Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(127,384)]
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, 0, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (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: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.26 | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.9.g.a.127.25 |
$q$-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 | ||||||||
\(3\) | 46.7654i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 795.016 | 1.27203 | 0.636013 | − | 0.771679i | \(-0.280583\pi\) | ||||
0.636013 | + | 0.771679i | \(0.280583\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2625.43i | 1.09347i | 0.837304 | + | 0.546737i | \(0.184130\pi\) | ||||
−0.837304 | + | 0.546737i | \(0.815870\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10097.9i | − 0.689699i | −0.938658 | − | 0.344850i | \(-0.887930\pi\) | ||||
0.938658 | − | 0.344850i | \(-0.112070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11030.0 | −0.386189 | −0.193095 | − | 0.981180i | \(-0.561852\pi\) | ||||
−0.193095 | + | 0.981180i | \(0.561852\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37179.2i | 0.734404i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 59630.3 | 0.713956 | 0.356978 | − | 0.934113i | \(-0.383807\pi\) | ||||
0.356978 | + | 0.934113i | \(0.383807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 135471.i | 1.03952i | 0.854312 | + | 0.519761i | \(0.173979\pi\) | ||||
−0.854312 | + | 0.519761i | \(0.826021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −122779. | −0.631318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 139801.i | − 0.499572i | −0.968301 | − | 0.249786i | \(-0.919640\pi\) | ||||
0.968301 | − | 0.249786i | \(-0.0803602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 241425. | 0.618049 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 102276.i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −621971. | −0.879383 | −0.439691 | − | 0.898149i | \(-0.644912\pi\) | ||||
−0.439691 | + | 0.898149i | \(0.644912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 334997.i | − 0.362739i | −0.983415 | − | 0.181370i | \(-0.941947\pi\) | ||||
0.983415 | − | 0.181370i | \(-0.0580530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 472231. | 0.398198 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.08726e6i | 1.39093i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −298771. | −0.159416 | −0.0797079 | − | 0.996818i | \(-0.525399\pi\) | ||||
−0.0797079 | + | 0.996818i | \(0.525399\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 515820.i | − 0.222967i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.49508e6 | −1.59075 | −0.795375 | − | 0.606117i | \(-0.792726\pi\) | ||||
−0.795375 | + | 0.606117i | \(0.792726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.61305e6i | 1.34932i | 0.738129 | + | 0.674660i | \(0.235710\pi\) | ||||
−0.738129 | + | 0.674660i | \(0.764290\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.73870e6 | −0.424008 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.76388e6i | 1.18120i | 0.806964 | + | 0.590600i | \(0.201109\pi\) | ||||
−0.806964 | + | 0.590600i | \(0.798891\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.12809e6 | −0.195686 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.78863e6i | 0.412203i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06426e7 | −1.34879 | −0.674393 | − | 0.738373i | \(-0.735595\pi\) | ||||
−0.674393 | + | 0.738373i | \(0.735595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 8.02798e6i | − 0.877315i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.33537e6 | −0.600168 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.68703e6i | 0.634381i | 0.948362 | + | 0.317191i | \(0.102739\pi\) | ||||
−0.948362 | + | 0.317191i | \(0.897261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82864e6 | 0.637639 | 0.318819 | − | 0.947816i | \(-0.396714\pi\) | ||||
0.318819 | + | 0.947816i | \(0.396714\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 5.74182e6i | − 0.364491i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.76899e6 | −0.491243 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.01447e7i | − 0.999680i | −0.866118 | − | 0.499840i | \(-0.833392\pi\) | ||||
0.866118 | − | 0.499840i | \(-0.166608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.53783e6 | 0.288428 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.28859e7i | − 0.507088i | −0.967324 | − | 0.253544i | \(-0.918404\pi\) | ||||
0.967324 | − | 0.253544i | \(-0.0815962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.72924e7 | −0.961060 | −0.480530 | − | 0.876978i | \(-0.659556\pi\) | ||||
−0.480530 | + | 0.876978i | \(0.659556\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.12903e7i | 0.356831i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.65113e7 | 0.754169 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.34620e7i | 0.859100i | 0.903043 | + | 0.429550i | \(0.141328\pi\) | ||||
−0.903043 | + | 0.429550i | \(0.858672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.64077e6i | − 0.0767152i | −0.999264 | − | 0.0383576i | \(-0.987787\pi\) | ||||
0.999264 | − | 0.0383576i | \(-0.0122126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.74070e7 | 0.908170 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.90867e7i | − 0.507712i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.49677e7 | −0.397941 | −0.198970 | − | 0.980006i | \(-0.563760\pi\) | ||||
−0.198970 | + | 0.980006i | \(0.563760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.89584e7i | − 0.422288i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.56663e7 | 0.209427 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.07702e8i | 1.32230i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99172e7 | 0.789763 | 0.394882 | − | 0.918732i | \(-0.370786\pi\) | ||||
0.394882 | + | 0.918732i | \(0.370786\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.20841e7i | 0.229900i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.54036e8 | −1.48026 | −0.740129 | − | 0.672464i | \(-0.765236\pi\) | ||||
−0.740129 | + | 0.672464i | \(0.765236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.81464e8i | 1.61228i | 0.591723 | + | 0.806141i | \(0.298448\pi\) | ||||
−0.591723 | + | 0.806141i | \(0.701552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.76115e7 | −0.803052 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.04547e7i | 0.537496i | 0.963211 | + | 0.268748i | \(0.0866098\pi\) | ||||
−0.963211 | + | 0.268748i | \(0.913390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.56300e8 | 1.81569 | 0.907847 | − | 0.419301i | \(-0.137725\pi\) | ||||
0.907847 | + | 0.419301i | \(0.137725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.39721e7i | − 0.0920387i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31677e8 | 1.42092 | 0.710459 | − | 0.703739i | \(-0.248488\pi\) | ||||
0.710459 | + | 0.703739i | \(0.248488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.11144e8i | − 0.635468i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.41225e7 | 0.128730 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.56555e8i | 0.780692i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.12392e8 | 0.524315 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.10214e8i | − 0.918420i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.18616e8 | −0.485852 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.08884e8i | 0.418550i | 0.977857 | + | 0.209275i | \(0.0671104\pi\) | ||||
−0.977857 | + | 0.209275i | \(0.932890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.15731e8 | −0.779030 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.97482e8i | 1.34969i | 0.737961 | + | 0.674843i | \(0.235789\pi\) | ||||
−0.737961 | + | 0.674843i | \(0.764211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.55671e8 | −1.13669 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 8.13109e7i | − 0.244801i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.96120e8 | −0.840592 | −0.420296 | − | 0.907387i | \(-0.638074\pi\) | ||||
−0.420296 | + | 0.907387i | \(0.638074\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.70397e8i | − 1.52798i | −0.645227 | − | 0.763991i | \(-0.723237\pi\) | ||||
0.645227 | − | 0.763991i | \(-0.276763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.69550e8 | −0.681966 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.11379e8i | 0.266355i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.94476e8 | −1.11860 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 5.27556e7i | − 0.112979i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.90505e8 | −0.792284 | −0.396142 | − | 0.918189i | \(-0.629651\pi\) | ||||
−0.396142 | + | 0.918189i | \(0.629651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 8.29215e8i | − 1.59500i | −0.603322 | − | 0.797498i | \(-0.706157\pi\) | ||||
0.603322 | − | 0.797498i | \(-0.293843\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.30411e8 | −0.237985 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.66328e8i | − 0.461413i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.15092e8 | −0.683197 | −0.341599 | − | 0.939846i | \(-0.610968\pi\) | ||||
−0.341599 | + | 0.939846i | \(0.610968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 4.97704e8i | − 0.778722i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.67037e8 | 0.546269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.74012e7i | − 0.0813150i | −0.999173 | − | 0.0406575i | \(-0.987055\pi\) | ||||
0.999173 | − | 0.0406575i | \(-0.0129453\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.75432e8 | 0.506518 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.10763e8i | 0.142407i | 0.997462 | + | 0.0712033i | \(0.0226839\pi\) | ||||
−0.997462 | + | 0.0712033i | \(0.977316\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.94071e8 | −0.850858 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.96276e8i | − 0.346507i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.35188e9 | −1.50922 | −0.754612 | − | 0.656171i | \(-0.772175\pi\) | ||||
−0.754612 | + | 0.656171i | \(0.772175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.33846e8i | 0.675820i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.59487e8 | −0.366260 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.03426e8i | 0.198150i | 0.995080 | + | 0.0990750i | \(0.0315884\pi\) | ||||
−0.995080 | + | 0.0990750i | \(0.968412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.31026e8 | 0.681112 | 0.340556 | − | 0.940224i | \(-0.389385\pi\) | ||||
0.340556 | + | 0.940224i | \(0.389385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.12875e8i | 0.368141i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.37528e8 | −0.202781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.02140e8i | − 0.492415i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.68518e8 | 0.210439 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.41990e8i | 0.632665i | 0.948648 | + | 0.316332i | \(0.102451\pi\) | ||||
−0.948648 | + | 0.316332i | \(0.897549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.63204e9 | −1.89698 | −0.948489 | − | 0.316809i | \(-0.897389\pi\) | ||||
−0.948489 | + | 0.316809i | \(0.897389\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 4.10085e8i | − 0.283619i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.48020e9 | −0.982780 | −0.491390 | − | 0.870940i | \(-0.663511\pi\) | ||||
−0.491390 | + | 0.870940i | \(0.663511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.37124e8i | − 0.0874381i | −0.999044 | − | 0.0437191i | \(-0.986079\pi\) | ||||
0.999044 | − | 0.0437191i | \(-0.0139206\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.42073e8 | 0.577166 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.63294e9i | − 0.961582i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.57366e9 | −2.02347 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.05744e8i | 0.166524i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.36798e9 | 0.716957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.83419e9i | − 1.42988i | −0.699186 | − | 0.714940i | \(-0.746454\pi\) | ||||
0.699186 | − | 0.714940i | \(-0.253546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.02616e8 | 0.292767 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.66745e9i | 1.71637i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79512e8 | 0.396646 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.27634e9i | − 0.554868i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.57720e8 | −0.275722 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.95932e9i | 1.19666i | 0.801249 | + | 0.598331i | \(0.204169\pi\) | ||||
−0.801249 | + | 0.598331i | \(0.795831\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.27997e8 | −0.206016 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.76691e9i | − 1.04206i | −0.853539 | − | 0.521029i | \(-0.825549\pi\) | ||||
0.853539 | − | 0.521029i | \(-0.174451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.33542e8 | 0.0485597 | 0.0242798 | − | 0.999705i | \(-0.492271\pi\) | ||||
0.0242798 | + | 0.999705i | \(0.492271\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.23981e9i | 0.435419i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.60887e9 | −0.545879 | −0.272939 | − | 0.962031i | \(-0.587996\pi\) | ||||
−0.272939 | + | 0.962031i | \(0.587996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.58238e9i | 1.50252i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.56486e9 | −0.496002 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.98543e9i | 1.52796i | 0.645241 | + | 0.763979i | \(0.276757\pi\) | ||||
−0.645241 | + | 0.763979i | \(0.723243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11322e8 | 0.240506 | 0.120253 | − | 0.992743i | \(-0.461629\pi\) | ||||
0.120253 | + | 0.992743i | \(0.461629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.96851e8 | −0.248918 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.49424e9i | − 0.401452i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.70262e8 | 0.0442915 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.10021e9i | − 1.53692i | −0.639901 | − | 0.768458i | \(-0.721025\pi\) | ||||
0.639901 | − | 0.768458i | \(-0.278975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41169e9 | −0.344554 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.21701e9i | 0.524332i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.64150e9 | −1.75164 | −0.875822 | − | 0.482634i | \(-0.839680\pi\) | ||||
−0.875822 | + | 0.482634i | \(0.839680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.84402e8i | − 0.174317i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.36025e9 | 0.293128 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4.62801e7i | − 0.00967323i | −0.999988 | − | 0.00483662i | \(-0.998460\pi\) | ||||
0.999988 | − | 0.00483662i | \(-0.00153955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.46101e9 | −1.71569 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.16762e9i | − 0.229751i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.33628e9 | 1.21011 | 0.605056 | − | 0.796183i | \(-0.293151\pi\) | ||||
0.605056 | + | 0.796183i | \(0.293151\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.57083e9i | 1.58908i | 0.607212 | + | 0.794540i | \(0.292288\pi\) | ||||
−0.607212 | + | 0.794540i | \(0.707712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.35425e9 | 0.243808 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.43789e9i | − 0.426268i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.18594e8 | −0.0541152 | −0.0270576 | − | 0.999634i | \(-0.508614\pi\) | ||||
−0.0270576 | + | 0.999634i | \(0.508614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.32639e8i | 0.120913i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.19967e10 | −1.92414 | −0.962070 | − | 0.272801i | \(-0.912050\pi\) | ||||
−0.962070 | + | 0.272801i | \(0.912050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.24269e9i | − 0.349643i | −0.984600 | − | 0.174821i | \(-0.944065\pi\) | ||||
0.984600 | − | 0.174821i | \(-0.0559348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.03672e9 | −0.763429 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.18015e10i | − 1.73944i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.41998e9 | −0.490267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.26970e9i | 0.455970i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.22665e9 | −0.166438 | −0.0832189 | − | 0.996531i | \(-0.526520\pi\) | ||||
−0.0832189 | + | 0.996531i | \(0.526520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.11131e9i | 0.806949i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.03277e9 | −0.132733 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.54200e9i | 0.192929i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.21113e10 | −1.47545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 7.20357e9i | − 0.854628i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.01891e9 | 0.811092 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.12906e10i | − 1.27105i | −0.772080 | − | 0.635526i | \(-0.780783\pi\) | ||||
0.772080 | − | 0.635526i | \(-0.219217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.48622e9 | −0.930852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.88837e9i | 0.522544i | 0.965265 | + | 0.261272i | \(0.0841419\pi\) | ||||
−0.965265 | + | 0.261272i | \(0.915858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.11505e10 | −1.16176 | −0.580880 | − | 0.813989i | \(-0.697292\pi\) | ||||
−0.580880 | + | 0.813989i | \(0.697292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.56484e9i | − 0.463642i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.34931e9 | −0.925854 | −0.462927 | − | 0.886396i | \(-0.653201\pi\) | ||||
−0.462927 | + | 0.886396i | \(0.653201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.28059e9i | 0.606510i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.29484e9 | −0.310323 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.07820e9i | 0.742172i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.66291e9 | −0.238684 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.19860e10i | 1.04829i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.51327e10 | −1.29161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66134e10i | 1.38404i | 0.721881 | + | 0.692018i | \(0.243278\pi\) | ||||
−0.721881 | + | 0.692018i | \(0.756722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.53412e8 | 0.0531386 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.60153e10i | − 1.27162i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.93404e10 | 1.49950 | 0.749749 | − | 0.661722i | \(-0.230174\pi\) | ||||
0.749749 | + | 0.661722i | \(0.230174\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.08345e10i | 0.820367i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.38276e9 | −0.250181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.21734e10i | 0.879497i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.19768e9 | 0.366888 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.33924e10i | − 1.61346i | −0.590923 | − | 0.806728i | \(-0.701236\pi\) | ||||
0.590923 | − | 0.806728i | \(-0.298764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.26158e9 | 0.556880 | 0.278440 | − | 0.960454i | \(-0.410183\pi\) | ||||
0.278440 | + | 0.960454i | \(0.410183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.12810e9i | 0.0743222i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.37397e9 | 0.346096 | 0.173048 | − | 0.984913i | \(-0.444638\pi\) | ||||
0.173048 | + | 0.984913i | \(0.444638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.02445e10i | − 0.645028i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.32137e9 | −0.450733 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 1.94858e9i | − 0.117312i | −0.998278 | − | 0.0586559i | \(-0.981319\pi\) | ||||
0.998278 | − | 0.0586559i | \(-0.0186815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36895e9 | −0.0806043 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.25603e9i | 0.302713i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.16979e10 | −1.22249 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.05117e10i | 0.579442i | 0.957111 | + | 0.289721i | \(0.0935626\pi\) | ||||
−0.957111 | + | 0.289721i | \(0.906437\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.83074e9 | 0.530250 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.79413e10i | − 1.47486i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.52843e10 | 0.789606 | 0.394803 | − | 0.918766i | \(-0.370813\pi\) | ||||
0.394803 | + | 0.918766i | \(0.370813\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 5.54713e9i | − 0.280507i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.86031e9 | 0.339608 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 9.70465e9i | − 0.470352i | −0.971953 | − | 0.235176i | \(-0.924433\pi\) | ||||
0.971953 | − | 0.235176i | \(-0.0755667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.09198e9 | −0.241650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.56132e10i | 0.725599i | 0.931867 | + | 0.362800i | \(0.118179\pi\) | ||||
−0.931867 | + | 0.362800i | \(0.881821\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.10769e10 | 0.959322 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.00887e10i | − 0.449773i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.20022e10 | 1.83432 | 0.917158 | − | 0.398525i | \(-0.130478\pi\) | ||||
0.917158 | + | 0.398525i | \(0.130478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 8.33636e9i | − 0.356672i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.85884e10 | −0.779242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.66028e10i | 1.09280i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.82342e10 | 0.734047 | 0.367024 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367024 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 1.66331e10i | − 0.656268i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.08304e10 | 0.805601 | 0.402801 | − | 0.915288i | \(-0.368037\pi\) | ||||
0.402801 | + | 0.915288i | \(0.368037\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.69500e9i | 0.140086i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.80254e9 | 0.141336 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.01695e9i | 0.109949i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.99212e9 | 0.0711904 | 0.0355952 | − | 0.999366i | \(-0.488667\pi\) | ||||
0.0355952 | + | 0.999366i | \(0.488667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.38482e10i | − 0.485316i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.01818e10 | −0.693680 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.89447e9i | − 0.0975837i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.66748e10 | 0.882181 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.20707e9i | 0.0716078i | 0.999359 | + | 0.0358039i | \(0.0113992\pi\) | ||||
−0.999359 | + | 0.0358039i | \(0.988601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.87341e10 | 1.23300 | 0.616502 | − | 0.787353i | \(-0.288549\pi\) | ||||
0.616502 | + | 0.787353i | \(0.288549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.26056e10i | − 0.393733i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.43963e10 | 0.441259 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.31790e10i | 0.697241i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.20869e9 | −0.153780 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.79774e10i | − 0.520975i | −0.965477 | − | 0.260488i | \(-0.916117\pi\) | ||||
0.965477 | − | 0.260488i | \(-0.0838833\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.58344e10 | −1.01941 | −0.509705 | − | 0.860349i | \(-0.670245\pi\) | ||||
−0.509705 | + | 0.860349i | \(0.670245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.31244e10i | − 0.645822i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.89390e10 | 0.519315 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 5.47851e10i | − 1.47504i | −0.675324 | − | 0.737521i | \(-0.735996\pi\) | ||||
0.675324 | − | 0.737521i | \(-0.264004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.46714e9 | 0.0652287 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.90120e9i | 0.127259i | 0.997974 | + | 0.0636294i | \(0.0202676\pi\) | ||||
−0.997974 | + | 0.0636294i | \(0.979732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.98497e10 | −0.506191 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.82621e10i | − 0.457425i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.43247e10 | 0.352452 | 0.176226 | − | 0.984350i | \(-0.443611\pi\) | ||||
0.176226 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.53908e10i | 1.09714i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.87786e10 | 0.920871 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 2.30224e10i | − 0.537161i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.28090e10 | −0.752191 | −0.376096 | − | 0.926581i | \(-0.622734\pi\) | ||||
−0.376096 | + | 0.926581i | \(0.622734\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6.09874e9i | − 0.137401i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.80132e10 | −1.94870 | −0.974348 | − | 0.225045i | \(-0.927747\pi\) | ||||
−0.974348 | + | 0.225045i | \(0.927747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36196e10i | 0.513983i | 0.966414 | + | 0.256992i | \(0.0827313\pi\) | ||||
−0.966414 | + | 0.256992i | \(0.917269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.24549e10 | 0.266397 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.39463e10i | 0.503466i | 0.967797 | + | 0.251733i | \(0.0810005\pi\) | ||||
−0.967797 | + | 0.251733i | \(0.919000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.28885e10 | 1.09312 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 1.94120e10i | − 0.394444i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.65821e10 | 0.930625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.27062e10i | 0.642475i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.32753e10 | 0.449595 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.18896e9i | 0.0795727i | 0.999208 | + | 0.0397864i | \(0.0126677\pi\) | ||||
−0.999208 | + | 0.0397864i | \(0.987332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.29543e9 | 0.0615647 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.71646e10i | 0.315389i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.55853e10 | 1.00460 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.65755e9i | 0.136136i | 0.997681 | + | 0.0680681i | \(0.0216835\pi\) | ||||
−0.997681 | + | 0.0680681i | \(0.978316\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.68439e9 | 0.0469472 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.78263e10i | 0.994946i | 0.867479 | + | 0.497473i | \(0.165739\pi\) | ||||
−0.867479 | + | 0.497473i | \(0.834261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.70883e10 | −0.627840 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.75572e10i | 0.292438i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.38312e10 | 0.554487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.98539e10i | 1.44922i | 0.689158 | + | 0.724611i | \(0.257981\pi\) | ||||
−0.689158 | + | 0.724611i | \(0.742019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.17989e9 | −0.0822184 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.89949e9i | 0.139025i | 0.997581 | + | 0.0695126i | \(0.0221444\pi\) | ||||
−0.997581 | + | 0.0695126i | \(0.977856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22461e11 | −1.88293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 3.24585e10i | − 0.491243i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.83459e10 | 0.422298 | 0.211149 | − | 0.977454i | \(-0.432279\pi\) | ||||
0.211149 | + | 0.977454i | \(0.432279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 7.16543e10i | − 1.05089i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.38555e10 | 0.200056 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.44267e11i | 2.05086i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.82030e10 | 0.814673 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 6.32212e10i | − 0.871351i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.48484e10 | 1.15158 | 0.575788 | − | 0.817599i | \(-0.304695\pi\) | ||||
0.575788 | + | 0.817599i | \(0.304695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.22214e11i | 1.63348i | 0.577003 | + | 0.816742i | \(0.304222\pi\) | ||||
−0.577003 | + | 0.816742i | \(0.695778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.96420e10 | −0.390185 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.99760e10i | − 0.258980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.87668e10 | 0.750428 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.68115e10i | − 0.211460i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.95805e10 | 0.614331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.60126e10i | 0.683708i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.51329e9 | −0.114402 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.13913e10i | 0.134965i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.26688e11 | 1.47892 | 0.739462 | − | 0.673198i | \(-0.235080\pi\) | ||||
0.739462 | + | 0.673198i | \(0.235080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.41867e10i | 0.393240i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.03763e11 | 2.30961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.79694e10i | 1.09431i | 0.837031 | + | 0.547156i | \(0.184290\pi\) | ||||
−0.837031 | + | 0.547156i | \(0.815710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.93082e10 | −0.212546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 8.42593e10i | − 0.914137i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.78522e10 | −0.939404 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.11081e10i | − 0.117076i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.25333e10 | −0.857449 | −0.428725 | − | 0.903435i | \(-0.641037\pi\) | ||||
−0.428725 | + | 0.903435i | \(0.641037\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 5.08818e10i | − 0.521093i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.81593e10 | 0.284296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.35561e11i | − 1.34928i | −0.738147 | − | 0.674640i | \(-0.764299\pi\) | ||||
0.738147 | − | 0.674640i | \(-0.235701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.84187e11 | 1.80744 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.25574e10i | 0.121497i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.20885e11 | −1.15325 | −0.576624 | − | 0.817010i | \(-0.695630\pi\) | ||||
−0.576624 | + | 0.817010i | \(0.695630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.61019e11i | − 1.51472i | −0.652998 | − | 0.757360i | \(-0.726489\pi\) | ||||
0.652998 | − | 0.757360i | \(-0.273511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.93760e10 | −0.365269 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 3.37514e10i | − 0.308760i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.39635e11 | 1.25977 | 0.629884 | − | 0.776689i | \(-0.283102\pi\) | ||||
0.629884 | + | 0.776689i | \(0.283102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1.23088e11i | − 1.09522i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.55860e9 | 0.0838861 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.07467e11i | 0.930257i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.91778e10 | 0.163748 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.23680e11i | − 1.04171i | −0.853646 | − | 0.520854i | \(-0.825614\pi\) | ||||
0.853646 | − | 0.520854i | \(-0.174386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.53825e10 | 0.377075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 6.92222e10i | − 0.567408i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.29499e11 | 1.04725 | 0.523623 | − | 0.851950i | \(-0.324580\pi\) | ||||
0.523623 | + | 0.851950i | \(0.324580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.24464e11i | 0.993061i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.41265e9 | 0.0504824 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 7.24974e10i | − 0.563139i | −0.959541 | − | 0.281569i | \(-0.909145\pi\) | ||||
0.959541 | − | 0.281569i | \(-0.0908549\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.03270e10 | −0.0791545 | −0.0395773 | − | 0.999217i | \(-0.512601\pi\) | ||||
−0.0395773 | + | 0.999217i | \(0.512601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.40564e10i | 0.333227i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.93531e10 | 0.666942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.17177e10i | 0.380964i | 0.981691 | + | 0.190482i | \(0.0610052\pi\) | ||||
−0.981691 | + | 0.190482i | \(0.938995\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.63651e10 | 0.555170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 6.35753e10i | − 0.456167i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.79758e11 | 1.27305 | 0.636527 | − | 0.771254i | \(-0.280370\pi\) | ||||
0.636527 | + | 0.771254i | \(0.280370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1.67124e11i | − 1.16825i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.69245e10 | −0.668795 | −0.334397 | − | 0.942432i | \(-0.608533\pi\) | ||||
−0.334397 | + | 0.942432i | \(0.608533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 7.61781e10i | − 0.518881i | −0.965759 | − | 0.259440i | \(-0.916462\pi\) | ||||
0.965759 | − | 0.259440i | \(-0.0835381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.42982e10 | −0.0961426 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.55510e10i | − 0.435138i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.88608e11 | −1.23606 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.39739e10i | 0.413935i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.78158e10 | −0.113816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18736e11i | 0.748972i | 0.927233 | + | 0.374486i | \(0.122181\pi\) | ||||
−0.927233 | + | 0.374486i | \(0.877819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.32542e11 | 0.825542 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.65642e10i | 0.532407i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.24428e10 | 0.0755719 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.81816e10i | 0.169029i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.38064e10 | −0.0817805 | −0.0408903 | − | 0.999164i | \(-0.513019\pi\) | ||||
−0.0408903 | + | 0.999164i | \(0.513019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.32942e10i | 0.370272i | 0.982713 | + | 0.185136i | \(0.0592725\pi\) | ||||
−0.982713 | + | 0.185136i | \(0.940728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.71510e11 | −0.990946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3.83819e10i | − 0.219033i | −0.993985 | − | 0.109516i | \(-0.965070\pi\) | ||||
0.993985 | − | 0.109516i | \(-0.0349302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.76227e10 | 0.437532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.11307e10i | 0.229004i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.77321e10 | 0.262517 | 0.131259 | − | 0.991348i | \(-0.458098\pi\) | ||||
0.131259 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.16005e11i | 1.71683i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.96885e10 | 0.320353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.78691e11i | − 0.947461i | −0.880670 | − | 0.473730i | \(-0.842907\pi\) | ||||
0.880670 | − | 0.473730i | \(-0.157093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.62385e11 | −0.850630 | −0.425315 | − | 0.905045i | \(-0.639837\pi\) | ||||
−0.425315 | + | 0.905045i | \(0.639837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.07585e10i | − 0.159188i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.82764e11 | −1.44590 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.69519e10i | 0.439315i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.38393e11 | −0.690894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 8.91506e10i | − 0.439779i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.25895e11 | 1.58861 | 0.794304 | − | 0.607520i | \(-0.207836\pi\) | ||||
0.794304 | + | 0.607520i | \(0.207836\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.46920e10i | − 0.118944i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.56252e11 | −1.21987 | −0.609934 | − | 0.792452i | \(-0.708804\pi\) | ||||
−0.609934 | + | 0.792452i | \(0.708804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.83563e11i | 0.863586i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.29396e11 | 0.601632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3.96209e10i | − 0.182071i | −0.995848 | − | 0.0910357i | \(-0.970982\pi\) | ||||
0.995848 | − | 0.0910357i | \(-0.0290177\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.35420e11 | −1.06925 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.24514e9i | 0.0280360i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.17387e11 | 0.520887 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.75065e11i | 1.64511i | 0.568687 | + | 0.822554i | \(0.307452\pi\) | ||||
−0.568687 | + | 0.822554i | \(0.692548\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.79803e10 | −0.251390 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 4.53475e11i | − 1.94363i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68043e11 | −1.13573 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 7.52392e10i | − 0.315163i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.96001e11 | −1.22580 | −0.612901 | − | 0.790160i | \(-0.709998\pi\) | ||||
−0.612901 | + | 0.790160i | \(0.709998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4.04749e10i | − 0.165716i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.14296e11 | −0.867478 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.04412e11i | − 1.61863i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.94063e11 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 7.31814e10i | − 0.286367i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.68328e10 | −0.181214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.85483e10i | 0.338810i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.33146e11 | −0.882167 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.88372e11i | − 0.704855i | −0.935839 | − | 0.352428i | \(-0.885356\pi\) | ||||
0.935839 | − | 0.352428i | \(-0.114644\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.76421e11 | −1.76299 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.79418e10i | 0.138856i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50159e11 | −0.543501 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.55301e11i | 1.27192i | 0.771723 | + | 0.635959i | \(0.219395\pi\) | ||||
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.75078e11i | 0.963354i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06552e11 | 0.369103 | 0.184551 | − | 0.982823i | \(-0.440917\pi\) | ||||
0.184551 | + | 0.982823i | \(0.440917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 4.19416e10i | − 0.143713i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.03419e11 | −0.689479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.71902e11i | − 0.911664i | −0.890066 | − | 0.455832i | \(-0.849342\pi\) | ||||
0.890066 | − | 0.455832i | \(-0.150658\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.98789e10 | 0.231778 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.45168e11i | 1.46073i | 0.683060 | + | 0.730363i | \(0.260649\pi\) | ||||
−0.683060 | + | 0.730363i | \(0.739351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.10457e11 | −1.00781 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.96237e9i | 0.0255717i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.84974e11 | −0.587738 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.05844e11i | 0.961479i | 0.876863 | + | 0.480740i | \(0.159632\pi\) | ||||
−0.876863 | + | 0.480740i | \(0.840368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.85279e11 | 0.887338 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.59239e11i | − 2.02887i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.31463e11 | 0.400330 | 0.200165 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200165 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 6.60183e10i | − 0.198929i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.23715e11 | 1.26338 | 0.631692 | − | 0.775219i | \(-0.282361\pi\) | ||||
0.631692 | + | 0.775219i | \(0.282361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.72899e11i | 1.98542i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.03679e11 | −0.302723 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.47875e10i | − 0.244991i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.39328e11 | −1.54223 | −0.771113 | − | 0.636699i | \(-0.780300\pi\) | ||||
−0.771113 | + | 0.636699i | \(0.780300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 3.57357e11i | − 1.01131i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.77304e10 | 0.0776673 | 0.0388336 | − | 0.999246i | \(-0.487636\pi\) | ||||
0.0388336 | + | 0.999246i | \(0.487636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 8.08767e10i | − 0.224190i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.66829e10 | 0.100642 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.08955e11i | − 1.65362i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30121e11 | −0.349738 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.36126e10i | 0.169237i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.30005e11 | −0.869044 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.92830e11i | 0.502662i | 0.967901 | + | 0.251331i | \(0.0808683\pi\) | ||||
−0.967901 | + | 0.251331i | \(0.919132\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.16431e9 | 0.00558484 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.08252e11i | 1.55374i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.73795e10 | −0.246249 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 3.95682e11i | − 0.990554i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.96593e11 | 1.23074 | 0.615371 | − | 0.788238i | \(-0.289006\pi\) | ||||
0.615371 | + | 0.788238i | \(0.289006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.43702e11i | 0.843325i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.46043e10 | 0.132647 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.75596e11i | 0.662842i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.91800e11 | 0.694868 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.96319e11i | 0.698658i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.18435e11 | −0.743407 | −0.371704 | − | 0.928351i | \(-0.621226\pi\) | ||||
−0.371704 | + | 0.928351i | \(0.621226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 7.47780e11i | − 1.72858i | −0.502991 | − | 0.864292i | \(-0.667767\pi\) | ||||
0.502991 | − | 0.864292i | \(-0.332233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00818e11 | −0.917456 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 4.56349e10i | − 0.103435i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.24937e11 | −1.40265 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.33320e10i | 0.140763i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.17778e11 | −0.479338 | −0.239669 | − | 0.970855i | \(-0.577039\pi\) | ||||
−0.239669 | + | 0.970855i | \(0.577039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.07755e11i | 1.32474i | 0.749179 | + | 0.662368i | \(0.230448\pi\) | ||||
−0.749179 | + | 0.662368i | \(0.769552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14009e11 | 0.246106 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.03109e11i | 0.220431i | 0.993908 | + | 0.110215i | \(0.0351541\pi\) | ||||
−0.993908 | + | 0.110215i | \(0.964846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.78415e11 | 1.01295 | 0.506474 | − | 0.862255i | \(-0.330949\pi\) | ||||
0.506474 | + | 0.862255i | \(0.330949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1.48992e10i | − 0.0312434i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.72685e10 | −0.139711 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.80586e10i | 0.181145i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.42621e10 | −0.0698092 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 9.56688e10i | − 0.193073i | −0.995329 | − | 0.0965367i | \(-0.969223\pi\) | ||||
0.995329 | − | 0.0965367i | \(-0.0307765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.13399e11 | −0.226686 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.61031e11i | − 1.11090i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51797e11 | −1.08231 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.95076e11i | 0.573325i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.04880e11 | 0.201866 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.17684e10i | 0.0796396i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.23586e11 | −1.36677 | −0.683383 | − | 0.730060i | \(-0.739492\pi\) | ||||
−0.683383 | + | 0.730060i | \(0.739492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 2.35544e11i | − 0.440766i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.92851e11 | 1.46983 | 0.734917 | − | 0.678157i | \(-0.237221\pi\) | ||||
0.734917 | + | 0.678157i | \(0.237221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.17760e10i | − 0.0399949i | −0.999800 | − | 0.0199975i | \(-0.993634\pi\) | ||||
0.999800 | − | 0.0199975i | \(-0.00636581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.51903e11 | 1.00427 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.20359e10i | 0.165926i | 0.996553 | + | 0.0829629i | \(0.0264383\pi\) | ||||
−0.996553 | + | 0.0829629i | \(0.973562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.07477e12 | −1.91977 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.59937e11i | − 0.283056i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.37896e11 | 0.592521 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.22195e11i | 0.386066i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.52909e11 | −0.263254 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.11419e11i | − 0.531267i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.09630e11 | 1.19959 | 0.599796 | − | 0.800153i | \(-0.295248\pi\) | ||||
0.599796 | + | 0.800153i | \(0.295248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 5.73650e10i | − 0.0960929i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.65687e11 | 1.60300 | 0.801499 | − | 0.597997i | \(-0.204036\pi\) | ||||
0.801499 | + | 0.597997i | \(0.204036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.29054e9i | 0.0152826i | 0.999971 | + | 0.00764131i | \(0.00243233\pi\) | ||||
−0.999971 | + | 0.00764131i | \(0.997568\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.85798e11 | −0.465892 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.20513e12i | 1.94689i | 0.228926 | + | 0.973444i | \(0.426479\pi\) | ||||
−0.228926 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.85867e11 | −0.457674 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.82979e10i | − 0.0766333i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.80841e11 | −1.22788 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.61727e11i | 0.252052i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.21120e10 | −0.111388 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.08358e11i | 0.318986i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.34620e11 | −0.962973 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.66387e11i | − 0.851849i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.81177e11 | 0.866391 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.50561e11i | 1.25683i | 0.777878 | + | 0.628415i | \(0.216296\pi\) | ||||
−0.777878 | + | 0.628415i | \(0.783704\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.36877e11 | 0.493420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.04501e11i | 0.296908i | 0.988919 | + | 0.148454i | \(0.0474296\pi\) | ||||
−0.988919 | + | 0.148454i | \(0.952570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.67641e10 | −0.0529104 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.28242e11i | 0.468284i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.04356e12 | −1.47585 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 5.59082e11i | − 0.783815i | −0.920005 | − | 0.391907i | \(-0.871815\pi\) | ||||
0.920005 | − | 0.391907i | \(-0.128185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.28009e11 | 0.733842 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.42131e11i | 0.195832i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.21308e10 | −0.0985267 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.96861e11i | − 0.537427i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.45154e11 | −1.13468 | −0.567340 | − | 0.823484i | \(-0.692027\pi\) | ||||
−0.567340 | + | 0.823484i | \(0.692027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.52824e11i | − 0.203420i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.28607e11 | −0.301691 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 4.78711e11i | − 0.626364i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.92001e10 | 0.0508544 | 0.0254272 | − | 0.999677i | \(-0.491905\pi\) | ||||
0.0254272 | + | 0.999677i | \(0.491905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.21457e11i | − 0.670743i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.60504e10 | −0.0459782 | −0.0229891 | − | 0.999736i | \(-0.507318\pi\) | ||||
−0.0229891 | + | 0.999736i | \(0.507318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.28415e11i | 0.794694i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.13476e11 | 0.267684 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 5.80923e11i | − 0.722301i | −0.932508 | − | 0.361151i | \(-0.882384\pi\) | ||||
0.932508 | − | 0.361151i | \(-0.117616\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.01034e11 | 0.371151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 4.37224e11i | − 0.534542i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45669e11 | 0.176602 | 0.0883009 | − | 0.996094i | \(-0.471856\pi\) | ||||
0.0883009 | + | 0.996094i | \(0.471856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.69395e11i | 0.804765i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.93714e11 | −0.350168 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 7.77443e11i | − 0.919166i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.40668e11 | 0.868420 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.54084e11i | − 0.179165i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.09251e12 | −2.41301 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.27650e12i | − 1.45988i | −0.683514 | − | 0.729938i | \(-0.739549\pi\) | ||||
0.683514 | − | 0.729938i | \(-0.260451\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.77780e11 | −0.428493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.14012e11i | 0.353239i | 0.984279 | + | 0.176620i | \(0.0565162\pi\) | ||||
−0.984279 | + | 0.176620i | \(0.943484\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.49754e12 | 1.67081 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.24532e11i | − 0.137804i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.03341e10 | 0.0113421 | 0.00567107 | − | 0.999984i | \(-0.498195\pi\) | ||||
0.00567107 | + | 0.999984i | \(0.498195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.52121e11i | 0.274459i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.60528e11 | −0.605232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.49178e11i | 0.481066i | 0.970641 | + | 0.240533i | \(0.0773222\pi\) | ||||
−0.970641 | + | 0.240533i | \(0.922678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.17678e12 | −1.25012 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 7.07685e11i | − 0.745712i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.44908e11 | 0.674082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.52082e12i | 1.57682i | 0.615149 | + | 0.788411i | \(0.289096\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.76933e11 | −0.799073 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.09016e11i | − 0.111223i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.35823e11 | −0.238675 | −0.119337 | − | 0.992854i | \(-0.538077\pi\) | ||||
−0.119337 | + | 0.992854i | \(0.538077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.05570e10i | 0.0306796i |
(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 | 384.9.g.a.127.26 | yes | 32 | |
4.3 | odd | 2 | inner | 384.9.g.a.127.25 | ✓ | 32 | |
8.3 | odd | 2 | 384.9.g.b.127.8 | yes | 32 | ||
8.5 | even | 2 | 384.9.g.b.127.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.g.a.127.25 | ✓ | 32 | 4.3 | odd | 2 | inner | |
384.9.g.a.127.26 | yes | 32 | 1.1 | even | 1 | trivial | |
384.9.g.b.127.7 | yes | 32 | 8.5 | even | 2 | ||
384.9.g.b.127.8 | yes | 32 | 8.3 | odd | 2 |