Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,17,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(8.11622719283\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 354217 x^{12} + 47647865256 x^{10} + \cdots + 84\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{34}\cdot 3^{10}\cdot 5^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(-336.317i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.17.c.a.2.7 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 336.317 | − | 336.317i | 1.31374 | − | 1.31374i | 0.395099 | − | 0.918638i | \(-0.370710\pi\) |
0.918638 | − | 0.395099i | \(-0.129290\pi\) | |||||||
\(3\) | 6051.53 | + | 6051.53i | 0.922349 | + | 0.922349i | 0.997195 | − | 0.0748461i | \(-0.0238465\pi\) |
−0.0748461 | + | 0.997195i | \(0.523847\pi\) | |||||||
\(4\) | − | 160682.i | − | 2.45181i | ||||||
\(5\) | 335305. | + | 200395.i | 0.858382 | + | 0.513011i | ||||
\(6\) | 4.07046e6 | 2.42345 | ||||||||
\(7\) | −371312. | + | 371312.i | −0.0644101 | + | 0.0644101i | −0.738578 | − | 0.674168i | \(-0.764502\pi\) |
0.674168 | + | 0.738578i | \(0.264502\pi\) | |||||||
\(8\) | −3.19992e7 | − | 3.19992e7i | −1.90730 | − | 1.90730i | ||||
\(9\) | 3.01954e7i | 0.701456i | ||||||||
\(10\) | 1.80165e8 | − | 4.53727e7i | 1.80165 | − | 0.453727i | ||||
\(11\) | −2.87674e8 | −1.34202 | −0.671010 | − | 0.741448i | \(-0.734139\pi\) | ||||
−0.671010 | + | 0.741448i | \(0.734139\pi\) | |||||||
\(12\) | 9.72372e8 | − | 9.72372e8i | 2.26143 | − | 2.26143i | ||||
\(13\) | −9.55195e7 | − | 9.55195e7i | −0.117097 | − | 0.117097i | 0.646130 | − | 0.763227i | \(-0.276386\pi\) |
−0.763227 | + | 0.646130i | \(0.776386\pi\) | |||||||
\(14\) | 2.49757e8i | 0.169236i | ||||||||
\(15\) | 8.16416e8 | + | 3.24181e9i | 0.318553 | + | 1.26490i | ||||
\(16\) | −1.09933e10 | −2.55957 | ||||||||
\(17\) | −6.35046e8 | + | 6.35046e8i | −0.0910362 | + | 0.0910362i | −0.751158 | − | 0.660122i | \(-0.770505\pi\) |
0.660122 | + | 0.751158i | \(0.270505\pi\) | |||||||
\(18\) | 1.01552e10 | + | 1.01552e10i | 0.921528 | + | 0.921528i | ||||
\(19\) | 1.35652e10i | 0.798726i | 0.916793 | + | 0.399363i | \(0.130769\pi\) | ||||
−0.916793 | + | 0.399363i | \(0.869231\pi\) | |||||||
\(20\) | 3.21999e10 | − | 5.38776e10i | 1.25781 | − | 2.10459i | ||||
\(21\) | −4.49401e9 | −0.118817 | ||||||||
\(22\) | −9.67496e10 | + | 9.67496e10i | −1.76306 | + | 1.76306i | ||||
\(23\) | 5.40328e10 | + | 5.40328e10i | 0.689978 | + | 0.689978i | 0.962227 | − | 0.272249i | \(-0.0877675\pi\) |
−0.272249 | + | 0.962227i | \(0.587767\pi\) | |||||||
\(24\) | − | 3.87288e11i | − | 3.51840i | ||||||
\(25\) | 7.22717e10 | + | 1.34387e11i | 0.473640 | + | 0.880719i | ||||
\(26\) | −6.42496e10 | −0.307669 | ||||||||
\(27\) | 7.77704e10 | − | 7.77704e10i | 0.275362 | − | 0.275362i | ||||
\(28\) | 5.96631e10 | + | 5.96631e10i | 0.157922 | + | 0.157922i | ||||
\(29\) | − | 1.69248e11i | − | 0.338330i | −0.985588 | − | 0.169165i | \(-0.945893\pi\) | ||
0.985588 | − | 0.169165i | \(-0.0541070\pi\) | |||||||
\(30\) | 1.36485e12 | + | 8.15700e11i | 2.08025 | + | 1.24326i | ||||
\(31\) | −1.28377e12 | −1.50520 | −0.752598 | − | 0.658480i | \(-0.771200\pi\) | ||||
−0.752598 | + | 0.658480i | \(0.771200\pi\) | |||||||
\(32\) | −1.60013e12 | + | 1.60013e12i | −1.45531 | + | 1.45531i | ||||
\(33\) | −1.74087e12 | − | 1.74087e12i | −1.23781 | − | 1.23781i | ||||
\(34\) | 4.27153e11i | 0.239195i | ||||||||
\(35\) | −1.98912e11 | + | 5.00939e10i | −0.0883316 | + | 0.0222454i | ||||
\(36\) | 4.85185e12 | 1.71984 | ||||||||
\(37\) | 2.40048e12 | − | 2.40048e12i | 0.683415 | − | 0.683415i | −0.277353 | − | 0.960768i | \(-0.589457\pi\) |
0.960768 | + | 0.277353i | \(0.0894571\pi\) | |||||||
\(38\) | 4.56221e12 | + | 4.56221e12i | 1.04932 | + | 1.04932i | ||||
\(39\) | − | 1.15608e12i | − | 0.216008i | ||||||
\(40\) | −4.31703e12 | − | 1.71420e13i | −0.658727 | − | 2.61566i | ||||
\(41\) | −5.05325e12 | −0.632849 | −0.316425 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316425 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(42\) | −1.51141e12 | + | 1.51141e12i | −0.156095 | + | 0.156095i | ||||
\(43\) | −8.53023e12 | − | 8.53023e12i | −0.729815 | − | 0.729815i | 0.240767 | − | 0.970583i | \(-0.422601\pi\) |
−0.970583 | + | 0.240767i | \(0.922601\pi\) | |||||||
\(44\) | 4.62240e13i | 3.29038i | ||||||||
\(45\) | −6.05100e12 | + | 1.01247e13i | −0.359854 | + | 0.602117i | ||||
\(46\) | 3.63443e13 | 1.81290 | ||||||||
\(47\) | 6.90127e12 | − | 6.90127e12i | 0.289832 | − | 0.289832i | −0.547182 | − | 0.837014i | \(-0.684299\pi\) |
0.837014 | + | 0.547182i | \(0.184299\pi\) | |||||||
\(48\) | −6.65262e13 | − | 6.65262e13i | −2.36082 | − | 2.36082i | ||||
\(49\) | 3.29572e13i | 0.991703i | ||||||||
\(50\) | 6.95028e13 | + | 2.08904e13i | 1.77927 | + | 0.534795i | ||||
\(51\) | −7.68600e12 | −0.167934 | ||||||||
\(52\) | −1.53483e13 | + | 1.53483e13i | −0.287100 | + | 0.287100i | ||||
\(53\) | 3.19201e13 | + | 3.19201e13i | 0.512694 | + | 0.512694i | 0.915351 | − | 0.402657i | \(-0.131913\pi\) |
−0.402657 | + | 0.915351i | \(0.631913\pi\) | |||||||
\(54\) | − | 5.23110e13i | − | 0.723507i | ||||||
\(55\) | −9.64587e13 | − | 5.76484e13i | −1.15197 | − | 0.688471i | ||||
\(56\) | 2.37634e13 | 0.245699 | ||||||||
\(57\) | −8.20903e13 | + | 8.20903e13i | −0.736704 | + | 0.736704i | ||||
\(58\) | −5.69210e13 | − | 5.69210e13i | −0.444476 | − | 0.444476i | ||||
\(59\) | − | 2.15375e14i | − | 1.46683i | −0.679783 | − | 0.733413i | \(-0.737926\pi\) | ||
0.679783 | − | 0.733413i | \(-0.262074\pi\) | |||||||
\(60\) | 5.20900e14 | − | 1.31183e14i | 3.10131 | − | 0.781032i | ||||
\(61\) | 2.85646e14 | 1.49001 | 0.745005 | − | 0.667058i | \(-0.232447\pi\) | ||||
0.745005 | + | 0.667058i | \(0.232447\pi\) | |||||||
\(62\) | −4.31753e14 | + | 4.31753e14i | −1.97743 | + | 1.97743i | ||||
\(63\) | −1.12119e13 | − | 1.12119e13i | −0.0451808 | − | 0.0451808i | ||||
\(64\) | 3.55844e14i | 1.26421i | ||||||||
\(65\) | −1.28866e13 | − | 5.11698e13i | −0.0404419 | − | 0.160586i | ||||
\(66\) | −1.17097e15 | −3.25232 | ||||||||
\(67\) | 3.15528e14 | − | 3.15528e14i | 0.777033 | − | 0.777033i | −0.202292 | − | 0.979325i | \(-0.564839\pi\) |
0.979325 | + | 0.202292i | \(0.0648390\pi\) | |||||||
\(68\) | 1.02041e14 | + | 1.02041e14i | 0.223204 | + | 0.223204i | ||||
\(69\) | 6.53963e14i | 1.27280i | ||||||||
\(70\) | −5.00500e13 | + | 8.37448e13i | −0.0868199 | + | 0.145269i | ||||
\(71\) | 3.15103e14 | 0.487962 | 0.243981 | − | 0.969780i | \(-0.421547\pi\) | ||||
0.243981 | + | 0.969780i | \(0.421547\pi\) | |||||||
\(72\) | 9.66228e14 | − | 9.66228e14i | 1.33789 | − | 1.33789i | ||||
\(73\) | −3.46889e14 | − | 3.46889e14i | −0.430137 | − | 0.430137i | 0.458538 | − | 0.888675i | \(-0.348373\pi\) |
−0.888675 | + | 0.458538i | \(0.848373\pi\) | |||||||
\(74\) | − | 1.61465e15i | − | 1.79566i | ||||||
\(75\) | −3.75893e14 | + | 1.25060e15i | −0.375469 | + | 1.24919i | ||||
\(76\) | 2.17968e15 | 1.95833 | ||||||||
\(77\) | 1.06817e14 | − | 1.06817e14i | 0.0864397 | − | 0.0864397i | ||||
\(78\) | −3.88809e14 | − | 3.88809e14i | −0.283778 | − | 0.283778i | ||||
\(79\) | 1.88973e15i | 1.24561i | 0.782377 | + | 0.622805i | \(0.214007\pi\) | ||||
−0.782377 | + | 0.622805i | \(0.785993\pi\) | |||||||
\(80\) | −3.68611e15 | − | 2.20300e15i | −2.19709 | − | 1.31309i | ||||
\(81\) | 2.24107e15 | 1.20942 | ||||||||
\(82\) | −1.69949e15 | + | 1.69949e15i | −0.831398 | + | 0.831398i | ||||
\(83\) | −2.43560e14 | − | 2.43560e14i | −0.108139 | − | 0.108139i | 0.650967 | − | 0.759106i | \(-0.274364\pi\) |
−0.759106 | + | 0.650967i | \(0.774364\pi\) | |||||||
\(84\) | 7.22106e14i | 0.291318i | ||||||||
\(85\) | −3.40194e14 | + | 8.56745e13i | −0.124846 | + | 0.0314413i | ||||
\(86\) | −5.73772e15 | −1.91757 | ||||||||
\(87\) | 1.02421e15 | − | 1.02421e15i | 0.312058 | − | 0.312058i | ||||
\(88\) | 9.20534e15 | + | 9.20534e15i | 2.55964 | + | 2.55964i | ||||
\(89\) | − | 4.86801e15i | − | 1.23661i | −0.785940 | − | 0.618303i | \(-0.787821\pi\) | ||
0.785940 | − | 0.618303i | \(-0.212179\pi\) | |||||||
\(90\) | 1.37004e15 | + | 5.44015e15i | 0.318269 | + | 1.26378i | ||||
\(91\) | 7.09350e13 | 0.0150844 | ||||||||
\(92\) | 8.68211e15 | − | 8.68211e15i | 1.69170 | − | 1.69170i | ||||
\(93\) | −7.76876e15 | − | 7.76876e15i | −1.38832 | − | 1.38832i | ||||
\(94\) | − | 4.64203e15i | − | 0.761526i | ||||||
\(95\) | −2.71840e15 | + | 4.54849e15i | −0.409755 | + | 0.685612i | ||||
\(96\) | −1.93664e16 | −2.68460 | ||||||||
\(97\) | −5.87093e15 | + | 5.87093e15i | −0.749089 | + | 0.749089i | −0.974308 | − | 0.225219i | \(-0.927690\pi\) |
0.225219 | + | 0.974308i | \(0.427690\pi\) | |||||||
\(98\) | 1.10841e16 | + | 1.10841e16i | 1.30284 | + | 1.30284i | ||||
\(99\) | − | 8.68642e15i | − | 0.941368i | ||||||
\(100\) | 2.15936e16 | − | 1.16128e16i | 2.15936 | − | 1.16128i | ||||
\(101\) | 6.45438e15 | 0.596051 | 0.298026 | − | 0.954558i | \(-0.403672\pi\) | ||||
0.298026 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(102\) | −2.58493e15 | + | 2.58493e15i | −0.220622 | + | 0.220622i | ||||
\(103\) | −2.00133e15 | − | 2.00133e15i | −0.157987 | − | 0.157987i | 0.623687 | − | 0.781674i | \(-0.285634\pi\) |
−0.781674 | + | 0.623687i | \(0.785634\pi\) | |||||||
\(104\) | 6.11310e15i | 0.446678i | ||||||||
\(105\) | −1.50687e15 | − | 9.00576e14i | −0.101991 | − | 0.0609545i | ||||
\(106\) | 2.14706e16 | 1.34709 | ||||||||
\(107\) | −2.03930e16 | + | 2.03930e16i | −1.18689 | + | 1.18689i | −0.208970 | + | 0.977922i | \(0.567011\pi\) |
−0.977922 | + | 0.208970i | \(0.932989\pi\) | |||||||
\(108\) | −1.24963e16 | − | 1.24963e16i | −0.675137 | − | 0.675137i | ||||
\(109\) | − | 1.82128e16i | − | 0.914038i | −0.889457 | − | 0.457019i | \(-0.848917\pi\) | ||
0.889457 | − | 0.457019i | \(-0.151083\pi\) | |||||||
\(110\) | −5.18288e16 | + | 1.30525e16i | −2.41785 | + | 0.608911i | ||||
\(111\) | 2.90532e16 | 1.26070 | ||||||||
\(112\) | 4.08193e15 | − | 4.08193e15i | 0.164862 | − | 0.164862i | ||||
\(113\) | 1.87445e16 | + | 1.87445e16i | 0.705093 | + | 0.705093i | 0.965499 | − | 0.260406i | \(-0.0838564\pi\) |
−0.260406 | + | 0.965499i | \(0.583856\pi\) | |||||||
\(114\) | 5.52167e16i | 1.93567i | ||||||||
\(115\) | 7.28960e15 | + | 2.89454e16i | 0.238298 | + | 0.946231i | ||||
\(116\) | −2.71951e16 | −0.829521 | ||||||||
\(117\) | 2.88424e15 | − | 2.88424e15i | 0.0821382 | − | 0.0821382i | ||||
\(118\) | −7.24341e16 | − | 7.24341e16i | −1.92702 | − | 1.92702i | ||||
\(119\) | − | 4.71600e14i | − | 0.0117273i | ||||||
\(120\) | 7.76106e16 | − | 1.29860e17i | 1.80498 | − | 3.02013i | ||||
\(121\) | 3.68066e16 | 0.801019 | ||||||||
\(122\) | 9.60676e16 | − | 9.60676e16i | 1.95748 | − | 1.95748i | ||||
\(123\) | −3.05799e16 | − | 3.05799e16i | −0.583708 | − | 0.583708i | ||||
\(124\) | 2.06278e17i | 3.69046i | ||||||||
\(125\) | −2.69739e15 | + | 5.95436e16i | −0.0452547 | + | 0.998975i | ||||
\(126\) | −7.54149e15 | −0.118712 | ||||||||
\(127\) | 5.06090e15 | − | 5.06090e15i | 0.0747821 | − | 0.0747821i | −0.668726 | − | 0.743509i | \(-0.733160\pi\) |
0.743509 | + | 0.668726i | \(0.233160\pi\) | |||||||
\(128\) | 1.48102e16 | + | 1.48102e16i | 0.205533 | + | 0.205533i | ||||
\(129\) | − | 1.03242e17i | − | 1.34629i | ||||||
\(130\) | −2.15432e16 | − | 1.28753e16i | −0.264098 | − | 0.157838i | ||||
\(131\) | −6.46825e16 | −0.745790 | −0.372895 | − | 0.927874i | \(-0.621635\pi\) | ||||
−0.372895 | + | 0.927874i | \(0.621635\pi\) | |||||||
\(132\) | −2.79726e17 | + | 2.79726e17i | −3.03488 | + | 3.03488i | ||||
\(133\) | −5.03692e15 | − | 5.03692e15i | −0.0514460 | − | 0.0514460i | ||||
\(134\) | − | 2.12235e17i | − | 2.04164i | ||||||
\(135\) | 4.16616e16 | − | 1.04921e16i | 0.377630 | − | 0.0951022i | ||||
\(136\) | 4.06420e16 | 0.347267 | ||||||||
\(137\) | 3.44238e16 | − | 3.44238e16i | 0.277392 | − | 0.277392i | −0.554675 | − | 0.832067i | \(-0.687157\pi\) |
0.832067 | + | 0.554675i | \(0.187157\pi\) | |||||||
\(138\) | 2.19939e17 | + | 2.19939e17i | 1.67213 | + | 1.67213i | ||||
\(139\) | 6.24994e16i | 0.448495i | 0.974532 | + | 0.224248i | \(0.0719924\pi\) | ||||
−0.974532 | + | 0.224248i | \(0.928008\pi\) | |||||||
\(140\) | 8.04918e15 | + | 3.19615e16i | 0.0545415 | + | 0.216573i | ||||
\(141\) | 8.35265e16 | 0.534652 | ||||||||
\(142\) | 1.05975e17 | − | 1.05975e17i | 0.641054 | − | 0.641054i | ||||
\(143\) | 2.74785e16 | + | 2.74785e16i | 0.157146 | + | 0.157146i | ||||
\(144\) | − | 3.31946e17i | − | 1.79543i | ||||||
\(145\) | 3.39165e16 | − | 5.67498e16i | 0.173567 | − | 0.290416i | ||||
\(146\) | −2.33329e17 | −1.13018 | ||||||||
\(147\) | −1.99441e17 | + | 1.99441e17i | −0.914696 | + | 0.914696i | ||||
\(148\) | −3.85714e17 | − | 3.85714e17i | −1.67561 | − | 1.67561i | ||||
\(149\) | 5.55029e16i | 0.228468i | 0.993454 | + | 0.114234i | \(0.0364413\pi\) | ||||
−0.993454 | + | 0.114234i | \(0.963559\pi\) | |||||||
\(150\) | 2.94179e17 | + | 5.47018e17i | 1.14784 | + | 2.13438i | ||||
\(151\) | 9.45707e16 | 0.349898 | 0.174949 | − | 0.984578i | \(-0.444024\pi\) | ||||
0.174949 | + | 0.984578i | \(0.444024\pi\) | |||||||
\(152\) | 4.34076e17 | − | 4.34076e17i | 1.52341 | − | 1.52341i | ||||
\(153\) | −1.91754e16 | − | 1.91754e16i | −0.0638578 | − | 0.0638578i | ||||
\(154\) | − | 7.18485e16i | − | 0.227118i | ||||||
\(155\) | −4.30454e17 | − | 2.57261e17i | −1.29203 | − | 0.772182i | ||||
\(156\) | −1.85761e17 | −0.529612 | ||||||||
\(157\) | 8.78341e16 | − | 8.78341e16i | 0.237939 | − | 0.237939i | −0.578057 | − | 0.815996i | \(-0.696189\pi\) |
0.815996 | + | 0.578057i | \(0.196189\pi\) | |||||||
\(158\) | 6.35547e17 | + | 6.35547e17i | 1.63641 | + | 1.63641i | ||||
\(159\) | 3.86332e17i | 0.945765i | ||||||||
\(160\) | −8.57189e17 | + | 2.15874e17i | −1.99580 | + | 0.502621i | ||||
\(161\) | −4.01260e16 | −0.0888831 | ||||||||
\(162\) | 7.53710e17 | − | 7.53710e17i | 1.58885 | − | 1.58885i | ||||
\(163\) | 4.20586e17 | + | 4.20586e17i | 0.844023 | + | 0.844023i | 0.989379 | − | 0.145357i | \(-0.0464330\pi\) |
−0.145357 | + | 0.989379i | \(0.546433\pi\) | |||||||
\(164\) | 8.11967e17i | 1.55163i | ||||||||
\(165\) | −2.34862e17 | − | 9.32584e17i | −0.427504 | − | 1.69753i | ||||
\(166\) | −1.63827e17 | −0.284132 | ||||||||
\(167\) | −4.62254e17 | + | 4.62254e17i | −0.764097 | + | 0.764097i | −0.977060 | − | 0.212963i | \(-0.931689\pi\) |
0.212963 | + | 0.977060i | \(0.431689\pi\) | |||||||
\(168\) | 1.43805e17 | + | 1.43805e17i | 0.226620 | + | 0.226620i | ||||
\(169\) | − | 6.47169e17i | − | 0.972577i | ||||||
\(170\) | −8.55994e16 | + | 1.43227e17i | −0.122710 | + | 0.205321i | ||||
\(171\) | −4.09606e17 | −0.560270 | ||||||||
\(172\) | −1.37065e18 | + | 1.37065e18i | −1.78937 | + | 1.78937i | ||||
\(173\) | −7.12705e17 | − | 7.12705e17i | −0.888261 | − | 0.888261i | 0.106095 | − | 0.994356i | \(-0.466165\pi\) |
−0.994356 | + | 0.106095i | \(0.966165\pi\) | |||||||
\(174\) | − | 6.88919e17i | − | 0.819925i | ||||||
\(175\) | −7.67347e16 | − | 2.30642e16i | −0.0872344 | − | 0.0262200i | ||||
\(176\) | 3.16248e18 | 3.43500 | ||||||||
\(177\) | 1.30335e18 | − | 1.30335e18i | 1.35293 | − | 1.35293i | ||||
\(178\) | −1.63719e18 | − | 1.63719e18i | −1.62458 | − | 1.62458i | ||||
\(179\) | 1.55328e18i | 1.47376i | 0.676026 | + | 0.736878i | \(0.263701\pi\) | ||||
−0.676026 | + | 0.736878i | \(0.736299\pi\) | |||||||
\(180\) | 1.62685e18 | + | 9.72286e17i | 1.47628 | + | 0.882296i | ||||
\(181\) | 3.83773e17 | 0.333155 | 0.166577 | − | 0.986028i | \(-0.446728\pi\) | ||||
0.166577 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(182\) | 2.38566e16 | − | 2.38566e16i | 0.0198170 | − | 0.0198170i | ||||
\(183\) | 1.72860e18 | + | 1.72860e18i | 1.37431 | + | 1.37431i | ||||
\(184\) | − | 3.45802e18i | − | 2.63199i | ||||||
\(185\) | 1.28594e18 | − | 3.23850e17i | 0.937231 | − | 0.236032i | ||||
\(186\) | −5.22553e18 | −3.64777 | ||||||||
\(187\) | 1.82686e17 | − | 1.82686e17i | 0.122172 | − | 0.122172i | ||||
\(188\) | −1.10891e18 | − | 1.10891e18i | −0.710613 | − | 0.710613i | ||||
\(189\) | 5.77541e16i | 0.0354722i | ||||||||
\(190\) | 6.15490e17 | + | 2.44398e18i | 0.362403 | + | 1.43902i | ||||
\(191\) | −2.69832e18 | −1.52344 | −0.761721 | − | 0.647905i | \(-0.775645\pi\) | ||||
−0.761721 | + | 0.647905i | \(0.775645\pi\) | |||||||
\(192\) | −2.15340e18 | + | 2.15340e18i | −1.16604 | + | 1.16604i | ||||
\(193\) | 1.53099e18 | + | 1.53099e18i | 0.795270 | + | 0.795270i | 0.982345 | − | 0.187076i | \(-0.0599010\pi\) |
−0.187076 | + | 0.982345i | \(0.559901\pi\) | |||||||
\(194\) | 3.94899e18i | 1.96821i | ||||||||
\(195\) | 2.31672e17 | − | 3.87639e17i | 0.110815 | − | 0.185418i | ||||
\(196\) | 5.29563e18 | 2.43147 | ||||||||
\(197\) | −3.07411e18 | + | 3.07411e18i | −1.35516 | + | 1.35516i | −0.475371 | + | 0.879785i | \(0.657686\pi\) |
−0.879785 | + | 0.475371i | \(0.842314\pi\) | |||||||
\(198\) | −2.92139e18 | − | 2.92139e18i | −1.23671 | − | 1.23671i | ||||
\(199\) | − | 7.37981e17i | − | 0.300069i | −0.988681 | − | 0.150034i | \(-0.952062\pi\) | ||
0.988681 | − | 0.150034i | \(-0.0479384\pi\) | |||||||
\(200\) | 1.98764e18 | − | 6.61291e18i | 0.776423 | − | 2.58317i | ||||
\(201\) | 3.81886e18 | 1.43339 | ||||||||
\(202\) | 2.17072e18 | − | 2.17072e18i | 0.783055 | − | 0.783055i | ||||
\(203\) | 6.28438e16 | + | 6.28438e16i | 0.0217919 | + | 0.0217919i | ||||
\(204\) | 1.23500e18i | 0.411743i | ||||||||
\(205\) | −1.69438e18 | − | 1.01265e18i | −0.543226 | − | 0.324659i | ||||
\(206\) | −1.34616e18 | −0.415107 | ||||||||
\(207\) | −1.63154e18 | + | 1.63154e18i | −0.483989 | + | 0.483989i | ||||
\(208\) | 1.05007e18 | + | 1.05007e18i | 0.299718 | + | 0.299718i | ||||
\(209\) | − | 3.90236e18i | − | 1.07191i | ||||||
\(210\) | −8.09663e17 | + | 2.03905e17i | −0.214067 | + | 0.0539106i | ||||
\(211\) | 1.14883e18 | 0.292413 | 0.146207 | − | 0.989254i | \(-0.453294\pi\) | ||||
0.146207 | + | 0.989254i | \(0.453294\pi\) | |||||||
\(212\) | 5.12899e18 | − | 5.12899e18i | 1.25703 | − | 1.25703i | ||||
\(213\) | 1.90686e18 | + | 1.90686e18i | 0.450072 | + | 0.450072i | ||||
\(214\) | 1.37170e19i | 3.11853i | ||||||||
\(215\) | −1.15082e18 | − | 4.56965e18i | −0.252057 | − | 1.00086i | ||||
\(216\) | −4.97718e18 | −1.05040 | ||||||||
\(217\) | 4.76678e17 | − | 4.76678e17i | 0.0969498 | − | 0.0969498i | ||||
\(218\) | −6.12526e18 | − | 6.12526e18i | −1.20081 | − | 1.20081i | ||||
\(219\) | − | 4.19842e18i | − | 0.793474i | ||||||
\(220\) | −9.26306e18 | + | 1.54992e19i | −1.68800 | + | 2.82441i | ||||
\(221\) | 1.21319e17 | 0.0213201 | ||||||||
\(222\) | 9.77108e18 | − | 9.77108e18i | 1.65622 | − | 1.65622i | ||||
\(223\) | −3.90465e18 | − | 3.90465e18i | −0.638474 | − | 0.638474i | 0.311705 | − | 0.950179i | \(-0.399100\pi\) |
−0.950179 | + | 0.311705i | \(0.899100\pi\) | |||||||
\(224\) | − | 1.18829e18i | − | 0.187473i | ||||||
\(225\) | −4.05786e18 | + | 2.18227e18i | −0.617785 | + | 0.332237i | ||||
\(226\) | 1.26082e19 | 1.85261 | ||||||||
\(227\) | −5.53218e18 | + | 5.53218e18i | −0.784674 | + | 0.784674i | −0.980616 | − | 0.195941i | \(-0.937224\pi\) |
0.195941 | + | 0.980616i | \(0.437224\pi\) | |||||||
\(228\) | 1.31904e19 | + | 1.31904e19i | 1.80626 | + | 1.80626i | ||||
\(229\) | − | 9.74806e18i | − | 1.28895i | −0.764627 | − | 0.644473i | \(-0.777077\pi\) | ||
0.764627 | − | 0.644473i | \(-0.222923\pi\) | |||||||
\(230\) | 1.21864e19 | + | 7.28321e18i | 1.55616 | + | 0.930037i | ||||
\(231\) | 1.29281e18 | 0.159455 | ||||||||
\(232\) | −5.41581e18 | + | 5.41581e18i | −0.645297 | + | 0.645297i | ||||
\(233\) | −4.13927e18 | − | 4.13927e18i | −0.476515 | − | 0.476515i | 0.427500 | − | 0.904015i | \(-0.359394\pi\) |
−0.904015 | + | 0.427500i | \(0.859394\pi\) | |||||||
\(234\) | − | 1.94004e18i | − | 0.215816i | ||||||
\(235\) | 3.69701e18 | − | 9.31054e17i | 0.397473 | − | 0.100100i | ||||
\(236\) | −3.46068e19 | −3.59638 | ||||||||
\(237\) | −1.14357e19 | + | 1.14357e19i | −1.14889 | + | 1.14889i | ||||
\(238\) | −1.58607e17 | − | 1.58607e17i | −0.0154066 | − | 0.0154066i | ||||
\(239\) | 1.16508e19i | 1.09439i | 0.837006 | + | 0.547194i | \(0.184304\pi\) | ||||
−0.837006 | + | 0.547194i | \(0.815696\pi\) | |||||||
\(240\) | −8.97509e18 | − | 3.56381e19i | −0.815359 | − | 3.23761i | ||||
\(241\) | 2.18771e19 | 1.92245 | 0.961223 | − | 0.275771i | \(-0.0889333\pi\) | ||||
0.961223 | + | 0.275771i | \(0.0889333\pi\) | |||||||
\(242\) | 1.23787e19 | − | 1.23787e19i | 1.05233 | − | 1.05233i | ||||
\(243\) | 1.02142e19 | + | 1.02142e19i | 0.840141 | + | 0.840141i | ||||
\(244\) | − | 4.58982e19i | − | 3.65323i | ||||||
\(245\) | −6.60445e18 | + | 1.10507e19i | −0.508754 | + | 0.851260i | ||||
\(246\) | −2.05691e19 | −1.53368 | ||||||||
\(247\) | 1.29574e18 | − | 1.29574e18i | 0.0935282 | − | 0.0935282i | ||||
\(248\) | 4.10796e19 | + | 4.10796e19i | 2.87086 | + | 2.87086i | ||||
\(249\) | − | 2.94782e18i | − | 0.199483i | ||||||
\(250\) | 1.91183e19 | + | 2.09327e19i | 1.25294 | + | 1.37184i | ||||
\(251\) | 7.95441e18 | 0.504915 | 0.252458 | − | 0.967608i | \(-0.418761\pi\) | ||||
0.252458 | + | 0.967608i | \(0.418761\pi\) | |||||||
\(252\) | −1.80155e18 | + | 1.80155e18i | −0.110775 | + | 0.110775i | ||||
\(253\) | −1.55438e19 | − | 1.55438e19i | −0.925964 | − | 0.925964i | ||||
\(254\) | − | 3.40413e18i | − | 0.196488i | ||||||
\(255\) | −2.57716e18 | − | 1.54024e18i | −0.144152 | − | 0.0861521i | ||||
\(256\) | −1.33587e19 | −0.724177 | ||||||||
\(257\) | 9.16947e18 | − | 9.16947e18i | 0.481814 | − | 0.481814i | −0.423897 | − | 0.905711i | \(-0.639338\pi\) |
0.905711 | + | 0.423897i | \(0.139338\pi\) | |||||||
\(258\) | −3.47220e19 | − | 3.47220e19i | −1.76867 | − | 1.76867i | ||||
\(259\) | 1.78265e18i | 0.0880377i | ||||||||
\(260\) | −8.22207e18 | + | 2.07064e18i | −0.393726 | + | 0.0991559i | ||||
\(261\) | 5.11051e18 | 0.237323 | ||||||||
\(262\) | −2.17538e19 | + | 2.17538e19i | −0.979772 | + | 0.979772i | ||||
\(263\) | 4.10589e18 | + | 4.10589e18i | 0.179375 | + | 0.179375i | 0.791083 | − | 0.611709i | \(-0.209517\pi\) |
−0.611709 | + | 0.791083i | \(0.709517\pi\) | |||||||
\(264\) | 1.11413e20i | 4.72176i | ||||||||
\(265\) | 4.30637e18 | + | 1.70996e19i | 0.177070 | + | 0.703104i | ||||
\(266\) | −3.38800e18 | −0.135173 | ||||||||
\(267\) | 2.94589e19 | − | 2.94589e19i | 1.14058 | − | 1.14058i | ||||
\(268\) | −5.06997e19 | − | 5.06997e19i | −1.90514 | − | 1.90514i | ||||
\(269\) | 8.31122e18i | 0.303142i | 0.988446 | + | 0.151571i | \(0.0484333\pi\) | ||||
−0.988446 | + | 0.151571i | \(0.951567\pi\) | |||||||
\(270\) | 1.04829e19 | − | 1.75402e19i | 0.371167 | − | 0.621046i | ||||
\(271\) | 9.25539e18 | 0.318156 | 0.159078 | − | 0.987266i | \(-0.449148\pi\) | ||||
0.159078 | + | 0.987266i | \(0.449148\pi\) | |||||||
\(272\) | 6.98125e18 | − | 6.98125e18i | 0.233014 | − | 0.233014i | ||||
\(273\) | 4.29265e17 | + | 4.29265e17i | 0.0139131 | + | 0.0139131i | ||||
\(274\) | − | 2.31546e19i | − | 0.728841i | ||||||
\(275\) | −2.07907e19 | − | 3.86597e19i | −0.635634 | − | 1.18194i | ||||
\(276\) | 1.05080e20 | 3.12067 | ||||||||
\(277\) | −4.75485e19 | + | 4.75485e19i | −1.37182 | + | 1.37182i | −0.514086 | + | 0.857739i | \(0.671869\pi\) |
−0.857739 | + | 0.514086i | \(0.828131\pi\) | |||||||
\(278\) | 2.10196e19 | + | 2.10196e19i | 0.589205 | + | 0.589205i | ||||
\(279\) | − | 3.87638e19i | − | 1.05583i | ||||||
\(280\) | 7.96798e18 | + | 4.76205e18i | 0.210904 | + | 0.126046i | ||||
\(281\) | 2.34503e19 | 0.603250 | 0.301625 | − | 0.953427i | \(-0.402471\pi\) | ||||
0.301625 | + | 0.953427i | \(0.402471\pi\) | |||||||
\(282\) | 2.80914e19 | − | 2.80914e19i | 0.702393 | − | 0.702393i | ||||
\(283\) | 8.97167e18 | + | 8.97167e18i | 0.218063 | + | 0.218063i | 0.807682 | − | 0.589619i | \(-0.200722\pi\) |
−0.589619 | + | 0.807682i | \(0.700722\pi\) | |||||||
\(284\) | − | 5.06314e19i | − | 1.19639i | ||||||
\(285\) | −4.39758e19 | + | 1.10748e19i | −1.01031 | + | 0.254436i | ||||
\(286\) | 1.84829e19 | 0.412898 | ||||||||
\(287\) | 1.87633e18 | − | 1.87633e18i | 0.0407619 | − | 0.0407619i | ||||
\(288\) | −4.83164e19 | − | 4.83164e19i | −1.02083 | − | 1.02083i | ||||
\(289\) | 4.78546e19i | 0.983425i | ||||||||
\(290\) | −7.67925e18 | − | 3.04926e19i | −0.153509 | − | 0.609552i | ||||
\(291\) | −7.10563e19 | −1.38184 | ||||||||
\(292\) | −5.57388e19 | + | 5.57388e19i | −1.05462 | + | 1.05462i | ||||
\(293\) | 3.01448e19 | + | 3.01448e19i | 0.554973 | + | 0.554973i | 0.927872 | − | 0.372899i | \(-0.121636\pi\) |
−0.372899 | + | 0.927872i | \(0.621636\pi\) | |||||||
\(294\) | 1.34151e20i | 2.40334i | ||||||||
\(295\) | 4.31600e19 | − | 7.22163e19i | 0.752498 | − | 1.25910i | ||||
\(296\) | −1.53627e20 | −2.60696 | ||||||||
\(297\) | −2.23725e19 | + | 2.23725e19i | −0.369542 | + | 0.369542i | ||||
\(298\) | 1.86665e19 | + | 1.86665e19i | 0.300147 | + | 0.300147i | ||||
\(299\) | − | 1.03224e19i | − | 0.161588i | ||||||
\(300\) | 2.00949e20 | + | 6.03993e19i | 3.06278 | + | 0.920580i | ||||
\(301\) | 6.33474e18 | 0.0940150 | ||||||||
\(302\) | 3.18057e19 | − | 3.18057e19i | 0.459674 | − | 0.459674i | ||||
\(303\) | 3.90589e19 | + | 3.90589e19i | 0.549767 | + | 0.549767i | ||||
\(304\) | − | 1.49126e20i | − | 2.04440i | ||||||
\(305\) | 9.57787e19 | + | 5.72420e19i | 1.27900 | + | 0.764392i | ||||
\(306\) | −1.28981e19 | −0.167785 | ||||||||
\(307\) | 4.61714e19 | − | 4.61714e19i | 0.585148 | − | 0.585148i | −0.351165 | − | 0.936313i | \(-0.614215\pi\) |
0.936313 | + | 0.351165i | \(0.114215\pi\) | |||||||
\(308\) | −1.71635e19 | − | 1.71635e19i | −0.211934 | − | 0.211934i | ||||
\(309\) | − | 2.42223e19i | − | 0.291439i | ||||||
\(310\) | −2.31290e20 | + | 5.82480e19i | −2.71184 | + | 0.682948i | ||||
\(311\) | −1.05199e20 | −1.20207 | −0.601034 | − | 0.799224i | \(-0.705244\pi\) | ||||
−0.601034 | + | 0.799224i | \(0.705244\pi\) | |||||||
\(312\) | −3.69936e19 | + | 3.69936e19i | −0.411993 | + | 0.411993i | ||||
\(313\) | −9.34620e19 | − | 9.34620e19i | −1.01457 | − | 1.01457i | −0.999892 | − | 0.0146733i | \(-0.995329\pi\) |
−0.0146733 | − | 0.999892i | \(-0.504671\pi\) | |||||||
\(314\) | − | 5.90802e19i | − | 0.625180i | ||||||
\(315\) | −1.51260e18 | − | 6.00621e18i | −0.0156042 | − | 0.0619607i | ||||
\(316\) | 3.03645e20 | 3.05400 | ||||||||
\(317\) | 1.12873e19 | − | 1.12873e19i | 0.110692 | − | 0.110692i | −0.649591 | − | 0.760283i | \(-0.725060\pi\) |
0.760283 | + | 0.649591i | \(0.225060\pi\) | |||||||
\(318\) | 1.29930e20 | + | 1.29930e20i | 1.24249 | + | 1.24249i | ||||
\(319\) | 4.86883e19i | 0.454045i | ||||||||
\(320\) | −7.13093e19 | + | 1.19316e20i | −0.648554 | + | 1.08518i | ||||
\(321\) | −2.46818e20 | −2.18946 | ||||||||
\(322\) | −1.34951e19 | + | 1.34951e19i | −0.116769 | + | 0.116769i | ||||
\(323\) | −8.61453e18 | − | 8.61453e18i | −0.0727129 | − | 0.0727129i | ||||
\(324\) | − | 3.60100e20i | − | 2.96526i | ||||||
\(325\) | 5.93323e18 | − | 1.97399e19i | 0.0476677 | − | 0.158591i | ||||
\(326\) | 2.82900e20 | 2.21765 | ||||||||
\(327\) | 1.10215e20 | − | 1.10215e20i | 0.843062 | − | 0.843062i | ||||
\(328\) | 1.61700e20 | + | 1.61700e20i | 1.20703 | + | 1.20703i | ||||
\(329\) | 5.12504e18i | 0.0373362i | ||||||||
\(330\) | −3.92632e20 | − | 2.34656e20i | −2.79173 | − | 1.66848i | ||||
\(331\) | −1.15661e20 | −0.802717 | −0.401358 | − | 0.915921i | \(-0.631462\pi\) | ||||
−0.401358 | + | 0.915921i | \(0.631462\pi\) | |||||||
\(332\) | −3.91357e19 | + | 3.91357e19i | −0.265136 | + | 0.265136i | ||||
\(333\) | 7.24834e19 | + | 7.24834e19i | 0.479385 | + | 0.479385i | ||||
\(334\) | 3.10927e20i | 2.00765i | ||||||||
\(335\) | 1.69029e20 | − | 4.25681e19i | 1.06562 | − | 0.268365i | ||||
\(336\) | 4.94039e19 | 0.304122 | ||||||||
\(337\) | 1.20713e20 | − | 1.20713e20i | 0.725628 | − | 0.725628i | −0.244118 | − | 0.969746i | \(-0.578498\pi\) |
0.969746 | + | 0.244118i | \(0.0784983\pi\) | |||||||
\(338\) | −2.17654e20 | − | 2.17654e20i | −1.27771 | − | 1.27771i | ||||
\(339\) | 2.26866e20i | 1.30068i | ||||||||
\(340\) | 1.37663e19 | + | 5.46631e19i | 0.0770881 | + | 0.306100i | ||||
\(341\) | 3.69307e20 | 2.02000 | ||||||||
\(342\) | −1.37757e20 | + | 1.37757e20i | −0.736048 | + | 0.736048i | ||||
\(343\) | −2.45772e19 | − | 2.45772e19i | −0.128286 | − | 0.128286i | ||||
\(344\) | 5.45921e20i | 2.78396i | ||||||||
\(345\) | −1.31051e20 | + | 2.19277e20i | −0.652961 | + | 1.09255i | ||||
\(346\) | −4.79389e20 | −2.33389 | ||||||||
\(347\) | −6.19151e19 | + | 6.19151e19i | −0.294551 | + | 0.294551i | −0.838875 | − | 0.544324i | \(-0.816786\pi\) |
0.544324 | + | 0.838875i | \(0.316786\pi\) | |||||||
\(348\) | −1.64572e20 | − | 1.64572e20i | −0.765108 | − | 0.765108i | ||||
\(349\) | − | 1.80830e20i | − | 0.821610i | −0.911723 | − | 0.410805i | \(-0.865248\pi\) | ||
0.911723 | − | 0.410805i | \(-0.134752\pi\) | |||||||
\(350\) | −3.35641e19 | + | 1.80503e19i | −0.149049 | + | 0.0801569i | ||||
\(351\) | −1.48572e19 | −0.0644881 | ||||||||
\(352\) | 4.60315e20 | − | 4.60315e20i | 1.95305 | − | 1.95305i | ||||
\(353\) | −5.63816e19 | − | 5.63816e19i | −0.233851 | − | 0.233851i | 0.580447 | − | 0.814298i | \(-0.302878\pi\) |
−0.814298 | + | 0.580447i | \(0.802878\pi\) | |||||||
\(354\) | − | 8.76675e20i | − | 3.55478i | ||||||
\(355\) | 1.05656e20 | + | 6.31451e19i | 0.418858 | + | 0.250330i | ||||
\(356\) | −7.82201e20 | −3.03193 | ||||||||
\(357\) | 2.85390e18 | − | 2.85390e18i | 0.0108167 | − | 0.0108167i | ||||
\(358\) | 5.22394e20 | + | 5.22394e20i | 1.93613 | + | 1.93613i | ||||
\(359\) | 3.98348e20i | 1.44380i | 0.691997 | + | 0.721901i | \(0.256731\pi\) | ||||
−0.691997 | + | 0.721901i | \(0.743269\pi\) | |||||||
\(360\) | 5.17609e20 | − | 1.30354e20i | 1.83477 | − | 0.462068i | ||||
\(361\) | 1.04427e20 | 0.362037 | ||||||||
\(362\) | 1.29069e20 | − | 1.29069e20i | 0.437678 | − | 0.437678i | ||||
\(363\) | 2.22736e20 | + | 2.22736e20i | 0.738819 | + | 0.738819i | ||||
\(364\) | − | 1.13980e19i | − | 0.0369842i | ||||||
\(365\) | −4.67990e19 | − | 1.85828e20i | −0.148557 | − | 0.589888i | ||||
\(366\) | 1.16271e21 | 3.61097 | ||||||||
\(367\) | −1.02197e20 | + | 1.02197e20i | −0.310535 | + | 0.310535i | −0.845117 | − | 0.534581i | \(-0.820469\pi\) |
0.534581 | + | 0.845117i | \(0.320469\pi\) | |||||||
\(368\) | −5.93999e20 | − | 5.93999e20i | −1.76605 | − | 1.76605i | ||||
\(369\) | − | 1.52585e20i | − | 0.443915i | ||||||
\(370\) | 3.23567e20 | − | 5.41399e20i | 0.921192 | − | 1.54136i | ||||
\(371\) | −2.37046e19 | −0.0660453 | ||||||||
\(372\) | −1.24830e21 | + | 1.24830e21i | −3.40389 | + | 3.40389i | ||||
\(373\) | −2.35792e20 | − | 2.35792e20i | −0.629301 | − | 0.629301i | 0.318591 | − | 0.947892i | \(-0.396790\pi\) |
−0.947892 | + | 0.318591i | \(0.896790\pi\) | |||||||
\(374\) | − | 1.22881e20i | − | 0.321005i | ||||||
\(375\) | −3.76653e20 | + | 3.44007e20i | −0.963145 | + | 0.879663i | ||||
\(376\) | −4.41670e20 | −1.10559 | ||||||||
\(377\) | −1.61665e19 | + | 1.61665e19i | −0.0396173 | + | 0.0396173i | ||||
\(378\) | 1.94237e19 | + | 1.94237e19i | 0.0466012 | + | 0.0466012i | ||||
\(379\) | − | 4.41886e20i | − | 1.03800i | −0.854775 | − | 0.518999i | \(-0.826305\pi\) | ||
0.854775 | − | 0.518999i | \(-0.173695\pi\) | |||||||
\(380\) | 7.30860e20 | + | 4.36798e20i | 1.68099 | + | 1.00464i | ||||
\(381\) | 6.12524e19 | 0.137950 | ||||||||
\(382\) | −9.07489e20 | + | 9.07489e20i | −2.00140 | + | 2.00140i | ||||
\(383\) | −6.14078e20 | − | 6.14078e20i | −1.32627 | − | 1.32627i | −0.908594 | − | 0.417680i | \(-0.862843\pi\) |
−0.417680 | − | 0.908594i | \(-0.637157\pi\) | |||||||
\(384\) | 1.79249e20i | 0.379147i | ||||||||
\(385\) | 5.72217e19 | − | 1.44107e19i | 0.118543 | − | 0.0298538i | ||||
\(386\) | 1.02980e21 | 2.08955 | ||||||||
\(387\) | 2.57573e20 | − | 2.57573e20i | 0.511933 | − | 0.511933i | ||||
\(388\) | 9.43353e20 | + | 9.43353e20i | 1.83663 | + | 1.83663i | ||||
\(389\) | − | 9.46296e19i | − | 0.180480i | −0.995920 | − | 0.0902402i | \(-0.971237\pi\) | ||
0.995920 | − | 0.0902402i | \(-0.0287635\pi\) | |||||||
\(390\) | −5.24544e19 | − | 2.08285e20i | −0.0980088 | − | 0.389171i | ||||
\(391\) | −6.86267e19 | −0.125626 | ||||||||
\(392\) | 1.05460e21 | − | 1.05460e21i | 1.89148 | − | 1.89148i | ||||
\(393\) | −3.91428e20 | − | 3.91428e20i | −0.687878 | − | 0.687878i | ||||
\(394\) | 2.06775e21i | 3.56064i | ||||||||
\(395\) | −3.78692e20 | + | 6.33636e20i | −0.639012 | + | 1.06921i | ||||
\(396\) | −1.39575e21 | −2.30806 | ||||||||
\(397\) | 7.84672e20 | − | 7.84672e20i | 1.27164 | − | 1.27164i | 0.326412 | − | 0.945228i | \(-0.394160\pi\) |
0.945228 | − | 0.326412i | \(-0.105840\pi\) | |||||||
\(398\) | −2.48195e20 | − | 2.48195e20i | −0.394211 | − | 0.394211i | ||||
\(399\) | − | 6.09621e19i | − | 0.0949024i | ||||||
\(400\) | −7.94503e20 | − | 1.47736e21i | −1.21232 | − | 2.25427i | ||||
\(401\) | −2.00662e20 | −0.300130 | −0.150065 | − | 0.988676i | \(-0.547948\pi\) | ||||
−0.150065 | + | 0.988676i | \(0.547948\pi\) | |||||||
\(402\) | 1.28435e21 | − | 1.28435e21i | 1.88310 | − | 1.88310i | ||||
\(403\) | 1.22625e20 | + | 1.22625e20i | 0.176254 | + | 0.176254i | ||||
\(404\) | − | 1.03710e21i | − | 1.46141i | ||||||
\(405\) | 7.51444e20 | + | 4.49099e20i | 1.03814 | + | 0.620444i | ||||
\(406\) | 4.22709e19 | 0.0572576 | ||||||||
\(407\) | −6.90556e20 | + | 6.90556e20i | −0.917157 | + | 0.917157i | ||||
\(408\) | 2.45946e20 | + | 2.45946e20i | 0.320301 | + | 0.320301i | ||||
\(409\) | 4.86410e20i | 0.621177i | 0.950544 | + | 0.310589i | \(0.100526\pi\) | ||||
−0.950544 | + | 0.310589i | \(0.899474\pi\) | |||||||
\(410\) | −9.10420e20 | + | 2.29280e20i | −1.14017 | + | 0.287141i | ||||
\(411\) | 4.16634e20 | 0.511705 | ||||||||
\(412\) | −3.21578e20 | + | 3.21578e20i | −0.387355 | + | 0.387355i | ||||
\(413\) | 7.99711e19 | + | 7.99711e19i | 0.0944784 | + | 0.0944784i | ||||
\(414\) | 1.09743e21i | 1.27167i | ||||||||
\(415\) | −3.28588e19 | − | 1.30475e20i | −0.0373480 | − | 0.148301i | ||||
\(416\) | 3.05687e20 | 0.340824 | ||||||||
\(417\) | −3.78217e20 | + | 3.78217e20i | −0.413669 | + | 0.413669i | ||||
\(418\) | −1.31243e21 | − | 1.31243e21i | −1.40820 | − | 1.40820i | ||||
\(419\) | − | 6.85131e19i | − | 0.0721210i | −0.999350 | − | 0.0360605i | \(-0.988519\pi\) | ||
0.999350 | − | 0.0360605i | \(-0.0114809\pi\) | |||||||
\(420\) | −1.44706e20 | + | 2.42126e20i | −0.149449 | + | 0.250062i | ||||
\(421\) | 6.59559e20 | 0.668339 | 0.334169 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334169 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(422\) | 3.86372e20 | − | 3.86372e20i | 0.384154 | − | 0.384154i | ||||
\(423\) | 2.08386e20 | + | 2.08386e20i | 0.203304 | + | 0.203304i | ||||
\(424\) | − | 2.04284e21i | − | 1.95572i | ||||||
\(425\) | −1.31238e20 | − | 3.94461e19i | −0.123296 | − | 0.0370589i | ||||
\(426\) | 1.28262e21 | 1.18255 | ||||||||
\(427\) | −1.06064e20 | + | 1.06064e20i | −0.0959718 | + | 0.0959718i | ||||
\(428\) | 3.27679e21 | + | 3.27679e21i | 2.91004 | + | 2.91004i | ||||
\(429\) | 3.32574e20i | 0.289888i | ||||||||
\(430\) | −1.92389e21 | − | 1.14981e21i | −1.64601 | − | 0.983736i | ||||
\(431\) | −8.29007e19 | −0.0696210 | −0.0348105 | − | 0.999394i | \(-0.511083\pi\) | ||||
−0.0348105 | + | 0.999394i | \(0.511083\pi\) | |||||||
\(432\) | −8.54953e20 | + | 8.54953e20i | −0.704810 | + | 0.704810i | ||||
\(433\) | 5.64309e20 | + | 5.64309e20i | 0.456682 | + | 0.456682i | 0.897565 | − | 0.440883i | \(-0.145335\pi\) |
−0.440883 | + | 0.897565i | \(0.645335\pi\) | |||||||
\(434\) | − | 3.20630e20i | − | 0.254733i | ||||||
\(435\) | 5.48670e20 | − | 1.38177e20i | 0.427954 | − | 0.107776i | ||||
\(436\) | −2.92646e21 | −2.24105 | ||||||||
\(437\) | −7.32967e20 | + | 7.32967e20i | −0.551103 | + | 0.551103i | ||||
\(438\) | −1.41200e21 | − | 1.41200e21i | −1.04242 | − | 1.04242i | ||||
\(439\) | − | 1.12569e21i | − | 0.816024i | −0.912976 | − | 0.408012i | \(-0.866222\pi\) | ||
0.912976 | − | 0.408012i | \(-0.133778\pi\) | |||||||
\(440\) | 1.24190e21 | + | 4.93131e21i | 0.884025 | + | 3.51027i | ||||
\(441\) | −9.95154e20 | −0.695635 | ||||||||
\(442\) | 4.08015e19 | − | 4.08015e19i | 0.0280090 | − | 0.0280090i | ||||
\(443\) | 8.58659e20 | + | 8.58659e20i | 0.578883 | + | 0.578883i | 0.934596 | − | 0.355712i | \(-0.115762\pi\) |
−0.355712 | + | 0.934596i | \(0.615762\pi\) | |||||||
\(444\) | − | 4.66833e21i | − | 3.09099i | ||||||
\(445\) | 9.75524e20 | − | 1.63227e21i | 0.634392 | − | 1.06148i | ||||
\(446\) | −2.62640e21 | −1.67757 | ||||||||
\(447\) | −3.35877e20 | + | 3.35877e20i | −0.210727 | + | 0.210727i | ||||
\(448\) | −1.32129e20 | − | 1.32129e20i | −0.0814280 | − | 0.0814280i | ||||
\(449\) | − | 1.05049e21i | − | 0.635948i | −0.948099 | − | 0.317974i | \(-0.896997\pi\) | ||
0.948099 | − | 0.317974i | \(-0.103003\pi\) | |||||||
\(450\) | −6.30794e20 | + | 2.09866e21i | −0.375135 | + | 1.24808i | ||||
\(451\) | 1.45369e21 | 0.849297 | ||||||||
\(452\) | 3.01191e21 | − | 3.01191e21i | 1.72876 | − | 1.72876i | ||||
\(453\) | 5.72298e20 | + | 5.72298e20i | 0.322728 | + | 0.322728i | ||||
\(454\) | 3.72113e21i | 2.06171i | ||||||||
\(455\) | 2.37849e19 | + | 1.42150e19i | 0.0129482 | + | 0.00773848i | ||||
\(456\) | 5.25365e21 | 2.81023 | ||||||||
\(457\) | 9.80238e20 | − | 9.80238e20i | 0.515231 | − | 0.515231i | −0.400894 | − | 0.916125i | \(-0.631300\pi\) |
0.916125 | + | 0.400894i | \(0.131300\pi\) | |||||||
\(458\) | −3.27844e21 | − | 3.27844e21i | −1.69334 | − | 1.69334i | ||||
\(459\) | 9.87756e19i | 0.0501358i | ||||||||
\(460\) | 4.65101e21 | − | 1.17131e21i | 2.31998 | − | 0.584263i | ||||
\(461\) | −2.84661e21 | −1.39547 | −0.697735 | − | 0.716356i | \(-0.745809\pi\) | ||||
−0.697735 | + | 0.716356i | \(0.745809\pi\) | |||||||
\(462\) | 4.34793e20 | − | 4.34793e20i | 0.209482 | − | 0.209482i | ||||
\(463\) | −5.66373e20 | − | 5.66373e20i | −0.268198 | − | 0.268198i | 0.560176 | − | 0.828374i | \(-0.310734\pi\) |
−0.828374 | + | 0.560176i | \(0.810734\pi\) | |||||||
\(464\) | 1.86059e21i | 0.865980i | ||||||||
\(465\) | −1.04809e21 | − | 4.16173e21i | −0.479484 | − | 1.90393i | ||||
\(466\) | −2.78421e21 | −1.25203 | ||||||||
\(467\) | −8.71716e20 | + | 8.71716e20i | −0.385337 | + | 0.385337i | −0.873020 | − | 0.487684i | \(-0.837842\pi\) |
0.487684 | + | 0.873020i | \(0.337842\pi\) | |||||||
\(468\) | −4.63446e20 | − | 4.63446e20i | −0.201388 | − | 0.201388i | ||||
\(469\) | 2.34318e20i | 0.100098i | ||||||||
\(470\) | 9.30238e20 | − | 1.55650e21i | 0.390671 | − | 0.653680i | ||||
\(471\) | 1.06306e21 | 0.438926 | ||||||||
\(472\) | −6.89182e21 | + | 6.89182e21i | −2.79768 | + | 2.79768i | ||||
\(473\) | 2.45393e21 | + | 2.45393e21i | 0.979427 | + | 0.979427i | ||||
\(474\) | 7.69206e21i | 3.01867i | ||||||||
\(475\) | −1.82299e21 | + | 9.80380e20i | −0.703453 | + | 0.378308i | ||||
\(476\) | −7.57776e19 | −0.0287531 | ||||||||
\(477\) | −9.63840e20 | + | 9.63840e20i | −0.359632 | + | 0.359632i | ||||
\(478\) | 3.91835e21 | + | 3.91835e21i | 1.43774 | + | 1.43774i | ||||
\(479\) | 4.50080e20i | 0.162407i | 0.996698 | + | 0.0812036i | \(0.0258764\pi\) | ||||
−0.996698 | + | 0.0812036i | \(0.974124\pi\) | |||||||
\(480\) | −6.49368e21 | − | 3.88094e21i | −2.30442 | − | 1.37723i | ||||
\(481\) | −4.58586e20 | −0.160052 | ||||||||
\(482\) | 7.35765e21 | − | 7.35765e21i | 2.52559 | − | 2.52559i | ||||
\(483\) | −2.42824e20 | − | 2.42824e20i | −0.0819812 | − | 0.0819812i | ||||
\(484\) | − | 5.91416e21i | − | 1.96395i | ||||||
\(485\) | −3.14506e21 | + | 7.92051e20i | −1.02730 | + | 0.258714i | ||||
\(486\) | 6.87038e21 | 2.20745 | ||||||||
\(487\) | 9.70460e20 | − | 9.70460e20i | 0.306723 | − | 0.306723i | −0.536914 | − | 0.843637i | \(-0.680410\pi\) |
0.843637 | + | 0.536914i | \(0.180410\pi\) | |||||||
\(488\) | −9.14045e21 | − | 9.14045e21i | −2.84190 | − | 2.84190i | ||||
\(489\) | 5.09038e21i | 1.55697i | ||||||||
\(490\) | 1.49536e21 | + | 5.93773e21i | 0.449962 | + | 1.78670i | ||||
\(491\) | 6.05872e20 | 0.179361 | 0.0896807 | − | 0.995971i | \(-0.471415\pi\) | ||||
0.0896807 | + | 0.995971i | \(0.471415\pi\) | |||||||
\(492\) | −4.91364e21 | + | 4.91364e21i | −1.43114 | + | 1.43114i | ||||
\(493\) | 1.07480e20 | + | 1.07480e20i | 0.0308002 | + | 0.0308002i | ||||
\(494\) | − | 8.71559e20i | − | 0.245743i | ||||||
\(495\) | 1.74071e21 | − | 2.91260e21i | 0.482932 | − | 0.808053i | ||||
\(496\) | 1.41128e22 | 3.85266 | ||||||||
\(497\) | −1.17002e20 | + | 1.17002e20i | −0.0314297 | + | 0.0314297i | ||||
\(498\) | −9.91402e20 | − | 9.91402e20i | −0.262069 | − | 0.262069i | ||||
\(499\) | − | 8.34117e20i | − | 0.216981i | −0.994097 | − | 0.108491i | \(-0.965398\pi\) | ||
0.994097 | − | 0.108491i | \(-0.0346018\pi\) | |||||||
\(500\) | 9.56758e21 | + | 4.33423e20i | 2.44930 | + | 0.110956i | ||||
\(501\) | −5.59469e21 | −1.40953 | ||||||||
\(502\) | 2.67520e21 | − | 2.67520e21i | 0.663326 | − | 0.663326i | ||||
\(503\) | −2.58150e21 | − | 2.58150e21i | −0.629982 | − | 0.629982i | 0.318081 | − | 0.948063i | \(-0.396961\pi\) |
−0.948063 | + | 0.318081i | \(0.896961\pi\) | |||||||
\(504\) | 7.17543e20i | 0.172347i | ||||||||
\(505\) | 2.16419e21 | + | 1.29343e21i | 0.511640 | + | 0.305781i | ||||
\(506\) | −1.04553e22 | −2.43295 | ||||||||
\(507\) | 3.91636e21 | − | 3.91636e21i | 0.897055 | − | 0.897055i | ||||
\(508\) | −8.13195e20 | − | 8.13195e20i | −0.183352 | − | 0.183352i | ||||
\(509\) | 4.00742e21i | 0.889453i | 0.895667 | + | 0.444726i | \(0.146699\pi\) | ||||
−0.895667 | + | 0.444726i | \(0.853301\pi\) | |||||||
\(510\) | −1.38475e21 | + | 3.48735e20i | −0.302559 | + | 0.0761963i | ||||
\(511\) | 2.57608e20 | 0.0554104 | ||||||||
\(512\) | −5.46336e21 | + | 5.46336e21i | −1.15691 | + | 1.15691i | ||||
\(513\) | 1.05497e21 | + | 1.05497e21i | 0.219939 | + | 0.219939i | ||||
\(514\) | − | 6.16770e21i | − | 1.26595i | ||||||
\(515\) | −2.70001e20 | − | 1.07212e21i | −0.0545642 | − | 0.216662i | ||||
\(516\) | −1.65891e22 | −3.30085 | ||||||||
\(517\) | −1.98532e21 | + | 1.98532e21i | −0.388960 | + | 0.388960i | ||||
\(518\) | 5.99536e20 | + | 5.99536e20i | 0.115658 | + | 0.115658i | ||||
\(519\) | − | 8.62591e21i | − | 1.63857i | ||||||
\(520\) | −1.22503e21 | + | 2.04975e21i | −0.229151 | + | 0.383420i | ||||
\(521\) | 1.01590e22 | 1.87133 | 0.935665 | − | 0.352889i | \(-0.114801\pi\) | ||||
0.935665 | + | 0.352889i | \(0.114801\pi\) | |||||||
\(522\) | 1.71875e21 | − | 1.71875e21i | 0.311780 | − | 0.311780i | ||||
\(523\) | −4.88787e20 | − | 4.88787e20i | −0.0873185 | − | 0.0873185i | 0.662098 | − | 0.749417i | \(-0.269666\pi\) |
−0.749417 | + | 0.662098i | \(0.769666\pi\) | |||||||
\(524\) | 1.03933e22i | 1.82854i | ||||||||
\(525\) | −3.24789e20 | − | 6.03936e20i | −0.0562765 | − | 0.104645i | ||||
\(526\) | 2.76176e21 | 0.471303 | ||||||||
\(527\) | 8.15252e20 | − | 8.15252e20i | 0.137027 | − | 0.137027i | ||||
\(528\) | 1.91379e22 | + | 1.91379e22i | 3.16827 | + | 3.16827i | ||||
\(529\) | − | 2.93515e20i | − | 0.0478613i | ||||||
\(530\) | 7.19920e21 | + | 4.30259e21i | 1.15632 | + | 0.691072i | ||||
\(531\) | 6.50332e21 | 1.02891 | ||||||||
\(532\) | −8.09342e20 | + | 8.09342e20i | −0.126136 | + | 0.126136i | ||||
\(533\) | 4.82684e20 | + | 4.82684e20i | 0.0741046 | + | 0.0741046i | ||||
\(534\) | − | 1.98150e22i | − | 2.99685i | ||||||
\(535\) | −1.09245e22 | + | 2.75123e21i | −1.62770 | + | 0.409918i | ||||
\(536\) | −2.01933e22 | −2.96407 | ||||||||
\(537\) | −9.39973e21 | + | 9.39973e21i | −1.35932 | + | 1.35932i | ||||
\(538\) | 2.79520e21 | + | 2.79520e21i | 0.398250 | + | 0.398250i | ||||
\(539\) | − | 9.48093e21i | − | 1.33089i | ||||||
\(540\) | −1.68588e21 | − | 6.69428e21i | −0.233173 | − | 0.925878i | ||||
\(541\) | 1.27581e21 | 0.173863 | 0.0869314 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869314 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(542\) | 3.11274e21 | − | 3.11274e21i | 0.417974 | − | 0.417974i | ||||
\(543\) | 2.32241e21 | + | 2.32241e21i | 0.307285 | + | 0.307285i | ||||
\(544\) | − | 2.03231e21i | − | 0.264971i | ||||||
\(545\) | 3.64975e21 | − | 6.10684e21i | 0.468911 | − | 0.784593i | ||||
\(546\) | 2.88738e20 | 0.0365564 | ||||||||
\(547\) | −5.75598e21 | + | 5.75598e21i | −0.718159 | + | 0.718159i | −0.968228 | − | 0.250069i | \(-0.919547\pi\) |
0.250069 | + | 0.968228i | \(0.419547\pi\) | |||||||
\(548\) | −5.53129e21 | − | 5.53129e21i | −0.680114 | − | 0.680114i | ||||
\(549\) | 8.62518e21i | 1.04518i | ||||||||
\(550\) | −1.99941e22 | − | 6.00964e21i | −2.38782 | − | 0.717706i | ||||
\(551\) | 2.29589e21 | 0.270233 | ||||||||
\(552\) | 2.09263e22 | − | 2.09263e22i | 2.42761 | − | 2.42761i | ||||
\(553\) | −7.01677e20 | − | 7.01677e20i | −0.0802299 | − | 0.0802299i | ||||
\(554\) | 3.19827e22i | 3.60444i | ||||||||
\(555\) | 9.74170e21 | + | 5.82211e21i | 1.08216 | + | 0.646750i | ||||
\(556\) | 1.00425e22 | 1.09963 | ||||||||
\(557\) | 2.85063e21 | − | 2.85063e21i | 0.307680 | − | 0.307680i | −0.536329 | − | 0.844009i | \(-0.680189\pi\) |
0.844009 | + | 0.536329i | \(0.180189\pi\) | |||||||
\(558\) | −1.30369e22 | − | 1.30369e22i | −1.38708 | − | 1.38708i | ||||
\(559\) | 1.62961e21i | 0.170918i | ||||||||
\(560\) | 2.18669e21 | − | 5.50696e20i | 0.226091 | − | 0.0569387i | ||||
\(561\) | 2.21106e21 | 0.225371 | ||||||||
\(562\) | 7.88672e21 | − | 7.88672e21i | 0.792512 | − | 0.792512i | ||||
\(563\) | 1.00638e22 | + | 1.00638e22i | 0.997000 | + | 0.997000i | 0.999996 | − | 0.00299588i | \(-0.000953621\pi\) |
−0.00299588 | + | 0.999996i | \(0.500954\pi\) | |||||||
\(564\) | − | 1.34212e22i | − | 1.31087i | ||||||
\(565\) | 2.52883e21 | + | 1.00414e22i | 0.243519 | + | 0.966960i | ||||
\(566\) | 6.03465e21 | 0.572955 | ||||||||
\(567\) | −8.32136e20 | + | 8.32136e20i | −0.0778986 | + | 0.0778986i | ||||
\(568\) | −1.00831e22 | − | 1.00831e22i | −0.930691 | − | 0.930691i | ||||
\(569\) | − | 1.48136e22i | − | 1.34822i | −0.738629 | − | 0.674112i | \(-0.764526\pi\) | ||
0.738629 | − | 0.674112i | \(-0.235474\pi\) | |||||||
\(570\) | −1.10651e22 | + | 1.85145e22i | −0.993020 | + | 1.66155i | ||||
\(571\) | 5.94204e21 | 0.525831 | 0.262916 | − | 0.964819i | \(-0.415316\pi\) | ||||
0.262916 | + | 0.964819i | \(0.415316\pi\) | |||||||
\(572\) | 4.41530e21 | − | 4.41530e21i | 0.385293 | − | 0.385293i | ||||
\(573\) | −1.63290e22 | − | 1.63290e22i | −1.40515 | − | 1.40515i | ||||
\(574\) | − | 1.26208e21i | − | 0.107101i | ||||||
\(575\) | −3.35627e21 | + | 1.11664e22i | −0.280876 | + | 0.934477i | ||||
\(576\) | −1.07448e22 | −0.886787 | ||||||||
\(577\) | 6.79999e21 | − | 6.79999e21i | 0.553480 | − | 0.553480i | −0.373963 | − | 0.927443i | \(-0.622001\pi\) |
0.927443 | + | 0.373963i | \(0.122001\pi\) | |||||||
\(578\) | 1.60943e22 | + | 1.60943e22i | 1.29196 | + | 1.29196i | ||||
\(579\) | 1.85297e22i | 1.46703i | ||||||||
\(580\) | −9.11868e21 | − | 5.44977e21i | −0.712046 | − | 0.425553i | ||||
\(581\) | 1.80873e20 | 0.0139305 | ||||||||
\(582\) | −2.38974e22 | + | 2.38974e22i | −1.81538 | + | 1.81538i | ||||
\(583\) | −9.18260e21 | − | 9.18260e21i | −0.688045 | − | 0.688045i | ||||
\(584\) | 2.22003e22i | 1.64080i | ||||||||
\(585\) | 1.54509e21 | − | 3.89115e20i | 0.112644 | − | 0.0283682i | ||||
\(586\) | 2.02764e22 | 1.45818 | ||||||||
\(587\) | 4.60252e21 | − | 4.60252e21i | 0.326505 | − | 0.326505i | −0.524751 | − | 0.851256i | \(-0.675841\pi\) |
0.851256 | + | 0.524751i | \(0.175841\pi\) | |||||||
\(588\) | 3.20467e22 | + | 3.20467e22i | 2.24266 | + | 2.24266i | ||||
\(589\) | − | 1.74146e22i | − | 1.20224i | ||||||
\(590\) | −9.77213e21 | − | 3.88030e22i | −0.665539 | − | 2.64271i | ||||
\(591\) | −3.72061e22 | −2.49985 | ||||||||
\(592\) | −2.63892e22 | + | 2.63892e22i | −1.74925 | + | 1.74925i | ||||
\(593\) | −1.38310e22 | − | 1.38310e22i | −0.904518 | − | 0.904518i | 0.0913053 | − | 0.995823i | \(-0.470896\pi\) |
−0.995823 | + | 0.0913053i | \(0.970896\pi\) | |||||||
\(594\) | 1.50485e22i | 0.970962i | ||||||||
\(595\) | 9.45062e19 | − | 1.58130e20i | 0.00601623 | − | 0.0100665i | ||||
\(596\) | 8.91831e21 | 0.560161 | ||||||||
\(597\) | 4.46591e21 | − | 4.46591e21i | 0.276768 | − | 0.276768i | ||||
\(598\) | −3.47159e21 | − | 3.47159e21i | −0.212285 | − | 0.212285i | ||||
\(599\) | − | 1.39652e22i | − | 0.842624i | −0.906916 | − | 0.421312i | \(-0.861570\pi\) | ||
0.906916 | − | 0.421312i | \(-0.138430\pi\) | |||||||
\(600\) | 5.20465e22 | − | 2.79900e22i | 3.09872 | − | 1.66645i | ||||
\(601\) | −4.28172e21 | −0.251549 | −0.125774 | − | 0.992059i | \(-0.540142\pi\) | ||||
−0.125774 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(602\) | 2.13048e21 | − | 2.13048e21i | 0.123511 | − | 0.123511i | ||||
\(603\) | 9.52748e21 | + | 9.52748e21i | 0.545054 | + | 0.545054i | ||||
\(604\) | − | 1.51958e22i | − | 0.857884i | ||||||
\(605\) | 1.23415e22 | + | 7.37586e21i | 0.687581 | + | 0.410932i | ||||
\(606\) | 2.62723e22 | 1.44450 | ||||||||
\(607\) | −8.39700e21 | + | 8.39700e21i | −0.455632 | + | 0.455632i | −0.897219 | − | 0.441586i | \(-0.854416\pi\) |
0.441586 | + | 0.897219i | \(0.354416\pi\) | |||||||
\(608\) | −2.17061e22 | − | 2.17061e22i | −1.16239 | − | 1.16239i | ||||
\(609\) | 7.60603e20i | 0.0401994i | ||||||||
\(610\) | 5.14634e22 | − | 1.29605e22i | 2.68448 | − | 0.676058i | ||||
\(611\) | −1.31841e21 | −0.0678768 | ||||||||
\(612\) | −3.08115e21 | + | 3.08115e21i | −0.156567 | + | 0.156567i | ||||
\(613\) | 3.28621e20 | + | 3.28621e20i | 0.0164820 | + | 0.0164820i | 0.715300 | − | 0.698818i | \(-0.246290\pi\) |
−0.698818 | + | 0.715300i | \(0.746290\pi\) | |||||||
\(614\) | − | 3.10564e22i | − | 1.53746i | ||||||
\(615\) | −4.12556e21 | − | 1.63817e22i | −0.201596 | − | 0.800493i | ||||
\(616\) | −6.83610e21 | −0.329733 | ||||||||
\(617\) | 4.84147e21 | − | 4.84147e21i | 0.230513 | − | 0.230513i | −0.582394 | − | 0.812907i | \(-0.697884\pi\) |
0.812907 | + | 0.582394i | \(0.197884\pi\) | |||||||
\(618\) | −8.14636e21 | − | 8.14636e21i | −0.382874 | − | 0.382874i | ||||
\(619\) | 2.47483e22i | 1.14821i | 0.818783 | + | 0.574104i | \(0.194649\pi\) | ||||
−0.818783 | + | 0.574104i | \(0.805351\pi\) | |||||||
\(620\) | −4.13372e22 | + | 6.91663e22i | −1.89325 | + | 3.16782i | ||||
\(621\) | 8.40431e21 | 0.379988 | ||||||||
\(622\) | −3.53802e22 | + | 3.53802e22i | −1.57920 | + | 1.57920i | ||||
\(623\) | 1.80755e21 | + | 1.80755e21i | 0.0796499 | + | 0.0796499i | ||||
\(624\) | 1.27091e22i | 0.552889i | ||||||||
\(625\) | −1.28367e22 | + | 1.94247e22i | −0.551331 | + | 0.834286i | ||||
\(626\) | −6.28657e22 | −2.66575 | ||||||||
\(627\) | 2.36152e22 | − | 2.36152e22i | 0.988672 | − | 0.988672i | ||||
\(628\) | −1.41134e22 | − | 1.41134e22i | −0.583383 | − | 0.583383i | ||||
\(629\) | 3.04883e21i | 0.124431i | ||||||||
\(630\) | −2.52870e21 | − | 1.51128e21i | −0.101900 | − | 0.0609003i | ||||
\(631\) | −2.87349e22 | −1.14334 | −0.571670 | − | 0.820484i | \(-0.693704\pi\) | ||||
−0.571670 | + | 0.820484i | \(0.693704\pi\) | |||||||
\(632\) | 6.04698e22 | − | 6.04698e22i | 2.37575 | − | 2.37575i | ||||
\(633\) | 6.95220e21 | + | 6.95220e21i | 0.269707 | + | 0.269707i | ||||
\(634\) | − | 7.59222e21i | − | 0.290840i | ||||||
\(635\) | 2.71112e21 | − | 6.82769e20i | 0.102556 | − | 0.0258276i | ||||
\(636\) | 6.20765e22 | 2.31884 | ||||||||
\(637\) | 3.14805e21 | − | 3.14805e21i | 0.116125 | − | 0.116125i | ||||
\(638\) | 1.63747e22 | + | 1.63747e22i | 0.596496 | + | 0.596496i | ||||
\(639\) | 9.51466e21i | 0.342284i | ||||||||
\(640\) | 1.99806e21 | + | 7.93385e21i | 0.0709853 | + | 0.281867i | ||||
\(641\) | 2.21002e22 | 0.775412 | 0.387706 | − | 0.921783i | \(-0.373268\pi\) | ||||
0.387706 | + | 0.921783i | \(0.373268\pi\) | |||||||
\(642\) | −8.30090e22 | + | 8.30090e22i | −2.87637 | + | 2.87637i | ||||
\(643\) | 2.95279e22 | + | 2.95279e22i | 1.01052 | + | 1.01052i | 0.999944 | + | 0.0105744i | \(0.00336601\pi\) |
0.0105744 | + | 0.999944i | \(0.496634\pi\) | |||||||
\(644\) | 6.44753e21i | 0.217925i | ||||||||
\(645\) | 2.06892e22 | − | 3.46176e22i | 0.690661 | − | 1.15563i | ||||
\(646\) | −5.79442e21 | −0.191051 | ||||||||
\(647\) | 1.86305e21 | − | 1.86305e21i | 0.0606723 | − | 0.0606723i | −0.676120 | − | 0.736792i | \(-0.736340\pi\) |
0.736792 | + | 0.676120i | \(0.236340\pi\) | |||||||
\(648\) | −7.17125e22 | − | 7.17125e22i | −2.30672 | − | 2.30672i | ||||
\(649\) | 6.19577e22i | 1.96851i | ||||||||
\(650\) | −4.64343e21 | − | 8.63431e21i | −0.145724 | − | 0.270970i | ||||
\(651\) | 5.76926e21 | 0.178843 | ||||||||
\(652\) | 6.75806e22 | − | 6.75806e22i | 2.06939 | − | 2.06939i | ||||
\(653\) | 8.24522e21 | + | 8.24522e21i | 0.249400 | + | 0.249400i | 0.820724 | − | 0.571324i | \(-0.193570\pi\) |
−0.571324 | + | 0.820724i | \(0.693570\pi\) | |||||||
\(654\) | − | 7.41344e22i | − | 2.21512i | ||||||
\(655\) | −2.16884e22 | − | 1.29620e22i | −0.640172 | − | 0.382598i | ||||
\(656\) | 5.55519e22 | 1.61982 | ||||||||
\(657\) | 1.04744e22 | − | 1.04744e22i | 0.301722 | − | 0.301722i | ||||
\(658\) | 1.72364e21 | + | 1.72364e21i | 0.0490500 | + | 0.0490500i | ||||
\(659\) | 4.75532e22i | 1.33689i | 0.743761 | + | 0.668446i | \(0.233040\pi\) | ||||
−0.743761 | + | 0.668446i | \(0.766960\pi\) | |||||||
\(660\) | −1.49849e23 | + | 3.77380e22i | −4.16202 | + | 1.04816i | ||||
\(661\) | 4.67704e22 | 1.28339 | 0.641697 | − | 0.766958i | \(-0.278231\pi\) | ||||
0.641697 | + | 0.766958i | \(0.278231\pi\) | |||||||
\(662\) | −3.88987e22 | + | 3.88987e22i | −1.05456 | + | 1.05456i | ||||
\(663\) | 7.34163e20 | + | 7.34163e20i | 0.0196646 | + | 0.0196646i | ||||
\(664\) | 1.55875e22i | 0.412506i | ||||||||
\(665\) | −6.79533e20 | − | 2.69828e21i | −0.0177680 | − | 0.0705527i | ||||
\(666\) | 4.87548e22 | 1.25957 | ||||||||
\(667\) | 9.14496e21 | − | 9.14496e21i | 0.233440 | − | 0.233440i | ||||
\(668\) | 7.42759e22 | + | 7.42759e22i | 1.87342 | + | 1.87342i | ||||
\(669\) | − | 4.72582e22i | − | 1.17779i | ||||||
\(670\) | 4.25308e22 | − | 7.11635e22i | 1.04738 | − | 1.75250i | ||||
\(671\) | −8.21729e22 | −1.99963 | ||||||||
\(672\) | 7.19099e21 | − | 7.19099e21i | 0.172916 | − | 0.172916i | ||||
\(673\) | −5.30419e22 | − | 5.30419e22i | −1.26037 | − | 1.26037i | −0.950913 | − | 0.309460i | \(-0.899852\pi\) |
−0.309460 | − | 0.950913i | \(-0.600148\pi\) | |||||||
\(674\) | − | 8.11955e22i | − | 1.90657i | ||||||
\(675\) | 1.60719e22 | + | 4.83074e21i | 0.372939 | + | 0.112094i | ||||
\(676\) | −1.03988e23 | −2.38458 | ||||||||
\(677\) | −2.71174e22 | + | 2.71174e22i | −0.614523 | + | 0.614523i | −0.944121 | − | 0.329598i | \(-0.893087\pi\) |
0.329598 | + | 0.944121i | \(0.393087\pi\) | |||||||
\(678\) | 7.62989e22 | + | 7.62989e22i | 1.70876 | + | 1.70876i | ||||
\(679\) | − | 4.35989e21i | − | 0.0964978i | ||||||
\(680\) | 1.36275e22 | + | 8.14444e21i | 0.298088 | + | 0.178152i | ||||
\(681\) | −6.69563e22 | −1.44749 | ||||||||
\(682\) | 1.24204e23 | − | 1.24204e23i | 2.65376 | − | 2.65376i | ||||
\(683\) | −1.17516e22 | − | 1.17516e22i | −0.248160 | − | 0.248160i | 0.572055 | − | 0.820215i | \(-0.306146\pi\) |
−0.820215 | + | 0.572055i | \(0.806146\pi\) | |||||||
\(684\) | 6.58164e22i | 1.37368i | ||||||||
\(685\) | 1.84408e22 | − | 4.64414e21i | 0.380414 | − | 0.0958033i | ||||
\(686\) | −1.65314e22 | −0.337068 | ||||||||
\(687\) | 5.89907e22 | − | 5.89907e22i | 1.18886 | − | 1.18886i | ||||
\(688\) | 9.37753e22 | + | 9.37753e22i | 1.86802 | + | 1.86802i | ||||
\(689\) | − | 6.09799e21i | − | 0.120070i | ||||||
\(690\) | 2.96721e22 | + | 1.17821e23i | 0.577504 | + | 2.29314i | ||||
\(691\) | 9.87813e21 | 0.190042 | 0.0950212 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950212 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(692\) | −1.14519e23 | + | 1.14519e23i | −2.17785 | + | 2.17785i | ||||
\(693\) | 3.22537e21 | + | 3.22537e21i | 0.0606336 | + | 0.0606336i | ||||
\(694\) | 4.16462e22i | 0.773926i | ||||||||
\(695\) | −1.25246e22 | + | 2.09564e22i | −0.230083 | + | 0.384980i | ||||
\(696\) | −6.55479e22 | −1.19038 | ||||||||
\(697\) | 3.20905e21 | − | 3.20905e21i | 0.0576122 | − | 0.0576122i | ||||
\(698\) | −6.08160e22 | − | 6.08160e22i | −1.07938 | − | 1.07938i | ||||
\(699\) | − | 5.00979e22i | − | 0.879026i | ||||||
\(700\) | −3.70599e21 | + | 1.23299e22i | −0.0642866 | + | 0.213882i | ||||
\(701\) | 6.05029e22 | 1.03760 | 0.518802 | − | 0.854894i | \(-0.326378\pi\) | ||||
0.518802 | + | 0.854894i | \(0.326378\pi\) | |||||||
\(702\) | −4.99672e21 | + | 4.99672e21i | −0.0847204 | + | 0.0847204i | ||||
\(703\) | 3.25630e22 | + | 3.25630e22i | 0.545861 | + | 0.545861i | ||||
\(704\) | − | 1.02367e23i | − | 1.69660i | ||||||
\(705\) | 2.80069e22 | + | 1.67383e22i | 0.458936 | + | 0.274282i | ||||
\(706\) | −3.79241e22 | −0.614438 | ||||||||
\(707\) | −2.39659e21 | + | 2.39659e21i | −0.0383917 | + | 0.0383917i | ||||
\(708\) | −2.09424e23 | − | 2.09424e23i | −3.31712 | − | 3.31712i | ||||
\(709\) | 4.31217e22i | 0.675345i | 0.941264 | + | 0.337672i | \(0.109640\pi\) | ||||
−0.941264 | + | 0.337672i | \(0.890360\pi\) | |||||||
\(710\) | 5.67706e22 | − | 1.42971e22i | 0.879138 | − | 0.221402i | ||||
\(711\) | −5.70610e22 | −0.873740 | ||||||||
\(712\) | −1.55772e23 | + | 1.55772e23i | −2.35858 | + | 2.35858i | ||||
\(713\) | −6.93656e22 | − | 6.93656e22i | −1.03855 | − | 1.03855i | ||||
\(714\) | − | 1.91963e21i | − | 0.0284205i | ||||||
\(715\) | 3.70714e21 | + | 1.47202e22i | 0.0542738 | + | 0.215509i | ||||
\(716\) | 2.49584e23 | 3.61337 | ||||||||
\(717\) | −7.05050e22 | + | 7.05050e22i | −1.00941 | + | 1.00941i | ||||
\(718\) | 1.33971e23 | + | 1.33971e23i | 1.89678 | + | 1.89678i | ||||
\(719\) | − | 8.16788e22i | − | 1.14361i | −0.820389 | − | 0.571805i | \(-0.806243\pi\) | ||
0.820389 | − | 0.571805i | \(-0.193757\pi\) | |||||||
\(720\) | 6.65203e22 | − | 1.11303e23i | 0.921074 | − | 1.54116i | ||||
\(721\) | 1.48624e21 | 0.0203519 | ||||||||
\(722\) | 3.51204e22 | − | 3.51204e22i | 0.475622 | − | 0.475622i | ||||
\(723\) | 1.32390e23 | + | 1.32390e23i | 1.77317 | + | 1.77317i | ||||
\(724\) | − | 6.16654e22i | − | 0.816833i | ||||||
\(725\) | 2.27448e22 | − | 1.22318e22i | 0.297973 | − | 0.160246i | ||||
\(726\) | 1.49820e23 | 1.94123 | ||||||||
\(727\) | −2.07289e22 | + | 2.07289e22i | −0.265645 | + | 0.265645i | −0.827343 | − | 0.561698i | \(-0.810148\pi\) |
0.561698 | + | 0.827343i | \(0.310148\pi\) | |||||||
\(728\) | −2.26986e21 | − | 2.26986e21i | −0.0287706 | − | 0.0287706i | ||||
\(729\) | 2.71518e22i | 0.340391i | ||||||||
\(730\) | −7.82365e22 | − | 4.67579e22i | −0.970122 | − | 0.579792i | ||||
\(731\) | 1.08342e22 | 0.132879 | ||||||||
\(732\) | 2.77754e23 | − | 2.77754e23i | 3.36955 | − | 3.36955i | ||||
\(733\) | −5.17301e22 | − | 5.17301e22i | −0.620743 | − | 0.620743i | 0.324978 | − | 0.945721i | \(-0.394643\pi\) |
−0.945721 | + | 0.324978i | \(0.894643\pi\) | |||||||
\(734\) | 6.87414e22i | 0.815924i | ||||||||
\(735\) | −1.06841e23 | + | 2.69068e22i | −1.25441 | + | 0.315910i | ||||
\(736\) | −1.72919e23 | −2.00826 | ||||||||
\(737\) | −9.07692e22 | + | 9.07692e22i | −1.04279 | + | 1.04279i | ||||
\(738\) | −5.13168e22 | − | 5.13168e22i | −0.583188 | − | 0.583188i | ||||
\(739\) | − | 6.59756e22i | − | 0.741699i | −0.928693 | − | 0.370850i | \(-0.879067\pi\) | ||
0.928693 | − | 0.370850i | \(-0.120933\pi\) | |||||||
\(740\) | −5.20370e22 | − | 2.06627e23i | −0.578706 | − | 2.29792i | ||||
\(741\) | 1.56824e22 | 0.172531 | ||||||||
\(742\) | −7.97227e21 | + | 7.97227e21i | −0.0867662 | + | 0.0867662i | ||||
\(743\) | −6.68400e22 | − | 6.68400e22i | −0.719658 | − | 0.719658i | 0.248877 | − | 0.968535i | \(-0.419939\pi\) |
−0.968535 | + | 0.248877i | \(0.919939\pi\) | |||||||
\(744\) | 4.97189e23i | 5.29587i | ||||||||
\(745\) | −1.11225e22 | + | 1.86104e22i | −0.117207 | + | 0.196113i | ||||
\(746\) | −1.58602e23 | −1.65347 | ||||||||
\(747\) | 7.35438e21 | − | 7.35438e21i | 0.0758545 | − | 0.0758545i | ||||
\(748\) | −2.93544e22 | − | 2.93544e22i | −0.299544 | − | 0.299544i | ||||
\(749\) | − | 1.51443e22i | − | 0.152896i | ||||||
\(750\) | −1.09796e22 | + | 2.42370e23i | −0.109673 | + | 2.42097i | ||||
\(751\) | 1.99115e23 | 1.96782 | 0.983910 | − | 0.178666i | \(-0.0571782\pi\) | ||||
0.983910 | + | 0.178666i | \(0.0571782\pi\) | |||||||
\(752\) | −7.58676e22 | + | 7.58676e22i | −0.741846 | + | 0.741846i | ||||
\(753\) | 4.81364e22 | + | 4.81364e22i | 0.465708 | + | 0.465708i | ||||
\(754\) | 1.08741e22i | 0.104094i | ||||||||
\(755\) | 3.17101e22 | + | 1.89515e22i | 0.300346 | + | 0.179501i | ||||
\(756\) | 9.28005e21 | 0.0869713 | ||||||||
\(757\) | −4.99979e21 | + | 4.99979e21i | −0.0463644 | + | 0.0463644i | −0.729909 | − | 0.683544i | \(-0.760438\pi\) |
0.683544 | + | 0.729909i | \(0.260438\pi\) | |||||||
\(758\) | −1.48614e23 | − | 1.48614e23i | −1.36366 | − | 1.36366i | ||||
\(759\) | − | 1.88128e23i | − | 1.70812i | ||||||
\(760\) | 2.32535e23 | − | 5.85614e22i | 2.08919 | − | 0.526142i | ||||
\(761\) | 1.23073e23 | 1.09417 | 0.547084 | − | 0.837078i | \(-0.315738\pi\) | ||||
0.547084 | + | 0.837078i | \(0.315738\pi\) | |||||||
\(762\) | 2.06002e22 | − | 2.06002e22i | 0.181231 | − | 0.181231i | ||||
\(763\) | 6.76261e21 | + | 6.76261e21i | 0.0588733 | + | 0.0588733i | ||||
\(764\) | 4.33571e23i | 3.73520i | ||||||||
\(765\) | −2.58697e21 | − | 1.02723e22i | −0.0220546 | − | 0.0875742i | ||||
\(766\) | −4.13050e23 | −3.48475 | ||||||||
\(767\) | −2.05725e22 | + | 2.05725e22i | −0.171761 | + | 0.171761i | ||||
\(768\) | −8.08406e22 | − | 8.08406e22i | −0.667944 | − | 0.667944i | ||||
\(769\) | 9.70633e22i | 0.793678i | 0.917888 | + | 0.396839i | \(0.129893\pi\) | ||||
−0.917888 | + | 0.396839i | \(0.870107\pi\) | |||||||
\(770\) | 1.43981e22 | − | 2.40912e22i | 0.116514 | − | 0.194954i | ||||
\(771\) | 1.10979e23 | 0.888801 | ||||||||
\(772\) | 2.46003e23 | − | 2.46003e23i | 1.94985 | − | 1.94985i | ||||
\(773\) | 3.65226e22 | + | 3.65226e22i | 0.286500 | + | 0.286500i | 0.835695 | − | 0.549194i | \(-0.185065\pi\) |
−0.549194 | + | 0.835695i | \(0.685065\pi\) | |||||||
\(774\) | − | 1.73253e23i | − | 1.34509i | ||||||
\(775\) | −9.27800e22 | − | 1.72522e23i | −0.712920 | − | 1.32565i | ||||
\(776\) | 3.75730e23 | 2.85748 | ||||||||
\(777\) | −1.07878e22 | + | 1.07878e22i | −0.0812015 | + | 0.0812015i | ||||
\(778\) | −3.18255e22 | − | 3.18255e22i | −0.237104 | − | 0.237104i | ||||
\(779\) | − | 6.85484e22i | − | 0.505473i | ||||||
\(780\) | −6.22867e22 | − | 3.72256e22i | −0.454609 | − | 0.271697i | ||||
\(781\) | −9.06471e22 | −0.654855 | ||||||||
\(782\) | −2.30803e22 | + | 2.30803e22i | −0.165039 | + | 0.165039i | ||||
\(783\) | −1.31625e22 | − | 1.31625e22i | −0.0931632 | − | 0.0931632i | ||||
\(784\) | − | 3.62308e23i | − | 2.53834i | ||||||
\(785\) | 4.70528e22 | − | 1.18498e22i | 0.326308 | − | 0.0821773i | ||||
\(786\) | −2.63288e23 | −1.80738 | ||||||||
\(787\) | 2.68452e22 | − | 2.68452e22i | 0.182419 | − | 0.182419i | −0.609990 | − | 0.792409i | \(-0.708827\pi\) |
0.792409 | + | 0.609990i | \(0.208827\pi\) | |||||||
\(788\) | 4.93954e23 | + | 4.93954e23i | 3.32259 | + | 3.32259i | ||||
\(789\) | 4.96938e22i | 0.330892i | ||||||||
\(790\) | 8.57420e22 | + | 3.40463e23i | 0.565167 | + | 2.24415i | ||||
\(791\) | −1.39201e22 | −0.0908303 | ||||||||
\(792\) | −2.77959e23 | + | 2.77959e23i | −1.79547 | + | 1.79547i | ||||
\(793\) | −2.72848e22 | − | 2.72848e22i | −0.174476 | − | 0.174476i | ||||
\(794\) | − | 5.27797e23i | − | 3.34120i | ||||||
\(795\) | −7.74189e22 | + | 1.29539e23i | −0.485188 | + | 0.811828i | ||||
\(796\) | −1.18580e23 | −0.735712 | ||||||||
\(797\) | −1.17771e23 | + | 1.17771e23i | −0.723389 | + | 0.723389i | −0.969294 | − | 0.245905i | \(-0.920915\pi\) |
0.245905 | + | 0.969294i | \(0.420915\pi\) | |||||||
\(798\) | −2.05026e22 | − | 2.05026e22i | −0.124677 | − | 0.124677i | ||||
\(799\) | 8.76525e21i | 0.0527703i | ||||||||
\(800\) | −3.30680e23 | − | 9.93925e22i | −1.97101 | − | 0.592426i | ||||
\(801\) | 1.46991e23 | 0.867424 | ||||||||
\(802\) | −6.74859e22 | + | 6.74859e22i | −0.394292 | + | 0.394292i | ||||
\(803\) | 9.97909e22 | + | 9.97909e22i | 0.577253 | + | 0.577253i | ||||
\(804\) | − | 6.13622e23i | − | 3.51441i | ||||||
\(805\) | −1.34545e22 | − | 8.04105e21i | −0.0762957 | − | 0.0455980i | ||||
\(806\) | 8.24816e22 | 0.463102 | ||||||||
\(807\) | −5.02956e22 | + | 5.02956e22i | −0.279603 | + | 0.279603i | ||||
\(808\) | −2.06535e23 | − | 2.06535e23i | −1.13685 | − | 1.13685i | ||||
\(809\) | 1.88036e23i | 1.02483i | 0.858738 | + | 0.512415i | \(0.171249\pi\) | ||||
−0.858738 | + | 0.512415i | \(0.828751\pi\) | |||||||
\(810\) | 4.03763e23 | − | 1.01683e23i | 2.17894 | − | 0.548745i | ||||
\(811\) | 2.08734e23 | 1.11539 | 0.557696 | − | 0.830045i | \(-0.311686\pi\) | ||||
0.557696 | + | 0.830045i | \(0.311686\pi\) | |||||||
\(812\) | 1.00979e22 | − | 1.00979e22i | 0.0534295 | − | 0.0534295i | ||||
\(813\) | 5.60093e22 | + | 5.60093e22i | 0.293451 | + | 0.293451i | ||||
\(814\) | 4.64492e23i | 2.40981i | ||||||||
\(815\) | 5.67415e22 | + | 2.25308e23i | 0.291501 | + | 1.15749i | ||||
\(816\) | 8.44945e22 | 0.429840 | ||||||||
\(817\) | 1.15714e23 | − | 1.15714e23i | 0.582922 | − | 0.582922i | ||||
\(818\) | 1.63588e23 | + | 1.63588e23i | 0.816064 | + | 0.816064i | ||||
\(819\) | 2.14191e21i | 0.0105811i | ||||||||
\(820\) | −1.62714e23 | + | 2.72257e23i | −0.796002 | + | 1.33189i | ||||
\(821\) | −3.99301e23 | −1.93444 | −0.967219 | − | 0.253943i | \(-0.918272\pi\) | ||||
−0.967219 | + | 0.253943i | \(0.918272\pi\) | |||||||
\(822\) | 1.40121e23 | − | 1.40121e23i | 0.672246 | − | 0.672246i | ||||
\(823\) | −2.36061e23 | − | 2.36061e23i | −1.12157 | − | 1.12157i | −0.991506 | − | 0.130063i | \(-0.958482\pi\) |
−0.130063 | − | 0.991506i | \(-0.541518\pi\) | |||||||
\(824\) | 1.28082e23i | 0.602658i | ||||||||
\(825\) | 1.08135e23 | − | 3.59766e23i | 0.503887 | − | 1.67644i | ||||
\(826\) | 5.37913e22 | 0.248240 | ||||||||
\(827\) | 2.74602e23 | − | 2.74602e23i | 1.25505 | − | 1.25505i | 0.301618 | − | 0.953429i | \(-0.402473\pi\) |
0.953429 | − | 0.301618i | \(-0.0975268\pi\) | |||||||
\(828\) | 2.62159e23 | + | 2.62159e23i | 1.18665 | + | 1.18665i | ||||
\(829\) | 3.35172e23i | 1.50256i | 0.659984 | + | 0.751280i | \(0.270563\pi\) | ||||
−0.659984 | + | 0.751280i | \(0.729437\pi\) | |||||||
\(830\) | −5.49320e22 | − | 3.28300e22i | −0.243894 | − | 0.145763i | ||||
\(831\) | −5.75482e23 | −2.53060 | ||||||||
\(832\) | 3.39900e22 | − | 3.39900e22i | 0.148035 | − | 0.148035i | ||||
\(833\) | −2.09293e22 | − | 2.09293e22i | −0.0902808 | − | 0.0902808i | ||||
\(834\) | 2.54402e23i | 1.08691i | ||||||||
\(835\) | −2.47630e23 | + | 6.23629e22i | −1.04788 | + | 0.263897i | ||||
\(836\) | −6.27039e23 | −2.62811 | ||||||||
\(837\) | −9.98392e22 | + | 9.98392e22i | −0.414474 | + | 0.414474i | ||||
\(838\) | −2.30421e22 | − | 2.30421e22i | −0.0947480 | − | 0.0947480i | ||||
\(839\) | − | 2.05076e23i | − | 0.835253i | −0.908619 | − | 0.417627i | \(-0.862862\pi\) | ||
0.908619 | − | 0.417627i | \(-0.137138\pi\) | |||||||
\(840\) | 1.94008e22 | + | 7.70362e22i | 0.0782681 | + | 0.310785i | ||||
\(841\) | 2.21602e23 | 0.885533 | ||||||||
\(842\) | 2.21821e23 | − | 2.21821e23i | 0.878022 | − | 0.878022i | ||||
\(843\) | 1.41910e23 | + | 1.41910e23i | 0.556407 | + | 0.556407i | ||||
\(844\) | − | 1.84597e23i | − | 0.716943i | ||||||
\(845\) | 1.29689e23 | − | 2.16999e23i | 0.498942 | − | 0.834842i | ||||
\(846\) | 1.40168e23 | 0.534177 | ||||||||
\(847\) | −1.36667e22 | + | 1.36667e22i | −0.0515937 | + | 0.0515937i | ||||
\(848\) | −3.50907e23 | − | 3.50907e23i | −1.31228 | − | 1.31228i | ||||
\(849\) | 1.08585e23i | 0.402260i | ||||||||
\(850\) | −5.74039e22 | + | 3.08711e22i | −0.210664 | + | 0.113292i | ||||
\(851\) | 2.59410e23 | 0.943083 | ||||||||
\(852\) | 3.06398e23 | − | 3.06398e23i | 1.10349 | − | 1.10349i | ||||
\(853\) | −2.20341e23 | − | 2.20341e23i | −0.786146 | − | 0.786146i | 0.194714 | − | 0.980860i | \(-0.437622\pi\) |
−0.980860 | + | 0.194714i | \(0.937622\pi\) | |||||||
\(854\) | 7.13420e22i | 0.252163i | ||||||||
\(855\) | −1.37343e23 | − | 8.20830e22i | −0.480926 | − | 0.287425i | ||||
\(856\) | 1.30512e24 | 4.52752 | ||||||||
\(857\) | 7.34874e22 | − | 7.34874e22i | 0.252561 | − | 0.252561i | −0.569459 | − | 0.822020i | \(-0.692847\pi\) |
0.822020 | + | 0.569459i | \(0.192847\pi\) | |||||||
\(858\) | 1.11850e23 | + | 1.11850e23i | 0.380836 | + | 0.380836i | ||||
\(859\) | − | 1.24022e23i | − | 0.418363i | −0.977877 | − | 0.209182i | \(-0.932920\pi\) | ||
0.977877 | − | 0.209182i | \(-0.0670800\pi\) | |||||||
\(860\) | −7.34260e23 | + | 1.84916e23i | −2.45393 | + | 0.617997i | ||||
\(861\) | 2.27094e22 | 0.0751934 | ||||||||
\(862\) | −2.78809e22 | + | 2.78809e22i | −0.0914637 | + | 0.0914637i | ||||
\(863\) | 3.75851e23 | + | 3.75851e23i | 1.22160 | + | 1.22160i | 0.967062 | + | 0.254539i | \(0.0819237\pi\) |
0.254539 | + | 0.967062i | \(0.418076\pi\) | |||||||
\(864\) | 2.48885e23i | 0.801474i | ||||||||
\(865\) | −9.61514e22 | − | 3.81796e23i | −0.306780 | − | 1.21816i | ||||
\(866\) | 3.79573e23 | 1.19992 | ||||||||
\(867\) | −2.89594e23 | + | 2.89594e23i | −0.907061 | + | 0.907061i | ||||
\(868\) | −7.65936e22 | − | 7.65936e22i | −0.237703 | − | 0.237703i | ||||
\(869\) | − | 5.43625e23i | − | 1.67163i | ||||||
\(870\) | 1.38056e23 | − | 2.30998e23i | 0.420630 | − | 0.703809i | ||||
\(871\) | −6.02782e22 | −0.181976 | ||||||||
\(872\) | −5.82794e23 | + | 5.82794e23i | −1.74335 | + | 1.74335i | ||||
\(873\) | −1.77275e23 | − | 1.77275e23i | −0.525452 | − | 0.525452i | ||||
\(874\) | 4.93018e23i | 1.44801i | ||||||||
\(875\) | −2.11076e22 | − | 2.31108e22i | −0.0614293 | − | 0.0672590i | ||||
\(876\) | −6.74610e23 | −1.94545 | ||||||||
\(877\) | 2.20730e21 | − | 2.20730e21i | 0.00630761 | − | 0.00630761i | −0.703946 | − | 0.710254i | \(-0.748580\pi\) |
0.710254 | + | 0.703946i | \(0.248580\pi\) | |||||||
\(878\) | −3.78589e23 | − | 3.78589e23i | −1.07204 | − | 1.07204i | ||||
\(879\) | 3.64845e23i | 1.02376i | ||||||||
\(880\) | 1.06040e24 | + | 6.33746e23i | 2.94854 | + | 1.76219i | ||||
\(881\) | −2.85602e23 | −0.786962 | −0.393481 | − | 0.919333i | \(-0.628729\pi\) | ||||
−0.393481 | + | 0.919333i | \(0.628729\pi\) | |||||||
\(882\) | −3.34687e23 | + | 3.34687e23i | −0.913882 | + | 0.913882i | ||||
\(883\) | 4.71788e23 | + | 4.71788e23i | 1.27662 | + | 1.27662i | 0.942548 | + | 0.334071i | \(0.108423\pi\) |
0.334071 | + | 0.942548i | \(0.391577\pi\) | |||||||
\(884\) | − | 1.94937e22i | − | 0.0522729i | ||||||
\(885\) | 6.98203e23 | − | 1.75835e23i | 1.85539 | − | 0.467261i | ||||
\(886\) | 5.77563e23 | 1.52100 | ||||||||
\(887\) | −6.85087e22 | + | 6.85087e22i | −0.178796 | + | 0.178796i | −0.790831 | − | 0.612035i | \(-0.790351\pi\) |
0.612035 | + | 0.790831i | \(0.290351\pi\) | |||||||
\(888\) | −9.29679e23 | − | 9.29679e23i | −2.40453 | − | 2.40453i | ||||
\(889\) | 3.75834e21i | 0.00963345i | ||||||||
\(890\) | −2.20875e23 | − | 8.77045e23i | −0.561081 | − | 2.22793i | ||||
\(891\) | −6.44698e23 | −1.62306 | ||||||||
\(892\) | −6.27407e23 | + | 6.27407e23i | −1.56542 | + | 1.56542i | ||||
\(893\) | 9.36171e22 | + | 9.36171e22i | 0.231496 | + | 0.231496i | ||||
\(894\) | 2.25922e23i | 0.553680i | ||||||||
\(895\) | −3.11270e23 | + | 5.20823e23i | −0.756053 | + | 1.26505i | ||||
\(896\) | −1.09984e22 | −0.0264769 | ||||||||
\(897\) | 6.24662e22 | − | 6.24662e22i | 0.149041 | − | 0.149041i | ||||
\(898\) | −3.53298e23 | − | 3.53298e23i | −0.835469 | − | 0.835469i | ||||
\(899\) | 2.17275e23i | 0.509252i | ||||||||
\(900\) | 3.50651e23 | + | 6.52026e23i | 0.814583 | + | 1.51469i | ||||
\(901\) | −4.05415e22 | −0.0933473 | ||||||||
\(902\) | 4.88900e23 | − | 4.88900e23i | 1.11575 | − | 1.11575i | ||||
\(903\) | 3.83349e22 | + | 3.83349e22i | 0.0867146 | + | 0.0867146i | ||||
\(904\) | − | 1.19962e24i | − | 2.68965i | ||||||
\(905\) | 1.28681e23 | + | 7.69062e22i | 0.285974 | + | 0.170912i | ||||
\(906\) | 3.84947e23 | 0.847960 | ||||||||
\(907\) | 4.67817e23 | − | 4.67817e23i | 1.02145 | − | 1.02145i | 0.0216864 | − | 0.999765i | \(-0.493096\pi\) |
0.999765 | − | 0.0216864i | \(-0.00690355\pi\) | |||||||
\(908\) | 8.88922e23 | + | 8.88922e23i | 1.92387 | + | 1.92387i | ||||
\(909\) | 1.94892e23i | 0.418103i | ||||||||
\(910\) | 1.27800e22 | − | 3.21851e21i | 0.0271769 | − | 0.00684422i | ||||
\(911\) | 3.34094e23 | 0.704242 | 0.352121 | − | 0.935954i | \(-0.385461\pi\) | ||||
0.352121 | + | 0.935954i | \(0.385461\pi\) | |||||||
\(912\) | 9.02442e23 | − | 9.02442e23i | 1.88565 | − | 1.88565i | ||||
\(913\) | 7.00659e22 | + | 7.00659e22i | 0.145124 | + | 0.145124i | ||||
\(914\) | − | 6.59341e23i | − | 1.35376i | ||||||
\(915\) | 2.33206e23 | + | 9.26010e23i | 0.474647 | + | 1.88472i | ||||
\(916\) | −1.56634e24 | −3.16025 | ||||||||
\(917\) | 2.40174e22 | − | 2.40174e22i | 0.0480364 | − | 0.0480364i | ||||
\(918\) | 3.32199e22 | + | 3.32199e22i | 0.0658653 | + | 0.0658653i | ||||
\(919\) | − | 3.79151e23i | − | 0.745226i | −0.927987 | − | 0.372613i | \(-0.878462\pi\) | ||
0.927987 | − | 0.372613i | \(-0.121538\pi\) | |||||||
\(920\) | 6.92969e23 | − | 1.15949e24i | 1.35024 | − | 2.25925i | ||||
\(921\) | 5.58815e23 | 1.07942 | ||||||||
\(922\) | −9.57363e23 | + | 9.57363e23i | −1.83328 | + | 1.83328i | ||||
\(923\) | −3.00985e22 | − | 3.00985e22i | −0.0571388 | − | 0.0571388i | ||||
\(924\) | − | 2.07731e23i | − | 0.390954i | ||||||
\(925\) | 4.96081e23 | + | 1.49107e23i | 0.925589 | + | 0.278204i | ||||
\(926\) | −3.80962e23 | −0.704683 | ||||||||
\(927\) | 6.04310e22 | − | 6.04310e22i | 0.110821 | − | 0.110821i | ||||
\(928\) | 2.70819e23 | + | 2.70819e23i | 0.492374 | + | 0.492374i | ||||
\(929\) | 8.70089e23i | 1.56833i | 0.620551 | + | 0.784166i | \(0.286909\pi\) | ||||
−0.620551 | + | 0.784166i | \(0.713091\pi\) | |||||||
\(930\) | −1.75215e24 | − | 1.04717e24i | −3.13118 | − | 1.87134i | ||||
\(931\) | −4.47071e23 | −0.792098 | ||||||||
\(932\) | −6.65106e23 | + | 6.65106e23i | −1.16833 | + | 1.16833i | ||||
\(933\) | −6.36616e23 | − | 6.36616e23i | −1.10873 | − | 1.10873i | ||||
\(934\) | 5.86346e23i | 1.01246i | ||||||||
\(935\) | 9.78651e22 | − | 2.46463e22i | 0.167546 | − | 0.0421948i | ||||
\(936\) | −1.84587e23 | −0.313325 | ||||||||
\(937\) | 3.54678e23 | − | 3.54678e23i | 0.596922 | − | 0.596922i | −0.342571 | − | 0.939492i | \(-0.611298\pi\) |
0.939492 | + | 0.342571i | \(0.111298\pi\) | |||||||
\(938\) | 7.88052e22 | + | 7.88052e22i | 0.131502 | + | 0.131502i | ||||
\(939\) | − | 1.13118e24i | − | 1.87157i | ||||||
\(940\) | −1.49604e23 | − | 5.94043e23i | −0.245425 | − | 0.974530i | ||||
\(941\) | −3.88142e23 | −0.631356 | −0.315678 | − | 0.948866i | \(-0.602232\pi\) | ||||
−0.315678 | + | 0.948866i | \(0.602232\pi\) | |||||||
\(942\) | 3.57526e23 | − | 3.57526e23i | 0.576634 | − | 0.576634i | ||||
\(943\) | −2.73042e23 | − | 2.73042e23i | −0.436652 | − | 0.436652i | ||||
\(944\) | 2.36768e24i | 3.75445i | ||||||||
\(945\) | −1.15736e22 | + | 1.93653e22i | −0.0181976 | + | 0.0304487i | ||||
\(946\) | 1.65059e24 | 2.57342 | ||||||||
\(947\) | −2.47270e23 | + | 2.47270e23i | −0.382271 | + | 0.382271i | −0.871920 | − | 0.489648i | \(-0.837125\pi\) |
0.489648 | + | 0.871920i | \(0.337125\pi\) | |||||||
\(948\) | 1.83752e24 | + | 1.83752e24i | 2.81686 | + | 2.81686i | ||||
\(949\) | 6.62693e22i | 0.100735i | ||||||||
\(950\) | −2.83383e23 | + | 9.42820e23i | −0.427155 | + | 1.42115i | ||||
\(951\) | 1.36611e23 | 0.204193 | ||||||||
\(952\) | −1.50908e22 | + | 1.50908e22i | −0.0223675 | + | 0.0223675i | ||||
\(953\) | −5.42046e23 | − | 5.42046e23i | −0.796697 | − | 0.796697i | 0.185876 | − | 0.982573i | \(-0.440488\pi\) |
−0.982573 | + | 0.185876i | \(0.940488\pi\) | |||||||
\(954\) | 6.48311e23i | 0.944923i | ||||||||
\(955\) | −9.04761e23 | − | 5.40729e23i | −1.30770 | − | 0.781543i | ||||
\(956\) | 1.87207e24 | 2.68323 | ||||||||
\(957\) | −2.94639e23 | + | 2.94639e23i | −0.418788 | + | 0.418788i | ||||
\(958\) | 1.51369e23 | + | 1.51369e23i | 0.213360 | + | 0.213360i | ||||
\(959\) | 2.55639e22i | 0.0357337i | ||||||||
\(960\) | −1.15358e24 | + | 2.90516e23i | −1.59910 | + | 0.402718i | ||||
\(961\) | 9.20637e23 | 1.26561 | ||||||||
\(962\) | −1.54230e23 | + | 1.54230e23i | −0.210266 | + | 0.210266i | ||||
\(963\) | −6.15774e23 | − | 6.15774e23i | −0.832552 | − | 0.832552i | ||||
\(964\) | − | 3.51526e24i | − | 4.71348i | ||||||
\(965\) | 2.06547e23 | + | 8.20153e23i | 0.274663 | + | 1.09063i | ||||
\(966\) | −1.63332e23 | −0.215404 | ||||||||
\(967\) | 9.52108e23 | − | 9.52108e23i | 1.24530 | − | 1.24530i | 0.287530 | − | 0.957772i | \(-0.407166\pi\) |
0.957772 | − | 0.287530i | \(-0.0928342\pi\) | |||||||
\(968\) | −1.17778e24 | − | 1.17778e24i | −1.52779 | − | 1.52779i | ||||
\(969\) | − | 1.04262e23i | − | 0.134133i | ||||||
\(970\) | −7.91357e23 | + | 1.32412e24i | −1.00971 | + | 1.68948i | ||||
\(971\) | −1.03461e24 | −1.30925 | −0.654624 | − | 0.755955i | \(-0.727173\pi\) | ||||
−0.654624 | + | 0.755955i | \(0.727173\pi\) | |||||||
\(972\) | 1.64123e24 | − | 1.64123e24i | 2.05987 | − | 2.05987i | ||||
\(973\) | −2.32068e22 | − | 2.32068e22i | −0.0288876 | − | 0.0288876i | ||||
\(974\) | − | 6.52764e23i | − | 0.805907i | ||||||
\(975\) | 1.55362e23 | − | 8.35517e22i | 0.190243 | − | 0.102310i | ||||
\(976\) | −3.14019e24 | −3.81379 | ||||||||
\(977\) | −7.39187e23 | + | 7.39187e23i | −0.890426 | + | 0.890426i | −0.994563 | − | 0.104137i | \(-0.966792\pi\) |
0.104137 | + | 0.994563i | \(0.466792\pi\) | |||||||
\(978\) | 1.71198e24 | + | 1.71198e24i | 2.04545 | + | 2.04545i | ||||
\(979\) | 1.40040e24i | 1.65955i | ||||||||
\(980\) | 1.77565e24 | + | 1.06122e24i | 2.08713 | + | 1.24737i | ||||
\(981\) | 5.49941e23 | 0.641157 | ||||||||
\(982\) | 2.03765e23 | − | 2.03765e23i | 0.235634 | − | 0.235634i | ||||
\(983\) | 3.16506e23 | + | 3.16506e23i | 0.363039 | + | 0.363039i | 0.864931 | − | 0.501892i | \(-0.167362\pi\) |
−0.501892 | + | 0.864931i | \(0.667362\pi\) | |||||||
\(984\) | 1.95707e24i | 2.22661i | ||||||||
\(985\) | −1.64680e24 | + | 4.14730e23i | −1.85845 | + | 0.468032i | ||||
\(986\) | 7.22949e22 | 0.0809268 | ||||||||
\(987\) | −3.10143e22 | + | 3.10143e22i | −0.0344370 | + | 0.0344370i | ||||
\(988\) | −2.08202e23 | − | 2.08202e23i | −0.229314 | − | 0.229314i | ||||
\(989\) | − | 9.21825e23i | − | 1.00711i | ||||||
\(990\) | −3.94126e23 | − | 1.56499e24i | −0.427124 | − | 1.69602i | ||||
\(991\) | 7.48684e23 | 0.804840 | 0.402420 | − | 0.915455i | \(-0.368169\pi\) | ||||
0.402420 | + | 0.915455i | \(0.368169\pi\) | |||||||
\(992\) | 2.05419e24 | − | 2.05419e24i | 2.19052 | − | 2.19052i | ||||
\(993\) | −6.99925e23 | − | 6.99925e23i | −0.740385 | − | 0.740385i | ||||
\(994\) | 7.86992e22i | 0.0825808i | ||||||||
\(995\) | 1.47888e23 | − | 2.47449e23i | 0.153938 | − | 0.257573i | ||||
\(996\) | −4.73662e23 | −0.489096 | ||||||||
\(997\) | 3.73374e23 | − | 3.73374e23i | 0.382457 | − | 0.382457i | −0.489529 | − | 0.871987i | \(-0.662831\pi\) |
0.871987 | + | 0.489529i | \(0.162831\pi\) | |||||||
\(998\) | −2.80527e23 | − | 2.80527e23i | −0.285057 | − | 0.285057i | ||||
\(999\) | − | 3.73373e23i | − | 0.376374i |
(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 | 5.17.c.a.3.7 | yes | 14 | |
3.2 | odd | 2 | 45.17.g.a.28.1 | 14 | |||
4.3 | odd | 2 | 80.17.p.c.33.2 | 14 | |||
5.2 | odd | 4 | inner | 5.17.c.a.2.7 | ✓ | 14 | |
5.3 | odd | 4 | 25.17.c.b.7.1 | 14 | |||
5.4 | even | 2 | 25.17.c.b.18.1 | 14 | |||
15.2 | even | 4 | 45.17.g.a.37.1 | 14 | |||
20.7 | even | 4 | 80.17.p.c.17.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.17.c.a.2.7 | ✓ | 14 | 5.2 | odd | 4 | inner | |
5.17.c.a.3.7 | yes | 14 | 1.1 | even | 1 | trivial | |
25.17.c.b.7.1 | 14 | 5.3 | odd | 4 | |||
25.17.c.b.18.1 | 14 | 5.4 | even | 2 | |||
45.17.g.a.28.1 | 14 | 3.2 | odd | 2 | |||
45.17.g.a.37.1 | 14 | 15.2 | even | 4 | |||
80.17.p.c.17.2 | 14 | 20.7 | even | 4 | |||
80.17.p.c.33.2 | 14 | 4.3 | odd | 2 |