Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,12,Mod(64,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.64");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(89.8961521255\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18433 x^{10} + 121088056 x^{8} + 340607607312 x^{6} + 380893885719552 x^{4} + \cdots + 14\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{6}\cdot 13^{4} \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.6 | ||
Root | \(-3.38741i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.64 |
Dual form | 117.12.b.b.64.7 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.38741i | − | 0.0748518i | −0.999299 | − | 0.0374259i | \(-0.988084\pi\) | ||
0.999299 | − | 0.0374259i | \(-0.0119158\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2036.53 | 0.994397 | ||||||||
\(5\) | − | 9091.88i | − | 1.30112i | −0.759453 | − | 0.650562i | \(-0.774533\pi\) | ||
0.759453 | − | 0.650562i | \(-0.225467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 45027.4i | − | 1.01260i | −0.862357 | − | 0.506300i | \(-0.831013\pi\) | ||
0.862357 | − | 0.506300i | \(-0.168987\pi\) | |||||||
\(8\) | − | 13836.0i | − | 0.149284i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −30797.9 | −0.0973915 | ||||||||
\(11\) | − | 810639.i | − | 1.51764i | −0.651303 | − | 0.758818i | \(-0.725777\pi\) | ||
0.651303 | − | 0.758818i | \(-0.274223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.11466e6 | − | 741417.i | 0.832632 | − | 0.553827i | ||||
\(14\) | −152526. | −0.0757950 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.12394e6 | 0.983223 | ||||||||
\(17\) | 851428. | 0.145438 | 0.0727192 | − | 0.997352i | \(-0.476832\pi\) | ||||
0.0727192 | + | 0.997352i | \(0.476832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.56605e6i | − | 0.701011i | −0.936561 | − | 0.350505i | \(-0.886010\pi\) | ||
0.936561 | − | 0.350505i | \(-0.113990\pi\) | |||||||
\(20\) | − | 1.85158e7i | − | 1.29383i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.74596e6 | −0.113598 | ||||||||
\(23\) | −3.69275e6 | −0.119632 | −0.0598159 | − | 0.998209i | \(-0.519051\pi\) | ||||
−0.0598159 | + | 0.998209i | \(0.519051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.38341e7 | −0.692923 | ||||||||
\(26\) | −2.51148e6 | − | 3.77580e6i | −0.0414550 | − | 0.0623240i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 9.16995e7i | − | 1.00693i | ||||||
\(29\) | 9.33625e7 | 0.845247 | 0.422623 | − | 0.906305i | \(-0.361109\pi\) | ||||
0.422623 | + | 0.906305i | \(0.361109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.61508e8i | − | 1.64057i | −0.571953 | − | 0.820286i | \(-0.693814\pi\) | ||
0.571953 | − | 0.820286i | \(-0.306186\pi\) | |||||||
\(32\) | − | 4.23055e7i | − | 0.222880i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.88413e6i | − | 0.0108863i | ||||||
\(35\) | −4.09384e8 | −1.31752 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.38221e8i | 1.27600i | 0.770036 | + | 0.638000i | \(0.220238\pi\) | ||||
−0.770036 | + | 0.638000i | \(0.779762\pi\) | |||||||
\(38\) | −2.56293e7 | −0.0524719 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.25795e8 | −0.194237 | ||||||||
\(41\) | 6.71292e8i | 0.904899i | 0.891790 | + | 0.452449i | \(0.149450\pi\) | ||||
−0.891790 | + | 0.452449i | \(0.850550\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.09294e9 | −1.13375 | −0.566876 | − | 0.823803i | \(-0.691848\pi\) | ||||
−0.566876 | + | 0.823803i | \(0.691848\pi\) | |||||||
\(44\) | − | 1.65089e9i | − | 1.50913i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25088e7i | 0.00895466i | ||||||||
\(47\) | 1.79698e9i | 1.14289i | 0.820641 | + | 0.571445i | \(0.193617\pi\) | ||||
−0.820641 | + | 0.571445i | \(0.806383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.01432e7 | −0.0253591 | ||||||||
\(50\) | 1.14610e8i | 0.0518665i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.27003e9 | − | 1.50991e9i | 0.827967 | − | 0.550724i | ||||
\(53\) | 5.82497e9 | 1.91327 | 0.956636 | − | 0.291287i | \(-0.0940835\pi\) | ||||
0.956636 | + | 0.291287i | \(0.0940835\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.37023e9 | −1.97463 | ||||||||
\(56\) | −6.22997e8 | −0.151165 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.16257e8i | − | 0.0632683i | ||||||
\(59\) | 4.74847e9i | 0.864704i | 0.901705 | + | 0.432352i | \(0.142316\pi\) | ||||
−0.901705 | + | 0.432352i | \(0.857684\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50495e9 | 0.986120 | 0.493060 | − | 0.869995i | \(-0.335878\pi\) | ||||
0.493060 | + | 0.869995i | \(0.335878\pi\) | |||||||
\(62\) | −8.85834e8 | −0.122800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.30252e9 | 0.966540 | ||||||||
\(65\) | −6.74087e9 | − | 1.01343e10i | −0.720597 | − | 1.08336i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.11940e9i | 0.734704i | 0.930082 | + | 0.367352i | \(0.119736\pi\) | ||||
−0.930082 | + | 0.367352i | \(0.880264\pi\) | |||||||
\(68\) | 1.73395e9 | 0.144623 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.38675e9i | 0.0986186i | ||||||||
\(71\) | 3.16640e9i | 0.208279i | 0.994563 | + | 0.104139i | \(0.0332088\pi\) | ||||
−0.994563 | + | 0.104139i | \(0.966791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.22937e9i | − | 0.464613i | −0.972643 | − | 0.232306i | \(-0.925373\pi\) | ||
0.972643 | − | 0.232306i | \(-0.0746272\pi\) | |||||||
\(74\) | 1.82317e9 | 0.0955110 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.54085e10i | − | 0.697083i | ||||||
\(77\) | −3.65010e10 | −1.53676 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.75500e9 | −0.137297 | −0.0686485 | − | 0.997641i | \(-0.521869\pi\) | ||||
−0.0686485 | + | 0.997641i | \(0.521869\pi\) | |||||||
\(80\) | − | 3.74943e10i | − | 1.27929i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.27394e9 | 0.0677333 | ||||||||
\(83\) | 6.60119e9i | 0.183947i | 0.995761 | + | 0.0919735i | \(0.0293175\pi\) | ||||
−0.995761 | + | 0.0919735i | \(0.970682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.74108e9i | − | 0.189233i | ||||||
\(86\) | 3.70222e9i | 0.0848634i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.12160e10 | −0.226559 | ||||||||
\(89\) | − | 5.68420e10i | − | 1.07901i | −0.841983 | − | 0.539503i | \(-0.818612\pi\) | ||
0.841983 | − | 0.539503i | \(-0.181388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.33841e10 | − | 5.01902e10i | −0.560805 | − | 0.843123i | ||||
\(92\) | −7.52038e9 | −0.118962 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.08709e9 | 0.0855474 | ||||||||
\(95\) | −6.87896e10 | −0.912101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.62006e11i | 1.91551i | 0.287578 | + | 0.957757i | \(0.407150\pi\) | ||||
−0.287578 | + | 0.957757i | \(0.592850\pi\) | |||||||
\(98\) | 1.69856e8i | 0.00189818i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.89040e10 | −0.689040 | ||||||||
\(101\) | −1.31282e11 | −1.24290 | −0.621450 | − | 0.783454i | \(-0.713456\pi\) | ||||
−0.621450 | + | 0.783454i | \(0.713456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.50452e10 | −0.467859 | −0.233929 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233929 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(104\) | −1.02582e10 | − | 1.54223e10i | −0.0826777 | − | 0.124299i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 1.97316e10i | − | 0.143212i | ||||||
\(107\) | −1.85072e11 | −1.27564 | −0.637822 | − | 0.770184i | \(-0.720164\pi\) | ||||
−0.637822 | + | 0.770184i | \(0.720164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.74414e10i | − | 0.170829i | −0.996346 | − | 0.0854143i | \(-0.972779\pi\) | ||
0.996346 | − | 0.0854143i | \(-0.0272214\pi\) | |||||||
\(110\) | 2.49660e10i | 0.147805i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.85690e11i | − | 0.995612i | ||||||
\(113\) | 1.64428e11 | 0.839547 | 0.419773 | − | 0.907629i | \(-0.362110\pi\) | ||||
0.419773 | + | 0.907629i | \(0.362110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.35740e10i | 0.155656i | ||||||||
\(116\) | 1.90135e11 | 0.840511 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.60850e10 | 0.0647247 | ||||||||
\(119\) | − | 3.83376e10i | − | 0.147271i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.71823e11 | −1.30322 | ||||||||
\(122\) | − | 2.20349e10i | − | 0.0738129i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.32567e11i | − | 1.63138i | ||||||
\(125\) | − | 1.36324e11i | − | 0.399546i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.48728e11 | 1.47379 | 0.736897 | − | 0.676005i | \(-0.236290\pi\) | ||||
0.736897 | + | 0.676005i | \(0.236290\pi\) | |||||||
\(128\) | − | 1.14766e11i | − | 0.295228i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.43291e10 | + | 2.28341e10i | −0.0810912 | + | 0.0539380i | ||||
\(131\) | −3.22742e11 | −0.730910 | −0.365455 | − | 0.930829i | \(-0.619087\pi\) | ||||
−0.365455 | + | 0.930829i | \(0.619087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.40680e11 | −0.709843 | ||||||||
\(134\) | 2.75037e10 | 0.0549940 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1.17803e10i | − | 0.0217117i | ||||||
\(137\) | − | 1.94892e11i | − | 0.345009i | −0.985009 | − | 0.172505i | \(-0.944814\pi\) | ||
0.985009 | − | 0.172505i | \(-0.0551859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.64756e11 | −1.08663 | −0.543314 | − | 0.839530i | \(-0.682831\pi\) | ||||
−0.543314 | + | 0.839530i | \(0.682831\pi\) | |||||||
\(140\) | −8.33721e11 | −1.31014 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.07259e10 | 0.0155901 | ||||||||
\(143\) | −6.01021e11 | − | 9.03584e11i | −0.840508 | − | 1.26363i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.48840e11i | − | 1.09977i | ||||||
\(146\) | −2.78762e10 | −0.0347771 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.09610e12i | 1.26885i | ||||||||
\(149\) | − | 4.29539e11i | − | 0.479157i | −0.970877 | − | 0.239578i | \(-0.922991\pi\) | ||
0.970877 | − | 0.239578i | \(-0.0770092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.20700e12i | 1.25122i | 0.780136 | + | 0.625610i | \(0.215150\pi\) | ||||
−0.780136 | + | 0.625610i | \(0.784850\pi\) | |||||||
\(152\) | −1.04684e11 | −0.104650 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.23644e11i | 0.115029i | ||||||||
\(155\) | −2.37760e12 | −2.13459 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.61496e10 | −0.0804450 | −0.0402225 | − | 0.999191i | \(-0.512807\pi\) | ||||
−0.0402225 | + | 0.999191i | \(0.512807\pi\) | |||||||
\(158\) | 1.27197e10i | 0.0102769i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.84636e11 | −0.289995 | ||||||||
\(161\) | 1.66275e11i | 0.121139i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.50626e12i | − | 1.02534i | −0.858586 | − | 0.512670i | \(-0.828656\pi\) | ||
0.858586 | − | 0.512670i | \(-0.171344\pi\) | |||||||
\(164\) | 1.36710e12i | 0.899829i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.23609e10 | 0.0137688 | ||||||||
\(167\) | − | 1.03474e12i | − | 0.616441i | −0.951315 | − | 0.308221i | \(-0.900266\pi\) | ||
0.951315 | − | 0.308221i | \(-0.0997335\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92762e11 | − | 1.65285e12i | 0.386551 | − | 0.922268i | ||||
\(170\) | −2.62222e10 | −0.0141645 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.22579e12 | −1.12740 | ||||||||
\(173\) | 1.11263e11 | 0.0545881 | 0.0272941 | − | 0.999627i | \(-0.491311\pi\) | ||||
0.0272941 | + | 0.999627i | \(0.491311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52346e12i | 0.701653i | ||||||||
\(176\) | − | 3.34302e12i | − | 1.49217i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.92547e11 | −0.0807656 | ||||||||
\(179\) | −2.06269e12 | −0.838964 | −0.419482 | − | 0.907764i | \(-0.637788\pi\) | ||||
−0.419482 | + | 0.907764i | \(0.637788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46724e12 | 1.32663 | 0.663317 | − | 0.748338i | \(-0.269148\pi\) | ||||
0.663317 | + | 0.748338i | \(0.269148\pi\) | |||||||
\(182\) | −1.70015e11 | + | 1.13086e11i | −0.0631093 | + | 0.0419773i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.10927e10i | 0.0178592i | ||||||||
\(185\) | 4.89344e12 | 1.66023 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.90200e11i | − | 0.220722i | ||||||
\(188\) | 3.65959e12i | 1.13649i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.33018e11i | 0.0682725i | ||||||||
\(191\) | 4.63569e12 | 1.31957 | 0.659783 | − | 0.751456i | \(-0.270648\pi\) | ||||
0.659783 | + | 0.751456i | \(0.270648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.13783e12i | − | 0.305852i | −0.988238 | − | 0.152926i | \(-0.951130\pi\) | ||
0.988238 | − | 0.152926i | \(-0.0488696\pi\) | |||||||
\(194\) | 5.48779e11 | 0.143380 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02118e11 | −0.0252170 | ||||||||
\(197\) | 2.32298e12i | 0.557803i | 0.960320 | + | 0.278901i | \(0.0899702\pi\) | ||||
−0.960320 | + | 0.278901i | \(0.910030\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.94354e11 | 0.0668618 | 0.0334309 | − | 0.999441i | \(-0.489357\pi\) | ||||
0.0334309 | + | 0.999441i | \(0.489357\pi\) | |||||||
\(200\) | 4.68127e11i | 0.103442i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.44704e11i | 0.0930333i | ||||||||
\(203\) | − | 4.20387e12i | − | 0.855897i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.10330e12 | 1.17739 | ||||||||
\(206\) | 1.86461e11i | 0.0350201i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.59678e12 | − | 3.05756e12i | 0.818663 | − | 0.544536i | ||||
\(209\) | −6.13333e12 | −1.06388 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00209e11 | 0.131719 | 0.0658597 | − | 0.997829i | \(-0.479021\pi\) | ||||
0.0658597 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(212\) | 1.18627e13 | 1.90255 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.26914e11i | 0.0954843i | ||||||||
\(215\) | 9.93684e12i | 1.47515i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17750e13 | −1.66124 | ||||||||
\(218\) | −9.29552e10 | −0.0127868 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.50097e13 | −1.96357 | ||||||||
\(221\) | 9.49050e11 | − | 6.31263e11i | 0.121097 | − | 0.0805477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.48493e13i | 1.80314i | 0.432631 | + | 0.901571i | \(0.357585\pi\) | ||||
−0.432631 | + | 0.901571i | \(0.642415\pi\) | |||||||
\(224\) | −1.90491e12 | −0.225689 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 5.56985e11i | − | 0.0628416i | ||||||
\(227\) | 1.57088e13i | 1.72982i | 0.501928 | + | 0.864910i | \(0.332624\pi\) | ||||
−0.501928 | + | 0.864910i | \(0.667376\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.72068e12i | 0.285485i | 0.989760 | + | 0.142742i | \(0.0455920\pi\) | ||||
−0.989760 | + | 0.142742i | \(0.954408\pi\) | |||||||
\(230\) | 1.13729e11 | 0.0116511 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.29176e12i | − | 0.126182i | ||||||
\(233\) | 8.42380e12 | 0.803620 | 0.401810 | − | 0.915723i | \(-0.368381\pi\) | ||||
0.401810 | + | 0.915723i | \(0.368381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63379e13 | 1.48704 | ||||||||
\(236\) | 9.67037e12i | 0.859859i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.29865e11 | −0.0110235 | ||||||||
\(239\) | − | 2.27825e13i | − | 1.88979i | −0.327374 | − | 0.944895i | \(-0.606164\pi\) | ||
0.327374 | − | 0.944895i | \(-0.393836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.32011e12i | 0.500761i | 0.968147 | + | 0.250381i | \(0.0805558\pi\) | ||||
−0.968147 | + | 0.250381i | \(0.919444\pi\) | |||||||
\(242\) | 1.25952e12i | 0.0975483i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.32475e13 | 0.980595 | ||||||||
\(245\) | 4.55896e11i | 0.0329953i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.60960e12 | − | 8.43356e12i | −0.388239 | − | 0.583684i | ||||
\(248\) | −3.61821e12 | −0.244912 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.61784e11 | −0.0299067 | ||||||||
\(251\) | −5.09290e12 | −0.322671 | −0.161335 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161335 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.99349e12i | 0.181558i | ||||||||
\(254\) | − | 1.85877e12i | − | 0.110316i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.66148e13 | 0.944442 | ||||||||
\(257\) | 2.23129e13 | 1.24144 | 0.620718 | − | 0.784034i | \(-0.286841\pi\) | ||||
0.620718 | + | 0.784034i | \(0.286841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.42347e13 | 1.29208 | ||||||||
\(260\) | −1.37280e13 | − | 2.06388e13i | −0.716560 | − | 1.07729i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.09326e12i | 0.0547099i | ||||||||
\(263\) | −1.02420e12 | −0.0501911 | −0.0250956 | − | 0.999685i | \(-0.507989\pi\) | ||||
−0.0250956 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.29599e13i | − | 2.48940i | ||||||
\(266\) | 1.15402e12i | 0.0531331i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.65354e13i | 0.730588i | ||||||||
\(269\) | 3.39292e13 | 1.46871 | 0.734355 | − | 0.678766i | \(-0.237485\pi\) | ||||
0.734355 | + | 0.678766i | \(0.237485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.37089e13i | 1.81651i | 0.418414 | + | 0.908257i | \(0.362586\pi\) | ||||
−0.418414 | + | 0.908257i | \(0.637414\pi\) | |||||||
\(272\) | 3.51123e12 | 0.142998 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.60178e11 | −0.0258246 | ||||||||
\(275\) | 2.74272e13i | 1.05160i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.69270e13 | 0.623651 | 0.311826 | − | 0.950139i | \(-0.399060\pi\) | ||||
0.311826 | + | 0.950139i | \(0.399060\pi\) | |||||||
\(278\) | 2.25180e12i | 0.0813361i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.66422e12i | 0.196685i | ||||||||
\(281\) | 4.31608e13i | 1.46962i | 0.678274 | + | 0.734809i | \(0.262728\pi\) | ||||
−0.678274 | + | 0.734809i | \(0.737272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.77458e13 | −1.56354 | −0.781772 | − | 0.623565i | \(-0.785684\pi\) | ||||
−0.781772 | + | 0.623565i | \(0.785684\pi\) | |||||||
\(284\) | 6.44846e12i | 0.207112i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.06081e12 | + | 2.03590e12i | −0.0945852 | + | 0.0629136i | ||||
\(287\) | 3.02265e13 | 0.916301 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.35470e13 | −0.978848 | ||||||||
\(290\) | −2.87537e12 | −0.0823198 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1.67593e13i | − | 0.462010i | ||||||
\(293\) | 1.64453e13i | 0.444908i | 0.974943 | + | 0.222454i | \(0.0714067\pi\) | ||||
−0.974943 | + | 0.222454i | \(0.928593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.31725e13 | 1.12509 | ||||||||
\(296\) | 7.44680e12 | 0.190487 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.45502e12 | −0.0358658 | ||||||||
\(299\) | −4.11615e12 | + | 2.73787e12i | −0.0996093 | + | 0.0662553i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.92121e13i | 1.14804i | ||||||||
\(302\) | 4.08860e12 | 0.0936561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 3.12019e13i | − | 0.689250i | ||||||
\(305\) | − | 5.91422e13i | − | 1.28306i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.79282e12i | 0.121235i | 0.998161 | + | 0.0606176i | \(0.0193070\pi\) | ||||
−0.998161 | + | 0.0606176i | \(0.980693\pi\) | |||||||
\(308\) | −7.43352e13 | −1.52815 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.05389e12i | 0.159778i | ||||||||
\(311\) | −6.88588e13 | −1.34208 | −0.671039 | − | 0.741422i | \(-0.734152\pi\) | ||||
−0.671039 | + | 0.741422i | \(0.734152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.94167e13 | −0.553477 | −0.276738 | − | 0.960945i | \(-0.589254\pi\) | ||||
−0.276738 | + | 0.960945i | \(0.589254\pi\) | |||||||
\(314\) | 3.25698e11i | 0.00602146i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.64715e12 | −0.136528 | ||||||||
\(317\) | − | 2.48320e13i | − | 0.435698i | −0.975983 | − | 0.217849i | \(-0.930096\pi\) | ||
0.975983 | − | 0.217849i | \(-0.0699040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.56832e13i | − | 1.28278i | ||||||
\(320\) | − | 7.54855e13i | − | 1.25759i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.63241e11 | 0.00906749 | ||||||||
\(323\) | − | 6.44195e12i | − | 0.101954i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.77134e13 | + | 2.50852e13i | −0.576949 | + | 0.383759i | ||||
\(326\) | −5.10231e12 | −0.0767486 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.28796e12 | 0.135087 | ||||||||
\(329\) | 8.09132e13 | 1.15729 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.37169e13i | − | 0.466438i | −0.972424 | − | 0.233219i | \(-0.925074\pi\) | ||
0.972424 | − | 0.233219i | \(-0.0749259\pi\) | |||||||
\(332\) | 1.34435e13i | 0.182916i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.50509e12 | −0.0461418 | ||||||||
\(335\) | 7.38206e13 | 0.955941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.98229e13 | −1.12570 | −0.562850 | − | 0.826559i | \(-0.690295\pi\) | ||||
−0.562850 | + | 0.826559i | \(0.690295\pi\) | |||||||
\(338\) | −5.59888e12 | − | 2.34667e12i | −0.0690335 | − | 0.0289341i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 1.57649e13i | − | 0.188173i | ||||||
\(341\) | −2.11988e14 | −2.48979 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.67761e13i | − | 0.986922i | ||||||
\(344\) | 1.51218e13i | 0.169251i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3.76894e11i | − | 0.00408602i | ||||||
\(347\) | −8.75394e13 | −0.934096 | −0.467048 | − | 0.884232i | \(-0.654682\pi\) | ||||
−0.467048 | + | 0.884232i | \(0.654682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.87065e13i | 0.400169i | 0.979779 | + | 0.200085i | \(0.0641217\pi\) | ||||
−0.979779 | + | 0.200085i | \(0.935878\pi\) | |||||||
\(350\) | 5.16059e12 | 0.0525201 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.42945e13 | −0.338251 | ||||||||
\(353\) | − | 3.24210e13i | − | 0.314822i | −0.987533 | − | 0.157411i | \(-0.949685\pi\) | ||
0.987533 | − | 0.157411i | \(-0.0503148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.87885e13 | 0.270996 | ||||||||
\(356\) | − | 1.15760e14i | − | 1.07296i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.98719e12i | 0.0627980i | ||||||||
\(359\) | 1.45534e14i | 1.28809i | 0.764990 | + | 0.644043i | \(0.222744\pi\) | ||||
−0.764990 | + | 0.644043i | \(0.777256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.92451e13 | 0.508584 | ||||||||
\(362\) | − | 1.17449e13i | − | 0.0993011i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.79876e13 | − | 1.02214e14i | −0.557663 | − | 0.838399i | ||||
\(365\) | −7.48205e13 | −0.604518 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.95668e13 | 0.545430 | 0.272715 | − | 0.962095i | \(-0.412078\pi\) | ||||
0.272715 | + | 0.962095i | \(0.412078\pi\) | |||||||
\(368\) | −1.52287e13 | −0.117625 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1.65761e13i | − | 0.124272i | ||||||
\(371\) | − | 2.62284e14i | − | 1.93738i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.20982e14 | 0.867604 | 0.433802 | − | 0.901008i | \(-0.357172\pi\) | ||||
0.433802 | + | 0.901008i | \(0.357172\pi\) | |||||||
\(374\) | −2.33799e12 | −0.0165215 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.48629e13 | 0.170615 | ||||||||
\(377\) | 1.04067e14 | − | 6.92206e13i | 0.703779 | − | 0.468120i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.22918e13i | − | 0.212117i | −0.994360 | − | 0.106059i | \(-0.966177\pi\) | ||
0.994360 | − | 0.106059i | \(-0.0338231\pi\) | |||||||
\(380\) | −1.40092e14 | −0.906991 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 1.57030e13i | − | 0.0987719i | ||||||
\(383\) | 6.60313e13i | 0.409408i | 0.978824 | + | 0.204704i | \(0.0656232\pi\) | ||||
−0.978824 | + | 0.204704i | \(0.934377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.31862e14i | 1.99951i | ||||||||
\(386\) | −3.85428e12 | −0.0228936 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.29929e14i | 1.90478i | ||||||||
\(389\) | −1.13990e14 | −0.648851 | −0.324426 | − | 0.945911i | \(-0.605171\pi\) | ||||
−0.324426 | + | 0.945911i | \(0.605171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.14411e12 | −0.0173991 | ||||||||
\(392\) | 6.93779e11i | 0.00378572i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.86887e12 | 0.0417525 | ||||||||
\(395\) | 3.41400e13i | 0.178640i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.68777e14i | − | 1.36787i | −0.729543 | − | 0.683935i | \(-0.760267\pi\) | ||
0.729543 | − | 0.683935i | \(-0.239733\pi\) | |||||||
\(398\) | − | 9.97097e11i | − | 0.00500473i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.39530e14 | −0.681297 | ||||||||
\(401\) | 3.43265e14i | 1.65324i | 0.562762 | + | 0.826619i | \(0.309739\pi\) | ||||
−0.562762 | + | 0.826619i | \(0.690261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.93886e14 | − | 2.91492e14i | −0.908593 | − | 1.36599i | ||||
\(404\) | −2.67358e14 | −1.23594 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.42402e13 | −0.0640655 | ||||||||
\(407\) | 4.36303e14 | 1.93650 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.66850e14i | 1.15289i | 0.817135 | + | 0.576446i | \(0.195561\pi\) | ||||
−0.817135 | + | 0.576446i | \(0.804439\pi\) | |||||||
\(410\) | − | 2.06744e13i | − | 0.0881294i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.12101e14 | −0.465237 | ||||||||
\(413\) | 2.13811e14 | 0.875599 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00172e13 | 0.239338 | ||||||||
\(416\) | −3.13660e13 | − | 4.71561e13i | −0.123437 | − | 0.185577i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.07761e13i | 0.0796333i | ||||||||
\(419\) | 2.13925e14 | 0.809253 | 0.404626 | − | 0.914482i | \(-0.367402\pi\) | ||||
0.404626 | + | 0.914482i | \(0.367402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.24393e14i | 0.458398i | 0.973380 | + | 0.229199i | \(0.0736107\pi\) | ||||
−0.973380 | + | 0.229199i | \(0.926389\pi\) | |||||||
\(422\) | − | 2.71063e12i | − | 0.00985944i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 8.05940e13i | − | 0.285621i | ||||||
\(425\) | −2.88073e13 | −0.100777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.92901e14i | − | 0.998545i | ||||||
\(428\) | −3.76903e14 | −1.26850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.36601e13 | 0.110418 | ||||||||
\(431\) | − | 3.23913e14i | − | 1.04907i | −0.851389 | − | 0.524535i | \(-0.824239\pi\) | ||
0.851389 | − | 0.524535i | \(-0.175761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.35022e13 | −0.0742036 | −0.0371018 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371018 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(434\) | 3.98868e13i | 0.124347i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 5.58851e13i | − | 0.169871i | ||||||
\(437\) | 2.79395e13i | 0.0838632i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.02014e14 | 1.17676 | 0.588379 | − | 0.808586i | \(-0.299767\pi\) | ||||
0.588379 | + | 0.808586i | \(0.299767\pi\) | |||||||
\(440\) | 1.01974e14i | 0.294781i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.13835e12 | − | 3.21482e12i | −0.00602914 | − | 0.00906430i | ||||
\(443\) | 3.08170e14 | 0.858164 | 0.429082 | − | 0.903265i | \(-0.358837\pi\) | ||||
0.429082 | + | 0.903265i | \(0.358837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.16800e14 | −1.40392 | ||||||||
\(446\) | 5.03007e13 | 0.134969 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.73841e14i | − | 0.978719i | ||||||
\(449\) | 1.99777e14i | 0.516643i | 0.966059 | + | 0.258322i | \(0.0831694\pi\) | ||||
−0.966059 | + | 0.258322i | \(0.916831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.44175e14 | 1.37331 | ||||||||
\(452\) | 3.34862e14 | 0.834843 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.32121e13 | 0.129480 | ||||||||
\(455\) | −4.56323e14 | + | 3.03524e14i | −1.09701 | + | 0.729677i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.57271e13i | − | 0.107309i | −0.998560 | − | 0.0536543i | \(-0.982913\pi\) | ||
0.998560 | − | 0.0536543i | \(-0.0170869\pi\) | |||||||
\(458\) | 9.21606e12 | 0.0213690 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.83744e13i | 0.154784i | ||||||||
\(461\) | − | 3.40488e14i | − | 0.761635i | −0.924650 | − | 0.380817i | \(-0.875643\pi\) | ||
0.924650 | − | 0.380817i | \(-0.124357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.63954e14i | 0.794971i | 0.917608 | + | 0.397486i | \(0.130117\pi\) | ||||
−0.917608 | + | 0.397486i | \(0.869883\pi\) | |||||||
\(464\) | 3.85021e14 | 0.831066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 2.85349e13i | − | 0.0601524i | ||||||
\(467\) | 1.10274e14 | 0.229738 | 0.114869 | − | 0.993381i | \(-0.463355\pi\) | ||||
0.114869 | + | 0.993381i | \(0.463355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.65596e14 | 0.743962 | ||||||||
\(470\) | − | 5.53431e13i | − | 0.111308i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.56995e13 | 0.129087 | ||||||||
\(473\) | 8.85976e14i | 1.72062i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.55991e14i | 0.485746i | ||||||||
\(476\) | − | 7.80755e13i | − | 0.146446i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.71737e13 | −0.141454 | ||||||||
\(479\) | 1.66407e14i | 0.301526i | 0.988570 | + | 0.150763i | \(0.0481731\pi\) | ||||
−0.988570 | + | 0.150763i | \(0.951827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.99046e14 | + | 5.99932e14i | 0.706684 | + | 1.06244i | ||||
\(482\) | 2.14088e13 | 0.0374829 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.57228e14 | −1.29592 | ||||||||
\(485\) | 1.47293e15 | 2.49232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.21283e13i | 0.0696891i | 0.999393 | + | 0.0348446i | \(0.0110936\pi\) | ||||
−0.999393 | + | 0.0348446i | \(0.988906\pi\) | |||||||
\(488\) | − | 9.00021e13i | − | 0.147212i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.54431e12 | 0.00246976 | ||||||||
\(491\) | −3.56448e13 | −0.0563700 | −0.0281850 | − | 0.999603i | \(-0.508973\pi\) | ||||
−0.0281850 | + | 0.999603i | \(0.508973\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.94914e13 | 0.122931 | ||||||||
\(494\) | −2.85679e13 | + | 1.90020e13i | −0.0436898 | + | 0.0290604i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.07844e15i | − | 1.61305i | ||||||
\(497\) | 1.42575e14 | 0.210903 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.70054e14i | 0.390748i | 0.980729 | + | 0.195374i | \(0.0625921\pi\) | ||||
−0.980729 | + | 0.195374i | \(0.937408\pi\) | |||||||
\(500\) | − | 2.77627e14i | − | 0.397307i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.72517e13i | 0.0241525i | ||||||||
\(503\) | 4.93264e14 | 0.683054 | 0.341527 | − | 0.939872i | \(-0.389056\pi\) | ||||
0.341527 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.19360e15i | 1.61717i | ||||||||
\(506\) | 1.01402e13 | 0.0135899 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.11750e15 | 1.46554 | ||||||||
\(509\) | 7.49682e14i | 0.972589i | 0.873795 | + | 0.486294i | \(0.161652\pi\) | ||||
−0.873795 | + | 0.486294i | \(0.838348\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.70548e14 | −0.470467 | ||||||||
\(512\) | − | 2.91321e14i | − | 0.365921i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 7.55830e13i | − | 0.0929238i | ||||||
\(515\) | 5.00464e14i | 0.608742i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.45670e15 | 1.73449 | ||||||||
\(518\) | − | 8.20928e13i | − | 0.0967145i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.40218e14 | + | 9.32664e13i | −0.161728 | + | 0.107574i | ||||
\(521\) | −1.28499e15 | −1.46654 | −0.733270 | − | 0.679938i | \(-0.762007\pi\) | ||||
−0.733270 | + | 0.679938i | \(0.762007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.71007e14 | 0.191097 | 0.0955486 | − | 0.995425i | \(-0.469539\pi\) | ||||
0.0955486 | + | 0.995425i | \(0.469539\pi\) | |||||||
\(524\) | −6.57273e14 | −0.726815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.46937e12i | 0.00375690i | ||||||||
\(527\) | − | 2.22655e14i | − | 0.238602i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.39173e14 | −0.985688 | ||||||||
\(530\) | −1.79397e14 | −0.186336 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.93803e14 | −0.705866 | ||||||||
\(533\) | 4.97707e14 | + | 7.48260e14i | 0.501157 | + | 0.753447i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.68265e15i | 1.65977i | ||||||||
\(536\) | 1.12340e14 | 0.109680 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.14932e14i | − | 0.109936i | ||||||
\(539\) | 4.06480e13i | 0.0384859i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.59371e15i | − | 1.47851i | −0.673424 | − | 0.739256i | \(-0.735177\pi\) | ||
0.673424 | − | 0.739256i | \(-0.264823\pi\) | |||||||
\(542\) | 1.48060e14 | 0.135969 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 3.60201e13i | − | 0.0324153i | ||||||
\(545\) | −2.49494e14 | −0.222269 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.12365e15 | 0.981073 | 0.490537 | − | 0.871421i | \(-0.336801\pi\) | ||||
0.490537 | + | 0.871421i | \(0.336801\pi\) | |||||||
\(548\) | − | 3.96902e14i | − | 0.343076i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.29072e13 | 0.0787145 | ||||||||
\(551\) | − | 7.06386e14i | − | 0.592527i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.69078e14i | 0.139027i | ||||||||
\(554\) | − | 5.73387e13i | − | 0.0466814i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.35379e15 | −1.08054 | ||||||||
\(557\) | − | 5.45822e14i | − | 0.431368i | −0.976463 | − | 0.215684i | \(-0.930802\pi\) | ||
0.976463 | − | 0.215684i | \(-0.0691981\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.21825e15 | + | 8.10321e14i | −0.943998 | + | 0.627903i | ||||
\(560\) | −1.68827e15 | −1.29541 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.46203e14 | 0.110004 | ||||||||
\(563\) | 1.07491e15 | 0.800897 | 0.400448 | − | 0.916319i | \(-0.368854\pi\) | ||||
0.400448 | + | 0.916319i | \(0.368854\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.49496e15i | − | 1.09235i | ||||||
\(566\) | 1.61735e14i | 0.117034i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.38102e13 | 0.0310928 | ||||||||
\(569\) | 3.71485e14 | 0.261110 | 0.130555 | − | 0.991441i | \(-0.458324\pi\) | ||||
0.130555 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.89713e14 | 0.406576 | 0.203288 | − | 0.979119i | \(-0.434837\pi\) | ||||
0.203288 | + | 0.979119i | \(0.434837\pi\) | |||||||
\(572\) | −1.22400e15 | − | 1.84017e15i | −0.835799 | − | 1.25655i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.02390e14i | − | 0.0685868i | ||||||
\(575\) | 1.24941e14 | 0.0828956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.47961e14i | − | 0.291590i | −0.989315 | − | 0.145795i | \(-0.953426\pi\) | ||
0.989315 | − | 0.145795i | \(-0.0465740\pi\) | |||||||
\(578\) | 1.13637e14i | 0.0732686i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 1.72869e15i | − | 1.09361i | ||||||
\(581\) | 2.97235e14 | 0.186265 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.72195e15i | − | 2.90365i | ||||||
\(584\) | −1.13861e14 | −0.0693594 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.57070e13 | 0.0333022 | ||||||||
\(587\) | − | 2.90281e14i | − | 0.171913i | −0.996299 | − | 0.0859567i | \(-0.972605\pi\) | ||
0.996299 | − | 0.0859567i | \(-0.0273947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.97858e15 | −1.15006 | ||||||||
\(590\) | − | 1.46243e14i | − | 0.0842148i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.21959e15i | 1.25459i | ||||||||
\(593\) | − | 1.53135e15i | − | 0.857581i | −0.903404 | − | 0.428790i | \(-0.858940\pi\) | ||
0.903404 | − | 0.428790i | \(-0.141060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.48561e14 | −0.191618 | ||||||||
\(596\) | − | 8.74767e14i | − | 0.476472i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.27427e12 | + | 1.39431e13i | 0.00495933 | + | 0.00745594i | ||||
\(599\) | 2.34047e14 | 0.124009 | 0.0620047 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620047 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.19750e15 | −1.14319 | −0.571597 | − | 0.820535i | \(-0.693676\pi\) | ||||
−0.571597 | + | 0.820535i | \(0.693676\pi\) | |||||||
\(602\) | 1.66701e14 | 0.0859327 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.45808e15i | 1.24421i | ||||||||
\(605\) | 3.38057e15i | 1.69565i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.02645e15 | 1.49072 | 0.745360 | − | 0.666662i | \(-0.232277\pi\) | ||||
0.745360 | + | 0.666662i | \(0.232277\pi\) | |||||||
\(608\) | −3.20086e14 | −0.156241 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00339e14 | −0.0960397 | ||||||||
\(611\) | 1.33231e15 | + | 2.00301e15i | 0.632963 | + | 0.951606i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.31524e15i | 0.613724i | 0.951754 | + | 0.306862i | \(0.0992791\pi\) | ||||
−0.951754 | + | 0.306862i | \(0.900721\pi\) | |||||||
\(614\) | 1.96226e13 | 0.00907468 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.05026e14i | 0.229414i | ||||||||
\(617\) | − | 7.90565e14i | − | 0.355934i | −0.984036 | − | 0.177967i | \(-0.943048\pi\) | ||
0.984036 | − | 0.177967i | \(-0.0569520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.75601e13i | 0.0254579i | 0.999919 | + | 0.0127290i | \(0.00405186\pi\) | ||||
−0.999919 | + | 0.0127290i | \(0.995948\pi\) | |||||||
\(620\) | −4.84204e15 | −2.12263 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.33253e14i | 0.100457i | ||||||||
\(623\) | −2.55945e15 | −1.09260 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.89150e15 | −1.21278 | ||||||||
\(626\) | 9.96462e13i | 0.0414288i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.95811e14 | −0.0799943 | ||||||||
\(629\) | 4.58256e14i | 0.185579i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.34887e15i | 1.33271i | 0.745633 | + | 0.666356i | \(0.232147\pi\) | ||||
−0.745633 | + | 0.666356i | \(0.767853\pi\) | |||||||
\(632\) | 5.19540e13i | 0.0204963i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.41160e13 | −0.0326128 | ||||||||
\(635\) | − | 4.98897e15i | − | 1.91759i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.58925e13 | + | 3.71771e13i | −0.0211148 | + | 0.0140446i | ||||
\(638\) | −2.56370e14 | −0.0960182 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.04344e15 | −0.384128 | ||||||||
\(641\) | 5.29783e14 | 0.193365 | 0.0966827 | − | 0.995315i | \(-0.469177\pi\) | ||||
0.0966827 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.01506e15i | − | 0.364194i | −0.983281 | − | 0.182097i | \(-0.941712\pi\) | ||
0.983281 | − | 0.182097i | \(-0.0582885\pi\) | |||||||
\(644\) | 3.38623e14i | 0.120460i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.18215e13 | −0.00763143 | ||||||||
\(647\) | −1.92293e14 | −0.0666793 | −0.0333396 | − | 0.999444i | \(-0.510614\pi\) | ||||
−0.0333396 | + | 0.999444i | \(0.510614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.84929e15 | 1.31231 | ||||||||
\(650\) | 8.49737e13 | + | 1.27751e14i | 0.0287251 | + | 0.0431857i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3.06753e15i | − | 1.01959i | ||||||
\(653\) | 2.34263e15 | 0.772114 | 0.386057 | − | 0.922475i | \(-0.373837\pi\) | ||||
0.386057 | + | 0.922475i | \(0.373837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.93433e15i | 0.951004i | ||||||||
\(656\) | 2.76836e15i | 0.889717i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 2.74086e14i | − | 0.0866253i | ||||||
\(659\) | −5.91488e15 | −1.85386 | −0.926928 | − | 0.375239i | \(-0.877560\pi\) | ||||
−0.926928 | + | 0.375239i | \(0.877560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.81720e15i | − | 1.48486i | −0.669922 | − | 0.742432i | \(-0.733672\pi\) | ||
0.669922 | − | 0.742432i | \(-0.266328\pi\) | |||||||
\(662\) | −1.14213e14 | −0.0349138 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.13337e13 | 0.0274604 | ||||||||
\(665\) | 3.09742e15i | 0.923594i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.44764e14 | −0.101118 | ||||||||
\(668\) | − | 2.10728e15i | − | 0.612988i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 2.50060e14i | − | 0.0715540i | ||||||
\(671\) | − | 5.27316e15i | − | 1.49657i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.84391e15 | −0.514821 | −0.257410 | − | 0.966302i | \(-0.582869\pi\) | ||||
−0.257410 | + | 0.966302i | \(0.582869\pi\) | |||||||
\(674\) | 3.04267e14i | 0.0842607i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.41083e15 | − | 3.36608e15i | 0.384385 | − | 0.917101i | ||||
\(677\) | 2.85026e15 | 0.770276 | 0.385138 | − | 0.922859i | \(-0.374154\pi\) | ||||
0.385138 | + | 0.922859i | \(0.374154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.29470e15 | 1.93965 | ||||||||
\(680\) | −1.07105e14 | −0.0282495 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.18091e14i | 0.186365i | ||||||||
\(683\) | − | 4.69918e15i | − | 1.20978i | −0.796308 | − | 0.604892i | \(-0.793216\pi\) | ||
0.796308 | − | 0.604892i | \(-0.206784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.77193e15 | −0.448899 | ||||||||
\(686\) | −2.93946e14 | −0.0738729 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.50720e15 | −1.11473 | ||||||||
\(689\) | 6.49285e15 | − | 4.31873e15i | 1.59305 | − | 1.05962i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.34559e15i | − | 0.566399i | −0.959061 | − | 0.283199i | \(-0.908604\pi\) | ||
0.959061 | − | 0.283199i | \(-0.0913958\pi\) | |||||||
\(692\) | 2.26590e14 | 0.0542823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.96532e14i | 0.0699188i | ||||||||
\(695\) | 6.04388e15i | 1.41384i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.71556e14i | 0.131607i | ||||||||
\(698\) | 1.31115e14 | 0.0299534 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.10257e15i | 0.697722i | ||||||||
\(701\) | −2.09935e15 | −0.468421 | −0.234210 | − | 0.972186i | \(-0.575250\pi\) | ||||
−0.234210 | + | 0.972186i | \(0.575250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.07221e15 | 0.894490 | ||||||||
\(704\) | − | 6.73034e15i | − | 1.46686i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.09823e14 | −0.0235650 | ||||||||
\(707\) | 5.91127e15i | 1.25856i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.10587e15i | − | 1.27995i | −0.768396 | − | 0.639975i | \(-0.778945\pi\) | ||
0.768396 | − | 0.639975i | \(-0.221055\pi\) | |||||||
\(710\) | − | 9.75185e13i | − | 0.0202846i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.86463e14 | −0.161079 | ||||||||
\(713\) | 9.65683e14i | 0.196265i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.21528e15 | + | 5.46441e15i | −1.64414 | + | 1.09360i | ||||
\(716\) | −4.20073e15 | −0.834263 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.92983e14 | 0.0964156 | ||||||||
\(719\) | −5.91981e15 | −1.14894 | −0.574472 | − | 0.818524i | \(-0.694793\pi\) | ||||
−0.574472 | + | 0.818524i | \(0.694793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47854e15i | 0.473754i | ||||||||
\(722\) | − | 2.00687e14i | − | 0.0380685i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.06112e15 | 1.31920 | ||||||||
\(725\) | −3.15884e15 | −0.585690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.61053e15 | 0.476748 | 0.238374 | − | 0.971173i | \(-0.423386\pi\) | ||||
0.238374 | + | 0.971173i | \(0.423386\pi\) | |||||||
\(728\) | −6.94429e14 | + | 4.61901e14i | −0.125865 | + | 0.0837194i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.53447e14i | 0.0452493i | ||||||||
\(731\) | −9.30556e14 | −0.164891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.10402e15i | 1.58914i | 0.607175 | + | 0.794568i | \(0.292303\pi\) | ||||
−0.607175 | + | 0.794568i | \(0.707697\pi\) | |||||||
\(734\) | − | 2.35651e14i | − | 0.0408264i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.56224e14i | 0.0266636i | ||||||||
\(737\) | 6.58190e15 | 1.11501 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.00804e15i | − | 0.335141i | −0.985860 | − | 0.167570i | \(-0.946408\pi\) | ||
0.985860 | − | 0.167570i | \(-0.0535921\pi\) | |||||||
\(740\) | 9.96561e15 | 1.65093 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.88461e14 | −0.145016 | ||||||||
\(743\) | 8.48953e15i | 1.37545i | 0.725971 | + | 0.687725i | \(0.241391\pi\) | ||||
−0.725971 | + | 0.687725i | \(0.758609\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.90531e15 | −0.623442 | ||||||||
\(746\) | − | 4.09815e14i | − | 0.0649417i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.40561e15i | − | 0.219486i | ||||||
\(749\) | 8.33331e15i | 1.29172i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.75001e15 | −0.878312 | −0.439156 | − | 0.898411i | \(-0.644722\pi\) | ||||
−0.439156 | + | 0.898411i | \(0.644722\pi\) | |||||||
\(752\) | 7.41062e15i | 1.12372i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.34478e14 | − | 3.52518e14i | −0.0350397 | − | 0.0526792i | ||||
\(755\) | 1.09739e16 | 1.62799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.57782e15 | 0.669317 | 0.334658 | − | 0.942339i | \(-0.391379\pi\) | ||||
0.334658 | + | 0.942339i | \(0.391379\pi\) | |||||||
\(758\) | −1.09385e14 | −0.0158774 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.51770e14i | 0.136162i | ||||||||
\(761\) | 3.71156e15i | 0.527158i | 0.964638 | + | 0.263579i | \(0.0849029\pi\) | ||||
−0.964638 | + | 0.263579i | \(0.915097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.23562e15 | −0.172981 | ||||||||
\(764\) | 9.44070e15 | 1.31217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.23675e14 | 0.0306450 | ||||||||
\(767\) | 3.52059e15 | + | 5.29291e15i | 0.478896 | + | 0.719980i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.37640e15i | − | 0.318658i | −0.987226 | − | 0.159329i | \(-0.949067\pi\) | ||
0.987226 | − | 0.159329i | \(-0.0509331\pi\) | |||||||
\(770\) | 1.12415e15 | 0.149667 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 2.31721e15i | − | 0.304138i | ||||||
\(773\) | − | 4.48843e15i | − | 0.584934i | −0.956276 | − | 0.292467i | \(-0.905524\pi\) | ||
0.956276 | − | 0.292467i | \(-0.0944762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.84788e15i | 1.13679i | ||||||||
\(776\) | 2.24150e15 | 0.285956 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.86132e14i | 0.0485677i | ||||||||
\(779\) | 5.07903e15 | 0.634344 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.56681e15 | 0.316091 | ||||||||
\(782\) | 1.06504e13i | 0.00130235i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.06788e14 | −0.0249337 | ||||||||
\(785\) | 8.74180e14i | 0.104669i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.79432e15i | 0.211856i | 0.994374 | + | 0.105928i | \(0.0337812\pi\) | ||||
−0.994374 | + | 0.105928i | \(0.966219\pi\) | |||||||
\(788\) | 4.73080e15i | 0.554677i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.15646e14 | 0.0133716 | ||||||||
\(791\) | − | 7.40378e15i | − | 0.850125i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.25079e15 | − | 4.82288e15i | 0.821074 | − | 0.546140i | ||||
\(794\) | −9.10458e14 | −0.102388 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.99459e14 | 0.0664872 | ||||||||
\(797\) | −1.29926e15 | −0.143111 | −0.0715556 | − | 0.997437i | \(-0.522796\pi\) | ||||
−0.0715556 | + | 0.997437i | \(0.522796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53000e15i | 0.166220i | ||||||||
\(800\) | 1.43137e15i | 0.154439i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.16278e15 | 0.123748 | ||||||||
\(803\) | −6.67105e15 | −0.705113 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.51175e15 | 0.157617 | ||||||||
\(806\) | −9.87401e14 | + | 6.56772e14i | −0.102247 | + | 0.0680099i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.81641e15i | 0.185545i | ||||||||
\(809\) | 1.71565e16 | 1.74065 | 0.870326 | − | 0.492476i | \(-0.163908\pi\) | ||||
0.870326 | + | 0.492476i | \(0.163908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.99602e15i | − | 0.900401i | −0.892928 | − | 0.450200i | \(-0.851353\pi\) | ||
0.892928 | − | 0.450200i | \(-0.148647\pi\) | |||||||
\(812\) | − | 8.56130e15i | − | 0.851102i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 1.47793e15i | − | 0.144951i | ||||||
\(815\) | −1.36947e16 | −1.33409 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.26921e15i | 0.794772i | ||||||||
\(818\) | 9.03929e14 | 0.0862961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.24295e16 | 1.17079 | ||||||||
\(821\) | − | 1.60428e16i | − | 1.50104i | −0.660848 | − | 0.750520i | \(-0.729803\pi\) | ||
0.660848 | − | 0.750520i | \(-0.270197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.49308e15 | −0.507128 | −0.253564 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253564 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(824\) | 7.61603e14i | 0.0698440i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 7.24266e14i | − | 0.0655402i | ||||||
\(827\) | 8.14813e15i | 0.732450i | 0.930526 | + | 0.366225i | \(0.119350\pi\) | ||||
−0.930526 | + | 0.366225i | \(0.880650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.98376e16 | 1.75971 | 0.879853 | − | 0.475246i | \(-0.157641\pi\) | ||||
0.879853 | + | 0.475246i | \(0.157641\pi\) | |||||||
\(830\) | − | 2.03303e14i | − | 0.0179149i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.25446e15 | − | 6.15563e15i | 0.804772 | − | 0.535296i | ||||
\(833\) | −4.26934e13 | −0.00368819 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.40775e15 | −0.802066 | ||||||||
\(836\) | −1.24907e16 | −1.05792 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 7.24651e14i | − | 0.0605741i | ||||||
\(839\) | − | 2.34908e15i | − | 0.195077i | −0.995232 | − | 0.0975387i | \(-0.968903\pi\) | ||
0.995232 | − | 0.0975387i | \(-0.0310970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.48395e15 | −0.285558 | ||||||||
\(842\) | 4.21368e14 | 0.0343119 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.62965e15 | 0.130981 | ||||||||
\(845\) | −1.50275e16 | − | 6.29850e15i | −1.19998 | − | 0.502951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.67423e16i | 1.31964i | ||||||||
\(848\) | 2.40218e16 | 1.88117 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.75821e13i | 0.00754338i | ||||||||
\(851\) | − | 1.98751e15i | − | 0.152650i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.56183e16i | − | 1.18417i | −0.805875 | − | 0.592086i | \(-0.798305\pi\) | ||
0.805875 | − | 0.592086i | \(-0.201695\pi\) | |||||||
\(854\) | −9.92175e14 | −0.0747429 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.56064e15i | 0.190434i | ||||||||
\(857\) | −1.24481e16 | −0.919834 | −0.459917 | − | 0.887962i | \(-0.652121\pi\) | ||||
−0.459917 | + | 0.887962i | \(0.652121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.17701e16 | −0.858651 | −0.429326 | − | 0.903150i | \(-0.641249\pi\) | ||||
−0.429326 | + | 0.903150i | \(0.641249\pi\) | |||||||
\(860\) | 2.02366e16i | 1.46689i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.09723e15 | −0.0785247 | ||||||||
\(863\) | − | 4.09282e15i | − | 0.291047i | −0.989355 | − | 0.145524i | \(-0.953513\pi\) | ||
0.989355 | − | 0.145524i | \(-0.0464867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.01159e15i | − | 0.0710259i | ||||||
\(866\) | 7.96115e13i | 0.00555428i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.39801e16 | −1.65194 | ||||||||
\(869\) | 3.04395e15i | 0.208367i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.01986e15 | + | 9.05035e15i | 0.406899 | + | 0.611738i | ||||
\(872\) | −3.79678e14 | −0.0255020 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.46426e13 | 0.00627731 | ||||||||
\(875\) | −6.13831e15 | −0.404580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.66555e16i | − | 1.08408i | −0.840354 | − | 0.542038i | \(-0.817653\pi\) | ||
0.840354 | − | 0.542038i | \(-0.182347\pi\) | |||||||
\(878\) | − | 1.36179e15i | − | 0.0880824i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.03943e16 | −1.94150 | ||||||||
\(881\) | −2.33295e16 | −1.48094 | −0.740472 | − | 0.672087i | \(-0.765398\pi\) | ||||
−0.740472 | + | 0.672087i | \(0.765398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.66211e14 | 0.0354972 | 0.0177486 | − | 0.999842i | \(-0.494350\pi\) | ||||
0.0177486 | + | 0.999842i | \(0.494350\pi\) | |||||||
\(884\) | 1.93277e15 | − | 1.28558e15i | 0.120418 | − | 0.0800964i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1.04390e15i | − | 0.0642352i | ||||||
\(887\) | −8.53270e15 | −0.521803 | −0.260901 | − | 0.965365i | \(-0.584020\pi\) | ||||
−0.260901 | + | 0.965365i | \(0.584020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.47078e16i | − | 1.49236i | ||||||
\(890\) | 1.75061e15i | 0.105086i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.02410e16i | 1.79304i | ||||||||
\(893\) | 1.35960e16 | 0.801177 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.87538e16i | 1.09160i | ||||||||
\(896\) | −5.16760e15 | −0.298948 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.76726e14 | 0.0386717 | ||||||||
\(899\) | − | 2.44150e16i | − | 1.38669i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.95954e15 | 0.278263 | ||||||||
\(902\) | − | 1.84334e15i | − | 0.102795i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.27502e15i | − | 0.125331i | ||||||
\(905\) | − | 3.15237e16i | − | 1.72612i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.92538e15 | 0.536917 | 0.268458 | − | 0.963291i | \(-0.413486\pi\) | ||||
0.268458 | + | 0.963291i | \(0.413486\pi\) | |||||||
\(908\) | 3.19914e16i | 1.72013i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.02816e15 | + | 1.54575e15i | 0.0546177 | + | 0.0821130i | ||||
\(911\) | −1.06854e16 | −0.564208 | −0.282104 | − | 0.959384i | \(-0.591032\pi\) | ||||
−0.282104 | + | 0.959384i | \(0.591032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.35118e15 | 0.279165 | ||||||||
\(914\) | −1.54896e14 | −0.00803225 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.54074e15i | 0.283885i | ||||||||
\(917\) | 1.45323e16i | 0.740119i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.16827e15 | −0.310405 | −0.155202 | − | 0.987883i | \(-0.549603\pi\) | ||||
−0.155202 | + | 0.987883i | \(0.549603\pi\) | |||||||
\(920\) | 4.64529e14 | 0.0232370 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.15337e15 | −0.0570098 | ||||||||
\(923\) | 2.34762e15 | + | 3.52945e15i | 0.115350 | + | 0.173420i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.82102e16i | − | 0.884170i | ||||||
\(926\) | 1.23286e15 | 0.0595051 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.94975e15i | − | 0.188389i | ||||||
\(929\) | − | 1.71984e16i | − | 0.815460i | −0.913103 | − | 0.407730i | \(-0.866320\pi\) | ||
0.913103 | − | 0.407730i | \(-0.133680\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.79386e14i | 0.0177770i | ||||||||
\(932\) | 1.71553e16 | 0.799117 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 3.73544e14i | − | 0.0171963i | ||||||
\(935\) | −6.27522e15 | −0.287187 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.38540e16 | −0.626626 | −0.313313 | − | 0.949650i | \(-0.601439\pi\) | ||||
−0.313313 | + | 0.949650i | \(0.601439\pi\) | |||||||
\(938\) | − | 1.23842e15i | − | 0.0556869i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.32725e16 | 1.47871 | ||||||||
\(941\) | − | 3.01742e16i | − | 1.33319i | −0.745419 | − | 0.666597i | \(-0.767750\pi\) | ||
0.745419 | − | 0.666597i | \(-0.232250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.47891e15i | − | 0.108255i | ||||||
\(944\) | 1.95824e16i | 0.850196i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00116e15 | 0.128792 | ||||||||
\(947\) | 1.47817e16i | 0.630665i | 0.948981 | + | 0.315333i | \(0.102116\pi\) | ||||
−0.948981 | + | 0.315333i | \(0.897884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.10140e15 | − | 9.17293e15i | −0.257315 | − | 0.386851i | ||||
\(950\) | 8.67145e14 | 0.0363590 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.30437e14 | −0.0219852 | ||||||||
\(953\) | 2.28957e16 | 0.943501 | 0.471750 | − | 0.881732i | \(-0.343622\pi\) | ||||
0.471750 | + | 0.881732i | \(0.343622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.21471e16i | − | 1.71692i | ||||||
\(956\) | − | 4.63972e16i | − | 1.87920i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.63687e14 | 0.0225698 | ||||||||
\(959\) | −8.77548e15 | −0.349356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.29779e16 | −1.69148 | ||||||||
\(962\) | 2.03221e15 | − | 1.35173e15i | 0.0795255 | − | 0.0528966i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.28711e16i | 0.497956i | ||||||||
\(965\) | −1.03450e16 | −0.397951 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.65782e16i | − | 1.39116i | −0.718448 | − | 0.695580i | \(-0.755147\pi\) | ||
0.718448 | − | 0.695580i | \(-0.244853\pi\) | |||||||
\(968\) | 5.14453e15i | 0.194550i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 4.98943e15i | − | 0.186555i | ||||||
\(971\) | −2.24568e16 | −0.834915 | −0.417458 | − | 0.908696i | \(-0.637079\pi\) | ||||
−0.417458 | + | 0.908696i | \(0.637079\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.99323e16i | 1.10032i | ||||||||
\(974\) | 1.42706e14 | 0.00521636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.68260e16 | 0.969575 | ||||||||
\(977\) | 2.77848e16i | 0.998590i | 0.866432 | + | 0.499295i | \(0.166408\pi\) | ||||
−0.866432 | + | 0.499295i | \(0.833592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.60783e16 | −1.63754 | ||||||||
\(980\) | 9.28444e14i | 0.0328105i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.20744e14i | 0.00421940i | ||||||||
\(983\) | 6.91991e15i | 0.240467i | 0.992746 | + | 0.120234i | \(0.0383644\pi\) | ||||
−0.992746 | + | 0.120234i | \(0.961636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.11202e16 | 0.725770 | ||||||||
\(986\) | − | 2.69270e14i | − | 0.00920163i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.14241e16 | − | 1.71752e16i | −0.386063 | − | 0.580413i | ||||
\(989\) | 4.03594e15 | 0.135633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.49174e16 | 1.49283 | 0.746414 | − | 0.665482i | \(-0.231774\pi\) | ||||
0.746414 | + | 0.665482i | \(0.231774\pi\) | |||||||
\(992\) | −1.10632e16 | −0.365651 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 4.82959e14i | − | 0.0157865i | ||||||
\(995\) | − | 2.67623e15i | − | 0.0869954i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.98182e16 | −1.60164 | −0.800819 | − | 0.598907i | \(-0.795602\pi\) | ||||
−0.800819 | + | 0.598907i | \(0.795602\pi\) | |||||||
\(998\) | 9.14782e14 | 0.0292482 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.12.b.b.64.6 | 12 | ||
3.2 | odd | 2 | 13.12.b.a.12.7 | yes | 12 | ||
12.11 | even | 2 | 208.12.f.b.129.4 | 12 | |||
13.12 | even | 2 | inner | 117.12.b.b.64.7 | 12 | ||
39.5 | even | 4 | 169.12.a.e.1.7 | 12 | |||
39.8 | even | 4 | 169.12.a.e.1.6 | 12 | |||
39.38 | odd | 2 | 13.12.b.a.12.6 | ✓ | 12 | ||
156.155 | even | 2 | 208.12.f.b.129.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.12.b.a.12.6 | ✓ | 12 | 39.38 | odd | 2 | ||
13.12.b.a.12.7 | yes | 12 | 3.2 | odd | 2 | ||
117.12.b.b.64.6 | 12 | 1.1 | even | 1 | trivial | ||
117.12.b.b.64.7 | 12 | 13.12 | even | 2 | inner | ||
169.12.a.e.1.6 | 12 | 39.8 | even | 4 | |||
169.12.a.e.1.7 | 12 | 39.5 | even | 4 | |||
208.12.f.b.129.3 | 12 | 156.155 | even | 2 | |||
208.12.f.b.129.4 | 12 | 12.11 | even | 2 |