Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.a (trivial) |
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: | yes |
Analytic conductor: | \(211.244930035\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −145.155 | −1.60375 | −0.801877 | − | 0.597490i | \(-0.796165\pi\) | ||||
−0.801877 | + | 0.597490i | \(0.796165\pi\) | |||||||
\(3\) | −2025.07 | −1.60381 | −0.801903 | − | 0.597455i | \(-0.796179\pi\) | ||||
−0.801903 | + | 0.597455i | \(0.796179\pi\) | |||||||
\(4\) | 12878.0 | 1.57202 | ||||||||
\(5\) | −10162.8 | −0.290876 | −0.145438 | − | 0.989367i | \(-0.546459\pi\) | ||||
−0.145438 | + | 0.989367i | \(0.546459\pi\) | |||||||
\(6\) | 293949. | 2.57211 | ||||||||
\(7\) | 345875. | 1.11117 | 0.555587 | − | 0.831459i | \(-0.312494\pi\) | ||||
0.555587 | + | 0.831459i | \(0.312494\pi\) | |||||||
\(8\) | −680200. | −0.917385 | ||||||||
\(9\) | 2.50658e6 | 1.57219 | ||||||||
\(10\) | 1.47518e6 | 0.466494 | ||||||||
\(11\) | 1.29462e6 | 0.220338 | 0.110169 | − | 0.993913i | \(-0.464861\pi\) | ||||
0.110169 | + | 0.993913i | \(0.464861\pi\) | |||||||
\(12\) | −2.60789e7 | −2.52122 | ||||||||
\(13\) | −2.93098e7 | −1.68415 | −0.842077 | − | 0.539358i | \(-0.818667\pi\) | ||||
−0.842077 | + | 0.539358i | \(0.818667\pi\) | |||||||
\(14\) | −5.02055e7 | −1.78205 | ||||||||
\(15\) | 2.05804e7 | 0.466509 | ||||||||
\(16\) | −6.76221e6 | −0.100765 | ||||||||
\(17\) | −7.66490e7 | −0.770173 | −0.385087 | − | 0.922880i | \(-0.625828\pi\) | ||||
−0.385087 | + | 0.922880i | \(0.625828\pi\) | |||||||
\(18\) | −3.63843e8 | −2.52141 | ||||||||
\(19\) | 1.13939e8 | 0.555614 | 0.277807 | − | 0.960637i | \(-0.410392\pi\) | ||||
0.277807 | + | 0.960637i | \(0.410392\pi\) | |||||||
\(20\) | −1.30877e8 | −0.457265 | ||||||||
\(21\) | −7.00421e8 | −1.78211 | ||||||||
\(22\) | −1.87921e8 | −0.353368 | ||||||||
\(23\) | −9.76784e8 | −1.37584 | −0.687920 | − | 0.725787i | \(-0.741476\pi\) | ||||
−0.687920 | + | 0.725787i | \(0.741476\pi\) | |||||||
\(24\) | 1.37745e9 | 1.47131 | ||||||||
\(25\) | −1.11742e9 | −0.915391 | ||||||||
\(26\) | 4.25447e9 | 2.70097 | ||||||||
\(27\) | −1.84739e9 | −0.917685 | ||||||||
\(28\) | 4.45418e9 | 1.74679 | ||||||||
\(29\) | 4.14550e9 | 1.29417 | 0.647083 | − | 0.762420i | \(-0.275989\pi\) | ||||
0.647083 | + | 0.762420i | \(0.275989\pi\) | |||||||
\(30\) | −2.98735e9 | −0.748165 | ||||||||
\(31\) | −5.83659e9 | −1.18116 | −0.590579 | − | 0.806980i | \(-0.701101\pi\) | ||||
−0.590579 | + | 0.806980i | \(0.701101\pi\) | |||||||
\(32\) | 6.55377e9 | 1.07899 | ||||||||
\(33\) | −2.62170e9 | −0.353380 | ||||||||
\(34\) | 1.11260e10 | 1.23517 | ||||||||
\(35\) | −3.51506e9 | −0.323214 | ||||||||
\(36\) | 3.22798e10 | 2.47152 | ||||||||
\(37\) | 3.87665e9 | 0.248396 | 0.124198 | − | 0.992257i | \(-0.460364\pi\) | ||||
0.124198 | + | 0.992257i | \(0.460364\pi\) | |||||||
\(38\) | −1.65388e10 | −0.891068 | ||||||||
\(39\) | 5.93545e10 | 2.70105 | ||||||||
\(40\) | 6.91274e9 | 0.266846 | ||||||||
\(41\) | −3.31987e10 | −1.09151 | −0.545753 | − | 0.837946i | \(-0.683756\pi\) | ||||
−0.545753 | + | 0.837946i | \(0.683756\pi\) | |||||||
\(42\) | 1.01670e11 | 2.85806 | ||||||||
\(43\) | −4.34571e10 | −1.04837 | −0.524186 | − | 0.851604i | \(-0.675631\pi\) | ||||
−0.524186 | + | 0.851604i | \(0.675631\pi\) | |||||||
\(44\) | 1.66722e10 | 0.346377 | ||||||||
\(45\) | −2.54739e10 | −0.457313 | ||||||||
\(46\) | 1.41785e11 | 2.20651 | ||||||||
\(47\) | 1.16895e11 | 1.58183 | 0.790916 | − | 0.611925i | \(-0.209605\pi\) | ||||
0.790916 | + | 0.611925i | \(0.209605\pi\) | |||||||
\(48\) | 1.36939e10 | 0.161607 | ||||||||
\(49\) | 2.27405e10 | 0.234707 | ||||||||
\(50\) | 1.62199e11 | 1.46806 | ||||||||
\(51\) | 1.55219e11 | 1.23521 | ||||||||
\(52\) | −3.77453e11 | −2.64753 | ||||||||
\(53\) | 3.23420e10 | 0.200435 | 0.100218 | − | 0.994966i | \(-0.468046\pi\) | ||||
0.100218 | + | 0.994966i | \(0.468046\pi\) | |||||||
\(54\) | 2.68158e11 | 1.47174 | ||||||||
\(55\) | −1.31570e10 | −0.0640912 | ||||||||
\(56\) | −2.35264e11 | −1.01937 | ||||||||
\(57\) | −2.30734e11 | −0.891098 | ||||||||
\(58\) | −6.01741e11 | −2.07552 | ||||||||
\(59\) | −4.58259e11 | −1.41440 | −0.707202 | − | 0.707012i | \(-0.750043\pi\) | ||||
−0.707202 | + | 0.707012i | \(0.750043\pi\) | |||||||
\(60\) | 2.65034e11 | 0.733363 | ||||||||
\(61\) | −7.04452e11 | −1.75068 | −0.875342 | − | 0.483505i | \(-0.839364\pi\) | ||||
−0.875342 | + | 0.483505i | \(0.839364\pi\) | |||||||
\(62\) | 8.47211e11 | 1.89429 | ||||||||
\(63\) | 8.66964e11 | 1.74698 | ||||||||
\(64\) | −8.95917e11 | −1.62966 | ||||||||
\(65\) | 2.97870e11 | 0.489880 | ||||||||
\(66\) | 3.80553e11 | 0.566734 | ||||||||
\(67\) | 7.66795e11 | 1.03560 | 0.517801 | − | 0.855501i | \(-0.326751\pi\) | ||||
0.517801 | + | 0.855501i | \(0.326751\pi\) | |||||||
\(68\) | −9.87087e11 | −1.21073 | ||||||||
\(69\) | 1.97806e12 | 2.20658 | ||||||||
\(70\) | 5.10229e11 | 0.518356 | ||||||||
\(71\) | −1.10301e12 | −1.02188 | −0.510939 | − | 0.859617i | \(-0.670702\pi\) | ||||
−0.510939 | + | 0.859617i | \(0.670702\pi\) | |||||||
\(72\) | −1.70498e12 | −1.44231 | ||||||||
\(73\) | 2.36793e12 | 1.83135 | 0.915674 | − | 0.401921i | \(-0.131657\pi\) | ||||
0.915674 | + | 0.401921i | \(0.131657\pi\) | |||||||
\(74\) | −5.62715e11 | −0.398366 | ||||||||
\(75\) | 2.26285e12 | 1.46811 | ||||||||
\(76\) | 1.46731e12 | 0.873439 | ||||||||
\(77\) | 4.47777e11 | 0.244834 | ||||||||
\(78\) | −8.61560e12 | −4.33182 | ||||||||
\(79\) | 7.79158e11 | 0.360620 | 0.180310 | − | 0.983610i | \(-0.442290\pi\) | ||||
0.180310 | + | 0.983610i | \(0.442290\pi\) | |||||||
\(80\) | 6.87229e10 | 0.0293101 | ||||||||
\(81\) | −2.55213e11 | −0.100404 | ||||||||
\(82\) | 4.81896e12 | 1.75050 | ||||||||
\(83\) | −6.47070e11 | −0.217242 | −0.108621 | − | 0.994083i | \(-0.534643\pi\) | ||||
−0.108621 | + | 0.994083i | \(0.534643\pi\) | |||||||
\(84\) | −9.02003e12 | −2.80151 | ||||||||
\(85\) | 7.78968e11 | 0.224025 | ||||||||
\(86\) | 6.30802e12 | 1.68133 | ||||||||
\(87\) | −8.39492e12 | −2.07559 | ||||||||
\(88\) | −8.80601e11 | −0.202135 | ||||||||
\(89\) | 1.00322e12 | 0.213974 | 0.106987 | − | 0.994260i | \(-0.465880\pi\) | ||||
0.106987 | + | 0.994260i | \(0.465880\pi\) | |||||||
\(90\) | 3.69767e12 | 0.733418 | ||||||||
\(91\) | −1.01375e13 | −1.87139 | ||||||||
\(92\) | −1.25790e13 | −2.16285 | ||||||||
\(93\) | 1.18195e13 | 1.89435 | ||||||||
\(94\) | −1.69679e13 | −2.53687 | ||||||||
\(95\) | −1.15794e12 | −0.161615 | ||||||||
\(96\) | −1.32718e13 | −1.73049 | ||||||||
\(97\) | 1.52626e13 | 1.86043 | 0.930213 | − | 0.367020i | \(-0.119622\pi\) | ||||
0.930213 | + | 0.367020i | \(0.119622\pi\) | |||||||
\(98\) | −3.30090e12 | −0.376411 | ||||||||
\(99\) | 3.24507e12 | 0.346414 | ||||||||
\(100\) | −1.43902e13 | −1.43902 | ||||||||
\(101\) | −1.76318e13 | −1.65275 | −0.826374 | − | 0.563121i | \(-0.809600\pi\) | ||||
−0.826374 | + | 0.563121i | \(0.809600\pi\) | |||||||
\(102\) | −2.25309e13 | −1.98097 | ||||||||
\(103\) | −4.93405e12 | −0.407157 | −0.203578 | − | 0.979059i | \(-0.565257\pi\) | ||||
−0.203578 | + | 0.979059i | \(0.565257\pi\) | |||||||
\(104\) | 1.99366e13 | 1.54502 | ||||||||
\(105\) | 7.11824e12 | 0.518372 | ||||||||
\(106\) | −4.69461e12 | −0.321448 | ||||||||
\(107\) | −2.84116e13 | −1.83021 | −0.915105 | − | 0.403216i | \(-0.867892\pi\) | ||||
−0.915105 | + | 0.403216i | \(0.867892\pi\) | |||||||
\(108\) | −2.37907e13 | −1.44262 | ||||||||
\(109\) | −1.38782e13 | −0.792614 | −0.396307 | − | 0.918118i | \(-0.629708\pi\) | ||||
−0.396307 | + | 0.918118i | \(0.629708\pi\) | |||||||
\(110\) | 1.90980e12 | 0.102787 | ||||||||
\(111\) | −7.85048e12 | −0.398379 | ||||||||
\(112\) | −2.33888e12 | −0.111967 | ||||||||
\(113\) | 1.35222e13 | 0.610993 | 0.305497 | − | 0.952193i | \(-0.401178\pi\) | ||||
0.305497 | + | 0.952193i | \(0.401178\pi\) | |||||||
\(114\) | 3.34922e13 | 1.42910 | ||||||||
\(115\) | 9.92686e12 | 0.400199 | ||||||||
\(116\) | 5.33858e13 | 2.03446 | ||||||||
\(117\) | −7.34675e13 | −2.64781 | ||||||||
\(118\) | 6.65187e13 | 2.26835 | ||||||||
\(119\) | −2.65110e13 | −0.855796 | ||||||||
\(120\) | −1.39988e13 | −0.427968 | ||||||||
\(121\) | −3.28467e13 | −0.951451 | ||||||||
\(122\) | 1.02255e14 | 2.80766 | ||||||||
\(123\) | 6.72296e13 | 1.75056 | ||||||||
\(124\) | −7.51637e13 | −1.85681 | ||||||||
\(125\) | 2.37619e13 | 0.557142 | ||||||||
\(126\) | −1.25844e14 | −2.80172 | ||||||||
\(127\) | −5.73033e13 | −1.21187 | −0.605934 | − | 0.795515i | \(-0.707201\pi\) | ||||
−0.605934 | + | 0.795515i | \(0.707201\pi\) | |||||||
\(128\) | 7.63585e13 | 1.53459 | ||||||||
\(129\) | 8.80036e13 | 1.68139 | ||||||||
\(130\) | −4.32374e13 | −0.785647 | ||||||||
\(131\) | −1.03566e13 | −0.179041 | −0.0895205 | − | 0.995985i | \(-0.528533\pi\) | ||||
−0.0895205 | + | 0.995985i | \(0.528533\pi\) | |||||||
\(132\) | −3.37623e13 | −0.555522 | ||||||||
\(133\) | 3.94086e13 | 0.617384 | ||||||||
\(134\) | −1.11304e14 | −1.66085 | ||||||||
\(135\) | 1.87746e13 | 0.266933 | ||||||||
\(136\) | 5.21366e13 | 0.706545 | ||||||||
\(137\) | −5.90787e13 | −0.763392 | −0.381696 | − | 0.924288i | \(-0.624660\pi\) | ||||
−0.381696 | + | 0.924288i | \(0.624660\pi\) | |||||||
\(138\) | −2.87125e14 | −3.53881 | ||||||||
\(139\) | 8.92735e13 | 1.04985 | 0.524924 | − | 0.851149i | \(-0.324094\pi\) | ||||
0.524924 | + | 0.851149i | \(0.324094\pi\) | |||||||
\(140\) | −4.52670e13 | −0.508100 | ||||||||
\(141\) | −2.36721e14 | −2.53695 | ||||||||
\(142\) | 1.60107e14 | 1.63884 | ||||||||
\(143\) | −3.79451e13 | −0.371084 | ||||||||
\(144\) | −1.69500e13 | −0.158422 | ||||||||
\(145\) | −4.21299e13 | −0.376442 | ||||||||
\(146\) | −3.43718e14 | −2.93703 | ||||||||
\(147\) | −4.60511e13 | −0.376424 | ||||||||
\(148\) | 4.99235e13 | 0.390485 | ||||||||
\(149\) | −3.00467e13 | −0.224950 | −0.112475 | − | 0.993655i | \(-0.535878\pi\) | ||||
−0.112475 | + | 0.993655i | \(0.535878\pi\) | |||||||
\(150\) | −3.28465e14 | −2.35448 | ||||||||
\(151\) | −1.09032e14 | −0.748521 | −0.374260 | − | 0.927324i | \(-0.622103\pi\) | ||||
−0.374260 | + | 0.927324i | \(0.622103\pi\) | |||||||
\(152\) | −7.75012e13 | −0.509712 | ||||||||
\(153\) | −1.92127e14 | −1.21086 | ||||||||
\(154\) | −6.49972e13 | −0.392654 | ||||||||
\(155\) | 5.93161e13 | 0.343571 | ||||||||
\(156\) | 7.64368e14 | 4.24612 | ||||||||
\(157\) | 2.21346e14 | 1.17957 | 0.589784 | − | 0.807561i | \(-0.299213\pi\) | ||||
0.589784 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(158\) | −1.13099e14 | −0.578345 | ||||||||
\(159\) | −6.54948e13 | −0.321459 | ||||||||
\(160\) | −6.66046e13 | −0.313852 | ||||||||
\(161\) | −3.37845e14 | −1.52880 | ||||||||
\(162\) | 3.70455e13 | 0.161023 | ||||||||
\(163\) | 2.75363e14 | 1.14997 | 0.574985 | − | 0.818164i | \(-0.305008\pi\) | ||||
0.574985 | + | 0.818164i | \(0.305008\pi\) | |||||||
\(164\) | −4.27533e14 | −1.71587 | ||||||||
\(165\) | 2.66438e13 | 0.102790 | ||||||||
\(166\) | 9.39255e13 | 0.348402 | ||||||||
\(167\) | −4.51190e14 | −1.60954 | −0.804771 | − | 0.593586i | \(-0.797712\pi\) | ||||
−0.804771 | + | 0.593586i | \(0.797712\pi\) | |||||||
\(168\) | 4.76426e14 | 1.63488 | ||||||||
\(169\) | 5.56192e14 | 1.83637 | ||||||||
\(170\) | −1.13071e14 | −0.359281 | ||||||||
\(171\) | 2.85597e14 | 0.873533 | ||||||||
\(172\) | −5.59641e14 | −1.64807 | ||||||||
\(173\) | −3.30467e14 | −0.937193 | −0.468596 | − | 0.883412i | \(-0.655240\pi\) | ||||
−0.468596 | + | 0.883412i | \(0.655240\pi\) | |||||||
\(174\) | 1.21857e15 | 3.32873 | ||||||||
\(175\) | −3.86488e14 | −1.01716 | ||||||||
\(176\) | −8.75450e12 | −0.0222023 | ||||||||
\(177\) | 9.28007e14 | 2.26843 | ||||||||
\(178\) | −1.45622e14 | −0.343161 | ||||||||
\(179\) | −4.56742e13 | −0.103783 | −0.0518915 | − | 0.998653i | \(-0.516525\pi\) | ||||
−0.0518915 | + | 0.998653i | \(0.516525\pi\) | |||||||
\(180\) | −3.28053e14 | −0.718908 | ||||||||
\(181\) | −6.46033e14 | −1.36567 | −0.682833 | − | 0.730575i | \(-0.739252\pi\) | ||||
−0.682833 | + | 0.730575i | \(0.739252\pi\) | |||||||
\(182\) | 1.47152e15 | 3.00124 | ||||||||
\(183\) | 1.42656e15 | 2.80776 | ||||||||
\(184\) | 6.64409e14 | 1.26217 | ||||||||
\(185\) | −3.93976e13 | −0.0722526 | ||||||||
\(186\) | −1.71566e15 | −3.03807 | ||||||||
\(187\) | −9.92314e13 | −0.169699 | ||||||||
\(188\) | 1.50538e15 | 2.48668 | ||||||||
\(189\) | −6.38965e14 | −1.01971 | ||||||||
\(190\) | 1.68081e14 | 0.259191 | ||||||||
\(191\) | 5.19900e14 | 0.774825 | 0.387412 | − | 0.921907i | \(-0.373369\pi\) | ||||
0.387412 | + | 0.921907i | \(0.373369\pi\) | |||||||
\(192\) | 1.81429e15 | 2.61366 | ||||||||
\(193\) | 5.43076e14 | 0.756376 | 0.378188 | − | 0.925729i | \(-0.376547\pi\) | ||||
0.378188 | + | 0.925729i | \(0.376547\pi\) | |||||||
\(194\) | −2.21545e15 | −2.98366 | ||||||||
\(195\) | −6.03207e14 | −0.785673 | ||||||||
\(196\) | 2.92852e14 | 0.368964 | ||||||||
\(197\) | 5.84517e13 | 0.0712470 | ||||||||
\(198\) | −4.71039e14 | −0.555563 | ||||||||
\(199\) | −5.89769e14 | −0.673189 | −0.336594 | − | 0.941650i | \(-0.609275\pi\) | ||||
−0.336594 | + | 0.941650i | \(0.609275\pi\) | |||||||
\(200\) | 7.60069e14 | 0.839766 | ||||||||
\(201\) | −1.55281e15 | −1.66091 | ||||||||
\(202\) | 2.55934e15 | 2.65060 | ||||||||
\(203\) | 1.43382e15 | 1.43804 | ||||||||
\(204\) | 1.99892e15 | 1.94178 | ||||||||
\(205\) | 3.37392e14 | 0.317493 | ||||||||
\(206\) | 7.16203e14 | 0.652979 | ||||||||
\(207\) | −2.44839e15 | −2.16308 | ||||||||
\(208\) | 1.98199e14 | 0.169703 | ||||||||
\(209\) | 1.47508e14 | 0.122423 | ||||||||
\(210\) | −1.03325e15 | −0.831341 | ||||||||
\(211\) | 7.79987e14 | 0.608487 | 0.304244 | − | 0.952594i | \(-0.401596\pi\) | ||||
0.304244 | + | 0.952594i | \(0.401596\pi\) | |||||||
\(212\) | 4.16501e14 | 0.315089 | ||||||||
\(213\) | 2.23367e15 | 1.63889 | ||||||||
\(214\) | 4.12409e15 | 2.93520 | ||||||||
\(215\) | 4.41646e14 | 0.304947 | ||||||||
\(216\) | 1.25659e15 | 0.841871 | ||||||||
\(217\) | −2.01873e15 | −1.31247 | ||||||||
\(218\) | 2.01450e15 | 1.27116 | ||||||||
\(219\) | −4.79523e15 | −2.93713 | ||||||||
\(220\) | −1.69436e14 | −0.100753 | ||||||||
\(221\) | 2.24657e15 | 1.29709 | ||||||||
\(222\) | 1.13954e15 | 0.638902 | ||||||||
\(223\) | 1.43792e15 | 0.782985 | 0.391493 | − | 0.920181i | \(-0.371959\pi\) | ||||
0.391493 | + | 0.920181i | \(0.371959\pi\) | |||||||
\(224\) | 2.26678e15 | 1.19894 | ||||||||
\(225\) | −2.80091e15 | −1.43917 | ||||||||
\(226\) | −1.96281e15 | −0.979882 | ||||||||
\(227\) | −3.72324e15 | −1.80615 | −0.903073 | − | 0.429486i | \(-0.858695\pi\) | ||||
−0.903073 | + | 0.429486i | \(0.858695\pi\) | |||||||
\(228\) | −2.97140e15 | −1.40083 | ||||||||
\(229\) | −2.18510e15 | −1.00125 | −0.500623 | − | 0.865666i | \(-0.666896\pi\) | ||||
−0.500623 | + | 0.865666i | \(0.666896\pi\) | |||||||
\(230\) | −1.44094e15 | −0.641821 | ||||||||
\(231\) | −9.06780e14 | −0.392667 | ||||||||
\(232\) | −2.81977e15 | −1.18725 | ||||||||
\(233\) | −2.22110e15 | −0.909401 | −0.454700 | − | 0.890645i | \(-0.650254\pi\) | ||||
−0.454700 | + | 0.890645i | \(0.650254\pi\) | |||||||
\(234\) | 1.06642e16 | 4.24644 | ||||||||
\(235\) | −1.18798e15 | −0.460117 | ||||||||
\(236\) | −5.90147e15 | −2.22348 | ||||||||
\(237\) | −1.57785e15 | −0.578364 | ||||||||
\(238\) | 3.84820e15 | 1.37249 | ||||||||
\(239\) | −4.73143e15 | −1.64212 | −0.821062 | − | 0.570838i | \(-0.806618\pi\) | ||||
−0.821062 | + | 0.570838i | \(0.806618\pi\) | |||||||
\(240\) | −1.39169e14 | −0.0470077 | ||||||||
\(241\) | 1.43724e15 | 0.472519 | 0.236259 | − | 0.971690i | \(-0.424078\pi\) | ||||
0.236259 | + | 0.971690i | \(0.424078\pi\) | |||||||
\(242\) | 4.76786e15 | 1.52589 | ||||||||
\(243\) | 3.46216e15 | 1.07871 | ||||||||
\(244\) | −9.07195e15 | −2.75212 | ||||||||
\(245\) | −2.31107e14 | −0.0682706 | ||||||||
\(246\) | −9.75873e15 | −2.80747 | ||||||||
\(247\) | −3.33953e15 | −0.935740 | ||||||||
\(248\) | 3.97005e15 | 1.08358 | ||||||||
\(249\) | 1.31036e15 | 0.348414 | ||||||||
\(250\) | −3.44916e15 | −0.893518 | ||||||||
\(251\) | 1.08501e15 | 0.273875 | 0.136938 | − | 0.990580i | \(-0.456274\pi\) | ||||
0.136938 | + | 0.990580i | \(0.456274\pi\) | |||||||
\(252\) | 1.11648e16 | 2.74629 | ||||||||
\(253\) | −1.26457e15 | −0.303150 | ||||||||
\(254\) | 8.31787e15 | 1.94354 | ||||||||
\(255\) | −1.57746e15 | −0.359293 | ||||||||
\(256\) | −3.74448e15 | −0.831442 | ||||||||
\(257\) | 4.84146e15 | 1.04812 | 0.524060 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524060 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(258\) | −1.27742e16 | −2.69653 | ||||||||
\(259\) | 1.34083e15 | 0.276011 | ||||||||
\(260\) | 3.83598e15 | 0.770104 | ||||||||
\(261\) | 1.03910e16 | 2.03468 | ||||||||
\(262\) | 1.50331e15 | 0.287138 | ||||||||
\(263\) | −4.14252e15 | −0.771885 | −0.385942 | − | 0.922523i | \(-0.626124\pi\) | ||||
−0.385942 | + | 0.922523i | \(0.626124\pi\) | |||||||
\(264\) | 1.78328e15 | 0.324186 | ||||||||
\(265\) | −3.28685e14 | −0.0583018 | ||||||||
\(266\) | −5.72036e15 | −0.990132 | ||||||||
\(267\) | −2.03159e15 | −0.343172 | ||||||||
\(268\) | 9.87480e15 | 1.62799 | ||||||||
\(269\) | 8.88717e15 | 1.43012 | 0.715062 | − | 0.699061i | \(-0.246399\pi\) | ||||
0.715062 | + | 0.699061i | \(0.246399\pi\) | |||||||
\(270\) | −2.72524e15 | −0.428094 | ||||||||
\(271\) | 5.37246e15 | 0.823896 | 0.411948 | − | 0.911207i | \(-0.364848\pi\) | ||||
0.411948 | + | 0.911207i | \(0.364848\pi\) | |||||||
\(272\) | 5.18316e14 | 0.0776063 | ||||||||
\(273\) | 2.05292e16 | 3.00134 | ||||||||
\(274\) | 8.57558e15 | 1.22429 | ||||||||
\(275\) | −1.44664e15 | −0.201696 | ||||||||
\(276\) | 2.54734e16 | 3.46879 | ||||||||
\(277\) | 9.67553e15 | 1.28693 | 0.643467 | − | 0.765474i | \(-0.277495\pi\) | ||||
0.643467 | + | 0.765474i | \(0.277495\pi\) | |||||||
\(278\) | −1.29585e16 | −1.68370 | ||||||||
\(279\) | −1.46299e16 | −1.85701 | ||||||||
\(280\) | 2.39094e15 | 0.296512 | ||||||||
\(281\) | −9.60785e15 | −1.16422 | −0.582110 | − | 0.813110i | \(-0.697773\pi\) | ||||
−0.582110 | + | 0.813110i | \(0.697773\pi\) | |||||||
\(282\) | 3.43612e16 | 4.06864 | ||||||||
\(283\) | −1.56977e16 | −1.81645 | −0.908225 | − | 0.418482i | \(-0.862562\pi\) | ||||
−0.908225 | + | 0.418482i | \(0.862562\pi\) | |||||||
\(284\) | −1.42045e16 | −1.60642 | ||||||||
\(285\) | 2.34490e15 | 0.259199 | ||||||||
\(286\) | 5.50793e15 | 0.595127 | ||||||||
\(287\) | −1.14826e16 | −1.21285 | ||||||||
\(288\) | 1.64276e16 | 1.69637 | ||||||||
\(289\) | −4.02951e15 | −0.406833 | ||||||||
\(290\) | 6.11537e15 | 0.603720 | ||||||||
\(291\) | −3.09078e16 | −2.98376 | ||||||||
\(292\) | 3.04943e16 | 2.87892 | ||||||||
\(293\) | 8.90199e14 | 0.0821954 | 0.0410977 | − | 0.999155i | \(-0.486915\pi\) | ||||
0.0410977 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(294\) | 6.68455e15 | 0.603691 | ||||||||
\(295\) | 4.65720e15 | 0.411417 | ||||||||
\(296\) | −2.63689e15 | −0.227875 | ||||||||
\(297\) | −2.39167e15 | −0.202201 | ||||||||
\(298\) | 4.36143e15 | 0.360764 | ||||||||
\(299\) | 2.86294e16 | 2.31712 | ||||||||
\(300\) | 2.91411e16 | 2.30790 | ||||||||
\(301\) | −1.50307e16 | −1.16492 | ||||||||
\(302\) | 1.58266e16 | 1.20044 | ||||||||
\(303\) | 3.57055e16 | 2.65069 | ||||||||
\(304\) | −7.70478e14 | −0.0559863 | ||||||||
\(305\) | 7.15921e15 | 0.509232 | ||||||||
\(306\) | 2.78882e16 | 1.94192 | ||||||||
\(307\) | 1.77890e16 | 1.21270 | 0.606348 | − | 0.795200i | \(-0.292634\pi\) | ||||
0.606348 | + | 0.795200i | \(0.292634\pi\) | |||||||
\(308\) | 5.76648e15 | 0.384885 | ||||||||
\(309\) | 9.99179e15 | 0.653000 | ||||||||
\(310\) | −8.61004e15 | −0.551003 | ||||||||
\(311\) | −4.48278e15 | −0.280934 | −0.140467 | − | 0.990085i | \(-0.544860\pi\) | ||||
−0.140467 | + | 0.990085i | \(0.544860\pi\) | |||||||
\(312\) | −4.03729e16 | −2.47791 | ||||||||
\(313\) | −1.49198e16 | −0.896862 | −0.448431 | − | 0.893817i | \(-0.648017\pi\) | ||||
−0.448431 | + | 0.893817i | \(0.648017\pi\) | |||||||
\(314\) | −3.21294e16 | −1.89174 | ||||||||
\(315\) | −8.81078e15 | −0.508155 | ||||||||
\(316\) | 1.00340e16 | 0.566903 | ||||||||
\(317\) | −1.64023e16 | −0.907859 | −0.453930 | − | 0.891038i | \(-0.649978\pi\) | ||||
−0.453930 | + | 0.891038i | \(0.649978\pi\) | |||||||
\(318\) | 9.50691e15 | 0.515541 | ||||||||
\(319\) | 5.36685e15 | 0.285154 | ||||||||
\(320\) | 9.10503e15 | 0.474031 | ||||||||
\(321\) | 5.75354e16 | 2.93530 | ||||||||
\(322\) | 4.90400e16 | 2.45181 | ||||||||
\(323\) | −8.73330e15 | −0.427919 | ||||||||
\(324\) | −3.28664e15 | −0.157837 | ||||||||
\(325\) | 3.27514e16 | 1.54166 | ||||||||
\(326\) | −3.99704e16 | −1.84427 | ||||||||
\(327\) | 2.81044e16 | 1.27120 | ||||||||
\(328\) | 2.25817e16 | 1.00133 | ||||||||
\(329\) | 4.04311e16 | 1.75769 | ||||||||
\(330\) | −3.86748e15 | −0.164850 | ||||||||
\(331\) | −4.04451e16 | −1.69038 | −0.845188 | − | 0.534469i | \(-0.820512\pi\) | ||||
−0.845188 | + | 0.534469i | \(0.820512\pi\) | |||||||
\(332\) | −8.33298e15 | −0.341509 | ||||||||
\(333\) | 9.71713e15 | 0.390527 | ||||||||
\(334\) | 6.54925e16 | 2.58131 | ||||||||
\(335\) | −7.79279e15 | −0.301232 | ||||||||
\(336\) | 4.73639e15 | 0.179573 | ||||||||
\(337\) | −3.09233e16 | −1.14998 | −0.574991 | − | 0.818160i | \(-0.694994\pi\) | ||||
−0.574991 | + | 0.818160i | \(0.694994\pi\) | |||||||
\(338\) | −8.07341e16 | −2.94509 | ||||||||
\(339\) | −2.73833e16 | −0.979914 | ||||||||
\(340\) | 1.00316e16 | 0.352173 | ||||||||
\(341\) | −7.55617e15 | −0.260255 | ||||||||
\(342\) | −4.14559e16 | −1.40093 | ||||||||
\(343\) | −2.56461e16 | −0.850374 | ||||||||
\(344\) | 2.95595e16 | 0.961762 | ||||||||
\(345\) | −2.01026e16 | −0.641842 | ||||||||
\(346\) | 4.79690e16 | 1.50303 | ||||||||
\(347\) | −4.75672e16 | −1.46274 | −0.731368 | − | 0.681983i | \(-0.761118\pi\) | ||||
−0.731368 | + | 0.681983i | \(0.761118\pi\) | |||||||
\(348\) | −1.08110e17 | −3.26288 | ||||||||
\(349\) | 1.75469e16 | 0.519797 | 0.259899 | − | 0.965636i | \(-0.416311\pi\) | ||||
0.259899 | + | 0.965636i | \(0.416311\pi\) | |||||||
\(350\) | 5.61007e16 | 1.63127 | ||||||||
\(351\) | 5.41466e16 | 1.54552 | ||||||||
\(352\) | 8.48465e15 | 0.237742 | ||||||||
\(353\) | 2.14820e16 | 0.590933 | 0.295467 | − | 0.955353i | \(-0.404525\pi\) | ||||
0.295467 | + | 0.955353i | \(0.404525\pi\) | |||||||
\(354\) | −1.34705e17 | −3.63800 | ||||||||
\(355\) | 1.12096e16 | 0.297240 | ||||||||
\(356\) | 1.29195e16 | 0.336372 | ||||||||
\(357\) | 5.36865e16 | 1.37253 | ||||||||
\(358\) | 6.62985e15 | 0.166442 | ||||||||
\(359\) | 9.72533e15 | 0.239768 | 0.119884 | − | 0.992788i | \(-0.461748\pi\) | ||||
0.119884 | + | 0.992788i | \(0.461748\pi\) | |||||||
\(360\) | 1.73273e16 | 0.419533 | ||||||||
\(361\) | −2.90709e16 | −0.691293 | ||||||||
\(362\) | 9.37751e16 | 2.19019 | ||||||||
\(363\) | 6.65168e16 | 1.52594 | ||||||||
\(364\) | −1.30551e17 | −2.94186 | ||||||||
\(365\) | −2.40648e16 | −0.532696 | ||||||||
\(366\) | −2.07073e17 | −4.50295 | ||||||||
\(367\) | −2.51912e16 | −0.538171 | −0.269085 | − | 0.963116i | \(-0.586721\pi\) | ||||
−0.269085 | + | 0.963116i | \(0.586721\pi\) | |||||||
\(368\) | 6.60522e15 | 0.138636 | ||||||||
\(369\) | −8.32152e16 | −1.71606 | ||||||||
\(370\) | 5.71876e15 | 0.115875 | ||||||||
\(371\) | 1.11863e16 | 0.222718 | ||||||||
\(372\) | 1.52212e17 | 2.97796 | ||||||||
\(373\) | 5.80195e16 | 1.11549 | 0.557746 | − | 0.830011i | \(-0.311666\pi\) | ||||
0.557746 | + | 0.830011i | \(0.311666\pi\) | |||||||
\(374\) | 1.44040e16 | 0.272155 | ||||||||
\(375\) | −4.81195e16 | −0.893547 | ||||||||
\(376\) | −7.95121e16 | −1.45115 | ||||||||
\(377\) | −1.21504e17 | −2.17957 | ||||||||
\(378\) | 9.27491e16 | 1.63536 | ||||||||
\(379\) | 2.67049e16 | 0.462845 | 0.231423 | − | 0.972853i | \(-0.425662\pi\) | ||||
0.231423 | + | 0.972853i | \(0.425662\pi\) | |||||||
\(380\) | −1.49119e16 | −0.254063 | ||||||||
\(381\) | 1.16043e17 | 1.94360 | ||||||||
\(382\) | −7.54662e16 | −1.24263 | ||||||||
\(383\) | −8.05130e16 | −1.30339 | −0.651695 | − | 0.758481i | \(-0.725942\pi\) | ||||
−0.651695 | + | 0.758481i | \(0.725942\pi\) | |||||||
\(384\) | −1.54631e17 | −2.46119 | ||||||||
\(385\) | −4.55067e15 | −0.0712165 | ||||||||
\(386\) | −7.88302e16 | −1.21304 | ||||||||
\(387\) | −1.08929e17 | −1.64824 | ||||||||
\(388\) | 1.96552e17 | 2.92463 | ||||||||
\(389\) | −1.30815e17 | −1.91419 | −0.957094 | − | 0.289779i | \(-0.906418\pi\) | ||||
−0.957094 | + | 0.289779i | \(0.906418\pi\) | |||||||
\(390\) | 8.75587e16 | 1.26003 | ||||||||
\(391\) | 7.48695e16 | 1.05963 | ||||||||
\(392\) | −1.54681e16 | −0.215316 | ||||||||
\(393\) | 2.09728e16 | 0.287147 | ||||||||
\(394\) | −8.48457e15 | −0.114263 | ||||||||
\(395\) | −7.91842e15 | −0.104896 | ||||||||
\(396\) | 4.17901e16 | 0.544572 | ||||||||
\(397\) | 1.86167e16 | 0.238651 | 0.119326 | − | 0.992855i | \(-0.461927\pi\) | ||||
0.119326 | + | 0.992855i | \(0.461927\pi\) | |||||||
\(398\) | 8.56080e16 | 1.07963 | ||||||||
\(399\) | −7.98052e16 | −0.990164 | ||||||||
\(400\) | 7.55623e15 | 0.0922391 | ||||||||
\(401\) | −1.20070e17 | −1.44210 | −0.721052 | − | 0.692881i | \(-0.756341\pi\) | ||||
−0.721052 | + | 0.692881i | \(0.756341\pi\) | |||||||
\(402\) | 2.25399e17 | 2.66368 | ||||||||
\(403\) | 1.71069e17 | 1.98925 | ||||||||
\(404\) | −2.27062e17 | −2.59816 | ||||||||
\(405\) | 2.59368e15 | 0.0292051 | ||||||||
\(406\) | −2.08127e17 | −2.30626 | ||||||||
\(407\) | 5.01879e15 | 0.0547312 | ||||||||
\(408\) | −1.05580e17 | −1.13316 | ||||||||
\(409\) | −1.76100e17 | −1.86020 | −0.930098 | − | 0.367313i | \(-0.880278\pi\) | ||||
−0.930098 | + | 0.367313i | \(0.880278\pi\) | |||||||
\(410\) | −4.89741e16 | −0.509180 | ||||||||
\(411\) | 1.19638e17 | 1.22433 | ||||||||
\(412\) | −6.35408e16 | −0.640060 | ||||||||
\(413\) | −1.58500e17 | −1.57165 | ||||||||
\(414\) | 3.55396e17 | 3.46905 | ||||||||
\(415\) | 6.57604e15 | 0.0631905 | ||||||||
\(416\) | −1.92090e17 | −1.81718 | ||||||||
\(417\) | −1.80785e17 | −1.68375 | ||||||||
\(418\) | −2.14115e16 | −0.196337 | ||||||||
\(419\) | 9.38626e16 | 0.847426 | 0.423713 | − | 0.905797i | \(-0.360727\pi\) | ||||
0.423713 | + | 0.905797i | \(0.360727\pi\) | |||||||
\(420\) | 9.16688e16 | 0.814894 | ||||||||
\(421\) | 1.10977e17 | 0.971407 | 0.485703 | − | 0.874124i | \(-0.338563\pi\) | ||||
0.485703 | + | 0.874124i | \(0.338563\pi\) | |||||||
\(422\) | −1.13219e17 | −0.975863 | ||||||||
\(423\) | 2.93007e17 | 2.48694 | ||||||||
\(424\) | −2.19990e16 | −0.183876 | ||||||||
\(425\) | 8.56492e16 | 0.705010 | ||||||||
\(426\) | −3.24228e17 | −2.62838 | ||||||||
\(427\) | −2.43652e17 | −1.94531 | ||||||||
\(428\) | −3.65885e17 | −2.87713 | ||||||||
\(429\) | 7.68415e16 | 0.595146 | ||||||||
\(430\) | −6.41072e16 | −0.489059 | ||||||||
\(431\) | −1.35233e17 | −1.01620 | −0.508102 | − | 0.861297i | \(-0.669653\pi\) | ||||
−0.508102 | + | 0.861297i | \(0.669653\pi\) | |||||||
\(432\) | 1.24924e16 | 0.0924703 | ||||||||
\(433\) | 9.96386e16 | 0.726534 | 0.363267 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363267 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(434\) | 2.93029e17 | 2.10488 | ||||||||
\(435\) | 8.53159e16 | 0.603740 | ||||||||
\(436\) | −1.78724e17 | −1.24601 | ||||||||
\(437\) | −1.11294e17 | −0.764436 | ||||||||
\(438\) | 6.96052e17 | 4.71043 | ||||||||
\(439\) | 1.63741e17 | 1.09178 | 0.545892 | − | 0.837855i | \(-0.316191\pi\) | ||||
0.545892 | + | 0.837855i | \(0.316191\pi\) | |||||||
\(440\) | 8.94938e15 | 0.0587963 | ||||||||
\(441\) | 5.70009e16 | 0.369004 | ||||||||
\(442\) | −3.26101e17 | −2.08021 | ||||||||
\(443\) | 7.00534e16 | 0.440357 | 0.220178 | − | 0.975460i | \(-0.429336\pi\) | ||||
0.220178 | + | 0.975460i | \(0.429336\pi\) | |||||||
\(444\) | −1.01099e17 | −0.626262 | ||||||||
\(445\) | −1.01955e16 | −0.0622399 | ||||||||
\(446\) | −2.08722e17 | −1.25571 | ||||||||
\(447\) | 6.08465e16 | 0.360776 | ||||||||
\(448\) | −3.09875e17 | −1.81084 | ||||||||
\(449\) | 7.90873e16 | 0.455518 | 0.227759 | − | 0.973718i | \(-0.426860\pi\) | ||||
0.227759 | + | 0.973718i | \(0.426860\pi\) | |||||||
\(450\) | 4.06566e17 | 2.30807 | ||||||||
\(451\) | −4.29797e16 | −0.240501 | ||||||||
\(452\) | 1.74139e17 | 0.960496 | ||||||||
\(453\) | 2.20797e17 | 1.20048 | ||||||||
\(454\) | 5.40448e17 | 2.89661 | ||||||||
\(455\) | 1.03026e17 | 0.544342 | ||||||||
\(456\) | 1.56945e17 | 0.817480 | ||||||||
\(457\) | 6.98717e16 | 0.358795 | 0.179397 | − | 0.983777i | \(-0.442585\pi\) | ||||
0.179397 | + | 0.983777i | \(0.442585\pi\) | |||||||
\(458\) | 3.17179e17 | 1.60575 | ||||||||
\(459\) | 1.41600e17 | 0.706776 | ||||||||
\(460\) | 1.27838e17 | 0.629123 | ||||||||
\(461\) | 1.57968e17 | 0.766502 | 0.383251 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383251 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(462\) | 1.31624e17 | 0.629740 | ||||||||
\(463\) | −2.34071e17 | −1.10426 | −0.552131 | − | 0.833758i | \(-0.686185\pi\) | ||||
−0.552131 | + | 0.833758i | \(0.686185\pi\) | |||||||
\(464\) | −2.80327e16 | −0.130406 | ||||||||
\(465\) | −1.20119e17 | −0.551021 | ||||||||
\(466\) | 3.22405e17 | 1.45845 | ||||||||
\(467\) | −5.92394e16 | −0.264272 | −0.132136 | − | 0.991232i | \(-0.542184\pi\) | ||||
−0.132136 | + | 0.991232i | \(0.542184\pi\) | |||||||
\(468\) | −9.46116e17 | −4.16243 | ||||||||
\(469\) | 2.65215e17 | 1.15073 | ||||||||
\(470\) | 1.72442e17 | 0.737915 | ||||||||
\(471\) | −4.48240e17 | −1.89180 | ||||||||
\(472\) | 3.11708e17 | 1.29755 | ||||||||
\(473\) | −5.62605e16 | −0.230997 | ||||||||
\(474\) | 2.29033e17 | 0.927553 | ||||||||
\(475\) | −1.27318e17 | −0.508604 | ||||||||
\(476\) | −3.41409e17 | −1.34533 | ||||||||
\(477\) | 8.10679e16 | 0.315123 | ||||||||
\(478\) | 6.86792e17 | 2.63356 | ||||||||
\(479\) | −2.37177e17 | −0.897205 | −0.448603 | − | 0.893731i | \(-0.648078\pi\) | ||||
−0.448603 | + | 0.893731i | \(0.648078\pi\) | |||||||
\(480\) | 1.34879e17 | 0.503357 | ||||||||
\(481\) | −1.13624e17 | −0.418337 | ||||||||
\(482\) | −2.08623e17 | −0.757804 | ||||||||
\(483\) | 6.84160e17 | 2.45189 | ||||||||
\(484\) | −4.23000e17 | −1.49570 | ||||||||
\(485\) | −1.55111e17 | −0.541154 | ||||||||
\(486\) | −5.02550e17 | −1.72999 | ||||||||
\(487\) | 1.18832e17 | 0.403641 | 0.201821 | − | 0.979423i | \(-0.435314\pi\) | ||||
0.201821 | + | 0.979423i | \(0.435314\pi\) | |||||||
\(488\) | 4.79168e17 | 1.60605 | ||||||||
\(489\) | −5.57630e17 | −1.84433 | ||||||||
\(490\) | 3.35464e16 | 0.109489 | ||||||||
\(491\) | −1.43052e17 | −0.460750 | −0.230375 | − | 0.973102i | \(-0.573995\pi\) | ||||
−0.230375 | + | 0.973102i | \(0.573995\pi\) | |||||||
\(492\) | 8.65784e17 | 2.75193 | ||||||||
\(493\) | −3.17748e17 | −0.996732 | ||||||||
\(494\) | 4.84750e17 | 1.50070 | ||||||||
\(495\) | −3.29790e16 | −0.100764 | ||||||||
\(496\) | 3.94682e16 | 0.119019 | ||||||||
\(497\) | −3.81503e17 | −1.13548 | ||||||||
\(498\) | −1.90206e17 | −0.558770 | ||||||||
\(499\) | 6.60855e15 | 0.0191625 | 0.00958126 | − | 0.999954i | \(-0.496950\pi\) | ||||
0.00958126 | + | 0.999954i | \(0.496950\pi\) | |||||||
\(500\) | 3.06006e17 | 0.875840 | ||||||||
\(501\) | 9.13691e17 | 2.58139 | ||||||||
\(502\) | −1.57494e17 | −0.439228 | ||||||||
\(503\) | −6.41119e17 | −1.76501 | −0.882504 | − | 0.470304i | \(-0.844144\pi\) | ||||
−0.882504 | + | 0.470304i | \(0.844144\pi\) | |||||||
\(504\) | −5.89709e17 | −1.60265 | ||||||||
\(505\) | 1.79188e17 | 0.480745 | ||||||||
\(506\) | 1.83558e17 | 0.486178 | ||||||||
\(507\) | −1.12633e18 | −2.94518 | ||||||||
\(508\) | −7.37953e17 | −1.90509 | ||||||||
\(509\) | −5.47621e17 | −1.39577 | −0.697887 | − | 0.716208i | \(-0.745876\pi\) | ||||
−0.697887 | + | 0.716208i | \(0.745876\pi\) | |||||||
\(510\) | 2.28977e17 | 0.576217 | ||||||||
\(511\) | 8.19009e17 | 2.03495 | ||||||||
\(512\) | −8.19983e16 | −0.201164 | ||||||||
\(513\) | −2.10489e17 | −0.509879 | ||||||||
\(514\) | −7.02762e17 | −1.68092 | ||||||||
\(515\) | 5.01438e16 | 0.118432 | ||||||||
\(516\) | 1.13331e18 | 2.64318 | ||||||||
\(517\) | 1.51335e17 | 0.348538 | ||||||||
\(518\) | −1.94629e17 | −0.442654 | ||||||||
\(519\) | 6.69219e17 | 1.50308 | ||||||||
\(520\) | −2.02611e17 | −0.449409 | ||||||||
\(521\) | −1.31923e15 | −0.00288985 | −0.00144492 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144492 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(522\) | −1.50831e18 | −3.26312 | ||||||||
\(523\) | −5.26578e17 | −1.12513 | −0.562564 | − | 0.826754i | \(-0.690185\pi\) | ||||
−0.562564 | + | 0.826754i | \(0.690185\pi\) | |||||||
\(524\) | −1.33372e17 | −0.281457 | ||||||||
\(525\) | 7.82665e17 | 1.63132 | ||||||||
\(526\) | 6.01309e17 | 1.23791 | ||||||||
\(527\) | 4.47369e17 | 0.909696 | ||||||||
\(528\) | 1.77285e16 | 0.0356082 | ||||||||
\(529\) | 4.50071e17 | 0.892934 | ||||||||
\(530\) | 4.77104e16 | 0.0935017 | ||||||||
\(531\) | −1.14867e18 | −2.22371 | ||||||||
\(532\) | 5.07505e17 | 0.970543 | ||||||||
\(533\) | 9.73048e17 | 1.83826 | ||||||||
\(534\) | 2.94895e17 | 0.550364 | ||||||||
\(535\) | 2.88741e17 | 0.532365 | ||||||||
\(536\) | −5.21574e17 | −0.950046 | ||||||||
\(537\) | 9.24935e16 | 0.166448 | ||||||||
\(538\) | −1.29002e18 | −2.29356 | ||||||||
\(539\) | 2.94403e16 | 0.0517149 | ||||||||
\(540\) | 2.41780e17 | 0.419625 | ||||||||
\(541\) | −7.09136e16 | −0.121604 | −0.0608020 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608020 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(542\) | −7.79840e17 | −1.32133 | ||||||||
\(543\) | 1.30826e18 | 2.19026 | ||||||||
\(544\) | −5.02340e17 | −0.831007 | ||||||||
\(545\) | 1.41042e17 | 0.230553 | ||||||||
\(546\) | −2.97992e18 | −4.81341 | ||||||||
\(547\) | −2.39261e17 | −0.381903 | −0.190952 | − | 0.981599i | \(-0.561157\pi\) | ||||
−0.190952 | + | 0.981599i | \(0.561157\pi\) | |||||||
\(548\) | −7.60817e17 | −1.20007 | ||||||||
\(549\) | −1.76577e18 | −2.75241 | ||||||||
\(550\) | 2.09987e17 | 0.323470 | ||||||||
\(551\) | 4.72333e17 | 0.719057 | ||||||||
\(552\) | −1.34547e18 | −2.02428 | ||||||||
\(553\) | 2.69491e17 | 0.400711 | ||||||||
\(554\) | −1.40445e18 | −2.06392 | ||||||||
\(555\) | 7.97828e16 | 0.115879 | ||||||||
\(556\) | 1.14967e18 | 1.65039 | ||||||||
\(557\) | 2.71586e17 | 0.385344 | 0.192672 | − | 0.981263i | \(-0.438285\pi\) | ||||
0.192672 | + | 0.981263i | \(0.438285\pi\) | |||||||
\(558\) | 2.12360e18 | 2.97818 | ||||||||
\(559\) | 1.27372e18 | 1.76562 | ||||||||
\(560\) | 2.37695e16 | 0.0325686 | ||||||||
\(561\) | 2.00950e17 | 0.272164 | ||||||||
\(562\) | 1.39463e18 | 1.86712 | ||||||||
\(563\) | 6.09127e17 | 0.806127 | 0.403064 | − | 0.915172i | \(-0.367945\pi\) | ||||
0.403064 | + | 0.915172i | \(0.367945\pi\) | |||||||
\(564\) | −3.04849e18 | −3.98815 | ||||||||
\(565\) | −1.37423e17 | −0.177723 | ||||||||
\(566\) | 2.27860e18 | 2.91314 | ||||||||
\(567\) | −8.82719e16 | −0.111566 | ||||||||
\(568\) | 7.50265e17 | 0.937456 | ||||||||
\(569\) | 5.16902e17 | 0.638525 | 0.319263 | − | 0.947666i | \(-0.396565\pi\) | ||||
0.319263 | + | 0.947666i | \(0.396565\pi\) | |||||||
\(570\) | −3.40375e17 | −0.415691 | ||||||||
\(571\) | −1.84006e17 | −0.222176 | −0.111088 | − | 0.993811i | \(-0.535434\pi\) | ||||
−0.111088 | + | 0.993811i | \(0.535434\pi\) | |||||||
\(572\) | −4.88658e17 | −0.583353 | ||||||||
\(573\) | −1.05283e18 | −1.24267 | ||||||||
\(574\) | 1.66676e18 | 1.94511 | ||||||||
\(575\) | 1.09148e18 | 1.25943 | ||||||||
\(576\) | −2.24569e18 | −2.56214 | ||||||||
\(577\) | 5.01932e16 | 0.0566243 | 0.0283121 | − | 0.999599i | \(-0.490987\pi\) | ||||
0.0283121 | + | 0.999599i | \(0.490987\pi\) | |||||||
\(578\) | 5.84904e17 | 0.652460 | ||||||||
\(579\) | −1.09977e18 | −1.21308 | ||||||||
\(580\) | −5.42549e17 | −0.591776 | ||||||||
\(581\) | −2.23805e17 | −0.241393 | ||||||||
\(582\) | 4.48643e18 | 4.78522 | ||||||||
\(583\) | 4.18706e16 | 0.0441636 | ||||||||
\(584\) | −1.61067e18 | −1.68005 | ||||||||
\(585\) | 7.46636e17 | 0.770186 | ||||||||
\(586\) | −1.29217e17 | −0.131821 | ||||||||
\(587\) | 1.04740e18 | 1.05674 | 0.528368 | − | 0.849016i | \(-0.322804\pi\) | ||||
0.528368 | + | 0.849016i | \(0.322804\pi\) | |||||||
\(588\) | −5.93046e17 | −0.591747 | ||||||||
\(589\) | −6.65014e17 | −0.656269 | ||||||||
\(590\) | −6.76016e17 | −0.659810 | ||||||||
\(591\) | −1.18369e17 | −0.114266 | ||||||||
\(592\) | −2.62147e16 | −0.0250296 | ||||||||
\(593\) | 1.41371e18 | 1.33507 | 0.667534 | − | 0.744579i | \(-0.267350\pi\) | ||||
0.667534 | + | 0.744579i | \(0.267350\pi\) | |||||||
\(594\) | 3.47163e17 | 0.324281 | ||||||||
\(595\) | 2.69426e17 | 0.248931 | ||||||||
\(596\) | −3.86941e17 | −0.353626 | ||||||||
\(597\) | 1.19432e18 | 1.07966 | ||||||||
\(598\) | −4.15570e18 | −3.71610 | ||||||||
\(599\) | −2.05968e17 | −0.182191 | −0.0910954 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910954 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(600\) | −1.53919e18 | −1.34682 | ||||||||
\(601\) | −9.31064e17 | −0.805927 | −0.402963 | − | 0.915216i | \(-0.632020\pi\) | ||||
−0.402963 | + | 0.915216i | \(0.632020\pi\) | |||||||
\(602\) | 2.18179e18 | 1.86825 | ||||||||
\(603\) | 1.92204e18 | 1.62817 | ||||||||
\(604\) | −1.40412e18 | −1.17669 | ||||||||
\(605\) | 3.33814e17 | 0.276755 | ||||||||
\(606\) | −5.18284e18 | −4.25105 | ||||||||
\(607\) | 2.63045e17 | 0.213454 | 0.106727 | − | 0.994288i | \(-0.465963\pi\) | ||||
0.106727 | + | 0.994288i | \(0.465963\pi\) | |||||||
\(608\) | 7.46729e17 | 0.599501 | ||||||||
\(609\) | −2.90359e18 | −2.30634 | ||||||||
\(610\) | −1.03920e18 | −0.816683 | ||||||||
\(611\) | −3.42618e18 | −2.66405 | ||||||||
\(612\) | −2.47422e18 | −1.90350 | ||||||||
\(613\) | −1.16532e18 | −0.887060 | −0.443530 | − | 0.896259i | \(-0.646274\pi\) | ||||
−0.443530 | + | 0.896259i | \(0.646274\pi\) | |||||||
\(614\) | −2.58216e18 | −1.94486 | ||||||||
\(615\) | −6.83241e17 | −0.509197 | ||||||||
\(616\) | −3.04578e17 | −0.224607 | ||||||||
\(617\) | −4.22470e17 | −0.308278 | −0.154139 | − | 0.988049i | \(-0.549260\pi\) | ||||
−0.154139 | + | 0.988049i | \(0.549260\pi\) | |||||||
\(618\) | −1.45036e18 | −1.04725 | ||||||||
\(619\) | 2.34248e18 | 1.67373 | 0.836866 | − | 0.547407i | \(-0.184385\pi\) | ||||
0.836866 | + | 0.547407i | \(0.184385\pi\) | |||||||
\(620\) | 7.63874e17 | 0.540102 | ||||||||
\(621\) | 1.80450e18 | 1.26259 | ||||||||
\(622\) | 6.50698e17 | 0.450549 | ||||||||
\(623\) | 3.46988e17 | 0.237762 | ||||||||
\(624\) | −4.01367e17 | −0.272171 | ||||||||
\(625\) | 1.12255e18 | 0.753332 | ||||||||
\(626\) | 2.16569e18 | 1.43835 | ||||||||
\(627\) | −2.98713e17 | −0.196343 | ||||||||
\(628\) | 2.85049e18 | 1.85431 | ||||||||
\(629\) | −2.97141e17 | −0.191308 | ||||||||
\(630\) | 1.27893e18 | 0.814954 | ||||||||
\(631\) | −1.03646e18 | −0.653678 | −0.326839 | − | 0.945080i | \(-0.605983\pi\) | ||||
−0.326839 | + | 0.945080i | \(0.605983\pi\) | |||||||
\(632\) | −5.29983e17 | −0.330827 | ||||||||
\(633\) | −1.57953e18 | −0.975895 | ||||||||
\(634\) | 2.38087e18 | 1.45598 | ||||||||
\(635\) | 5.82362e17 | 0.352504 | ||||||||
\(636\) | −8.43443e17 | −0.505341 | ||||||||
\(637\) | −6.66520e17 | −0.395282 | ||||||||
\(638\) | −7.79026e17 | −0.457317 | ||||||||
\(639\) | −2.76478e18 | −1.60659 | ||||||||
\(640\) | −7.76016e17 | −0.446376 | ||||||||
\(641\) | 2.48877e18 | 1.41712 | 0.708561 | − | 0.705650i | \(-0.249345\pi\) | ||||
0.708561 | + | 0.705650i | \(0.249345\pi\) | |||||||
\(642\) | −8.35156e18 | −4.70750 | ||||||||
\(643\) | 1.68962e18 | 0.942797 | 0.471399 | − | 0.881920i | \(-0.343749\pi\) | ||||
0.471399 | + | 0.881920i | \(0.343749\pi\) | |||||||
\(644\) | −4.35078e18 | −2.40330 | ||||||||
\(645\) | −8.94363e17 | −0.489075 | ||||||||
\(646\) | 1.26768e18 | 0.686277 | ||||||||
\(647\) | 3.24216e18 | 1.73763 | 0.868813 | − | 0.495141i | \(-0.164884\pi\) | ||||
0.868813 | + | 0.495141i | \(0.164884\pi\) | |||||||
\(648\) | 1.73596e17 | 0.0921090 | ||||||||
\(649\) | −5.93272e17 | −0.311647 | ||||||||
\(650\) | −4.75404e18 | −2.47244 | ||||||||
\(651\) | 4.08807e18 | 2.10495 | ||||||||
\(652\) | 3.54614e18 | 1.80778 | ||||||||
\(653\) | −2.68182e18 | −1.35361 | −0.676806 | − | 0.736161i | \(-0.736637\pi\) | ||||
−0.676806 | + | 0.736161i | \(0.736637\pi\) | |||||||
\(654\) | −4.07949e18 | −2.03869 | ||||||||
\(655\) | 1.05252e17 | 0.0520788 | ||||||||
\(656\) | 2.24496e17 | 0.109985 | ||||||||
\(657\) | 5.93542e18 | 2.87923 | ||||||||
\(658\) | −5.86878e18 | −2.81890 | ||||||||
\(659\) | 6.03146e17 | 0.286858 | 0.143429 | − | 0.989661i | \(-0.454187\pi\) | ||||
0.143429 | + | 0.989661i | \(0.454187\pi\) | |||||||
\(660\) | 3.43119e17 | 0.161588 | ||||||||
\(661\) | 2.93438e18 | 1.36838 | 0.684190 | − | 0.729304i | \(-0.260156\pi\) | ||||
0.684190 | + | 0.729304i | \(0.260156\pi\) | |||||||
\(662\) | 5.87081e18 | 2.71095 | ||||||||
\(663\) | −4.54946e18 | −2.08028 | ||||||||
\(664\) | 4.40137e17 | 0.199295 | ||||||||
\(665\) | −4.00502e17 | −0.179582 | ||||||||
\(666\) | −1.41049e18 | −0.626308 | ||||||||
\(667\) | −4.04926e18 | −1.78056 | ||||||||
\(668\) | −5.81043e18 | −2.53024 | ||||||||
\(669\) | −2.91189e18 | −1.25576 | ||||||||
\(670\) | 1.13116e18 | 0.483102 | ||||||||
\(671\) | −9.11999e17 | −0.385743 | ||||||||
\(672\) | −4.59039e18 | −1.92287 | ||||||||
\(673\) | 3.11819e18 | 1.29361 | 0.646807 | − | 0.762654i | \(-0.276104\pi\) | ||||
0.646807 | + | 0.762654i | \(0.276104\pi\) | |||||||
\(674\) | 4.48867e18 | 1.84429 | ||||||||
\(675\) | 2.06431e18 | 0.840041 | ||||||||
\(676\) | 7.16265e18 | 2.88682 | ||||||||
\(677\) | 2.72429e18 | 1.08749 | 0.543747 | − | 0.839249i | \(-0.317005\pi\) | ||||
0.543747 | + | 0.839249i | \(0.317005\pi\) | |||||||
\(678\) | 3.97483e18 | 1.57154 | ||||||||
\(679\) | 5.27895e18 | 2.06726 | ||||||||
\(680\) | −5.29854e17 | −0.205517 | ||||||||
\(681\) | 7.53982e18 | 2.89671 | ||||||||
\(682\) | 1.09682e18 | 0.417384 | ||||||||
\(683\) | 3.95022e18 | 1.48897 | 0.744487 | − | 0.667637i | \(-0.232694\pi\) | ||||
0.744487 | + | 0.667637i | \(0.232694\pi\) | |||||||
\(684\) | 3.67793e18 | 1.37321 | ||||||||
\(685\) | 6.00405e17 | 0.222053 | ||||||||
\(686\) | 3.72267e18 | 1.36379 | ||||||||
\(687\) | 4.42498e18 | 1.60580 | ||||||||
\(688\) | 2.93866e17 | 0.105639 | ||||||||
\(689\) | −9.47939e17 | −0.337563 | ||||||||
\(690\) | 2.91799e18 | 1.02936 | ||||||||
\(691\) | 3.49814e18 | 1.22245 | 0.611223 | − | 0.791458i | \(-0.290678\pi\) | ||||
0.611223 | + | 0.791458i | \(0.290678\pi\) | |||||||
\(692\) | −4.25577e18 | −1.47329 | ||||||||
\(693\) | 1.12239e18 | 0.384926 | ||||||||
\(694\) | 6.90462e18 | 2.34587 | ||||||||
\(695\) | −9.07269e17 | −0.305376 | ||||||||
\(696\) | 5.71023e18 | 1.90412 | ||||||||
\(697\) | 2.54465e18 | 0.840648 | ||||||||
\(698\) | −2.54702e18 | −0.833626 | ||||||||
\(699\) | 4.49789e18 | 1.45850 | ||||||||
\(700\) | −4.97720e18 | −1.59900 | ||||||||
\(701\) | −2.04271e18 | −0.650190 | −0.325095 | − | 0.945681i | \(-0.605396\pi\) | ||||
−0.325095 | + | 0.945681i | \(0.605396\pi\) | |||||||
\(702\) | −7.85966e18 | −2.47864 | ||||||||
\(703\) | 4.41701e17 | 0.138013 | ||||||||
\(704\) | −1.15987e18 | −0.359078 | ||||||||
\(705\) | 2.40575e18 | 0.737939 | ||||||||
\(706\) | −3.11822e18 | −0.947711 | ||||||||
\(707\) | −6.09839e18 | −1.83649 | ||||||||
\(708\) | 1.19509e19 | 3.56602 | ||||||||
\(709\) | 6.55708e17 | 0.193870 | 0.0969348 | − | 0.995291i | \(-0.469096\pi\) | ||||
0.0969348 | + | 0.995291i | \(0.469096\pi\) | |||||||
\(710\) | −1.62714e18 | −0.476700 | ||||||||
\(711\) | 1.95302e18 | 0.566963 | ||||||||
\(712\) | −6.82389e17 | −0.196296 | ||||||||
\(713\) | 5.70109e18 | 1.62508 | ||||||||
\(714\) | −7.79288e18 | −2.20120 | ||||||||
\(715\) | 3.85629e17 | 0.107939 | ||||||||
\(716\) | −5.88194e17 | −0.163149 | ||||||||
\(717\) | 9.58148e18 | 2.63365 | ||||||||
\(718\) | −1.41168e18 | −0.384528 | ||||||||
\(719\) | 3.13690e18 | 0.846765 | 0.423382 | − | 0.905951i | \(-0.360843\pi\) | ||||
0.423382 | + | 0.905951i | \(0.360843\pi\) | |||||||
\(720\) | 1.72260e17 | 0.0460811 | ||||||||
\(721\) | −1.70656e18 | −0.452422 | ||||||||
\(722\) | 4.21979e18 | 1.10866 | ||||||||
\(723\) | −2.91052e18 | −0.757829 | ||||||||
\(724\) | −8.31963e18 | −2.14686 | ||||||||
\(725\) | −4.63227e18 | −1.18467 | ||||||||
\(726\) | −9.65525e18 | −2.44723 | ||||||||
\(727\) | −3.16136e18 | −0.794146 | −0.397073 | − | 0.917787i | \(-0.629974\pi\) | ||||
−0.397073 | + | 0.917787i | \(0.629974\pi\) | |||||||
\(728\) | 6.89555e18 | 1.71678 | ||||||||
\(729\) | −6.60422e18 | −1.62964 | ||||||||
\(730\) | 3.49314e18 | 0.854313 | ||||||||
\(731\) | 3.33094e18 | 0.807429 | ||||||||
\(732\) | 1.83713e19 | 4.41386 | ||||||||
\(733\) | −3.49551e18 | −0.832405 | −0.416202 | − | 0.909272i | \(-0.636639\pi\) | ||||
−0.416202 | + | 0.909272i | \(0.636639\pi\) | |||||||
\(734\) | 3.65664e18 | 0.863093 | ||||||||
\(735\) | 4.68008e17 | 0.109493 | ||||||||
\(736\) | −6.40162e18 | −1.48451 | ||||||||
\(737\) | 9.92709e17 | 0.228183 | ||||||||
\(738\) | 1.20791e19 | 2.75213 | ||||||||
\(739\) | 6.65779e18 | 1.50363 | 0.751816 | − | 0.659374i | \(-0.229178\pi\) | ||||
0.751816 | + | 0.659374i | \(0.229178\pi\) | |||||||
\(740\) | −5.07363e17 | −0.113583 | ||||||||
\(741\) | 6.76278e18 | 1.50075 | ||||||||
\(742\) | −1.62375e18 | −0.357185 | ||||||||
\(743\) | 6.25592e18 | 1.36416 | 0.682078 | − | 0.731279i | \(-0.261076\pi\) | ||||
0.682078 | + | 0.731279i | \(0.261076\pi\) | |||||||
\(744\) | −8.03962e18 | −1.73785 | ||||||||
\(745\) | 3.05358e17 | 0.0654325 | ||||||||
\(746\) | −8.42183e18 | −1.78897 | ||||||||
\(747\) | −1.62193e18 | −0.341546 | ||||||||
\(748\) | −1.27790e18 | −0.266771 | ||||||||
\(749\) | −9.82685e18 | −2.03368 | ||||||||
\(750\) | 6.98479e18 | 1.43303 | ||||||||
\(751\) | −2.91968e18 | −0.593849 | −0.296925 | − | 0.954901i | \(-0.595961\pi\) | ||||
−0.296925 | + | 0.954901i | \(0.595961\pi\) | |||||||
\(752\) | −7.90469e17 | −0.159393 | ||||||||
\(753\) | −2.19721e18 | −0.439242 | ||||||||
\(754\) | 1.76369e19 | 3.49550 | ||||||||
\(755\) | 1.10807e18 | 0.217727 | ||||||||
\(756\) | −8.22861e18 | −1.60300 | ||||||||
\(757\) | −1.42277e17 | −0.0274796 | −0.0137398 | − | 0.999906i | \(-0.504374\pi\) | ||||
−0.0137398 | + | 0.999906i | \(0.504374\pi\) | |||||||
\(758\) | −3.87635e18 | −0.742289 | ||||||||
\(759\) | 2.56083e18 | 0.486194 | ||||||||
\(760\) | 7.87629e17 | 0.148263 | ||||||||
\(761\) | −1.21558e16 | −0.00226874 | −0.00113437 | − | 0.999999i | \(-0.500361\pi\) | ||||
−0.00113437 | + | 0.999999i | \(0.500361\pi\) | |||||||
\(762\) | −1.68443e19 | −3.11706 | ||||||||
\(763\) | −4.80013e18 | −0.880732 | ||||||||
\(764\) | 6.69529e18 | 1.21804 | ||||||||
\(765\) | 1.95255e18 | 0.352211 | ||||||||
\(766\) | 1.16869e19 | 2.09031 | ||||||||
\(767\) | 1.34315e19 | 2.38207 | ||||||||
\(768\) | 7.58283e18 | 1.33347 | ||||||||
\(769\) | −2.25480e18 | −0.393175 | −0.196588 | − | 0.980486i | \(-0.562986\pi\) | ||||
−0.196588 | + | 0.980486i | \(0.562986\pi\) | |||||||
\(770\) | 6.60553e17 | 0.114214 | ||||||||
\(771\) | −9.80428e18 | −1.68098 | ||||||||
\(772\) | 6.99374e18 | 1.18904 | ||||||||
\(773\) | −1.60398e17 | −0.0270415 | −0.0135208 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135208 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(774\) | 1.58116e19 | 2.64338 | ||||||||
\(775\) | 6.52192e18 | 1.08122 | ||||||||
\(776\) | −1.03816e19 | −1.70673 | ||||||||
\(777\) | −2.71528e18 | −0.442668 | ||||||||
\(778\) | 1.89884e19 | 3.06988 | ||||||||
\(779\) | −3.78262e18 | −0.606456 | ||||||||
\(780\) | −7.76812e18 | −1.23510 | ||||||||
\(781\) | −1.42798e18 | −0.225159 | ||||||||
\(782\) | −1.08677e19 | −1.69939 | ||||||||
\(783\) | −7.65834e18 | −1.18764 | ||||||||
\(784\) | −1.53776e17 | −0.0236501 | ||||||||
\(785\) | −2.24949e18 | −0.343108 | ||||||||
\(786\) | −3.04431e18 | −0.460513 | ||||||||
\(787\) | 1.55309e17 | 0.0233002 | 0.0116501 | − | 0.999932i | \(-0.496292\pi\) | ||||
0.0116501 | + | 0.999932i | \(0.496292\pi\) | |||||||
\(788\) | 7.52743e17 | 0.112002 | ||||||||
\(789\) | 8.38889e18 | 1.23795 | ||||||||
\(790\) | 1.14940e18 | 0.168227 | ||||||||
\(791\) | 4.67698e18 | 0.678919 | ||||||||
\(792\) | −2.20730e18 | −0.317795 | ||||||||
\(793\) | 2.06474e19 | 2.94842 | ||||||||
\(794\) | −2.70231e18 | −0.382738 | ||||||||
\(795\) | 6.65611e17 | 0.0935048 | ||||||||
\(796\) | −7.59506e18 | −1.05827 | ||||||||
\(797\) | 8.03018e18 | 1.10980 | 0.554902 | − | 0.831916i | \(-0.312756\pi\) | ||||
0.554902 | + | 0.831916i | \(0.312756\pi\) | |||||||
\(798\) | 1.15841e19 | 1.58798 | ||||||||
\(799\) | −8.95989e18 | −1.21828 | ||||||||
\(800\) | −7.32331e18 | −0.987695 | ||||||||
\(801\) | 2.51465e18 | 0.336408 | ||||||||
\(802\) | 1.74288e19 | 2.31278 | ||||||||
\(803\) | 3.06558e18 | 0.403516 | ||||||||
\(804\) | −1.99972e19 | −2.61098 | ||||||||
\(805\) | 3.43345e18 | 0.444691 | ||||||||
\(806\) | −2.48316e19 | −3.19027 | ||||||||
\(807\) | −1.79971e19 | −2.29364 | ||||||||
\(808\) | 1.19931e19 | 1.51621 | ||||||||
\(809\) | −1.04069e19 | −1.30513 | −0.652567 | − | 0.757731i | \(-0.726308\pi\) | ||||
−0.652567 | + | 0.757731i | \(0.726308\pi\) | |||||||
\(810\) | −3.76486e17 | −0.0468378 | ||||||||
\(811\) | 4.35231e18 | 0.537136 | 0.268568 | − | 0.963261i | \(-0.413450\pi\) | ||||
0.268568 | + | 0.963261i | \(0.413450\pi\) | |||||||
\(812\) | 1.84648e19 | 2.26064 | ||||||||
\(813\) | −1.08796e19 | −1.32137 | ||||||||
\(814\) | −7.28503e17 | −0.0877754 | ||||||||
\(815\) | −2.79846e18 | −0.334499 | ||||||||
\(816\) | −1.04963e18 | −0.124465 | ||||||||
\(817\) | −4.95145e18 | −0.582491 | ||||||||
\(818\) | 2.55619e19 | 2.98329 | ||||||||
\(819\) | −2.54106e19 | −2.94218 | ||||||||
\(820\) | 4.34494e18 | 0.499107 | ||||||||
\(821\) | −4.07100e18 | −0.463949 | −0.231975 | − | 0.972722i | \(-0.574519\pi\) | ||||
−0.231975 | + | 0.972722i | \(0.574519\pi\) | |||||||
\(822\) | −1.73661e19 | −1.96353 | ||||||||
\(823\) | −1.12410e19 | −1.26097 | −0.630484 | − | 0.776202i | \(-0.717144\pi\) | ||||
−0.630484 | + | 0.776202i | \(0.717144\pi\) | |||||||
\(824\) | 3.35614e18 | 0.373519 | ||||||||
\(825\) | 2.92954e18 | 0.323481 | ||||||||
\(826\) | 2.30072e19 | 2.52054 | ||||||||
\(827\) | −5.36960e18 | −0.583655 | −0.291828 | − | 0.956471i | \(-0.594263\pi\) | ||||
−0.291828 | + | 0.956471i | \(0.594263\pi\) | |||||||
\(828\) | −3.15304e19 | −3.40042 | ||||||||
\(829\) | −1.15117e19 | −1.23179 | −0.615893 | − | 0.787830i | \(-0.711205\pi\) | ||||
−0.615893 | + | 0.787830i | \(0.711205\pi\) | |||||||
\(830\) | −9.54546e17 | −0.101342 | ||||||||
\(831\) | −1.95936e19 | −2.06399 | ||||||||
\(832\) | 2.62592e19 | 2.74460 | ||||||||
\(833\) | −1.74303e18 | −0.180765 | ||||||||
\(834\) | 2.62419e19 | 2.70032 | ||||||||
\(835\) | 4.58535e18 | 0.468178 | ||||||||
\(836\) | 1.89961e18 | 0.192452 | ||||||||
\(837\) | 1.07824e19 | 1.08393 | ||||||||
\(838\) | −1.36246e19 | −1.35906 | ||||||||
\(839\) | −4.36647e18 | −0.432193 | −0.216097 | − | 0.976372i | \(-0.569333\pi\) | ||||
−0.216097 | + | 0.976372i | \(0.569333\pi\) | |||||||
\(840\) | −4.84182e18 | −0.475547 | ||||||||
\(841\) | 6.92453e18 | 0.674864 | ||||||||
\(842\) | −1.61090e19 | −1.55790 | ||||||||
\(843\) | 1.94566e19 | 1.86718 | ||||||||
\(844\) | 1.00447e19 | 0.956557 | ||||||||
\(845\) | −5.65246e18 | −0.534157 | ||||||||
\(846\) | −4.25315e19 | −3.98844 | ||||||||
\(847\) | −1.13608e19 | −1.05723 | ||||||||
\(848\) | −2.18703e17 | −0.0201968 | ||||||||
\(849\) | 3.17889e19 | 2.91323 | ||||||||
\(850\) | −1.24324e19 | −1.13066 | ||||||||
\(851\) | −3.78665e18 | −0.341753 | ||||||||
\(852\) | 2.87652e19 | 2.57638 | ||||||||
\(853\) | −6.93088e17 | −0.0616056 | −0.0308028 | − | 0.999525i | \(-0.509806\pi\) | ||||
−0.0308028 | + | 0.999525i | \(0.509806\pi\) | |||||||
\(854\) | 3.53674e19 | 3.11980 | ||||||||
\(855\) | −2.90247e18 | −0.254090 | ||||||||
\(856\) | 1.93256e19 | 1.67901 | ||||||||
\(857\) | 9.79130e18 | 0.844239 | 0.422119 | − | 0.906540i | \(-0.361286\pi\) | ||||
0.422119 | + | 0.906540i | \(0.361286\pi\) | |||||||
\(858\) | −1.11539e19 | −0.954467 | ||||||||
\(859\) | 8.47286e18 | 0.719572 | 0.359786 | − | 0.933035i | \(-0.382850\pi\) | ||||
0.359786 | + | 0.933035i | \(0.382850\pi\) | |||||||
\(860\) | 5.68752e18 | 0.479384 | ||||||||
\(861\) | 2.32530e19 | 1.94518 | ||||||||
\(862\) | 1.96298e19 | 1.62974 | ||||||||
\(863\) | 1.39686e18 | 0.115102 | 0.0575508 | − | 0.998343i | \(-0.481671\pi\) | ||||
0.0575508 | + | 0.998343i | \(0.481671\pi\) | |||||||
\(864\) | −1.21074e19 | −0.990170 | ||||||||
\(865\) | 3.35847e18 | 0.272607 | ||||||||
\(866\) | −1.44631e19 | −1.16518 | ||||||||
\(867\) | 8.16004e18 | 0.652481 | ||||||||
\(868\) | −2.59972e19 | −2.06324 | ||||||||
\(869\) | 1.00871e18 | 0.0794584 | ||||||||
\(870\) | −1.23840e19 | −0.968250 | ||||||||
\(871\) | −2.24746e19 | −1.74411 | ||||||||
\(872\) | 9.43997e18 | 0.727132 | ||||||||
\(873\) | 3.82570e19 | 2.92495 | ||||||||
\(874\) | 1.61549e19 | 1.22597 | ||||||||
\(875\) | 8.21864e18 | 0.619081 | ||||||||
\(876\) | −6.17531e19 | −4.61723 | ||||||||
\(877\) | 8.92989e18 | 0.662748 | 0.331374 | − | 0.943499i | \(-0.392488\pi\) | ||||
0.331374 | + | 0.943499i | \(0.392488\pi\) | |||||||
\(878\) | −2.37678e19 | −1.75095 | ||||||||
\(879\) | −1.80271e18 | −0.131825 | ||||||||
\(880\) | 8.89702e16 | 0.00645814 | ||||||||
\(881\) | 1.28545e19 | 0.926218 | 0.463109 | − | 0.886301i | \(-0.346734\pi\) | ||||
0.463109 | + | 0.886301i | \(0.346734\pi\) | |||||||
\(882\) | −8.27397e18 | −0.591791 | ||||||||
\(883\) | −6.29105e18 | −0.446661 | −0.223331 | − | 0.974743i | \(-0.571693\pi\) | ||||
−0.223331 | + | 0.974743i | \(0.571693\pi\) | |||||||
\(884\) | 2.89314e19 | 2.03906 | ||||||||
\(885\) | −9.43115e18 | −0.659832 | ||||||||
\(886\) | −1.01686e19 | −0.706224 | ||||||||
\(887\) | 8.99934e18 | 0.620450 | 0.310225 | − | 0.950663i | \(-0.399596\pi\) | ||||
0.310225 | + | 0.950663i | \(0.399596\pi\) | |||||||
\(888\) | 5.33989e18 | 0.365467 | ||||||||
\(889\) | −1.98198e19 | −1.34660 | ||||||||
\(890\) | 1.47993e18 | 0.0998175 | ||||||||
\(891\) | −3.30404e17 | −0.0221228 | ||||||||
\(892\) | 1.85176e19 | 1.23087 | ||||||||
\(893\) | 1.33189e19 | 0.878889 | ||||||||
\(894\) | −8.83219e18 | −0.578595 | ||||||||
\(895\) | 4.64178e17 | 0.0301880 | ||||||||
\(896\) | 2.64105e19 | 1.70520 | ||||||||
\(897\) | −5.79765e19 | −3.71622 | ||||||||
\(898\) | −1.14799e19 | −0.730539 | ||||||||
\(899\) | −2.41956e19 | −1.52861 | ||||||||
\(900\) | −3.60701e19 | −2.26241 | ||||||||
\(901\) | −2.47898e18 | −0.154370 | ||||||||
\(902\) | 6.23873e18 | 0.385703 | ||||||||
\(903\) | 3.04383e19 | 1.86831 | ||||||||
\(904\) | −9.19777e18 | −0.560516 | ||||||||
\(905\) | 6.56551e18 | 0.397240 | ||||||||
\(906\) | −3.20499e19 | −1.92528 | ||||||||
\(907\) | 2.22298e19 | 1.32583 | 0.662915 | − | 0.748694i | \(-0.269319\pi\) | ||||
0.662915 | + | 0.748694i | \(0.269319\pi\) | |||||||
\(908\) | −4.79480e19 | −2.83931 | ||||||||
\(909\) | −4.41955e19 | −2.59844 | ||||||||
\(910\) | −1.49547e19 | −0.872990 | ||||||||
\(911\) | 2.10175e18 | 0.121818 | 0.0609091 | − | 0.998143i | \(-0.480600\pi\) | ||||
0.0609091 | + | 0.998143i | \(0.480600\pi\) | |||||||
\(912\) | 1.56027e18 | 0.0897912 | ||||||||
\(913\) | −8.37711e17 | −0.0478667 | ||||||||
\(914\) | −1.01422e19 | −0.575418 | ||||||||
\(915\) | −1.44979e19 | −0.816710 | ||||||||
\(916\) | −2.81398e19 | −1.57398 | ||||||||
\(917\) | −3.58208e18 | −0.198946 | ||||||||
\(918\) | −2.05540e19 | −1.13349 | ||||||||
\(919\) | −2.10844e19 | −1.15454 | −0.577272 | − | 0.816552i | \(-0.695883\pi\) | ||||
−0.577272 | + | 0.816552i | \(0.695883\pi\) | |||||||
\(920\) | −6.75225e18 | −0.367137 | ||||||||
\(921\) | −3.60239e19 | −1.94493 | ||||||||
\(922\) | −2.29299e19 | −1.22928 | ||||||||
\(923\) | 3.23290e19 | 1.72100 | ||||||||
\(924\) | −1.16775e19 | −0.617281 | ||||||||
\(925\) | −4.33184e18 | −0.227380 | ||||||||
\(926\) | 3.39767e19 | 1.77096 | ||||||||
\(927\) | −1.23676e19 | −0.640129 | ||||||||
\(928\) | 2.71686e19 | 1.39639 | ||||||||
\(929\) | −2.72627e18 | −0.139145 | −0.0695723 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695723 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(930\) | 1.74359e19 | 0.883702 | ||||||||
\(931\) | 2.59103e18 | 0.130406 | ||||||||
\(932\) | −2.86034e19 | −1.42960 | ||||||||
\(933\) | 9.07793e18 | 0.450564 | ||||||||
\(934\) | 8.59890e18 | 0.423827 | ||||||||
\(935\) | 1.00847e18 | 0.0493614 | ||||||||
\(936\) | 4.99726e19 | 2.42906 | ||||||||
\(937\) | −3.00915e19 | −1.45257 | −0.726285 | − | 0.687394i | \(-0.758755\pi\) | ||||
−0.726285 | + | 0.687394i | \(0.758755\pi\) | |||||||
\(938\) | −3.84974e19 | −1.84549 | ||||||||
\(939\) | 3.02137e19 | 1.43839 | ||||||||
\(940\) | −1.52989e19 | −0.723316 | ||||||||
\(941\) | −1.54939e19 | −0.727490 | −0.363745 | − | 0.931499i | \(-0.618502\pi\) | ||||
−0.363745 | + | 0.931499i | \(0.618502\pi\) | |||||||
\(942\) | 6.50643e19 | 3.03398 | ||||||||
\(943\) | 3.24280e19 | 1.50174 | ||||||||
\(944\) | 3.09884e18 | 0.142522 | ||||||||
\(945\) | 6.49368e18 | 0.296609 | ||||||||
\(946\) | 8.16650e18 | 0.370462 | ||||||||
\(947\) | −7.49897e18 | −0.337852 | −0.168926 | − | 0.985629i | \(-0.554030\pi\) | ||||
−0.168926 | + | 0.985629i | \(0.554030\pi\) | |||||||
\(948\) | −2.03196e19 | −0.909202 | ||||||||
\(949\) | −6.94038e19 | −3.08427 | ||||||||
\(950\) | 1.84808e19 | 0.815676 | ||||||||
\(951\) | 3.32157e19 | 1.45603 | ||||||||
\(952\) | 1.80328e19 | 0.785095 | ||||||||
\(953\) | 6.28397e18 | 0.271725 | 0.135863 | − | 0.990728i | \(-0.456619\pi\) | ||||
0.135863 | + | 0.990728i | \(0.456619\pi\) | |||||||
\(954\) | −1.17674e19 | −0.505379 | ||||||||
\(955\) | −5.28364e18 | −0.225378 | ||||||||
\(956\) | −6.09315e19 | −2.58146 | ||||||||
\(957\) | −1.08682e19 | −0.457332 | ||||||||
\(958\) | 3.44275e19 | 1.43890 | ||||||||
\(959\) | −2.04338e19 | −0.848261 | ||||||||
\(960\) | −1.84383e19 | −0.760253 | ||||||||
\(961\) | 9.64822e18 | 0.395135 | ||||||||
\(962\) | 1.64931e19 | 0.670910 | ||||||||
\(963\) | −7.12160e19 | −2.87744 | ||||||||
\(964\) | 1.85088e19 | 0.742811 | ||||||||
\(965\) | −5.51917e18 | −0.220012 | ||||||||
\(966\) | −9.93094e19 | −3.93223 | ||||||||
\(967\) | −4.43950e19 | −1.74607 | −0.873035 | − | 0.487657i | \(-0.837852\pi\) | ||||
−0.873035 | + | 0.487657i | \(0.837852\pi\) | |||||||
\(968\) | 2.23423e19 | 0.872847 | ||||||||
\(969\) | 1.76855e19 | 0.686300 | ||||||||
\(970\) | 2.25151e19 | 0.867877 | ||||||||
\(971\) | −2.37034e19 | −0.907581 | −0.453790 | − | 0.891108i | \(-0.649929\pi\) | ||||
−0.453790 | + | 0.891108i | \(0.649929\pi\) | |||||||
\(972\) | 4.45857e19 | 1.69576 | ||||||||
\(973\) | 3.08775e19 | 1.16656 | ||||||||
\(974\) | −1.72491e19 | −0.647341 | ||||||||
\(975\) | −6.63239e19 | −2.47252 | ||||||||
\(976\) | 4.76365e18 | 0.176407 | ||||||||
\(977\) | −2.43638e19 | −0.896254 | −0.448127 | − | 0.893970i | \(-0.647909\pi\) | ||||
−0.448127 | + | 0.893970i | \(0.647909\pi\) | |||||||
\(978\) | 8.09429e19 | 2.95785 | ||||||||
\(979\) | 1.29879e18 | 0.0471467 | ||||||||
\(980\) | −2.97620e18 | −0.107323 | ||||||||
\(981\) | −3.47869e19 | −1.24614 | ||||||||
\(982\) | 2.07648e19 | 0.738930 | ||||||||
\(983\) | −1.91129e19 | −0.675662 | −0.337831 | − | 0.941207i | \(-0.609693\pi\) | ||||
−0.337831 | + | 0.941207i | \(0.609693\pi\) | |||||||
\(984\) | −4.57296e19 | −1.60594 | ||||||||
\(985\) | −5.94033e17 | −0.0207241 | ||||||||
\(986\) | 4.61228e19 | 1.59851 | ||||||||
\(987\) | −8.18758e19 | −2.81899 | ||||||||
\(988\) | −4.30065e19 | −1.47101 | ||||||||
\(989\) | 4.24482e19 | 1.44239 | ||||||||
\(990\) | 4.78708e18 | 0.161600 | ||||||||
\(991\) | 2.98770e19 | 1.00198 | 0.500989 | − | 0.865453i | \(-0.332970\pi\) | ||||
0.500989 | + | 0.865453i | \(0.332970\pi\) | |||||||
\(992\) | −3.82516e19 | −1.27445 | ||||||||
\(993\) | 8.19040e19 | 2.71104 | ||||||||
\(994\) | 5.53771e19 | 1.82104 | ||||||||
\(995\) | 5.99370e18 | 0.195815 | ||||||||
\(996\) | 1.68749e19 | 0.547715 | ||||||||
\(997\) | −2.20460e19 | −0.710905 | −0.355453 | − | 0.934694i | \(-0.615673\pi\) | ||||
−0.355453 | + | 0.934694i | \(0.615673\pi\) | |||||||
\(998\) | −9.59265e17 | −0.0307320 | ||||||||
\(999\) | −7.16167e18 | −0.227949 |
(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 | 197.14.a.b.1.13 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.b.1.13 | ✓ | 109 | 1.1 | even | 1 | trivial |