Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,9,Mod(319,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("320.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.h (of order \(2\), degree \(1\), not 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: | \(130.361155220\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 1394 x^{14} + 1332306 x^{12} - 657883370 x^{10} + 233333110300 x^{8} - 45644912663250 x^{6} + \cdots + 23\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{99}\cdot 3^{9}\cdot 5^{10} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.5 | ||
Root | \(11.1856 + 6.45800i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.319 |
Dual form | 320.9.h.f.319.6 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −77.4652 | −0.956361 | −0.478181 | − | 0.878262i | \(-0.658704\pi\) | ||||
−0.478181 | + | 0.878262i | \(0.658704\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −586.915 | − | 214.840i | −0.939064 | − | 0.343744i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2766.32 | −1.15215 | −0.576076 | − | 0.817396i | \(-0.695417\pi\) | ||||
−0.576076 | + | 0.817396i | \(0.695417\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −560.136 | −0.0853736 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18778.9i | 1.28262i | 0.767280 | + | 0.641312i | \(0.221610\pi\) | ||||
−0.767280 | + | 0.641312i | \(0.778390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38629.0i | 1.35251i | 0.736668 | + | 0.676255i | \(0.236398\pi\) | ||||
−0.736668 | + | 0.676255i | \(0.763602\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 45465.5 | + | 16642.6i | 0.898084 | + | 0.328743i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 76484.1i | − | 0.915747i | −0.889017 | − | 0.457874i | \(-0.848611\pi\) | ||
0.889017 | − | 0.457874i | \(-0.151389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33574.4i | 0.257629i | 0.991669 | + | 0.128814i | \(0.0411172\pi\) | ||||
−0.991669 | + | 0.128814i | \(0.958883\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 214293. | 1.10187 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 222381. | 0.794670 | 0.397335 | − | 0.917674i | \(-0.369935\pi\) | ||||
0.397335 | + | 0.917674i | \(0.369935\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 298313. | + | 252185.i | 0.763681 | + | 0.645594i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 551641. | 1.03801 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −651811. | −0.921573 | −0.460786 | − | 0.887511i | \(-0.652433\pi\) | ||||
−0.460786 | + | 0.887511i | \(0.652433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.03876e6i | − | 1.12478i | −0.826872 | − | 0.562390i | \(-0.809882\pi\) | ||
0.826872 | − | 0.562390i | \(-0.190118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.45471e6i | − | 1.22665i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.62359e6 | + | 594315.i | 1.08194 | + | 0.396045i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.60818e6i | − | 1.39165i | −0.718210 | − | 0.695827i | \(-0.755038\pi\) | ||
0.718210 | − | 0.695827i | \(-0.244962\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.99241e6i | − | 1.29349i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.22496e6 | 1.49516 | 0.747580 | − | 0.664172i | \(-0.231216\pi\) | ||||
0.747580 | + | 0.664172i | \(0.231216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 865193. | 0.253069 | 0.126535 | − | 0.991962i | \(-0.459615\pi\) | ||||
0.126535 | + | 0.991962i | \(0.459615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 328752. | + | 120339.i | 0.0801712 | + | 0.0293466i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.55589e6 | −0.318851 | −0.159425 | − | 0.987210i | \(-0.550964\pi\) | ||||
−0.159425 | + | 0.987210i | \(0.550964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.88771e6 | 0.327454 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.92486e6i | 0.875785i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.13581e7i | 1.43947i | 0.694250 | + | 0.719734i | \(0.255736\pi\) | ||||
−0.694250 | + | 0.719734i | \(0.744264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.03445e6 | − | 1.10216e7i | 0.440894 | − | 1.20447i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.60085e6i | − | 0.246386i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.73206e7i | 1.42940i | 0.699431 | + | 0.714700i | \(0.253437\pi\) | ||||
−0.699431 | + | 0.714700i | \(0.746563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.27787e6 | −0.453412 | −0.226706 | − | 0.973963i | \(-0.572796\pi\) | ||||
−0.226706 | + | 0.973963i | \(0.572796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.54951e6 | 0.0983633 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.29905e6 | − | 2.26720e7i | 0.464917 | − | 1.27009i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.69260e7 | 1.83245 | 0.916226 | − | 0.400661i | \(-0.131219\pi\) | ||||
0.916226 | + | 0.400661i | \(0.131219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.72268e7 | −0.759992 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.42036e7i | − | 0.952458i | −0.879321 | − | 0.476229i | \(-0.842003\pi\) | ||
0.879321 | − | 0.476229i | \(-0.157997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.21399e7i | 1.48389i | 0.670461 | + | 0.741945i | \(0.266096\pi\) | ||||
−0.670461 | + | 0.741945i | \(0.733904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.31089e7 | − | 1.95356e7i | −0.730354 | − | 0.617421i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.19484e7i | − | 1.47778i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.05498e7i | 0.784332i | 0.919894 | + | 0.392166i | \(0.128274\pi\) | ||||
−0.919894 | + | 0.392166i | \(0.871726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.90579e7 | −0.907338 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.71605e7 | 0.572301 | 0.286151 | − | 0.958185i | \(-0.407624\pi\) | ||||
0.286151 | + | 0.958185i | \(0.407624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.64318e7 | + | 4.48897e7i | −0.314782 | + | 0.859945i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.04927e7 | 0.881356 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.34588e7 | −0.533274 | −0.266637 | − | 0.963797i | \(-0.585913\pi\) | ||||
−0.266637 | + | 0.963797i | \(0.585913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.06860e8i | − | 1.55830i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.04677e7i | 1.07570i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.21313e6 | − | 1.97053e7i | 0.0885583 | − | 0.241930i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.14836e8i | 1.29715i | 0.761152 | + | 0.648574i | \(0.224634\pi\) | ||||
−0.761152 | + | 0.648574i | \(0.775366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.05187e7i | − | 0.109502i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67657e6 | 0.0161115 | 0.00805577 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805577 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13496e8 | 1.00840 | 0.504201 | − | 0.863587i | \(-0.331787\pi\) | ||||
0.504201 | + | 0.863587i | \(0.331787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.25772e8 | − | 4.60387e7i | −1.03473 | − | 0.378762i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.58492e7 | 0.731229 | 0.365614 | − | 0.930766i | \(-0.380859\pi\) | ||||
0.365614 | + | 0.930766i | \(0.380859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.28668e7 | 0.587049 | 0.293525 | − | 0.955952i | \(-0.405172\pi\) | ||||
0.293525 | + | 0.955952i | \(0.405172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.02043e8i | 1.33092i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.02658e8i | − | 0.629622i | −0.949154 | − | 0.314811i | \(-0.898059\pi\) | ||
0.949154 | − | 0.314811i | \(-0.101941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.30519e8 | − | 4.77763e7i | −0.746246 | − | 0.273163i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.16375e7i | − | 0.115469i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.11579e8i | 1.05508i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.38288e8 | −0.645125 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.27288e8 | −1.42991 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.20905e8 | − | 2.12101e8i | −0.495226 | − | 0.868764i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.03106e8 | −0.396340 | −0.198170 | − | 0.980168i | \(-0.563500\pi\) | ||||
−0.198170 | + | 0.980168i | \(0.563500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.70224e7 | −0.242025 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.08809e8i | − | 0.369470i | −0.982788 | − | 0.184735i | \(-0.940857\pi\) | ||
0.982788 | − | 0.184735i | \(-0.0591427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 9.28776e7i | − | 0.296828i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.23766e8 | − | 1.18514e8i | −0.974756 | − | 0.356809i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.52729e8i | 0.433549i | 0.976222 | + | 0.216774i | \(0.0695536\pi\) | ||||
−0.976222 | + | 0.216774i | \(0.930446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.20534e8i | 0.858648i | 0.903151 | + | 0.429324i | \(0.141248\pi\) | ||||
−0.903151 | + | 0.429324i | \(0.858752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.20527e8 | 0.304936 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.25411e8 | −1.73476 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.82557e8 | + | 1.40035e8i | 0.865415 | + | 0.316785i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.46232e8 | −0.313164 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.06879e8 | −1.83994 | −0.919972 | − | 0.391985i | \(-0.871789\pi\) | ||||
−0.919972 | + | 0.391985i | \(0.871789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.61728e7i | − | 0.146518i | −0.997313 | − | 0.0732592i | \(-0.976660\pi\) | ||
0.997313 | − | 0.0732592i | \(-0.0233400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.28415e7i | 0.0781806i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.23167e8 | + | 6.09663e8i | −0.386636 | + | 1.05624i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.20359e8i | 1.51481i | 0.652944 | + | 0.757406i | \(0.273534\pi\) | ||||
−0.652944 | + | 0.757406i | \(0.726466\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 8.79858e8i | − | 1.37665i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.15177e8 | −0.915581 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.80213e8 | 0.538613 | 0.269306 | − | 0.963055i | \(-0.413206\pi\) | ||||
0.269306 | + | 0.963055i | \(0.413206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.12530e8 | + | 8.53792e8i | −0.421654 | + | 1.15190i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.25104e9 | 1.60844 | 0.804219 | − | 0.594333i | \(-0.202584\pi\) | ||||
0.804219 | + | 0.594333i | \(0.202584\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.76472e8 | −0.829283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.88063e7i | − | 0.0219947i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.69241e8i | − | 0.747133i | −0.927603 | − | 0.373566i | \(-0.878135\pi\) | ||
0.927603 | − | 0.373566i | \(-0.121865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.25228e8 | − | 6.97624e8i | −0.879876 | − | 0.743823i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.34174e9i | − | 1.36702i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.43467e8i | 0.431966i | 0.976397 | + | 0.215983i | \(0.0692956\pi\) | ||||
−0.976397 | + | 0.215983i | \(0.930704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.71276e9 | −1.59581 | −0.797907 | − | 0.602781i | \(-0.794059\pi\) | ||||
−0.797907 | + | 0.602781i | \(0.794059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.86317e8 | 0.433625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.60341e8 | + | 1.53078e9i | −0.478372 | + | 1.30685i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.43629e9 | 1.17456 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.52601e9 | −1.19594 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.30115e9i | 1.72906i | 0.502578 | + | 0.864532i | \(0.332385\pi\) | ||||
−0.502578 | + | 0.864532i | \(0.667615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.20124e9i | 0.865765i | 0.901450 | + | 0.432883i | \(0.142504\pi\) | ||||
−0.901450 | + | 0.432883i | \(0.857496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.42888e8 | + | 1.75629e9i | −0.444628 | + | 1.21467i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.12445e9i | 0.746580i | 0.927715 | + | 0.373290i | \(0.121770\pi\) | ||||
−0.927715 | + | 0.373290i | \(0.878230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.25000e9i | − | 1.43473i | −0.696697 | − | 0.717365i | \(-0.745348\pi\) | ||
0.696697 | − | 0.717365i | \(-0.254652\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.86048e9 | −1.75249 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.80312e9 | 1.06179 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.47969e9 | − | 9.07690e8i | −1.40405 | − | 0.513952i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.24564e8 | −0.0678438 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.30491e8 | −0.330441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.18331e9i | − | 1.60601i | −0.595969 | − | 0.803007i | \(-0.703232\pi\) | ||
0.595969 | − | 0.803007i | \(-0.296768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.87493e9i | 0.910894i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.07795e8 | − | 1.85878e8i | −0.237648 | − | 0.0869909i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.87354e9i | 1.29592i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3.26437e9i | − | 1.41913i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.95451e9 | 1.23856 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.56237e9 | 1.44052 | 0.720260 | − | 0.693704i | \(-0.244022\pi\) | ||||
0.720260 | + | 0.693704i | \(0.244022\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.67096e8 | − | 1.41258e8i | −0.0651981 | − | 0.0551167i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.62541e9 | −1.36538 | −0.682689 | − | 0.730709i | \(-0.739190\pi\) | ||||
−0.682689 | + | 0.730709i | \(0.739190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.49920e8 | −0.236330 | −0.118165 | − | 0.992994i | \(-0.537701\pi\) | ||||
−0.118165 | + | 0.992994i | \(0.537701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.02420e9i | 1.41329i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.18657e9i | − | 0.402597i | −0.979530 | − | 0.201299i | \(-0.935484\pi\) | ||
0.979530 | − | 0.201299i | \(-0.0645162\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.13175e8 | + | 3.34267e8i | 0.299421 | + | 0.109603i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.36655e9i | − | 0.750105i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.67879e9i | 0.514522i | 0.966342 | + | 0.257261i | \(0.0828201\pi\) | ||||
−0.966342 | + | 0.257261i | \(0.917180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.27098e9 | −1.85895 | −0.929474 | − | 0.368888i | \(-0.879738\pi\) | ||||
−0.929474 | + | 0.368888i | \(0.879738\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.93683e8 | −0.170266 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.10792e9 | − | 4.05555e8i | −0.307500 | − | 0.112560i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.29695e9 | −0.348446 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.10399e9 | −0.547327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.52982e9i | − | 1.89710i | −0.316632 | − | 0.948548i | \(-0.602552\pi\) | ||
0.316632 | − | 0.948548i | \(-0.397448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.17608e9i | 1.01926i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.27290e9 | − | 3.47739e9i | 0.301046 | − | 0.822418i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.46963e9i | − | 0.336880i | −0.985712 | − | 0.168440i | \(-0.946127\pi\) | ||
0.985712 | − | 0.168440i | \(-0.0538729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.21506e9i | 1.60340i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65103e8 | 0.0786780 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.91195e9 | 0.817656 | 0.408828 | − | 0.912611i | \(-0.365938\pi\) | ||||
0.408828 | + | 0.912611i | \(0.365938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44017e9 | − | 6.66623e9i | 0.494808 | − | 1.35175i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.59190e9 | 0.510003 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.45528e9 | −0.659894 | −0.329947 | − | 0.943999i | \(-0.607031\pi\) | ||||
−0.329947 | + | 0.943999i | \(0.607031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.91923e9i | 1.28286i | 0.767180 | + | 0.641432i | \(0.221659\pi\) | ||||
−0.767180 | + | 0.641432i | \(0.778341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.27795e9i | 1.49029i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.73576e9 | + | 5.60199e9i | −0.828055 | + | 0.979515i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.71800e9i | − | 0.801381i | −0.916213 | − | 0.400690i | \(-0.868770\pi\) | ||
0.916213 | − | 0.400690i | \(-0.131230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.81846e8i | 0.0960265i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.72838e8 | −0.107916 | −0.0539580 | − | 0.998543i | \(-0.517184\pi\) | ||||
−0.0539580 | + | 0.998543i | \(0.517184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.27935e9 | 1.44668 | 0.723339 | − | 0.690493i | \(-0.242606\pi\) | ||||
0.723339 | + | 0.690493i | \(0.242606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.58767e8 | + | 1.52648e9i | −0.0846937 | + | 0.231372i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.16876e10 | −1.72265 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.12593e9 | 0.161407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8.89577e9i | − | 1.24054i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.06323e9i | − | 0.551316i | −0.961256 | − | 0.275658i | \(-0.911104\pi\) | ||
0.961256 | − | 0.275658i | \(-0.0888957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.72114e9 | − | 1.01657e10i | 0.491347 | − | 1.34230i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.03592e10i | 1.33138i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.59038e9i | 1.07480i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.39340e9 | −0.291574 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.29876e8 | −0.0154085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.68457e9 | + | 1.34874e9i | 0.425783 | + | 0.155857i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.05058e9 | −0.906304 | −0.453152 | − | 0.891433i | \(-0.649700\pi\) | ||||
−0.453152 | + | 0.891433i | \(0.649700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.79203e9 | −0.964396 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.49045e9i | − | 0.373113i | −0.982444 | − | 0.186556i | \(-0.940267\pi\) | ||
0.982444 | − | 0.186556i | \(-0.0597327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.23084e10i | − | 1.28241i | −0.767371 | − | 0.641203i | \(-0.778436\pi\) | ||
0.767371 | − | 0.641203i | \(-0.221564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.09432e8 | − | 3.32897e8i | −0.0923694 | − | 0.0338118i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.41977e10i | 1.40599i | 0.711197 | + | 0.702993i | \(0.248153\pi\) | ||||
−0.711197 | + | 0.702993i | \(0.751847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.22403e10i | − | 1.18203i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.42498e9 | −0.699319 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.56791e9 | 0.235923 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.74167e9 | + | 1.15235e10i | −0.873173 | + | 1.03289i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.41929e9 | −0.561431 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.30408e9 | 0.367364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.62596e10i | 1.35456i | 0.735727 | + | 0.677278i | \(0.236841\pi\) | ||||
−0.735727 | + | 0.677278i | \(0.763159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.46094e9i | 0.118810i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.16724e10 | − | 7.93317e9i | −1.72079 | − | 0.629894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.64424e9i | − | 0.282545i | −0.989971 | − | 0.141272i | \(-0.954881\pi\) | ||
0.989971 | − | 0.141272i | \(-0.0451194\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.95245e9i | 0.602146i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95067e10 | 1.44267 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.07253e10 | 0.774875 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.01107e10 | + | 3.70101e9i | 0.713680 | + | 0.261242i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.11705e10 | −1.46020 | −0.730101 | − | 0.683340i | \(-0.760527\pi\) | ||||
−0.730101 | + | 0.683340i | \(0.760527\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.13163e9 | −0.211091 | −0.105545 | − | 0.994415i | \(-0.533659\pi\) | ||||
−0.105545 | + | 0.994415i | \(0.533659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.13093e10i | 1.40392i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.38374e9i | − | 0.411128i | −0.978644 | − | 0.205564i | \(-0.934097\pi\) | ||
0.978644 | − | 0.205564i | \(-0.0659028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.19989e9 | + | 1.42054e10i | −0.327401 | + | 0.894419i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.63900e10i | − | 1.00904i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.14937e10i | 0.691962i | 0.938242 | + | 0.345981i | \(0.112454\pi\) | ||||
−0.938242 | + | 0.345981i | \(0.887546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.58563e10 | 0.933627 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.07125e10 | 0.616973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.05332e9 | − | 2.47325e10i | 0.510078 | − | 1.39347i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.11024e10 | −1.16323 | −0.581617 | − | 0.813463i | \(-0.697580\pi\) | ||||
−0.581617 | + | 0.813463i | \(0.697580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.36655e9 | −0.127647 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.14201e10i | − | 1.65849i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.32356e9i | − | 0.120038i | −0.998197 | − | 0.0600191i | \(-0.980884\pi\) | ||
0.998197 | − | 0.0600191i | \(-0.0191162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.36591e9 | + | 1.64304e10i | 0.473615 | + | 0.830852i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.51788e10i | − | 1.24644i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.87748e9i | − | 0.381795i | −0.981610 | − | 0.190898i | \(-0.938860\pi\) | ||
0.981610 | − | 0.190898i | \(-0.0611399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.98710e9 | 0.379044 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.16820e10 | 1.47237 | 0.736186 | − | 0.676780i | \(-0.236625\pi\) | ||||
0.736186 | + | 0.676780i | \(0.236625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11606e10 | + | 3.04893e10i | −0.507977 | + | 1.38773i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.84626e8 | −0.0216054 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.57187e10 | 1.55990 | 0.779951 | − | 0.625840i | \(-0.215244\pi\) | ||||
0.779951 | + | 0.625840i | \(0.215244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.70086e10i | − | 0.727717i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.42891e9i | 0.353347i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.56331e9 | − | 1.79301e10i | 0.269609 | − | 0.736538i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.01725e9i | 0.363004i | 0.983391 | + | 0.181502i | \(0.0580960\pi\) | ||||
−0.983391 | + | 0.181502i | \(0.941904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.19478e9i | 0.283874i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.84446e10 | 0.713332 | 0.356666 | − | 0.934232i | \(-0.383913\pi\) | ||||
0.356666 | + | 0.934232i | \(0.383913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.01262e10 | 1.52128 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.29237e10 | + | 8.39119e9i | 0.852048 | + | 0.311892i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.89788e10 | 1.78497 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.11180e10 | 1.46939 | 0.734697 | − | 0.678395i | \(-0.237324\pi\) | ||||
0.734697 | + | 0.678395i | \(0.237324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.18312e10i | − | 0.414629i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.79141e10i | − | 1.64689i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.59409e10 | − | 5.83514e9i | −0.537427 | − | 0.196725i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.48302e10i | − | 0.821177i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.56118e10i | − | 1.47986i | −0.672683 | − | 0.739931i | \(-0.734858\pi\) | ||
0.672683 | − | 0.739931i | \(-0.265142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.43826e10 | 0.457834 | 0.228917 | − | 0.973446i | \(-0.426482\pi\) | ||||
0.228917 | + | 0.973446i | \(0.426482\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.71510e8 | 0.0272214 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.92882e10 | − | 2.28162e10i | 0.591201 | − | 0.699339i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.73666e10 | 0.522399 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.61941e10 | 1.65906 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.99136e10i | 0.577087i | 0.957467 | + | 0.288544i | \(0.0931710\pi\) | ||||
−0.957467 | + | 0.288544i | \(0.906829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.13608e10i | − | 0.323190i | −0.986857 | − | 0.161595i | \(-0.948336\pi\) | ||
0.986857 | − | 0.161595i | \(-0.0516638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.96349e10 | − | 1.08478e10i | −0.827650 | − | 0.302961i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.46633e9i | 0.204730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.17463e10i | − | 0.854743i | −0.904076 | − | 0.427372i | \(-0.859440\pi\) | ||
0.904076 | − | 0.427372i | \(-0.140560\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05737e9 | −0.0279559 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.49996e10 | −0.649111 | −0.324555 | − | 0.945867i | \(-0.605215\pi\) | ||||
−0.324555 | + | 0.945867i | \(0.605215\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.96375e10 | + | 7.18829e9i | 0.500778 | + | 0.183310i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.02516e10 | 1.75965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.89675e10 | −0.712732 | −0.356366 | − | 0.934347i | \(-0.615984\pi\) | ||||
−0.356366 | + | 0.934347i | \(0.615984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.93402e10i | 1.91773i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.90074e9i | 0.140124i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.29578e10 | + | 6.27178e10i | −0.535655 | + | 1.46334i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.50928e10i | 0.346023i | 0.984920 | + | 0.173012i | \(0.0553499\pi\) | ||||
−0.984920 | + | 0.173012i | \(0.944650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 4.21917e10i | − | 0.950554i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.37841e10 | 0.748012 | 0.374006 | − | 0.927426i | \(-0.377984\pi\) | ||||
0.374006 | + | 0.927426i | \(0.377984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.45040e9 | −0.0968445 | −0.0484223 | − | 0.998827i | \(-0.515419\pi\) | ||||
−0.0484223 | + | 0.998827i | \(0.515419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.72877e10 | − | 4.72277e10i | 0.369764 | − | 1.01015i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.15089e10 | 0.662470 | 0.331235 | − | 0.943548i | \(-0.392535\pi\) | ||||
0.331235 | + | 0.943548i | \(0.392535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.02149e11 | −2.11126 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.12958e10i | − | 1.44871i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.62474e10i | 0.324593i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.46698e9 | + | 1.00157e10i | −0.166324 | + | 0.196746i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.36208e9i | − | 0.122893i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.58978e9i | 0.0301992i | 0.999886 | + | 0.0150996i | \(0.00480653\pi\) | ||||
−0.999886 | + | 0.0150996i | \(0.995193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00752e11 | 1.88223 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.76548e10 | 0.875626 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.46713e10 | − | 6.73987e10i | 0.445886 | − | 1.21810i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.45450e10 | −1.68083 | −0.840413 | − | 0.541947i | \(-0.817687\pi\) | ||||
−0.840413 | + | 0.541947i | \(0.817687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.94533e10 | −0.515108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.07795e10i | 1.56193i | 0.624574 | + | 0.780966i | \(0.285273\pi\) | ||||
−0.624574 | + | 0.780966i | \(0.714727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.98532e10i | 0.843928i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.25984e9 | + | 6.17360e9i | −0.0376407 | + | 0.102830i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.69547e10i | 1.09738i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.75766e10i | 1.25121i | 0.780142 | + | 0.625603i | \(0.215147\pi\) | ||||
−0.780142 | + | 0.625603i | \(0.784853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.69119e10 | −1.53825 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.36077e10 | −0.993659 | −0.496830 | − | 0.867848i | \(-0.665503\pi\) | ||||
−0.496830 | + | 0.867848i | \(0.665503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.84006e8 | − | 3.60195e8i | −0.0151298 | − | 0.00553824i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.24031e10 | 0.793094 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.93388e10 | 0.288110 | 0.144055 | − | 0.989570i | \(-0.453986\pi\) | ||||
0.144055 | + | 0.989570i | \(0.453986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.16572e11i | − | 1.70967i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.85210e10i | 0.267421i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.66127e10 | − | 2.43836e10i | −0.946953 | − | 0.346631i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.92179e10i | − | 0.408966i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.18429e10i | 0.714529i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.07366e11 | 1.45720 | 0.728598 | − | 0.684942i | \(-0.240172\pi\) | ||||
0.728598 | + | 0.684942i | \(0.240172\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.40757e11 | −1.88132 | −0.940661 | − | 0.339347i | \(-0.889794\pi\) | ||||
−0.940661 | + | 0.339347i | \(0.889794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.39265e10 | + | 5.40416e10i | 0.841479 | + | 0.711363i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.94485e10 | −1.03001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.88576e10 | −0.368499 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.70187e9i | − | 0.122033i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.63206e11i | 2.02222i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.62553e10 | − | 2.05922e10i | −0.686670 | − | 0.251355i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3.43533e10i | − | 0.413116i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.54491e10i | 0.420001i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.50605e10 | −0.175812 | −0.0879062 | − | 0.996129i | \(-0.528018\pi\) | ||||
−0.0879062 | + | 0.996129i | \(0.528018\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.32679e11 | 1.52617 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.86357e10 | − | 1.78031e10i | −0.551276 | − | 0.201794i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.59183e10 | −0.512905 | −0.256453 | − | 0.966557i | \(-0.582554\pi\) | ||||
−0.256453 | + | 0.966557i | \(0.582554\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.51646e9 | 0.0387094 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.18842e10i | − | 0.237424i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.45104e10i | − | 0.903670i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.34070e10 | − | 1.18582e11i | 0.457496 | − | 1.24982i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.70367e11i | − | 1.76996i | −0.465627 | − | 0.884981i | \(-0.654171\pi\) | ||
0.465627 | − | 0.884981i | \(-0.345829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.34216e10i | 0.342279i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11262e11 | −1.12330 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.69946e10 | 0.567283 | 0.283642 | − | 0.958930i | \(-0.408457\pi\) | ||||
0.283642 | + | 0.958930i | \(0.408457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.20551e10 | + | 6.02517e10i | −0.216429 | + | 0.591256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.08047e11 | 1.04539 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.84498e9 | −0.0939217 | −0.0469608 | − | 0.998897i | \(-0.514954\pi\) | ||||
−0.0469608 | + | 0.998897i | \(0.514954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.60223e11i | 1.50723i | 0.657314 | + | 0.753617i | \(0.271693\pi\) | ||||
−0.657314 | + | 0.753617i | \(0.728307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.78259e11i | − | 1.65361i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.63392e10 | + | 5.60813e10i | 0.606874 | + | 0.513034i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.28831e9i | 0.0747761i | 0.999301 | + | 0.0373880i | \(0.0119038\pi\) | ||||
−0.999301 | + | 0.0373880i | \(0.988096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 9.30543e10i | − | 0.827984i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.51344e10 | −0.659378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.13293e11 | −1.84630 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.64860e9 | + | 1.26994e10i | −0.0396916 | + | 0.108432i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.23397e10 | −0.272385 | −0.136193 | − | 0.990682i | \(-0.543487\pi\) | ||||
−0.136193 | + | 0.990682i | \(0.543487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.48757e10 | 0.289776 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 8.71060e10i | − | 0.714000i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.22957e10i | − | 0.342041i | −0.985268 | − | 0.171020i | \(-0.945294\pi\) | ||
0.985268 | − | 0.171020i | \(-0.0547064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.54557e10 | − | 1.24179e11i | 0.362677 | − | 0.990787i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.74297e11i | 1.37212i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.31039e11i | 1.79464i | 0.441381 | + | 0.897320i | \(0.354489\pi\) | ||||
−0.441381 | + | 0.897320i | \(0.645511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.77311e10 | 0.519147 | 0.259573 | − | 0.965723i | \(-0.416418\pi\) | ||||
0.259573 | + | 0.965723i | \(0.416418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.06836e10 | −0.156443 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.11634e10 | + | 2.97098e10i | 0.605814 | + | 0.221758i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.53753e9 | −0.0407907 | −0.0203954 | − | 0.999792i | \(-0.506492\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.39679e11 | −1.01546 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.01025e10i | − | 0.431249i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.98304e11i | − | 1.40439i | −0.711983 | − | 0.702197i | \(-0.752203\pi\) | ||
0.711983 | − | 0.702197i | \(-0.247797\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.92090e11 | + | 7.03144e10i | 1.34278 | + | 0.491523i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.63115e10i | 0.388559i | 0.980946 | + | 0.194279i | \(0.0622368\pi\) | ||||
−0.980946 | + | 0.194279i | \(0.937763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.07195e10i | − | 0.141129i | −0.997507 | − | 0.0705646i | \(-0.977520\pi\) | ||
0.997507 | − | 0.0705646i | \(-0.0224801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.22675e11 | 0.824875 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.25577e10 | 0.614413 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.53931e10 | + | 1.50460e11i | 0.166416 | + | 0.986056i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.88412e10 | 0.316021 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.99485e11 | −1.27440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23968e11i | 0.781972i | 0.920397 | + | 0.390986i | \(0.127866\pi\) | ||||
−0.920397 | + | 0.390986i | \(0.872134\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.46596e11i | 1.53593i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.05142e10 | + | 2.21512e10i | 0.372188 | + | 0.136239i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.29204e10i | 0.442885i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.35573e10i | 0.0813148i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28203e11 | −1.35173 | −0.675864 | − | 0.737026i | \(-0.736229\pi\) | ||||
−0.675864 | + | 0.737026i | \(0.736229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.01445e11 | −0.593454 | −0.296727 | − | 0.954962i | \(-0.595895\pi\) | ||||
−0.296727 | + | 0.954962i | \(0.595895\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.93364e10 | + | 1.43991e10i | 0.227277 | + | 0.0831947i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.69107e10 | 0.267704 | 0.133852 | − | 0.991001i | \(-0.457265\pi\) | ||||
0.133852 | + | 0.991001i | \(0.457265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.25261e11 | −1.83338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.22599e11i | − | 1.23937i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.35671e11i | 0.746164i | 0.927798 | + | 0.373082i | \(0.121699\pi\) | ||||
−0.927798 | + | 0.373082i | \(0.878301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.33765e10 | + | 6.38616e10i | −0.127003 | + | 0.346956i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.36041e10i | − | 0.126685i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.08963e11i | − | 0.577747i | −0.957367 | − | 0.288873i | \(-0.906719\pi\) | ||
0.957367 | − | 0.288873i | \(-0.0932806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.92896e11 | −1.53429 | −0.767145 | − | 0.641474i | \(-0.778323\pi\) | ||||
−0.767145 | + | 0.641474i | \(0.778323\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.28872e11 | −1.18451 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.99538e10 | + | 5.45112e10i | −0.102033 | + | 0.278740i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.44951e11 | −0.732346 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.75960e11 | −1.37766 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.17891e11i | − | 0.581557i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.87465e10i | − | 0.286366i | −0.989696 | − | 0.143183i | \(-0.954266\pi\) | ||
0.989696 | − | 0.143183i | \(-0.0457338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.64561e11 | + | 1.39116e11i | 0.792707 | + | 0.670133i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.37409e11i | 1.60621i | 0.595837 | + | 0.803105i | \(0.296820\pi\) | ||||
−0.595837 | + | 0.803105i | \(0.703180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.17672e11i | − | 1.49451i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.80843e11 | 1.30580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.03880e11 | −0.936898 | −0.468449 | − | 0.883490i | \(-0.655187\pi\) | ||||
−0.468449 | + | 0.883490i | \(0.655187\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.28122e10 | − | 8.96387e10i | 0.149030 | − | 0.407130i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.03462e10 | 0.226016 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.38752e11 | −1.94690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.14740e11i | 0.941889i | 0.882163 | + | 0.470945i | \(0.156087\pi\) | ||||
−0.882163 | + | 0.470945i | \(0.843913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.90982e10i | 0.126163i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.88635e10 | − | 1.88126e11i | 0.295155 | − | 0.806325i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.23143e11i | − | 1.36919i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.19182e10i | 0.385028i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.87506e10 | 0.284711 | 0.142356 | − | 0.989816i | \(-0.454532\pi\) | ||||
0.142356 | + | 0.989816i | \(0.454532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.75683e10 | 0.358530 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.07393e10 | − | 2.58941e10i | −0.286355 | − | 0.104820i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.63793e9 | −0.0185629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.61613e11 | −1.82681 | −0.913405 | − | 0.407052i | \(-0.866557\pi\) | ||||
−0.913405 | + | 0.407052i | \(0.866557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.71120e10i | − | 0.0669612i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.31000e11i | − | 0.893830i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.25754e11 | + | 1.55847e11i | 1.62905 | + | 0.596313i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.30048e11i | − | 0.492069i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.60395e11i | − | 0.600173i | −0.953912 | − | 0.300087i | \(-0.902984\pi\) | ||
0.953912 | − | 0.300087i | \(-0.0970156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.13967e11 | −1.16183 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.85783e11 | 1.77782 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.94444e11 | − | 1.64377e11i | −0.703787 | − | 0.594962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.50548e11 | 0.538936 | 0.269468 | − | 0.963009i | \(-0.413152\pi\) | ||||
0.269468 | + | 0.963009i | \(0.413152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.02249e11 | 1.07017 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.61735e10i | − | 0.231747i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.60328e11i | 1.59460i | 0.603584 | + | 0.797300i | \(0.293739\pi\) | ||||
−0.603584 | + | 0.797300i | \(0.706261\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.58256e10 | + | 3.14164e10i | 0.294081 | + | 0.107648i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.93429e11i | 2.35035i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.28300e10i | 0.277722i | 0.990312 | + | 0.138861i | \(0.0443441\pi\) | ||||
−0.990312 | + | 0.138861i | \(0.955656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00468e11 | 0.333240 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.13495e10 | 0.201306 | 0.100653 | − | 0.994922i | \(-0.467907\pi\) | ||||
0.100653 | + | 0.994922i | \(0.467907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.32261e11 | + | 1.94834e11i | 1.72782 | + | 0.632469i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.52135e10 | −0.0488594 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.65149e11 | −0.842487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.54621e11i | 1.11482i | 0.830238 | + | 0.557409i | \(0.188205\pi\) | ||||
−0.830238 | + | 0.557409i | \(0.811795\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.83299e11i | 1.81431i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.63649e10 | + | 4.47069e10i | −0.0503647 | + | 0.137590i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.91287e10i | − | 0.271415i | −0.990749 | − | 0.135708i | \(-0.956669\pi\) | ||
0.990749 | − | 0.135708i | \(-0.0433307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.23501e11i | − | 0.974784i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.57826e9 | 0.00470586 | 0.00235293 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235293 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.29236e11 | −0.676370 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.20406e9 | − | 2.51443e10i | 0.0268741 | − | 0.0734166i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.69076e11 | −1.93328 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.83818e11 | −1.09754 | −0.548769 | − | 0.835974i | \(-0.684903\pi\) | ||||
−0.548769 | + | 0.835974i | \(0.684903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.13845e11i | 0.322179i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.96655e10i | − | 0.279143i | −0.990212 | − | 0.139572i | \(-0.955427\pi\) | ||
0.990212 | − | 0.139572i | \(-0.0445725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.61960e11 | − | 3.09875e11i | 0.726152 | − | 0.858973i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.58916e11i | − | 1.53343i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.41851e11i | 0.385196i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.54516e11 | 1.22165 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.59565e11 | −0.956601 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.97730e11 | − | 5.40172e11i | 0.520707 | − | 1.42250i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.42072e11 | 0.891699 | 0.445850 | − | 0.895108i | \(-0.352902\pi\) | ||||
0.445850 | + | 0.895108i | \(0.352902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.03040e11 | −0.781974 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.83985e11i | 0.725421i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.42508e11i | − | 0.613244i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.89028e11 | + | 5.16401e11i | −0.473215 | + | 1.29276i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.59158e11i | 0.394453i | 0.980358 | + | 0.197227i | \(0.0631935\pi\) | ||||
−0.980358 | + | 0.197227i | \(0.936807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19001e11i | 0.291987i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.87415e10 | 0.0455275 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.91340e11 | −1.90327 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.61056e11 | + | 1.32164e11i | 0.859789 | + | 0.314725i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.67664e11 | 0.631097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.05240e11 | 0.479147 | 0.239574 | − | 0.970878i | \(-0.422992\pi\) | ||||
0.239574 | + | 0.970878i | \(0.422992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.69411e11i | − | 1.77859i | −0.457337 | − | 0.889294i | \(-0.651197\pi\) | ||
0.457337 | − | 0.889294i | \(-0.348803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.36000e11i | − | 1.22688i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.23153e11 | − | 8.16849e10i | −0.505791 | − | 0.185145i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.90484e10i | 0.0651979i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.98562e10i | 0.133037i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.68809e10 | 0.103187 | 0.0515933 | − | 0.998668i | \(-0.483570\pi\) | ||||
0.0515933 | + | 0.998668i | \(0.483570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.89198e11 | −0.848342 | −0.424171 | − | 0.905582i | \(-0.639434\pi\) | ||||
−0.424171 | + | 0.905582i | \(0.639434\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.66857e11 | − | 4.33959e11i | 0.791919 | − | 0.936770i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.45057e11 | −0.310112 | −0.155056 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155056 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.47485e11 | 0.947459 | 0.473730 | − | 0.880670i | \(-0.342907\pi\) | ||||
0.473730 | + | 0.880670i | \(0.342907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.65481e11i | 0.766409i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.44380e11i | − | 0.299865i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.34252e11 | − | 2.68772e11i | −1.51043 | − | 0.552890i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.73021e11i | − | 1.16753i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.70318e9i | − | 0.0195824i | −0.999952 | − | 0.00979121i | \(-0.996883\pi\) | ||
0.999952 | − | 0.00979121i | \(-0.00311669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.53890e10 | −0.150704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.21216e10 | 0.103207 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.97031e11 | + | 1.45333e11i | 0.778750 | + | 0.285061i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.82549e11 | 0.743282 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.18827e11 | −1.38355 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.80011e11i | − | 1.10591i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.23212e11i | 0.799395i | 0.916647 | + | 0.399697i | \(0.130885\pi\) | ||||
−0.916647 | + | 0.399697i | \(0.869115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.04033e9 | + | 1.10377e10i | −0.00756053 | + | 0.0206544i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.71291e11i | 1.24448i | 0.782827 | + | 0.622239i | \(0.213777\pi\) | ||||
−0.782827 | + | 0.622239i | \(0.786223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3.79497e11i | − | 0.697005i | −0.937308 | − | 0.348502i | \(-0.886690\pi\) | ||
0.937308 | − | 0.348502i | \(-0.113310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.05382e11 | 1.64748 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.15242e11 | −0.568330 | −0.284165 | − | 0.958775i | \(-0.591716\pi\) | ||||
−0.284165 | + | 0.958775i | \(0.591716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.43779e11 | + | 3.92787e11i | −0.256822 | + | 0.701605i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.72208e10 | −0.154363 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.73692e11 | −1.00600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.42642e12i | 2.47841i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.43235e10i | − | 0.110742i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.34461e11 | + | 5.86738e11i | 0.570575 | + | 1.00095i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.04593e12i | − | 1.76809i | −0.467405 | − | 0.884043i | \(-0.654811\pi\) | ||
0.467405 | − | 0.884043i | \(-0.345189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.14759e11i | 0.527257i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.83612e10 | 0.113476 | 0.0567382 | − | 0.998389i | \(-0.481930\pi\) | ||||
0.0567382 | + | 0.998389i | \(0.481930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.76186e11 | −1.27680 | −0.638400 | − | 0.769705i | \(-0.720403\pi\) | ||||
−0.638400 | + | 0.769705i | \(0.720403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.88259e11 | + | 7.87488e11i | −0.469905 | + | 1.28372i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.37333e11 | 0.383409 | 0.191705 | − | 0.981453i | \(-0.438598\pi\) | ||||
0.191705 | + | 0.981453i | \(0.438598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.85223e11 | 0.456644 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 7.33465e11i | − | 1.16377i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.22381e10i | − | 0.0821451i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.52744e10 | − | 2.60278e11i | 0.148486 | − | 0.405644i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.65456e11i | − | 1.02790i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.77074e11i | 1.03657i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.68714e11 | 1.31819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.85405e11 | 0.278850 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.00524e12 | + | 3.67969e11i | 1.49857 | + | 0.548551i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.84438e11 | 1.45465 | 0.727326 | − | 0.686292i | \(-0.240763\pi\) | ||||
0.727326 | + | 0.686292i | \(0.240763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.39109e8 | −0.00137550 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.01816e11i | − | 0.873756i | −0.899521 | − | 0.436878i | \(-0.856084\pi\) | ||
0.899521 | − | 0.436878i | \(-0.143916\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.10043e11i | 0.734047i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.85426e11 | − | 1.04480e11i | −0.407202 | − | 0.149056i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.01000e11i | 0.425686i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.81576e11i | 0.955548i | 0.878483 | + | 0.477774i | \(0.158556\pi\) | ||||
−0.878483 | + | 0.477774i | \(0.841444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.23640e11 | 0.866753 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.34960e11 | 1.28821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.57745e11 | − | 7.78054e11i | 0.898443 | − | 1.06278i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.35734e10 | −0.0860908 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.14720e11 | −0.825306 | −0.412653 | − | 0.910888i | \(-0.635398\pi\) | ||||
−0.412653 | + | 0.910888i | \(0.635398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.33788e10i | 0.0843616i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.70389e11i | 0.356830i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.42979e11 | − | 3.08572e11i | −1.10299 | − | 0.403747i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.96324e11i | 0.903344i | 0.892184 | + | 0.451672i | \(0.149172\pi\) | ||||
−0.892184 | + | 0.451672i | \(0.850828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.53476e11i | 1.22644i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.95595e11 | 0.887152 | 0.443576 | − | 0.896237i | \(-0.353710\pi\) | ||||
0.443576 | + | 0.896237i | \(0.353710\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.39553e11 | 1.18816 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.95639e11 | + | 3.27848e11i | 1.12307 | + | 0.411098i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.10922e11 | 0.759601 | 0.379800 | − | 0.925068i | \(-0.375993\pi\) | ||||
0.379800 | + | 0.925068i | \(0.375993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.62782e12 | −2.00698 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.09983e12i | − | 1.34463i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.33023e12i | − | 1.61271i | −0.591431 | − | 0.806356i | \(-0.701437\pi\) | ||
0.591431 | − | 0.806356i | \(-0.298563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.94378e11 | − | 1.35058e12i | 0.594355 | − | 1.62370i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.48197e11i | 1.13045i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 4.22496e11i | − | 0.499514i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26128e11 | −0.265131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.36886e10 | −0.0624276 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.58074e11 | − | 7.05025e11i | 0.297601 | − | 0.813009i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.24211e11 | 0.828246 | 0.414123 | − | 0.910221i | \(-0.364088\pi\) | ||||
0.414123 | + | 0.910221i | \(0.364088\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.98924e11 | −0.225627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.63532e11i | 0.296453i | 0.988953 | + | 0.148226i | \(0.0473564\pi\) | ||||
−0.988953 | + | 0.148226i | \(0.952644\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.86699e11i | − | 0.989293i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.54641e11 | − | 8.92673e11i | 0.835068 | − | 0.987812i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.12946e12i | − | 1.23963i | −0.784748 | − | 0.619815i | \(-0.787208\pi\) | ||
0.784748 | − | 0.619815i | \(-0.212792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.28320e11i | − | 0.683991i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.64167e10 | −0.0501185 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.31157e12 | 1.40468 | 0.702339 | − | 0.711843i | \(-0.252139\pi\) | ||||
0.702339 | + | 0.711843i | \(0.252139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.41577e11 | − | 6.59958e11i | 0.256632 | − | 0.701086i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.33417e11 | −0.351333 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.92403e11 | 0.201106 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.89727e11i | 0.507761i | 0.967236 | + | 0.253881i | \(0.0817071\pi\) | ||||
−0.967236 | + | 0.253881i | \(0.918293\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.25955e12i | − | 1.29545i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.83389e11 | + | 1.32056e12i | −0.493179 | + | 1.34730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.63334e11i | 0.974981i | 0.873128 | + | 0.487490i | \(0.162088\pi\) | ||||
−0.873128 | + | 0.487490i | \(0.837912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.43878e12i | − | 1.44455i |
(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 | 320.9.h.f.319.5 | 16 | ||
4.3 | odd | 2 | inner | 320.9.h.f.319.11 | 16 | ||
5.4 | even | 2 | inner | 320.9.h.f.319.12 | 16 | ||
8.3 | odd | 2 | 80.9.h.d.79.6 | yes | 16 | ||
8.5 | even | 2 | 80.9.h.d.79.12 | yes | 16 | ||
20.19 | odd | 2 | inner | 320.9.h.f.319.6 | 16 | ||
40.3 | even | 4 | 400.9.b.m.351.6 | 16 | |||
40.13 | odd | 4 | 400.9.b.m.351.11 | 16 | |||
40.19 | odd | 2 | 80.9.h.d.79.11 | yes | 16 | ||
40.27 | even | 4 | 400.9.b.m.351.12 | 16 | |||
40.29 | even | 2 | 80.9.h.d.79.5 | ✓ | 16 | ||
40.37 | odd | 4 | 400.9.b.m.351.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.9.h.d.79.5 | ✓ | 16 | 40.29 | even | 2 | ||
80.9.h.d.79.6 | yes | 16 | 8.3 | odd | 2 | ||
80.9.h.d.79.11 | yes | 16 | 40.19 | odd | 2 | ||
80.9.h.d.79.12 | yes | 16 | 8.5 | even | 2 | ||
320.9.h.f.319.5 | 16 | 1.1 | even | 1 | trivial | ||
320.9.h.f.319.6 | 16 | 20.19 | odd | 2 | inner | ||
320.9.h.f.319.11 | 16 | 4.3 | odd | 2 | inner | ||
320.9.h.f.319.12 | 16 | 5.4 | even | 2 | inner | ||
400.9.b.m.351.5 | 16 | 40.37 | odd | 4 | |||
400.9.b.m.351.6 | 16 | 40.3 | even | 4 | |||
400.9.b.m.351.11 | 16 | 40.13 | odd | 4 | |||
400.9.b.m.351.12 | 16 | 40.27 | even | 4 |