Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,9,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(72.1060139808\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.11 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.9.c.a.58.70 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 25.1007i | − | 1.56879i | −0.620261 | − | 0.784395i | \(-0.712973\pi\) | ||
0.620261 | − | 0.784395i | \(-0.287027\pi\) | |||||||
\(3\) | −46.7654 | −0.577350 | ||||||||
\(4\) | −374.043 | −1.46110 | ||||||||
\(5\) | 458.555 | 0.733687 | 0.366844 | − | 0.930283i | \(-0.380438\pi\) | ||||
0.366844 | + | 0.930283i | \(0.380438\pi\) | |||||||
\(6\) | 1173.84i | 0.905742i | ||||||||
\(7\) | −1157.18 | −0.481959 | −0.240979 | − | 0.970530i | \(-0.577469\pi\) | ||||
−0.240979 | + | 0.970530i | \(0.577469\pi\) | |||||||
\(8\) | 2962.95i | 0.723377i | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | − | 11510.0i | − | 1.15100i | ||||||
\(11\) | − | 15446.5i | − | 1.05502i | −0.849550 | − | 0.527509i | \(-0.823126\pi\) | ||
0.849550 | − | 0.527509i | \(-0.176874\pi\) | |||||||
\(12\) | 17492.3 | 0.843569 | ||||||||
\(13\) | 19712.2i | 0.690179i | 0.938570 | + | 0.345090i | \(0.112151\pi\) | ||||
−0.938570 | + | 0.345090i | \(0.887849\pi\) | |||||||
\(14\) | 29046.0i | 0.756092i | ||||||||
\(15\) | −21444.5 | −0.423595 | ||||||||
\(16\) | −21382.9 | −0.326277 | ||||||||
\(17\) | −208.117 | −0.00249179 | −0.00124590 | − | 0.999999i | \(-0.500397\pi\) | ||||
−0.00124590 | + | 0.999999i | \(0.500397\pi\) | |||||||
\(18\) | − | 54895.1i | − | 0.522930i | ||||||
\(19\) | −32459.5 | −0.249074 | −0.124537 | − | 0.992215i | \(-0.539744\pi\) | ||||
−0.124537 | + | 0.992215i | \(0.539744\pi\) | |||||||
\(20\) | −171519. | −1.07199 | ||||||||
\(21\) | 54116.1 | 0.278259 | ||||||||
\(22\) | −387717. | −1.65510 | ||||||||
\(23\) | − | 244303.i | − | 0.873005i | −0.899703 | − | 0.436502i | \(-0.856217\pi\) | ||
0.899703 | − | 0.436502i | \(-0.143783\pi\) | |||||||
\(24\) | − | 138564.i | − | 0.417642i | ||||||
\(25\) | −180353. | −0.461703 | ||||||||
\(26\) | 494789. | 1.08275 | ||||||||
\(27\) | −102276. | −0.192450 | ||||||||
\(28\) | 432836. | 0.704192 | ||||||||
\(29\) | −920152. | −1.30097 | −0.650485 | − | 0.759519i | \(-0.725435\pi\) | ||||
−0.650485 | + | 0.759519i | \(0.725435\pi\) | |||||||
\(30\) | 538270.i | 0.664531i | ||||||||
\(31\) | 725461.i | 0.785538i | 0.919637 | + | 0.392769i | \(0.128483\pi\) | ||||
−0.919637 | + | 0.392769i | \(0.871517\pi\) | |||||||
\(32\) | 1.29524e6i | 1.23524i | ||||||||
\(33\) | 722362.i | 0.609115i | ||||||||
\(34\) | 5223.87i | 0.00390910i | ||||||||
\(35\) | −530631. | −0.353607 | ||||||||
\(36\) | −818032. | −0.487035 | ||||||||
\(37\) | 2.65720e6i | 1.41781i | 0.705306 | + | 0.708903i | \(0.250810\pi\) | ||||
−0.705306 | + | 0.708903i | \(0.749190\pi\) | |||||||
\(38\) | 814755.i | 0.390744i | ||||||||
\(39\) | − | 921849.i | − | 0.398475i | ||||||
\(40\) | 1.35868e6i | 0.530733i | ||||||||
\(41\) | 3.07208e6 | 1.08717 | 0.543584 | − | 0.839355i | \(-0.317067\pi\) | ||||
0.543584 | + | 0.839355i | \(0.317067\pi\) | |||||||
\(42\) | − | 1.35835e6i | − | 0.436530i | ||||||
\(43\) | 5.98941e6i | 1.75190i | 0.482400 | + | 0.875951i | \(0.339765\pi\) | ||||
−0.482400 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(44\) | 5.77766e6i | 1.54149i | ||||||||
\(45\) | 1.00286e6 | 0.244562 | ||||||||
\(46\) | −6.13215e6 | −1.36956 | ||||||||
\(47\) | − | 8.25605e6i | − | 1.69192i | −0.533243 | − | 0.845962i | \(-0.679027\pi\) | ||
0.533243 | − | 0.845962i | \(-0.320973\pi\) | |||||||
\(48\) | 999980. | 0.188376 | ||||||||
\(49\) | −4.42573e6 | −0.767716 | ||||||||
\(50\) | 4.52697e6i | 0.724315i | ||||||||
\(51\) | 9732.67 | 0.00143864 | ||||||||
\(52\) | − | 7.37321e6i | − | 1.00842i | ||||||
\(53\) | 7.09542e6 | 0.899238 | 0.449619 | − | 0.893220i | \(-0.351560\pi\) | ||||
0.449619 | + | 0.893220i | \(0.351560\pi\) | |||||||
\(54\) | 2.56719e6i | 0.301914i | ||||||||
\(55\) | − | 7.08307e6i | − | 0.774053i | ||||||
\(56\) | − | 3.42868e6i | − | 0.348638i | ||||||
\(57\) | 1.51798e6 | 0.143803 | ||||||||
\(58\) | 2.30964e7i | 2.04095i | ||||||||
\(59\) | 1.16388e7 | + | 3.37193e6i | 0.960502 | + | 0.278273i | ||||
\(60\) | 8.02115e6 | 0.618916 | ||||||||
\(61\) | 7.65261e6i | 0.552701i | 0.961057 | + | 0.276351i | \(0.0891251\pi\) | ||||
−0.961057 | + | 0.276351i | \(0.910875\pi\) | |||||||
\(62\) | 1.82096e7 | 1.23235 | ||||||||
\(63\) | −2.53076e6 | −0.160653 | ||||||||
\(64\) | 2.70374e7 | 1.61155 | ||||||||
\(65\) | 9.03913e6i | 0.506376i | ||||||||
\(66\) | 1.81318e7 | 0.955573 | ||||||||
\(67\) | 1.47421e7i | 0.731579i | 0.930698 | + | 0.365790i | \(0.119201\pi\) | ||||
−0.930698 | + | 0.365790i | \(0.880799\pi\) | |||||||
\(68\) | 77844.7 | 0.00364077 | ||||||||
\(69\) | 1.14249e7i | 0.504030i | ||||||||
\(70\) | 1.33192e7i | 0.554735i | ||||||||
\(71\) | 3.87749e6 | 0.152587 | 0.0762935 | − | 0.997085i | \(-0.475691\pi\) | ||||
0.0762935 | + | 0.997085i | \(0.475691\pi\) | |||||||
\(72\) | 6.47998e6i | 0.241126i | ||||||||
\(73\) | − | 1.72671e7i | − | 0.608035i | −0.952666 | − | 0.304018i | \(-0.901672\pi\) | ||
0.952666 | − | 0.304018i | \(-0.0983282\pi\) | |||||||
\(74\) | 6.66974e7 | 2.22424 | ||||||||
\(75\) | 8.43426e6 | 0.266564 | ||||||||
\(76\) | 1.21412e7 | 0.363923 | ||||||||
\(77\) | 1.78744e7i | 0.508475i | ||||||||
\(78\) | −2.31390e7 | −0.625124 | ||||||||
\(79\) | −6.10409e7 | −1.56716 | −0.783579 | − | 0.621293i | \(-0.786608\pi\) | ||||
−0.783579 | + | 0.621293i | \(0.786608\pi\) | |||||||
\(80\) | −9.80523e6 | −0.239386 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | − | 7.71112e7i | − | 1.70554i | ||||||
\(83\) | 7.83794e6i | 0.165154i | 0.996585 | + | 0.0825771i | \(0.0263151\pi\) | ||||
−0.996585 | + | 0.0825771i | \(0.973685\pi\) | |||||||
\(84\) | −2.02417e7 | −0.406565 | ||||||||
\(85\) | −95433.0 | −0.00182820 | ||||||||
\(86\) | 1.50338e8 | 2.74837 | ||||||||
\(87\) | 4.30313e7 | 0.751116 | ||||||||
\(88\) | 4.57673e7 | 0.763176 | ||||||||
\(89\) | − | 8.95553e7i | − | 1.42735i | −0.700476 | − | 0.713676i | \(-0.747029\pi\) | ||
0.700476 | − | 0.713676i | \(-0.252971\pi\) | |||||||
\(90\) | − | 2.51724e7i | − | 0.383667i | ||||||
\(91\) | − | 2.28106e7i | − | 0.332638i | ||||||
\(92\) | 9.13796e7i | 1.27555i | ||||||||
\(93\) | − | 3.39265e7i | − | 0.453531i | ||||||
\(94\) | −2.07232e8 | −2.65428 | ||||||||
\(95\) | −1.48845e7 | −0.182742 | ||||||||
\(96\) | − | 6.05724e7i | − | 0.713165i | ||||||
\(97\) | 1.08068e8i | 1.22070i | 0.792131 | + | 0.610351i | \(0.208971\pi\) | ||||
−0.792131 | + | 0.610351i | \(0.791029\pi\) | |||||||
\(98\) | 1.11089e8i | 1.20439i | ||||||||
\(99\) | − | 3.37815e7i | − | 0.351672i | ||||||
\(100\) | 6.74596e7 | 0.674596 | ||||||||
\(101\) | 4.86906e7i | 0.467907i | 0.972248 | + | 0.233954i | \(0.0751664\pi\) | ||||
−0.972248 | + | 0.233954i | \(0.924834\pi\) | |||||||
\(102\) | − | 244296.i | − | 0.00225692i | ||||||
\(103\) | − | 1.01995e8i | − | 0.906213i | −0.891456 | − | 0.453106i | \(-0.850316\pi\) | ||
0.891456 | − | 0.453106i | \(-0.149684\pi\) | |||||||
\(104\) | −5.84064e7 | −0.499260 | ||||||||
\(105\) | 2.48152e7 | 0.204155 | ||||||||
\(106\) | − | 1.78100e8i | − | 1.41072i | ||||||
\(107\) | −6.84585e6 | −0.0522267 | −0.0261133 | − | 0.999659i | \(-0.508313\pi\) | ||||
−0.0261133 | + | 0.999659i | \(0.508313\pi\) | |||||||
\(108\) | 3.82556e7 | 0.281190 | ||||||||
\(109\) | 2.20679e8i | 1.56334i | 0.623690 | + | 0.781672i | \(0.285633\pi\) | ||||
−0.623690 | + | 0.781672i | \(0.714367\pi\) | |||||||
\(110\) | −1.77790e8 | −1.21433 | ||||||||
\(111\) | − | 1.24265e8i | − | 0.818571i | ||||||
\(112\) | 2.47439e7 | 0.157252 | ||||||||
\(113\) | − | 1.71332e8i | − | 1.05081i | −0.850851 | − | 0.525406i | \(-0.823913\pi\) | ||
0.850851 | − | 0.525406i | \(-0.176087\pi\) | |||||||
\(114\) | − | 3.81023e7i | − | 0.225596i | ||||||
\(115\) | − | 1.12026e8i | − | 0.640513i | ||||||
\(116\) | 3.44176e8 | 1.90086 | ||||||||
\(117\) | 4.31106e7i | 0.230060i | ||||||||
\(118\) | 8.46377e7 | − | 2.92140e8i | 0.436552 | − | 1.50683i | ||||
\(119\) | 240829. | 0.00120094 | ||||||||
\(120\) | − | 6.35390e7i | − | 0.306419i | ||||||
\(121\) | −2.42358e7 | −0.113062 | ||||||||
\(122\) | 1.92086e8 | 0.867073 | ||||||||
\(123\) | −1.43667e8 | −0.627677 | ||||||||
\(124\) | − | 2.71354e8i | − | 1.14775i | ||||||
\(125\) | −2.61824e8 | −1.07243 | ||||||||
\(126\) | 6.35237e7i | 0.252031i | ||||||||
\(127\) | 4.65901e8 | 1.79093 | 0.895464 | − | 0.445133i | \(-0.146844\pi\) | ||||
0.895464 | + | 0.445133i | \(0.146844\pi\) | |||||||
\(128\) | − | 3.47074e8i | − | 1.29295i | ||||||
\(129\) | − | 2.80097e8i | − | 1.01146i | ||||||
\(130\) | 2.26888e8 | 0.794398 | ||||||||
\(131\) | − | 1.18641e6i | − | 0.00402857i | −0.999998 | − | 0.00201429i | \(-0.999359\pi\) | ||
0.999998 | − | 0.00201429i | \(-0.000641168\pi\) | |||||||
\(132\) | − | 2.70194e8i | − | 0.889980i | ||||||
\(133\) | 3.75616e7 | 0.120043 | ||||||||
\(134\) | 3.70037e8 | 1.14769 | ||||||||
\(135\) | −4.68991e7 | −0.141198 | ||||||||
\(136\) | − | 616641.i | − | 0.00180251i | ||||||
\(137\) | 2.77000e8 | 0.786317 | 0.393159 | − | 0.919471i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919471i | \(0.371382\pi\) | |||||||
\(138\) | 2.86772e8 | 0.790717 | ||||||||
\(139\) | 1.50839e8 | 0.404067 | 0.202034 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202034 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(140\) | 1.98479e8 | 0.516657 | ||||||||
\(141\) | 3.86097e8i | 0.976833i | ||||||||
\(142\) | − | 9.73276e7i | − | 0.239377i | ||||||
\(143\) | 3.04485e8 | 0.728151 | ||||||||
\(144\) | −4.67644e7 | −0.108759 | ||||||||
\(145\) | −4.21940e8 | −0.954506 | ||||||||
\(146\) | −4.33416e8 | −0.953881 | ||||||||
\(147\) | 2.06971e8 | 0.443241 | ||||||||
\(148\) | − | 9.93906e8i | − | 2.07156i | ||||||
\(149\) | 4.59699e8i | 0.932670i | 0.884608 | + | 0.466335i | \(0.154426\pi\) | ||||
−0.884608 | + | 0.466335i | \(0.845574\pi\) | |||||||
\(150\) | − | 2.11705e8i | − | 0.418184i | ||||||
\(151\) | − | 3.23489e7i | − | 0.0622231i | −0.999516 | − | 0.0311116i | \(-0.990095\pi\) | ||
0.999516 | − | 0.0311116i | \(-0.00990472\pi\) | |||||||
\(152\) | − | 9.61760e7i | − | 0.180174i | ||||||
\(153\) | −455152. | −0.000830597 | ||||||||
\(154\) | 4.48660e8 | 0.797690 | ||||||||
\(155\) | 3.32664e8i | 0.576340i | ||||||||
\(156\) | 3.44811e8i | 0.582214i | ||||||||
\(157\) | 6.79121e8i | 1.11776i | 0.829249 | + | 0.558880i | \(0.188769\pi\) | ||||
−0.829249 | + | 0.558880i | \(0.811231\pi\) | |||||||
\(158\) | 1.53217e9i | 2.45854i | ||||||||
\(159\) | −3.31820e8 | −0.519175 | ||||||||
\(160\) | 5.93939e8i | 0.906279i | ||||||||
\(161\) | 2.82703e8i | 0.420752i | ||||||||
\(162\) | − | 1.20056e8i | − | 0.174310i | ||||||
\(163\) | 8.90583e8 | 1.26161 | 0.630803 | − | 0.775943i | \(-0.282726\pi\) | ||||
0.630803 | + | 0.775943i | \(0.282726\pi\) | |||||||
\(164\) | −1.14909e9 | −1.58847 | ||||||||
\(165\) | 3.31242e8i | 0.446900i | ||||||||
\(166\) | 1.96737e8 | 0.259092 | ||||||||
\(167\) | −1.07002e8 | −0.137571 | −0.0687853 | − | 0.997631i | \(-0.521912\pi\) | ||||
−0.0687853 | + | 0.997631i | \(0.521912\pi\) | |||||||
\(168\) | 1.60343e8i | 0.201286i | ||||||||
\(169\) | 4.27159e8 | 0.523652 | ||||||||
\(170\) | 2.39543e6i | 0.00286806i | ||||||||
\(171\) | −7.09889e7 | −0.0830245 | ||||||||
\(172\) | − | 2.24029e9i | − | 2.55971i | ||||||
\(173\) | 1.00080e9i | 1.11728i | 0.829410 | + | 0.558640i | \(0.188677\pi\) | ||||
−0.829410 | + | 0.558640i | \(0.811323\pi\) | |||||||
\(174\) | − | 1.08011e9i | − | 1.17834i | ||||||
\(175\) | 2.08701e8 | 0.222522 | ||||||||
\(176\) | 3.30291e8i | 0.344228i | ||||||||
\(177\) | −5.44290e8 | − | 1.57690e8i | −0.554546 | − | 0.160661i | ||||
\(178\) | −2.24790e9 | −2.23922 | ||||||||
\(179\) | 5.84466e8i | 0.569308i | 0.958630 | + | 0.284654i | \(0.0918787\pi\) | ||||
−0.958630 | + | 0.284654i | \(0.908121\pi\) | |||||||
\(180\) | −3.75112e8 | −0.357331 | ||||||||
\(181\) | 2.10696e9 | 1.96310 | 0.981548 | − | 0.191215i | \(-0.0612428\pi\) | ||||
0.981548 | + | 0.191215i | \(0.0612428\pi\) | |||||||
\(182\) | −5.72562e8 | −0.521839 | ||||||||
\(183\) | − | 3.57877e8i | − | 0.319102i | ||||||
\(184\) | 7.23857e8 | 0.631512 | ||||||||
\(185\) | 1.21847e9i | 1.04023i | ||||||||
\(186\) | −8.51576e8 | −0.711495 | ||||||||
\(187\) | 3.21468e6i | 0.00262888i | ||||||||
\(188\) | 3.08812e9i | 2.47208i | ||||||||
\(189\) | 1.18352e8 | 0.0927530 | ||||||||
\(190\) | 3.73610e8i | 0.286684i | ||||||||
\(191\) | 4.70580e8i | 0.353590i | 0.984248 | + | 0.176795i | \(0.0565730\pi\) | ||||
−0.984248 | + | 0.176795i | \(0.943427\pi\) | |||||||
\(192\) | −1.26441e9 | −0.930431 | ||||||||
\(193\) | −1.59781e9 | −1.15158 | −0.575791 | − | 0.817597i | \(-0.695306\pi\) | ||||
−0.575791 | + | 0.817597i | \(0.695306\pi\) | |||||||
\(194\) | 2.71257e9 | 1.91502 | ||||||||
\(195\) | − | 4.22718e8i | − | 0.292356i | ||||||
\(196\) | 1.65541e9 | 1.12171 | ||||||||
\(197\) | −3.39150e8 | −0.225178 | −0.112589 | − | 0.993642i | \(-0.535914\pi\) | ||||
−0.112589 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(198\) | −8.47938e8 | −0.551701 | ||||||||
\(199\) | −2.20463e9 | −1.40580 | −0.702898 | − | 0.711290i | \(-0.748111\pi\) | ||||
−0.702898 | + | 0.711290i | \(0.748111\pi\) | |||||||
\(200\) | − | 5.34376e8i | − | 0.333985i | ||||||
\(201\) | − | 6.89422e8i | − | 0.422377i | ||||||
\(202\) | 1.22217e9 | 0.734048 | ||||||||
\(203\) | 1.06478e9 | 0.627014 | ||||||||
\(204\) | −3.64043e6 | −0.00210200 | ||||||||
\(205\) | 1.40872e9 | 0.797642 | ||||||||
\(206\) | −2.56014e9 | −1.42166 | ||||||||
\(207\) | − | 5.34290e8i | − | 0.291002i | ||||||
\(208\) | − | 4.21504e8i | − | 0.225190i | ||||||
\(209\) | 5.01386e8i | 0.262777i | ||||||||
\(210\) | − | 6.22877e8i | − | 0.320277i | ||||||
\(211\) | 1.23787e9i | 0.624517i | 0.949997 | + | 0.312259i | \(0.101086\pi\) | ||||
−0.949997 | + | 0.312259i | \(0.898914\pi\) | |||||||
\(212\) | −2.65399e9 | −1.31388 | ||||||||
\(213\) | −1.81332e8 | −0.0880961 | ||||||||
\(214\) | 1.71835e8i | 0.0819327i | ||||||||
\(215\) | 2.74647e9i | 1.28535i | ||||||||
\(216\) | − | 3.03039e8i | − | 0.139214i | ||||||
\(217\) | − | 8.39491e8i | − | 0.378597i | ||||||
\(218\) | 5.53918e9 | 2.45256 | ||||||||
\(219\) | 8.07504e8i | 0.351049i | ||||||||
\(220\) | 2.64937e9i | 1.13097i | ||||||||
\(221\) | − | 4.10245e6i | − | 0.00171978i | ||||||
\(222\) | −3.11913e9 | −1.28417 | ||||||||
\(223\) | 3.28091e9 | 1.32671 | 0.663353 | − | 0.748307i | \(-0.269133\pi\) | ||||
0.663353 | + | 0.748307i | \(0.269133\pi\) | |||||||
\(224\) | − | 1.49883e9i | − | 0.595334i | ||||||
\(225\) | −3.94431e8 | −0.153901 | ||||||||
\(226\) | −4.30055e9 | −1.64851 | ||||||||
\(227\) | 3.93777e8i | 0.148302i | 0.997247 | + | 0.0741509i | \(0.0236247\pi\) | ||||
−0.997247 | + | 0.0741509i | \(0.976375\pi\) | |||||||
\(228\) | −5.67790e8 | −0.210111 | ||||||||
\(229\) | 1.21372e9i | 0.441344i | 0.975348 | + | 0.220672i | \(0.0708250\pi\) | ||||
−0.975348 | + | 0.220672i | \(0.929175\pi\) | |||||||
\(230\) | −2.81193e9 | −1.00483 | ||||||||
\(231\) | − | 8.35904e8i | − | 0.293568i | ||||||
\(232\) | − | 2.72637e9i | − | 0.941093i | ||||||
\(233\) | 3.02094e9i | 1.02499i | 0.858691 | + | 0.512493i | \(0.171278\pi\) | ||||
−0.858691 | + | 0.512493i | \(0.828722\pi\) | |||||||
\(234\) | 1.08210e9 | 0.360916 | ||||||||
\(235\) | − | 3.78585e9i | − | 1.24134i | ||||||
\(236\) | −4.35339e9 | − | 1.26125e9i | −1.40339 | − | 0.406586i | ||||
\(237\) | 2.85460e9 | 0.904799 | ||||||||
\(238\) | − | 6.04497e6i | − | 0.00188402i | ||||||
\(239\) | 1.27278e8 | 0.0390087 | 0.0195043 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195043 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(240\) | 4.58545e8 | 0.138209 | ||||||||
\(241\) | 2.47599e9 | 0.733974 | 0.366987 | − | 0.930226i | \(-0.380389\pi\) | ||||
0.366987 | + | 0.930226i | \(0.380389\pi\) | |||||||
\(242\) | 6.08333e8i | 0.177370i | ||||||||
\(243\) | −2.23677e8 | −0.0641500 | ||||||||
\(244\) | − | 2.86241e9i | − | 0.807555i | ||||||
\(245\) | −2.02944e9 | −0.563264 | ||||||||
\(246\) | 3.60613e9i | 0.984694i | ||||||||
\(247\) | − | 6.39849e8i | − | 0.171905i | ||||||
\(248\) | −2.14951e9 | −0.568241 | ||||||||
\(249\) | − | 3.66544e8i | − | 0.0953518i | ||||||
\(250\) | 6.57197e9i | 1.68242i | ||||||||
\(251\) | 2.75745e9 | 0.694725 | 0.347363 | − | 0.937731i | \(-0.387077\pi\) | ||||
0.347363 | + | 0.937731i | \(0.387077\pi\) | |||||||
\(252\) | 9.46612e8 | 0.234731 | ||||||||
\(253\) | −3.77362e9 | −0.921035 | ||||||||
\(254\) | − | 1.16944e10i | − | 2.80959i | ||||||
\(255\) | 4.46296e6 | 0.00105551 | ||||||||
\(256\) | −1.79022e9 | −0.416818 | ||||||||
\(257\) | −7.67874e9 | −1.76018 | −0.880091 | − | 0.474805i | \(-0.842518\pi\) | ||||
−0.880091 | + | 0.474805i | \(0.842518\pi\) | |||||||
\(258\) | −7.03061e9 | −1.58677 | ||||||||
\(259\) | − | 3.07486e9i | − | 0.683324i | ||||||
\(260\) | − | 3.38102e9i | − | 0.739868i | ||||||
\(261\) | −2.01237e9 | −0.433657 | ||||||||
\(262\) | −2.97798e7 | −0.00631999 | ||||||||
\(263\) | 1.52171e9 | 0.318060 | 0.159030 | − | 0.987274i | \(-0.449163\pi\) | ||||
0.159030 | + | 0.987274i | \(0.449163\pi\) | |||||||
\(264\) | −2.14032e9 | −0.440620 | ||||||||
\(265\) | 3.25364e9 | 0.659760 | ||||||||
\(266\) | − | 9.42820e8i | − | 0.188323i | ||||||
\(267\) | 4.18809e9i | 0.824083i | ||||||||
\(268\) | − | 5.51419e9i | − | 1.06891i | ||||||
\(269\) | − | 1.90338e9i | − | 0.363509i | −0.983344 | − | 0.181755i | \(-0.941822\pi\) | ||
0.983344 | − | 0.181755i | \(-0.0581777\pi\) | |||||||
\(270\) | 1.17720e9i | 0.221510i | ||||||||
\(271\) | −9.32770e9 | −1.72941 | −0.864704 | − | 0.502281i | \(-0.832494\pi\) | ||||
−0.864704 | + | 0.502281i | \(0.832494\pi\) | |||||||
\(272\) | 4.45015e6 | 0.000813015 | ||||||||
\(273\) | 1.06675e9i | 0.192049i | ||||||||
\(274\) | − | 6.95289e9i | − | 1.23357i | ||||||
\(275\) | 2.78582e9i | 0.487104i | ||||||||
\(276\) | − | 4.27340e9i | − | 0.736440i | ||||||
\(277\) | −1.02882e10 | −1.74752 | −0.873760 | − | 0.486357i | \(-0.838325\pi\) | ||||
−0.873760 | + | 0.486357i | \(0.838325\pi\) | |||||||
\(278\) | − | 3.78615e9i | − | 0.633897i | ||||||
\(279\) | 1.58658e9i | 0.261846i | ||||||||
\(280\) | − | 1.57224e9i | − | 0.255791i | ||||||
\(281\) | −3.50624e9 | −0.562362 | −0.281181 | − | 0.959655i | \(-0.590726\pi\) | ||||
−0.281181 | + | 0.959655i | \(0.590726\pi\) | |||||||
\(282\) | 9.69130e9 | 1.53245 | ||||||||
\(283\) | 6.78254e9i | 1.05742i | 0.848803 | + | 0.528709i | \(0.177324\pi\) | ||||
−0.848803 | + | 0.528709i | \(0.822676\pi\) | |||||||
\(284\) | −1.45035e9 | −0.222946 | ||||||||
\(285\) | 6.96077e8 | 0.105506 | ||||||||
\(286\) | − | 7.64277e9i | − | 1.14232i | ||||||
\(287\) | −3.55495e9 | −0.523970 | ||||||||
\(288\) | 2.83269e9i | 0.411746i | ||||||||
\(289\) | −6.97571e9 | −0.999994 | ||||||||
\(290\) | 1.05910e10i | 1.49742i | ||||||||
\(291\) | − | 5.05383e9i | − | 0.704772i | ||||||
\(292\) | 6.45865e9i | 0.888404i | ||||||||
\(293\) | −1.05002e9 | −0.142471 | −0.0712353 | − | 0.997460i | \(-0.522694\pi\) | ||||
−0.0712353 | + | 0.997460i | \(0.522694\pi\) | |||||||
\(294\) | − | 5.19511e9i | − | 0.695353i | ||||||
\(295\) | 5.33700e9 | + | 1.54622e9i | 0.704708 | + | 0.204165i | ||||
\(296\) | −7.87315e9 | −1.02561 | ||||||||
\(297\) | 1.57981e9i | 0.203038i | ||||||||
\(298\) | 1.15387e10 | 1.46316 | ||||||||
\(299\) | 4.81574e9 | 0.602530 | ||||||||
\(300\) | −3.15477e9 | −0.389478 | ||||||||
\(301\) | − | 6.93084e9i | − | 0.844344i | ||||||
\(302\) | −8.11979e8 | −0.0976151 | ||||||||
\(303\) | − | 2.27703e9i | − | 0.270146i | ||||||
\(304\) | 6.94079e8 | 0.0812670 | ||||||||
\(305\) | 3.50914e9i | 0.405510i | ||||||||
\(306\) | 1.14246e7i | 0.00130303i | ||||||||
\(307\) | −1.07373e9 | −0.120876 | −0.0604380 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604380 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(308\) | − | 6.68580e9i | − | 0.742935i | ||||||
\(309\) | 4.76984e9i | 0.523202i | ||||||||
\(310\) | 8.35007e9 | 0.904156 | ||||||||
\(311\) | 1.79518e9 | 0.191896 | 0.0959480 | − | 0.995386i | \(-0.469412\pi\) | ||||
0.0959480 | + | 0.995386i | \(0.469412\pi\) | |||||||
\(312\) | 2.73140e9 | 0.288248 | ||||||||
\(313\) | 1.29198e10i | 1.34611i | 0.739594 | + | 0.673053i | \(0.235017\pi\) | ||||
−0.739594 | + | 0.673053i | \(0.764983\pi\) | |||||||
\(314\) | 1.70464e10 | 1.75353 | ||||||||
\(315\) | −1.16049e9 | −0.117869 | ||||||||
\(316\) | 2.28319e10 | 2.28978 | ||||||||
\(317\) | −1.77264e10 | −1.75543 | −0.877715 | − | 0.479183i | \(-0.840933\pi\) | ||||
−0.877715 | + | 0.479183i | \(0.840933\pi\) | |||||||
\(318\) | 8.32890e9i | 0.814478i | ||||||||
\(319\) | 1.42131e10i | 1.37255i | ||||||||
\(320\) | 1.23981e10 | 1.18238 | ||||||||
\(321\) | 3.20149e8 | 0.0301531 | ||||||||
\(322\) | 7.09602e9 | 0.660072 | ||||||||
\(323\) | 6.75537e6 | 0.000620639 | ||||||||
\(324\) | −1.78904e9 | −0.162345 | ||||||||
\(325\) | − | 3.55515e9i | − | 0.318658i | ||||||
\(326\) | − | 2.23542e10i | − | 1.97920i | ||||||
\(327\) | − | 1.03201e10i | − | 0.902597i | ||||||
\(328\) | 9.10242e9i | 0.786433i | ||||||||
\(329\) | 9.55376e9i | 0.815438i | ||||||||
\(330\) | 8.31440e9 | 0.701092 | ||||||||
\(331\) | 1.70745e10 | 1.42245 | 0.711223 | − | 0.702967i | \(-0.248142\pi\) | ||||
0.711223 | + | 0.702967i | \(0.248142\pi\) | |||||||
\(332\) | − | 2.93173e9i | − | 0.241308i | ||||||
\(333\) | 5.81129e9i | 0.472602i | ||||||||
\(334\) | 2.68582e9i | 0.215820i | ||||||||
\(335\) | 6.76008e9i | 0.536750i | ||||||||
\(336\) | −1.15716e9 | −0.0907895 | ||||||||
\(337\) | 5.55679e9i | 0.430828i | 0.976523 | + | 0.215414i | \(0.0691102\pi\) | ||||
−0.976523 | + | 0.215414i | \(0.930890\pi\) | |||||||
\(338\) | − | 1.07220e10i | − | 0.821501i | ||||||
\(339\) | 8.01242e9i | 0.606687i | ||||||||
\(340\) | 3.56960e7 | 0.00267119 | ||||||||
\(341\) | 1.12058e10 | 0.828757 | ||||||||
\(342\) | 1.78187e9i | 0.130248i | ||||||||
\(343\) | 1.17923e10 | 0.851966 | ||||||||
\(344\) | −1.77463e10 | −1.26729 | ||||||||
\(345\) | 5.23894e9i | 0.369800i | ||||||||
\(346\) | 2.51207e10 | 1.75278 | ||||||||
\(347\) | 6.91524e9i | 0.476968i | 0.971146 | + | 0.238484i | \(0.0766505\pi\) | ||||
−0.971146 | + | 0.238484i | \(0.923349\pi\) | |||||||
\(348\) | −1.60955e10 | −1.09746 | ||||||||
\(349\) | − | 5.11294e9i | − | 0.344643i | −0.985041 | − | 0.172321i | \(-0.944873\pi\) | ||
0.985041 | − | 0.172321i | \(-0.0551268\pi\) | |||||||
\(350\) | − | 5.23853e9i | − | 0.349090i | ||||||
\(351\) | − | 2.01608e9i | − | 0.132825i | ||||||
\(352\) | 2.00070e10 | 1.30320 | ||||||||
\(353\) | − | 6.28088e9i | − | 0.404503i | −0.979334 | − | 0.202251i | \(-0.935174\pi\) | ||
0.979334 | − | 0.202251i | \(-0.0648258\pi\) | |||||||
\(354\) | −3.95811e9 | + | 1.36620e10i | −0.252043 | + | 0.869967i | ||||
\(355\) | 1.77804e9 | 0.111951 | ||||||||
\(356\) | 3.34975e10i | 2.08551i | ||||||||
\(357\) | −1.12625e7 | −0.000693363 | ||||||||
\(358\) | 1.46705e10 | 0.893125 | ||||||||
\(359\) | −4.64931e9 | −0.279905 | −0.139952 | − | 0.990158i | \(-0.544695\pi\) | ||||
−0.139952 | + | 0.990158i | \(0.544695\pi\) | |||||||
\(360\) | 2.97142e9i | 0.176911i | ||||||||
\(361\) | −1.59299e10 | −0.937962 | ||||||||
\(362\) | − | 5.28860e10i | − | 3.07969i | ||||||
\(363\) | 1.13339e9 | 0.0652761 | ||||||||
\(364\) | 8.53215e9i | 0.486019i | ||||||||
\(365\) | − | 7.91793e9i | − | 0.446108i | ||||||
\(366\) | −8.98296e9 | −0.500605 | ||||||||
\(367\) | 4.38244e9i | 0.241575i | 0.992678 | + | 0.120787i | \(0.0385419\pi\) | ||||
−0.992678 | + | 0.120787i | \(0.961458\pi\) | |||||||
\(368\) | 5.22390e9i | 0.284842i | ||||||||
\(369\) | 6.71863e9 | 0.362389 | ||||||||
\(370\) | 3.05844e10 | 1.63190 | ||||||||
\(371\) | −8.21070e9 | −0.433395 | ||||||||
\(372\) | 1.26900e10i | 0.662656i | ||||||||
\(373\) | 6.57158e9 | 0.339496 | 0.169748 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169748 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(374\) | 8.06906e7 | 0.00412417 | ||||||||
\(375\) | 1.22443e10 | 0.619169 | ||||||||
\(376\) | 2.44623e10 | 1.22390 | ||||||||
\(377\) | − | 1.81382e10i | − | 0.897903i | ||||||
\(378\) | − | 2.97071e9i | − | 0.145510i | ||||||
\(379\) | −8.80802e8 | −0.0426895 | −0.0213448 | − | 0.999772i | \(-0.506795\pi\) | ||||
−0.0213448 | + | 0.999772i | \(0.506795\pi\) | |||||||
\(380\) | 5.56743e9 | 0.267005 | ||||||||
\(381\) | −2.17880e10 | −1.03399 | ||||||||
\(382\) | 1.18119e10 | 0.554709 | ||||||||
\(383\) | −2.17036e10 | −1.00864 | −0.504320 | − | 0.863517i | \(-0.668257\pi\) | ||||
−0.504320 | + | 0.863517i | \(0.668257\pi\) | |||||||
\(384\) | 1.62310e10i | 0.746486i | ||||||||
\(385\) | 8.19640e9i | 0.373061i | ||||||||
\(386\) | 4.01060e10i | 1.80659i | ||||||||
\(387\) | 1.30988e10i | 0.583968i | ||||||||
\(388\) | − | 4.04220e10i | − | 1.78357i | ||||||
\(389\) | −1.91308e10 | −0.835478 | −0.417739 | − | 0.908567i | \(-0.637177\pi\) | ||||
−0.417739 | + | 0.908567i | \(0.637177\pi\) | |||||||
\(390\) | −1.06105e10 | −0.458646 | ||||||||
\(391\) | 5.08435e7i | 0.00217535i | ||||||||
\(392\) | − | 1.31132e10i | − | 0.555348i | ||||||
\(393\) | 5.54831e7i | 0.00232590i | ||||||||
\(394\) | 8.51288e9i | 0.353258i | ||||||||
\(395\) | −2.79906e10 | −1.14980 | ||||||||
\(396\) | 1.26357e10i | 0.513830i | ||||||||
\(397\) | − | 2.75869e10i | − | 1.11056i | −0.831664 | − | 0.555279i | \(-0.812611\pi\) | ||
0.831664 | − | 0.555279i | \(-0.187389\pi\) | |||||||
\(398\) | 5.53375e10i | 2.20540i | ||||||||
\(399\) | −1.75658e9 | −0.0693069 | ||||||||
\(400\) | 3.85646e9 | 0.150643 | ||||||||
\(401\) | − | 4.26888e10i | − | 1.65096i | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||
0.564433 | − | 0.825479i | \(-0.309095\pi\) | |||||||
\(402\) | −1.73049e10 | −0.662622 | ||||||||
\(403\) | −1.43004e10 | −0.542162 | ||||||||
\(404\) | − | 1.82124e10i | − | 0.683661i | ||||||
\(405\) | 2.19325e9 | 0.0815208 | ||||||||
\(406\) | − | 2.67268e10i | − | 0.983654i | ||||||
\(407\) | 4.10444e10 | 1.49581 | ||||||||
\(408\) | 2.88374e7i | 0.00104068i | ||||||||
\(409\) | − | 1.58000e9i | − | 0.0564631i | −0.999601 | − | 0.0282315i | \(-0.991012\pi\) | ||
0.999601 | − | 0.0282315i | \(-0.00898757\pi\) | |||||||
\(410\) | − | 3.53597e10i | − | 1.25133i | ||||||
\(411\) | −1.29540e10 | −0.453980 | ||||||||
\(412\) | 3.81505e10i | 1.32407i | ||||||||
\(413\) | −1.34682e10 | − | 3.90194e9i | −0.462922 | − | 0.134116i | ||||
\(414\) | −1.34110e10 | −0.456521 | ||||||||
\(415\) | 3.59412e9i | 0.121172i | ||||||||
\(416\) | −2.55321e10 | −0.852536 | ||||||||
\(417\) | −7.05403e9 | −0.233288 | ||||||||
\(418\) | 1.25851e10 | 0.412242 | ||||||||
\(419\) | 1.53991e10i | 0.499620i | 0.968295 | + | 0.249810i | \(0.0803682\pi\) | ||||
−0.968295 | + | 0.249810i | \(0.919632\pi\) | |||||||
\(420\) | −9.28194e9 | −0.298292 | ||||||||
\(421\) | 4.73339e10i | 1.50676i | 0.657586 | + | 0.753380i | \(0.271578\pi\) | ||||
−0.657586 | + | 0.753380i | \(0.728422\pi\) | |||||||
\(422\) | 3.10713e10 | 0.979737 | ||||||||
\(423\) | − | 1.80560e10i | − | 0.563975i | ||||||
\(424\) | 2.10234e10i | 0.650488i | ||||||||
\(425\) | 3.75344e7 | 0.00115047 | ||||||||
\(426\) | 4.55156e9i | 0.138204i | ||||||||
\(427\) | − | 8.85547e9i | − | 0.266379i | ||||||
\(428\) | 2.56064e9 | 0.0763087 | ||||||||
\(429\) | −1.42393e10 | −0.420398 | ||||||||
\(430\) | 6.89382e10 | 2.01644 | ||||||||
\(431\) | 1.05757e10i | 0.306478i | 0.988189 | + | 0.153239i | \(0.0489704\pi\) | ||||
−0.988189 | + | 0.153239i | \(0.951030\pi\) | |||||||
\(432\) | 2.18696e9 | 0.0627921 | ||||||||
\(433\) | 1.93675e9 | 0.0550964 | 0.0275482 | − | 0.999620i | \(-0.491230\pi\) | ||||
0.0275482 | + | 0.999620i | \(0.491230\pi\) | |||||||
\(434\) | −2.10718e10 | −0.593939 | ||||||||
\(435\) | 1.97322e10 | 0.551084 | ||||||||
\(436\) | − | 8.25433e10i | − | 2.28421i | ||||||
\(437\) | 7.92994e9i | 0.217442i | ||||||||
\(438\) | 2.02689e10 | 0.550723 | ||||||||
\(439\) | 1.52316e9 | 0.0410097 | 0.0205048 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205048 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(440\) | 2.09868e10 | 0.559932 | ||||||||
\(441\) | −9.67907e9 | −0.255905 | ||||||||
\(442\) | −1.02974e8 | −0.00269798 | ||||||||
\(443\) | − | 5.44692e10i | − | 1.41428i | −0.707072 | − | 0.707142i | \(-0.749984\pi\) | ||
0.707072 | − | 0.707142i | \(-0.250016\pi\) | |||||||
\(444\) | 4.64804e10i | 1.19602i | ||||||||
\(445\) | − | 4.10660e10i | − | 1.04723i | ||||||
\(446\) | − | 8.23530e10i | − | 2.08132i | ||||||
\(447\) | − | 2.14980e10i | − | 0.538478i | ||||||
\(448\) | −3.12872e10 | −0.776702 | ||||||||
\(449\) | −3.04171e10 | −0.748398 | −0.374199 | − | 0.927348i | \(-0.622082\pi\) | ||||
−0.374199 | + | 0.927348i | \(0.622082\pi\) | |||||||
\(450\) | 9.90048e9i | 0.241438i | ||||||||
\(451\) | − | 4.74529e10i | − | 1.14698i | ||||||
\(452\) | 6.40856e10i | 1.53535i | ||||||||
\(453\) | 1.51281e9i | 0.0359245i | ||||||||
\(454\) | 9.88405e9 | 0.232655 | ||||||||
\(455\) | − | 1.04599e10i | − | 0.244052i | ||||||
\(456\) | 4.49771e9i | 0.104024i | ||||||||
\(457\) | 6.39260e8i | 0.0146559i | 0.999973 | + | 0.00732795i | \(0.00233258\pi\) | ||||
−0.999973 | + | 0.00732795i | \(0.997667\pi\) | |||||||
\(458\) | 3.04652e10 | 0.692376 | ||||||||
\(459\) | 2.12853e7 | 0.000479546 | ||||||||
\(460\) | 4.19026e10i | 0.935856i | ||||||||
\(461\) | −1.63617e10 | −0.362263 | −0.181132 | − | 0.983459i | \(-0.557976\pi\) | ||||
−0.181132 | + | 0.983459i | \(0.557976\pi\) | |||||||
\(462\) | −2.09817e10 | −0.460547 | ||||||||
\(463\) | − | 8.06345e10i | − | 1.75468i | −0.479874 | − | 0.877338i | \(-0.659317\pi\) | ||
0.479874 | − | 0.877338i | \(-0.340683\pi\) | |||||||
\(464\) | 1.96755e10 | 0.424477 | ||||||||
\(465\) | − | 1.55571e10i | − | 0.332750i | ||||||
\(466\) | 7.58275e10 | 1.60799 | ||||||||
\(467\) | 1.34566e10i | 0.282924i | 0.989944 | + | 0.141462i | \(0.0451803\pi\) | ||||
−0.989944 | + | 0.141462i | \(0.954820\pi\) | |||||||
\(468\) | − | 1.61252e10i | − | 0.336141i | ||||||
\(469\) | − | 1.70593e10i | − | 0.352591i | ||||||
\(470\) | −9.50274e10 | −1.94741 | ||||||||
\(471\) | − | 3.17593e10i | − | 0.645339i | ||||||
\(472\) | −9.99088e9 | + | 3.44851e10i | −0.201296 | + | 0.694805i | ||||
\(473\) | 9.25154e10 | 1.84829 | ||||||||
\(474\) | − | 7.16524e10i | − | 1.41944i | ||||||
\(475\) | 5.85416e9 | 0.114998 | ||||||||
\(476\) | −9.00805e7 | −0.00175470 | ||||||||
\(477\) | 1.55177e10 | 0.299746 | ||||||||
\(478\) | − | 3.19476e9i | − | 0.0611964i | ||||||
\(479\) | 1.40052e10 | 0.266041 | 0.133021 | − | 0.991113i | \(-0.457532\pi\) | ||||
0.133021 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(480\) | − | 2.77758e10i | − | 0.523240i | ||||||
\(481\) | −5.23793e10 | −0.978541 | ||||||||
\(482\) | − | 6.21490e10i | − | 1.15145i | ||||||
\(483\) | − | 1.32207e10i | − | 0.242921i | ||||||
\(484\) | 9.06521e9 | 0.165195 | ||||||||
\(485\) | 4.95550e10i | 0.895613i | ||||||||
\(486\) | 5.61445e9i | 0.100638i | ||||||||
\(487\) | 1.25982e10 | 0.223972 | 0.111986 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111986 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(488\) | −2.26743e10 | −0.399812 | ||||||||
\(489\) | −4.16484e10 | −0.728389 | ||||||||
\(490\) | 5.09402e10i | 0.883643i | ||||||||
\(491\) | −6.06960e9 | −0.104432 | −0.0522161 | − | 0.998636i | \(-0.516628\pi\) | ||||
−0.0522161 | + | 0.998636i | \(0.516628\pi\) | |||||||
\(492\) | 5.37376e10 | 0.917102 | ||||||||
\(493\) | 1.91499e8 | 0.00324175 | ||||||||
\(494\) | −1.60606e10 | −0.269684 | ||||||||
\(495\) | − | 1.54907e10i | − | 0.258018i | ||||||
\(496\) | − | 1.55125e10i | − | 0.256303i | ||||||
\(497\) | −4.48697e9 | −0.0735406 | ||||||||
\(498\) | −9.20050e9 | −0.149587 | ||||||||
\(499\) | −9.92585e10 | −1.60090 | −0.800452 | − | 0.599397i | \(-0.795407\pi\) | ||||
−0.800452 | + | 0.599397i | \(0.795407\pi\) | |||||||
\(500\) | 9.79336e10 | 1.56694 | ||||||||
\(501\) | 5.00398e9 | 0.0794264 | ||||||||
\(502\) | − | 6.92139e10i | − | 1.08988i | ||||||
\(503\) | 2.23408e10i | 0.349001i | 0.984657 | + | 0.174500i | \(0.0558310\pi\) | ||||
−0.984657 | + | 0.174500i | \(0.944169\pi\) | |||||||
\(504\) | − | 7.49852e9i | − | 0.116213i | ||||||
\(505\) | 2.23273e10i | 0.343298i | ||||||||
\(506\) | 9.47204e10i | 1.44491i | ||||||||
\(507\) | −1.99763e10 | −0.302331 | ||||||||
\(508\) | −1.74267e11 | −2.61674 | ||||||||
\(509\) | 1.18747e11i | 1.76909i | 0.466456 | + | 0.884545i | \(0.345531\pi\) | ||||
−0.466456 | + | 0.884545i | \(0.654469\pi\) | |||||||
\(510\) | − | 1.12023e8i | − | 0.00165587i | ||||||
\(511\) | 1.99812e10i | 0.293048i | ||||||||
\(512\) | − | 4.39153e10i | − | 0.639052i | ||||||
\(513\) | 3.31982e9 | 0.0479342 | ||||||||
\(514\) | 1.92741e11i | 2.76136i | ||||||||
\(515\) | − | 4.67703e10i | − | 0.664877i | ||||||
\(516\) | 1.04768e11i | 1.47785i | ||||||||
\(517\) | −1.27527e11 | −1.78501 | ||||||||
\(518\) | −7.71811e10 | −1.07199 | ||||||||
\(519\) | − | 4.68027e10i | − | 0.645062i | ||||||
\(520\) | −2.67825e10 | −0.366301 | ||||||||
\(521\) | −5.20004e10 | −0.705758 | −0.352879 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352879 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(522\) | 5.05119e10i | 0.680317i | ||||||||
\(523\) | −1.48520e10 | −0.198509 | −0.0992543 | − | 0.995062i | \(-0.531646\pi\) | ||||
−0.0992543 | + | 0.995062i | \(0.531646\pi\) | |||||||
\(524\) | 4.43770e8i | 0.00588617i | ||||||||
\(525\) | −9.75998e9 | −0.128473 | ||||||||
\(526\) | − | 3.81959e10i | − | 0.498969i | ||||||
\(527\) | − | 1.50981e8i | − | 0.00195740i | ||||||
\(528\) | − | 1.54462e10i | − | 0.198740i | ||||||
\(529\) | 1.86272e10 | 0.237862 | ||||||||
\(530\) | − | 8.16685e10i | − | 1.03503i | ||||||
\(531\) | 2.54539e10 | + | 7.37442e9i | 0.320167 | + | 0.0927576i | ||||
\(532\) | −1.40496e10 | −0.175396 | ||||||||
\(533\) | 6.05575e10i | 0.750341i | ||||||||
\(534\) | 1.05124e11 | 1.29281 | ||||||||
\(535\) | −3.13920e9 | −0.0383181 | ||||||||
\(536\) | −4.36803e10 | −0.529208 | ||||||||
\(537\) | − | 2.73328e10i | − | 0.328690i | ||||||
\(538\) | −4.77760e10 | −0.570270 | ||||||||
\(539\) | 6.83621e10i | 0.809954i | ||||||||
\(540\) | 1.75423e10 | 0.206305 | ||||||||
\(541\) | − | 6.49767e10i | − | 0.758522i | −0.925290 | − | 0.379261i | \(-0.876178\pi\) | ||
0.925290 | − | 0.379261i | \(-0.123822\pi\) | |||||||
\(542\) | 2.34131e11i | 2.71308i | ||||||||
\(543\) | −9.85327e10 | −1.13339 | ||||||||
\(544\) | − | 2.69562e8i | − | 0.00307796i | ||||||
\(545\) | 1.01193e11i | 1.14701i | ||||||||
\(546\) | 2.67761e10 | 0.301284 | ||||||||
\(547\) | −4.70937e10 | −0.526034 | −0.263017 | − | 0.964791i | \(-0.584717\pi\) | ||||
−0.263017 | + | 0.964791i | \(0.584717\pi\) | |||||||
\(548\) | −1.03610e11 | −1.14889 | ||||||||
\(549\) | 1.67363e10i | 0.184234i | ||||||||
\(550\) | 6.99259e10 | 0.764165 | ||||||||
\(551\) | 2.98677e10 | 0.324037 | ||||||||
\(552\) | −3.38514e10 | −0.364604 | ||||||||
\(553\) | 7.06355e10 | 0.755305 | ||||||||
\(554\) | 2.58242e11i | 2.74149i | ||||||||
\(555\) | − | 5.69822e10i | − | 0.600575i | ||||||
\(556\) | −5.64201e10 | −0.590385 | ||||||||
\(557\) | −4.72589e10 | −0.490979 | −0.245490 | − | 0.969399i | \(-0.578949\pi\) | ||||
−0.245490 | + | 0.969399i | \(0.578949\pi\) | |||||||
\(558\) | 3.98243e10 | 0.410782 | ||||||||
\(559\) | −1.18064e11 | −1.20913 | ||||||||
\(560\) | 1.13464e10 | 0.115374 | ||||||||
\(561\) | − | 1.50336e8i | − | 0.00151779i | ||||||
\(562\) | 8.80089e10i | 0.882229i | ||||||||
\(563\) | 4.73136e9i | 0.0470925i | 0.999723 | + | 0.0235463i | \(0.00749570\pi\) | ||||
−0.999723 | + | 0.0235463i | \(0.992504\pi\) | |||||||
\(564\) | − | 1.44417e11i | − | 1.42726i | ||||||
\(565\) | − | 7.85652e10i | − | 0.770968i | ||||||
\(566\) | 1.70246e11 | 1.65887 | ||||||||
\(567\) | −5.53477e9 | −0.0535509 | ||||||||
\(568\) | 1.14888e10i | 0.110378i | ||||||||
\(569\) | − | 1.46316e9i | − | 0.0139586i | −0.999976 | − | 0.00697932i | \(-0.997778\pi\) | ||
0.999976 | − | 0.00697932i | \(-0.00222160\pi\) | |||||||
\(570\) | − | 1.74720e10i | − | 0.165517i | ||||||
\(571\) | 1.36252e11i | 1.28173i | 0.767652 | + | 0.640867i | \(0.221425\pi\) | ||||
−0.767652 | + | 0.640867i | \(0.778575\pi\) | |||||||
\(572\) | −1.13890e11 | −1.06391 | ||||||||
\(573\) | − | 2.20069e10i | − | 0.204145i | ||||||
\(574\) | 8.92317e10i | 0.821999i | ||||||||
\(575\) | 4.40606e10i | 0.403069i | ||||||||
\(576\) | 5.91307e10 | 0.537184 | ||||||||
\(577\) | −2.11877e11 | −1.91152 | −0.955762 | − | 0.294142i | \(-0.904966\pi\) | ||||
−0.955762 | + | 0.294142i | \(0.904966\pi\) | |||||||
\(578\) | 1.75095e11i | 1.56878i | ||||||||
\(579\) | 7.47220e10 | 0.664866 | ||||||||
\(580\) | 1.57824e11 | 1.39463 | ||||||||
\(581\) | − | 9.06993e9i | − | 0.0795975i | ||||||
\(582\) | −1.26854e11 | −1.10564 | ||||||||
\(583\) | − | 1.09599e11i | − | 0.948712i | ||||||
\(584\) | 5.11617e10 | 0.439839 | ||||||||
\(585\) | 1.97686e10i | 0.168792i | ||||||||
\(586\) | 2.63561e10i | 0.223507i | ||||||||
\(587\) | 8.76572e10i | 0.738304i | 0.929369 | + | 0.369152i | \(0.120352\pi\) | ||||
−0.929369 | + | 0.369152i | \(0.879648\pi\) | |||||||
\(588\) | −7.74160e10 | −0.647622 | ||||||||
\(589\) | − | 2.35481e10i | − | 0.195657i | ||||||
\(590\) | 3.88110e10 | − | 1.33962e11i | 0.320293 | − | 1.10554i | ||||
\(591\) | 1.58605e10 | 0.130007 | ||||||||
\(592\) | − | 5.68186e10i | − | 0.462598i | ||||||
\(593\) | −3.49038e10 | −0.282263 | −0.141132 | − | 0.989991i | \(-0.545074\pi\) | ||||
−0.141132 | + | 0.989991i | \(0.545074\pi\) | |||||||
\(594\) | 3.96541e10 | 0.318524 | ||||||||
\(595\) | 1.10433e8 | 0.000881115 | ||||||||
\(596\) | − | 1.71947e11i | − | 1.36273i | ||||||
\(597\) | 1.03100e11 | 0.811637 | ||||||||
\(598\) | − | 1.20878e11i | − | 0.945244i | ||||||
\(599\) | 1.94116e10 | 0.150784 | 0.0753918 | − | 0.997154i | \(-0.475979\pi\) | ||||
0.0753918 | + | 0.997154i | \(0.475979\pi\) | |||||||
\(600\) | 2.49903e10i | 0.192826i | ||||||||
\(601\) | 6.35319e10i | 0.486960i | 0.969906 | + | 0.243480i | \(0.0782891\pi\) | ||||
−0.969906 | + | 0.243480i | \(0.921711\pi\) | |||||||
\(602\) | −1.73969e11 | −1.32460 | ||||||||
\(603\) | 3.22411e10i | 0.243860i | ||||||||
\(604\) | 1.20999e10i | 0.0909145i | ||||||||
\(605\) | −1.11134e10 | −0.0829519 | ||||||||
\(606\) | −5.71550e10 | −0.423803 | ||||||||
\(607\) | 8.61311e10 | 0.634462 | 0.317231 | − | 0.948348i | \(-0.397247\pi\) | ||||
0.317231 | + | 0.948348i | \(0.397247\pi\) | |||||||
\(608\) | − | 4.20429e10i | − | 0.307665i | ||||||
\(609\) | −4.97950e10 | −0.362007 | ||||||||
\(610\) | 8.80818e10 | 0.636160 | ||||||||
\(611\) | 1.62745e11 | 1.16773 | ||||||||
\(612\) | 1.70246e8 | 0.00121359 | ||||||||
\(613\) | − | 5.93916e10i | − | 0.420613i | −0.977635 | − | 0.210307i | \(-0.932554\pi\) | ||
0.977635 | − | 0.210307i | \(-0.0674463\pi\) | |||||||
\(614\) | 2.69512e10i | 0.189629i | ||||||||
\(615\) | −6.58791e10 | −0.460519 | ||||||||
\(616\) | −5.29611e10 | −0.367819 | ||||||||
\(617\) | 2.34982e11 | 1.62142 | 0.810708 | − | 0.585450i | \(-0.199082\pi\) | ||||
0.810708 | + | 0.585450i | \(0.199082\pi\) | |||||||
\(618\) | 1.19726e11 | 0.820795 | ||||||||
\(619\) | 1.33083e10 | 0.0906486 | 0.0453243 | − | 0.998972i | \(-0.485568\pi\) | ||||
0.0453243 | + | 0.998972i | \(0.485568\pi\) | |||||||
\(620\) | − | 1.24430e11i | − | 0.842093i | ||||||
\(621\) | 2.49863e10i | 0.168010i | ||||||||
\(622\) | − | 4.50601e10i | − | 0.301045i | ||||||
\(623\) | 1.03632e11i | 0.687925i | ||||||||
\(624\) | 1.97118e10i | 0.130013i | ||||||||
\(625\) | −4.96106e10 | −0.325128 | ||||||||
\(626\) | 3.24296e11 | 2.11176 | ||||||||
\(627\) | − | 2.34475e10i | − | 0.151714i | ||||||
\(628\) | − | 2.54020e11i | − | 1.63316i | ||||||
\(629\) | − | 5.53008e8i | − | 0.00353288i | ||||||
\(630\) | 2.91291e10i | 0.184912i | ||||||||
\(631\) | 1.02889e10 | 0.0649009 | 0.0324505 | − | 0.999473i | \(-0.489669\pi\) | ||||
0.0324505 | + | 0.999473i | \(0.489669\pi\) | |||||||
\(632\) | − | 1.80861e11i | − | 1.13365i | ||||||
\(633\) | − | 5.78893e10i | − | 0.360565i | ||||||
\(634\) | 4.44944e11i | 2.75390i | ||||||||
\(635\) | 2.13641e11 | 1.31398 | ||||||||
\(636\) | 1.24115e11 | 0.758570 | ||||||||
\(637\) | − | 8.72409e10i | − | 0.529862i | ||||||
\(638\) | 3.56759e11 | 2.15324 | ||||||||
\(639\) | 8.48007e9 | 0.0508623 | ||||||||
\(640\) | − | 1.59152e11i | − | 0.948622i | ||||||
\(641\) | 1.09157e11 | 0.646574 | 0.323287 | − | 0.946301i | \(-0.395212\pi\) | ||||
0.323287 | + | 0.946301i | \(0.395212\pi\) | |||||||
\(642\) | − | 8.03595e9i | − | 0.0473039i | ||||||
\(643\) | 4.76191e10 | 0.278572 | 0.139286 | − | 0.990252i | \(-0.455519\pi\) | ||||
0.139286 | + | 0.990252i | \(0.455519\pi\) | |||||||
\(644\) | − | 1.05743e11i | − | 0.614763i | ||||||
\(645\) | − | 1.28440e11i | − | 0.742097i | ||||||
\(646\) | − | 1.69564e8i | − | 0.000973654i | ||||||
\(647\) | −2.74577e11 | −1.56692 | −0.783461 | − | 0.621441i | \(-0.786548\pi\) | ||||
−0.783461 | + | 0.621441i | \(0.786548\pi\) | |||||||
\(648\) | 1.41717e10i | 0.0803753i | ||||||||
\(649\) | 5.20846e10 | − | 1.79778e11i | 0.293583 | − | 1.01335i | ||||
\(650\) | −8.92366e10 | −0.499907 | ||||||||
\(651\) | 3.92591e10i | 0.218583i | ||||||||
\(652\) | −3.33116e11 | −1.84334 | ||||||||
\(653\) | −2.39958e11 | −1.31972 | −0.659862 | − | 0.751387i | \(-0.729385\pi\) | ||||
−0.659862 | + | 0.751387i | \(0.729385\pi\) | |||||||
\(654\) | −2.59042e11 | −1.41599 | ||||||||
\(655\) | − | 5.44036e8i | − | 0.00295571i | ||||||
\(656\) | −6.56900e10 | −0.354718 | ||||||||
\(657\) | − | 3.77632e10i | − | 0.202678i | ||||||
\(658\) | 2.39806e11 | 1.27925 | ||||||||
\(659\) | 2.41605e11i | 1.28105i | 0.767939 | + | 0.640523i | \(0.221282\pi\) | ||||
−0.767939 | + | 0.640523i | \(0.778718\pi\) | |||||||
\(660\) | − | 1.23899e11i | − | 0.652967i | ||||||
\(661\) | 4.97939e10 | 0.260838 | 0.130419 | − | 0.991459i | \(-0.458368\pi\) | ||||
0.130419 | + | 0.991459i | \(0.458368\pi\) | |||||||
\(662\) | − | 4.28581e11i | − | 2.23152i | ||||||
\(663\) | 1.91852e8i | 0.000992917i | ||||||||
\(664\) | −2.32235e10 | −0.119469 | ||||||||
\(665\) | 1.72240e10 | 0.0880741 | ||||||||
\(666\) | 1.45867e11 | 0.741414 | ||||||||
\(667\) | 2.24796e11i | 1.13575i | ||||||||
\(668\) | 4.00233e10 | 0.201005 | ||||||||
\(669\) | −1.53433e11 | −0.765974 | ||||||||
\(670\) | 1.69682e11 | 0.842049 | ||||||||
\(671\) | 1.18206e11 | 0.583109 | ||||||||
\(672\) | 7.00933e10i | 0.343716i | ||||||||
\(673\) | 4.04861e11i | 1.97354i | 0.162128 | + | 0.986770i | \(0.448164\pi\) | ||||
−0.162128 | + | 0.986770i | \(0.551836\pi\) | |||||||
\(674\) | 1.39479e11 | 0.675880 | ||||||||
\(675\) | 1.84457e10 | 0.0888547 | ||||||||
\(676\) | −1.59776e11 | −0.765111 | ||||||||
\(677\) | −4.01952e11 | −1.91346 | −0.956731 | − | 0.290973i | \(-0.906021\pi\) | ||||
−0.956731 | + | 0.290973i | \(0.906021\pi\) | |||||||
\(678\) | 2.01117e11 | 0.951765 | ||||||||
\(679\) | − | 1.25054e11i | − | 0.588327i | ||||||
\(680\) | − | 2.82764e8i | − | 0.00132248i | ||||||
\(681\) | − | 1.84151e10i | − | 0.0856221i | ||||||
\(682\) | − | 2.81274e11i | − | 1.30015i | ||||||
\(683\) | 1.28178e11i | 0.589019i | 0.955648 | + | 0.294510i | \(0.0951563\pi\) | ||||
−0.955648 | + | 0.294510i | \(0.904844\pi\) | |||||||
\(684\) | 2.65529e10 | 0.121308 | ||||||||
\(685\) | 1.27020e11 | 0.576911 | ||||||||
\(686\) | − | 2.95995e11i | − | 1.33656i | ||||||
\(687\) | − | 5.67601e10i | − | 0.254810i | ||||||
\(688\) | − | 1.28071e11i | − | 0.571606i | ||||||
\(689\) | 1.39866e11i | 0.620636i | ||||||||
\(690\) | 1.31501e11 | 0.580139 | ||||||||
\(691\) | − | 1.72925e11i | − | 0.758483i | −0.925298 | − | 0.379241i | \(-0.876185\pi\) | ||
0.925298 | − | 0.379241i | \(-0.123815\pi\) | |||||||
\(692\) | − | 3.74342e11i | − | 1.63246i | ||||||
\(693\) | 3.90914e10i | 0.169492i | ||||||||
\(694\) | 1.73577e11 | 0.748264 | ||||||||
\(695\) | 6.91678e10 | 0.296459 | ||||||||
\(696\) | 1.27500e11i | 0.543340i | ||||||||
\(697\) | −6.39352e8 | −0.00270900 | ||||||||
\(698\) | −1.28338e11 | −0.540673 | ||||||||
\(699\) | − | 1.41275e11i | − | 0.591776i | ||||||
\(700\) | −7.80631e10 | −0.325127 | ||||||||
\(701\) | − | 5.06019e10i | − | 0.209554i | −0.994496 | − | 0.104777i | \(-0.966587\pi\) | ||
0.994496 | − | 0.104777i | \(-0.0334128\pi\) | |||||||
\(702\) | −5.06050e10 | −0.208375 | ||||||||
\(703\) | − | 8.62514e10i | − | 0.353138i | ||||||
\(704\) | − | 4.17633e11i | − | 1.70022i | ||||||
\(705\) | 1.77047e11i | 0.716690i | ||||||||
\(706\) | −1.57654e11 | −0.634580 | ||||||||
\(707\) | − | 5.63439e10i | − | 0.225512i | ||||||
\(708\) | 2.03588e11 | + | 5.89827e10i | 0.810250 | + | 0.234742i | ||||
\(709\) | 2.68732e11 | 1.06349 | 0.531746 | − | 0.846904i | \(-0.321536\pi\) | ||||
0.531746 | + | 0.846904i | \(0.321536\pi\) | |||||||
\(710\) | − | 4.46300e10i | − | 0.175628i | ||||||
\(711\) | −1.33496e11 | −0.522386 | ||||||||
\(712\) | 2.65348e11 | 1.03251 | ||||||||
\(713\) | 1.77232e11 | 0.685779 | ||||||||
\(714\) | 2.82695e8i | 0.00108774i | ||||||||
\(715\) | 1.39623e11 | 0.534235 | ||||||||
\(716\) | − | 2.18615e11i | − | 0.831819i | ||||||
\(717\) | −5.95219e9 | −0.0225217 | ||||||||
\(718\) | 1.16701e11i | 0.439112i | ||||||||
\(719\) | 2.69631e11i | 1.00891i | 0.863437 | + | 0.504457i | \(0.168307\pi\) | ||||
−0.863437 | + | 0.504457i | \(0.831693\pi\) | |||||||
\(720\) | −2.14440e10 | −0.0797952 | ||||||||
\(721\) | 1.18027e11i | 0.436757i | ||||||||
\(722\) | 3.99852e11i | 1.47147i | ||||||||
\(723\) | −1.15791e11 | −0.423760 | ||||||||
\(724\) | −7.88093e11 | −2.86829 | ||||||||
\(725\) | 1.65952e11 | 0.600662 | ||||||||
\(726\) | − | 2.84489e10i | − | 0.102405i | ||||||
\(727\) | −3.93515e11 | −1.40872 | −0.704358 | − | 0.709845i | \(-0.748765\pi\) | ||||
−0.704358 | + | 0.709845i | \(0.748765\pi\) | |||||||
\(728\) | 6.75868e10 | 0.240623 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | −1.98745e11 | −0.699850 | ||||||||
\(731\) | − | 1.24650e9i | − | 0.00436538i | ||||||
\(732\) | 1.33861e11i | 0.466242i | ||||||||
\(733\) | −2.39451e11 | −0.829471 | −0.414736 | − | 0.909942i | \(-0.636126\pi\) | ||||
−0.414736 | + | 0.909942i | \(0.636126\pi\) | |||||||
\(734\) | 1.10002e11 | 0.378980 | ||||||||
\(735\) | 9.49075e10 | 0.325200 | ||||||||
\(736\) | 3.16431e11 | 1.07837 | ||||||||
\(737\) | 2.27715e11 | 0.771829 | ||||||||
\(738\) | − | 1.68642e11i | − | 0.568513i | ||||||
\(739\) | − | 3.89964e11i | − | 1.30751i | −0.756704 | − | 0.653757i | \(-0.773192\pi\) | ||
0.756704 | − | 0.653757i | \(-0.226808\pi\) | |||||||
\(740\) | − | 4.55760e11i | − | 1.51988i | ||||||
\(741\) | 2.99228e10i | 0.0992496i | ||||||||
\(742\) | 2.06094e11i | 0.679907i | ||||||||
\(743\) | 3.43743e11 | 1.12792 | 0.563960 | − | 0.825802i | \(-0.309277\pi\) | ||||
0.563960 | + | 0.825802i | \(0.309277\pi\) | |||||||
\(744\) | 1.00523e11 | 0.328074 | ||||||||
\(745\) | 2.10797e11i | 0.684289i | ||||||||
\(746\) | − | 1.64951e11i | − | 0.532598i | ||||||
\(747\) | 1.71416e10i | 0.0550514i | ||||||||
\(748\) | − | 1.20243e9i | − | 0.00384108i | ||||||
\(749\) | 7.92190e9 | 0.0251711 | ||||||||
\(750\) | − | 3.07340e11i | − | 0.971347i | ||||||
\(751\) | 1.75253e10i | 0.0550942i | 0.999621 | + | 0.0275471i | \(0.00876962\pi\) | ||||
−0.999621 | + | 0.0275471i | \(0.991230\pi\) | |||||||
\(752\) | 1.76538e11i | 0.552037i | ||||||||
\(753\) | −1.28953e11 | −0.401100 | ||||||||
\(754\) | −4.55282e11 | −1.40862 | ||||||||
\(755\) | − | 1.48337e10i | − | 0.0456523i | ||||||
\(756\) | −4.42687e10 | −0.135522 | ||||||||
\(757\) | −4.13727e11 | −1.25988 | −0.629942 | − | 0.776642i | \(-0.716921\pi\) | ||||
−0.629942 | + | 0.776642i | \(0.716921\pi\) | |||||||
\(758\) | 2.21087e10i | 0.0669709i | ||||||||
\(759\) | 1.76475e11 | 0.531760 | ||||||||
\(760\) | − | 4.41020e10i | − | 0.132191i | ||||||
\(761\) | −2.30836e10 | −0.0688281 | −0.0344141 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344141 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(762\) | 5.46893e11i | 1.62212i | ||||||||
\(763\) | − | 2.55366e11i | − | 0.753467i | ||||||
\(764\) | − | 1.76017e11i | − | 0.516632i | ||||||
\(765\) | −2.08712e8 | −0.000609399 | ||||||||
\(766\) | 5.44774e11i | 1.58235i | ||||||||
\(767\) | −6.64682e10 | + | 2.29426e11i | −0.192058 | + | 0.662919i | ||||
\(768\) | 8.37203e10 | 0.240650 | ||||||||
\(769\) | 4.05959e11i | 1.16085i | 0.814313 | + | 0.580426i | \(0.197114\pi\) | ||||
−0.814313 | + | 0.580426i | \(0.802886\pi\) | |||||||
\(770\) | 2.05735e11 | 0.585255 | ||||||||
\(771\) | 3.59099e11 | 1.01624 | ||||||||
\(772\) | 5.97648e11 | 1.68258 | ||||||||
\(773\) | − | 6.15256e11i | − | 1.72321i | −0.507580 | − | 0.861604i | \(-0.669460\pi\) | ||
0.507580 | − | 0.861604i | \(-0.330540\pi\) | |||||||
\(774\) | 3.28789e11 | 0.916123 | ||||||||
\(775\) | − | 1.30839e11i | − | 0.362685i | ||||||
\(776\) | −3.20200e11 | −0.883027 | ||||||||
\(777\) | 1.43797e11i | 0.394517i | ||||||||
\(778\) | 4.80196e11i | 1.31069i | ||||||||
\(779\) | −9.97181e10 | −0.270785 | ||||||||
\(780\) | 1.58115e11i | 0.427163i | ||||||||
\(781\) | − | 5.98937e10i | − | 0.160982i | ||||||
\(782\) | 1.27621e9 | 0.00341266 | ||||||||
\(783\) | 9.41093e10 | 0.250372 | ||||||||
\(784\) | 9.46350e10 | 0.250488 | ||||||||
\(785\) | 3.11414e11i | 0.820086i | ||||||||
\(786\) | 1.39266e9 | 0.00364885 | ||||||||
\(787\) | 4.31469e11 | 1.12473 | 0.562367 | − | 0.826887i | \(-0.309891\pi\) | ||||
0.562367 | + | 0.826887i | \(0.309891\pi\) | |||||||
\(788\) | 1.26857e11 | 0.329009 | ||||||||
\(789\) | −7.11633e10 | −0.183632 | ||||||||
\(790\) | 7.02582e11i | 1.80380i | ||||||||
\(791\) | 1.98263e11i | 0.506448i | ||||||||
\(792\) | 1.00093e11 | 0.254392 | ||||||||
\(793\) | −1.50850e11 | −0.381463 | ||||||||
\(794\) | −6.92450e11 | −1.74223 | ||||||||
\(795\) | −1.52158e11 | −0.380912 | ||||||||
\(796\) | 8.24624e11 | 2.05402 | ||||||||
\(797\) | − | 6.75255e11i | − | 1.67353i | −0.547559 | − | 0.836767i | \(-0.684443\pi\) | ||
0.547559 | − | 0.836767i | \(-0.315557\pi\) | |||||||
\(798\) | 4.40913e10i | 0.108728i | ||||||||
\(799\) | 1.71822e9i | 0.00421593i | ||||||||
\(800\) | − | 2.33600e11i | − | 0.570313i | ||||||
\(801\) | − | 1.95857e11i | − | 0.475784i | ||||||
\(802\) | −1.07152e12 | −2.59001 | ||||||||
\(803\) | −2.66717e11 | −0.641488 | ||||||||
\(804\) | 2.57873e11i | 0.617138i | ||||||||
\(805\) | 1.29635e11i | 0.308701i | ||||||||
\(806\) | 3.58951e11i | 0.850539i | ||||||||
\(807\) | 8.90121e10i | 0.209872i | ||||||||
\(808\) | −1.44268e11 | −0.338473 | ||||||||
\(809\) | 5.04940e11i | 1.17881i | 0.807836 | + | 0.589407i | \(0.200639\pi\) | ||||
−0.807836 | + | 0.589407i | \(0.799361\pi\) | |||||||
\(810\) | − | 5.50521e10i | − | 0.127889i | ||||||
\(811\) | 5.69434e11i | 1.31632i | 0.752880 | + | 0.658158i | \(0.228664\pi\) | ||||
−0.752880 | + | 0.658158i | \(0.771336\pi\) | |||||||
\(812\) | −3.98275e11 | −0.916133 | ||||||||
\(813\) | 4.36214e11 | 0.998474 | ||||||||
\(814\) | − | 1.03024e12i | − | 2.34661i | ||||||
\(815\) | 4.08381e11 | 0.925625 | ||||||||
\(816\) | −2.08113e8 | −0.000469394 | ||||||||
\(817\) | − | 1.94413e11i | − | 0.436353i | ||||||
\(818\) | −3.96591e10 | −0.0885787 | ||||||||
\(819\) | − | 4.98868e10i | − | 0.110879i | ||||||
\(820\) | −5.26920e11 | −1.16544 | ||||||||
\(821\) | − | 1.63936e11i | − | 0.360829i | −0.983591 | − | 0.180415i | \(-0.942256\pi\) | ||
0.983591 | − | 0.180415i | \(-0.0577440\pi\) | |||||||
\(822\) | 3.25154e11i | 0.712200i | ||||||||
\(823\) | 2.58267e11i | 0.562950i | 0.959569 | + | 0.281475i | \(0.0908236\pi\) | ||||
−0.959569 | + | 0.281475i | \(0.909176\pi\) | |||||||
\(824\) | 3.02207e11 | 0.655534 | ||||||||
\(825\) | − | 1.30280e11i | − | 0.281230i | ||||||
\(826\) | −9.79413e10 | + | 3.38060e11i | −0.210400 | + | 0.726228i | ||||
\(827\) | −5.92922e11 | −1.26758 | −0.633790 | − | 0.773505i | \(-0.718502\pi\) | ||||
−0.633790 | + | 0.773505i | \(0.718502\pi\) | |||||||
\(828\) | 1.99847e11i | 0.425184i | ||||||||
\(829\) | 5.43949e11 | 1.15170 | 0.575851 | − | 0.817555i | \(-0.304671\pi\) | ||||
0.575851 | + | 0.817555i | \(0.304671\pi\) | |||||||
\(830\) | 9.02149e10 | 0.190093 | ||||||||
\(831\) | 4.81134e11 | 1.00893 | ||||||||
\(832\) | 5.32966e11i | 1.11226i | ||||||||
\(833\) | 9.21070e8 | 0.00191299 | ||||||||
\(834\) | 1.77061e11i | 0.365981i | ||||||||
\(835\) | −4.90662e10 | −0.100934 | ||||||||
\(836\) | − | 1.87540e11i | − | 0.383945i | ||||||
\(837\) | − | 7.41972e10i | − | 0.151177i | ||||||
\(838\) | 3.86528e11 | 0.783800 | ||||||||
\(839\) | 5.31991e11i | 1.07363i | 0.843698 | + | 0.536817i | \(0.180374\pi\) | ||||
−0.843698 | + | 0.536817i | \(0.819626\pi\) | |||||||
\(840\) | 7.35262e10i | 0.147681i | ||||||||
\(841\) | 3.46433e11 | 0.692525 | ||||||||
\(842\) | 1.18811e12 | 2.36379 | ||||||||
\(843\) | 1.63971e11 | 0.324680 | ||||||||
\(844\) | − | 4.63016e11i | − | 0.912485i | ||||||
\(845\) | 1.95876e11 | 0.384197 | ||||||||
\(846\) | −4.53217e11 | −0.884759 | ||||||||
\(847\) | 2.80452e10 | 0.0544910 | ||||||||
\(848\) | −1.51721e11 | −0.293401 | ||||||||
\(849\) | − | 3.17188e11i | − | 0.610500i | ||||||
\(850\) | − | 9.42139e8i | − | 0.00180484i | ||||||
\(851\) | 6.49160e11 | 1.23775 | ||||||||
\(852\) | 6.78261e10 | 0.128718 | ||||||||
\(853\) | −2.83381e11 | −0.535272 | −0.267636 | − | 0.963520i | \(-0.586242\pi\) | ||||
−0.267636 | + | 0.963520i | \(0.586242\pi\) | |||||||
\(854\) | −2.22278e11 | −0.417893 | ||||||||
\(855\) | −3.25523e10 | −0.0609140 | ||||||||
\(856\) | − | 2.02839e10i | − | 0.0377796i | ||||||
\(857\) | − | 6.15389e11i | − | 1.14084i | −0.821351 | − | 0.570422i | \(-0.806780\pi\) | ||
0.821351 | − | 0.570422i | \(-0.193220\pi\) | |||||||
\(858\) | 3.57417e11i | 0.659517i | ||||||||
\(859\) | 7.26155e11i | 1.33370i | 0.745194 | + | 0.666848i | \(0.232357\pi\) | ||||
−0.745194 | + | 0.666848i | \(0.767643\pi\) | |||||||
\(860\) | − | 1.02730e12i | − | 1.87803i | ||||||
\(861\) | 1.66249e11 | 0.302514 | ||||||||
\(862\) | 2.65456e11 | 0.480799 | ||||||||
\(863\) | − | 9.20163e10i | − | 0.165891i | −0.996554 | − | 0.0829453i | \(-0.973567\pi\) | ||
0.996554 | − | 0.0829453i | \(-0.0264327\pi\) | |||||||
\(864\) | − | 1.32472e11i | − | 0.237722i | ||||||
\(865\) | 4.58921e11i | 0.819735i | ||||||||
\(866\) | − | 4.86138e10i | − | 0.0864347i | ||||||
\(867\) | 3.26222e11 | 0.577347 | ||||||||
\(868\) | 3.14006e11i | 0.553170i | ||||||||
\(869\) | 9.42869e11i | 1.65338i | ||||||||
\(870\) | − | 4.95291e11i | − | 0.864536i | ||||||
\(871\) | −2.90600e11 | −0.504921 | ||||||||
\(872\) | −6.53861e11 | −1.13089 | ||||||||
\(873\) | 2.36344e11i | 0.406900i | ||||||||
\(874\) | 1.99047e11 | 0.341122 | ||||||||
\(875\) | 3.02979e11 | 0.516868 | ||||||||
\(876\) | − | 3.02041e11i | − | 0.512920i | ||||||
\(877\) | −1.17827e12 | −1.99180 | −0.995902 | − | 0.0904371i | \(-0.971174\pi\) | ||||
−0.995902 | + | 0.0904371i | \(0.971174\pi\) | |||||||
\(878\) | − | 3.82322e10i | − | 0.0643356i | ||||||
\(879\) | 4.91044e10 | 0.0822555 | ||||||||
\(880\) | 1.51457e11i | 0.252556i | ||||||||
\(881\) | 4.69478e11i | 0.779312i | 0.920960 | + | 0.389656i | \(0.127406\pi\) | ||||
−0.920960 | + | 0.389656i | \(0.872594\pi\) | |||||||
\(882\) | 2.42951e11i | 0.401462i | ||||||||
\(883\) | 4.37028e11 | 0.718897 | 0.359449 | − | 0.933165i | \(-0.382965\pi\) | ||||
0.359449 | + | 0.933165i | \(0.382965\pi\) | |||||||
\(884\) | 1.53449e9i | 0.00251278i | ||||||||
\(885\) | −2.49587e11 | − | 7.23093e10i | −0.406864 | − | 0.117875i | ||||
\(886\) | −1.36721e12 | −2.21871 | ||||||||
\(887\) | − | 1.06371e12i | − | 1.71843i | −0.511619 | − | 0.859213i | \(-0.670954\pi\) | ||
0.511619 | − | 0.859213i | \(-0.329046\pi\) | |||||||
\(888\) | 3.68191e11 | 0.592136 | ||||||||
\(889\) | −5.39132e11 | −0.863153 | ||||||||
\(890\) | −1.03078e12 | −1.64289 | ||||||||
\(891\) | − | 7.38802e10i | − | 0.117224i | ||||||
\(892\) | −1.22720e12 | −1.93846 | ||||||||
\(893\) | 2.67987e11i | 0.421414i | ||||||||
\(894\) | −5.39613e11 | −0.844759 | ||||||||
\(895\) | 2.68010e11i | 0.417694i | ||||||||
\(896\) | 4.01628e11i | 0.623149i | ||||||||
\(897\) | −2.25210e11 | −0.347871 | ||||||||
\(898\) | 7.63490e11i | 1.17408i | ||||||||
\(899\) | − | 6.67535e11i | − | 1.02196i | ||||||
\(900\) | 1.47534e11 | 0.224865 | ||||||||
\(901\) | −1.47668e9 | −0.00224071 | ||||||||
\(902\) | −1.19110e12 | −1.79937 | ||||||||
\(903\) | 3.24123e11i | 0.487482i | ||||||||
\(904\) | 5.07649e11 | 0.760134 | ||||||||
\(905\) | 9.66155e11 | 1.44030 | ||||||||
\(906\) | 3.79725e10 | 0.0563581 | ||||||||
\(907\) | −4.03385e11 | −0.596061 | −0.298031 | − | 0.954556i | \(-0.596330\pi\) | ||||
−0.298031 | + | 0.954556i | \(0.596330\pi\) | |||||||
\(908\) | − | 1.47289e11i | − | 0.216685i | ||||||
\(909\) | 1.06486e11i | 0.155969i | ||||||||
\(910\) | −2.62551e11 | −0.382867 | ||||||||
\(911\) | 3.61782e11 | 0.525259 | 0.262629 | − | 0.964897i | \(-0.415410\pi\) | ||||
0.262629 | + | 0.964897i | \(0.415410\pi\) | |||||||
\(912\) | −3.24588e10 | −0.0469195 | ||||||||
\(913\) | 1.21069e11 | 0.174241 | ||||||||
\(914\) | 1.60458e10 | 0.0229920 | ||||||||
\(915\) | − | 1.64106e11i | − | 0.234121i | ||||||
\(916\) | − | 4.53984e11i | − | 0.644849i | ||||||
\(917\) | 1.37290e9i | 0.00194161i | ||||||||
\(918\) | − | 5.34276e8i | − | 0.000752307i | ||||||
\(919\) | − | 1.08862e11i | − | 0.152621i | −0.997084 | − | 0.0763104i | \(-0.975686\pi\) | ||
0.997084 | − | 0.0763104i | \(-0.0243140\pi\) | |||||||
\(920\) | 3.31928e11 | 0.463332 | ||||||||
\(921\) | 5.02132e10 | 0.0697878 | ||||||||
\(922\) | 4.10689e11i | 0.568315i | ||||||||
\(923\) | 7.64339e10i | 0.105312i | ||||||||
\(924\) | 3.12664e11i | 0.428934i | ||||||||
\(925\) | − | 4.79233e11i | − | 0.654605i | ||||||
\(926\) | −2.02398e12 | −2.75272 | ||||||||
\(927\) | − | 2.23063e11i | − | 0.302071i | ||||||
\(928\) | − | 1.19182e12i | − | 1.60701i | ||||||
\(929\) | 1.62456e11i | 0.218109i | 0.994036 | + | 0.109055i | \(0.0347823\pi\) | ||||
−0.994036 | + | 0.109055i | \(0.965218\pi\) | |||||||
\(930\) | −3.90494e11 | −0.522015 | ||||||||
\(931\) | 1.43657e11 | 0.191218 | ||||||||
\(932\) | − | 1.12996e12i | − | 1.49761i | ||||||
\(933\) | −8.39521e10 | −0.110791 | ||||||||
\(934\) | 3.37771e11 | 0.443848 | ||||||||
\(935\) | 1.47411e9i | 0.00192878i | ||||||||
\(936\) | −1.27735e11 | −0.166420 | ||||||||
\(937\) | − | 1.28792e12i | − | 1.67083i | −0.549621 | − | 0.835414i | \(-0.685228\pi\) | ||
0.549621 | − | 0.835414i | \(-0.314772\pi\) | |||||||
\(938\) | −4.28201e11 | −0.553141 | ||||||||
\(939\) | − | 6.04200e11i | − | 0.777175i | ||||||
\(940\) | 1.41607e12i | 1.81373i | ||||||||
\(941\) | 1.27329e12i | 1.62394i | 0.583702 | + | 0.811968i | \(0.301604\pi\) | ||||
−0.583702 | + | 0.811968i | \(0.698396\pi\) | |||||||
\(942\) | −7.97180e11 | −1.01240 | ||||||||
\(943\) | − | 7.50517e11i | − | 0.949103i | ||||||
\(944\) | −2.48870e11 | − | 7.21017e10i | −0.313390 | − | 0.0907941i | ||||
\(945\) | 5.42708e10 | 0.0680517 | ||||||||
\(946\) | − | 2.32220e12i | − | 2.89958i | ||||||
\(947\) | −1.44714e12 | −1.79933 | −0.899663 | − | 0.436585i | \(-0.856188\pi\) | ||||
−0.899663 | + | 0.436585i | \(0.856188\pi\) | |||||||
\(948\) | −1.06774e12 | −1.32201 | ||||||||
\(949\) | 3.40373e11 | 0.419654 | ||||||||
\(950\) | − | 1.46943e11i | − | 0.180408i | ||||||
\(951\) | 8.28982e11 | 1.01350 | ||||||||
\(952\) | 7.13566e8i | 0.000868733i | ||||||||
\(953\) | 1.00260e12 | 1.21550 | 0.607749 | − | 0.794129i | \(-0.292073\pi\) | ||||
0.607749 | + | 0.794129i | \(0.292073\pi\) | |||||||
\(954\) | − | 3.89504e11i | − | 0.470239i | ||||||
\(955\) | 2.15787e11i | 0.259425i | ||||||||
\(956\) | −4.76073e10 | −0.0569957 | ||||||||
\(957\) | − | 6.64683e11i | − | 0.792440i | ||||||
\(958\) | − | 3.51541e11i | − | 0.417363i | ||||||
\(959\) | −3.20540e11 | −0.378972 | ||||||||
\(960\) | −5.79802e11 | −0.682645 | ||||||||
\(961\) | 3.26597e11 | 0.382929 | ||||||||
\(962\) | 1.31475e12i | 1.53513i | ||||||||
\(963\) | −1.49719e10 | −0.0174089 | ||||||||
\(964\) | −9.26127e11 | −1.07241 | ||||||||
\(965\) | −7.32681e11 | −0.844901 | ||||||||
\(966\) | −3.31848e11 | −0.381093 | ||||||||
\(967\) | 5.84657e11i | 0.668644i | 0.942459 | + | 0.334322i | \(0.108507\pi\) | ||||
−0.942459 | + | 0.334322i | \(0.891493\pi\) | |||||||
\(968\) | − | 7.18094e10i | − | 0.0817862i | ||||||
\(969\) | −3.15918e8 | −0.000358326 | ||||||||
\(970\) | 1.24386e12 | 1.40503 | ||||||||
\(971\) | 9.28306e11 | 1.04427 | 0.522137 | − | 0.852862i | \(-0.325135\pi\) | ||||
0.522137 | + | 0.852862i | \(0.325135\pi\) | |||||||
\(972\) | 8.36649e10 | 0.0937299 | ||||||||
\(973\) | −1.74548e11 | −0.194744 | ||||||||
\(974\) | − | 3.16224e11i | − | 0.351366i | ||||||
\(975\) | 1.66258e11i | 0.183977i | ||||||||
\(976\) | − | 1.63635e11i | − | 0.180334i | ||||||
\(977\) | − | 5.48065e11i | − | 0.601525i | −0.953699 | − | 0.300762i | \(-0.902759\pi\) | ||
0.953699 | − | 0.300762i | \(-0.0972411\pi\) | |||||||
\(978\) | 1.04540e12i | 1.14269i | ||||||||
\(979\) | −1.38332e12 | −1.50588 | ||||||||
\(980\) | 7.59097e11 | 0.822987 | ||||||||
\(981\) | 4.82624e11i | 0.521115i | ||||||||
\(982\) | 1.52351e11i | 0.163832i | ||||||||
\(983\) | − | 9.21559e11i | − | 0.986982i | −0.869751 | − | 0.493491i | \(-0.835721\pi\) | ||
0.869751 | − | 0.493491i | \(-0.164279\pi\) | |||||||
\(984\) | − | 4.25678e11i | − | 0.454047i | ||||||
\(985\) | −1.55519e11 | −0.165210 | ||||||||
\(986\) | − | 4.80676e9i | − | 0.00508563i | ||||||
\(987\) | − | 4.46785e11i | − | 0.470793i | ||||||
\(988\) | 2.39331e11i | 0.251172i | ||||||||
\(989\) | 1.46323e12 | 1.52942 | ||||||||
\(990\) | −3.88826e11 | −0.404776 | ||||||||
\(991\) | − | 1.58431e12i | − | 1.64265i | −0.570460 | − | 0.821326i | \(-0.693235\pi\) | ||
0.570460 | − | 0.821326i | \(-0.306765\pi\) | |||||||
\(992\) | −9.39647e11 | −0.970327 | ||||||||
\(993\) | −7.98495e11 | −0.821249 | ||||||||
\(994\) | 1.12626e11i | 0.115370i | ||||||||
\(995\) | −1.01094e12 | −1.03142 | ||||||||
\(996\) | 1.37103e11i | 0.139319i | ||||||||
\(997\) | 1.86682e12 | 1.88939 | 0.944695 | − | 0.327949i | \(-0.106358\pi\) | ||||
0.944695 | + | 0.327949i | \(0.106358\pi\) | |||||||
\(998\) | 2.49145e12i | 2.51148i | ||||||||
\(999\) | − | 2.71767e11i | − | 0.272857i |
(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 | 177.9.c.a.58.11 | ✓ | 80 | |
59.58 | odd | 2 | inner | 177.9.c.a.58.70 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.9.c.a.58.11 | ✓ | 80 | 1.1 | even | 1 | trivial | |
177.9.c.a.58.70 | yes | 80 | 59.58 | odd | 2 | inner |