Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,12,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14674544448\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + \cdots + 34431558027300 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.9 | ||
Root | \(20.8472 - 5.89062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.12.b.a.5.10 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 43.6944 | − | 11.7812i | 0.965519 | − | 0.260331i | ||||
\(3\) | 381.717i | 0.906932i | 0.891274 | + | 0.453466i | \(0.149813\pi\) | ||||
−0.891274 | + | 0.453466i | \(0.850187\pi\) | |||||||
\(4\) | 1770.40 | − | 1029.55i | 0.864455 | − | 0.502709i | ||||
\(5\) | 8937.55i | 1.27904i | 0.768775 | + | 0.639519i | \(0.220867\pi\) | ||||
−0.768775 | + | 0.639519i | \(0.779133\pi\) | |||||||
\(6\) | 4497.10 | + | 16678.9i | 0.236103 | + | 0.875661i | ||||
\(7\) | 10175.0 | 0.228821 | 0.114410 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114410 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(8\) | 65227.5 | − | 65843.1i | 0.703778 | − | 0.710420i | ||||
\(9\) | 31439.0 | 0.177474 | ||||||||
\(10\) | 105295. | + | 390521.i | 0.332973 | + | 1.23494i | ||||
\(11\) | 408594.i | 0.764948i | 0.923966 | + | 0.382474i | \(0.124928\pi\) | ||||
−0.923966 | + | 0.382474i | \(0.875072\pi\) | |||||||
\(12\) | 392996. | + | 675794.i | 0.455923 | + | 0.784002i | ||||
\(13\) | − | 1.94255e6i | − | 1.45106i | −0.688193 | − | 0.725528i | \(-0.741596\pi\) | ||
0.688193 | − | 0.725528i | \(-0.258404\pi\) | |||||||
\(14\) | 444591. | − | 119874.i | 0.220931 | − | 0.0595692i | ||||
\(15\) | −3.41162e6 | −1.16000 | ||||||||
\(16\) | 2.07436e6 | − | 3.64544e6i | 0.494567 | − | 0.869140i | ||||
\(17\) | −9.64991e6 | −1.64837 | −0.824184 | − | 0.566322i | \(-0.808366\pi\) | ||||
−0.824184 | + | 0.566322i | \(0.808366\pi\) | |||||||
\(18\) | 1.37371e6 | − | 370391.i | 0.171355 | − | 0.0462020i | ||||
\(19\) | − | 1.27489e7i | − | 1.18121i | −0.806959 | − | 0.590607i | \(-0.798888\pi\) | ||
0.806959 | − | 0.590607i | \(-0.201112\pi\) | |||||||
\(20\) | 9.20165e6 | + | 1.58231e7i | 0.642985 | + | 1.10567i | ||||
\(21\) | 3.88398e6i | 0.207525i | ||||||||
\(22\) | 4.81374e6 | + | 1.78533e7i | 0.199140 | + | 0.738572i | ||||
\(23\) | 2.34581e7 | 0.759957 | 0.379979 | − | 0.924995i | \(-0.375931\pi\) | ||||
0.379979 | + | 0.924995i | \(0.375931\pi\) | |||||||
\(24\) | 2.51334e7 | + | 2.48984e7i | 0.644303 | + | 0.638279i | ||||
\(25\) | −3.10517e7 | −0.635939 | ||||||||
\(26\) | −2.28857e7 | − | 8.48786e7i | −0.377755 | − | 1.40102i | ||||
\(27\) | 7.96209e7i | 1.06789i | ||||||||
\(28\) | 1.80139e7 | − | 1.04757e7i | 0.197805 | − | 0.115030i | ||||
\(29\) | − | 4.83134e7i | − | 0.437400i | −0.975792 | − | 0.218700i | \(-0.929818\pi\) | ||
0.975792 | − | 0.218700i | \(-0.0701815\pi\) | |||||||
\(30\) | −1.49069e8 | + | 4.01931e7i | −1.12000 | + | 0.301984i | ||||
\(31\) | 2.63557e8 | 1.65343 | 0.826714 | − | 0.562622i | \(-0.190207\pi\) | ||||
0.826714 | + | 0.562622i | \(0.190207\pi\) | |||||||
\(32\) | 4.76903e7 | − | 1.83724e8i | 0.251250 | − | 0.967922i | ||||
\(33\) | −1.55967e8 | −0.693756 | ||||||||
\(34\) | −4.21647e8 | + | 1.13688e8i | −1.59153 | + | 0.429121i | ||||
\(35\) | 9.09397e7i | 0.292671i | ||||||||
\(36\) | 5.56598e7 | − | 3.23680e7i | 0.153419 | − | 0.0892179i | ||||
\(37\) | − | 7.91290e7i | − | 0.187597i | −0.995591 | − | 0.0937985i | \(-0.970099\pi\) | ||
0.995591 | − | 0.0937985i | \(-0.0299010\pi\) | |||||||
\(38\) | −1.50198e8 | − | 5.57057e8i | −0.307507 | − | 1.14048i | ||||
\(39\) | 7.41505e8 | 1.31601 | ||||||||
\(40\) | 5.88476e8 | + | 5.82974e8i | 0.908655 | + | 0.900159i | ||||
\(41\) | −6.96380e8 | −0.938718 | −0.469359 | − | 0.883008i | \(-0.655515\pi\) | ||||
−0.469359 | + | 0.883008i | \(0.655515\pi\) | |||||||
\(42\) | 4.57581e7 | + | 1.69708e8i | 0.0540252 | + | 0.200369i | ||||
\(43\) | 4.03606e8i | 0.418679i | 0.977843 | + | 0.209339i | \(0.0671314\pi\) | ||||
−0.977843 | + | 0.209339i | \(0.932869\pi\) | |||||||
\(44\) | 4.20667e8 | + | 7.23376e8i | 0.384546 | + | 0.661263i | ||||
\(45\) | 2.80988e8i | 0.226996i | ||||||||
\(46\) | 1.02499e9 | − | 2.76365e8i | 0.733753 | − | 0.197840i | ||||
\(47\) | −5.59625e8 | −0.355925 | −0.177963 | − | 0.984037i | \(-0.556951\pi\) | ||||
−0.177963 | + | 0.984037i | \(0.556951\pi\) | |||||||
\(48\) | 1.39153e9 | + | 7.91820e8i | 0.788251 | + | 0.448538i | ||||
\(49\) | −1.87380e9 | −0.947641 | ||||||||
\(50\) | −1.35679e9 | + | 3.65828e8i | −0.614012 | + | 0.165555i | ||||
\(51\) | − | 3.68354e9i | − | 1.49496i | ||||||
\(52\) | −1.99995e9 | − | 3.43910e9i | −0.729459 | − | 1.25437i | ||||
\(53\) | − | 2.88775e9i | − | 0.948510i | −0.880388 | − | 0.474255i | \(-0.842717\pi\) | ||
0.880388 | − | 0.474255i | \(-0.157283\pi\) | |||||||
\(54\) | 9.38032e8 | + | 3.47899e9i | 0.278005 | + | 1.03107i | ||||
\(55\) | −3.65183e9 | −0.978397 | ||||||||
\(56\) | 6.63690e8 | − | 6.69954e8i | 0.161039 | − | 0.162559i | ||||
\(57\) | 4.86648e9 | 1.07128 | ||||||||
\(58\) | −5.69191e8 | − | 2.11102e9i | −0.113869 | − | 0.422318i | ||||
\(59\) | 9.84523e9i | 1.79283i | 0.443213 | + | 0.896417i | \(0.353839\pi\) | ||||
−0.443213 | + | 0.896417i | \(0.646161\pi\) | |||||||
\(60\) | −6.03994e9 | + | 3.51243e9i | −1.00277 | + | 0.583143i | ||||
\(61\) | 5.65364e9i | 0.857066i | 0.903526 | + | 0.428533i | \(0.140969\pi\) | ||||
−0.903526 | + | 0.428533i | \(0.859031\pi\) | |||||||
\(62\) | 1.15160e10 | − | 3.10503e9i | 1.59642 | − | 0.430439i | ||||
\(63\) | 3.19892e8 | 0.0406098 | ||||||||
\(64\) | −8.06933e7 | − | 8.58956e9i | −0.00939394 | − | 0.999956i | ||||
\(65\) | 1.73617e10 | 1.85596 | ||||||||
\(66\) | −6.81489e9 | + | 1.83749e9i | −0.669834 | + | 0.180606i | ||||
\(67\) | − | 1.28196e10i | − | 1.16001i | −0.814613 | − | 0.580005i | \(-0.803051\pi\) | ||
0.814613 | − | 0.580005i | \(-0.196949\pi\) | |||||||
\(68\) | −1.70842e10 | + | 9.93505e9i | −1.42494 | + | 0.828650i | ||||
\(69\) | 8.95435e9i | 0.689230i | ||||||||
\(70\) | 1.07138e9 | + | 3.97356e9i | 0.0761913 | + | 0.282579i | ||||
\(71\) | −3.63445e9 | −0.239066 | −0.119533 | − | 0.992830i | \(-0.538140\pi\) | ||||
−0.119533 | + | 0.992830i | \(0.538140\pi\) | |||||||
\(72\) | 2.05069e9 | − | 2.07004e9i | 0.124902 | − | 0.126081i | ||||
\(73\) | −2.56732e9 | −0.144945 | −0.0724727 | − | 0.997370i | \(-0.523089\pi\) | ||||
−0.0724727 | + | 0.997370i | \(0.523089\pi\) | |||||||
\(74\) | −9.32237e8 | − | 3.45749e9i | −0.0488373 | − | 0.181129i | ||||
\(75\) | − | 1.18530e10i | − | 0.576754i | ||||||
\(76\) | −1.31256e10 | − | 2.25707e10i | −0.593807 | − | 1.02111i | ||||
\(77\) | 4.15744e9i | 0.175036i | ||||||||
\(78\) | 3.23996e10 | − | 8.73585e9i | 1.27063 | − | 0.342598i | ||||
\(79\) | −2.59475e10 | −0.948739 | −0.474370 | − | 0.880326i | \(-0.657324\pi\) | ||||
−0.474370 | + | 0.880326i | \(0.657324\pi\) | |||||||
\(80\) | 3.25813e10 | + | 1.85397e10i | 1.11166 | + | 0.632570i | ||||
\(81\) | −2.48233e10 | −0.791029 | ||||||||
\(82\) | −3.04279e10 | + | 8.20422e9i | −0.906350 | + | 0.244377i | ||||
\(83\) | 3.80496e10i | 1.06028i | 0.847910 | + | 0.530140i | \(0.177860\pi\) | ||||
−0.847910 | + | 0.530140i | \(0.822140\pi\) | |||||||
\(84\) | 3.99874e9 | + | 6.87621e9i | 0.104325 | + | 0.179396i | ||||
\(85\) | − | 8.62466e10i | − | 2.10833i | ||||||
\(86\) | 4.75498e9 | + | 1.76353e10i | 0.108995 | + | 0.404243i | ||||
\(87\) | 1.84420e10 | 0.396692 | ||||||||
\(88\) | 2.69031e10 | + | 2.66515e10i | 0.543434 | + | 0.538353i | ||||
\(89\) | −2.00557e10 | −0.380709 | −0.190354 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190354 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(90\) | 3.31039e9 | + | 1.22776e10i | 0.0590942 | + | 0.219169i | ||||
\(91\) | − | 1.97655e10i | − | 0.332032i | ||||||
\(92\) | 4.15303e10 | − | 2.41512e10i | 0.656949 | − | 0.382038i | ||||
\(93\) | 1.00604e11i | 1.49955i | ||||||||
\(94\) | −2.44525e10 | + | 6.59307e9i | −0.343653 | + | 0.0926584i | ||||
\(95\) | 1.13944e11 | 1.51082 | ||||||||
\(96\) | 7.01305e10 | + | 1.82042e10i | 0.877840 | + | 0.227866i | ||||
\(97\) | −6.90643e10 | −0.816600 | −0.408300 | − | 0.912848i | \(-0.633878\pi\) | ||||
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(98\) | −8.18744e10 | + | 2.20756e10i | −0.914966 | + | 0.246700i | ||||
\(99\) | 1.28458e10i | 0.135758i | ||||||||
\(100\) | −5.49741e10 | + | 3.19693e10i | −0.549741 | + | 0.319693i | ||||
\(101\) | − | 3.00032e10i | − | 0.284053i | −0.989863 | − | 0.142027i | \(-0.954638\pi\) | ||
0.989863 | − | 0.142027i | \(-0.0453619\pi\) | |||||||
\(102\) | −4.33966e10 | − | 1.60950e11i | −0.389184 | − | 1.44341i | ||||
\(103\) | 4.46196e10 | 0.379246 | 0.189623 | − | 0.981857i | \(-0.439273\pi\) | ||||
0.189623 | + | 0.981857i | \(0.439273\pi\) | |||||||
\(104\) | −1.27904e11 | − | 1.26708e11i | −1.03086 | − | 1.02122i | ||||
\(105\) | −3.47132e10 | −0.265432 | ||||||||
\(106\) | −3.40212e10 | − | 1.26178e11i | −0.246927 | − | 0.915805i | ||||
\(107\) | − | 1.84556e10i | − | 0.127209i | −0.997975 | − | 0.0636044i | \(-0.979740\pi\) | ||
0.997975 | − | 0.0636044i | \(-0.0202596\pi\) | |||||||
\(108\) | 8.19736e10 | + | 1.40961e11i | 0.536838 | + | 0.923143i | ||||
\(109\) | − | 9.05577e8i | − | 0.00563741i | −0.999996 | − | 0.00281871i | \(-0.999103\pi\) | ||
0.999996 | − | 0.00281871i | \(-0.000897223\pi\) | |||||||
\(110\) | −1.59564e11 | + | 4.30230e10i | −0.944662 | + | 0.254707i | ||||
\(111\) | 3.02049e10 | 0.170138 | ||||||||
\(112\) | 2.11067e10 | − | 3.70924e10i | 0.113167 | − | 0.198877i | ||||
\(113\) | 1.77827e11 | 0.907957 | 0.453978 | − | 0.891013i | \(-0.350004\pi\) | ||||
0.453978 | + | 0.891013i | \(0.350004\pi\) | |||||||
\(114\) | 2.12638e11 | − | 5.73332e10i | 1.03434 | − | 0.278888i | ||||
\(115\) | 2.09658e11i | 0.972014i | ||||||||
\(116\) | −4.97410e10 | − | 8.55342e10i | −0.219885 | − | 0.378112i | ||||
\(117\) | − | 6.10719e10i | − | 0.257525i | ||||||
\(118\) | 1.15989e11 | + | 4.30182e11i | 0.466730 | + | 1.73102i | ||||
\(119\) | −9.81879e10 | −0.377181 | ||||||||
\(120\) | −2.22531e11 | + | 2.24631e11i | −0.816383 | + | 0.824088i | ||||
\(121\) | 1.18363e11 | 0.414855 | ||||||||
\(122\) | 6.66069e10 | + | 2.47033e11i | 0.223121 | + | 0.827514i | ||||
\(123\) | − | 2.65820e11i | − | 0.851353i | ||||||
\(124\) | 4.66603e11 | − | 2.71345e11i | 1.42932 | − | 0.831194i | ||||
\(125\) | 1.58877e11i | 0.465648i | ||||||||
\(126\) | 1.39775e10 | − | 3.76873e9i | 0.0392095 | − | 0.0105720i | ||||
\(127\) | −5.40179e11 | −1.45083 | −0.725417 | − | 0.688310i | \(-0.758353\pi\) | ||||
−0.725417 | + | 0.688310i | \(0.758353\pi\) | |||||||
\(128\) | −1.04721e11 | − | 3.74365e11i | −0.269390 | − | 0.963031i | ||||
\(129\) | −1.54063e11 | −0.379713 | ||||||||
\(130\) | 7.58607e11 | − | 2.04542e11i | 1.79196 | − | 0.483163i | ||||
\(131\) | − | 2.23934e11i | − | 0.507141i | −0.967317 | − | 0.253570i | \(-0.918395\pi\) | ||
0.967317 | − | 0.253570i | \(-0.0816049\pi\) | |||||||
\(132\) | −2.76125e11 | + | 1.60576e11i | −0.599721 | + | 0.348757i | ||||
\(133\) | − | 1.29720e11i | − | 0.270286i | ||||||
\(134\) | −1.51030e11 | − | 5.60143e11i | −0.301986 | − | 1.12001i | ||||
\(135\) | −7.11616e11 | −1.36587 | ||||||||
\(136\) | −6.29439e11 | + | 6.35380e11i | −1.16008 | + | 1.17103i | ||||
\(137\) | 3.35319e11 | 0.593602 | 0.296801 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296801 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(138\) | 1.05493e11 | + | 3.91255e11i | 0.179428 | + | 0.665465i | ||||
\(139\) | 2.72700e10i | 0.0445763i | 0.999752 | + | 0.0222881i | \(0.00709512\pi\) | ||||
−0.999752 | + | 0.0222881i | \(0.992905\pi\) | |||||||
\(140\) | 9.36269e10 | + | 1.61000e11i | 0.147128 | + | 0.253001i | ||||
\(141\) | − | 2.13618e11i | − | 0.322800i | ||||||
\(142\) | −1.58805e11 | + | 4.28184e10i | −0.230823 | + | 0.0622363i | ||||
\(143\) | 7.93714e11 | 1.10998 | ||||||||
\(144\) | 6.52159e10 | − | 1.14609e11i | 0.0877728 | − | 0.154250i | ||||
\(145\) | 4.31803e11 | 0.559451 | ||||||||
\(146\) | −1.12178e11 | + | 3.02462e10i | −0.139948 | + | 0.0377338i | ||||
\(147\) | − | 7.15260e11i | − | 0.859446i | ||||||
\(148\) | −8.14671e10 | − | 1.40090e11i | −0.0943068 | − | 0.162169i | ||||
\(149\) | 1.14880e12i | 1.28151i | 0.767747 | + | 0.640753i | \(0.221378\pi\) | ||||
−0.767747 | + | 0.640753i | \(0.778622\pi\) | |||||||
\(150\) | −1.39643e11 | − | 5.17909e11i | −0.150147 | − | 0.556867i | ||||
\(151\) | 4.51160e11 | 0.467689 | 0.233845 | − | 0.972274i | \(-0.424869\pi\) | ||||
0.233845 | + | 0.972274i | \(0.424869\pi\) | |||||||
\(152\) | −8.39428e11 | − | 8.31579e11i | −0.839158 | − | 0.831312i | ||||
\(153\) | −3.03384e11 | −0.292543 | ||||||||
\(154\) | 4.89798e10 | + | 1.81657e11i | 0.0455673 | + | 0.169001i | ||||
\(155\) | 2.35556e12i | 2.11480i | ||||||||
\(156\) | 1.31276e12 | − | 7.63416e11i | 1.13763 | − | 0.661570i | ||||
\(157\) | − | 8.98082e10i | − | 0.0751395i | −0.999294 | − | 0.0375697i | \(-0.988038\pi\) | ||
0.999294 | − | 0.0375697i | \(-0.0119616\pi\) | |||||||
\(158\) | −1.13376e12 | + | 3.05694e11i | −0.916026 | + | 0.246986i | ||||
\(159\) | 1.10230e12 | 0.860234 | ||||||||
\(160\) | 1.64204e12 | + | 4.26235e11i | 1.23801 | + | 0.321358i | ||||
\(161\) | 2.38686e11 | 0.173894 | ||||||||
\(162\) | −1.08464e12 | + | 2.92449e11i | −0.763754 | + | 0.205929i | ||||
\(163\) | − | 3.45737e11i | − | 0.235350i | −0.993052 | − | 0.117675i | \(-0.962456\pi\) | ||
0.993052 | − | 0.117675i | \(-0.0375441\pi\) | |||||||
\(164\) | −1.23287e12 | + | 7.16957e11i | −0.811480 | + | 0.471902i | ||||
\(165\) | − | 1.39396e12i | − | 0.887340i | ||||||
\(166\) | 4.48271e11 | + | 1.66255e12i | 0.276024 | + | 1.02372i | ||||
\(167\) | 6.61651e11 | 0.394174 | 0.197087 | − | 0.980386i | \(-0.436852\pi\) | ||||
0.197087 | + | 0.980386i | \(0.436852\pi\) | |||||||
\(168\) | 2.55733e11 | + | 2.53342e11i | 0.147430 | + | 0.146051i | ||||
\(169\) | −1.98134e12 | −1.10556 | ||||||||
\(170\) | −1.01609e12 | − | 3.76849e12i | −0.548863 | − | 2.03563i | ||||
\(171\) | − | 4.00813e11i | − | 0.209635i | ||||||
\(172\) | 4.15532e11 | + | 7.14546e11i | 0.210474 | + | 0.361929i | ||||
\(173\) | − | 2.94318e12i | − | 1.44399i | −0.691900 | − | 0.721993i | \(-0.743226\pi\) | ||
0.691900 | − | 0.721993i | \(-0.256774\pi\) | |||||||
\(174\) | 8.05814e11 | − | 2.17270e11i | 0.383014 | − | 0.103271i | ||||
\(175\) | −3.15952e11 | −0.145516 | ||||||||
\(176\) | 1.48950e12 | + | 8.47571e11i | 0.664846 | + | 0.378318i | ||||
\(177\) | −3.75809e12 | −1.62598 | ||||||||
\(178\) | −8.76322e11 | + | 2.36281e11i | −0.367582 | + | 0.0991103i | ||||
\(179\) | − | 8.70295e11i | − | 0.353977i | −0.984213 | − | 0.176988i | \(-0.943364\pi\) | ||
0.984213 | − | 0.176988i | \(-0.0566355\pi\) | |||||||
\(180\) | 2.89291e11 | + | 4.97462e11i | 0.114113 | + | 0.196228i | ||||
\(181\) | 4.02698e12i | 1.54080i | 0.637559 | + | 0.770401i | \(0.279944\pi\) | ||||
−0.637559 | + | 0.770401i | \(0.720056\pi\) | |||||||
\(182\) | −2.32862e11 | − | 8.63641e11i | −0.0864382 | − | 0.320583i | ||||
\(183\) | −2.15809e12 | −0.777301 | ||||||||
\(184\) | 1.53011e12 | − | 1.54455e12i | 0.534841 | − | 0.539889i | ||||
\(185\) | 7.07219e11 | 0.239944 | ||||||||
\(186\) | 1.18524e12 | + | 4.39585e12i | 0.390379 | + | 1.44784i | ||||
\(187\) | − | 3.94289e12i | − | 1.26092i | ||||||
\(188\) | −9.90762e11 | + | 5.76161e11i | −0.307681 | + | 0.178927i | ||||
\(189\) | 8.10143e11i | 0.244355i | ||||||||
\(190\) | 4.97872e12 | − | 1.34240e12i | 1.45872 | − | 0.393313i | ||||
\(191\) | 5.16393e12 | 1.46993 | 0.734965 | − | 0.678105i | \(-0.237199\pi\) | ||||
0.734965 | + | 0.678105i | \(0.237199\pi\) | |||||||
\(192\) | 3.27878e12 | − | 3.08020e10i | 0.906892 | − | 0.00851966i | ||||
\(193\) | 2.61981e12 | 0.704214 | 0.352107 | − | 0.935960i | \(-0.385465\pi\) | ||||
0.352107 | + | 0.935960i | \(0.385465\pi\) | |||||||
\(194\) | −3.01773e12 | + | 8.13663e11i | −0.788443 | + | 0.212586i | ||||
\(195\) | 6.62724e12i | 1.68323i | ||||||||
\(196\) | −3.31738e12 | + | 1.92916e12i | −0.819193 | + | 0.476388i | ||||
\(197\) | 9.51398e11i | 0.228453i | 0.993455 | + | 0.114227i | \(0.0364390\pi\) | ||||
−0.993455 | + | 0.114227i | \(0.963561\pi\) | |||||||
\(198\) | 1.51339e11 | + | 5.61289e11i | 0.0353421 | + | 0.131077i | ||||
\(199\) | −7.34864e12 | −1.66923 | −0.834613 | − | 0.550837i | \(-0.814309\pi\) | ||||
−0.834613 | + | 0.550837i | \(0.814309\pi\) | |||||||
\(200\) | −2.02543e12 | + | 2.04454e12i | −0.447560 | + | 0.451784i | ||||
\(201\) | 4.89344e12 | 1.05205 | ||||||||
\(202\) | −3.53475e11 | − | 1.31097e12i | −0.0739479 | − | 0.274259i | ||||
\(203\) | − | 4.91589e11i | − | 0.100086i | ||||||
\(204\) | −3.79238e12 | − | 6.52135e12i | −0.751529 | − | 1.29232i | ||||
\(205\) | − | 6.22393e12i | − | 1.20066i | ||||||
\(206\) | 1.94963e12 | − | 5.25674e11i | 0.366169 | − | 0.0987294i | ||||
\(207\) | 7.37499e11 | 0.134873 | ||||||||
\(208\) | −7.08145e12 | − | 4.02956e12i | −1.26117 | − | 0.717644i | ||||
\(209\) | 5.20912e12 | 0.903567 | ||||||||
\(210\) | −1.51678e12 | + | 4.08965e11i | −0.256280 | + | 0.0691003i | ||||
\(211\) | − | 6.80722e11i | − | 0.112051i | −0.998429 | − | 0.0560256i | \(-0.982157\pi\) | ||
0.998429 | − | 0.0560256i | \(-0.0178428\pi\) | |||||||
\(212\) | −2.97308e12 | − | 5.11248e12i | −0.476825 | − | 0.819945i | ||||
\(213\) | − | 1.38733e12i | − | 0.216817i | ||||||
\(214\) | −2.17430e11 | − | 8.06406e11i | −0.0331164 | − | 0.122823i | ||||
\(215\) | −3.60725e12 | −0.535506 | ||||||||
\(216\) | 5.24248e12 | + | 5.19347e12i | 0.758650 | + | 0.751557i | ||||
\(217\) | 2.68170e12 | 0.378339 | ||||||||
\(218\) | −1.06688e10 | − | 3.95687e10i | −0.00146759 | − | 0.00544303i | ||||
\(219\) | − | 9.79991e11i | − | 0.131456i | ||||||
\(220\) | −6.46521e12 | + | 3.75973e12i | −0.845781 | + | 0.491850i | ||||
\(221\) | 1.87454e13i | 2.39187i | ||||||||
\(222\) | 1.31979e12 | − | 3.55851e11i | 0.164271 | − | 0.0442922i | ||||
\(223\) | −1.19442e12 | −0.145037 | −0.0725187 | − | 0.997367i | \(-0.523104\pi\) | ||||
−0.0725187 | + | 0.997367i | \(0.523104\pi\) | |||||||
\(224\) | 4.85249e11 | − | 1.86939e12i | 0.0574911 | − | 0.221481i | ||||
\(225\) | −9.76236e11 | −0.112863 | ||||||||
\(226\) | 7.77003e12 | − | 2.09502e12i | 0.876650 | − | 0.236369i | ||||
\(227\) | − | 5.02675e12i | − | 0.553535i | −0.960937 | − | 0.276768i | \(-0.910737\pi\) | ||
0.960937 | − | 0.276768i | \(-0.0892632\pi\) | |||||||
\(228\) | 8.61564e12 | − | 5.01028e12i | 0.926074 | − | 0.538543i | ||||
\(229\) | − | 2.86620e12i | − | 0.300754i | −0.988629 | − | 0.150377i | \(-0.951951\pi\) | ||
0.988629 | − | 0.150377i | \(-0.0480487\pi\) | |||||||
\(230\) | 2.47003e12 | + | 9.16087e12i | 0.253046 | + | 0.938499i | ||||
\(231\) | −1.58697e12 | −0.158746 | ||||||||
\(232\) | −3.18110e12 | − | 3.15136e12i | −0.310737 | − | 0.307832i | ||||
\(233\) | −9.05833e12 | −0.864153 | −0.432077 | − | 0.901837i | \(-0.642219\pi\) | ||||
−0.432077 | + | 0.901837i | \(0.642219\pi\) | |||||||
\(234\) | −7.19503e11 | − | 2.66850e12i | −0.0670417 | − | 0.248645i | ||||
\(235\) | − | 5.00168e12i | − | 0.455242i | ||||||
\(236\) | 1.01361e13 | + | 1.74300e13i | 0.901274 | + | 1.54982i | ||||
\(237\) | − | 9.90461e12i | − | 0.860442i | ||||||
\(238\) | −4.29026e12 | + | 1.15678e12i | −0.364176 | + | 0.0981919i | ||||
\(239\) | 1.48753e13 | 1.23389 | 0.616947 | − | 0.787005i | \(-0.288369\pi\) | ||||
0.616947 | + | 0.787005i | \(0.288369\pi\) | |||||||
\(240\) | −7.07693e12 | + | 1.24368e13i | −0.573698 | + | 1.00820i | ||||
\(241\) | 1.65832e12 | 0.131394 | 0.0656969 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656969 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(242\) | 5.17180e12 | − | 1.39446e12i | 0.400551 | − | 0.108000i | ||||
\(243\) | 4.62911e12i | 0.350480i | ||||||||
\(244\) | 5.82070e12 | + | 1.00092e13i | 0.430855 | + | 0.740896i | ||||
\(245\) | − | 1.67472e13i | − | 1.21207i | ||||||
\(246\) | −3.13169e12 | − | 1.16149e13i | −0.221634 | − | 0.821998i | ||||
\(247\) | −2.47654e13 | −1.71401 | ||||||||
\(248\) | 1.71912e13 | − | 1.73534e13i | 1.16365 | − | 1.17463i | ||||
\(249\) | −1.45242e13 | −0.961601 | ||||||||
\(250\) | 1.87177e12 | + | 6.94206e12i | 0.121223 | + | 0.449592i | ||||
\(251\) | 1.60614e13i | 1.01760i | 0.860883 | + | 0.508802i | \(0.169912\pi\) | ||||
−0.860883 | + | 0.508802i | \(0.830088\pi\) | |||||||
\(252\) | 5.66339e11 | − | 3.29345e11i | 0.0351054 | − | 0.0204149i | ||||
\(253\) | 9.58481e12i | 0.581327i | ||||||||
\(254\) | −2.36028e13 | + | 6.36398e12i | −1.40081 | + | 0.377697i | ||||
\(255\) | 3.29218e13 | 1.91211 | ||||||||
\(256\) | −8.98623e12 | − | 1.51239e13i | −0.510808 | − | 0.859695i | ||||
\(257\) | −2.90477e13 | −1.61614 | −0.808072 | − | 0.589084i | \(-0.799489\pi\) | ||||
−0.808072 | + | 0.589084i | \(0.799489\pi\) | |||||||
\(258\) | −6.73171e12 | + | 1.81506e12i | −0.366621 | + | 0.0988512i | ||||
\(259\) | − | 8.05138e11i | − | 0.0429261i | ||||||
\(260\) | 3.07372e13 | − | 1.78747e13i | 1.60439 | − | 0.933006i | ||||
\(261\) | − | 1.51892e12i | − | 0.0776271i | ||||||
\(262\) | −2.63822e12 | − | 9.78468e12i | −0.132024 | − | 0.489654i | ||||
\(263\) | −7.15627e12 | −0.350695 | −0.175348 | − | 0.984507i | \(-0.556105\pi\) | ||||
−0.175348 | + | 0.984507i | \(0.556105\pi\) | |||||||
\(264\) | −1.01733e13 | + | 1.02694e13i | −0.488250 | + | 0.492858i | ||||
\(265\) | 2.58094e13 | 1.21318 | ||||||||
\(266\) | −1.52827e12 | − | 5.66806e12i | −0.0703639 | − | 0.260967i | ||||
\(267\) | − | 7.65561e12i | − | 0.345277i | ||||||
\(268\) | −1.31984e13 | − | 2.26958e13i | −0.583147 | − | 1.00278i | ||||
\(269\) | − | 9.77777e12i | − | 0.423255i | −0.977350 | − | 0.211627i | \(-0.932124\pi\) | ||
0.977350 | − | 0.211627i | \(-0.0678764\pi\) | |||||||
\(270\) | −3.10936e13 | + | 8.38371e12i | −1.31878 | + | 0.355579i | ||||
\(271\) | 3.73866e13 | 1.55376 | 0.776882 | − | 0.629647i | \(-0.216800\pi\) | ||||
0.776882 | + | 0.629647i | \(0.216800\pi\) | |||||||
\(272\) | −2.00174e13 | + | 3.51781e13i | −0.815228 | + | 1.43266i | ||||
\(273\) | 7.54482e12 | 0.301130 | ||||||||
\(274\) | 1.46516e13 | − | 3.95048e12i | 0.573134 | − | 0.154533i | ||||
\(275\) | − | 1.26875e13i | − | 0.486460i | ||||||
\(276\) | 9.21894e12 | + | 1.58528e13i | 0.346482 | + | 0.595808i | ||||
\(277\) | 2.28097e13i | 0.840391i | 0.907433 | + | 0.420196i | \(0.138039\pi\) | ||||
−0.907433 | + | 0.420196i | \(0.861961\pi\) | |||||||
\(278\) | 3.21274e11 | + | 1.19155e12i | 0.0116046 | + | 0.0430392i | ||||
\(279\) | 8.28598e12 | 0.293441 | ||||||||
\(280\) | 5.98775e12 | + | 5.93176e12i | 0.207919 | + | 0.205975i | ||||
\(281\) | −8.47235e12 | −0.288482 | −0.144241 | − | 0.989543i | \(-0.546074\pi\) | ||||
−0.144241 | + | 0.989543i | \(0.546074\pi\) | |||||||
\(282\) | −2.51669e12 | − | 9.33393e12i | −0.0840349 | − | 0.311670i | ||||
\(283\) | 5.48093e13i | 1.79485i | 0.441163 | + | 0.897427i | \(0.354566\pi\) | ||||
−0.441163 | + | 0.897427i | \(0.645434\pi\) | |||||||
\(284\) | −6.43445e12 | + | 3.74185e12i | −0.206662 | + | 0.120181i | ||||
\(285\) | 4.34944e13i | 1.37021i | ||||||||
\(286\) | 3.46809e13 | − | 9.35093e12i | 1.07171 | − | 0.288963i | ||||
\(287\) | −7.08567e12 | −0.214798 | ||||||||
\(288\) | 1.49934e12 | − | 5.77610e12i | 0.0445903 | − | 0.171781i | ||||
\(289\) | 5.88488e13 | 1.71712 | ||||||||
\(290\) | 1.88674e13 | − | 5.08718e12i | 0.540161 | − | 0.145642i | ||||
\(291\) | − | 2.63630e13i | − | 0.740601i | ||||||
\(292\) | −4.54520e12 | + | 2.64318e12i | −0.125299 | + | 0.0728655i | ||||
\(293\) | − | 5.59919e13i | − | 1.51479i | −0.652955 | − | 0.757396i | \(-0.726471\pi\) | ||
0.652955 | − | 0.757396i | \(-0.273529\pi\) | |||||||
\(294\) | −8.42665e12 | − | 3.12529e13i | −0.223740 | − | 0.829812i | ||||
\(295\) | −8.79923e13 | −2.29310 | ||||||||
\(296\) | −5.21010e12 | − | 5.16138e12i | −0.133273 | − | 0.132027i | ||||
\(297\) | −3.25326e13 | −0.816879 | ||||||||
\(298\) | 1.35343e13 | + | 5.01962e13i | 0.333616 | + | 1.23732i | ||||
\(299\) | − | 4.55685e13i | − | 1.10274i | ||||||
\(300\) | −1.22032e13 | − | 2.09846e13i | −0.289940 | − | 0.498578i | ||||
\(301\) | 4.10670e12i | 0.0958025i | ||||||||
\(302\) | 1.97132e13 | − | 5.31522e12i | 0.451563 | − | 0.121754i | ||||
\(303\) | 1.14527e13 | 0.257617 | ||||||||
\(304\) | −4.64754e13 | − | 2.64459e13i | −1.02664 | − | 0.584189i | ||||
\(305\) | −5.05297e13 | −1.09622 | ||||||||
\(306\) | −1.32562e13 | + | 3.57423e12i | −0.282456 | + | 0.0761580i | ||||
\(307\) | − | 3.49392e13i | − | 0.731226i | −0.930767 | − | 0.365613i | \(-0.880859\pi\) | ||
0.930767 | − | 0.365613i | \(-0.119141\pi\) | |||||||
\(308\) | 4.28029e12 | + | 7.36036e12i | 0.0879922 | + | 0.151311i | ||||
\(309\) | 1.70321e13i | 0.343950i | ||||||||
\(310\) | 2.77514e13 | + | 1.02925e14i | 0.550548 | + | 2.04188i | ||||
\(311\) | −8.77394e13 | −1.71006 | −0.855032 | − | 0.518575i | \(-0.826463\pi\) | ||||
−0.855032 | + | 0.518575i | \(0.826463\pi\) | |||||||
\(312\) | 4.83665e13 | − | 4.88230e13i | 0.926178 | − | 0.934919i | ||||
\(313\) | 9.47630e13 | 1.78297 | 0.891487 | − | 0.453046i | \(-0.149663\pi\) | ||||
0.891487 | + | 0.453046i | \(0.149663\pi\) | |||||||
\(314\) | −1.05805e12 | − | 3.92412e12i | −0.0195611 | − | 0.0725486i | ||||
\(315\) | 2.85905e12i | 0.0519415i | ||||||||
\(316\) | −4.59376e13 | + | 2.67142e13i | −0.820143 | + | 0.476940i | ||||
\(317\) | − | 7.45724e13i | − | 1.30844i | −0.756306 | − | 0.654218i | \(-0.772998\pi\) | ||
0.756306 | − | 0.654218i | \(-0.227002\pi\) | |||||||
\(318\) | 4.81645e13 | − | 1.29865e13i | 0.830573 | − | 0.223946i | ||||
\(319\) | 1.97405e13 | 0.334588 | ||||||||
\(320\) | 7.67696e13 | − | 7.21201e11i | 1.27898 | − | 0.0120152i | ||||
\(321\) | 7.04482e12 | 0.115370 | ||||||||
\(322\) | 1.04293e13 | − | 2.81202e12i | 0.167898 | − | 0.0452700i | ||||
\(323\) | 1.23026e14i | 1.94707i | ||||||||
\(324\) | −4.39473e13 | + | 2.55568e13i | −0.683809 | + | 0.397658i | ||||
\(325\) | 6.03196e13i | 0.922783i | ||||||||
\(326\) | −4.07321e12 | − | 1.51068e13i | −0.0612688 | − | 0.227235i | ||||
\(327\) | 3.45674e11 | 0.00511275 | ||||||||
\(328\) | −4.54231e13 | + | 4.58518e13i | −0.660649 | + | 0.666884i | ||||
\(329\) | −5.69419e12 | −0.0814431 | ||||||||
\(330\) | −1.64226e13 | − | 6.09085e13i | −0.231002 | − | 0.856744i | ||||
\(331\) | − | 9.05611e13i | − | 1.25282i | −0.779495 | − | 0.626409i | \(-0.784524\pi\) | ||
0.779495 | − | 0.626409i | \(-0.215476\pi\) | |||||||
\(332\) | 3.91739e13 | + | 6.73631e13i | 0.533012 | + | 0.916564i | ||||
\(333\) | − | 2.48774e12i | − | 0.0332936i | ||||||
\(334\) | 2.89105e13 | − | 7.79507e12i | 0.380583 | − | 0.102616i | ||||
\(335\) | 1.14575e14 | 1.48370 | ||||||||
\(336\) | 1.41588e13 | + | 8.05677e12i | 0.180368 | + | 0.102635i | ||||
\(337\) | 3.77207e13 | 0.472733 | 0.236366 | − | 0.971664i | \(-0.424043\pi\) | ||||
0.236366 | + | 0.971664i | \(0.424043\pi\) | |||||||
\(338\) | −8.65737e13 | + | 2.33427e13i | −1.06744 | + | 0.287812i | ||||
\(339\) | 6.78794e13i | 0.823455i | ||||||||
\(340\) | −8.87950e13 | − | 1.52691e14i | −1.05988 | − | 1.82255i | ||||
\(341\) | 1.07688e14i | 1.26479i | ||||||||
\(342\) | −4.72208e12 | − | 1.75133e13i | −0.0545745 | − | 0.202407i | ||||
\(343\) | −3.91852e13 | −0.445661 | ||||||||
\(344\) | 2.65747e13 | + | 2.63262e13i | 0.297438 | + | 0.294657i | ||||
\(345\) | −8.00299e13 | −0.881551 | ||||||||
\(346\) | −3.46743e13 | − | 1.28601e14i | −0.375915 | − | 1.39420i | ||||
\(347\) | − | 4.95297e13i | − | 0.528510i | −0.964453 | − | 0.264255i | \(-0.914874\pi\) | ||
0.964453 | − | 0.264255i | \(-0.0851261\pi\) | |||||||
\(348\) | 3.26499e13 | − | 1.89870e13i | 0.342922 | − | 0.199421i | ||||
\(349\) | − | 4.22844e13i | − | 0.437160i | −0.975819 | − | 0.218580i | \(-0.929858\pi\) | ||
0.975819 | − | 0.218580i | \(-0.0701425\pi\) | |||||||
\(350\) | −1.38053e13 | + | 3.72230e12i | −0.140499 | + | 0.0378824i | ||||
\(351\) | 1.54668e14 | 1.54957 | ||||||||
\(352\) | 7.50684e13 | + | 1.94860e13i | 0.740410 | + | 0.192193i | ||||
\(353\) | −5.42310e13 | −0.526607 | −0.263304 | − | 0.964713i | \(-0.584812\pi\) | ||||
−0.263304 | + | 0.964713i | \(0.584812\pi\) | |||||||
\(354\) | −1.64208e14 | + | 4.42750e13i | −1.56991 | + | 0.423293i | ||||
\(355\) | − | 3.24831e13i | − | 0.305775i | ||||||
\(356\) | −3.55067e13 | + | 2.06483e13i | −0.329106 | + | 0.191386i | ||||
\(357\) | − | 3.74800e13i | − | 0.342078i | ||||||
\(358\) | −1.02532e13 | − | 3.80270e13i | −0.0921512 | − | 0.341771i | ||||
\(359\) | 1.11001e14 | 0.982441 | 0.491220 | − | 0.871035i | \(-0.336551\pi\) | ||||
0.491220 | + | 0.871035i | \(0.336551\pi\) | |||||||
\(360\) | 1.85011e13 | + | 1.83281e13i | 0.161263 | + | 0.159755i | ||||
\(361\) | −4.60446e13 | −0.395266 | ||||||||
\(362\) | 4.74428e13 | + | 1.75956e14i | 0.401119 | + | 1.48767i | ||||
\(363\) | 4.51812e13i | 0.376245i | ||||||||
\(364\) | −2.03495e13 | − | 3.49929e13i | −0.166915 | − | 0.287027i | ||||
\(365\) | − | 2.29456e13i | − | 0.185391i | ||||||
\(366\) | −9.42966e13 | + | 2.54250e13i | −0.750499 | + | 0.202356i | ||||
\(367\) | −1.37111e14 | −1.07500 | −0.537502 | − | 0.843262i | \(-0.680632\pi\) | ||||
−0.537502 | + | 0.843262i | \(0.680632\pi\) | |||||||
\(368\) | 4.86605e13 | − | 8.55149e13i | 0.375849 | − | 0.660509i | ||||
\(369\) | −2.18935e13 | −0.166598 | ||||||||
\(370\) | 3.09015e13 | − | 8.33192e12i | 0.231670 | − | 0.0624648i | ||||
\(371\) | − | 2.93829e13i | − | 0.217039i | ||||||
\(372\) | 1.03577e14 | + | 1.78110e14i | 0.753837 | + | 1.29629i | ||||
\(373\) | − | 1.24348e14i | − | 0.891744i | −0.895097 | − | 0.445872i | \(-0.852894\pi\) | ||
0.895097 | − | 0.445872i | \(-0.147106\pi\) | |||||||
\(374\) | −4.64521e13 | − | 1.72282e14i | −0.328255 | − | 1.21744i | ||||
\(375\) | −6.06463e13 | −0.422311 | ||||||||
\(376\) | −3.65029e13 | + | 3.68474e13i | −0.250492 | + | 0.252856i | ||||
\(377\) | −9.38512e13 | −0.634691 | ||||||||
\(378\) | 9.54449e12 | + | 3.53987e13i | 0.0636133 | + | 0.235930i | ||||
\(379\) | 2.76010e14i | 1.81305i | 0.422157 | + | 0.906523i | \(0.361273\pi\) | ||||
−0.422157 | + | 0.906523i | \(0.638727\pi\) | |||||||
\(380\) | 2.01727e14 | − | 1.17311e14i | 1.30603 | − | 0.759502i | ||||
\(381\) | − | 2.06196e14i | − | 1.31581i | ||||||
\(382\) | 2.25635e14 | − | 6.08374e13i | 1.41925 | − | 0.382668i | ||||
\(383\) | 1.30866e14 | 0.811396 | 0.405698 | − | 0.914007i | \(-0.367028\pi\) | ||||
0.405698 | + | 0.914007i | \(0.367028\pi\) | |||||||
\(384\) | 1.42902e14 | − | 3.99740e13i | 0.873404 | − | 0.244318i | ||||
\(385\) | −3.71574e13 | −0.223878 | ||||||||
\(386\) | 1.14471e14 | − | 3.08646e13i | 0.679933 | − | 0.183329i | ||||
\(387\) | 1.26890e13i | 0.0743047i | ||||||||
\(388\) | −1.22272e14 | + | 7.11051e13i | −0.705914 | + | 0.410512i | ||||
\(389\) | 2.65449e14i | 1.51098i | 0.655161 | + | 0.755489i | \(0.272601\pi\) | ||||
−0.655161 | + | 0.755489i | \(0.727399\pi\) | |||||||
\(390\) | 7.80771e13 | + | 2.89573e14i | 0.438196 | + | 1.62519i | ||||
\(391\) | −2.26368e14 | −1.25269 | ||||||||
\(392\) | −1.22223e14 | + | 1.23377e14i | −0.666929 | + | 0.673223i | ||||
\(393\) | 8.54795e13 | 0.459942 | ||||||||
\(394\) | 1.12086e13 | + | 4.15708e13i | 0.0594735 | + | 0.220576i | ||||
\(395\) | − | 2.31907e14i | − | 1.21347i | ||||||
\(396\) | 1.32254e13 | + | 2.27422e13i | 0.0682470 | + | 0.117357i | ||||
\(397\) | 2.55728e14i | 1.30146i | 0.759309 | + | 0.650730i | \(0.225537\pi\) | ||||
−0.759309 | + | 0.650730i | \(0.774463\pi\) | |||||||
\(398\) | −3.21095e14 | + | 8.65761e13i | −1.61167 | + | 0.434551i | ||||
\(399\) | 4.95165e13 | 0.245131 | ||||||||
\(400\) | −6.44125e13 | + | 1.13197e14i | −0.314514 | + | 0.552720i | ||||
\(401\) | 4.93538e13 | 0.237698 | 0.118849 | − | 0.992912i | \(-0.462079\pi\) | ||||
0.118849 | + | 0.992912i | \(0.462079\pi\) | |||||||
\(402\) | 2.13816e14 | − | 5.76508e13i | 1.01577 | − | 0.273881i | ||||
\(403\) | − | 5.11973e14i | − | 2.39922i | ||||||
\(404\) | −3.08898e13 | − | 5.31178e13i | −0.142796 | − | 0.245551i | ||||
\(405\) | − | 2.21860e14i | − | 1.01176i | ||||||
\(406\) | −5.79153e12 | − | 2.14797e13i | −0.0260555 | − | 0.0966351i | ||||
\(407\) | 3.23316e13 | 0.143502 | ||||||||
\(408\) | −2.42535e14 | − | 2.40268e14i | −1.06205 | − | 1.05212i | ||||
\(409\) | 2.01464e14 | 0.870400 | 0.435200 | − | 0.900334i | \(-0.356678\pi\) | ||||
0.435200 | + | 0.900334i | \(0.356678\pi\) | |||||||
\(410\) | −7.33256e13 | − | 2.71951e14i | −0.312568 | − | 1.15926i | ||||
\(411\) | 1.27997e14i | 0.538357i | ||||||||
\(412\) | 7.89947e13 | − | 4.59380e13i | 0.327841 | − | 0.190650i | ||||
\(413\) | 1.00175e14i | 0.410238i | ||||||||
\(414\) | 3.22246e13 | − | 8.68865e12i | 0.130222 | − | 0.0351116i | ||||
\(415\) | −3.40070e14 | −1.35614 | ||||||||
\(416\) | −3.56893e14 | − | 9.26409e13i | −1.40451 | − | 0.364577i | ||||
\(417\) | −1.04094e13 | −0.0404276 | ||||||||
\(418\) | 2.27610e14 | − | 6.13699e13i | 0.872411 | − | 0.235226i | ||||
\(419\) | 3.36722e14i | 1.27378i | 0.770954 | + | 0.636891i | \(0.219780\pi\) | ||||
−0.770954 | + | 0.636891i | \(0.780220\pi\) | |||||||
\(420\) | −6.14565e13 | + | 3.57390e13i | −0.229455 | + | 0.133435i | ||||
\(421\) | 1.20703e12i | 0.00444800i | 0.999998 | + | 0.00222400i | \(0.000707922\pi\) | ||||
−0.999998 | + | 0.00222400i | \(0.999292\pi\) | |||||||
\(422\) | −8.01975e12 | − | 2.97438e13i | −0.0291704 | − | 0.108188i | ||||
\(423\) | −1.75941e13 | −0.0631675 | ||||||||
\(424\) | −1.90138e14 | − | 1.88360e14i | −0.673841 | − | 0.667540i | ||||
\(425\) | 2.99646e14 | 1.04826 | ||||||||
\(426\) | −1.63445e13 | − | 6.06187e13i | −0.0564441 | − | 0.209341i | ||||
\(427\) | 5.75259e13i | 0.196115i | ||||||||
\(428\) | −1.90009e13 | − | 3.26739e13i | −0.0639491 | − | 0.109966i | ||||
\(429\) | 3.02974e14i | 1.00668i | ||||||||
\(430\) | −1.57617e14 | + | 4.24979e13i | −0.517042 | + | 0.139409i | ||||
\(431\) | −1.87948e13 | −0.0608714 | −0.0304357 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304357 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(432\) | 2.90253e14 | + | 1.65163e14i | 0.928145 | + | 0.528142i | ||||
\(433\) | 3.13621e14 | 0.990197 | 0.495098 | − | 0.868837i | \(-0.335132\pi\) | ||||
0.495098 | + | 0.868837i | \(0.335132\pi\) | |||||||
\(434\) | 1.17175e14 | − | 3.15937e13i | 0.365294 | − | 0.0984934i | ||||
\(435\) | 1.64827e14i | 0.507384i | ||||||||
\(436\) | −9.32336e11 | − | 1.60324e12i | −0.00283398 | − | 0.00487329i | ||||
\(437\) | − | 2.99065e14i | − | 0.897672i | ||||||
\(438\) | −1.15455e13 | − | 4.28201e13i | −0.0342220 | − | 0.126923i | ||||
\(439\) | 4.95205e14 | 1.44954 | 0.724771 | − | 0.688990i | \(-0.241946\pi\) | ||||
0.724771 | + | 0.688990i | \(0.241946\pi\) | |||||||
\(440\) | −2.38199e14 | + | 2.40448e14i | −0.688574 | + | 0.695073i | ||||
\(441\) | −5.89103e13 | −0.168182 | ||||||||
\(442\) | 2.20845e14 | + | 8.19071e14i | 0.622679 | + | 2.30940i | ||||
\(443\) | 2.99673e14i | 0.834500i | 0.908792 | + | 0.417250i | \(0.137006\pi\) | ||||
−0.908792 | + | 0.417250i | \(0.862994\pi\) | |||||||
\(444\) | 5.34749e13 | − | 3.10974e13i | 0.147077 | − | 0.0855299i | ||||
\(445\) | − | 1.79249e14i | − | 0.486941i | ||||||
\(446\) | −5.21894e13 | + | 1.40717e13i | −0.140036 | + | 0.0377577i | ||||
\(447\) | −4.38517e14 | −1.16224 | ||||||||
\(448\) | −8.21055e11 | − | 8.73988e13i | −0.00214953 | − | 0.228811i | ||||
\(449\) | 2.49937e14 | 0.646362 | 0.323181 | − | 0.946337i | \(-0.395248\pi\) | ||||
0.323181 | + | 0.946337i | \(0.395248\pi\) | |||||||
\(450\) | −4.26561e13 | + | 1.15013e13i | −0.108971 | + | 0.0293817i | ||||
\(451\) | − | 2.84536e14i | − | 0.718070i | ||||||
\(452\) | 3.14825e14 | − | 1.83081e14i | 0.784888 | − | 0.456438i | ||||
\(453\) | 1.72215e14i | 0.424162i | ||||||||
\(454\) | −5.92214e13 | − | 2.19641e14i | −0.144102 | − | 0.534449i | ||||
\(455\) | 1.76655e14 | 0.424681 | ||||||||
\(456\) | 3.17428e14 | − | 3.20424e14i | 0.753943 | − | 0.761059i | ||||
\(457\) | −7.22584e14 | −1.69570 | −0.847851 | − | 0.530235i | \(-0.822104\pi\) | ||||
−0.847851 | + | 0.530235i | \(0.822104\pi\) | |||||||
\(458\) | −3.37674e13 | − | 1.25237e14i | −0.0782955 | − | 0.290383i | ||||
\(459\) | − | 7.68334e14i | − | 1.76027i | ||||||
\(460\) | 2.15853e14 | + | 3.71179e14i | 0.488641 | + | 0.840263i | ||||
\(461\) | 2.69171e13i | 0.0602107i | 0.999547 | + | 0.0301054i | \(0.00958428\pi\) | ||||
−0.999547 | + | 0.0301054i | \(0.990416\pi\) | |||||||
\(462\) | −6.93416e13 | + | 1.86964e13i | −0.153272 | + | 0.0413265i | ||||
\(463\) | −6.06138e13 | −0.132396 | −0.0661982 | − | 0.997806i | \(-0.521087\pi\) | ||||
−0.0661982 | + | 0.997806i | \(0.521087\pi\) | |||||||
\(464\) | −1.76123e14 | − | 1.00219e14i | −0.380161 | − | 0.216323i | ||||
\(465\) | −8.99156e14 | −1.91798 | ||||||||
\(466\) | −3.95799e14 | + | 1.06718e14i | −0.834357 | + | 0.224966i | ||||
\(467\) | 2.97151e13i | 0.0619063i | 0.999521 | + | 0.0309531i | \(0.00985426\pi\) | ||||
−0.999521 | + | 0.0309531i | \(0.990146\pi\) | |||||||
\(468\) | −6.28765e13 | − | 1.08122e14i | −0.129460 | − | 0.222619i | ||||
\(469\) | − | 1.30439e14i | − | 0.265434i | ||||||
\(470\) | −5.89259e13 | − | 2.18545e14i | −0.118514 | − | 0.439545i | ||||
\(471\) | 3.42813e13 | 0.0681464 | ||||||||
\(472\) | 6.48241e14 | + | 6.42179e14i | 1.27366 | + | 1.26176i | ||||
\(473\) | −1.64911e14 | −0.320267 | ||||||||
\(474\) | −1.16689e14 | − | 4.32776e14i | −0.224000 | − | 0.830774i | ||||
\(475\) | 3.95876e14i | 0.751180i | ||||||||
\(476\) | −1.73832e14 | + | 1.01089e14i | −0.326056 | + | 0.189612i | ||||
\(477\) | − | 9.07879e13i | − | 0.168336i | ||||||
\(478\) | 6.49968e14 | − | 1.75250e14i | 1.19135 | − | 0.321221i | ||||
\(479\) | 1.21025e14 | 0.219296 | 0.109648 | − | 0.993970i | \(-0.465028\pi\) | ||||
0.109648 | + | 0.993970i | \(0.465028\pi\) | |||||||
\(480\) | −1.62701e14 | + | 6.26795e14i | −0.291450 | + | 1.12279i | ||||
\(481\) | −1.53712e14 | −0.272214 | ||||||||
\(482\) | 7.24594e13 | − | 1.95371e13i | 0.126863 | − | 0.0342059i | ||||
\(483\) | 9.11106e13i | 0.157710i | ||||||||
\(484\) | 2.09550e14 | − | 1.21860e14i | 0.358624 | − | 0.208552i | ||||
\(485\) | − | 6.17266e14i | − | 1.04446i | ||||||
\(486\) | 5.45366e13 | + | 2.02266e14i | 0.0912408 | + | 0.338395i | ||||
\(487\) | 6.01563e14 | 0.995111 | 0.497556 | − | 0.867432i | \(-0.334231\pi\) | ||||
0.497556 | + | 0.867432i | \(0.334231\pi\) | |||||||
\(488\) | 3.72253e14 | + | 3.68773e14i | 0.608877 | + | 0.603184i | ||||
\(489\) | 1.31974e14 | 0.213446 | ||||||||
\(490\) | −1.97302e14 | − | 7.31757e14i | −0.315539 | − | 1.17028i | ||||
\(491\) | − | 8.74926e13i | − | 0.138364i | −0.997604 | − | 0.0691820i | \(-0.977961\pi\) | ||
0.997604 | − | 0.0691820i | \(-0.0220389\pi\) | |||||||
\(492\) | −2.73675e14 | − | 4.70609e14i | −0.427983 | − | 0.735957i | ||||
\(493\) | 4.66220e14i | 0.720995i | ||||||||
\(494\) | −1.08211e15 | + | 2.91767e14i | −1.65491 | + | 0.446209i | ||||
\(495\) | −1.14810e14 | −0.173640 | ||||||||
\(496\) | 5.46713e14 | − | 9.60781e14i | 0.817730 | − | 1.43706i | ||||
\(497\) | −3.69806e13 | −0.0547033 | ||||||||
\(498\) | −6.34625e14 | + | 1.71113e14i | −0.928445 | + | 0.250335i | ||||
\(499\) | 8.99853e14i | 1.30202i | 0.759068 | + | 0.651011i | \(0.225655\pi\) | ||||
−0.759068 | + | 0.651011i | \(0.774345\pi\) | |||||||
\(500\) | 1.63572e14 | + | 2.81277e14i | 0.234085 | + | 0.402532i | ||||
\(501\) | 2.52564e14i | 0.357489i | ||||||||
\(502\) | 1.89224e14 | + | 7.01796e14i | 0.264914 | + | 0.982517i | ||||
\(503\) | 6.87292e14 | 0.951738 | 0.475869 | − | 0.879516i | \(-0.342134\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342134\pi\) | |||||||
\(504\) | 2.08658e13 | − | 2.10627e13i | 0.0285803 | − | 0.0288500i | ||||
\(505\) | 2.68155e14 | 0.363315 | ||||||||
\(506\) | 1.12921e14 | + | 4.18803e14i | 0.151338 | + | 0.561283i | ||||
\(507\) | − | 7.56313e14i | − | 1.00267i | ||||||
\(508\) | −9.56336e14 | + | 5.56141e14i | −1.25418 | + | 0.729347i | ||||
\(509\) | 1.78689e14i | 0.231819i | 0.993260 | + | 0.115910i | \(0.0369783\pi\) | ||||
−0.993260 | + | 0.115910i | \(0.963022\pi\) | |||||||
\(510\) | 1.43850e15 | − | 3.87860e14i | 1.84618 | − | 0.497781i | ||||
\(511\) | −2.61225e13 | −0.0331666 | ||||||||
\(512\) | −5.70826e14 | − | 5.54962e14i | −0.717000 | − | 0.697073i | ||||
\(513\) | 1.01508e15 | 1.26141 | ||||||||
\(514\) | −1.26922e15 | + | 3.42218e14i | −1.56042 | + | 0.420732i | ||||
\(515\) | 3.98790e14i | 0.485070i | ||||||||
\(516\) | −2.72754e14 | + | 1.58616e14i | −0.328245 | + | 0.190885i | ||||
\(517\) | − | 2.28659e14i | − | 0.272264i | ||||||
\(518\) | −9.48553e12 | − | 3.51800e13i | −0.0111750 | − | 0.0414460i | ||||
\(519\) | 1.12346e15 | 1.30960 | ||||||||
\(520\) | 1.13246e15 | − | 1.14315e15i | 1.30618 | − | 1.31851i | ||||
\(521\) | 3.87660e14 | 0.442429 | 0.221215 | − | 0.975225i | \(-0.428998\pi\) | ||||
0.221215 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(522\) | −1.78948e13 | − | 6.63685e13i | −0.0202088 | − | 0.0749505i | ||||
\(523\) | 3.70738e14i | 0.414293i | 0.978310 | + | 0.207146i | \(0.0664177\pi\) | ||||
−0.978310 | + | 0.207146i | \(0.933582\pi\) | |||||||
\(524\) | −2.30551e14 | − | 3.96454e14i | −0.254944 | − | 0.438400i | ||||
\(525\) | − | 1.20604e14i | − | 0.131973i | ||||||
\(526\) | −3.12689e14 | + | 8.43097e13i | −0.338603 | + | 0.0912969i | ||||
\(527\) | −2.54330e15 | −2.72546 | ||||||||
\(528\) | −3.23532e14 | + | 5.68568e14i | −0.343108 | + | 0.602971i | ||||
\(529\) | −4.02529e14 | −0.422465 | ||||||||
\(530\) | 1.12773e15 | − | 3.04067e14i | 1.17135 | − | 0.315829i | ||||
\(531\) | 3.09524e14i | 0.318182i | ||||||||
\(532\) | −1.33553e14 | − | 2.29658e14i | −0.135875 | − | 0.233651i | ||||
\(533\) | 1.35275e15i | 1.36213i | ||||||||
\(534\) | −9.01925e13 | − | 3.34507e14i | −0.0898863 | − | 0.333372i | ||||
\(535\) | 1.64948e14 | 0.162705 | ||||||||
\(536\) | −8.44079e14 | − | 8.36187e14i | −0.824094 | − | 0.816388i | ||||
\(537\) | 3.32207e14 | 0.321033 | ||||||||
\(538\) | −1.15194e14 | − | 4.27234e14i | −0.110186 | − | 0.408661i | ||||
\(539\) | − | 7.65621e14i | − | 0.724896i | ||||||
\(540\) | −1.25985e15 | + | 7.32643e14i | −1.18073 | + | 0.686636i | ||||
\(541\) | − | 1.32152e15i | − | 1.22599i | −0.790086 | − | 0.612995i | \(-0.789964\pi\) | ||
0.790086 | − | 0.612995i | \(-0.210036\pi\) | |||||||
\(542\) | 1.63359e15 | − | 4.40460e14i | 1.50019 | − | 0.404493i | ||||
\(543\) | −1.53717e15 | −1.39740 | ||||||||
\(544\) | −4.60207e14 | + | 1.77292e15i | −0.414152 | + | 1.59549i | ||||
\(545\) | 8.09364e12 | 0.00721046 | ||||||||
\(546\) | 3.29667e14 | − | 8.88874e13i | 0.290747 | − | 0.0783936i | ||||
\(547\) | − | 1.58642e15i | − | 1.38513i | −0.721357 | − | 0.692563i | \(-0.756481\pi\) | ||
0.721357 | − | 0.692563i | \(-0.243519\pi\) | |||||||
\(548\) | 5.93651e14 | − | 3.45228e14i | 0.513143 | − | 0.298409i | ||||
\(549\) | 1.77745e14i | 0.152107i | ||||||||
\(550\) | −1.49475e14 | − | 5.54375e14i | −0.126641 | − | 0.469687i | ||||
\(551\) | −6.15943e14 | −0.516662 | ||||||||
\(552\) | 5.89582e14 | + | 5.84069e14i | 0.489643 | + | 0.485064i | ||||
\(553\) | −2.64016e14 | −0.217091 | ||||||||
\(554\) | 2.68727e14 | + | 9.96658e14i | 0.218780 | + | 0.811414i | ||||
\(555\) | 2.69958e14i | 0.217613i | ||||||||
\(556\) | 2.80758e13 | + | 4.82789e13i | 0.0224089 | + | 0.0385342i | ||||
\(557\) | − | 1.21582e15i | − | 0.960869i | −0.877031 | − | 0.480435i | \(-0.840479\pi\) | ||
0.877031 | − | 0.480435i | \(-0.159521\pi\) | |||||||
\(558\) | 3.62051e14 | − | 9.76191e13i | 0.283323 | − | 0.0763918i | ||||
\(559\) | 7.84025e14 | 0.607526 | ||||||||
\(560\) | 3.31515e14 | + | 1.88642e14i | 0.254372 | + | 0.144745i | ||||
\(561\) | 1.50507e15 | 1.14356 | ||||||||
\(562\) | −3.70194e14 | + | 9.98148e13i | −0.278535 | + | 0.0751009i | ||||
\(563\) | − | 2.27297e15i | − | 1.69355i | −0.531951 | − | 0.846775i | \(-0.678541\pi\) | ||
0.531951 | − | 0.846775i | \(-0.321459\pi\) | |||||||
\(564\) | −2.19931e14 | − | 3.78191e14i | −0.162275 | − | 0.279046i | ||||
\(565\) | 1.58933e15i | 1.16131i | ||||||||
\(566\) | 6.45722e14 | + | 2.39486e15i | 0.467256 | + | 1.73297i | ||||
\(567\) | −2.52578e14 | −0.181004 | ||||||||
\(568\) | −2.37066e14 | + | 2.39304e14i | −0.168249 | + | 0.169837i | ||||
\(569\) | −3.01866e14 | −0.212176 | −0.106088 | − | 0.994357i | \(-0.533833\pi\) | ||||
−0.106088 | + | 0.994357i | \(0.533833\pi\) | |||||||
\(570\) | 5.12418e14 | + | 1.90046e15i | 0.356708 | + | 1.32296i | ||||
\(571\) | 2.23731e15i | 1.54251i | 0.636529 | + | 0.771253i | \(0.280370\pi\) | ||||
−0.636529 | + | 0.771253i | \(0.719630\pi\) | |||||||
\(572\) | 1.40519e15 | − | 8.17167e14i | 0.959530 | − | 0.557998i | ||||
\(573\) | 1.97116e15i | 1.33313i | ||||||||
\(574\) | −3.09604e14 | + | 8.34780e13i | −0.207392 | + | 0.0559186i | ||||
\(575\) | −7.28414e14 | −0.483287 | ||||||||
\(576\) | −2.53692e12 | − | 2.70047e14i | −0.00166718 | − | 0.177466i | ||||
\(577\) | −1.67626e15 | −1.09113 | −0.545564 | − | 0.838069i | \(-0.683684\pi\) | ||||
−0.545564 | + | 0.838069i | \(0.683684\pi\) | |||||||
\(578\) | 2.57137e15 | − | 6.93312e14i | 1.65791 | − | 0.447019i | ||||
\(579\) | 1.00003e15i | 0.638675i | ||||||||
\(580\) | 7.64467e14 | − | 4.44563e14i | 0.483620 | − | 0.281241i | ||||
\(581\) | 3.87155e14i | 0.242614i | ||||||||
\(582\) | −3.10589e14 | − | 1.15192e15i | −0.192801 | − | 0.715064i | ||||
\(583\) | 1.17991e15 | 0.725561 | ||||||||
\(584\) | −1.67460e14 | + | 1.69040e14i | −0.102009 | + | 0.102972i | ||||
\(585\) | 5.45833e14 | 0.329384 | ||||||||
\(586\) | −6.59654e14 | − | 2.44653e15i | −0.394348 | − | 1.46256i | ||||
\(587\) | 1.50304e15i | 0.890144i | 0.895495 | + | 0.445072i | \(0.146822\pi\) | ||||
−0.895495 | + | 0.445072i | \(0.853178\pi\) | |||||||
\(588\) | −7.36395e14 | − | 1.26630e15i | −0.432052 | − | 0.742953i | ||||
\(589\) | − | 3.36007e15i | − | 1.95305i | ||||||
\(590\) | −3.84477e15 | + | 1.03666e15i | −2.21403 | + | 0.596966i | ||||
\(591\) | −3.63165e14 | −0.207192 | ||||||||
\(592\) | −2.88460e14 | − | 1.64142e14i | −0.163048 | − | 0.0927792i | ||||
\(593\) | −1.38749e14 | −0.0777015 | −0.0388507 | − | 0.999245i | \(-0.512370\pi\) | ||||
−0.0388507 | + | 0.999245i | \(0.512370\pi\) | |||||||
\(594\) | −1.42149e15 | + | 3.83274e14i | −0.788713 | + | 0.212659i | ||||
\(595\) | − | 8.77560e14i | − | 0.482429i | ||||||
\(596\) | 1.18275e15 | + | 2.03384e15i | 0.644225 | + | 1.10780i | ||||
\(597\) | − | 2.80510e15i | − | 1.51387i | ||||||
\(598\) | −5.36853e14 | − | 1.99109e15i | −0.287077 | − | 1.06472i | ||||
\(599\) | 1.44893e15 | 0.767717 | 0.383859 | − | 0.923392i | \(-0.374595\pi\) | ||||
0.383859 | + | 0.923392i | \(0.374595\pi\) | |||||||
\(600\) | −7.80437e14 | − | 7.73140e14i | −0.409738 | − | 0.405906i | ||||
\(601\) | −7.86748e13 | −0.0409285 | −0.0204643 | − | 0.999791i | \(-0.506514\pi\) | ||||
−0.0204643 | + | 0.999791i | \(0.506514\pi\) | |||||||
\(602\) | 4.83820e13 | + | 1.79440e14i | 0.0249404 | + | 0.0924992i | ||||
\(603\) | − | 4.03034e14i | − | 0.205872i | ||||||
\(604\) | 7.98735e14 | − | 4.64491e14i | 0.404296 | − | 0.235112i | ||||
\(605\) | 1.05788e15i | 0.530616i | ||||||||
\(606\) | 5.00421e14 | − | 1.34927e14i | 0.248734 | − | 0.0670657i | ||||
\(607\) | 1.57249e15 | 0.774550 | 0.387275 | − | 0.921964i | \(-0.373416\pi\) | ||||
0.387275 | + | 0.921964i | \(0.373416\pi\) | |||||||
\(608\) | −2.34228e15 | − | 6.08000e14i | −1.14332 | − | 0.296779i | ||||
\(609\) | 1.87648e14 | 0.0907713 | ||||||||
\(610\) | −2.20787e15 | + | 5.95303e14i | −1.05842 | + | 0.285380i | ||||
\(611\) | 1.08710e15i | 0.516467i | ||||||||
\(612\) | −5.37112e14 | + | 3.12348e14i | −0.252890 | + | 0.147064i | ||||
\(613\) | 8.60982e14i | 0.401755i | 0.979616 | + | 0.200878i | \(0.0643794\pi\) | ||||
−0.979616 | + | 0.200878i | \(0.935621\pi\) | |||||||
\(614\) | −4.11627e14 | − | 1.52665e15i | −0.190361 | − | 0.706013i | ||||
\(615\) | 2.37578e15 | 1.08891 | ||||||||
\(616\) | 2.73739e14 | + | 2.71179e14i | 0.124349 | + | 0.123186i | ||||
\(617\) | −9.54957e14 | −0.429947 | −0.214974 | − | 0.976620i | \(-0.568967\pi\) | ||||
−0.214974 | + | 0.976620i | \(0.568967\pi\) | |||||||
\(618\) | 2.00659e14 | + | 7.44206e14i | 0.0895409 | + | 0.332090i | ||||
\(619\) | 1.65458e13i | 0.00731793i | 0.999993 | + | 0.00365896i | \(0.00116469\pi\) | ||||
−0.999993 | + | 0.00365896i | \(0.998835\pi\) | |||||||
\(620\) | 2.42516e15 | + | 4.17029e15i | 1.06313 | + | 1.82815i | ||||
\(621\) | 1.86775e15i | 0.811550i | ||||||||
\(622\) | −3.83372e15 | + | 1.03368e15i | −1.65110 | + | 0.445183i | ||||
\(623\) | −2.04067e14 | −0.0871141 | ||||||||
\(624\) | 1.53815e15 | − | 2.70311e15i | 0.650854 | − | 1.14380i | ||||
\(625\) | −2.93617e15 | −1.23152 | ||||||||
\(626\) | 4.14062e15 | − | 1.11643e15i | 1.72150 | − | 0.464164i | ||||
\(627\) | 1.98841e15i | 0.819474i | ||||||||
\(628\) | −9.24620e13 | − | 1.58997e14i | −0.0377733 | − | 0.0649547i | ||||
\(629\) | 7.63587e14i | 0.309229i | ||||||||
\(630\) | 3.36832e13 | + | 1.24925e14i | 0.0135220 | + | 0.0501505i | ||||
\(631\) | 2.66470e15 | 1.06044 | 0.530221 | − | 0.847859i | \(-0.322109\pi\) | ||||
0.530221 | + | 0.847859i | \(0.322109\pi\) | |||||||
\(632\) | −1.69249e15 | + | 1.70847e15i | −0.667702 | + | 0.674004i | ||||
\(633\) | 2.59843e14 | 0.101623 | ||||||||
\(634\) | −8.78556e14 | − | 3.25840e15i | −0.340626 | − | 1.26332i | ||||
\(635\) | − | 4.82788e15i | − | 1.85567i | ||||||
\(636\) | 1.95152e15 | − | 1.13487e15i | 0.743634 | − | 0.432448i | ||||
\(637\) | 3.63994e15i | 1.37508i | ||||||||
\(638\) | 8.62551e14 | − | 2.32568e14i | 0.323051 | − | 0.0871036i | ||||
\(639\) | −1.14264e14 | −0.0424281 | ||||||||
\(640\) | 3.34591e15 | − | 9.35954e14i | 1.23175 | − | 0.344560i | ||||
\(641\) | 2.68473e15 | 0.979901 | 0.489951 | − | 0.871750i | \(-0.337015\pi\) | ||||
0.489951 | + | 0.871750i | \(0.337015\pi\) | |||||||
\(642\) | 3.07819e14 | − | 8.29967e13i | 0.111392 | − | 0.0300343i | ||||
\(643\) | − | 4.42246e14i | − | 0.158673i | −0.996848 | − | 0.0793367i | \(-0.974720\pi\) | ||
0.996848 | − | 0.0793367i | \(-0.0252802\pi\) | |||||||
\(644\) | 4.22571e14 | − | 2.45739e14i | 0.150324 | − | 0.0874182i | ||||
\(645\) | − | 1.37695e15i | − | 0.485668i | ||||||
\(646\) | 1.44940e15 | + | 5.37554e15i | 0.506884 | + | 1.87994i | ||||
\(647\) | −3.79844e15 | −1.31714 | −0.658570 | − | 0.752520i | \(-0.728838\pi\) | ||||
−0.658570 | + | 0.752520i | \(0.728838\pi\) | |||||||
\(648\) | −1.61916e15 | + | 1.63444e15i | −0.556708 | + | 0.561963i | ||||
\(649\) | −4.02270e15 | −1.37142 | ||||||||
\(650\) | 7.10639e14 | + | 2.63563e15i | 0.240229 | + | 0.890965i | ||||
\(651\) | 1.02365e15i | 0.343128i | ||||||||
\(652\) | −3.55953e14 | − | 6.12094e14i | −0.118313 | − | 0.203449i | ||||
\(653\) | − | 5.25844e15i | − | 1.73314i | −0.499052 | − | 0.866572i | \(-0.666318\pi\) | ||
0.499052 | − | 0.866572i | \(-0.333682\pi\) | |||||||
\(654\) | 1.51040e13 | − | 4.07247e12i | 0.00493646 | − | 0.00133101i | ||||
\(655\) | 2.00142e15 | 0.648652 | ||||||||
\(656\) | −1.44454e15 | + | 2.53861e15i | −0.464258 | + | 0.815877i | ||||
\(657\) | −8.07141e13 | −0.0257241 | ||||||||
\(658\) | −2.48804e14 | + | 6.70846e13i | −0.0786349 | + | 0.0212022i | ||||
\(659\) | 3.68455e15i | 1.15482i | 0.816454 | + | 0.577410i | \(0.195937\pi\) | ||||
−0.816454 | + | 0.577410i | \(0.804063\pi\) | |||||||
\(660\) | −1.43515e15 | − | 2.46788e15i | −0.446074 | − | 0.767066i | ||||
\(661\) | − | 1.45382e15i | − | 0.448130i | −0.974574 | − | 0.224065i | \(-0.928067\pi\) | ||
0.974574 | − | 0.224065i | \(-0.0719327\pi\) | |||||||
\(662\) | −1.06692e15 | − | 3.95702e15i | −0.326147 | − | 1.20962i | ||||
\(663\) | −7.15546e15 | −2.16927 | ||||||||
\(664\) | 2.50530e15 | + | 2.48188e15i | 0.753244 | + | 0.746201i | ||||
\(665\) | 1.15938e15 | 0.345707 | ||||||||
\(666\) | −2.93086e13 | − | 1.08700e14i | −0.00866737 | − | 0.0321457i | ||||
\(667\) | − | 1.13334e15i | − | 0.332405i | ||||||
\(668\) | 1.17139e15 | − | 6.81202e14i | 0.340746 | − | 0.198155i | ||||
\(669\) | − | 4.55930e14i | − | 0.131539i | ||||||
\(670\) | 5.00631e15 | − | 1.34984e15i | 1.43254 | − | 0.386252i | ||||
\(671\) | −2.31004e15 | −0.655611 | ||||||||
\(672\) | 7.13579e14 | + | 1.85228e14i | 0.200868 | + | 0.0521406i | ||||
\(673\) | 4.59102e15 | 1.28182 | 0.640909 | − | 0.767617i | \(-0.278557\pi\) | ||||
0.640909 | + | 0.767617i | \(0.278557\pi\) | |||||||
\(674\) | 1.64818e15 | − | 4.44397e14i | 0.456432 | − | 0.123067i | ||||
\(675\) | − | 2.47237e15i | − | 0.679113i | ||||||
\(676\) | −3.50778e15 | + | 2.03989e15i | −0.955709 | + | 0.555776i | ||||
\(677\) | − | 2.08953e15i | − | 0.564691i | −0.959313 | − | 0.282345i | \(-0.908888\pi\) | ||
0.959313 | − | 0.282345i | \(-0.0911124\pi\) | |||||||
\(678\) | 7.99704e14 | + | 2.96595e15i | 0.214371 | + | 0.795062i | ||||
\(679\) | −7.02730e14 | −0.186855 | ||||||||
\(680\) | −5.67874e15 | − | 5.62564e15i | −1.49780 | − | 1.48379i | ||||
\(681\) | 1.91880e15 | 0.502019 | ||||||||
\(682\) | 1.26869e15 | + | 4.70535e15i | 0.329263 | + | 1.22118i | ||||
\(683\) | 3.35863e14i | 0.0864667i | 0.999065 | + | 0.0432333i | \(0.0137659\pi\) | ||||
−0.999065 | + | 0.0432333i | \(0.986234\pi\) | |||||||
\(684\) | −4.12657e14 | − | 7.09602e14i | −0.105385 | − | 0.181220i | ||||
\(685\) | 2.99693e15i | 0.759240i | ||||||||
\(686\) | −1.71218e15 | + | 4.61650e14i | −0.430294 | + | 0.116019i | ||||
\(687\) | 1.09408e15 | 0.272763 | ||||||||
\(688\) | 1.47132e15 | + | 8.37225e14i | 0.363891 | + | 0.207065i | ||||
\(689\) | −5.60960e15 | −1.37634 | ||||||||
\(690\) | −3.49686e15 | + | 9.42852e14i | −0.851155 | + | 0.229495i | ||||
\(691\) | − | 6.13314e14i | − | 0.148099i | −0.997255 | − | 0.0740497i | \(-0.976408\pi\) | ||
0.997255 | − | 0.0740497i | \(-0.0235923\pi\) | |||||||
\(692\) | −3.03015e15 | − | 5.21062e15i | −0.725906 | − | 1.24826i | ||||
\(693\) | 1.30706e14i | 0.0310644i | ||||||||
\(694\) | −5.83521e14 | − | 2.16417e15i | −0.137588 | − | 0.510287i | ||||
\(695\) | −2.43727e14 | −0.0570148 | ||||||||
\(696\) | 1.20293e15 | − | 1.21428e15i | 0.279183 | − | 0.281818i | ||||
\(697\) | 6.72000e15 | 1.54735 | ||||||||
\(698\) | −4.98163e14 | − | 1.84759e15i | −0.113806 | − | 0.422087i | ||||
\(699\) | − | 3.45772e15i | − | 0.783728i | ||||||
\(700\) | −5.59362e14 | + | 3.25288e14i | −0.125792 | + | 0.0731524i | ||||
\(701\) | 7.14041e15i | 1.59321i | 0.604498 | + | 0.796606i | \(0.293374\pi\) | ||||
−0.604498 | + | 0.796606i | \(0.706626\pi\) | |||||||
\(702\) | 6.75811e15 | − | 1.82218e15i | 1.49614 | − | 0.403400i | ||||
\(703\) | −1.00881e15 | −0.221592 | ||||||||
\(704\) | 3.50964e15 | − | 3.29708e13i | 0.764914 | − | 0.00718587i | ||||
\(705\) | 1.90923e15 | 0.412874 | ||||||||
\(706\) | −2.36959e15 | + | 6.38909e14i | −0.508450 | + | 0.137092i | ||||
\(707\) | − | 3.05283e14i | − | 0.0649973i | ||||||
\(708\) | −6.65335e15 | + | 3.86914e15i | −1.40559 | + | 0.817394i | ||||
\(709\) | 1.70696e15i | 0.357823i | 0.983865 | + | 0.178911i | \(0.0572576\pi\) | ||||
−0.983865 | + | 0.178911i | \(0.942742\pi\) | |||||||
\(710\) | −3.82691e14 | − | 1.41933e15i | −0.0796027 | − | 0.295231i | ||||
\(711\) | −8.15765e14 | −0.168377 | ||||||||
\(712\) | −1.30818e15 | + | 1.32053e15i | −0.267934 | + | 0.270463i | ||||
\(713\) | 6.18254e15 | 1.25653 | ||||||||
\(714\) | −4.41561e14 | − | 1.63767e15i | −0.0890534 | − | 0.330282i | ||||
\(715\) | 7.09386e15i | 1.41971i | ||||||||
\(716\) | −8.96011e14 | − | 1.54077e15i | −0.177947 | − | 0.305997i | ||||
\(717\) | 5.67816e15i | 1.11906i | ||||||||
\(718\) | 4.85011e15 | − | 1.30773e15i | 0.948566 | − | 0.255760i | ||||
\(719\) | 7.81443e15 | 1.51666 | 0.758330 | − | 0.651870i | \(-0.226015\pi\) | ||||
0.758330 | + | 0.651870i | \(0.226015\pi\) | |||||||
\(720\) | 1.02432e15 | + | 5.82871e14i | 0.197292 | + | 0.112265i | ||||
\(721\) | 4.54005e14 | 0.0867793 | ||||||||
\(722\) | −2.01189e15 | + | 5.42463e14i | −0.381637 | + | 0.102900i | ||||
\(723\) | 6.33009e14i | 0.119165i | ||||||||
\(724\) | 4.14597e15 | + | 7.12938e15i | 0.774576 | + | 1.33196i | ||||
\(725\) | 1.50021e15i | 0.278160i | ||||||||
\(726\) | 5.32290e14 | + | 1.97417e15i | 0.0979484 | + | 0.363272i | ||||
\(727\) | 9.77013e12 | 0.00178427 | 0.000892136 | − | 1.00000i | \(-0.499716\pi\) | ||||
0.000892136 | 1.00000i | \(0.499716\pi\) | ||||||||
\(728\) | −1.30142e15 | − | 1.28925e15i | −0.235882 | − | 0.233677i | ||||
\(729\) | −6.16439e15 | −1.10889 | ||||||||
\(730\) | −2.70327e14 | − | 1.00259e15i | −0.0482630 | − | 0.178998i | ||||
\(731\) | − | 3.89476e15i | − | 0.690137i | ||||||
\(732\) | −3.82070e15 | + | 2.22186e15i | −0.671942 | + | 0.390756i | ||||
\(733\) | − | 1.07577e16i | − | 1.87780i | −0.344191 | − | 0.938900i | \(-0.611847\pi\) | ||
0.344191 | − | 0.938900i | \(-0.388153\pi\) | |||||||
\(734\) | −5.99100e15 | + | 1.61534e15i | −1.03794 | + | 0.279857i | ||||
\(735\) | 6.39267e15 | 1.09926 | ||||||||
\(736\) | 1.11872e15 | − | 4.30981e15i | 0.190939 | − | 0.735580i | ||||
\(737\) | 5.23799e15 | 0.887346 | ||||||||
\(738\) | −9.56624e14 | + | 2.57933e14i | −0.160854 | + | 0.0433707i | ||||
\(739\) | − | 1.55149e14i | − | 0.0258944i | −0.999916 | − | 0.0129472i | \(-0.995879\pi\) | ||
0.999916 | − | 0.0129472i | \(-0.00412133\pi\) | |||||||
\(740\) | 1.25206e15 | − | 7.28117e14i | 0.207421 | − | 0.120622i | ||||
\(741\) | − | 9.45339e15i | − | 1.55449i | ||||||
\(742\) | −3.46167e14 | − | 1.28387e15i | −0.0565020 | − | 0.209555i | ||||
\(743\) | −6.27422e15 | −1.01653 | −0.508266 | − | 0.861200i | \(-0.669713\pi\) | ||||
−0.508266 | + | 0.861200i | \(0.669713\pi\) | |||||||
\(744\) | 6.62410e15 | + | 6.56216e15i | 1.06531 | + | 1.05535i | ||||
\(745\) | −1.02675e16 | −1.63910 | ||||||||
\(746\) | −1.46497e15 | − | 5.43332e15i | −0.232149 | − | 0.860996i | ||||
\(747\) | 1.19624e15i | 0.188172i | ||||||||
\(748\) | −4.05940e15 | − | 6.98051e15i | −0.633874 | − | 1.09000i | ||||
\(749\) | − | 1.87786e14i | − | 0.0291080i | ||||||
\(750\) | −2.64990e15 | + | 7.14488e14i | −0.407749 | + | 0.109941i | ||||
\(751\) | −6.57869e15 | −1.00489 | −0.502447 | − | 0.864608i | \(-0.667567\pi\) | ||||
−0.502447 | + | 0.864608i | \(0.667567\pi\) | |||||||
\(752\) | −1.16086e15 | + | 2.04008e15i | −0.176029 | + | 0.309349i | ||||
\(753\) | −6.13093e15 | −0.922898 | ||||||||
\(754\) | −4.10077e15 | + | 1.10568e15i | −0.612806 | + | 0.165230i | ||||
\(755\) | 4.03226e15i | 0.598192i | ||||||||
\(756\) | 8.34082e14 | + | 1.43428e15i | 0.122840 | + | 0.211234i | ||||
\(757\) | 2.54343e15i | 0.371871i | 0.982562 | + | 0.185935i | \(0.0595315\pi\) | ||||
−0.982562 | + | 0.185935i | \(0.940468\pi\) | |||||||
\(758\) | 3.25174e15 | + | 1.20601e16i | 0.471992 | + | 1.75053i | ||||
\(759\) | −3.65869e15 | −0.527225 | ||||||||
\(760\) | 7.43228e15 | − | 7.50243e15i | 1.06328 | − | 1.07332i | ||||
\(761\) | −5.98810e15 | −0.850498 | −0.425249 | − | 0.905076i | \(-0.639813\pi\) | ||||
−0.425249 | + | 0.905076i | \(0.639813\pi\) | |||||||
\(762\) | −2.42924e15 | − | 9.00960e15i | −0.342545 | − | 1.27044i | ||||
\(763\) | − | 9.21426e12i | − | 0.00128996i | ||||||
\(764\) | 9.14224e15 | − | 5.31651e15i | 1.27069 | − | 0.738947i | ||||
\(765\) | − | 2.71151e15i | − | 0.374173i | ||||||
\(766\) | 5.71810e15 | − | 1.54176e15i | 0.783418 | − | 0.211232i | ||||
\(767\) | 1.91249e16 | 2.60150 | ||||||||
\(768\) | 5.77306e15 | − | 3.43020e15i | 0.779685 | − | 0.463268i | ||||
\(769\) | −7.50045e15 | −1.00576 | −0.502878 | − | 0.864358i | \(-0.667725\pi\) | ||||
−0.502878 | + | 0.864358i | \(0.667725\pi\) | |||||||
\(770\) | −1.62357e15 | + | 4.37760e14i | −0.216158 | + | 0.0582823i | ||||
\(771\) | − | 1.10880e16i | − | 1.46573i | ||||||
\(772\) | 4.63813e15 | − | 2.69722e15i | 0.608762 | − | 0.354015i | ||||
\(773\) | 6.98863e15i | 0.910762i | 0.890297 | + | 0.455381i | \(0.150497\pi\) | ||||
−0.890297 | + | 0.455381i | \(0.849503\pi\) | |||||||
\(774\) | 1.49492e14 | + | 5.54437e14i | 0.0193438 | + | 0.0717426i | ||||
\(775\) | −8.18390e15 | −1.05148 | ||||||||
\(776\) | −4.50489e15 | + | 4.54741e15i | −0.574705 | + | 0.580129i | ||||
\(777\) | 3.07335e14 | 0.0389311 | ||||||||
\(778\) | 3.12732e15 | + | 1.15986e16i | 0.393355 | + | 1.45888i | ||||
\(779\) | 8.87809e15i | 1.10883i | ||||||||
\(780\) | 6.82307e15 | + | 1.17329e16i | 0.846173 | + | 1.45507i | ||||
\(781\) | − | 1.48501e15i | − | 0.182873i | ||||||
\(782\) | −9.89103e15 | + | 2.66690e15i | −1.20950 | + | 0.326114i | ||||
\(783\) | 3.84675e15 | 0.467094 | ||||||||
\(784\) | −3.88693e15 | + | 6.83080e15i | −0.468672 | + | 0.823632i | ||||
\(785\) | 8.02666e14 | 0.0961063 | ||||||||
\(786\) | 3.73498e15 | − | 1.00705e15i | 0.444083 | − | 0.119737i | ||||
\(787\) | − | 2.82969e15i | − | 0.334102i | −0.985948 | − | 0.167051i | \(-0.946576\pi\) | ||
0.985948 | − | 0.167051i | \(-0.0534244\pi\) | |||||||
\(788\) | 9.79510e14 | + | 1.68436e15i | 0.114846 | + | 0.197488i | ||||
\(789\) | − | 2.73167e15i | − | 0.318057i | ||||||
\(790\) | −2.73216e15 | − | 1.01331e16i | −0.315905 | − | 1.17163i | ||||
\(791\) | 1.80939e15 | 0.207759 | ||||||||
\(792\) | 8.45806e14 | + | 8.37897e14i | 0.0964456 | + | 0.0955438i | ||||
\(793\) | 1.09825e16 | 1.24365 | ||||||||
\(794\) | 3.01280e15 | + | 1.11739e16i | 0.338811 | + | 1.25659i | ||||
\(795\) | 9.85189e15i | 1.10027i | ||||||||
\(796\) | −1.30101e16 | + | 7.56578e15i | −1.44297 | + | 0.839136i | ||||
\(797\) | − | 7.15437e15i | − | 0.788044i | −0.919101 | − | 0.394022i | \(-0.871083\pi\) | ||
0.919101 | − | 0.394022i | \(-0.128917\pi\) | |||||||
\(798\) | 2.16359e15 | − | 5.83366e14i | 0.236679 | − | 0.0638153i | ||||
\(799\) | 5.40033e15 | 0.586696 | ||||||||
\(800\) | −1.48087e15 | + | 5.70494e15i | −0.159779 | + | 0.615540i | ||||
\(801\) | −6.30532e14 | −0.0675660 | ||||||||
\(802\) | 2.15648e15 | − | 5.81449e14i | 0.229502 | − | 0.0618803i | ||||
\(803\) | − | 1.04899e15i | − | 0.110876i | ||||||
\(804\) | 8.66337e15 | − | 5.03804e15i | 0.909450 | − | 0.528875i | ||||
\(805\) | 2.13327e15i | 0.222417i | ||||||||
\(806\) | −6.03168e15 | − | 2.23704e16i | −0.624591 | − | 2.31649i | ||||
\(807\) | 3.73234e15 | 0.383864 | ||||||||
\(808\) | −1.97550e15 | − | 1.95703e15i | −0.201797 | − | 0.199910i | ||||
\(809\) | −6.06373e15 | −0.615209 | −0.307605 | − | 0.951514i | \(-0.599527\pi\) | ||||
−0.307605 | + | 0.951514i | \(0.599527\pi\) | |||||||
\(810\) | −2.61378e15 | − | 9.69403e15i | −0.263392 | − | 0.976870i | ||||
\(811\) | − | 1.25004e16i | − | 1.25115i | −0.780164 | − | 0.625576i | \(-0.784864\pi\) | ||
0.780164 | − | 0.625576i | \(-0.215136\pi\) | |||||||
\(812\) | −5.06115e14 | − | 8.70312e14i | −0.0503142 | − | 0.0865200i | ||||
\(813\) | 1.42711e16i | 1.40916i | ||||||||
\(814\) | 1.41271e15 | − | 3.80906e14i | 0.138554 | − | 0.0373580i | ||||
\(815\) | 3.09004e15 | 0.301021 | ||||||||
\(816\) | −1.34281e16 | − | 7.64099e15i | −1.29933 | − | 0.739356i | ||||
\(817\) | 5.14554e15 | 0.494549 | ||||||||
\(818\) | 8.80284e15 | − | 2.37349e15i | 0.840388 | − | 0.226592i | ||||
\(819\) | − | 6.21407e14i | − | 0.0589271i | ||||||
\(820\) | −6.40784e15 | − | 1.10189e16i | −0.603581 | − | 1.03791i | ||||
\(821\) | 9.11023e15i | 0.852397i | 0.904630 | + | 0.426198i | \(0.140147\pi\) | ||||
−0.904630 | + | 0.426198i | \(0.859853\pi\) | |||||||
\(822\) | 1.50796e15 | + | 5.59276e15i | 0.140151 | + | 0.519794i | ||||
\(823\) | −1.90354e16 | −1.75737 | −0.878683 | − | 0.477407i | \(-0.841577\pi\) | ||||
−0.878683 | + | 0.477407i | \(0.841577\pi\) | |||||||
\(824\) | 2.91042e15 | − | 2.93789e15i | 0.266905 | − | 0.269424i | ||||
\(825\) | 4.84305e15 | 0.441187 | ||||||||
\(826\) | 1.18019e15 | + | 4.37710e15i | 0.106798 | + | 0.396092i | ||||
\(827\) | 6.03027e15i | 0.542071i | 0.962569 | + | 0.271036i | \(0.0873661\pi\) | ||||
−0.962569 | + | 0.271036i | \(0.912634\pi\) | |||||||
\(828\) | 1.30567e15 | − | 7.59291e14i | 0.116592 | − | 0.0678018i | ||||
\(829\) | − | 1.35457e16i | − | 1.20158i | −0.799408 | − | 0.600788i | \(-0.794854\pi\) | ||
0.799408 | − | 0.600788i | \(-0.205146\pi\) | |||||||
\(830\) | −1.48592e16 | + | 4.00645e15i | −1.30938 | + | 0.353045i | ||||
\(831\) | −8.70687e15 | −0.762178 | ||||||||
\(832\) | −1.66857e16 | + | 1.56751e14i | −1.45099 | + | 0.0136311i | ||||
\(833\) | 1.80820e16 | 1.56206 | ||||||||
\(834\) | −4.54834e14 | + | 1.22636e14i | −0.0390337 | + | 0.0105246i | ||||
\(835\) | 5.91354e15i | 0.504164i | ||||||||
\(836\) | 9.22226e15 | − | 5.36305e15i | 0.781093 | − | 0.454231i | ||||
\(837\) | 2.09846e16i | 1.76568i | ||||||||
\(838\) | 3.96701e15 | + | 1.47129e16i | 0.331605 | + | 1.22986i | ||||
\(839\) | 5.63944e15 | 0.468322 | 0.234161 | − | 0.972198i | \(-0.424766\pi\) | ||||
0.234161 | + | 0.972198i | \(0.424766\pi\) | |||||||
\(840\) | −2.26426e15 | + | 2.28563e15i | −0.186805 | + | 0.188569i | ||||
\(841\) | 9.86633e15 | 0.808682 | ||||||||
\(842\) | 1.42203e13 | + | 5.27403e13i | 0.00115795 | + | 0.00429463i | ||||
\(843\) | − | 3.23404e15i | − | 0.261634i | ||||||
\(844\) | −7.00837e14 | − | 1.20515e15i | −0.0563292 | − | 0.0968633i | ||||
\(845\) | − | 1.77084e16i | − | 1.41406i | ||||||
\(846\) | −7.68762e14 | + | 2.07280e14i | −0.0609895 | + | 0.0164445i | ||||
\(847\) | 1.20434e15 | 0.0949275 | ||||||||
\(848\) | −1.05271e16 | − | 5.99023e15i | −0.824388 | − | 0.469101i | ||||
\(849\) | −2.09217e16 | −1.62781 | ||||||||
\(850\) | 1.30929e16 | − | 3.53020e15i | 1.01212 | − | 0.272895i | ||||
\(851\) | − | 1.85621e15i | − | 0.142566i | ||||||
\(852\) | −1.42833e15 | − | 2.45614e15i | −0.108996 | − | 0.187428i | ||||
\(853\) | − | 2.66012e15i | − | 0.201689i | −0.994902 | − | 0.100844i | \(-0.967846\pi\) | ||
0.994902 | − | 0.100844i | \(-0.0321544\pi\) | |||||||
\(854\) | 6.77726e14 | + | 2.51356e15i | 0.0510547 | + | 0.189353i | ||||
\(855\) | 3.58229e15 | 0.268131 | ||||||||
\(856\) | −1.21517e15 | − | 1.20381e15i | −0.0903717 | − | 0.0895267i | ||||
\(857\) | 6.62417e15 | 0.489482 | 0.244741 | − | 0.969588i | \(-0.421297\pi\) | ||||
0.244741 | + | 0.969588i | \(0.421297\pi\) | |||||||
\(858\) | 3.56941e15 | + | 1.32383e16i | 0.262070 | + | 0.971967i | ||||
\(859\) | − | 2.28112e16i | − | 1.66412i | −0.554683 | − | 0.832062i | \(-0.687161\pi\) | ||
0.554683 | − | 0.832062i | \(-0.312839\pi\) | |||||||
\(860\) | −6.38629e15 | + | 3.71384e15i | −0.462922 | + | 0.269204i | ||||
\(861\) | − | 2.70472e15i | − | 0.194807i | ||||||
\(862\) | −8.21229e14 | + | 2.21426e14i | −0.0587725 | + | 0.0158467i | ||||
\(863\) | −2.00538e16 | −1.42606 | −0.713031 | − | 0.701133i | \(-0.752678\pi\) | ||||
−0.713031 | + | 0.701133i | \(0.752678\pi\) | |||||||
\(864\) | 1.46282e16 | + | 3.79714e15i | 1.03363 | + | 0.268307i | ||||
\(865\) | 2.63048e16 | 1.84691 | ||||||||
\(866\) | 1.37035e16 | − | 3.69484e15i | 0.956054 | − | 0.257779i | ||||
\(867\) | 2.24636e16i | 1.55731i | ||||||||
\(868\) | 4.74769e15 | − | 2.76094e15i | 0.327057 | − | 0.190195i | ||||
\(869\) | − | 1.06020e16i | − | 0.725736i | ||||||
\(870\) | 1.94186e15 | + | 7.20201e15i | 0.132088 | + | 0.489889i | ||||
\(871\) | −2.49026e16 | −1.68324 | ||||||||
\(872\) | −5.96260e13 | − | 5.90685e13i | −0.00400493 | − | 0.00396748i | ||||
\(873\) | −2.17131e15 | −0.144925 | ||||||||
\(874\) | −3.52336e15 | − | 1.30675e16i | −0.233692 | − | 0.866720i | ||||
\(875\) | 1.61658e15i | 0.106550i | ||||||||
\(876\) | −1.00895e15 | − | 1.73498e15i | −0.0660840 | − | 0.113638i | ||||
\(877\) | 2.76399e16i | 1.79903i | 0.436887 | + | 0.899516i | \(0.356081\pi\) | ||||
−0.436887 | + | 0.899516i | \(0.643919\pi\) | |||||||
\(878\) | 2.16377e16 | − | 5.83413e15i | 1.39956 | − | 0.377361i | ||||
\(879\) | 2.13731e16 | 1.37381 | ||||||||
\(880\) | −7.57521e15 | + | 1.33125e16i | −0.483883 | + | 0.850364i | ||||
\(881\) | −2.51486e16 | −1.59642 | −0.798208 | − | 0.602382i | \(-0.794218\pi\) | ||||
−0.798208 | + | 0.602382i | \(0.794218\pi\) | |||||||
\(882\) | −2.57405e15 | + | 6.94036e14i | −0.162383 | + | 0.0437829i | ||||
\(883\) | 1.31245e16i | 0.822810i | 0.911453 | + | 0.411405i | \(0.134962\pi\) | ||||
−0.911453 | + | 0.411405i | \(0.865038\pi\) | |||||||
\(884\) | 1.92993e16 | + | 3.31870e16i | 1.20242 | + | 2.06767i | ||||
\(885\) | − | 3.35882e16i | − | 2.07969i | ||||||
\(886\) | 3.53051e15 | + | 1.30940e16i | 0.217246 | + | 0.805726i | ||||
\(887\) | −5.71207e15 | −0.349312 | −0.174656 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174656 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(888\) | 1.97019e15 | − | 1.98878e15i | 0.119739 | − | 0.120869i | ||||
\(889\) | −5.49633e15 | −0.331981 | ||||||||
\(890\) | −2.11177e15 | − | 7.83218e15i | −0.126766 | − | 0.470151i | ||||
\(891\) | − | 1.01426e16i | − | 0.605096i | ||||||
\(892\) | −2.11460e15 | + | 1.22971e15i | −0.125378 | + | 0.0729116i | ||||
\(893\) | 7.13461e15i | 0.420424i | ||||||||
\(894\) | −1.91608e16 | + | 5.16628e15i | −1.12216 | + | 0.302567i | ||||
\(895\) | 7.77831e15 | 0.452750 | ||||||||
\(896\) | −1.06554e15 | − | 3.80917e15i | −0.0616420 | − | 0.220362i | ||||
\(897\) | 1.73943e16 | 1.00011 | ||||||||
\(898\) | 1.09208e16 | − | 2.94457e15i | 0.624075 | − | 0.168268i | ||||
\(899\) | − | 1.27333e16i | − | 0.723209i | ||||||
\(900\) | −1.72833e15 | + | 1.00508e15i | −0.0975649 | + | 0.0567372i | ||||
\(901\) | 2.78665e16i | 1.56349i | ||||||||
\(902\) | −3.35219e15 | − | 1.24327e16i | −0.186936 | − | 0.693310i | ||||
\(903\) | −1.56760e15 | −0.0868864 | ||||||||
\(904\) | 1.15992e16 | − | 1.17086e16i | 0.639000 | − | 0.645031i | ||||
\(905\) | −3.59913e16 | −1.97075 | ||||||||
\(906\) | 2.02891e15 | + | 7.52485e15i | 0.110423 | + | 0.409537i | ||||
\(907\) | − | 1.52922e16i | − | 0.827235i | −0.910451 | − | 0.413618i | \(-0.864265\pi\) | ||
0.910451 | − | 0.413618i | \(-0.135735\pi\) | |||||||
\(908\) | −5.17529e15 | − | 8.89938e15i | −0.278267 | − | 0.478506i | ||||
\(909\) | − | 9.43271e14i | − | 0.0504121i | ||||||
\(910\) | 7.71884e15 | − | 2.08121e15i | 0.410038 | − | 0.110558i | ||||
\(911\) | −5.29684e14 | −0.0279683 | −0.0139842 | − | 0.999902i | \(-0.504451\pi\) | ||||
−0.0139842 | + | 0.999902i | \(0.504451\pi\) | |||||||
\(912\) | 1.00948e16 | − | 1.77404e16i | 0.529820 | − | 0.931093i | ||||
\(913\) | −1.55468e16 | −0.811058 | ||||||||
\(914\) | −3.15729e16 | + | 8.51294e15i | −1.63723 | + | 0.441444i | ||||
\(915\) | − | 1.92881e16i | − | 0.994198i | ||||||
\(916\) | −2.95089e15 | − | 5.07433e15i | −0.151192 | − | 0.259988i | ||||
\(917\) | − | 2.27853e15i | − | 0.116044i | ||||||
\(918\) | −9.05193e15 | − | 3.35719e16i | −0.458254 | − | 1.69958i | ||||
\(919\) | 2.61618e16 | 1.31654 | 0.658268 | − | 0.752783i | \(-0.271289\pi\) | ||||
0.658268 | + | 0.752783i | \(0.271289\pi\) | |||||||
\(920\) | 1.38045e16 | + | 1.36754e16i | 0.690539 | + | 0.684082i | ||||
\(921\) | 1.33369e16 | 0.663173 | ||||||||
\(922\) | 3.17117e14 | + | 1.17613e15i | 0.0156747 | + | 0.0581346i | ||||
\(923\) | 7.06011e15i | 0.346898i | ||||||||
\(924\) | −2.80957e15 | + | 1.63386e15i | −0.137229 | + | 0.0798030i | ||||
\(925\) | 2.45709e15i | 0.119300i | ||||||||
\(926\) | −2.64848e15 | + | 7.14105e14i | −0.127831 | + | 0.0344669i | ||||
\(927\) | 1.40280e15 | 0.0673063 | ||||||||
\(928\) | −8.87631e15 | − | 2.30408e15i | −0.423369 | − | 0.109896i | ||||
\(929\) | −2.14173e16 | −1.01550 | −0.507749 | − | 0.861505i | \(-0.669522\pi\) | ||||
−0.507749 | + | 0.861505i | \(0.669522\pi\) | |||||||
\(930\) | −3.92881e16 | + | 1.05932e16i | −1.85185 | + | 0.499309i | ||||
\(931\) | 2.38889e16i | 1.11937i | ||||||||
\(932\) | −1.60369e16 | + | 9.32600e15i | −0.747022 | + | 0.434418i | ||||
\(933\) | − | 3.34916e16i | − | 1.55091i | ||||||
\(934\) | 3.50081e14 | + | 1.29838e15i | 0.0161161 | + | 0.0597717i | ||||
\(935\) | 3.52398e16 | 1.61276 | ||||||||
\(936\) | −4.02116e15 | − | 3.98356e15i | −0.182951 | − | 0.181240i | ||||
\(937\) | 1.84540e16 | 0.834685 | 0.417343 | − | 0.908749i | \(-0.362961\pi\) | ||||
0.417343 | + | 0.908749i | \(0.362961\pi\) | |||||||
\(938\) | −1.53673e15 | − | 5.69946e15i | −0.0691008 | − | 0.256282i | ||||
\(939\) | 3.61727e16i | 1.61704i | ||||||||
\(940\) | −5.14947e15 | − | 8.85499e15i | −0.228854 | − | 0.393536i | ||||
\(941\) | − | 1.10663e16i | − | 0.488946i | −0.969656 | − | 0.244473i | \(-0.921385\pi\) | ||
0.969656 | − | 0.244473i | \(-0.0786149\pi\) | |||||||
\(942\) | 1.49790e15 | − | 4.03877e14i | 0.0657967 | − | 0.0177406i | ||||
\(943\) | −1.63357e16 | −0.713385 | ||||||||
\(944\) | 3.58902e16 | + | 2.04226e16i | 1.55822 | + | 0.886675i | ||||
\(945\) | −7.24070e15 | −0.312540 | ||||||||
\(946\) | −7.20568e15 | + | 1.94285e15i | −0.309224 | + | 0.0833756i | ||||
\(947\) | − | 1.56625e16i | − | 0.668244i | −0.942530 | − | 0.334122i | \(-0.891560\pi\) | ||
0.942530 | − | 0.334122i | \(-0.108440\pi\) | |||||||
\(948\) | −1.01973e16 | − | 1.75352e16i | −0.432552 | − | 0.743814i | ||||
\(949\) | 4.98715e15i | 0.210324i | ||||||||
\(950\) | 4.66391e15 | + | 1.72976e16i | 0.195556 | + | 0.725279i | ||||
\(951\) | 2.84656e16 | 1.18666 | ||||||||
\(952\) | −6.40455e15 | + | 6.46500e15i | −0.265452 | + | 0.267957i | ||||
\(953\) | 2.46314e16 | 1.01503 | 0.507515 | − | 0.861643i | \(-0.330564\pi\) | ||||
0.507515 | + | 0.861643i | \(0.330564\pi\) | |||||||
\(954\) | −1.06959e15 | − | 3.96693e15i | −0.0438231 | − | 0.162532i | ||||
\(955\) | 4.61529e16i | 1.88010i | ||||||||
\(956\) | 2.63353e16 | − | 1.53149e16i | 1.06665 | − | 0.620290i | ||||
\(957\) | 7.53530e15i | 0.303448i | ||||||||
\(958\) | 5.28812e15 | − | 1.42583e15i | 0.211734 | − | 0.0570895i | ||||
\(959\) | 3.41188e15 | 0.135829 | ||||||||
\(960\) | 2.75295e14 | + | 2.93043e16i | 0.0108970 | + | 1.15995i | ||||
\(961\) | 4.40539e16 | 1.73383 | ||||||||
\(962\) | −6.71636e15 | + | 1.81092e15i | −0.262828 | + | 0.0708657i | ||||
\(963\) | − | 5.80226e14i | − | 0.0225763i | ||||||
\(964\) | 2.93590e15 | − | 1.70732e15i | 0.113584 | − | 0.0660529i | ||||
\(965\) | 2.34147e16i | 0.900717i | ||||||||
\(966\) | 1.07340e15 | + | 3.98102e15i | 0.0410568 | + | 0.152272i | ||||
\(967\) | 1.75674e16 | 0.668130 | 0.334065 | − | 0.942550i | \(-0.391579\pi\) | ||||
0.334065 | + | 0.942550i | \(0.391579\pi\) | |||||||
\(968\) | 7.72052e15 | − | 7.79339e15i | 0.291966 | − | 0.294721i | ||||
\(969\) | −4.69611e16 | −1.76586 | ||||||||
\(970\) | −7.27216e15 | − | 2.69711e16i | −0.271906 | − | 1.00845i | ||||
\(971\) | − | 1.47579e15i | − | 0.0548679i | −0.999624 | − | 0.0274339i | \(-0.991266\pi\) | ||
0.999624 | − | 0.0274339i | \(-0.00873359\pi\) | |||||||
\(972\) | 4.76589e15 | + | 8.19540e15i | 0.176189 | + | 0.302974i | ||||
\(973\) | 2.77472e14i | 0.0102000i | ||||||||
\(974\) | 2.62849e16 | − | 7.08715e15i | 0.960799 | − | 0.259058i | ||||
\(975\) | −2.30250e16 | −0.836902 | ||||||||
\(976\) | 2.06100e16 | + | 1.17277e16i | 0.744910 | + | 0.423876i | ||||
\(977\) | −3.43891e16 | −1.23595 | −0.617975 | − | 0.786198i | \(-0.712047\pi\) | ||||
−0.617975 | + | 0.786198i | \(0.712047\pi\) | |||||||
\(978\) | 5.76651e15 | − | 1.55481e15i | 0.206086 | − | 0.0555667i | ||||
\(979\) | − | 8.19463e15i | − | 0.291222i | ||||||
\(980\) | −1.72420e16 | − | 2.96492e16i | −0.609319 | − | 1.04778i | ||||
\(981\) | − | 2.84705e13i | − | 0.00100049i | ||||||
\(982\) | −1.03077e15 | − | 3.82294e15i | −0.0360204 | − | 0.133593i | ||||
\(983\) | −3.64560e16 | −1.26685 | −0.633424 | − | 0.773805i | \(-0.718351\pi\) | ||||
−0.633424 | + | 0.773805i | \(0.718351\pi\) | |||||||
\(984\) | −1.75024e16 | − | 1.73388e16i | −0.604819 | − | 0.599163i | ||||
\(985\) | −8.50317e15 | −0.292201 | ||||||||
\(986\) | 5.49264e15 | + | 2.03712e16i | 0.187697 | + | 0.696135i | ||||
\(987\) | − | 2.17357e15i | − | 0.0738634i | ||||||
\(988\) | −4.38448e16 | + | 2.54972e16i | −1.48168 | + | 0.861647i | ||||
\(989\) | 9.46782e15i | 0.318178i | ||||||||
\(990\) | −5.01655e15 | + | 1.35260e15i | −0.167653 | + | 0.0452040i | ||||
\(991\) | −1.42245e16 | −0.472750 | −0.236375 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236375 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(992\) | 1.25691e16 | − | 4.84217e16i | 0.415423 | − | 1.60039i | ||||
\(993\) | 3.45687e16 | 1.13622 | ||||||||
\(994\) | −1.61585e15 | + | 4.35677e14i | −0.0528171 | + | 0.0142410i | ||||
\(995\) | − | 6.56789e16i | − | 2.13500i | ||||||
\(996\) | −2.57137e16 | + | 1.49533e16i | −0.831261 | + | 0.483406i | ||||
\(997\) | − | 6.02174e16i | − | 1.93597i | −0.251009 | − | 0.967985i | \(-0.580762\pi\) | ||
0.251009 | − | 0.967985i | \(-0.419238\pi\) | |||||||
\(998\) | 1.06014e16 | + | 3.93185e16i | 0.338957 | + | 1.25713i | ||||
\(999\) | 6.30032e15 | 0.200333 |
(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 | 8.12.b.a.5.9 | ✓ | 10 | |
3.2 | odd | 2 | 72.12.d.b.37.2 | 10 | |||
4.3 | odd | 2 | 32.12.b.a.17.3 | 10 | |||
8.3 | odd | 2 | 32.12.b.a.17.8 | 10 | |||
8.5 | even | 2 | inner | 8.12.b.a.5.10 | yes | 10 | |
16.3 | odd | 4 | 256.12.a.o.1.8 | 10 | |||
16.5 | even | 4 | 256.12.a.p.1.8 | 10 | |||
16.11 | odd | 4 | 256.12.a.o.1.3 | 10 | |||
16.13 | even | 4 | 256.12.a.p.1.3 | 10 | |||
24.5 | odd | 2 | 72.12.d.b.37.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.12.b.a.5.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8.12.b.a.5.10 | yes | 10 | 8.5 | even | 2 | inner | |
32.12.b.a.17.3 | 10 | 4.3 | odd | 2 | |||
32.12.b.a.17.8 | 10 | 8.3 | odd | 2 | |||
72.12.d.b.37.1 | 10 | 24.5 | odd | 2 | |||
72.12.d.b.37.2 | 10 | 3.2 | odd | 2 | |||
256.12.a.o.1.3 | 10 | 16.11 | odd | 4 | |||
256.12.a.o.1.8 | 10 | 16.3 | odd | 4 | |||
256.12.a.p.1.3 | 10 | 16.13 | even | 4 | |||
256.12.a.p.1.8 | 10 | 16.5 | even | 4 |