||||
0.981153 | − | 0.193232i | \(-0.0618969\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 4.35973e7i | − 0.0997090i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.51246e6 | −0.0170462 | −0.00852311 | − | 0.999964i | \(-0.502713\pi\) | ||||
−0.00852311 | + | 0.999964i | \(0.502713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.03848e8 | −0.233788 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.38026e8i | − 0.308302i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 9.60927e8i | − 2.12963i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.93147e8 | −0.424727 | −0.212364 | − | 0.977191i | \(-0.568116\pi\) | ||||
−0.212364 | + | 0.977191i | \(0.568116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.86760e8 | 0.407494 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.25486e8i | 0.271679i | 0.990731 | + | 0.135839i | \(0.0433731\pi\) | ||||
−0.990731 | + | 0.135839i | \(0.956627\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.56795e8i | 0.336843i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.12516e7 | −0.109256 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.83437e8 | 0.388037 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.25654e8i | 1.52327i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.52896e7i | 0.115175i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.03488e9 | −2.13934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.71718e8 | 1.17289 | 0.586445 | − | 0.809989i | \(-0.300527\pi\) | ||||
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 5.53573e7i | − 0.112705i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.27253e8i | 0.863287i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.60284e8 | −1.92566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.40690e8 | −0.877064 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.13512e8i | 0.816796i | 0.912804 | + | 0.408398i | \(0.133912\pi\) | ||||
−0.912804 | + | 0.408398i | \(0.866088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.38382e8i | 0.859433i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.34143e8 | −0.650182 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.08379e9 | 2.09314 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.58574e7i | − 0.164585i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 8.34496e7i | − 0.158783i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.21028e8 | 0.795180 | 0.397590 | − | 0.917563i | \(-0.369847\pi\) | ||||
0.397590 | + | 0.917563i | \(0.369847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.42556e7 | 0.101714 | 0.0508572 | − | 0.998706i | \(-0.483805\pi\) | ||||
0.0508572 | + | 0.998706i | \(0.483805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.47065e8i | − 0.459768i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1.35274e9i | − 2.49887i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.32399e9 | 2.42784 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.89097e8 | 0.344217 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.90848e8i | − 0.525578i | −0.964853 | − | 0.262789i | \(-0.915358\pi\) | ||||
0.964853 | − | 0.262789i | \(-0.0846423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.58287e8i | − 0.642734i | −0.946955 | − | 0.321367i | \(-0.895858\pi\) | ||||
0.946955 | − | 0.321367i | \(-0.104142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.12896e8 | −1.09150 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.49604e8 | 0.971702 | 0.485851 | − | 0.874042i | \(-0.338510\pi\) | ||||
0.485851 | + | 0.874042i | \(0.338510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.91879e8i | 0.336794i | 0.985719 | + | 0.168397i | \(0.0538591\pi\) | ||||
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 3.57297e8i | − 0.622625i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.29370e8 | −0.223819 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.26232e8 | 1.59096 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.60603e7i | − 0.0444430i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 8.59129e8i | − 1.45470i | −0.686269 | − | 0.727348i | \(-0.740753\pi\) | ||||
0.686269 | − | 0.727348i | \(-0.259247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.81780e8 | 0.641838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.15998e8 | 0.527475 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6.79648e8i | − 1.12645i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.25452e8i | − 0.535596i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.68923e8 | 0.276036 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.97268e7 | −0.0320086 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.92564e8i | 1.27699i | 0.769626 | + | 0.638495i | \(0.220442\pi\) | ||||
−0.769626 | + | 0.638495i | \(0.779558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.66257e8i | 0.745979i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.82625e8 | 0.449022 | 0.224511 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224511 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.51038e8 | 0.711596 | 0.355798 | − | 0.934563i | \(-0.384209\pi\) | ||||
0.355798 | + | 0.934563i | \(0.384209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 7.89245e7i | − 0.123652i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.56438e8i | 0.865734i | 0.901458 | + | 0.432867i | \(0.142498\pi\) | ||||
−0.901458 | + | 0.432867i | \(0.857502\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.07747e9 | −1.66478 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.45349e8 | −0.376468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5.03526e8i | − 0.767295i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 9.19983e8i | − 1.39228i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.19000e8 | 0.178856 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.79506e8 | −0.566492 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.73043e8i | 0.701296i | 0.936507 | + | 0.350648i | \(0.114039\pi\) | ||||
−0.936507 | + | 0.350648i | \(0.885961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.10774e8i | 0.457592i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.82594e8 | 0.413271 | 0.206636 | − | 0.978418i | \(-0.433749\pi\) | ||||
0.206636 | + | 0.978418i | \(0.433749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.66922e8 | 0.242454 | 0.121227 | − | 0.992625i | \(-0.461317\pi\) | ||||
0.121227 | + | 0.992625i | \(0.461317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.01943e9i | − 1.47071i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 5.01664e8i | − 0.718857i | −0.933173 | − | 0.359428i | \(-0.882972\pi\) | ||||
0.933173 | − | 0.359428i | \(-0.117028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.08669e9 | 1.54668 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.01867e8 | 0.144012 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.48087e9i | − 2.07952i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.79209e9i | − 2.49972i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.27834e7 | 0.100845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.00416e8 | 0.138205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 4.17996e8i | − 0.571476i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.69654e8i | − 0.773656i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.70843e9 | 2.30489 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11909.6 | −1.59615e−5 0 | −7.98077e−6 | − | 1.00000i | \(-0.500003\pi\) | ||||
−7.98077e−6 | 1.00000i | \(0.500003\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.75899e8i | 0.367332i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.13710e8i | 0.414929i | 0.978243 | + | 0.207464i | \(0.0665211\pi\) | ||||
−0.978243 | + | 0.207464i | \(0.933479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.15899e8 | −0.809276 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.01875e9 | −1.32985 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.73651e8i | − 0.354886i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.77960e8i | 0.229285i | 0.993407 | + | 0.114642i | \(0.0365722\pi\) | ||||
−0.993407 | + | 0.114642i | \(0.963428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.49057e8 | −1.08682 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.21144e9 | −1.54062 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77321e8i | 0.350395i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21807e8i | 0.152909i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.99728e8 | −0.249110 | −0.124555 | − | 0.992213i | \(-0.539750\pi\) | ||||
−0.124555 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.37015e8 | 0.541561 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 4.31984e8i | − 0.531891i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 9.79883e8i | − 1.19878i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.50949e9 | −1.83490 | −0.917450 | − | 0.397852i | \(-0.869756\pi\) | ||||
−0.917450 | + | 0.397852i | \(0.869756\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.39433e8 | 0.651539 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.62445e9i | 1.94957i | 0.223150 | + | 0.974784i | \(0.428366\pi\) | ||||
−0.223150 | + | 0.974784i | \(0.571634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 3.03780e7i | − 0.0362264i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00609e8 | 0.237714 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.64857e8 | −0.900597 | −0.450298 | − | 0.892878i | \(-0.648682\pi\) | ||||
−0.450298 | + | 0.892878i | \(0.648682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.80933e9i | 2.11699i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1.20793e8i | − 0.140443i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.12339e9 | 1.29794 | 0.648968 | − | 0.760815i | \(-0.275201\pi\) | ||||
0.648968 | + | 0.760815i | \(0.275201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.63145e9 | −1.87311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.92516e8i | 0.447838i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 6.19822e8i | − 0.702767i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.40173e8 | 0.946670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.10914e8 | 0.348146 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.91796e8i | 0.881112i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 9.82431e8i | − 1.08648i | −0.839577 | − | 0.543241i | \(-0.817197\pi\) | ||||
0.839577 | − | 0.543241i | \(-0.182803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.42246e8 | −0.486063 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.00598e9 | 1.09883 | 0.549414 | − | 0.835550i | \(-0.314851\pi\) | ||||
0.549414 | + | 0.835550i | \(0.314851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.19515e6i | − 0.00455417i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.02320e9i | − 1.10394i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.50555e7 | 0.0161440 | 0.00807199 | − | 0.999967i | \(-0.497431\pi\) | ||||
0.00807199 | + | 0.999967i | \(0.497431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.37217e9 | −2.52812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.33936e7i | − 0.0989260i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.01319e9i | 1.06667i | 0.845905 | + | 0.533333i | \(0.179061\pi\) | ||||
−0.845905 | + | 0.533333i | \(0.820939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.50095e9 | −2.61695 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.37151e8 | −0.662660 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.19260e8i | − 0.226658i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.84753e9i | 1.89832i | 0.314791 | + | 0.949161i | \(0.398066\pi\) | ||||
−0.314791 | + | 0.949161i | \(0.601934\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.67256e8 | 0.579337 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.88938e8 | 0.191801 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.12629e8i | 0.517270i | 0.965975 | + | 0.258635i | \(0.0832727\pi\) | ||||
−0.965975 | + | 0.258635i | \(0.916727\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 4.60923e7i | − 0.0462309i |
(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 | 384.7.b.a.319.4 | yes | 4 | |
4.3 | odd | 2 | inner | 384.7.b.a.319.2 | yes | 4 | |
8.3 | odd | 2 | inner | 384.7.b.a.319.3 | yes | 4 | |
8.5 | even | 2 | inner | 384.7.b.a.319.1 | ✓ | 4 | |
16.3 | odd | 4 | 768.7.g.b.511.1 | 2 | |||
16.5 | even | 4 | 768.7.g.a.511.1 | 2 | |||
16.11 | odd | 4 | 768.7.g.a.511.2 | 2 | |||
16.13 | even | 4 | 768.7.g.b.511.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.a.319.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
384.7.b.a.319.2 | yes | 4 | 4.3 | odd | 2 | inner | |
384.7.b.a.319.3 | yes | 4 | 8.3 | odd | 2 | inner | |
384.7.b.a.319.4 | yes | 4 | 1.1 | even | 1 | trivial | |
768.7.g.a.511.1 | 2 | 16.5 | even | 4 | |||
768.7.g.a.511.2 | 2 | 16.11 | odd | 4 | |||
768.7.g.b.511.1 | 2 | 16.3 | odd | 4 | |||
768.7.g.b.511.2 | 2 | 16.13 | even | 4 |