Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,9,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), degree \(2\), 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: | \(4.07378610061\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{601})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 301x^{2} + 22500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(-12.7577i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.7 |
Dual form | 10.9.c.b.3.2 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | + | 8.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 82.7883 | − | 82.7883i | 1.02208 | − | 1.02208i | 0.0223265 | − | 0.999751i | \(-0.492893\pi\) |
0.999751 | − | 0.0223265i | \(-0.00710733\pi\) | |||||||
\(4\) | 128.000i | 0.500000i | ||||||||
\(5\) | −33.6352 | − | 624.094i | −0.0538164 | − | 0.998551i | ||||
\(6\) | 1324.61 | 1.02208 | ||||||||
\(7\) | 2718.55 | + | 2718.55i | 1.13226 | + | 1.13226i | 0.989801 | + | 0.142458i | \(0.0455006\pi\) |
0.142458 | + | 0.989801i | \(0.454499\pi\) | |||||||
\(8\) | −1024.00 | + | 1024.00i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 7146.79i | − | 1.08928i | ||||||
\(10\) | 4723.67 | − | 5261.84i | 0.472367 | − | 0.526184i | ||||
\(11\) | −20966.3 | −1.43203 | −0.716013 | − | 0.698087i | \(-0.754035\pi\) | ||||
−0.716013 | + | 0.698087i | \(0.754035\pi\) | |||||||
\(12\) | 10596.9 | + | 10596.9i | 0.511039 | + | 0.511039i | ||||
\(13\) | −8095.66 | + | 8095.66i | −0.283452 | + | 0.283452i | −0.834484 | − | 0.551032i | \(-0.814234\pi\) |
0.551032 | + | 0.834484i | \(0.314234\pi\) | |||||||
\(14\) | 43496.9i | 1.13226i | ||||||||
\(15\) | −54452.3 | − | 48883.1i | −1.07560 | − | 0.965592i | ||||
\(16\) | −16384.0 | −0.250000 | ||||||||
\(17\) | −3141.02 | − | 3141.02i | −0.0376076 | − | 0.0376076i | 0.688053 | − | 0.725661i | \(-0.258466\pi\) |
−0.725661 | + | 0.688053i | \(0.758466\pi\) | |||||||
\(18\) | 57174.3 | − | 57174.3i | 0.544642 | − | 0.544642i | ||||
\(19\) | 69201.5i | 0.531008i | 0.964110 | + | 0.265504i | \(0.0855383\pi\) | ||||
−0.964110 | + | 0.265504i | \(0.914462\pi\) | |||||||
\(20\) | 79884.1 | − | 4305.31i | 0.499275 | − | 0.0269082i | ||||
\(21\) | 450129. | 2.31451 | ||||||||
\(22\) | −167730. | − | 167730.i | −0.716013 | − | 0.716013i | ||||
\(23\) | 1084.70 | − | 1084.70i | 0.00387615 | − | 0.00387615i | −0.705166 | − | 0.709042i | \(-0.749128\pi\) |
0.709042 | + | 0.705166i | \(0.249128\pi\) | |||||||
\(24\) | 169550.i | 0.511039i | ||||||||
\(25\) | −388362. | + | 41983.1i | −0.994208 | + | 0.107477i | ||||
\(26\) | −129531. | −0.283452 | ||||||||
\(27\) | −48496.5 | − | 48496.5i | −0.0912547 | − | 0.0912547i | ||||
\(28\) | −347975. | + | 347975.i | −0.566129 | + | 0.566129i | ||||
\(29\) | 120633.i | 0.170558i | 0.996357 | + | 0.0852792i | \(0.0271782\pi\) | ||||
−0.996357 | + | 0.0852792i | \(0.972822\pi\) | |||||||
\(30\) | −44553.6 | − | 826683.i | −0.0550045 | − | 1.02060i | ||||
\(31\) | 826466. | 0.894908 | 0.447454 | − | 0.894307i | \(-0.352331\pi\) | ||||
0.447454 | + | 0.894307i | \(0.352331\pi\) | |||||||
\(32\) | −131072. | − | 131072.i | −0.125000 | − | 0.125000i | ||||
\(33\) | −1.73576e6 | + | 1.73576e6i | −1.46364 | + | 1.46364i | ||||
\(34\) | − | 50256.4i | − | 0.0376076i | ||||||
\(35\) | 1.60519e6 | − | 1.78807e6i | 1.06968 | − | 1.19155i | ||||
\(36\) | 914789. | 0.544642 | ||||||||
\(37\) | −1.17029e6 | − | 1.17029e6i | −0.624434 | − | 0.624434i | 0.322228 | − | 0.946662i | \(-0.395568\pi\) |
−0.946662 | + | 0.322228i | \(0.895568\pi\) | |||||||
\(38\) | −553612. | + | 553612.i | −0.265504 | + | 0.265504i | ||||
\(39\) | 1.34045e6i | 0.579419i | ||||||||
\(40\) | 673515. | + | 604630.i | 0.263092 | + | 0.236184i | ||||
\(41\) | 1.74660e6 | 0.618099 | 0.309049 | − | 0.951046i | \(-0.399989\pi\) | ||||
0.309049 | + | 0.951046i | \(0.399989\pi\) | |||||||
\(42\) | 3.60103e6 | + | 3.60103e6i | 1.15726 | + | 1.15726i | ||||
\(43\) | 3.03222e6 | − | 3.03222e6i | 0.886925 | − | 0.886925i | −0.107302 | − | 0.994226i | \(-0.534221\pi\) |
0.994226 | + | 0.107302i | \(0.0342211\pi\) | |||||||
\(44\) | − | 2.68368e6i | − | 0.716013i | ||||||
\(45\) | −4.46027e6 | + | 240384.i | −1.08771 | + | 0.0586213i | ||||
\(46\) | 17355.3 | 0.00387615 | ||||||||
\(47\) | −5.83610e6 | − | 5.83610e6i | −1.19600 | − | 1.19600i | −0.975354 | − | 0.220646i | \(-0.929183\pi\) |
−0.220646 | − | 0.975354i | \(-0.570817\pi\) | |||||||
\(48\) | −1.35640e6 | + | 1.35640e6i | −0.255519 | + | 0.255519i | ||||
\(49\) | 9.01626e6i | 1.56402i | ||||||||
\(50\) | −3.44276e6 | − | 2.77103e6i | −0.550842 | − | 0.443365i | ||||
\(51\) | −520080. | −0.0768758 | ||||||||
\(52\) | −1.03625e6 | − | 1.03625e6i | −0.141726 | − | 0.141726i | ||||
\(53\) | 1.97703e6 | − | 1.97703e6i | 0.250559 | − | 0.250559i | −0.570641 | − | 0.821200i | \(-0.693305\pi\) |
0.821200 | + | 0.570641i | \(0.193305\pi\) | |||||||
\(54\) | − | 775944.i | − | 0.0912547i | ||||||
\(55\) | 705206. | + | 1.30849e7i | 0.0770664 | + | 1.42995i | ||||
\(56\) | −5.56760e6 | −0.566129 | ||||||||
\(57\) | 5.72907e6 | + | 5.72907e6i | 0.542731 | + | 0.542731i | ||||
\(58\) | −965061. | + | 965061.i | −0.0852792 | + | 0.0852792i | ||||
\(59\) | − | 1.58356e7i | − | 1.30685i | −0.756990 | − | 0.653427i | \(-0.773331\pi\) | ||
0.756990 | − | 0.653427i | \(-0.226669\pi\) | |||||||
\(60\) | 6.25703e6 | − | 6.96989e6i | 0.482796 | − | 0.537800i | ||||
\(61\) | −2.51723e6 | −0.181804 | −0.0909019 | − | 0.995860i | \(-0.528975\pi\) | ||||
−0.0909019 | + | 0.995860i | \(0.528975\pi\) | |||||||
\(62\) | 6.61173e6 | + | 6.61173e6i | 0.447454 | + | 0.447454i | ||||
\(63\) | 1.94289e7 | − | 1.94289e7i | 1.23335 | − | 1.23335i | ||||
\(64\) | − | 2.09715e6i | − | 0.125000i | ||||||
\(65\) | 5.32476e6 | + | 4.78016e6i | 0.298295 | + | 0.267787i | ||||
\(66\) | −2.77722e7 | −1.46364 | ||||||||
\(67\) | 1.47668e7 | + | 1.47668e7i | 0.732802 | + | 0.732802i | 0.971174 | − | 0.238372i | \(-0.0766138\pi\) |
−0.238372 | + | 0.971174i | \(0.576614\pi\) | |||||||
\(68\) | 402051. | − | 402051.i | 0.0188038 | − | 0.0188038i | ||||
\(69\) | − | 179602.i | − | 0.00792344i | ||||||
\(70\) | 2.71461e7 | − | 1.46303e6i | 1.13062 | − | 0.0609341i | ||||
\(71\) | −8.22222e6 | −0.323561 | −0.161780 | − | 0.986827i | \(-0.551724\pi\) | ||||
−0.161780 | + | 0.986827i | \(0.551724\pi\) | |||||||
\(72\) | 7.31831e6 | + | 7.31831e6i | 0.272321 | + | 0.272321i | ||||
\(73\) | −3.03744e7 | + | 3.03744e7i | −1.06959 | + | 1.06959i | −0.0721980 | + | 0.997390i | \(0.523001\pi\) |
−0.997390 | + | 0.0721980i | \(0.976999\pi\) | |||||||
\(74\) | − | 1.87246e7i | − | 0.624434i | ||||||
\(75\) | −2.86761e7 | + | 3.56275e7i | −0.906307 | + | 1.12601i | ||||
\(76\) | −8.85779e6 | −0.265504 | ||||||||
\(77\) | −5.69980e7 | − | 5.69980e7i | −1.62142 | − | 1.62142i | ||||
\(78\) | −1.07236e7 | + | 1.07236e7i | −0.289710 | + | 0.289710i | ||||
\(79\) | − | 4.69738e7i | − | 1.20600i | −0.797741 | − | 0.603000i | \(-0.793972\pi\) | ||
0.797741 | − | 0.603000i | \(-0.206028\pi\) | |||||||
\(80\) | 551080. | + | 1.02252e7i | 0.0134541 | + | 0.249638i | ||||
\(81\) | 3.88602e7 | 0.902745 | ||||||||
\(82\) | 1.39728e7 | + | 1.39728e7i | 0.309049 | + | 0.309049i | ||||
\(83\) | 2.81305e7 | − | 2.81305e7i | 0.592740 | − | 0.592740i | −0.345630 | − | 0.938371i | \(-0.612335\pi\) |
0.938371 | + | 0.345630i | \(0.112335\pi\) | |||||||
\(84\) | 5.76165e7i | 1.15726i | ||||||||
\(85\) | −1.85465e6 | + | 2.06594e6i | −0.0355292 | + | 0.0395770i | ||||
\(86\) | 4.85155e7 | 0.886925 | ||||||||
\(87\) | 9.98697e6 | + | 9.98697e6i | 0.174324 | + | 0.174324i | ||||
\(88\) | 2.14695e7 | − | 2.14695e7i | 0.358006 | − | 0.358006i | ||||
\(89\) | 7.91918e7i | 1.26218i | 0.775711 | + | 0.631088i | \(0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(90\) | −3.76052e7 | − | 3.37591e7i | −0.573163 | − | 0.514542i | ||||
\(91\) | −4.40170e7 | −0.641881 | ||||||||
\(92\) | 138842. | + | 138842.i | 0.00193807 | + | 0.00193807i | ||||
\(93\) | 6.84217e7 | − | 6.84217e7i | 0.914665 | − | 0.914665i | ||||
\(94\) | − | 9.33776e7i | − | 1.19600i | ||||||
\(95\) | 4.31883e7 | − | 2.32761e6i | 0.530238 | − | 0.0285769i | ||||
\(96\) | −2.17024e7 | −0.255519 | ||||||||
\(97\) | 1.47530e6 | + | 1.47530e6i | 0.0166645 | + | 0.0166645i | 0.715390 | − | 0.698725i | \(-0.246249\pi\) |
−0.698725 | + | 0.715390i | \(0.746249\pi\) | |||||||
\(98\) | −7.21301e7 | + | 7.21301e7i | −0.782010 | + | 0.782010i | ||||
\(99\) | 1.49842e8i | 1.55988i | ||||||||
\(100\) | −5.37384e6 | − | 4.97104e7i | −0.0537384 | − | 0.497104i | ||||
\(101\) | 1.61256e8 | 1.54964 | 0.774818 | − | 0.632185i | \(-0.217842\pi\) | ||||
0.774818 | + | 0.632185i | \(0.217842\pi\) | |||||||
\(102\) | −4.16064e6 | − | 4.16064e6i | −0.0384379 | − | 0.0384379i | ||||
\(103\) | −1.34152e8 | + | 1.34152e8i | −1.19192 | + | 1.19192i | −0.215397 | + | 0.976526i | \(0.569105\pi\) |
−0.976526 | + | 0.215397i | \(0.930895\pi\) | |||||||
\(104\) | − | 1.65799e7i | − | 0.141726i | ||||||
\(105\) | −1.51402e7 | − | 2.80923e8i | −0.124559 | − | 2.31116i | ||||
\(106\) | 3.16325e7 | 0.250559 | ||||||||
\(107\) | 2.02907e7 | + | 2.02907e7i | 0.154796 | + | 0.154796i | 0.780256 | − | 0.625460i | \(-0.215089\pi\) |
−0.625460 | + | 0.780256i | \(0.715089\pi\) | |||||||
\(108\) | 6.20755e6 | − | 6.20755e6i | 0.0456274 | − | 0.0456274i | ||||
\(109\) | − | 5.27998e7i | − | 0.374047i | −0.982355 | − | 0.187023i | \(-0.940116\pi\) | ||
0.982355 | − | 0.187023i | \(-0.0598840\pi\) | |||||||
\(110\) | −9.90379e7 | + | 1.10321e8i | −0.676442 | + | 0.753508i | ||||
\(111\) | −1.93772e8 | −1.27644 | ||||||||
\(112\) | −4.45408e7 | − | 4.45408e7i | −0.283065 | − | 0.283065i | ||||
\(113\) | −1.25553e8 | + | 1.25553e8i | −0.770041 | + | 0.770041i | −0.978113 | − | 0.208073i | \(-0.933281\pi\) |
0.208073 | + | 0.978113i | \(0.433281\pi\) | |||||||
\(114\) | 9.16651e7i | 0.542731i | ||||||||
\(115\) | −713442. | − | 640474.i | −0.00407913 | − | 0.00366193i | ||||
\(116\) | −1.54410e7 | −0.0852792 | ||||||||
\(117\) | 5.78580e7 | + | 5.78580e7i | 0.308759 | + | 0.308759i | ||||
\(118\) | 1.26685e8 | − | 1.26685e8i | 0.653427 | − | 0.653427i | ||||
\(119\) | − | 1.70781e7i | − | 0.0851631i | ||||||
\(120\) | 1.05815e8 | − | 5.70287e6i | 0.510298 | − | 0.0275022i | ||||
\(121\) | 2.25226e8 | 1.05070 | ||||||||
\(122\) | −2.01378e7 | − | 2.01378e7i | −0.0909019 | − | 0.0909019i | ||||
\(123\) | 1.44598e8 | − | 1.44598e8i | 0.631745 | − | 0.631745i | ||||
\(124\) | 1.05788e8i | 0.447454i | ||||||||
\(125\) | 3.92641e7 | + | 2.40963e8i | 0.160826 | + | 0.986983i | ||||
\(126\) | 3.10863e8 | 1.23335 | ||||||||
\(127\) | −9.69572e7 | − | 9.69572e7i | −0.372705 | − | 0.372705i | 0.495757 | − | 0.868462i | \(-0.334891\pi\) |
−0.868462 | + | 0.495757i | \(0.834891\pi\) | |||||||
\(128\) | 1.67772e7 | − | 1.67772e7i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 5.02064e8i | − | 1.81301i | ||||||
\(130\) | 4.35679e6 | + | 8.08393e7i | 0.0152543 | + | 0.283041i | ||||
\(131\) | 6.19413e7 | 0.210327 | 0.105164 | − | 0.994455i | \(-0.466463\pi\) | ||||
0.105164 | + | 0.994455i | \(0.466463\pi\) | |||||||
\(132\) | −2.22178e8 | − | 2.22178e8i | −0.731820 | − | 0.731820i | ||||
\(133\) | −1.88128e8 | + | 1.88128e8i | −0.601238 | + | 0.601238i | ||||
\(134\) | 2.36268e8i | 0.732802i | ||||||||
\(135\) | −2.86352e7 | + | 3.18976e7i | −0.0862115 | + | 0.0960335i | ||||
\(136\) | 6.43282e6 | 0.0188038 | ||||||||
\(137\) | 8.79898e6 | + | 8.79898e6i | 0.0249776 | + | 0.0249776i | 0.719485 | − | 0.694508i | \(-0.244378\pi\) |
−0.694508 | + | 0.719485i | \(0.744378\pi\) | |||||||
\(138\) | 1.43681e6 | − | 1.43681e6i | 0.00396172 | − | 0.00396172i | ||||
\(139\) | 2.71570e7i | 0.0727482i | 0.999338 | + | 0.0363741i | \(0.0115808\pi\) | ||||
−0.999338 | + | 0.0363741i | \(0.988419\pi\) | |||||||
\(140\) | 2.28873e8 | + | 2.05465e8i | 0.595776 | + | 0.534842i | ||||
\(141\) | −9.66321e8 | −2.44481 | ||||||||
\(142\) | −6.57777e7 | − | 6.57777e7i | −0.161780 | − | 0.161780i | ||||
\(143\) | 1.69736e8 | − | 1.69736e8i | 0.405910 | − | 0.405910i | ||||
\(144\) | 1.17093e8i | 0.272321i | ||||||||
\(145\) | 7.52862e7 | − | 4.05751e6i | 0.170311 | − | 0.00917883i | ||||
\(146\) | −4.85991e8 | −1.06959 | ||||||||
\(147\) | 7.46441e8 | + | 7.46441e8i | 1.59855 | + | 1.59855i | ||||
\(148\) | 1.49797e8 | − | 1.49797e8i | 0.312217 | − | 0.312217i | ||||
\(149\) | 553367.i | 0.00112271i | 1.00000 | 0.000561355i | \(0.000178685\pi\) | |||||
−1.00000 | 0.000561355i | \(0.999821\pi\) | ||||||||
\(150\) | −5.14429e8 | + | 5.56113e7i | −1.01616 | + | 0.109850i | ||||
\(151\) | −1.27298e8 | −0.244858 | −0.122429 | − | 0.992477i | \(-0.539068\pi\) | ||||
−0.122429 | + | 0.992477i | \(0.539068\pi\) | |||||||
\(152\) | −7.08623e7 | − | 7.08623e7i | −0.132752 | − | 0.132752i | ||||
\(153\) | −2.24482e7 | + | 2.24482e7i | −0.0409653 | + | 0.0409653i | ||||
\(154\) | − | 9.11968e8i | − | 1.62142i | ||||||
\(155\) | −2.77984e7 | − | 5.15793e8i | −0.0481607 | − | 0.893611i | ||||
\(156\) | −1.71578e8 | −0.289710 | ||||||||
\(157\) | 5.28456e8 | + | 5.28456e8i | 0.869782 | + | 0.869782i | 0.992448 | − | 0.122666i | \(-0.0391443\pi\) |
−0.122666 | + | 0.992448i | \(0.539144\pi\) | |||||||
\(158\) | 3.75791e8 | − | 3.75791e8i | 0.603000 | − | 0.603000i | ||||
\(159\) | − | 3.27350e8i | − | 0.512182i | ||||||
\(160\) | −7.73926e7 | + | 8.62099e7i | −0.118092 | + | 0.131546i | ||||
\(161\) | 5.89765e6 | 0.00877760 | ||||||||
\(162\) | 3.10882e8 | + | 3.10882e8i | 0.451372 | + | 0.451372i | ||||
\(163\) | 2.09644e8 | − | 2.09644e8i | 0.296983 | − | 0.296983i | −0.542848 | − | 0.839831i | \(-0.682654\pi\) |
0.839831 | + | 0.542848i | \(0.182654\pi\) | |||||||
\(164\) | 2.23565e8i | 0.309049i | ||||||||
\(165\) | 1.14166e9 | + | 1.02490e9i | 1.54029 | + | 1.38275i | ||||
\(166\) | 4.50087e8 | 0.592740 | ||||||||
\(167\) | −7.26269e8 | − | 7.26269e8i | −0.933753 | − | 0.933753i | 0.0641853 | − | 0.997938i | \(-0.479555\pi\) |
−0.997938 | + | 0.0641853i | \(0.979555\pi\) | |||||||
\(168\) | −4.60932e8 | + | 4.60932e8i | −0.578628 | + | 0.578628i | ||||
\(169\) | 6.84651e8i | 0.839310i | ||||||||
\(170\) | −3.13647e7 | + | 1.69039e6i | −0.0375531 | + | 0.00202391i | ||||
\(171\) | 4.94569e8 | 0.578418 | ||||||||
\(172\) | 3.88124e8 | + | 3.88124e8i | 0.443462 | + | 0.443462i | ||||
\(173\) | 6.00999e8 | − | 6.00999e8i | 0.670949 | − | 0.670949i | −0.286986 | − | 0.957935i | \(-0.592653\pi\) |
0.957935 | + | 0.286986i | \(0.0926533\pi\) | |||||||
\(174\) | 1.59791e8i | 0.174324i | ||||||||
\(175\) | −1.16992e9 | − | 9.41650e8i | −1.24739 | − | 1.00401i | ||||
\(176\) | 3.43512e8 | 0.358006 | ||||||||
\(177\) | −1.31100e9 | − | 1.31100e9i | −1.33571 | − | 1.33571i | ||||
\(178\) | −6.33534e8 | + | 6.33534e8i | −0.631088 | + | 0.631088i | ||||
\(179\) | 9.25251e8i | 0.901255i | 0.892712 | + | 0.450627i | \(0.148800\pi\) | ||||
−0.892712 | + | 0.450627i | \(0.851200\pi\) | |||||||
\(180\) | −3.07692e7 | − | 5.70915e8i | −0.0293107 | − | 0.543853i | ||||
\(181\) | −8.31703e8 | −0.774914 | −0.387457 | − | 0.921888i | \(-0.626647\pi\) | ||||
−0.387457 | + | 0.921888i | \(0.626647\pi\) | |||||||
\(182\) | −3.52136e8 | − | 3.52136e8i | −0.320941 | − | 0.320941i | ||||
\(183\) | −2.08397e8 | + | 2.08397e8i | −0.185818 | + | 0.185818i | ||||
\(184\) | 2.22147e6i | 0.00193807i | ||||||||
\(185\) | −6.91008e8 | + | 7.69734e8i | −0.589924 | + | 0.657134i | ||||
\(186\) | 1.09475e9 | 0.914665 | ||||||||
\(187\) | 6.58556e7 | + | 6.58556e7i | 0.0538551 | + | 0.0538551i | ||||
\(188\) | 7.47021e8 | − | 7.47021e8i | 0.598000 | − | 0.598000i | ||||
\(189\) | − | 2.63681e8i | − | 0.206648i | ||||||
\(190\) | 3.64127e8 | + | 3.26885e8i | 0.279408 | + | 0.250831i | ||||
\(191\) | 1.17089e9 | 0.879799 | 0.439900 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439900 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(192\) | −1.73620e8 | − | 1.73620e8i | −0.127760 | − | 0.127760i | ||||
\(193\) | −1.41003e9 | + | 1.41003e9i | −1.01624 | + | 1.01624i | −0.0163773 | + | 0.999866i | \(0.505213\pi\) |
−0.999866 | + | 0.0163773i | \(0.994787\pi\) | |||||||
\(194\) | 2.36047e7i | 0.0166645i | ||||||||
\(195\) | 8.36568e8 | − | 4.50864e7i | 0.578579 | − | 0.0311822i | ||||
\(196\) | −1.15408e9 | −0.782010 | ||||||||
\(197\) | −7.98017e8 | − | 7.98017e8i | −0.529843 | − | 0.529843i | 0.390683 | − | 0.920525i | \(-0.372239\pi\) |
−0.920525 | + | 0.390683i | \(0.872239\pi\) | |||||||
\(198\) | −1.19873e9 | + | 1.19873e9i | −0.779941 | + | 0.779941i | ||||
\(199\) | − | 3.89588e8i | − | 0.248424i | −0.992256 | − | 0.124212i | \(-0.960360\pi\) | ||
0.992256 | − | 0.124212i | \(-0.0396402\pi\) | |||||||
\(200\) | 3.54692e8 | − | 4.40674e8i | 0.221683 | − | 0.275421i | ||||
\(201\) | 2.44503e9 | 1.49796 | ||||||||
\(202\) | 1.29005e9 | + | 1.29005e9i | 0.774818 | + | 0.774818i | ||||
\(203\) | −3.27946e8 | + | 3.27946e8i | −0.193116 | + | 0.193116i | ||||
\(204\) | − | 6.65702e7i | − | 0.0384379i | ||||||
\(205\) | −5.87473e7 | − | 1.09004e9i | −0.0332638 | − | 0.617203i | ||||
\(206\) | −2.14643e9 | −1.19192 | ||||||||
\(207\) | −7.75216e6 | − | 7.75216e6i | −0.00422222 | − | 0.00422222i | ||||
\(208\) | 1.32639e8 | − | 1.32639e8i | 0.0708629 | − | 0.0708629i | ||||
\(209\) | − | 1.45090e9i | − | 0.760417i | ||||||
\(210\) | 2.12626e9 | − | 2.36850e9i | 1.09330 | − | 1.21786i | ||||
\(211\) | 3.73042e9 | 1.88204 | 0.941019 | − | 0.338354i | \(-0.109870\pi\) | ||||
0.941019 | + | 0.338354i | \(0.109870\pi\) | |||||||
\(212\) | 2.53060e8 | + | 2.53060e8i | 0.125280 | + | 0.125280i | ||||
\(213\) | −6.80703e8 | + | 6.80703e8i | −0.330704 | + | 0.330704i | ||||
\(214\) | 3.24651e8i | 0.154796i | ||||||||
\(215\) | −1.99438e9 | − | 1.79040e9i | −0.933370 | − | 0.837908i | ||||
\(216\) | 9.93209e7 | 0.0456274 | ||||||||
\(217\) | 2.24679e9 | + | 2.24679e9i | 1.01327 | + | 1.01327i | ||||
\(218\) | 4.22398e8 | − | 4.22398e8i | 0.187023 | − | 0.187023i | ||||
\(219\) | 5.02929e9i | 2.18640i | ||||||||
\(220\) | −1.67487e9 | + | 9.02664e7i | −0.714975 | + | 0.0385332i | ||||
\(221\) | 5.08574e7 | 0.0213199 | ||||||||
\(222\) | −1.55018e9 | − | 1.55018e9i | −0.638220 | − | 0.638220i | ||||
\(223\) | 2.58624e9 | − | 2.58624e9i | 1.04580 | − | 1.04580i | 0.0469003 | − | 0.998900i | \(-0.485066\pi\) |
0.998900 | − | 0.0469003i | \(-0.0149343\pi\) | |||||||
\(224\) | − | 7.12652e8i | − | 0.283065i | ||||||
\(225\) | 3.00045e8 | + | 2.77554e9i | 0.117073 | + | 1.08297i | ||||
\(226\) | −2.00885e9 | −0.770041 | ||||||||
\(227\) | 2.28574e8 | + | 2.28574e8i | 0.0860844 | + | 0.0860844i | 0.748838 | − | 0.662753i | \(-0.230612\pi\) |
−0.662753 | + | 0.748838i | \(0.730612\pi\) | |||||||
\(228\) | −7.33321e8 | + | 7.33321e8i | −0.271366 | + | 0.271366i | ||||
\(229\) | − | 4.29778e9i | − | 1.56280i | −0.624033 | − | 0.781398i | \(-0.714507\pi\) | ||
0.624033 | − | 0.781398i | \(-0.285493\pi\) | |||||||
\(230\) | −583749. | − | 1.08313e7i | −0.000208600 | − | 0.00387053i | ||||
\(231\) | −9.43752e9 | −3.31444 | ||||||||
\(232\) | −1.23528e8 | − | 1.23528e8i | −0.0426396 | − | 0.0426396i | ||||
\(233\) | 2.83013e8 | − | 2.83013e8i | 0.0960247 | − | 0.0960247i | −0.657463 | − | 0.753487i | \(-0.728370\pi\) |
0.753487 | + | 0.657463i | \(0.228370\pi\) | |||||||
\(234\) | 9.25728e8i | 0.308759i | ||||||||
\(235\) | −3.44598e9 | + | 3.83858e9i | −1.12990 | + | 1.25863i | ||||
\(236\) | 2.02696e9 | 0.653427 | ||||||||
\(237\) | −3.88888e9 | − | 3.88888e9i | −1.23263 | − | 1.23263i | ||||
\(238\) | 1.36625e8 | − | 1.36625e8i | 0.0425815 | − | 0.0425815i | ||||
\(239\) | 5.19198e9i | 1.59126i | 0.605782 | + | 0.795630i | \(0.292860\pi\) | ||||
−0.605782 | + | 0.795630i | \(0.707140\pi\) | |||||||
\(240\) | 8.92146e8 | + | 8.00900e8i | 0.268900 | + | 0.241398i | ||||
\(241\) | 4.53061e9 | 1.34304 | 0.671519 | − | 0.740987i | \(-0.265642\pi\) | ||||
0.671519 | + | 0.740987i | \(0.265642\pi\) | |||||||
\(242\) | 1.80181e9 | + | 1.80181e9i | 0.525349 | + | 0.525349i | ||||
\(243\) | 3.53535e9 | − | 3.53535e9i | 1.01393 | − | 1.01393i | ||||
\(244\) | − | 3.22205e8i | − | 0.0909019i | ||||||
\(245\) | 5.62700e9 | − | 3.03264e8i | 1.56175 | − | 0.0841699i | ||||
\(246\) | 2.31357e9 | 0.631745 | ||||||||
\(247\) | −5.60232e8 | − | 5.60232e8i | −0.150515 | − | 0.150515i | ||||
\(248\) | −8.46301e8 | + | 8.46301e8i | −0.223727 | + | 0.223727i | ||||
\(249\) | − | 4.65774e9i | − | 1.21165i | ||||||
\(250\) | −1.61359e9 | + | 2.24181e9i | −0.413079 | + | 0.573904i | ||||
\(251\) | −3.40464e9 | −0.857780 | −0.428890 | − | 0.903357i | \(-0.641095\pi\) | ||||
−0.428890 | + | 0.903357i | \(0.641095\pi\) | |||||||
\(252\) | 2.48690e9 | + | 2.48690e9i | 0.616675 | + | 0.616675i | ||||
\(253\) | −2.27422e7 | + | 2.27422e7i | −0.00555074 | + | 0.00555074i | ||||
\(254\) | − | 1.55132e9i | − | 0.372705i | ||||||
\(255\) | 1.74930e7 | + | 3.24579e8i | 0.00413717 | + | 0.0767643i | ||||
\(256\) | 2.68435e8 | 0.0625000 | ||||||||
\(257\) | 3.01159e7 | + | 3.01159e7i | 0.00690341 | + | 0.00690341i | 0.710550 | − | 0.703647i | \(-0.248446\pi\) |
−0.703647 | + | 0.710550i | \(0.748446\pi\) | |||||||
\(258\) | 4.01651e9 | − | 4.01651e9i | 0.906505 | − | 0.906505i | ||||
\(259\) | − | 6.36299e9i | − | 1.41404i | ||||||
\(260\) | −6.11860e8 | + | 6.81569e8i | −0.133893 | + | 0.149148i | ||||
\(261\) | 8.62136e8 | 0.185786 | ||||||||
\(262\) | 4.95531e8 | + | 4.95531e8i | 0.105164 | + | 0.105164i | ||||
\(263\) | −2.01502e9 | + | 2.01502e9i | −0.421169 | + | 0.421169i | −0.885606 | − | 0.464437i | \(-0.846257\pi\) |
0.464437 | + | 0.885606i | \(0.346257\pi\) | |||||||
\(264\) | − | 3.55484e9i | − | 0.731820i | ||||||
\(265\) | −1.30035e9 | − | 1.16736e9i | −0.263680 | − | 0.236712i | ||||
\(266\) | −3.01005e9 | −0.601238 | ||||||||
\(267\) | 6.55615e9 | + | 6.55615e9i | 1.29004 | + | 1.29004i | ||||
\(268\) | −1.89015e9 | + | 1.89015e9i | −0.366401 | + | 0.366401i | ||||
\(269\) | 9.53840e9i | 1.82166i | 0.412785 | + | 0.910828i | \(0.364556\pi\) | ||||
−0.412785 | + | 0.910828i | \(0.635444\pi\) | |||||||
\(270\) | −4.84262e8 | + | 2.60991e7i | −0.0911225 | + | 0.00491100i | ||||
\(271\) | −3.84233e9 | −0.712390 | −0.356195 | − | 0.934412i | \(-0.615926\pi\) | ||||
−0.356195 | + | 0.934412i | \(0.615926\pi\) | |||||||
\(272\) | 5.14625e7 | + | 5.14625e7i | 0.00940190 | + | 0.00940190i | ||||
\(273\) | −3.64409e9 | + | 3.64409e9i | −0.656052 | + | 0.656052i | ||||
\(274\) | 1.40784e8i | 0.0249776i | ||||||||
\(275\) | 8.14252e9 | − | 8.80230e8i | 1.42373 | − | 0.153910i | ||||
\(276\) | 2.29890e7 | 0.00396172 | ||||||||
\(277\) | −2.80174e9 | − | 2.80174e9i | −0.475892 | − | 0.475892i | 0.427923 | − | 0.903815i | \(-0.359245\pi\) |
−0.903815 | + | 0.427923i | \(0.859245\pi\) | |||||||
\(278\) | −2.17256e8 | + | 2.17256e8i | −0.0363741 | + | 0.0363741i | ||||
\(279\) | − | 5.90658e9i | − | 0.974809i | ||||||
\(280\) | 1.87267e8 | + | 3.47471e9i | 0.0304670 | + | 0.565309i | ||||
\(281\) | −8.28718e9 | −1.32917 | −0.664586 | − | 0.747212i | \(-0.731392\pi\) | ||||
−0.664586 | + | 0.747212i | \(0.731392\pi\) | |||||||
\(282\) | −7.73057e9 | − | 7.73057e9i | −1.22240 | − | 1.22240i | ||||
\(283\) | −7.40766e7 | + | 7.40766e7i | −0.0115488 | + | 0.0115488i | −0.712858 | − | 0.701309i | \(-0.752599\pi\) |
0.701309 | + | 0.712858i | \(0.252599\pi\) | |||||||
\(284\) | − | 1.05244e9i | − | 0.161780i | ||||||
\(285\) | 3.38278e9 | − | 3.76818e9i | 0.512737 | − | 0.571152i | ||||
\(286\) | 2.71578e9 | 0.405910 | ||||||||
\(287\) | 4.74822e9 | + | 4.74822e9i | 0.699848 | + | 0.699848i | ||||
\(288\) | −9.36744e8 | + | 9.36744e8i | −0.136160 | + | 0.136160i | ||||
\(289\) | − | 6.95603e9i | − | 0.997171i | ||||||
\(290\) | 6.34749e8 | + | 5.69829e8i | 0.0897450 | + | 0.0805662i | ||||
\(291\) | 2.44274e8 | 0.0340648 | ||||||||
\(292\) | −3.88793e9 | − | 3.88793e9i | −0.534794 | − | 0.534794i | ||||
\(293\) | −6.33070e9 | + | 6.33070e9i | −0.858977 | + | 0.858977i | −0.991218 | − | 0.132241i | \(-0.957783\pi\) |
0.132241 | + | 0.991218i | \(0.457783\pi\) | |||||||
\(294\) | 1.19431e10i | 1.59855i | ||||||||
\(295\) | −9.88292e9 | + | 5.32635e8i | −1.30496 | + | 0.0703302i | ||||
\(296\) | 2.39675e9 | 0.312217 | ||||||||
\(297\) | 1.01679e9 | + | 1.01679e9i | 0.130679 | + | 0.130679i | ||||
\(298\) | −4.42693e6 | + | 4.42693e6i | −0.000561355 | + | 0.000561355i | ||||
\(299\) | 1.75628e7i | 0.00219740i | ||||||||
\(300\) | −4.56033e9 | − | 3.67054e9i | −0.563003 | − | 0.453154i | ||||
\(301\) | 1.64865e10 | 2.00846 | ||||||||
\(302\) | −1.01838e9 | − | 1.01838e9i | −0.122429 | − | 0.122429i | ||||
\(303\) | 1.33501e10 | − | 1.33501e10i | 1.58385 | − | 1.58385i | ||||
\(304\) | − | 1.13380e9i | − | 0.132752i | ||||||
\(305\) | 8.46676e7 | + | 1.57099e9i | 0.00978403 | + | 0.181540i | ||||
\(306\) | −3.59172e8 | −0.0409653 | ||||||||
\(307\) | 4.80692e9 | + | 4.80692e9i | 0.541144 | + | 0.541144i | 0.923864 | − | 0.382720i | \(-0.125013\pi\) |
−0.382720 | + | 0.923864i | \(0.625013\pi\) | |||||||
\(308\) | 7.29574e9 | − | 7.29574e9i | 0.810712 | − | 0.810712i | ||||
\(309\) | 2.22124e10i | 2.43648i | ||||||||
\(310\) | 3.90396e9 | − | 4.34873e9i | 0.422725 | − | 0.470886i | ||||
\(311\) | 1.06468e10 | 1.13809 | 0.569047 | − | 0.822305i | \(-0.307312\pi\) | ||||
0.569047 | + | 0.822305i | \(0.307312\pi\) | |||||||
\(312\) | −1.37262e9 | − | 1.37262e9i | −0.144855 | − | 0.144855i | ||||
\(313\) | −1.05889e10 | + | 1.05889e10i | −1.10325 | + | 1.10325i | −0.109236 | + | 0.994016i | \(0.534840\pi\) |
−0.994016 | + | 0.109236i | \(0.965160\pi\) | |||||||
\(314\) | 8.45530e9i | 0.869782i | ||||||||
\(315\) | −1.27790e10 | − | 1.14720e10i | −1.29794 | − | 1.16519i | ||||
\(316\) | 6.01265e9 | 0.603000 | ||||||||
\(317\) | −9.51101e9 | − | 9.51101e9i | −0.941867 | − | 0.941867i | 0.0565338 | − | 0.998401i | \(-0.481995\pi\) |
−0.998401 | + | 0.0565338i | \(0.981995\pi\) | |||||||
\(318\) | 2.61880e9 | − | 2.61880e9i | 0.256091 | − | 0.256091i | ||||
\(319\) | − | 2.52922e9i | − | 0.244244i | ||||||
\(320\) | −1.30882e9 | + | 7.05382e7i | −0.124819 | + | 0.00672705i | ||||
\(321\) | 3.35966e9 | 0.316428 | ||||||||
\(322\) | 4.71812e7 | + | 4.71812e7i | 0.00438880 | + | 0.00438880i | ||||
\(323\) | 2.17364e8 | − | 2.17364e8i | 0.0199699 | − | 0.0199699i | ||||
\(324\) | 4.97411e9i | 0.451372i | ||||||||
\(325\) | 2.80417e9 | − | 3.48393e9i | 0.251345 | − | 0.312274i | ||||
\(326\) | 3.35430e9 | 0.296983 | ||||||||
\(327\) | −4.37120e9 | − | 4.37120e9i | −0.382305 | − | 0.382305i | ||||
\(328\) | −1.78852e9 | + | 1.78852e9i | −0.154525 | + | 0.154525i | ||||
\(329\) | − | 3.17315e10i | − | 2.70836i | ||||||
\(330\) | 9.34125e8 | + | 1.73325e10i | 0.0787679 | + | 1.46152i | ||||
\(331\) | −1.31018e10 | −1.09149 | −0.545744 | − | 0.837952i | \(-0.683753\pi\) | ||||
−0.545744 | + | 0.837952i | \(0.683753\pi\) | |||||||
\(332\) | 3.60070e9 | + | 3.60070e9i | 0.296370 | + | 0.296370i | ||||
\(333\) | −8.36381e9 | + | 8.36381e9i | −0.680186 | + | 0.680186i | ||||
\(334\) | − | 1.16203e10i | − | 0.933753i | ||||||
\(335\) | 8.71918e9 | − | 9.71254e9i | 0.692303 | − | 0.771176i | ||||
\(336\) | −7.37491e9 | −0.578628 | ||||||||
\(337\) | 1.33341e10 | + | 1.33341e10i | 1.03382 | + | 1.03382i | 0.999408 | + | 0.0344141i | \(0.0109565\pi\) |
0.0344141 | + | 0.999408i | \(0.489043\pi\) | |||||||
\(338\) | −5.47721e9 | + | 5.47721e9i | −0.419655 | + | 0.419655i | ||||
\(339\) | 2.07886e10i | 1.57408i | ||||||||
\(340\) | −2.64441e8 | − | 2.37395e8i | −0.0197885 | − | 0.0177646i | ||||
\(341\) | −1.73279e10 | −1.28153 | ||||||||
\(342\) | 3.95655e9 | + | 3.95655e9i | 0.289209 | + | 0.289209i | ||||
\(343\) | −8.83927e9 | + | 8.83927e9i | −0.638616 | + | 0.638616i | ||||
\(344\) | 6.20998e9i | 0.443462i | ||||||||
\(345\) | −1.12088e8 | + | 6.04094e6i | −0.00791196 | + | 0.000426411i | ||||
\(346\) | 9.61599e9 | 0.670949 | ||||||||
\(347\) | −1.09024e10 | − | 1.09024e10i | −0.751973 | − | 0.751973i | 0.222874 | − | 0.974847i | \(-0.428456\pi\) |
−0.974847 | + | 0.222874i | \(0.928456\pi\) | |||||||
\(348\) | −1.27833e9 | + | 1.27833e9i | −0.0871619 | + | 0.0871619i | ||||
\(349\) | 9.67778e9i | 0.652340i | 0.945311 | + | 0.326170i | \(0.105758\pi\) | ||||
−0.945311 | + | 0.326170i | \(0.894242\pi\) | |||||||
\(350\) | −1.82613e9 | − | 1.68925e10i | −0.121692 | − | 1.12570i | ||||
\(351\) | 7.85223e8 | 0.0517326 | ||||||||
\(352\) | 2.74809e9 | + | 2.74809e9i | 0.179003 | + | 0.179003i | ||||
\(353\) | 6.27335e9 | − | 6.27335e9i | 0.404018 | − | 0.404018i | −0.475628 | − | 0.879646i | \(-0.657779\pi\) |
0.879646 | + | 0.475628i | \(0.157779\pi\) | |||||||
\(354\) | − | 2.09761e10i | − | 1.33571i | ||||||
\(355\) | 2.76556e8 | + | 5.13144e9i | 0.0174129 | + | 0.323092i | ||||
\(356\) | −1.01365e10 | −0.631088 | ||||||||
\(357\) | −1.41386e9 | − | 1.41386e9i | −0.0870432 | − | 0.0870432i | ||||
\(358\) | −7.40201e9 | + | 7.40201e9i | −0.450627 | + | 0.450627i | ||||
\(359\) | 7.91205e9i | 0.476334i | 0.971224 | + | 0.238167i | \(0.0765465\pi\) | ||||
−0.971224 | + | 0.238167i | \(0.923454\pi\) | |||||||
\(360\) | 4.32116e9 | − | 4.81347e9i | 0.257271 | − | 0.286582i | ||||
\(361\) | 1.21947e10 | 0.718031 | ||||||||
\(362\) | −6.65362e9 | − | 6.65362e9i | −0.387457 | − | 0.387457i | ||||
\(363\) | 1.86461e10 | − | 1.86461e10i | 1.07389 | − | 1.07389i | ||||
\(364\) | − | 5.63417e9i | − | 0.320941i | ||||||
\(365\) | 1.99782e10 | + | 1.79349e10i | 1.12560 | + | 1.01048i | ||||
\(366\) | −3.33435e9 | −0.185818 | ||||||||
\(367\) | 6.65934e9 | + | 6.65934e9i | 0.367085 | + | 0.367085i | 0.866413 | − | 0.499328i | \(-0.166420\pi\) |
−0.499328 | + | 0.866413i | \(0.666420\pi\) | |||||||
\(368\) | −1.77718e7 | + | 1.77718e7i | −0.000969036 | + | 0.000969036i | ||||
\(369\) | − | 1.24826e10i | − | 0.673285i | ||||||
\(370\) | −1.16859e10 | + | 6.29808e8i | −0.623529 | + | 0.0336048i | ||||
\(371\) | 1.07493e10 | 0.567396 | ||||||||
\(372\) | 8.75798e9 | + | 8.75798e9i | 0.457333 | + | 0.457333i | ||||
\(373\) | 1.63417e10 | − | 1.63417e10i | 0.844230 | − | 0.844230i | −0.145176 | − | 0.989406i | \(-0.546375\pi\) |
0.989406 | + | 0.145176i | \(0.0463748\pi\) | |||||||
\(374\) | 1.05369e9i | 0.0538551i | ||||||||
\(375\) | 2.31995e10 | + | 1.66983e10i | 1.17315 | + | 0.844396i | ||||
\(376\) | 1.19523e10 | 0.598000 | ||||||||
\(377\) | −9.76602e8 | − | 9.76602e8i | −0.0483450 | − | 0.0483450i | ||||
\(378\) | 2.10945e9 | − | 2.10945e9i | 0.103324 | − | 0.103324i | ||||
\(379\) | − | 9.14573e9i | − | 0.443263i | −0.975130 | − | 0.221632i | \(-0.928862\pi\) | ||
0.975130 | − | 0.221632i | \(-0.0711382\pi\) | |||||||
\(380\) | 2.97934e8 | + | 5.52810e9i | 0.0142885 | + | 0.265119i | ||||
\(381\) | −1.60538e10 | −0.761867 | ||||||||
\(382\) | 9.36714e9 | + | 9.36714e9i | 0.439900 | + | 0.439900i | ||||
\(383\) | −6.52966e9 | + | 6.52966e9i | −0.303456 | + | 0.303456i | −0.842364 | − | 0.538909i | \(-0.818837\pi\) |
0.538909 | + | 0.842364i | \(0.318837\pi\) | |||||||
\(384\) | − | 2.77791e9i | − | 0.127760i | ||||||
\(385\) | −3.36550e10 | + | 3.74892e10i | −1.53181 | + | 1.70633i | ||||
\(386\) | −2.25604e10 | −1.01624 | ||||||||
\(387\) | −2.16706e10 | − | 2.16706e10i | −0.966112 | − | 0.966112i | ||||
\(388\) | −1.88838e8 | + | 1.88838e8i | −0.00833225 | + | 0.00833225i | ||||
\(389\) | − | 2.04596e10i | − | 0.893507i | −0.894657 | − | 0.446754i | \(-0.852580\pi\) | ||
0.894657 | − | 0.446754i | \(-0.147420\pi\) | |||||||
\(390\) | 7.05324e9 | + | 6.33186e9i | 0.304881 | + | 0.273699i | ||||
\(391\) | −6.81417e6 | −0.000291545 | ||||||||
\(392\) | −9.23265e9 | − | 9.23265e9i | −0.391005 | − | 0.391005i | ||||
\(393\) | 5.12801e9 | − | 5.12801e9i | 0.214971 | − | 0.214971i | ||||
\(394\) | − | 1.27683e10i | − | 0.529843i | ||||||
\(395\) | −2.93161e10 | + | 1.57998e9i | −1.20425 | + | 0.0649026i | ||||
\(396\) | −1.91797e10 | −0.779941 | ||||||||
\(397\) | −7.68996e9 | − | 7.68996e9i | −0.309572 | − | 0.309572i | 0.535171 | − | 0.844744i | \(-0.320247\pi\) |
−0.844744 | + | 0.535171i | \(0.820247\pi\) | |||||||
\(398\) | 3.11670e9 | − | 3.11670e9i | 0.124212 | − | 0.124212i | ||||
\(399\) | 3.11496e10i | 1.22902i | ||||||||
\(400\) | 6.36293e9 | − | 6.87851e8i | 0.248552 | − | 0.0268692i | ||||
\(401\) | −5.85624e9 | −0.226486 | −0.113243 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113243 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(402\) | 1.95602e10 | + | 1.95602e10i | 0.748980 | + | 0.748980i | ||||
\(403\) | −6.69079e9 | + | 6.69079e9i | −0.253663 | + | 0.253663i | ||||
\(404\) | 2.06407e10i | 0.774818i | ||||||||
\(405\) | −1.30707e9 | − | 2.42524e10i | −0.0485825 | − | 0.901437i | ||||
\(406\) | −5.24714e9 | −0.193116 | ||||||||
\(407\) | 2.45366e10 | + | 2.45366e10i | 0.894205 | + | 0.894205i | ||||
\(408\) | 5.32562e8 | − | 5.32562e8i | 0.0192189 | − | 0.0192189i | ||||
\(409\) | 1.32972e10i | 0.475191i | 0.971364 | + | 0.237596i | \(0.0763593\pi\) | ||||
−0.971364 | + | 0.237596i | \(0.923641\pi\) | |||||||
\(410\) | 8.25036e9 | − | 9.19032e9i | 0.291970 | − | 0.325233i | ||||
\(411\) | 1.45690e9 | 0.0510580 | ||||||||
\(412\) | −1.71715e10 | − | 1.71715e10i | −0.595962 | − | 0.595962i | ||||
\(413\) | 4.30500e10 | − | 4.30500e10i | 1.47970 | − | 1.47970i | ||||
\(414\) | − | 1.24034e8i | − | 0.00422222i | ||||||
\(415\) | −1.85022e10 | − | 1.66099e10i | −0.623780 | − | 0.559982i | ||||
\(416\) | 2.12223e9 | 0.0708629 | ||||||||
\(417\) | 2.24828e9 | + | 2.24828e9i | 0.0743542 | + | 0.0743542i | ||||
\(418\) | 1.16072e10 | − | 1.16072e10i | 0.380209 | − | 0.380209i | ||||
\(419\) | − | 6.98994e9i | − | 0.226786i | −0.993550 | − | 0.113393i | \(-0.963828\pi\) | ||
0.993550 | − | 0.113393i | \(-0.0361720\pi\) | |||||||
\(420\) | 3.59581e10 | − | 1.93794e9i | 1.15558 | − | 0.0622793i | ||||
\(421\) | −2.54099e10 | −0.808864 | −0.404432 | − | 0.914568i | \(-0.632531\pi\) | ||||
−0.404432 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(422\) | 2.98434e10 | + | 2.98434e10i | 0.941019 | + | 0.941019i | ||||
\(423\) | −4.17094e10 | + | 4.17094e10i | −1.30278 | + | 1.30278i | ||||
\(424\) | 4.04896e9i | 0.125280i | ||||||||
\(425\) | 1.35173e9 | + | 1.08799e9i | 0.0414317 | + | 0.0333478i | ||||
\(426\) | −1.08912e10 | −0.330704 | ||||||||
\(427\) | −6.84322e9 | − | 6.84322e9i | −0.205849 | − | 0.205849i | ||||
\(428\) | −2.59720e9 | + | 2.59720e9i | −0.0773982 | + | 0.0773982i | ||||
\(429\) | − | 2.81043e10i | − | 0.829743i | ||||||
\(430\) | −1.63183e9 | − | 3.02782e10i | −0.0477311 | − | 0.885639i | ||||
\(431\) | 3.72373e10 | 1.07912 | 0.539559 | − | 0.841948i | \(-0.318591\pi\) | ||||
0.539559 | + | 0.841948i | \(0.318591\pi\) | |||||||
\(432\) | 7.94567e8 | + | 7.94567e8i | 0.0228137 | + | 0.0228137i | ||||
\(433\) | 1.34378e10 | − | 1.34378e10i | 0.382277 | − | 0.382277i | −0.489645 | − | 0.871922i | \(-0.662874\pi\) |
0.871922 | + | 0.489645i | \(0.162874\pi\) | |||||||
\(434\) | 3.59487e10i | 1.01327i | ||||||||
\(435\) | 5.89689e9 | − | 6.56872e9i | 0.164690 | − | 0.183453i | ||||
\(436\) | 6.75837e9 | 0.187023 | ||||||||
\(437\) | 7.50632e7 | + | 7.50632e7i | 0.00205826 | + | 0.00205826i | ||||
\(438\) | −4.02343e10 | + | 4.02343e10i | −1.09320 | + | 1.09320i | ||||
\(439\) | − | 4.19540e10i | − | 1.12957i | −0.825237 | − | 0.564787i | \(-0.808958\pi\) | ||
0.825237 | − | 0.564787i | \(-0.191042\pi\) | |||||||
\(440\) | −1.41211e10 | − | 1.26768e10i | −0.376754 | − | 0.338221i | ||||
\(441\) | 6.44373e10 | 1.70366 | ||||||||
\(442\) | 4.06859e8 | + | 4.06859e8i | 0.0106599 | + | 0.0106599i | ||||
\(443\) | −3.76709e10 | + | 3.76709e10i | −0.978119 | + | 0.978119i | −0.999766 | − | 0.0216469i | \(-0.993109\pi\) |
0.0216469 | + | 0.999766i | \(0.493109\pi\) | |||||||
\(444\) | − | 2.48029e10i | − | 0.638220i | ||||||
\(445\) | 4.94231e10 | − | 2.66363e9i | 1.26035 | − | 0.0679258i | ||||
\(446\) | 4.13798e10 | 1.04580 | ||||||||
\(447\) | 4.58122e7 | + | 4.58122e7i | 0.00114750 | + | 0.00114750i | ||||
\(448\) | 5.70122e9 | − | 5.70122e9i | 0.141532 | − | 0.141532i | ||||
\(449\) | 5.05667e10i | 1.24417i | 0.782950 | + | 0.622085i | \(0.213714\pi\) | ||||
−0.782950 | + | 0.622085i | \(0.786286\pi\) | |||||||
\(450\) | −1.98040e10 | + | 2.46047e10i | −0.482951 | + | 0.600023i | ||||
\(451\) | −3.66197e10 | −0.885133 | ||||||||
\(452\) | −1.60708e10 | − | 1.60708e10i | −0.385020 | − | 0.385020i | ||||
\(453\) | −1.05388e10 | + | 1.05388e10i | −0.250264 | + | 0.250264i | ||||
\(454\) | 3.65719e9i | 0.0860844i | ||||||||
\(455\) | 1.48052e9 | + | 2.74708e10i | 0.0345437 | + | 0.640951i | ||||
\(456\) | −1.17331e10 | −0.271366 | ||||||||
\(457\) | 1.52066e10 | + | 1.52066e10i | 0.348631 | + | 0.348631i | 0.859599 | − | 0.510968i | \(-0.170713\pi\) |
−0.510968 | + | 0.859599i | \(0.670713\pi\) | |||||||
\(458\) | 3.43822e10 | − | 3.43822e10i | 0.781398 | − | 0.781398i | ||||
\(459\) | 3.04657e8i | 0.00686374i | ||||||||
\(460\) | 8.19806e7 | − | 9.13206e7i | 0.00183096 | − | 0.00203956i | ||||
\(461\) | −2.73791e10 | −0.606199 | −0.303100 | − | 0.952959i | \(-0.598021\pi\) | ||||
−0.303100 | + | 0.952959i | \(0.598021\pi\) | |||||||
\(462\) | −7.55002e10 | − | 7.55002e10i | −1.65722 | − | 1.65722i | ||||
\(463\) | 3.53408e10 | − | 3.53408e10i | 0.769046 | − | 0.769046i | −0.208893 | − | 0.977939i | \(-0.566986\pi\) |
0.977939 | + | 0.208893i | \(0.0669859\pi\) | |||||||
\(464\) | − | 1.97645e9i | − | 0.0426396i | ||||||
\(465\) | −4.50030e10 | − | 4.04002e10i | −0.962563 | − | 0.864116i | ||||
\(466\) | 4.52821e9 | 0.0960247 | ||||||||
\(467\) | −4.85998e10 | − | 4.85998e10i | −1.02180 | − | 1.02180i | −0.999757 | − | 0.0220454i | \(-0.992982\pi\) |
−0.0220454 | − | 0.999757i | \(-0.507018\pi\) | |||||||
\(468\) | −7.40583e9 | + | 7.40583e9i | −0.154380 | + | 0.154380i | ||||
\(469\) | 8.02885e10i | 1.65944i | ||||||||
\(470\) | −5.82764e10 | + | 3.14078e9i | −1.19427 | + | 0.0643644i | ||||
\(471\) | 8.75000e10 | 1.77797 | ||||||||
\(472\) | 1.62157e10 | + | 1.62157e10i | 0.326713 | + | 0.326713i | ||||
\(473\) | −6.35744e10 | + | 6.35744e10i | −1.27010 | + | 1.27010i | ||||
\(474\) | − | 6.22221e10i | − | 1.23263i | ||||||
\(475\) | −2.90529e9 | − | 2.68753e10i | −0.0570710 | − | 0.527932i | ||||
\(476\) | 2.18600e9 | 0.0425815 | ||||||||
\(477\) | −1.41294e10 | − | 1.41294e10i | −0.272930 | − | 0.272930i | ||||
\(478\) | −4.15358e10 | + | 4.15358e10i | −0.795630 | + | 0.795630i | ||||
\(479\) | 5.06476e10i | 0.962093i | 0.876695 | + | 0.481047i | \(0.159743\pi\) | ||||
−0.876695 | + | 0.481047i | \(0.840257\pi\) | |||||||
\(480\) | 7.29967e8 | + | 1.35444e10i | 0.0137511 | + | 0.255149i | ||||
\(481\) | 1.89485e10 | 0.353994 | ||||||||
\(482\) | 3.62449e10 | + | 3.62449e10i | 0.671519 | + | 0.671519i | ||||
\(483\) | 4.88257e8 | − | 4.88257e8i | 0.00897139 | − | 0.00897139i | ||||
\(484\) | 2.88290e10i | 0.525349i | ||||||||
\(485\) | 8.71102e8 | − | 9.70346e8i | 0.0157435 | − | 0.0175372i | ||||
\(486\) | 5.65657e10 | 1.01393 | ||||||||
\(487\) | 3.99713e9 | + | 3.99713e9i | 0.0710612 | + | 0.0710612i | 0.741744 | − | 0.670683i | \(-0.233999\pi\) |
−0.670683 | + | 0.741744i | \(0.733999\pi\) | |||||||
\(488\) | 2.57764e9 | − | 2.57764e9i | 0.0454510 | − | 0.0454510i | ||||
\(489\) | − | 3.47121e10i | − | 0.607079i | ||||||
\(490\) | 4.74421e10 | + | 4.25899e10i | 0.822962 | + | 0.738792i | ||||
\(491\) | 4.99004e10 | 0.858575 | 0.429288 | − | 0.903168i | \(-0.358765\pi\) | ||||
0.429288 | + | 0.903168i | \(0.358765\pi\) | |||||||
\(492\) | 1.85085e10 | + | 1.85085e10i | 0.315872 | + | 0.315872i | ||||
\(493\) | 3.78910e8 | − | 3.78910e8i | 0.00641429 | − | 0.00641429i | ||||
\(494\) | − | 8.96371e9i | − | 0.150515i | ||||||
\(495\) | 9.35153e10 | − | 5.03996e9i | 1.55762 | − | 0.0839472i | ||||
\(496\) | −1.35408e10 | −0.223727 | ||||||||
\(497\) | −2.23525e10 | − | 2.23525e10i | −0.366354 | − | 0.366354i | ||||
\(498\) | 3.72619e10 | − | 3.72619e10i | 0.605826 | − | 0.605826i | ||||
\(499\) | − | 7.43519e10i | − | 1.19920i | −0.800302 | − | 0.599598i | \(-0.795327\pi\) | ||
0.800302 | − | 0.599598i | \(-0.204673\pi\) | |||||||
\(500\) | −3.08432e10 | + | 5.02580e9i | −0.493491 | + | 0.0804128i | ||||
\(501\) | −1.20253e11 | −1.90873 | ||||||||
\(502\) | −2.72371e10 | − | 2.72371e10i | −0.428890 | − | 0.428890i | ||||
\(503\) | 5.52095e10 | − | 5.52095e10i | 0.862465 | − | 0.862465i | −0.129158 | − | 0.991624i | \(-0.541228\pi\) |
0.991624 | + | 0.129158i | \(0.0412276\pi\) | |||||||
\(504\) | 3.97904e10i | 0.616675i | ||||||||
\(505\) | −5.42387e9 | − | 1.00639e11i | −0.0833958 | − | 1.54739i | ||||
\(506\) | −3.63876e8 | −0.00555074 | ||||||||
\(507\) | 5.66811e10 | + | 5.66811e10i | 0.857840 | + | 0.857840i | ||||
\(508\) | 1.24105e10 | − | 1.24105e10i | 0.186352 | − | 0.186352i | ||||
\(509\) | 1.27030e10i | 0.189249i | 0.995513 | + | 0.0946245i | \(0.0301650\pi\) | ||||
−0.995513 | + | 0.0946245i | \(0.969835\pi\) | |||||||
\(510\) | −2.45669e9 | + | 2.73658e9i | −0.0363136 | + | 0.0404508i | ||||
\(511\) | −1.65149e11 | −2.42210 | ||||||||
\(512\) | 2.14748e9 | + | 2.14748e9i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 3.35603e9 | − | 3.35603e9i | 0.0484570 | − | 0.0484570i | ||||
\(514\) | 4.81855e8i | 0.00690341i | ||||||||
\(515\) | 8.82358e10 | + | 7.92113e10i | 1.25434 | + | 1.12605i | ||||
\(516\) | 6.42642e10 | 0.906505 | ||||||||
\(517\) | 1.22361e11 | + | 1.22361e11i | 1.71270 | + | 1.71270i | ||||
\(518\) | 5.09039e10 | − | 5.09039e10i | 0.707021 | − | 0.707021i | ||||
\(519\) | − | 9.95114e10i | − | 1.37152i | ||||||
\(520\) | −1.03474e10 | + | 5.57670e8i | −0.141520 | + | 0.00762717i | ||||
\(521\) | −3.13323e10 | −0.425247 | −0.212623 | − | 0.977134i | \(-0.568201\pi\) | ||||
−0.212623 | + | 0.977134i | \(0.568201\pi\) | |||||||
\(522\) | 6.89709e9 | + | 6.89709e9i | 0.0928932 | + | 0.0928932i | ||||
\(523\) | −1.15624e10 | + | 1.15624e10i | −0.154539 | + | 0.154539i | −0.780142 | − | 0.625603i | \(-0.784853\pi\) |
0.625603 | + | 0.780142i | \(0.284853\pi\) | |||||||
\(524\) | 7.92849e9i | 0.105164i | ||||||||
\(525\) | −1.74813e11 | + | 1.88978e10i | −2.30111 | + | 0.248756i | ||||
\(526\) | −3.22403e10 | −0.421169 | ||||||||
\(527\) | −2.59595e9 | − | 2.59595e9i | −0.0336553 | − | 0.0336553i | ||||
\(528\) | 2.84387e10 | − | 2.84387e10i | 0.365910 | − | 0.365910i | ||||
\(529\) | 7.83086e10i | 0.999970i | ||||||||
\(530\) | −1.06397e9 | − | 1.97417e10i | −0.0134842 | − | 0.250196i | ||||
\(531\) | −1.13174e11 | −1.42353 | ||||||||
\(532\) | −2.40804e10 | − | 2.40804e10i | −0.300619 | − | 0.300619i | ||||
\(533\) | −1.41399e10 | + | 1.41399e10i | −0.175201 | + | 0.175201i | ||||
\(534\) | 1.04898e11i | 1.29004i | ||||||||
\(535\) | 1.19808e10 | − | 1.33458e10i | 0.146242 | − | 0.162903i | ||||
\(536\) | −3.02424e10 | −0.366401 | ||||||||
\(537\) | 7.65999e10 | + | 7.65999e10i | 0.921152 | + | 0.921152i | ||||
\(538\) | −7.63072e10 | + | 7.63072e10i | −0.910828 | + | 0.910828i | ||||
\(539\) | − | 1.89038e11i | − | 2.23972i | ||||||
\(540\) | −4.08289e9 | − | 3.66531e9i | −0.0480168 | − | 0.0431058i | ||||
\(541\) | 1.21976e11 | 1.42392 | 0.711961 | − | 0.702219i | \(-0.247807\pi\) | ||||
0.711961 | + | 0.702219i | \(0.247807\pi\) | |||||||
\(542\) | −3.07387e10 | − | 3.07387e10i | −0.356195 | − | 0.356195i | ||||
\(543\) | −6.88552e10 | + | 6.88552e10i | −0.792022 | + | 0.792022i | ||||
\(544\) | 8.23401e8i | 0.00940190i | ||||||||
\(545\) | −3.29520e10 | + | 1.77593e9i | −0.373505 | + | 0.0201298i | ||||
\(546\) | −5.83054e10 | −0.656052 | ||||||||
\(547\) | −1.11157e11 | − | 1.11157e11i | −1.24161 | − | 1.24161i | −0.959331 | − | 0.282283i | \(-0.908908\pi\) |
−0.282283 | − | 0.959331i | \(-0.591092\pi\) | |||||||
\(548\) | −1.12627e9 | + | 1.12627e9i | −0.0124888 | + | 0.0124888i | ||||
\(549\) | 1.79901e10i | 0.198036i | ||||||||
\(550\) | 7.21820e10 | + | 5.80983e10i | 0.788820 | + | 0.634911i | ||||
\(551\) | −8.34796e9 | −0.0905678 | ||||||||
\(552\) | 1.83912e8 | + | 1.83912e8i | 0.00198086 | + | 0.00198086i | ||||
\(553\) | 1.27701e11 | − | 1.27701e11i | 1.36550 | − | 1.36550i | ||||
\(554\) | − | 4.48278e10i | − | 0.475892i | ||||||
\(555\) | 6.51758e9 | + | 1.20932e11i | 0.0686933 | + | 1.27459i | ||||
\(556\) | −3.47609e9 | −0.0363741 | ||||||||
\(557\) | −2.14972e10 | − | 2.14972e10i | −0.223337 | − | 0.223337i | 0.586565 | − | 0.809902i | \(-0.300480\pi\) |
−0.809902 | + | 0.586565i | \(0.800480\pi\) | |||||||
\(558\) | 4.72526e10 | − | 4.72526e10i | 0.487404 | − | 0.487404i | ||||
\(559\) | 4.90957e10i | 0.502801i | ||||||||
\(560\) | −2.62995e10 | + | 2.92958e10i | −0.267421 | + | 0.297888i | ||||
\(561\) | 1.09041e10 | 0.110088 | ||||||||
\(562\) | −6.62974e10 | − | 6.62974e10i | −0.664586 | − | 0.664586i | ||||
\(563\) | −2.68020e10 | + | 2.68020e10i | −0.266768 | + | 0.266768i | −0.827796 | − | 0.561029i | \(-0.810406\pi\) |
0.561029 | + | 0.827796i | \(0.310406\pi\) | |||||||
\(564\) | − | 1.23689e11i | − | 1.22240i | ||||||
\(565\) | 8.25800e10 | + | 7.41340e10i | 0.810366 | + | 0.727484i | ||||
\(566\) | −1.18523e9 | −0.0115488 | ||||||||
\(567\) | 1.05644e11 | + | 1.05644e11i | 1.02214 | + | 1.02214i | ||||
\(568\) | 8.41955e9 | − | 8.41955e9i | 0.0808901 | − | 0.0808901i | ||||
\(569\) | − | 9.52278e10i | − | 0.908479i | −0.890880 | − | 0.454240i | \(-0.849911\pi\) | ||
0.890880 | − | 0.454240i | \(-0.150089\pi\) | |||||||
\(570\) | 5.72077e10 | − | 3.08318e9i | 0.541945 | − | 0.0292078i | ||||
\(571\) | 1.93929e11 | 1.82431 | 0.912154 | − | 0.409848i | \(-0.134418\pi\) | ||||
0.912154 | + | 0.409848i | \(0.134418\pi\) | |||||||
\(572\) | 2.17262e10 | + | 2.17262e10i | 0.202955 | + | 0.202955i | ||||
\(573\) | 9.69361e10 | − | 9.69361e10i | 0.899223 | − | 0.899223i | ||||
\(574\) | 7.59716e10i | 0.699848i | ||||||||
\(575\) | −3.75719e8 | + | 4.66798e8i | −0.00343710 | + | 0.00427029i | ||||
\(576\) | −1.49879e10 | −0.136160 | ||||||||
\(577\) | −1.25849e11 | − | 1.25849e11i | −1.13540 | − | 1.13540i | −0.989265 | − | 0.146131i | \(-0.953318\pi\) |
−0.146131 | − | 0.989265i | \(-0.546682\pi\) | |||||||
\(578\) | 5.56482e10 | − | 5.56482e10i | 0.498586 | − | 0.498586i | ||||
\(579\) | 2.33467e11i | 2.07736i | ||||||||
\(580\) | 5.19361e8 | + | 9.63663e9i | 0.00458942 | + | 0.0851556i | ||||
\(581\) | 1.52948e11 | 1.34227 | ||||||||
\(582\) | 1.95420e9 | + | 1.95420e9i | 0.0170324 | + | 0.0170324i | ||||
\(583\) | −4.14510e10 | + | 4.14510e10i | −0.358807 | + | 0.358807i | ||||
\(584\) | − | 6.22068e10i | − | 0.534794i | ||||||
\(585\) | 3.41628e10 | − | 3.80549e10i | 0.291696 | − | 0.324928i | ||||
\(586\) | −1.01291e11 | −0.858977 | ||||||||
\(587\) | 3.41535e10 | + | 3.41535e10i | 0.287662 | + | 0.287662i | 0.836155 | − | 0.548493i | \(-0.184798\pi\) |
−0.548493 | + | 0.836155i | \(0.684798\pi\) | |||||||
\(588\) | −9.55444e10 | + | 9.55444e10i | −0.799275 | + | 0.799275i | ||||
\(589\) | 5.71927e10i | 0.475203i | ||||||||
\(590\) | −8.33244e10 | − | 7.48023e10i | −0.687645 | − | 0.617315i | ||||
\(591\) | −1.32133e11 | −1.08308 | ||||||||
\(592\) | 1.91740e10 | + | 1.91740e10i | 0.156108 | + | 0.156108i | ||||
\(593\) | −1.67663e11 | + | 1.67663e11i | −1.35588 | + | 1.35588i | −0.476939 | + | 0.878937i | \(0.658254\pi\) |
−0.878937 | + | 0.476939i | \(0.841746\pi\) | |||||||
\(594\) | 1.62687e10i | 0.130679i | ||||||||
\(595\) | −1.06583e10 | + | 5.74426e8i | −0.0850397 | + | 0.00458317i | ||||
\(596\) | −7.08309e7 | −0.000561355 | ||||||||
\(597\) | −3.22533e10 | − | 3.22533e10i | −0.253908 | − | 0.253908i | ||||
\(598\) | −1.40502e8 | + | 1.40502e8i | −0.00109870 | + | 0.00109870i | ||||
\(599\) | − | 2.21439e11i | − | 1.72007i | −0.510231 | − | 0.860037i | \(-0.670440\pi\) | ||
0.510231 | − | 0.860037i | \(-0.329560\pi\) | |||||||
\(600\) | −7.11825e9 | − | 6.58470e10i | −0.0549248 | − | 0.508078i | ||||
\(601\) | −2.25242e11 | −1.72644 | −0.863220 | − | 0.504828i | \(-0.831556\pi\) | ||||
−0.863220 | + | 0.504828i | \(0.831556\pi\) | |||||||
\(602\) | 1.31892e11 | + | 1.31892e11i | 1.00423 | + | 1.00423i | ||||
\(603\) | 1.05535e11 | − | 1.05535e11i | 0.798229 | − | 0.798229i | ||||
\(604\) | − | 1.62942e10i | − | 0.122429i | ||||||
\(605\) | −7.57554e9 | − | 1.40562e11i | −0.0565447 | − | 1.04917i | ||||
\(606\) | 2.13601e11 | 1.58385 | ||||||||
\(607\) | −8.03075e10 | − | 8.03075e10i | −0.591563 | − | 0.591563i | 0.346490 | − | 0.938054i | \(-0.387373\pi\) |
−0.938054 | + | 0.346490i | \(0.887373\pi\) | |||||||
\(608\) | 9.07038e9 | − | 9.07038e9i | 0.0663760 | − | 0.0663760i | ||||
\(609\) | 5.43002e10i | 0.394759i | ||||||||
\(610\) | −1.18906e10 | + | 1.32452e10i | −0.0858782 | + | 0.0956622i | ||||
\(611\) | 9.44942e10 | 0.678017 | ||||||||
\(612\) | −2.87338e9 | − | 2.87338e9i | −0.0204827 | − | 0.0204827i | ||||
\(613\) | −5.38969e10 | + | 5.38969e10i | −0.381700 | + | 0.381700i | −0.871714 | − | 0.490014i | \(-0.836992\pi\) |
0.490014 | + | 0.871714i | \(0.336992\pi\) | |||||||
\(614\) | 7.69107e10i | 0.541144i | ||||||||
\(615\) | −9.51063e10 | − | 8.53791e10i | −0.664827 | − | 0.596831i | ||||
\(616\) | 1.16732e11 | 0.810712 | ||||||||
\(617\) | −1.37064e10 | − | 1.37064e10i | −0.0945766 | − | 0.0945766i | 0.658235 | − | 0.752812i | \(-0.271303\pi\) |
−0.752812 | + | 0.658235i | \(0.771303\pi\) | |||||||
\(618\) | −1.77699e11 | + | 1.77699e11i | −1.21824 | + | 1.21824i | ||||
\(619\) | 1.67460e11i | 1.14064i | 0.821423 | + | 0.570320i | \(0.193181\pi\) | ||||
−0.821423 | + | 0.570320i | \(0.806819\pi\) | |||||||
\(620\) | 6.60215e10 | − | 3.55819e9i | 0.446806 | − | 0.0240804i | ||||
\(621\) | −1.05209e8 | −0.000707433 | ||||||||
\(622\) | 8.51746e10 | + | 8.51746e10i | 0.569047 | + | 0.569047i | ||||
\(623\) | −2.15287e11 | + | 2.15287e11i | −1.42911 | + | 1.42911i | ||||
\(624\) | − | 2.19620e10i | − | 0.144855i | ||||||
\(625\) | 1.49063e11 | − | 3.26093e10i | 0.976897 | − | 0.213708i | ||||
\(626\) | −1.69423e11 | −1.10325 | ||||||||
\(627\) | −1.20117e11 | − | 1.20117e11i | −0.777205 | − | 0.777205i | ||||
\(628\) | −6.76424e10 | + | 6.76424e10i | −0.434891 | + | 0.434891i | ||||
\(629\) | 7.35182e9i | 0.0469669i | ||||||||
\(630\) | −1.04559e10 | − | 1.94008e11i | −0.0663745 | − | 1.23156i | ||||
\(631\) | 9.05920e10 | 0.571442 | 0.285721 | − | 0.958313i | \(-0.407767\pi\) | ||||
0.285721 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(632\) | 4.81012e10 | + | 4.81012e10i | 0.301500 | + | 0.301500i | ||||
\(633\) | 3.08835e11 | − | 3.08835e11i | 1.92359 | − | 1.92359i | ||||
\(634\) | − | 1.52176e11i | − | 0.941867i | ||||||
\(635\) | −5.72493e10 | + | 6.37716e10i | −0.352107 | + | 0.392223i | ||||
\(636\) | 4.19008e10 | 0.256091 | ||||||||
\(637\) | −7.29926e10 | − | 7.29926e10i | −0.443324 | − | 0.443324i | ||||
\(638\) | 2.02338e10 | − | 2.02338e10i | 0.122122 | − | 0.122122i | ||||
\(639\) | 5.87625e10i | 0.352449i | ||||||||
\(640\) | −1.10349e10 | − | 9.90626e9i | −0.0657730 | − | 0.0590459i | ||||
\(641\) | −2.71517e10 | −0.160829 | −0.0804147 | − | 0.996761i | \(-0.525624\pi\) | ||||
−0.0804147 | + | 0.996761i | \(0.525624\pi\) | |||||||
\(642\) | 2.68773e10 | + | 2.68773e10i | 0.158214 | + | 0.158214i | ||||
\(643\) | −2.63399e10 | + | 2.63399e10i | −0.154089 | + | 0.154089i | −0.779941 | − | 0.625853i | \(-0.784751\pi\) |
0.625853 | + | 0.779941i | \(0.284751\pi\) | |||||||
\(644\) | 7.54900e8i | 0.00438880i | ||||||||
\(645\) | −3.13335e11 | + | 1.68870e10i | −1.81038 | + | 0.0975697i | ||||
\(646\) | 3.47782e9 | 0.0199699 | ||||||||
\(647\) | −2.14034e9 | − | 2.14034e9i | −0.0122142 | − | 0.0122142i | 0.700973 | − | 0.713188i | \(-0.252749\pi\) |
−0.713188 | + | 0.700973i | \(0.752749\pi\) | |||||||
\(648\) | −3.97928e10 | + | 3.97928e10i | −0.225686 | + | 0.225686i | ||||
\(649\) | 3.32014e11i | 1.87145i | ||||||||
\(650\) | 5.03048e10 | − | 5.43810e9i | 0.281810 | − | 0.0304645i | ||||
\(651\) | 3.72016e11 | 2.07127 | ||||||||
\(652\) | 2.68344e10 | + | 2.68344e10i | 0.148491 | + | 0.148491i | ||||
\(653\) | 1.29525e11 | − | 1.29525e11i | 0.712364 | − | 0.712364i | −0.254665 | − | 0.967029i | \(-0.581965\pi\) |
0.967029 | + | 0.254665i | \(0.0819653\pi\) | |||||||
\(654\) | − | 6.99392e10i | − | 0.382305i | ||||||
\(655\) | −2.08341e9 | − | 3.86572e10i | −0.0113190 | − | 0.210022i | ||||
\(656\) | −2.86163e10 | −0.154525 | ||||||||
\(657\) | 2.17080e11 | + | 2.17080e11i | 1.16509 | + | 1.16509i | ||||
\(658\) | 2.53852e11 | − | 2.53852e11i | 1.35418 | − | 1.35418i | ||||
\(659\) | 1.29660e11i | 0.687485i | 0.939064 | + | 0.343742i | \(0.111695\pi\) | ||||
−0.939064 | + | 0.343742i | \(0.888305\pi\) | |||||||
\(660\) | −1.31187e11 | + | 1.46133e11i | −0.691376 | + | 0.770144i | ||||
\(661\) | 4.35428e10 | 0.228092 | 0.114046 | − | 0.993475i | \(-0.463619\pi\) | ||||
0.114046 | + | 0.993475i | \(0.463619\pi\) | |||||||
\(662\) | −1.04814e11 | − | 1.04814e11i | −0.545744 | − | 0.545744i | ||||
\(663\) | 4.21039e9 | − | 4.21039e9i | 0.0217906 | − | 0.0217906i | ||||
\(664\) | 5.76112e10i | 0.296370i | ||||||||
\(665\) | 1.23737e11 | + | 1.11082e11i | 0.632724 | + | 0.568011i | ||||
\(666\) | −1.33821e11 | −0.680186 | ||||||||
\(667\) | 1.30851e8 | + | 1.30851e8i | 0.000661109 | + | 0.000661109i | ||||
\(668\) | 9.29625e10 | − | 9.29625e10i | 0.466876 | − | 0.466876i | ||||
\(669\) | − | 4.28220e11i | − | 2.13778i | ||||||
\(670\) | 1.47454e11 | − | 7.94694e9i | 0.731740 | − | 0.0394367i | ||||
\(671\) | 5.27769e10 | 0.260348 | ||||||||
\(672\) | −5.89993e10 | − | 5.89993e10i | −0.289314 | − | 0.289314i | ||||
\(673\) | 1.08117e11 | − | 1.08117e11i | 0.527028 | − | 0.527028i | −0.392657 | − | 0.919685i | \(-0.628444\pi\) |
0.919685 | + | 0.392657i | \(0.128444\pi\) | |||||||
\(674\) | 2.13346e11i | 1.03382i | ||||||||
\(675\) | 2.08703e10 | + | 1.67982e10i | 0.100534 | + | 0.0809184i | ||||
\(676\) | −8.76353e10 | −0.419655 | ||||||||
\(677\) | −7.02840e10 | − | 7.02840e10i | −0.334581 | − | 0.334581i | 0.519742 | − | 0.854323i | \(-0.326028\pi\) |
−0.854323 | + | 0.519742i | \(0.826028\pi\) | |||||||
\(678\) | −1.66309e11 | + | 1.66309e11i | −0.787041 | + | 0.787041i | ||||
\(679\) | 8.02135e9i | 0.0377371i | ||||||||
\(680\) | −2.16369e8 | − | 4.01469e9i | −0.00101195 | − | 0.0187766i | ||||
\(681\) | 3.78466e10 | 0.175970 | ||||||||
\(682\) | −1.38623e11 | − | 1.38623e11i | −0.640766 | − | 0.640766i | ||||
\(683\) | −1.25091e11 | + | 1.25091e11i | −0.574834 | + | 0.574834i | −0.933475 | − | 0.358642i | \(-0.883240\pi\) |
0.358642 | + | 0.933475i | \(0.383240\pi\) | |||||||
\(684\) | 6.33048e10i | 0.289209i | ||||||||
\(685\) | 5.19544e9 | − | 5.78735e9i | 0.0235972 | − | 0.0262856i | ||||
\(686\) | −1.41428e11 | −0.638616 | ||||||||
\(687\) | −3.55806e11 | − | 3.55806e11i | −1.59730 | − | 1.59730i | ||||
\(688\) | −4.96799e10 | + | 4.96799e10i | −0.221731 | + | 0.221731i | ||||
\(689\) | 3.20108e10i | 0.142043i | ||||||||
\(690\) | −9.45034e8 | − | 8.48379e8i | −0.00416918 | − | 0.00374277i | ||||
\(691\) | −1.67070e11 | −0.732800 | −0.366400 | − | 0.930457i | \(-0.619410\pi\) | ||||
−0.366400 | + | 0.930457i | \(0.619410\pi\) | |||||||
\(692\) | 7.69279e10 | + | 7.69279e10i | 0.335475 | + | 0.335475i | ||||
\(693\) | −4.07353e11 | + | 4.07353e11i | −1.76619 | + | 1.76619i | ||||
\(694\) | − | 1.74438e11i | − | 0.751973i | ||||||
\(695\) | 1.69485e10 | − | 9.13431e8i | 0.0726427 | − | 0.00391504i | ||||
\(696\) | −2.04533e10 | −0.0871619 | ||||||||
\(697\) | −5.48611e9 | − | 5.48611e9i | −0.0232452 | − | 0.0232452i | ||||
\(698\) | −7.74223e10 | + | 7.74223e10i | −0.326170 | + | 0.326170i | ||||
\(699\) | − | 4.68603e10i | − | 0.196289i | ||||||
\(700\) | 1.20531e11 | − | 1.49749e11i | 0.502004 | − | 0.623696i | ||||
\(701\) | 1.66014e11 | 0.687498 | 0.343749 | − | 0.939062i | \(-0.388303\pi\) | ||||
0.343749 | + | 0.939062i | \(0.388303\pi\) | |||||||
\(702\) | 6.28178e9 | + | 6.28178e9i | 0.0258663 | + | 0.0258663i | ||||
\(703\) | 8.09858e10 | − | 8.09858e10i | 0.331579 | − | 0.331579i | ||||
\(704\) | 4.39695e10i | 0.179003i | ||||||||
\(705\) | 3.25024e10 | + | 6.03075e11i | 0.131571 | + | 2.44127i | ||||
\(706\) | 1.00374e11 | 0.404018 | ||||||||
\(707\) | 4.38382e11 | + | 4.38382e11i | 1.75459 | + | 1.75459i | ||||
\(708\) | 1.67808e11 | − | 1.67808e11i | 0.667853 | − | 0.667853i | ||||
\(709\) | − | 3.71810e11i | − | 1.47142i | −0.677297 | − | 0.735710i | \(-0.736849\pi\) | ||
0.677297 | − | 0.735710i | \(-0.263151\pi\) | |||||||
\(710\) | −3.88391e10 | + | 4.32640e10i | −0.152839 | + | 0.170252i | ||||
\(711\) | −3.35712e11 | −1.31368 | ||||||||
\(712\) | −8.10924e10 | − | 8.10924e10i | −0.315544 | − | 0.315544i | ||||
\(713\) | 8.96472e8 | − | 8.96472e8i | 0.00346879 | − | 0.00346879i | ||||
\(714\) | − | 2.26218e10i | − | 0.0870432i | ||||||
\(715\) | −1.11640e11 | − | 1.00222e11i | −0.427167 | − | 0.383477i | ||||
\(716\) | −1.18432e11 | −0.450627 | ||||||||
\(717\) | 4.29835e11 | + | 4.29835e11i | 1.62639 | + | 1.62639i | ||||
\(718\) | −6.32964e10 | + | 6.32964e10i | −0.238167 | + | 0.238167i | ||||
\(719\) | − | 3.16803e11i | − | 1.18543i | −0.805414 | − | 0.592713i | \(-0.798057\pi\) | ||
0.805414 | − | 0.592713i | \(-0.201943\pi\) | |||||||
\(720\) | 7.30771e10 | − | 3.93845e9i | 0.271926 | − | 0.0146553i | ||||
\(721\) | −7.29399e11 | −2.69913 | ||||||||
\(722\) | 9.75577e10 | + | 9.75577e10i | 0.359015 | + | 0.359015i | ||||
\(723\) | 3.75081e11 | − | 3.75081e11i | 1.37269 | − | 1.37269i | ||||
\(724\) | − | 1.06458e11i | − | 0.387457i | ||||||
\(725\) | −5.06454e9 | − | 4.68492e10i | −0.0183311 | − | 0.169570i | ||||
\(726\) | 2.98338e11 | 1.07389 | ||||||||
\(727\) | 1.86694e11 | + | 1.86694e11i | 0.668333 | + | 0.668333i | 0.957330 | − | 0.288997i | \(-0.0933218\pi\) |
−0.288997 | + | 0.957330i | \(0.593322\pi\) | |||||||
\(728\) | 4.50734e10 | − | 4.50734e10i | 0.160470 | − | 0.160470i | ||||
\(729\) | − | 3.30410e11i | − | 1.16988i | ||||||
\(730\) | 1.63464e10 | + | 3.03304e11i | 0.0575614 | + | 1.06804i | ||||
\(731\) | −1.90485e10 | −0.0667102 | ||||||||
\(732\) | −2.66748e10 | − | 2.66748e10i | −0.0929088 | − | 0.0929088i | ||||
\(733\) | 8.03537e10 | − | 8.03537e10i | 0.278349 | − | 0.278349i | −0.554101 | − | 0.832450i | \(-0.686938\pi\) |
0.832450 | + | 0.554101i | \(0.186938\pi\) | |||||||
\(734\) | 1.06549e11i | 0.367085i | ||||||||
\(735\) | 4.40743e11 | − | 4.90956e11i | 1.51020 | − | 1.68226i | ||||
\(736\) | −2.84349e8 | −0.000969036 | ||||||||
\(737\) | −3.09604e11 | − | 3.09604e11i | −1.04939 | − | 1.04939i | ||||
\(738\) | 9.98606e10 | − | 9.98606e10i | 0.336642 | − | 0.336642i | ||||
\(739\) | 2.44359e11i | 0.819315i | 0.912239 | + | 0.409658i | \(0.134352\pi\) | ||||
−0.912239 | + | 0.409658i | \(0.865648\pi\) | |||||||
\(740\) | −9.85260e10 | − | 8.84490e10i | −0.328567 | − | 0.294962i | ||||
\(741\) | −9.27613e10 | −0.307676 | ||||||||
\(742\) | 8.59947e10 | + | 8.59947e10i | 0.283698 | + | 0.283698i | ||||
\(743\) | 1.76095e10 | − | 1.76095e10i | 0.0577818 | − | 0.0577818i | −0.677625 | − | 0.735407i | \(-0.736991\pi\) |
0.735407 | + | 0.677625i | \(0.236991\pi\) | |||||||
\(744\) | 1.40128e11i | 0.457333i | ||||||||
\(745\) | 3.45353e8 | − | 1.86126e7i | 0.00112108 | − | 6.04202e-5i | ||||
\(746\) | 2.61466e11 | 0.844230 | ||||||||
\(747\) | −2.01042e11 | − | 2.01042e11i | −0.645662 | − | 0.645662i | ||||
\(748\) | −8.42952e9 | + | 8.42952e9i | −0.0269275 | + | 0.0269275i | ||||
\(749\) | 1.10322e11i | 0.350539i | ||||||||
\(750\) | 5.20097e10 | + | 3.19182e11i | 0.164376 | + | 1.00877i | ||||
\(751\) | 9.35354e10 | 0.294047 | 0.147023 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147023 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(752\) | 9.56187e10 | + | 9.56187e10i | 0.299000 | + | 0.299000i | ||||
\(753\) | −2.81864e11 | + | 2.81864e11i | −0.876717 | + | 0.876717i | ||||
\(754\) | − | 1.56256e10i | − | 0.0483450i | ||||||
\(755\) | 4.28170e9 | + | 7.94460e10i | 0.0131774 | + | 0.244503i | ||||
\(756\) | 3.37511e10 | 0.103324 | ||||||||
\(757\) | 6.80194e10 | + | 6.80194e10i | 0.207133 | + | 0.207133i | 0.803048 | − | 0.595915i | \(-0.203210\pi\) |
−0.595915 | + | 0.803048i | \(0.703210\pi\) | |||||||
\(758\) | 7.31659e10 | − | 7.31659e10i | 0.221632 | − | 0.221632i | ||||
\(759\) | 3.76558e9i | 0.0113466i | ||||||||
\(760\) | −4.18413e10 | + | 4.66082e10i | −0.125415 | + | 0.139704i | ||||
\(761\) | 1.73217e11 | 0.516478 | 0.258239 | − | 0.966081i | \(-0.416858\pi\) | ||||
0.258239 | + | 0.966081i | \(0.416858\pi\) | |||||||
\(762\) | −1.28431e11 | − | 1.28431e11i | −0.380933 | − | 0.380933i | ||||
\(763\) | 1.43539e11 | − | 1.43539e11i | 0.423518 | − | 0.423518i | ||||
\(764\) | 1.49874e11i | 0.439900i | ||||||||
\(765\) | 1.47649e10 | + | 1.32548e10i | 0.0431106 | + | 0.0387014i | ||||
\(766\) | −1.04475e11 | −0.303456 | ||||||||
\(767\) | 1.28200e11 | + | 1.28200e11i | 0.370430 | + | 0.370430i | ||||
\(768\) | 2.22233e10 | − | 2.22233e10i | 0.0638798 | − | 0.0638798i | ||||
\(769\) | 6.23925e11i | 1.78413i | 0.451905 | + | 0.892066i | \(0.350745\pi\) | ||||
−0.451905 | + | 0.892066i | \(0.649255\pi\) | |||||||
\(770\) | −5.69154e11 | + | 3.06742e10i | −1.61907 | + | 0.0872592i | ||||
\(771\) | 4.98649e9 | 0.0141116 | ||||||||
\(772\) | −1.80483e11 | − | 1.80483e11i | −0.508122 | − | 0.508122i | ||||
\(773\) | −2.80444e11 | + | 2.80444e11i | −0.785466 | + | 0.785466i | −0.980747 | − | 0.195281i | \(-0.937438\pi\) |
0.195281 | + | 0.980747i | \(0.437438\pi\) | |||||||
\(774\) | − | 3.46730e11i | − | 0.966112i | ||||||
\(775\) | −3.20968e11 | + | 3.46976e10i | −0.889724 | + | 0.0961818i | ||||
\(776\) | −3.02141e9 | −0.00833225 | ||||||||
\(777\) | −5.26781e11 | − | 5.26781e11i | −1.44526 | − | 1.44526i | ||||
\(778\) | 1.63677e11 | − | 1.63677e11i | 0.446754 | − | 0.446754i | ||||
\(779\) | 1.20867e11i | 0.328215i | ||||||||
\(780\) | 5.77106e9 | + | 1.07081e11i | 0.0155911 | + | 0.289290i | ||||
\(781\) | 1.72389e11 | 0.463347 | ||||||||
\(782\) | −5.45133e7 | − | 5.45133e7i | −0.000145773 | − | 0.000145773i | ||||
\(783\) | 5.85026e9 | − | 5.85026e9i | 0.0155643 | − | 0.0155643i | ||||
\(784\) | − | 1.47722e11i | − | 0.391005i | ||||||
\(785\) | 3.12032e11 | − | 3.47581e11i | 0.821713 | − | 0.915330i | ||||
\(786\) | 8.20482e10 | 0.214971 | ||||||||
\(787\) | −2.18147e10 | − | 2.18147e10i | −0.0568656 | − | 0.0568656i | 0.678102 | − | 0.734968i | \(-0.262803\pi\) |
−0.734968 | + | 0.678102i | \(0.762803\pi\) | |||||||
\(788\) | 1.02146e11 | − | 1.02146e11i | 0.264921 | − | 0.264921i | ||||
\(789\) | 3.33640e11i | 0.860934i | ||||||||
\(790\) | −2.47169e11 | − | 2.21889e11i | −0.634578 | − | 0.569675i | ||||
\(791\) | −6.82646e11 | −1.74377 | ||||||||
\(792\) | −1.53438e11 | − | 1.53438e11i | −0.389971 | − | 0.389971i | ||||
\(793\) | 2.03786e10 | − | 2.03786e10i | 0.0515326 | − | 0.0515326i | ||||
\(794\) | − | 1.23039e11i | − | 0.309572i | ||||||
\(795\) | −2.04297e11 | + | 1.10105e10i | −0.511439 | + | 0.0275638i | ||||
\(796\) | 4.98672e10 | 0.124212 | ||||||||
\(797\) | 1.10772e11 | + | 1.10772e11i | 0.274534 | + | 0.274534i | 0.830922 | − | 0.556389i | \(-0.187813\pi\) |
−0.556389 | + | 0.830922i | \(0.687813\pi\) | |||||||
\(798\) | −2.49197e11 | + | 2.49197e11i | −0.614512 | + | 0.614512i | ||||
\(799\) | 3.66627e10i | 0.0899574i | ||||||||
\(800\) | 5.64062e10 | + | 4.54006e10i | 0.137711 | + | 0.110841i | ||||
\(801\) | 5.65967e11 | 1.37487 | ||||||||
\(802\) | −4.68499e10 | − | 4.68499e10i | −0.113243 | − | 0.113243i | ||||
\(803\) | 6.36839e11 | − | 6.36839e11i | 1.53168 | − | 1.53168i | ||||
\(804\) | 3.12964e11i | 0.748980i | ||||||||
\(805\) | −1.98369e8 | − | 3.68069e9i | −0.000472379 | − | 0.00876488i | ||||
\(806\) | −1.07053e11 | −0.253663 | ||||||||
\(807\) | 7.89668e11 | + | 7.89668e11i | 1.86187 | + | 1.86187i | ||||
\(808\) | −1.65126e11 | + | 1.65126e11i | −0.387409 | + | 0.387409i | ||||
\(809\) | − | 2.98150e11i | − | 0.696051i | −0.937485 | − | 0.348025i | \(-0.886852\pi\) | ||
0.937485 | − | 0.348025i | \(-0.113148\pi\) | |||||||
\(810\) | 1.83563e11 | − | 2.04476e11i | 0.426427 | − | 0.475010i | ||||
\(811\) | 6.76978e11 | 1.56492 | 0.782458 | − | 0.622704i | \(-0.213966\pi\) | ||||
0.782458 | + | 0.622704i | \(0.213966\pi\) | |||||||
\(812\) | −4.19771e10 | − | 4.19771e10i | −0.0965581 | − | 0.0965581i | ||||
\(813\) | −3.18100e11 | + | 3.18100e11i | −0.728118 | + | 0.728118i | ||||
\(814\) | 3.92586e11i | 0.894205i | ||||||||
\(815\) | −1.37889e11 | − | 1.23786e11i | −0.312535 | − | 0.280570i | ||||
\(816\) | 8.52099e9 | 0.0192189 | ||||||||
\(817\) | 2.09834e11 | + | 2.09834e11i | 0.470964 | + | 0.470964i | ||||
\(818\) | −1.06378e11 | + | 1.06378e11i | −0.237596 | + | 0.237596i | ||||
\(819\) | 3.14580e11i | 0.699191i | ||||||||
\(820\) | 1.39525e11 | − | 7.51965e9i | 0.308601 | − | 0.0166319i | ||||
\(821\) | −4.64293e10 | −0.102193 | −0.0510963 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510963 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(822\) | 1.16552e10 | + | 1.16552e10i | 0.0255290 | + | 0.0255290i | ||||
\(823\) | −5.00668e11 | + | 5.00668e11i | −1.09132 | + | 1.09132i | −0.0959282 | + | 0.995388i | \(0.530582\pi\) |
−0.995388 | + | 0.0959282i | \(0.969418\pi\) | |||||||
\(824\) | − | 2.74743e11i | − | 0.595962i | ||||||
\(825\) | 6.01232e11 | − | 7.46977e11i | 1.29786 | − | 1.61247i | ||||
\(826\) | 6.88800e11 | 1.47970 | ||||||||
\(827\) | −6.00312e11 | − | 6.00312e11i | −1.28338 | − | 1.28338i | −0.938732 | − | 0.344648i | \(-0.887998\pi\) |
−0.344648 | − | 0.938732i | \(-0.612002\pi\) | |||||||
\(828\) | 9.92276e8 | − | 9.92276e8i | 0.00211111 | − | 0.00211111i | ||||
\(829\) | − | 8.51434e11i | − | 1.80274i | −0.433051 | − | 0.901370i | \(-0.642563\pi\) | ||
0.433051 | − | 0.901370i | \(-0.357437\pi\) | |||||||
\(830\) | −1.51388e10 | − | 2.80897e11i | −0.0318991 | − | 0.591881i | ||||
\(831\) | −4.63902e11 | −0.972797 | ||||||||
\(832\) | 1.69778e10 | + | 1.69778e10i | 0.0354315 | + | 0.0354315i | ||||
\(833\) | 2.83203e10 | − | 2.83203e10i | 0.0588190 | − | 0.0588190i | ||||
\(834\) | 3.59724e10i | 0.0743542i | ||||||||
\(835\) | −4.28832e11 | + | 4.77689e11i | −0.882148 | + | 0.982651i | ||||
\(836\) | 1.85715e11 | 0.380209 | ||||||||
\(837\) | −4.00807e10 | − | 4.00807e10i | −0.0816646 | − | 0.0816646i | ||||
\(838\) | 5.59195e10 | − | 5.59195e10i | 0.113393 | − | 0.113393i | ||||
\(839\) | − | 2.72456e11i | − | 0.549856i | −0.961465 | − | 0.274928i | \(-0.911346\pi\) | ||
0.961465 | − | 0.274928i | \(-0.0886540\pi\) | |||||||
\(840\) | 3.03168e11 | + | 2.72161e11i | 0.608929 | + | 0.546650i | ||||
\(841\) | 4.85694e11 | 0.970910 | ||||||||
\(842\) | −2.03280e11 | − | 2.03280e11i | −0.404432 | − | 0.404432i | ||||
\(843\) | −6.86081e11 | + | 6.86081e11i | −1.35852 | + | 1.35852i | ||||
\(844\) | 4.77494e11i | 0.941019i | ||||||||
\(845\) | 4.27287e11 | − | 2.30284e10i | 0.838094 | − | 0.0451686i | ||||
\(846\) | −6.67350e11 | −1.30278 | ||||||||
\(847\) | 6.12290e11 | + | 6.12290e11i | 1.18966 | + | 1.18966i | ||||
\(848\) | −3.23917e10 | + | 3.23917e10i | −0.0626398 | + | 0.0626398i | ||||
\(849\) | 1.22653e10i | 0.0236075i | ||||||||
\(850\) | 2.10992e9 | + | 1.95177e10i | 0.00404194 | + | 0.0373898i | ||||
\(851\) | −2.53884e9 | −0.00484079 | ||||||||
\(852\) | −8.71300e10 | − | 8.71300e10i | −0.165352 | − | 0.165352i | ||||
\(853\) | −1.59406e11 | + | 1.59406e11i | −0.301099 | + | 0.301099i | −0.841444 | − | 0.540345i | \(-0.818294\pi\) |
0.540345 | + | 0.841444i | \(0.318294\pi\) | |||||||
\(854\) | − | 1.09491e11i | − | 0.205849i | ||||||
\(855\) | −1.66349e10 | − | 3.08657e11i | −0.0311284 | − | 0.577580i | ||||
\(856\) | −4.15553e10 | −0.0773982 | ||||||||
\(857\) | −3.08378e11 | − | 3.08378e11i | −0.571690 | − | 0.571690i | 0.360910 | − | 0.932601i | \(-0.382466\pi\) |
−0.932601 | + | 0.360910i | \(0.882466\pi\) | |||||||
\(858\) | 2.24834e11 | − | 2.24834e11i | 0.414871 | − | 0.414871i | ||||
\(859\) | − | 7.24487e11i | − | 1.33063i | −0.746562 | − | 0.665316i | \(-0.768297\pi\) | ||
0.746562 | − | 0.665316i | \(-0.231703\pi\) | |||||||
\(860\) | 2.29171e11 | − | 2.55281e11i | 0.418954 | − | 0.466685i | ||||
\(861\) | 7.86194e11 | 1.43060 | ||||||||
\(862\) | 2.97898e11 | + | 2.97898e11i | 0.539559 | + | 0.539559i | ||||
\(863\) | −4.20245e10 | + | 4.20245e10i | −0.0757634 | + | 0.0757634i | −0.743973 | − | 0.668210i | \(-0.767061\pi\) |
0.668210 | + | 0.743973i | \(0.267061\pi\) | |||||||
\(864\) | 1.27131e10i | 0.0228137i | ||||||||
\(865\) | −3.95295e11 | − | 3.54865e11i | −0.706085 | − | 0.633869i | ||||
\(866\) | 2.15006e11 | 0.382277 | ||||||||
\(867\) | −5.75877e11 | − | 5.75877e11i | −1.01919 | − | 1.01919i | ||||
\(868\) | −2.87589e11 | + | 2.87589e11i | −0.506634 | + | 0.506634i | ||||
\(869\) | 9.84867e11i | 1.72702i | ||||||||
\(870\) | 9.97249e10 | − | 5.37462e9i | 0.174071 | − | 0.00938147i | ||||
\(871\) | −2.39094e11 | −0.415428 | ||||||||
\(872\) | 5.40670e10 | + | 5.40670e10i | 0.0935117 | + | 0.0935117i | ||||
\(873\) | 1.05436e10 | − | 1.05436e10i | 0.0181524 | − | 0.0181524i | ||||
\(874\) | 1.20101e9i | 0.00205826i | ||||||||
\(875\) | −5.48328e11 | + | 7.61811e11i | −0.935424 | + | 1.29962i | ||||
\(876\) | −6.43749e11 | −1.09320 | ||||||||
\(877\) | −6.58815e11 | − | 6.58815e11i | −1.11369 | − | 1.11369i | −0.992647 | − | 0.121045i | \(-0.961376\pi\) |
−0.121045 | − | 0.992647i | \(-0.538624\pi\) | |||||||
\(878\) | 3.35632e11 | − | 3.35632e11i | 0.564787 | − | 0.564787i | ||||
\(879\) | 1.04822e12i | 1.75588i | ||||||||
\(880\) | −1.15541e10 | − | 2.14384e11i | −0.0192666 | − | 0.357488i | ||||
\(881\) | −4.01192e11 | −0.665961 | −0.332981 | − | 0.942934i | \(-0.608054\pi\) | ||||
−0.332981 | + | 0.942934i | \(0.608054\pi\) | |||||||
\(882\) | 5.15499e11 | + | 5.15499e11i | 0.851831 | + | 0.851831i | ||||
\(883\) | 5.60683e11 | − | 5.60683e11i | 0.922306 | − | 0.922306i | −0.0748864 | − | 0.997192i | \(-0.523859\pi\) |
0.997192 | + | 0.0748864i | \(0.0238594\pi\) | |||||||
\(884\) | 6.50974e9i | 0.0106599i | ||||||||
\(885\) | −7.74094e11 | + | 8.62286e11i | −1.26189 | + | 1.40565i | ||||
\(886\) | −6.02735e11 | −0.978119 | ||||||||
\(887\) | −2.69741e11 | − | 2.69741e11i | −0.435765 | − | 0.435765i | 0.454819 | − | 0.890584i | \(-0.349704\pi\) |
−0.890584 | + | 0.454819i | \(0.849704\pi\) | |||||||
\(888\) | 1.98423e11 | − | 1.98423e11i | 0.319110 | − | 0.319110i | ||||
\(889\) | − | 5.27167e11i | − | 0.843997i | ||||||
\(890\) | 4.16694e11 | + | 3.74076e11i | 0.664136 | + | 0.596211i | ||||
\(891\) | −8.14754e11 | −1.29275 | ||||||||
\(892\) | 3.31038e11 | + | 3.31038e11i | 0.522900 | + | 0.522900i | ||||
\(893\) | 4.03867e11 | − | 4.03867e11i | 0.635086 | − | 0.635086i | ||||
\(894\) | 7.32996e8i | 0.00114750i | ||||||||
\(895\) | 5.77444e11 | − | 3.11210e10i | 0.899949 | − | 0.0485023i | ||||
\(896\) | 9.12195e10 | 0.141532 | ||||||||
\(897\) | 1.45399e9 | + | 1.45399e9i | 0.00224591 | + | 0.00224591i | ||||
\(898\) | −4.04534e11 | + | 4.04534e11i | −0.622085 | + | 0.622085i | ||||
\(899\) | 9.96988e10i | 0.152634i | ||||||||
\(900\) | −3.55270e11 | + | 3.84057e10i | −0.541487 | + | 0.0585364i | ||||
\(901\) | −1.24198e10 | −0.0188459 | ||||||||
\(902\) | −2.92958e11 | − | 2.92958e11i | −0.442567 | − | 0.442567i | ||||
\(903\) | 1.36489e12 | − | 1.36489e12i | 2.05280 | − | 2.05280i | ||||
\(904\) | − | 2.57133e11i | − | 0.385020i | ||||||
\(905\) | 2.79745e10 | + | 5.19061e11i | 0.0417031 | + | 0.773791i | ||||
\(906\) | −1.68621e11 | −0.250264 | ||||||||
\(907\) | 6.28908e11 | + | 6.28908e11i | 0.929305 | + | 0.929305i | 0.997661 | − | 0.0683564i | \(-0.0217755\pi\) |
−0.0683564 | + | 0.997661i | \(0.521775\pi\) | |||||||
\(908\) | −2.92575e10 | + | 2.92575e10i | −0.0430422 | + | 0.0430422i | ||||
\(909\) | − | 1.15246e12i | − | 1.68799i | ||||||
\(910\) | −2.07922e11 | + | 2.31610e11i | −0.303204 | + | 0.337747i | ||||
\(911\) | 1.00441e12 | 1.45827 | 0.729134 | − | 0.684371i | \(-0.239923\pi\) | ||||
0.729134 | + | 0.684371i | \(0.239923\pi\) | |||||||
\(912\) | −9.38651e10 | − | 9.38651e10i | −0.135683 | − | 0.135683i | ||||
\(913\) | −5.89791e11 | + | 5.89791e11i | −0.848819 | + | 0.848819i | ||||
\(914\) | 2.43305e11i | 0.348631i | ||||||||
\(915\) | 1.37069e11 | + | 1.23050e11i | 0.195548 | + | 0.175548i | ||||
\(916\) | 5.50116e11 | 0.781398 | ||||||||
\(917\) | 1.68391e11 | + | 1.68391e11i | 0.238145 | + | 0.238145i | ||||
\(918\) | −2.43726e9 | + | 2.43726e9i | −0.00343187 | + | 0.00343187i | ||||
\(919\) | − | 1.58868e11i | − | 0.222727i | −0.993780 | − | 0.111364i | \(-0.964478\pi\) | ||
0.993780 | − | 0.111364i | \(-0.0355218\pi\) | |||||||
\(920\) | 1.38641e9 | − | 7.47198e7i | 0.00193526 | − | 0.000104300i | ||||
\(921\) | 7.95912e11 | 1.10618 | ||||||||
\(922\) | −2.19033e11 | − | 2.19033e11i | −0.303100 | − | 0.303100i | ||||
\(923\) | 6.65643e10 | − | 6.65643e10i | 0.0917138 | − | 0.0917138i | ||||
\(924\) | − | 1.20800e12i | − | 1.65722i | ||||||
\(925\) | 5.03629e11 | + | 4.05364e11i | 0.687929 | + | 0.553705i | ||||
\(926\) | 5.65453e11 | 0.769046 | ||||||||
\(927\) | 9.58757e11 | + | 9.58757e11i | 1.29834 | + | 1.29834i | ||||
\(928\) | 1.58116e10 | − | 1.58116e10i | 0.0213198 | − | 0.0213198i | ||||
\(929\) | 5.94996e11i | 0.798824i | 0.916772 | + | 0.399412i | \(0.130786\pi\) | ||||
−0.916772 | + | 0.399412i | \(0.869214\pi\) | |||||||
\(930\) | −3.68221e10 | − | 6.83225e11i | −0.0492240 | − | 0.913340i | ||||
\(931\) | −6.23939e11 | −0.830507 | ||||||||
\(932\) | 3.62257e10 | + | 3.62257e10i | 0.0480124 | + | 0.0480124i | ||||
\(933\) | 8.81432e11 | − | 8.81432e11i | 1.16322 | − | 1.16322i | ||||
\(934\) | − | 7.77597e11i | − | 1.02180i | ||||||
\(935\) | 3.88851e10 | − | 4.33152e10i | 0.0508787 | − | 0.0566753i | ||||
\(936\) | −1.18493e11 | −0.154380 | ||||||||
\(937\) | −2.52202e11 | − | 2.52202e11i | −0.327182 | − | 0.327182i | 0.524332 | − | 0.851514i | \(-0.324315\pi\) |
−0.851514 | + | 0.524332i | \(0.824315\pi\) | |||||||
\(938\) | −6.42308e11 | + | 6.42308e11i | −0.829721 | + | 0.829721i | ||||
\(939\) | 1.75328e12i | 2.25522i | ||||||||
\(940\) | −4.91338e11 | − | 4.41085e11i | −0.629316 | − | 0.564951i | ||||
\(941\) | −9.55354e11 | −1.21845 | −0.609223 | − | 0.792999i | \(-0.708518\pi\) | ||||
−0.609223 | + | 0.792999i | \(0.708518\pi\) | |||||||
\(942\) | 7.00000e11 | + | 7.00000e11i | 0.888985 | + | 0.888985i | ||||
\(943\) | 1.89454e9 | − | 1.89454e9i | 0.00239584 | − | 0.00239584i | ||||
\(944\) | 2.59451e11i | 0.326713i | ||||||||
\(945\) | −1.64562e11 | + | 8.86896e9i | −0.206349 | + | 0.0111210i | ||||
\(946\) | −1.01719e12 | −1.27010 | ||||||||
\(947\) | −5.84413e11 | − | 5.84413e11i | −0.726641 | − | 0.726641i | 0.243308 | − | 0.969949i | \(-0.421767\pi\) |
−0.969949 | + | 0.243308i | \(0.921767\pi\) | |||||||
\(948\) | 4.97777e11 | − | 4.97777e11i | 0.616313 | − | 0.616313i | ||||
\(949\) | − | 4.91802e11i | − | 0.606353i | ||||||
\(950\) | 1.91760e11 | − | 2.38244e11i | 0.235431 | − | 0.292502i | ||||
\(951\) | −1.57480e12 | −1.92532 | ||||||||
\(952\) | 1.74880e10 | + | 1.74880e10i | 0.0212908 | + | 0.0212908i | ||||
\(953\) | −4.48597e11 | + | 4.48597e11i | −0.543857 | + | 0.543857i | −0.924657 | − | 0.380801i | \(-0.875648\pi\) |
0.380801 | + | 0.924657i | \(0.375648\pi\) | |||||||
\(954\) | − | 2.26071e11i | − | 0.272930i | ||||||
\(955\) | −3.93832e10 | − | 7.30747e11i | −0.0473476 | − | 0.878524i | ||||
\(956\) | −6.64573e11 | −0.795630 | ||||||||
\(957\) | −2.09390e11 | − | 2.09390e11i | −0.249636 | − | 0.249636i | ||||
\(958\) | −4.05181e11 | + | 4.05181e11i | −0.481047 | + | 0.481047i | ||||
\(959\) | 4.78410e10i | 0.0565621i | ||||||||
\(960\) | −1.02515e11 | + | 1.14195e11i | −0.120699 | + | 0.134450i | ||||
\(961\) | −1.69845e11 | −0.199140 | ||||||||
\(962\) | 1.51588e11 | + | 1.51588e11i | 0.176997 | + | 0.176997i | ||||
\(963\) | 1.45013e11 | − | 1.45013e11i | 0.168617 | − | 0.168617i | ||||
\(964\) | 5.79918e11i | 0.671519i | ||||||||
\(965\) | 9.27415e11 | + | 8.32562e11i | 1.06946 | + | 0.960080i | ||||
\(966\) | 7.81210e9 | 0.00897139 | ||||||||
\(967\) | 3.45450e11 | + | 3.45450e11i | 0.395075 | + | 0.395075i | 0.876492 | − | 0.481417i | \(-0.159878\pi\) |
−0.481417 | + | 0.876492i | \(0.659878\pi\) | |||||||
\(968\) | −2.30632e11 | + | 2.30632e11i | −0.262674 | + | 0.262674i | ||||
\(969\) | − | 3.59903e10i | − | 0.0408216i | ||||||
\(970\) | 1.47316e10 | − | 7.93951e8i | 0.0166404 | − | 0.000896823i | ||||
\(971\) | −4.22522e10 | −0.0475306 | −0.0237653 | − | 0.999718i | \(-0.507565\pi\) | ||||
−0.0237653 | + | 0.999718i | \(0.507565\pi\) | |||||||
\(972\) | 4.52525e11 | + | 4.52525e11i | 0.506965 | + | 0.506965i | ||||
\(973\) | −7.38277e10 | + | 7.38277e10i | −0.0823697 | + | 0.0823697i | ||||
\(974\) | 6.39541e10i | 0.0710612i | ||||||||
\(975\) | −5.62764e10 | − | 5.20581e11i | −0.0622741 | − | 0.576063i | ||||
\(976\) | 4.12423e10 | 0.0454510 | ||||||||
\(977\) | 1.20249e12 | + | 1.20249e12i | 1.31978 | + | 1.31978i | 0.913944 | + | 0.405840i | \(0.133021\pi\) |
0.405840 | + | 0.913944i | \(0.366979\pi\) | |||||||
\(978\) | 2.77697e11 | − | 2.77697e11i | 0.303540 | − | 0.303540i | ||||
\(979\) | − | 1.66036e12i | − | 1.80747i | ||||||
\(980\) | 3.88178e10 | + | 7.20256e11i | 0.0420849 | + | 0.780877i | ||||
\(981\) | −3.77349e11 | −0.407443 | ||||||||
\(982\) | 3.99204e11 | + | 3.99204e11i | 0.429288 | + | 0.429288i | ||||
\(983\) | −3.99506e11 | + | 3.99506e11i | −0.427867 | + | 0.427867i | −0.887901 | − | 0.460034i | \(-0.847837\pi\) |
0.460034 | + | 0.887901i | \(0.347837\pi\) | |||||||
\(984\) | 2.96136e11i | 0.315872i | ||||||||
\(985\) | −4.71196e11 | + | 5.24879e11i | −0.500561 | + | 0.557589i | ||||
\(986\) | 6.06256e9 | 0.00641429 | ||||||||
\(987\) | −2.62700e12 | − | 2.62700e12i | −2.76816 | − | 2.76816i | ||||
\(988\) | 7.17097e10 | − | 7.17097e10i | 0.0752576 | − | 0.0752576i | ||||
\(989\) | − | 6.57812e9i | − | 0.00687570i | ||||||
\(990\) | 7.88442e11 | + | 7.07803e11i | 0.820784 | + | 0.736837i | ||||
\(991\) | 1.64837e12 | 1.70907 | 0.854533 | − | 0.519396i | \(-0.173843\pi\) | ||||
0.854533 | + | 0.519396i | \(0.173843\pi\) | |||||||
\(992\) | −1.08327e11 | − | 1.08327e11i | −0.111863 | − | 0.111863i | ||||
\(993\) | −1.08467e12 | + | 1.08467e12i | −1.11558 | + | 1.11558i | ||||
\(994\) | − | 3.57641e11i | − | 0.366354i | ||||||
\(995\) | −2.43139e11 | + | 1.31039e10i | −0.248064 | + | 0.0133693i | ||||
\(996\) | 5.96191e11 | 0.605826 | ||||||||
\(997\) | −6.07220e11 | − | 6.07220e11i | −0.614562 | − | 0.614562i | 0.329570 | − | 0.944131i | \(-0.393096\pi\) |
−0.944131 | + | 0.329570i | \(0.893096\pi\) | |||||||
\(998\) | 5.94815e11 | − | 5.94815e11i | 0.599598 | − | 0.599598i | ||||
\(999\) | 1.13510e11i | 0.113965i |
(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 | 10.9.c.b.7.2 | yes | 4 | |
3.2 | odd | 2 | 90.9.g.a.37.1 | 4 | |||
4.3 | odd | 2 | 80.9.p.a.17.1 | 4 | |||
5.2 | odd | 4 | 50.9.c.b.43.1 | 4 | |||
5.3 | odd | 4 | inner | 10.9.c.b.3.2 | ✓ | 4 | |
5.4 | even | 2 | 50.9.c.b.7.1 | 4 | |||
15.8 | even | 4 | 90.9.g.a.73.1 | 4 | |||
20.3 | even | 4 | 80.9.p.a.33.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.9.c.b.3.2 | ✓ | 4 | 5.3 | odd | 4 | inner | |
10.9.c.b.7.2 | yes | 4 | 1.1 | even | 1 | trivial | |
50.9.c.b.7.1 | 4 | 5.4 | even | 2 | |||
50.9.c.b.43.1 | 4 | 5.2 | odd | 4 | |||
80.9.p.a.17.1 | 4 | 4.3 | odd | 2 | |||
80.9.p.a.33.1 | 4 | 20.3 | even | 4 | |||
90.9.g.a.37.1 | 4 | 3.2 | odd | 2 | |||
90.9.g.a.73.1 | 4 | 15.8 | even | 4 |