Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.7");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (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: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 49316 x^{17} + 18276332 x^{16} - 230627572 x^{15} + 1992333560 x^{14} - 394917674060 x^{13} + 80687382741790 x^{12} + \cdots + 14\!\cdots\!04 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{34}\cdot 5^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.4 | ||
Root | \(17.5986 - 17.5986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.7 |
Dual form | 15.11.f.a.13.4 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −19.3738 | − | 19.3738i | −0.605432 | − | 0.605432i | 0.336317 | − | 0.941749i | \(-0.390819\pi\) |
−0.941749 | + | 0.336317i | \(0.890819\pi\) | |||||||
\(3\) | −99.2043 | + | 99.2043i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 273.309i | − | 0.266904i | ||||||
\(5\) | −2998.53 | + | 880.025i | −0.959530 | + | 0.281608i | ||||
\(6\) | 3843.94 | 0.494333 | ||||||||
\(7\) | 3127.99 | + | 3127.99i | 0.186113 | + | 0.186113i | 0.794013 | − | 0.607901i | \(-0.207988\pi\) |
−0.607901 | + | 0.794013i | \(0.707988\pi\) | |||||||
\(8\) | −25133.9 | + | 25133.9i | −0.767024 | + | 0.767024i | ||||
\(9\) | − | 19683.0i | − | 0.333333i | ||||||
\(10\) | 75142.5 | + | 41043.6i | 0.751425 | + | 0.410436i | ||||
\(11\) | 230381. | 1.43048 | 0.715242 | − | 0.698877i | \(-0.246316\pi\) | ||||
0.715242 | + | 0.698877i | \(0.246316\pi\) | |||||||
\(12\) | 27113.5 | + | 27113.5i | 0.108963 | + | 0.108963i | ||||
\(13\) | 287704. | − | 287704.i | 0.774871 | − | 0.774871i | −0.204083 | − | 0.978954i | \(-0.565421\pi\) |
0.978954 | + | 0.204083i | \(0.0654212\pi\) | |||||||
\(14\) | − | 121202.i | − | 0.225357i | ||||||
\(15\) | 210165. | − | 384769.i | 0.276760 | − | 0.506692i | ||||
\(16\) | 694009. | 0.661859 | ||||||||
\(17\) | 1.39122e6 | + | 1.39122e6i | 0.979832 | + | 0.979832i | 0.999801 | − | 0.0199685i | \(-0.00635660\pi\) |
−0.0199685 | + | 0.999801i | \(0.506357\pi\) | |||||||
\(18\) | −381335. | + | 381335.i | −0.201811 | + | 0.201811i | ||||
\(19\) | 323424.i | 0.130618i | 0.997865 | + | 0.0653092i | \(0.0208034\pi\) | ||||
−0.997865 | + | 0.0653092i | \(0.979197\pi\) | |||||||
\(20\) | 240519. | + | 819526.i | 0.0751622 | + | 0.256102i | ||||
\(21\) | −620621. | −0.151960 | ||||||||
\(22\) | −4.46336e6 | − | 4.46336e6i | −0.866061 | − | 0.866061i | ||||
\(23\) | −7.28021e6 | + | 7.28021e6i | −1.13111 | + | 1.13111i | −0.141116 | + | 0.989993i | \(0.545069\pi\) |
−0.989993 | + | 0.141116i | \(0.954931\pi\) | |||||||
\(24\) | − | 4.98677e6i | − | 0.626273i | ||||||
\(25\) | 8.21674e6 | − | 5.27756e6i | 0.841394 | − | 0.540422i | ||||
\(26\) | −1.11479e7 | −0.938264 | ||||||||
\(27\) | 1.95264e6 | + | 1.95264e6i | 0.136083 | + | 0.136083i | ||||
\(28\) | 854910. | − | 854910.i | 0.0496741 | − | 0.0496741i | ||||
\(29\) | − | 5.58509e6i | − | 0.272295i | −0.990689 | − | 0.136148i | \(-0.956528\pi\) | ||
0.990689 | − | 0.136148i | \(-0.0434721\pi\) | |||||||
\(30\) | −1.15262e7 | + | 3.38276e6i | −0.474327 | + | 0.139208i | ||||
\(31\) | −3.90283e6 | −0.136324 | −0.0681618 | − | 0.997674i | \(-0.521713\pi\) | ||||
−0.0681618 | + | 0.997674i | \(0.521713\pi\) | |||||||
\(32\) | 1.22914e7 | + | 1.22914e7i | 0.366314 | + | 0.366314i | ||||
\(33\) | −2.28548e7 | + | 2.28548e7i | −0.583993 | + | 0.583993i | ||||
\(34\) | − | 5.39066e7i | − | 1.18644i | ||||||
\(35\) | −1.21321e7 | − | 6.62667e6i | −0.230991 | − | 0.126170i | ||||
\(36\) | −5.37955e6 | −0.0889679 | ||||||||
\(37\) | 8.90358e7 | + | 8.90358e7i | 1.28397 | + | 1.28397i | 0.938387 | + | 0.345586i | \(0.112320\pi\) |
0.345586 | + | 0.938387i | \(0.387680\pi\) | |||||||
\(38\) | 6.26596e6 | − | 6.26596e6i | 0.0790806 | − | 0.0790806i | ||||
\(39\) | 5.70830e7i | 0.632679i | ||||||||
\(40\) | 5.32462e7 | − | 9.74830e7i | 0.519982 | − | 0.951983i | ||||
\(41\) | −3.06972e7 | −0.264960 | −0.132480 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132480 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(42\) | 1.20238e7 | + | 1.20238e7i | 0.0920016 | + | 0.0920016i | ||||
\(43\) | 5.99364e7 | − | 5.99364e7i | 0.407707 | − | 0.407707i | −0.473231 | − | 0.880938i | \(-0.656913\pi\) |
0.880938 | + | 0.473231i | \(0.156913\pi\) | |||||||
\(44\) | − | 6.29653e7i | − | 0.381802i | ||||||
\(45\) | 1.73215e7 | + | 5.90201e7i | 0.0938693 | + | 0.319843i | ||||
\(46\) | 2.82091e8 | 1.36962 | ||||||||
\(47\) | 1.25579e8 | + | 1.25579e8i | 0.547555 | + | 0.547555i | 0.925733 | − | 0.378178i | \(-0.123449\pi\) |
−0.378178 | + | 0.925733i | \(0.623449\pi\) | |||||||
\(48\) | −6.88487e7 | + | 6.88487e7i | −0.270203 | + | 0.270203i | ||||
\(49\) | − | 2.62907e8i | − | 0.930724i | ||||||
\(50\) | −2.61436e8 | − | 5.69431e7i | −0.836596 | − | 0.182218i | ||||
\(51\) | −2.76030e8 | −0.800030 | ||||||||
\(52\) | −7.86322e7 | − | 7.86322e7i | −0.206816 | − | 0.206816i | ||||
\(53\) | −2.38773e8 | + | 2.38773e8i | −0.570960 | + | 0.570960i | −0.932397 | − | 0.361437i | \(-0.882286\pi\) |
0.361437 | + | 0.932397i | \(0.382286\pi\) | |||||||
\(54\) | − | 7.56602e7i | − | 0.164778i | ||||||
\(55\) | −6.90804e8 | + | 2.02741e8i | −1.37259 | + | 0.402836i | ||||
\(56\) | −1.57237e8 | −0.285506 | ||||||||
\(57\) | −3.20851e7 | − | 3.20851e7i | −0.0533247 | − | 0.0533247i | ||||
\(58\) | −1.08205e8 | + | 1.08205e8i | −0.164856 | + | 0.164856i | ||||
\(59\) | 1.52981e8i | 0.213982i | 0.994260 | + | 0.106991i | \(0.0341215\pi\) | ||||
−0.994260 | + | 0.106991i | \(0.965878\pi\) | |||||||
\(60\) | −1.05161e8 | − | 5.74400e7i | −0.135238 | − | 0.0738684i | ||||
\(61\) | 9.12337e8 | 1.08021 | 0.540103 | − | 0.841599i | \(-0.318385\pi\) | ||||
0.540103 | + | 0.841599i | \(0.318385\pi\) | |||||||
\(62\) | 7.56127e7 | + | 7.56127e7i | 0.0825347 | + | 0.0825347i | ||||
\(63\) | 6.15683e7 | − | 6.15683e7i | 0.0620375 | − | 0.0620375i | ||||
\(64\) | − | 1.18693e9i | − | 1.10541i | ||||||
\(65\) | −6.09503e8 | + | 1.11588e9i | −0.525302 | + | 0.961721i | ||||
\(66\) | 8.85570e8 | 0.707136 | ||||||||
\(67\) | 1.02130e8 | + | 1.02130e8i | 0.0756445 | + | 0.0756445i | 0.743917 | − | 0.668272i | \(-0.232966\pi\) |
−0.668272 | + | 0.743917i | \(0.732966\pi\) | |||||||
\(68\) | 3.80234e8 | − | 3.80234e8i | 0.261521 | − | 0.261521i | ||||
\(69\) | − | 1.44446e9i | − | 0.923547i | ||||||
\(70\) | 1.06661e8 | + | 3.63429e8i | 0.0634623 | + | 0.216237i | ||||
\(71\) | 3.21746e9 | 1.78329 | 0.891643 | − | 0.452740i | \(-0.149553\pi\) | ||||
0.891643 | + | 0.452740i | \(0.149553\pi\) | |||||||
\(72\) | 4.94710e8 | + | 4.94710e8i | 0.255675 | + | 0.255675i | ||||
\(73\) | −1.64457e9 | + | 1.64457e9i | −0.793299 | + | 0.793299i | −0.982029 | − | 0.188730i | \(-0.939563\pi\) |
0.188730 | + | 0.982029i | \(0.439563\pi\) | |||||||
\(74\) | − | 3.44993e9i | − | 1.55472i | ||||||
\(75\) | −2.91579e8 | + | 1.33869e9i | −0.122871 | + | 0.564124i | ||||
\(76\) | 8.83948e7 | 0.0348625 | ||||||||
\(77\) | 7.20630e8 | + | 7.20630e8i | 0.266231 | + | 0.266231i | ||||
\(78\) | 1.10592e9 | − | 1.10592e9i | 0.383045 | − | 0.383045i | ||||
\(79\) | 4.86313e9i | 1.58045i | 0.612817 | + | 0.790225i | \(0.290036\pi\) | ||||
−0.612817 | + | 0.790225i | \(0.709964\pi\) | |||||||
\(80\) | −2.08101e9 | + | 6.10745e8i | −0.635073 | + | 0.186385i | ||||
\(81\) | −3.87420e8 | −0.111111 | ||||||||
\(82\) | 5.94723e8 | + | 5.94723e8i | 0.160415 | + | 0.160415i | ||||
\(83\) | 2.32096e9 | − | 2.32096e9i | 0.589220 | − | 0.589220i | −0.348200 | − | 0.937420i | \(-0.613207\pi\) |
0.937420 | + | 0.348200i | \(0.113207\pi\) | |||||||
\(84\) | 1.69622e8i | 0.0405588i | ||||||||
\(85\) | −5.39593e9 | − | 2.94731e9i | −1.21611 | − | 0.664249i | ||||
\(86\) | −2.32239e9 | −0.493678 | ||||||||
\(87\) | 5.54065e8 | + | 5.54065e8i | 0.111164 | + | 0.111164i | ||||
\(88\) | −5.79036e9 | + | 5.79036e9i | −1.09722 | + | 1.09722i | ||||
\(89\) | − | 7.27765e9i | − | 1.30329i | −0.758524 | − | 0.651646i | \(-0.774079\pi\) | ||
0.758524 | − | 0.651646i | \(-0.225921\pi\) | |||||||
\(90\) | 8.07860e8 | − | 1.47903e9i | 0.136812 | − | 0.250475i | ||||
\(91\) | 1.79987e9 | 0.288426 | ||||||||
\(92\) | 1.98975e9 | + | 1.98975e9i | 0.301897 | + | 0.301897i | ||||
\(93\) | 3.87177e8 | − | 3.87177e8i | 0.0556538 | − | 0.0556538i | ||||
\(94\) | − | 4.86589e9i | − | 0.663015i | ||||||
\(95\) | −2.84621e8 | − | 9.69797e8i | −0.0367832 | − | 0.125332i | ||||
\(96\) | −2.43873e9 | −0.299094 | ||||||||
\(97\) | 9.72979e8 | + | 9.72979e8i | 0.113304 | + | 0.113304i | 0.761486 | − | 0.648182i | \(-0.224470\pi\) |
−0.648182 | + | 0.761486i | \(0.724470\pi\) | |||||||
\(98\) | −5.09351e9 | + | 5.09351e9i | −0.563490 | + | 0.563490i | ||||
\(99\) | − | 4.53459e9i | − | 0.476828i | ||||||
\(100\) | −1.44241e9 | − | 2.24571e9i | −0.144241 | − | 0.224571i | ||||
\(101\) | −5.83910e9 | −0.555571 | −0.277785 | − | 0.960643i | \(-0.589600\pi\) | ||||
−0.277785 | + | 0.960643i | \(0.589600\pi\) | |||||||
\(102\) | 5.34777e9 | + | 5.34777e9i | 0.484364 | + | 0.484364i | ||||
\(103\) | 2.62735e9 | − | 2.62735e9i | 0.226637 | − | 0.226637i | −0.584649 | − | 0.811286i | \(-0.698768\pi\) |
0.811286 | + | 0.584649i | \(0.198768\pi\) | |||||||
\(104\) | 1.44622e10i | 1.18869i | ||||||||
\(105\) | 1.86095e9 | − | 5.46162e8i | 0.145810 | − | 0.0427932i | ||||
\(106\) | 9.25188e9 | 0.691355 | ||||||||
\(107\) | 9.66716e8 | + | 9.66716e8i | 0.0689255 | + | 0.0689255i | 0.740729 | − | 0.671804i | \(-0.234480\pi\) |
−0.671804 | + | 0.740729i | \(0.734480\pi\) | |||||||
\(108\) | 5.33674e8 | − | 5.33674e8i | 0.0363210 | − | 0.0363210i | ||||
\(109\) | 1.71835e9i | 0.111681i | 0.998440 | + | 0.0558403i | \(0.0177838\pi\) | ||||
−0.998440 | + | 0.0558403i | \(0.982216\pi\) | |||||||
\(110\) | 1.73114e10 | + | 9.45566e9i | 1.07490 | + | 0.587122i | ||||
\(111\) | −1.76655e10 | −1.04836 | ||||||||
\(112\) | 2.17086e9 | + | 2.17086e9i | 0.123180 | + | 0.123180i | ||||
\(113\) | 1.05676e10 | − | 1.05676e10i | 0.573566 | − | 0.573566i | −0.359557 | − | 0.933123i | \(-0.617072\pi\) |
0.933123 | + | 0.359557i | \(0.117072\pi\) | |||||||
\(114\) | 1.24322e9i | 0.0645690i | ||||||||
\(115\) | 1.54232e10 | − | 2.82367e10i | 0.766804 | − | 1.40386i | ||||
\(116\) | −1.52646e9 | −0.0726766 | ||||||||
\(117\) | −5.66288e9 | − | 5.66288e9i | −0.258290 | − | 0.258290i | ||||
\(118\) | 2.96382e9 | − | 2.96382e9i | 0.129551 | − | 0.129551i | ||||
\(119\) | 8.70346e9i | 0.364718i | ||||||||
\(120\) | 4.38848e9 | + | 1.49530e10i | 0.176363 | + | 0.600927i | ||||
\(121\) | 2.71380e10 | 1.04629 | ||||||||
\(122\) | −1.76755e10 | − | 1.76755e10i | −0.653991 | − | 0.653991i | ||||
\(123\) | 3.04530e9 | − | 3.04530e9i | 0.108169 | − | 0.108169i | ||||
\(124\) | 1.06668e9i | 0.0363852i | ||||||||
\(125\) | −1.99938e10 | + | 2.30559e10i | −0.655155 | + | 0.755494i | ||||
\(126\) | −2.38563e9 | −0.0751190 | ||||||||
\(127\) | −1.38358e10 | − | 1.38358e10i | −0.418779 | − | 0.418779i | 0.466003 | − | 0.884783i | \(-0.345693\pi\) |
−0.884783 | + | 0.466003i | \(0.845693\pi\) | |||||||
\(128\) | −1.04089e10 | + | 1.04089e10i | −0.302940 | + | 0.302940i | ||||
\(129\) | 1.18919e10i | 0.332891i | ||||||||
\(130\) | 3.34272e10 | − | 9.81039e9i | 0.900292 | − | 0.264222i | ||||
\(131\) | −2.03264e10 | −0.526871 | −0.263436 | − | 0.964677i | \(-0.584856\pi\) | ||||
−0.263436 | + | 0.964677i | \(0.584856\pi\) | |||||||
\(132\) | 6.24643e9 | + | 6.24643e9i | 0.155870 | + | 0.155870i | ||||
\(133\) | −1.01167e9 | + | 1.01167e9i | −0.0243097 | + | 0.0243097i | ||||
\(134\) | − | 3.95728e9i | − | 0.0915952i | ||||||
\(135\) | −7.57342e9 | − | 4.13668e9i | −0.168897 | − | 0.0922535i | ||||
\(136\) | −6.99335e10 | −1.50311 | ||||||||
\(137\) | −5.02310e10 | − | 5.02310e10i | −1.04080 | − | 1.04080i | −0.999131 | − | 0.0416734i | \(-0.986731\pi\) |
−0.0416734 | − | 0.999131i | \(-0.513269\pi\) | |||||||
\(138\) | −2.79847e10 | + | 2.79847e10i | −0.559145 | + | 0.559145i | ||||
\(139\) | 9.64298e10i | 1.85839i | 0.369589 | + | 0.929195i | \(0.379499\pi\) | ||||
−0.369589 | + | 0.929195i | \(0.620501\pi\) | |||||||
\(140\) | −1.81113e9 | + | 3.31582e9i | −0.0336752 | + | 0.0616524i | ||||
\(141\) | −2.49160e10 | −0.447077 | ||||||||
\(142\) | −6.23344e10 | − | 6.23344e10i | −1.07966 | − | 1.07966i | ||||
\(143\) | 6.62816e10 | − | 6.62816e10i | 1.10844 | − | 1.10844i | ||||
\(144\) | − | 1.36602e10i | − | 0.220620i | ||||||
\(145\) | 4.91501e9 | + | 1.67470e10i | 0.0766805 | + | 0.261275i | ||||
\(146\) | 6.37231e10 | 0.960578 | ||||||||
\(147\) | 2.60815e10 | + | 2.60815e10i | 0.379967 | + | 0.379967i | ||||
\(148\) | 2.43343e10 | − | 2.43343e10i | 0.342697 | − | 0.342697i | ||||
\(149\) | 1.12032e11i | 1.52550i | 0.646694 | + | 0.762750i | \(0.276151\pi\) | ||||
−0.646694 | + | 0.762750i | \(0.723849\pi\) | |||||||
\(150\) | 3.15846e10 | − | 2.02866e10i | 0.415929 | − | 0.267149i | ||||
\(151\) | 6.20370e10 | 0.790253 | 0.395127 | − | 0.918627i | \(-0.370701\pi\) | ||||
0.395127 | + | 0.918627i | \(0.370701\pi\) | |||||||
\(152\) | −8.12889e9 | − | 8.12889e9i | −0.100188 | − | 0.100188i | ||||
\(153\) | 2.73834e10 | − | 2.73834e10i | 0.326611 | − | 0.326611i | ||||
\(154\) | − | 2.79227e10i | − | 0.322370i | ||||||
\(155\) | 1.17027e10 | − | 3.43458e9i | 0.130806 | − | 0.0383898i | ||||
\(156\) | 1.56013e10 | 0.168864 | ||||||||
\(157\) | 1.11725e11 | + | 1.11725e11i | 1.17125 | + | 1.17125i | 0.981911 | + | 0.189344i | \(0.0606360\pi\) |
0.189344 | + | 0.981911i | \(0.439364\pi\) | |||||||
\(158\) | 9.42176e10 | − | 9.42176e10i | 0.956856 | − | 0.956856i | ||||
\(159\) | − | 4.73746e10i | − | 0.466187i | ||||||
\(160\) | −4.76730e10 | − | 2.60395e10i | −0.454646 | − | 0.248332i | ||||
\(161\) | −4.55449e10 | −0.421027 | ||||||||
\(162\) | 7.50582e9 | + | 7.50582e9i | 0.0672702 | + | 0.0672702i | ||||
\(163\) | −7.98259e10 | + | 7.98259e10i | −0.693754 | + | 0.693754i | −0.963056 | − | 0.269302i | \(-0.913207\pi\) |
0.269302 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(164\) | 8.38984e9i | 0.0707188i | ||||||||
\(165\) | 4.84180e10 | − | 8.86435e10i | 0.395901 | − | 0.724815i | ||||
\(166\) | −8.99318e10 | −0.713465 | ||||||||
\(167\) | −1.41288e10 | − | 1.41288e10i | −0.108773 | − | 0.108773i | 0.650626 | − | 0.759399i | \(-0.274507\pi\) |
−0.759399 | + | 0.650626i | \(0.774507\pi\) | |||||||
\(168\) | 1.55986e10 | − | 1.55986e10i | 0.116557 | − | 0.116557i | ||||
\(169\) | − | 2.76888e10i | − | 0.200850i | ||||||
\(170\) | 4.74391e10 | + | 1.61640e11i | 0.334112 | + | 1.13843i | ||||
\(171\) | 6.36596e9 | 0.0435395 | ||||||||
\(172\) | −1.63812e10 | − | 1.63812e10i | −0.108818 | − | 0.108818i | ||||
\(173\) | −1.21959e11 | + | 1.21959e11i | −0.787018 | + | 0.787018i | −0.981004 | − | 0.193986i | \(-0.937858\pi\) |
0.193986 | + | 0.981004i | \(0.437858\pi\) | |||||||
\(174\) | − | 2.14687e10i | − | 0.134605i | ||||||
\(175\) | 4.22101e10 | + | 9.19373e9i | 0.257173 | + | 0.0560146i | ||||
\(176\) | 1.59887e11 | 0.946779 | ||||||||
\(177\) | −1.51763e10 | − | 1.51763e10i | −0.0873576 | − | 0.0873576i | ||||
\(178\) | −1.40996e11 | + | 1.40996e11i | −0.789054 | + | 0.789054i | ||||
\(179\) | − | 9.05533e10i | − | 0.492764i | −0.969173 | − | 0.246382i | \(-0.920758\pi\) | ||
0.969173 | − | 0.246382i | \(-0.0792418\pi\) | |||||||
\(180\) | 1.61307e10 | − | 4.73413e9i | 0.0853673 | − | 0.0250541i | ||||
\(181\) | −3.62000e11 | −1.86344 | −0.931722 | − | 0.363174i | \(-0.881693\pi\) | ||||
−0.931722 | + | 0.363174i | \(0.881693\pi\) | |||||||
\(182\) | −3.48704e10 | − | 3.48704e10i | −0.174623 | − | 0.174623i | ||||
\(183\) | −9.05078e10 | + | 9.05078e10i | −0.440992 | + | 0.440992i | ||||
\(184\) | − | 3.65959e11i | − | 1.73518i | ||||||
\(185\) | −3.45330e11 | − | 1.88623e11i | −1.59359 | − | 0.870433i | ||||
\(186\) | −1.50022e10 | −0.0673893 | ||||||||
\(187\) | 3.20511e11 | + | 3.20511e11i | 1.40163 | + | 1.40163i | ||||
\(188\) | 3.43219e10 | − | 3.43219e10i | 0.146144 | − | 0.146144i | ||||
\(189\) | 1.22157e10i | 0.0506534i | ||||||||
\(190\) | −1.32745e10 | + | 2.43029e10i | −0.0536105 | + | 0.0981499i | ||||
\(191\) | 4.77485e11 | 1.87842 | 0.939210 | − | 0.343344i | \(-0.111560\pi\) | ||||
0.939210 | + | 0.343344i | \(0.111560\pi\) | |||||||
\(192\) | 1.17749e11 | + | 1.17749e11i | 0.451284 | + | 0.451284i | ||||
\(193\) | 2.48930e10 | − | 2.48930e10i | 0.0929587 | − | 0.0929587i | −0.659098 | − | 0.752057i | \(-0.729062\pi\) |
0.752057 | + | 0.659098i | \(0.229062\pi\) | |||||||
\(194\) | − | 3.77007e10i | − | 0.137196i | ||||||
\(195\) | −5.02344e10 | − | 1.71165e11i | −0.178168 | − | 0.607075i | ||||
\(196\) | −7.18548e10 | −0.248414 | ||||||||
\(197\) | −3.26049e11 | − | 3.26049e11i | −1.09888 | − | 1.09888i | −0.994541 | − | 0.104342i | \(-0.966726\pi\) |
−0.104342 | − | 0.994541i | \(-0.533274\pi\) | |||||||
\(198\) | −8.78523e10 | + | 8.78523e10i | −0.288687 | + | 0.288687i | ||||
\(199\) | − | 1.34833e11i | − | 0.432047i | −0.976388 | − | 0.216024i | \(-0.930691\pi\) | ||
0.976388 | − | 0.216024i | \(-0.0693088\pi\) | |||||||
\(200\) | −7.38729e10 | + | 3.39164e11i | −0.230853 | + | 1.05989i | ||||
\(201\) | −2.02634e10 | −0.0617635 | ||||||||
\(202\) | 1.13126e11 | + | 1.13126e11i | 0.336360 | + | 0.336360i | ||||
\(203\) | 1.74701e10 | − | 1.74701e10i | 0.0506776 | − | 0.0506776i | ||||
\(204\) | 7.54417e10i | 0.213531i | ||||||||
\(205\) | 9.20466e10 | − | 2.70143e10i | 0.254237 | − | 0.0746148i | ||||
\(206\) | −1.01803e11 | −0.274427 | ||||||||
\(207\) | 1.43296e11 | + | 1.43296e11i | 0.377036 | + | 0.377036i | ||||
\(208\) | 1.99669e11 | − | 1.99669e11i | 0.512855 | − | 0.512855i | ||||
\(209\) | 7.45108e10i | 0.186848i | ||||||||
\(210\) | −4.66350e10 | − | 2.54725e10i | −0.114187 | − | 0.0623699i | ||||
\(211\) | 6.66286e11 | 1.59312 | 0.796560 | − | 0.604560i | \(-0.206651\pi\) | ||||
0.796560 | + | 0.604560i | \(0.206651\pi\) | |||||||
\(212\) | 6.52588e10 | + | 6.52588e10i | 0.152391 | + | 0.152391i | ||||
\(213\) | −3.19186e11 | + | 3.19186e11i | −0.728023 | + | 0.728023i | ||||
\(214\) | − | 3.74580e10i | − | 0.0834595i | ||||||
\(215\) | −1.26975e11 | + | 2.32466e11i | −0.276393 | + | 0.506020i | ||||
\(216\) | −9.81547e10 | −0.208758 | ||||||||
\(217\) | −1.22080e10 | − | 1.22080e10i | −0.0253715 | − | 0.0253715i | ||||
\(218\) | 3.32909e10 | − | 3.32909e10i | 0.0676151 | − | 0.0676151i | ||||
\(219\) | − | 3.26296e11i | − | 0.647726i | ||||||
\(220\) | 5.54110e10 | + | 1.88803e11i | 0.107518 | + | 0.366350i | ||||
\(221\) | 8.00520e11 | 1.51849 | ||||||||
\(222\) | 3.42248e11 | + | 3.42248e11i | 0.634711 | + | 0.634711i | ||||
\(223\) | 4.60329e11 | − | 4.60329e11i | 0.834726 | − | 0.834726i | −0.153433 | − | 0.988159i | \(-0.549033\pi\) |
0.988159 | + | 0.153433i | \(0.0490328\pi\) | |||||||
\(224\) | 7.68951e10i | 0.136351i | ||||||||
\(225\) | −1.03878e11 | − | 1.61730e11i | −0.180141 | − | 0.280465i | ||||
\(226\) | −4.09469e11 | −0.694510 | ||||||||
\(227\) | −2.28848e11 | − | 2.28848e11i | −0.379680 | − | 0.379680i | 0.491307 | − | 0.870986i | \(-0.336519\pi\) |
−0.870986 | + | 0.491307i | \(0.836519\pi\) | |||||||
\(228\) | −8.76915e9 | + | 8.76915e9i | −0.0142326 | + | 0.0142326i | ||||
\(229\) | − | 5.54642e11i | − | 0.880716i | −0.897822 | − | 0.440358i | \(-0.854852\pi\) | ||
0.897822 | − | 0.440358i | \(-0.145148\pi\) | |||||||
\(230\) | −8.45858e11 | + | 2.48247e11i | −1.31419 | + | 0.385696i | ||||
\(231\) | −1.42979e11 | −0.217377 | ||||||||
\(232\) | 1.40375e11 | + | 1.40375e11i | 0.208857 | + | 0.208857i | ||||
\(233\) | 1.45797e11 | − | 1.45797e11i | 0.212309 | − | 0.212309i | −0.592939 | − | 0.805248i | \(-0.702032\pi\) |
0.805248 | + | 0.592939i | \(0.202032\pi\) | |||||||
\(234\) | 2.19423e11i | 0.312755i | ||||||||
\(235\) | −4.87065e11 | − | 2.66040e11i | −0.679591 | − | 0.371199i | ||||
\(236\) | 4.18110e10 | 0.0571125 | ||||||||
\(237\) | −4.82444e11 | − | 4.82444e11i | −0.645216 | − | 0.645216i | ||||
\(238\) | 1.68619e11 | − | 1.68619e11i | 0.220812 | − | 0.220812i | ||||
\(239\) | 9.95227e11i | 1.27624i | 0.769937 | + | 0.638120i | \(0.220288\pi\) | ||||
−0.769937 | + | 0.638120i | \(0.779712\pi\) | |||||||
\(240\) | 1.45856e11 | − | 2.67034e11i | 0.183176 | − | 0.335359i | ||||
\(241\) | −5.91275e11 | −0.727285 | −0.363642 | − | 0.931539i | \(-0.618467\pi\) | ||||
−0.363642 | + | 0.931539i | \(0.618467\pi\) | |||||||
\(242\) | −5.25766e11 | − | 5.25766e11i | −0.633455 | − | 0.633455i | ||||
\(243\) | 3.84338e10 | − | 3.84338e10i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 2.49350e11i | − | 0.288311i | ||||||
\(245\) | 2.31364e11 | + | 7.88333e11i | 0.262099 | + | 0.893057i | ||||
\(246\) | −1.17998e11 | −0.130978 | ||||||||
\(247\) | 9.30505e10 | + | 9.30505e10i | 0.101212 | + | 0.101212i | ||||
\(248\) | 9.80931e10 | − | 9.80931e10i | 0.104563 | − | 0.104563i | ||||
\(249\) | 4.60499e11i | 0.481096i | ||||||||
\(250\) | 8.34036e11 | − | 5.93247e10i | 0.854053 | − | 0.0607485i | ||||
\(251\) | −2.15028e11 | −0.215837 | −0.107919 | − | 0.994160i | \(-0.534419\pi\) | ||||
−0.107919 | + | 0.994160i | \(0.534419\pi\) | |||||||
\(252\) | −1.68272e10 | − | 1.68272e10i | −0.0165580 | − | 0.0165580i | ||||
\(253\) | −1.67722e12 | + | 1.67722e12i | −1.61803 | + | 1.61803i | ||||
\(254\) | 5.36104e11i | 0.507085i | ||||||||
\(255\) | 8.27685e11 | − | 2.42914e11i | 0.767652 | − | 0.225295i | ||||
\(256\) | −8.12094e11 | −0.738595 | ||||||||
\(257\) | −1.29066e12 | − | 1.29066e12i | −1.15119 | − | 1.15119i | −0.986314 | − | 0.164875i | \(-0.947278\pi\) |
−0.164875 | − | 0.986314i | \(-0.552722\pi\) | |||||||
\(258\) | 2.30392e11 | − | 2.30392e11i | 0.201543 | − | 0.201543i | ||||
\(259\) | 5.57007e11i | 0.477927i | ||||||||
\(260\) | 3.04979e11 | + | 1.66583e11i | 0.256687 | + | 0.140205i | ||||
\(261\) | −1.09931e11 | −0.0907651 | ||||||||
\(262\) | 3.93801e11 | + | 3.93801e11i | 0.318985 | + | 0.318985i | ||||
\(263\) | 8.67165e11 | − | 8.67165e11i | 0.689164 | − | 0.689164i | −0.272883 | − | 0.962047i | \(-0.587977\pi\) |
0.962047 | + | 0.272883i | \(0.0879772\pi\) | |||||||
\(264\) | − | 1.14886e12i | − | 0.895873i | ||||||
\(265\) | 5.05841e11 | − | 9.26093e11i | 0.387066 | − | 0.708639i | ||||
\(266\) | 3.91998e10 | 0.0294358 | ||||||||
\(267\) | 7.21975e11 | + | 7.21975e11i | 0.532066 | + | 0.532066i | ||||
\(268\) | 2.79130e10 | − | 2.79130e10i | 0.0201898 | − | 0.0201898i | ||||
\(269\) | − | 6.98198e11i | − | 0.495698i | −0.968799 | − | 0.247849i | \(-0.920276\pi\) | ||
0.968799 | − | 0.247849i | \(-0.0797237\pi\) | |||||||
\(270\) | 6.65828e10 | + | 2.26869e11i | 0.0464027 | + | 0.158109i | ||||
\(271\) | 1.42090e12 | 0.972116 | 0.486058 | − | 0.873927i | \(-0.338434\pi\) | ||||
0.486058 | + | 0.873927i | \(0.338434\pi\) | |||||||
\(272\) | 9.65521e11 | + | 9.65521e11i | 0.648510 | + | 0.648510i | ||||
\(273\) | −1.78555e11 | + | 1.78555e11i | −0.117750 | + | 0.117750i | ||||
\(274\) | 1.94634e12i | 1.26027i | ||||||||
\(275\) | 1.89298e12 | − | 1.21585e12i | 1.20360 | − | 0.773066i | ||||
\(276\) | −3.94783e11 | −0.246498 | ||||||||
\(277\) | −8.78959e11 | − | 8.78959e11i | −0.538976 | − | 0.538976i | 0.384252 | − | 0.923228i | \(-0.374459\pi\) |
−0.923228 | + | 0.384252i | \(0.874459\pi\) | |||||||
\(278\) | 1.86821e12 | − | 1.86821e12i | 1.12513 | − | 1.12513i | ||||
\(279\) | 7.68193e10i | 0.0454412i | ||||||||
\(280\) | 4.71480e11 | − | 1.38373e11i | 0.273951 | − | 0.0804007i | ||||
\(281\) | 1.50905e12 | 0.861335 | 0.430668 | − | 0.902511i | \(-0.358278\pi\) | ||||
0.430668 | + | 0.902511i | \(0.358278\pi\) | |||||||
\(282\) | 4.82717e11 | + | 4.82717e11i | 0.270675 | + | 0.270675i | ||||
\(283\) | −1.51591e12 | + | 1.51591e12i | −0.835104 | + | 0.835104i | −0.988210 | − | 0.153106i | \(-0.951073\pi\) |
0.153106 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(284\) | − | 8.79361e11i | − | 0.475965i | ||||||
\(285\) | 1.24444e11 | + | 6.79724e10i | 0.0661833 | + | 0.0361500i | ||||
\(286\) | −2.56826e12 | −1.34217 | ||||||||
\(287\) | −9.60208e10 | − | 9.60208e10i | −0.0493124 | − | 0.0493124i | ||||
\(288\) | 2.41933e11 | − | 2.41933e11i | 0.122105 | − | 0.122105i | ||||
\(289\) | 1.85500e12i | 0.920142i | ||||||||
\(290\) | 2.29232e11 | − | 4.19677e11i | 0.111760 | − | 0.204609i | ||||
\(291\) | −1.93048e11 | −0.0925123 | ||||||||
\(292\) | 4.49475e11 | + | 4.49475e11i | 0.211734 | + | 0.211734i | ||||
\(293\) | −1.62088e12 | + | 1.62088e12i | −0.750606 | + | 0.750606i | −0.974592 | − | 0.223986i | \(-0.928093\pi\) |
0.223986 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(294\) | − | 1.01060e12i | − | 0.460088i | ||||||
\(295\) | −1.34627e11 | − | 4.58717e11i | −0.0602589 | − | 0.205322i | ||||
\(296\) | −4.47562e12 | −1.96968 | ||||||||
\(297\) | 4.49851e11 | + | 4.49851e11i | 0.194664 | + | 0.194664i | ||||
\(298\) | 2.17050e12 | − | 2.17050e12i | 0.923587 | − | 0.923587i | ||||
\(299\) | 4.18909e12i | 1.75293i | ||||||||
\(300\) | 3.65877e11 | + | 7.96913e10i | 0.150567 | + | 0.0327948i | ||||
\(301\) | 3.74961e11 | 0.151759 | ||||||||
\(302\) | −1.20189e12 | − | 1.20189e12i | −0.478445 | − | 0.478445i | ||||
\(303\) | 5.79264e11 | − | 5.79264e11i | 0.226811 | − | 0.226811i | ||||
\(304\) | 2.24459e11i | 0.0864510i | ||||||||
\(305\) | −2.73567e12 | + | 8.02879e11i | −1.03649 | + | 0.304194i | ||||
\(306\) | −1.06104e12 | −0.395481 | ||||||||
\(307\) | −2.69296e12 | − | 2.69296e12i | −0.987503 | − | 0.987503i | 0.0124200 | − | 0.999923i | \(-0.496046\pi\) |
−0.999923 | + | 0.0124200i | \(0.996046\pi\) | |||||||
\(308\) | 1.96955e11 | − | 1.96955e11i | 0.0710581 | − | 0.0710581i | ||||
\(309\) | 5.21288e11i | 0.185048i | ||||||||
\(310\) | −2.93268e11 | − | 1.60186e11i | −0.102437 | − | 0.0559520i | ||||
\(311\) | −3.25599e11 | −0.111913 | −0.0559566 | − | 0.998433i | \(-0.517821\pi\) | ||||
−0.0559566 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(312\) | −1.43472e12 | − | 1.43472e12i | −0.485280 | − | 0.485280i | ||||
\(313\) | −6.24856e11 | + | 6.24856e11i | −0.207997 | + | 0.207997i | −0.803416 | − | 0.595418i | \(-0.796986\pi\) |
0.595418 | + | 0.803416i | \(0.296986\pi\) | |||||||
\(314\) | − | 4.32907e12i | − | 1.41823i | ||||||
\(315\) | −1.30433e11 | + | 2.38796e11i | −0.0420566 | + | 0.0769971i | ||||
\(316\) | 1.32914e12 | 0.421828 | ||||||||
\(317\) | 2.66764e12 | + | 2.66764e12i | 0.833356 | + | 0.833356i | 0.987974 | − | 0.154619i | \(-0.0494149\pi\) |
−0.154619 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(318\) | −9.17827e11 | + | 9.17827e11i | −0.282244 | + | 0.282244i | ||||
\(319\) | − | 1.28670e12i | − | 0.389514i | ||||||
\(320\) | 1.04453e12 | + | 3.55905e12i | 0.311294 | + | 1.06068i | ||||
\(321\) | −1.91805e11 | −0.0562775 | ||||||||
\(322\) | 8.82379e11 | + | 8.82379e11i | 0.254904 | + | 0.254904i | ||||
\(323\) | −4.49955e11 | + | 4.49955e11i | −0.127984 | + | 0.127984i | ||||
\(324\) | 1.05886e11i | 0.0296560i | ||||||||
\(325\) | 8.45614e11 | − | 3.88237e12i | 0.233214 | − | 1.07073i | ||||
\(326\) | 3.09307e12 | 0.840042 | ||||||||
\(327\) | −1.70467e11 | − | 1.70467e11i | −0.0455934 | − | 0.0455934i | ||||
\(328\) | 7.71540e11 | − | 7.71540e11i | 0.203231 | − | 0.203231i | ||||
\(329\) | 7.85620e11i | 0.203814i | ||||||||
\(330\) | −2.65541e12 | + | 7.79323e11i | −0.678518 | + | 0.199135i | ||||
\(331\) | 6.37656e12 | 1.60489 | 0.802447 | − | 0.596723i | \(-0.203531\pi\) | ||||
0.802447 | + | 0.596723i | \(0.203531\pi\) | |||||||
\(332\) | −6.34340e11 | − | 6.34340e11i | −0.157265 | − | 0.157265i | ||||
\(333\) | 1.75249e12 | − | 1.75249e12i | 0.427991 | − | 0.427991i | ||||
\(334\) | 5.47456e11i | 0.131709i | ||||||||
\(335\) | −3.96115e11 | − | 2.16362e11i | −0.0938852 | − | 0.0512810i | ||||
\(336\) | −4.30717e11 | −0.100576 | ||||||||
\(337\) | 4.60234e10 | + | 4.60234e10i | 0.0105884 | + | 0.0105884i | 0.712381 | − | 0.701793i | \(-0.247617\pi\) |
−0.701793 | + | 0.712381i | \(0.747617\pi\) | |||||||
\(338\) | −5.36439e11 | + | 5.36439e11i | −0.121601 | + | 0.121601i | ||||
\(339\) | 2.09670e12i | 0.468314i | ||||||||
\(340\) | −8.05527e11 | + | 1.47476e12i | −0.177291 | + | 0.324583i | ||||
\(341\) | −8.99137e11 | −0.195009 | ||||||||
\(342\) | −1.23333e11 | − | 1.23333e11i | −0.0263602 | − | 0.0263602i | ||||
\(343\) | 1.70595e12 | − | 1.70595e12i | 0.359332 | − | 0.359332i | ||||
\(344\) | 3.01286e12i | 0.625442i | ||||||||
\(345\) | 1.27116e12 | + | 4.33125e12i | 0.260078 | + | 0.886171i | ||||
\(346\) | 4.72564e12 | 0.952972 | ||||||||
\(347\) | −8.26438e11 | − | 8.26438e11i | −0.164272 | − | 0.164272i | 0.620184 | − | 0.784456i | \(-0.287058\pi\) |
−0.784456 | + | 0.620184i | \(0.787058\pi\) | |||||||
\(348\) | 1.51431e11 | − | 1.51431e11i | 0.0296701 | − | 0.0296701i | ||||
\(349\) | − | 8.53882e12i | − | 1.64919i | −0.565723 | − | 0.824595i | \(-0.691403\pi\) | ||
0.565723 | − | 0.824595i | \(-0.308597\pi\) | |||||||
\(350\) | −6.39653e11 | − | 9.95889e11i | −0.121788 | − | 0.189614i | ||||
\(351\) | 1.12356e12 | 0.210893 | ||||||||
\(352\) | 2.83172e12 | + | 2.83172e12i | 0.524006 | + | 0.524006i | ||||
\(353\) | −1.40537e12 | + | 1.40537e12i | −0.256399 | + | 0.256399i | −0.823588 | − | 0.567189i | \(-0.808031\pi\) |
0.567189 | + | 0.823588i | \(0.308031\pi\) | |||||||
\(354\) | 5.88048e11i | 0.105778i | ||||||||
\(355\) | −9.64764e12 | + | 2.83144e12i | −1.71111 | + | 0.502187i | ||||
\(356\) | −1.98905e12 | −0.347853 | ||||||||
\(357\) | −8.63421e11 | − | 8.63421e11i | −0.148896 | − | 0.148896i | ||||
\(358\) | −1.75437e12 | + | 1.75437e12i | −0.298335 | + | 0.298335i | ||||
\(359\) | − | 8.59688e12i | − | 1.44168i | −0.693102 | − | 0.720840i | \(-0.743756\pi\) | ||
0.693102 | − | 0.720840i | \(-0.256244\pi\) | |||||||
\(360\) | −1.91876e12 | − | 1.04804e12i | −0.317328 | − | 0.173327i | ||||
\(361\) | 6.02646e12 | 0.982939 | ||||||||
\(362\) | 7.01333e12 | + | 7.01333e12i | 1.12819 | + | 1.12819i | ||||
\(363\) | −2.69220e12 | + | 2.69220e12i | −0.427144 | + | 0.427144i | ||||
\(364\) | − | 4.91922e11i | − | 0.0769821i | ||||||
\(365\) | 3.48402e12 | − | 6.37854e12i | 0.537795 | − | 0.984593i | ||||
\(366\) | 3.50697e12 | 0.533981 | ||||||||
\(367\) | 4.00237e11 | + | 4.00237e11i | 0.0601156 | + | 0.0601156i | 0.736525 | − | 0.676410i | \(-0.236465\pi\) |
−0.676410 | + | 0.736525i | \(0.736465\pi\) | |||||||
\(368\) | −5.05253e12 | + | 5.05253e12i | −0.748635 | + | 0.748635i | ||||
\(369\) | 6.04214e11i | 0.0883199i | ||||||||
\(370\) | 3.03602e12 | + | 1.03447e13i | 0.437821 | + | 1.49180i | ||||
\(371\) | −1.49376e12 | −0.212526 | ||||||||
\(372\) | −1.05819e11 | − | 1.05819e11i | −0.0148542 | − | 0.0148542i | ||||
\(373\) | 2.97007e11 | − | 2.97007e11i | 0.0411361 | − | 0.0411361i | −0.686240 | − | 0.727376i | \(-0.740740\pi\) |
0.727376 | + | 0.686240i | \(0.240740\pi\) | |||||||
\(374\) | − | 1.24190e13i | − | 1.69719i | ||||||
\(375\) | −3.03774e11 | − | 4.27071e12i | −0.0409632 | − | 0.575895i | ||||
\(376\) | −6.31257e12 | −0.839976 | ||||||||
\(377\) | −1.60685e12 | − | 1.60685e12i | −0.210994 | − | 0.210994i | ||||
\(378\) | 2.36665e11 | − | 2.36665e11i | 0.0306672 | − | 0.0306672i | ||||
\(379\) | 1.15290e12i | 0.147433i | 0.997279 | + | 0.0737165i | \(0.0234860\pi\) | ||||
−0.997279 | + | 0.0737165i | \(0.976514\pi\) | |||||||
\(380\) | −2.65055e11 | + | 7.77896e10i | −0.0334516 | + | 0.00981757i | ||||
\(381\) | 2.74514e12 | 0.341932 | ||||||||
\(382\) | −9.25071e12 | − | 9.25071e12i | −1.13726 | − | 1.13726i | ||||
\(383\) | −1.27369e12 | + | 1.27369e12i | −0.154550 | + | 0.154550i | −0.780147 | − | 0.625597i | \(-0.784856\pi\) |
0.625597 | + | 0.780147i | \(0.284856\pi\) | |||||||
\(384\) | − | 2.06522e12i | − | 0.247350i | ||||||
\(385\) | −2.79500e12 | − | 1.52666e12i | −0.330429 | − | 0.180484i | ||||
\(386\) | −9.64544e11 | −0.112560 | ||||||||
\(387\) | −1.17973e12 | − | 1.17973e12i | −0.135902 | − | 0.135902i | ||||
\(388\) | 2.65924e11 | − | 2.65924e11i | 0.0302412 | − | 0.0302412i | ||||
\(389\) | 3.23506e12i | 0.363191i | 0.983373 | + | 0.181595i | \(0.0581261\pi\) | ||||
−0.983373 | + | 0.181595i | \(0.941874\pi\) | |||||||
\(390\) | −2.34289e12 | + | 4.28936e12i | −0.259674 | + | 0.475411i | ||||
\(391\) | −2.02568e13 | −2.21659 | ||||||||
\(392\) | 6.60785e12 | + | 6.60785e12i | 0.713888 | + | 0.713888i | ||||
\(393\) | 2.01647e12 | − | 2.01647e12i | 0.215094 | − | 0.215094i | ||||
\(394\) | 1.26336e13i | 1.33060i | ||||||||
\(395\) | −4.27968e12 | − | 1.45823e13i | −0.445067 | − | 1.51649i | ||||
\(396\) | −1.23935e12 | −0.127267 | ||||||||
\(397\) | 8.49815e12 | + | 8.49815e12i | 0.861731 | + | 0.861731i | 0.991539 | − | 0.129808i | \(-0.0414362\pi\) |
−0.129808 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(398\) | −2.61223e12 | + | 2.61223e12i | −0.261575 | + | 0.261575i | ||||
\(399\) | − | 2.00724e11i | − | 0.0198488i | ||||||
\(400\) | 5.70249e12 | − | 3.66268e12i | 0.556884 | − | 0.357683i | ||||
\(401\) | −2.58787e12 | −0.249586 | −0.124793 | − | 0.992183i | \(-0.539827\pi\) | ||||
−0.124793 | + | 0.992183i | \(0.539827\pi\) | |||||||
\(402\) | 3.92579e11 | + | 3.92579e11i | 0.0373936 | + | 0.0373936i | ||||
\(403\) | −1.12286e12 | + | 1.12286e12i | −0.105633 | + | 0.105633i | ||||
\(404\) | 1.59588e12i | 0.148284i | ||||||||
\(405\) | 1.16169e12 | − | 3.40940e11i | 0.106614 | − | 0.0312898i | ||||
\(406\) | −6.76926e11 | −0.0613636 | ||||||||
\(407\) | 2.05121e13 | + | 2.05121e13i | 1.83670 | + | 1.83670i | ||||
\(408\) | 6.93771e12 | − | 6.93771e12i | 0.613642 | − | 0.613642i | ||||
\(409\) | − | 4.14544e12i | − | 0.362205i | −0.983464 | − | 0.181102i | \(-0.942033\pi\) | ||
0.983464 | − | 0.181102i | \(-0.0579666\pi\) | |||||||
\(410\) | −2.30667e12 | − | 1.25992e12i | −0.199097 | − | 0.108749i | ||||
\(411\) | 9.96627e12 | 0.849814 | ||||||||
\(412\) | −7.18078e11 | − | 7.18078e11i | −0.0604903 | − | 0.0604903i | ||||
\(413\) | −4.78523e11 | + | 4.78523e11i | −0.0398247 | + | 0.0398247i | ||||
\(414\) | − | 5.55240e12i | − | 0.456540i | ||||||
\(415\) | −4.91697e12 | + | 9.00197e12i | −0.399445 | + | 0.731303i | ||||
\(416\) | 7.07260e12 | 0.567692 | ||||||||
\(417\) | −9.56625e12 | − | 9.56625e12i | −0.758685 | − | 0.758685i | ||||
\(418\) | 1.44356e12 | − | 1.44356e12i | 0.113124 | − | 0.113124i | ||||
\(419\) | 6.01062e12i | 0.465424i | 0.972546 | + | 0.232712i | \(0.0747600\pi\) | ||||
−0.972546 | + | 0.232712i | \(0.925240\pi\) | |||||||
\(420\) | −1.49271e11 | − | 5.08615e11i | −0.0114217 | − | 0.0389173i | ||||
\(421\) | 6.72155e12 | 0.508228 | 0.254114 | − | 0.967174i | \(-0.418216\pi\) | ||||
0.254114 | + | 0.967174i | \(0.418216\pi\) | |||||||
\(422\) | −1.29085e13 | − | 1.29085e13i | −0.964526 | − | 0.964526i | ||||
\(423\) | 2.47177e12 | − | 2.47177e12i | 0.182518 | − | 0.182518i | ||||
\(424\) | − | 1.20026e13i | − | 0.875880i | ||||||
\(425\) | 1.87736e13 | + | 4.08905e12i | 1.35395 | + | 0.294902i | ||||
\(426\) | 1.23677e13 | 0.881537 | ||||||||
\(427\) | 2.85379e12 | + | 2.85379e12i | 0.201040 | + | 0.201040i | ||||
\(428\) | 2.64213e11 | − | 2.64213e11i | 0.0183965 | − | 0.0183965i | ||||
\(429\) | 1.31508e13i | 0.905038i | ||||||||
\(430\) | 6.96377e12 | − | 2.04376e12i | 0.473698 | − | 0.139024i | ||||
\(431\) | −6.69149e12 | −0.449921 | −0.224961 | − | 0.974368i | \(-0.572225\pi\) | ||||
−0.224961 | + | 0.974368i | \(0.572225\pi\) | |||||||
\(432\) | 1.35515e12 | + | 1.35515e12i | 0.0900676 | + | 0.0900676i | ||||
\(433\) | 8.76838e12 | − | 8.76838e12i | 0.576076 | − | 0.576076i | −0.357744 | − | 0.933820i | \(-0.616454\pi\) |
0.933820 | + | 0.357744i | \(0.116454\pi\) | |||||||
\(434\) | 4.73032e11i | 0.0307215i | ||||||||
\(435\) | −2.14897e12 | − | 1.17379e12i | −0.137970 | − | 0.0753605i | ||||
\(436\) | 4.69640e11 | 0.0298080 | ||||||||
\(437\) | −2.35460e12 | − | 2.35460e12i | −0.147744 | − | 0.147744i | ||||
\(438\) | −6.32161e12 | + | 6.32161e12i | −0.392154 | + | 0.392154i | ||||
\(439\) | 1.28383e13i | 0.787378i | 0.919244 | + | 0.393689i | \(0.128801\pi\) | ||||
−0.919244 | + | 0.393689i | \(0.871199\pi\) | |||||||
\(440\) | 1.22669e13 | − | 2.24582e13i | 0.743827 | − | 1.36180i | ||||
\(441\) | −5.17479e12 | −0.310241 | ||||||||
\(442\) | −1.55091e13 | − | 1.55091e13i | −0.919341 | − | 0.919341i | ||||
\(443\) | 3.12846e12 | − | 3.12846e12i | 0.183363 | − | 0.183363i | −0.609457 | − | 0.792819i | \(-0.708612\pi\) |
0.792819 | + | 0.609457i | \(0.208612\pi\) | |||||||
\(444\) | 4.82814e12i | 0.279811i | ||||||||
\(445\) | 6.40452e12 | + | 2.18223e13i | 0.367017 | + | 1.25055i | ||||
\(446\) | −1.78367e13 | −1.01074 | ||||||||
\(447\) | −1.11141e13 | − | 1.11141e13i | −0.622783 | − | 0.622783i | ||||
\(448\) | 3.71271e12 | − | 3.71271e12i | 0.205732 | − | 0.205732i | ||||
\(449\) | 1.72912e13i | 0.947532i | 0.880651 | + | 0.473766i | \(0.157106\pi\) | ||||
−0.880651 | + | 0.473766i | \(0.842894\pi\) | |||||||
\(450\) | −1.12081e12 | + | 5.14585e12i | −0.0607393 | + | 0.278865i | ||||
\(451\) | −7.07206e12 | −0.379021 | ||||||||
\(452\) | −2.88822e12 | − | 2.88822e12i | −0.153087 | − | 0.153087i | ||||
\(453\) | −6.15434e12 | + | 6.15434e12i | −0.322620 | + | 0.322620i | ||||
\(454\) | 8.86731e12i | 0.459740i | ||||||||
\(455\) | −5.39697e12 | + | 1.58393e12i | −0.276754 | + | 0.0812232i | ||||
\(456\) | 1.61284e12 | 0.0818028 | ||||||||
\(457\) | −7.97734e12 | − | 7.97734e12i | −0.400200 | − | 0.400200i | 0.478104 | − | 0.878303i | \(-0.341324\pi\) |
−0.878303 | + | 0.478104i | \(0.841324\pi\) | |||||||
\(458\) | −1.07455e13 | + | 1.07455e13i | −0.533214 | + | 0.533214i | ||||
\(459\) | 5.43311e12i | 0.266677i | ||||||||
\(460\) | −7.71735e12 | − | 4.21529e12i | −0.374696 | − | 0.204663i | ||||
\(461\) | −1.02581e13 | −0.492677 | −0.246339 | − | 0.969184i | \(-0.579228\pi\) | ||||
−0.246339 | + | 0.969184i | \(0.579228\pi\) | |||||||
\(462\) | 2.77006e12 | + | 2.77006e12i | 0.131607 | + | 0.131607i | ||||
\(463\) | 2.71629e12 | − | 2.71629e12i | 0.127665 | − | 0.127665i | −0.640387 | − | 0.768052i | \(-0.721226\pi\) |
0.768052 | + | 0.640387i | \(0.221226\pi\) | |||||||
\(464\) | − | 3.87610e12i | − | 0.180221i | ||||||
\(465\) | −8.20237e11 | + | 1.50169e12i | −0.0377289 | + | 0.0690741i | ||||
\(466\) | −5.64929e12 | −0.257078 | ||||||||
\(467\) | −2.20310e13 | − | 2.20310e13i | −0.991859 | − | 0.991859i | 0.00810801 | − | 0.999967i | \(-0.497419\pi\) |
−0.999967 | + | 0.00810801i | \(0.997419\pi\) | |||||||
\(468\) | −1.54772e12 | + | 1.54772e12i | −0.0689386 | + | 0.0689386i | ||||
\(469\) | 6.38921e11i | 0.0281568i | ||||||||
\(470\) | 4.28210e12 | + | 1.45905e13i | 0.186710 | + | 0.636182i | ||||
\(471\) | −2.21672e13 | −0.956325 | ||||||||
\(472\) | −3.84499e12 | − | 3.84499e12i | −0.164129 | − | 0.164129i | ||||
\(473\) | 1.38082e13 | − | 1.38082e13i | 0.583218 | − | 0.583218i | ||||
\(474\) | 1.86936e13i | 0.781269i | ||||||||
\(475\) | 1.70689e12 | + | 2.65749e12i | 0.0705891 | + | 0.109902i | ||||
\(476\) | 2.37874e12 | 0.0973446 | ||||||||
\(477\) | 4.69976e12 | + | 4.69976e12i | 0.190320 | + | 0.190320i | ||||
\(478\) | 1.92814e13 | − | 1.92814e13i | 0.772677 | − | 0.772677i | ||||
\(479\) | − | 3.71794e12i | − | 0.147443i | −0.997279 | − | 0.0737217i | \(-0.976512\pi\) | ||
0.997279 | − | 0.0737217i | \(-0.0234877\pi\) | |||||||
\(480\) | 7.31260e12 | − | 2.14614e12i | 0.286989 | − | 0.0842272i | ||||
\(481\) | 5.12319e13 | 1.98983 | ||||||||
\(482\) | 1.14553e13 | + | 1.14553e13i | 0.440322 | + | 0.440322i | ||||
\(483\) | 4.51825e12 | − | 4.51825e12i | 0.171884 | − | 0.171884i | ||||
\(484\) | − | 7.41706e12i | − | 0.279258i | ||||||
\(485\) | −3.77375e12 | − | 2.06126e12i | −0.140626 | − | 0.0768112i | ||||
\(486\) | −1.48922e12 | −0.0549259 | ||||||||
\(487\) | −7.76585e12 | − | 7.76585e12i | −0.283494 | − | 0.283494i | 0.551007 | − | 0.834501i | \(-0.314244\pi\) |
−0.834501 | + | 0.551007i | \(0.814244\pi\) | |||||||
\(488\) | −2.29305e13 | + | 2.29305e13i | −0.828544 | + | 0.828544i | ||||
\(489\) | − | 1.58381e13i | − | 0.566448i | ||||||
\(490\) | 1.07906e13 | − | 1.97554e13i | 0.382002 | − | 0.699369i | ||||
\(491\) | −2.81134e13 | −0.985159 | −0.492580 | − | 0.870267i | \(-0.663946\pi\) | ||||
−0.492580 | + | 0.870267i | \(0.663946\pi\) | |||||||
\(492\) | −8.32309e11 | − | 8.32309e11i | −0.0288708 | − | 0.0288708i | ||||
\(493\) | 7.77009e12 | − | 7.77009e12i | 0.266804 | − | 0.266804i | ||||
\(494\) | − | 3.60549e12i | − | 0.122555i | ||||||
\(495\) | 3.99055e12 | + | 1.35971e13i | 0.134279 | + | 0.457531i | ||||
\(496\) | −2.70860e12 | −0.0902269 | ||||||||
\(497\) | 1.00642e13 | + | 1.00642e13i | 0.331892 | + | 0.331892i | ||||
\(498\) | 8.92162e12 | − | 8.92162e12i | 0.291271 | − | 0.291271i | ||||
\(499\) | − | 3.18691e12i | − | 0.103007i | −0.998673 | − | 0.0515035i | \(-0.983599\pi\) | ||
0.998673 | − | 0.0515035i | \(-0.0164013\pi\) | |||||||
\(500\) | 6.30138e12 | + | 5.46448e12i | 0.201644 | + | 0.174863i | ||||
\(501\) | 2.80327e12 | 0.0888129 | ||||||||
\(502\) | 4.16592e12 | + | 4.16592e12i | 0.130675 | + | 0.130675i | ||||
\(503\) | 1.22457e13 | − | 1.22457e13i | 0.380315 | − | 0.380315i | −0.490900 | − | 0.871216i | \(-0.663332\pi\) |
0.871216 | + | 0.490900i | \(0.163332\pi\) | |||||||
\(504\) | 3.09490e12i | 0.0951686i | ||||||||
\(505\) | 1.75087e13 | − | 5.13855e12i | 0.533086 | − | 0.156453i | ||||
\(506\) | 6.49884e13 | 1.95922 | ||||||||
\(507\) | 2.74685e12 | + | 2.74685e12i | 0.0819966 | + | 0.0819966i | ||||
\(508\) | −3.78145e12 | + | 3.78145e12i | −0.111774 | + | 0.111774i | ||||
\(509\) | 1.15777e13i | 0.338870i | 0.985541 | + | 0.169435i | \(0.0541943\pi\) | ||||
−0.985541 | + | 0.169435i | \(0.945806\pi\) | |||||||
\(510\) | −2.07416e13 | − | 1.13293e13i | −0.601162 | − | 0.328361i | ||||
\(511\) | −1.02884e13 | −0.295286 | ||||||||
\(512\) | 2.63921e13 | + | 2.63921e13i | 0.750110 | + | 0.750110i | ||||
\(513\) | −6.31531e11 | + | 6.31531e11i | −0.0177749 | + | 0.0177749i | ||||
\(514\) | 5.00101e13i | 1.39393i | ||||||||
\(515\) | −5.56604e12 | + | 1.01903e13i | −0.153642 | + | 0.281288i | ||||
\(516\) | 3.25017e12 | 0.0888499 | ||||||||
\(517\) | 2.89310e13 | + | 2.89310e13i | 0.783269 | + | 0.783269i | ||||
\(518\) | 1.07914e13 | − | 1.07914e13i | 0.289352 | − | 0.289352i | ||||
\(519\) | − | 2.41978e13i | − | 0.642598i | ||||||
\(520\) | −1.27271e13 | − | 4.33654e13i | −0.334744 | − | 1.14058i | ||||
\(521\) | −2.03576e13 | −0.530319 | −0.265160 | − | 0.964205i | \(-0.585425\pi\) | ||||
−0.265160 | + | 0.964205i | \(0.585425\pi\) | |||||||
\(522\) | 2.12979e12 | + | 2.12979e12i | 0.0549521 | + | 0.0549521i | ||||
\(523\) | −4.62281e13 | + | 4.62281e13i | −1.18140 | + | 1.18140i | −0.202021 | + | 0.979381i | \(0.564751\pi\) |
−0.979381 | + | 0.202021i | \(0.935249\pi\) | |||||||
\(524\) | 5.55540e12i | 0.140624i | ||||||||
\(525\) | −5.09948e12 | + | 3.27537e12i | −0.127858 | + | 0.0821227i | ||||
\(526\) | −3.36006e13 | −0.834485 | ||||||||
\(527\) | −5.42970e12 | − | 5.42970e12i | −0.133574 | − | 0.133574i | ||||
\(528\) | −1.58614e13 | + | 1.58614e13i | −0.386521 | + | 0.386521i | ||||
\(529\) | − | 6.45764e13i | − | 1.55882i | ||||||
\(530\) | −2.77421e13 | + | 8.14189e12i | −0.663375 | + | 0.194691i | ||||
\(531\) | 3.01112e12 | 0.0713272 | ||||||||
\(532\) | 2.76499e11 | + | 2.76499e11i | 0.00648836 | + | 0.00648836i | ||||
\(533\) | −8.83172e12 | + | 8.83172e12i | −0.205310 | + | 0.205310i | ||||
\(534\) | − | 2.79748e13i | − | 0.644260i | ||||||
\(535\) | −3.74946e12 | − | 2.04799e12i | −0.0855461 | − | 0.0467261i | ||||
\(536\) | −5.13382e12 | −0.116042 | ||||||||
\(537\) | 8.98328e12 | + | 8.98328e12i | 0.201170 | + | 0.201170i | ||||
\(538\) | −1.35268e13 | + | 1.35268e13i | −0.300112 | + | 0.300112i | ||||
\(539\) | − | 6.05687e13i | − | 1.33139i | ||||||
\(540\) | −1.13059e12 | + | 2.06989e12i | −0.0246228 | + | 0.0450793i | ||||
\(541\) | −2.10515e13 | −0.454251 | −0.227126 | − | 0.973865i | \(-0.572933\pi\) | ||||
−0.227126 | + | 0.973865i | \(0.572933\pi\) | |||||||
\(542\) | −2.75283e13 | − | 2.75283e13i | −0.588550 | − | 0.588550i | ||||
\(543\) | 3.59120e13 | − | 3.59120e13i | 0.760747 | − | 0.760747i | ||||
\(544\) | 3.42002e13i | 0.717852i | ||||||||
\(545\) | −1.51219e12 | − | 5.15251e12i | −0.0314501 | − | 0.107161i | ||||
\(546\) | 6.91860e12 | 0.142579 | ||||||||
\(547\) | 4.15569e13 | + | 4.15569e13i | 0.848606 | + | 0.848606i | 0.989959 | − | 0.141353i | \(-0.0451453\pi\) |
−0.141353 | + | 0.989959i | \(0.545145\pi\) | |||||||
\(548\) | −1.37286e13 | + | 1.37286e13i | −0.277795 | + | 0.277795i | ||||
\(549\) | − | 1.79575e13i | − | 0.360068i | ||||||
\(550\) | −6.02299e13 | − | 1.31186e13i | −1.19674 | − | 0.260660i | ||||
\(551\) | 1.80635e12 | 0.0355668 | ||||||||
\(552\) | 3.63048e13 | + | 3.63048e13i | 0.708383 | + | 0.708383i | ||||
\(553\) | −1.52119e13 | + | 1.52119e13i | −0.294142 | + | 0.294142i | ||||
\(554\) | 3.40576e13i | 0.652627i | ||||||||
\(555\) | 5.29704e13 | − | 1.55460e13i | 1.00593 | − | 0.295226i | ||||
\(556\) | 2.63552e13 | 0.496011 | ||||||||
\(557\) | −5.59600e12 | − | 5.59600e12i | −0.104376 | − | 0.104376i | 0.652990 | − | 0.757366i | \(-0.273514\pi\) |
−0.757366 | + | 0.652990i | \(0.773514\pi\) | |||||||
\(558\) | 1.48828e12 | − | 1.48828e12i | 0.0275116 | − | 0.0275116i | ||||
\(559\) | − | 3.44879e13i | − | 0.631840i | ||||||
\(560\) | −8.41979e12 | − | 4.59897e12i | −0.152884 | − | 0.0835066i | ||||
\(561\) | −6.35921e13 | −1.14443 | ||||||||
\(562\) | −2.92361e13 | − | 2.92361e13i | −0.521480 | − | 0.521480i | ||||
\(563\) | 4.89913e13 | − | 4.89913e13i | 0.866118 | − | 0.866118i | −0.125922 | − | 0.992040i | \(-0.540189\pi\) |
0.992040 | + | 0.125922i | \(0.0401888\pi\) | |||||||
\(564\) | 6.80976e12i | 0.119326i | ||||||||
\(565\) | −2.23875e13 | + | 4.09869e13i | −0.388833 | + | 0.711874i | ||||
\(566\) | 5.87379e13 | 1.01120 | ||||||||
\(567\) | −1.21185e12 | − | 1.21185e12i | −0.0206792 | − | 0.0206792i | ||||
\(568\) | −8.08670e13 | + | 8.08670e13i | −1.36782 | + | 1.36782i | ||||
\(569\) | − | 7.04691e13i | − | 1.18151i | −0.806851 | − | 0.590755i | \(-0.798830\pi\) | ||
0.806851 | − | 0.590755i | \(-0.201170\pi\) | |||||||
\(570\) | −1.09407e12 | − | 3.72784e12i | −0.0181832 | − | 0.0619559i | ||||
\(571\) | 6.55472e13 | 1.07988 | 0.539938 | − | 0.841705i | \(-0.318448\pi\) | ||||
0.539938 | + | 0.841705i | \(0.318448\pi\) | |||||||
\(572\) | −1.81154e13 | − | 1.81154e13i | −0.295847 | − | 0.295847i | ||||
\(573\) | −4.73686e13 | + | 4.73686e13i | −0.766862 | + | 0.766862i | ||||
\(574\) | 3.72058e12i | 0.0597106i | ||||||||
\(575\) | −2.13978e13 | + | 9.82413e13i | −0.340432 | + | 1.56299i | ||||
\(576\) | −2.33623e13 | −0.368472 | ||||||||
\(577\) | −3.36364e13 | − | 3.36364e13i | −0.525933 | − | 0.525933i | 0.393424 | − | 0.919357i | \(-0.371290\pi\) |
−0.919357 | + | 0.393424i | \(0.871290\pi\) | |||||||
\(578\) | 3.59385e13 | − | 3.59385e13i | 0.557083 | − | 0.557083i | ||||
\(579\) | 4.93898e12i | 0.0759004i | ||||||||
\(580\) | 4.57713e12 | − | 1.34332e12i | 0.0697353 | − | 0.0204663i | ||||
\(581\) | 1.45199e13 | 0.219322 | ||||||||
\(582\) | 3.74007e12 | + | 3.74007e12i | 0.0560099 | + | 0.0560099i | ||||
\(583\) | −5.50087e13 | + | 5.50087e13i | −0.816749 | + | 0.816749i | ||||
\(584\) | − | 8.26686e13i | − | 1.21696i | ||||||
\(585\) | 2.19638e13 | + | 1.19968e13i | 0.320574 | + | 0.175101i | ||||
\(586\) | 6.28052e13 | 0.908882 | ||||||||
\(587\) | 1.69574e13 | + | 1.69574e13i | 0.243315 | + | 0.243315i | 0.818220 | − | 0.574905i | \(-0.194961\pi\) |
−0.574905 | + | 0.818220i | \(0.694961\pi\) | |||||||
\(588\) | 7.12831e12 | − | 7.12831e12i | 0.101414 | − | 0.101414i | ||||
\(589\) | − | 1.26227e12i | − | 0.0178064i | ||||||
\(590\) | −6.27887e12 | + | 1.14953e13i | −0.0878257 | + | 0.160791i | ||||
\(591\) | 6.46909e13 | 0.897235 | ||||||||
\(592\) | 6.17916e13 | + | 6.17916e13i | 0.849809 | + | 0.849809i | ||||
\(593\) | 2.05210e13 | − | 2.05210e13i | 0.279850 | − | 0.279850i | −0.553199 | − | 0.833049i | \(-0.686593\pi\) |
0.833049 | + | 0.553199i | \(0.186593\pi\) | |||||||
\(594\) | − | 1.74307e13i | − | 0.235712i | ||||||
\(595\) | −7.65926e12 | − | 2.60976e13i | −0.102708 | − | 0.349958i | ||||
\(596\) | 3.06195e13 | 0.407161 | ||||||||
\(597\) | 1.33760e13 | + | 1.33760e13i | 0.176383 | + | 0.176383i | ||||
\(598\) | 8.11588e13 | − | 8.11588e13i | 1.06128 | − | 1.06128i | ||||
\(599\) | 7.92364e13i | 1.02752i | 0.857934 | + | 0.513760i | \(0.171748\pi\) | ||||
−0.857934 | + | 0.513760i | \(0.828252\pi\) | |||||||
\(600\) | −2.63180e13 | − | 4.09750e13i | −0.338452 | − | 0.526942i | ||||
\(601\) | −3.80901e13 | −0.485781 | −0.242890 | − | 0.970054i | \(-0.578096\pi\) | ||||
−0.242890 | + | 0.970054i | \(0.578096\pi\) | |||||||
\(602\) | −7.26443e12 | − | 7.26443e12i | −0.0918796 | − | 0.0918796i | ||||
\(603\) | 2.01022e12 | − | 2.01022e12i | 0.0252148 | − | 0.0252148i | ||||
\(604\) | − | 1.69553e13i | − | 0.210921i | ||||||
\(605\) | −8.13740e13 | + | 2.38821e13i | −1.00394 | + | 0.294642i | ||||
\(606\) | −2.24451e13 | −0.274637 | ||||||||
\(607\) | 2.93515e13 | + | 2.93515e13i | 0.356194 | + | 0.356194i | 0.862408 | − | 0.506214i | \(-0.168955\pi\) |
−0.506214 | + | 0.862408i | \(0.668955\pi\) | |||||||
\(608\) | −3.97535e12 | + | 3.97535e12i | −0.0478473 | + | 0.0478473i | ||||
\(609\) | 3.46622e12i | 0.0413780i | ||||||||
\(610\) | 6.85553e13 | + | 3.74456e13i | 0.811693 | + | 0.443355i | ||||
\(611\) | 7.22592e13 | 0.848569 | ||||||||
\(612\) | −7.48414e12 | − | 7.48414e12i | −0.0871736 | − | 0.0871736i | ||||
\(613\) | 1.13080e14 | − | 1.13080e14i | 1.30642 | − | 1.30642i | 0.382443 | − | 0.923979i | \(-0.375083\pi\) |
0.923979 | − | 0.382443i | \(-0.124917\pi\) | |||||||
\(614\) | 1.04346e14i | 1.19573i | ||||||||
\(615\) | −6.45148e12 | + | 1.18114e13i | −0.0733304 | + | 0.134253i | ||||
\(616\) | −3.62244e13 | −0.408412 | ||||||||
\(617\) | −7.40831e13 | − | 7.40831e13i | −0.828502 | − | 0.828502i | 0.158808 | − | 0.987310i | \(-0.449235\pi\) |
−0.987310 | + | 0.158808i | \(0.949235\pi\) | |||||||
\(618\) | 1.00993e13 | − | 1.00993e13i | 0.112034 | − | 0.112034i | ||||
\(619\) | − | 8.58743e12i | − | 0.0944953i | −0.998883 | − | 0.0472476i | \(-0.984955\pi\) | ||
0.998883 | − | 0.0472476i | \(-0.0150450\pi\) | |||||||
\(620\) | −9.38704e11 | − | 3.19847e12i | −0.0102464 | − | 0.0349127i | ||||
\(621\) | −2.84312e13 | −0.307849 | ||||||||
\(622\) | 6.30810e12 | + | 6.30810e12i | 0.0677559 | + | 0.0677559i | ||||
\(623\) | 2.27645e13 | − | 2.27645e13i | 0.242559 | − | 0.242559i | ||||
\(624\) | 3.96161e13i | 0.418744i | ||||||||
\(625\) | 3.96621e13 | − | 8.67287e13i | 0.415888 | − | 0.909416i | ||||
\(626\) | 2.42117e13 | 0.251857 | ||||||||
\(627\) | −7.39179e12 | − | 7.39179e12i | −0.0762802 | − | 0.0762802i | ||||
\(628\) | 3.05354e13 | − | 3.05354e13i | 0.312612 | − | 0.312612i | ||||
\(629\) | 2.47737e14i | 2.51616i | ||||||||
\(630\) | 7.15338e12 | − | 2.09941e12i | 0.0720789 | − | 0.0211541i | ||||
\(631\) | −9.17553e13 | −0.917243 | −0.458621 | − | 0.888632i | \(-0.651657\pi\) | ||||
−0.458621 | + | 0.888632i | \(0.651657\pi\) | |||||||
\(632\) | −1.22229e14 | − | 1.22229e14i | −1.21224 | − | 1.21224i | ||||
\(633\) | −6.60985e13 | + | 6.60985e13i | −0.650388 | + | 0.650388i | ||||
\(634\) | − | 1.03365e14i | − | 1.00908i | ||||||
\(635\) | 5.36629e13 | + | 2.93112e13i | 0.519763 | + | 0.283900i | ||||
\(636\) | −1.29479e13 | −0.124427 | ||||||||
\(637\) | −7.56393e13 | − | 7.56393e13i | −0.721191 | − | 0.721191i | ||||
\(638\) | −2.49283e13 | + | 2.49283e13i | −0.235824 | + | 0.235824i | ||||
\(639\) | − | 6.33292e13i | − | 0.594428i | ||||||
\(640\) | 2.20514e13 | − | 4.03717e13i | 0.205370 | − | 0.375990i | ||||
\(641\) | −1.50268e14 | −1.38860 | −0.694298 | − | 0.719688i | \(-0.744285\pi\) | ||||
−0.694298 | + | 0.719688i | \(0.744285\pi\) | |||||||
\(642\) | 3.71600e12 | + | 3.71600e12i | 0.0340722 | + | 0.0340722i | ||||
\(643\) | −8.46613e13 | + | 8.46613e13i | −0.770248 | + | 0.770248i | −0.978150 | − | 0.207902i | \(-0.933336\pi\) |
0.207902 | + | 0.978150i | \(0.433336\pi\) | |||||||
\(644\) | 1.24478e13i | 0.112374i | ||||||||
\(645\) | −1.04652e13 | − | 3.56582e13i | −0.0937448 | − | 0.319419i | ||||
\(646\) | 1.74347e13 | 0.154971 | ||||||||
\(647\) | 6.78537e13 | + | 6.78537e13i | 0.598483 | + | 0.598483i | 0.939909 | − | 0.341425i | \(-0.110910\pi\) |
−0.341425 | + | 0.939909i | \(0.610910\pi\) | |||||||
\(648\) | 9.73737e12 | − | 9.73737e12i | 0.0852249 | − | 0.0852249i | ||||
\(649\) | 3.52438e13i | 0.306097i | ||||||||
\(650\) | −9.15991e13 | + | 5.88335e13i | −0.789449 | + | 0.507058i | ||||
\(651\) | 2.42218e12 | 0.0207158 | ||||||||
\(652\) | 2.18172e13 | + | 2.18172e13i | 0.185165 | + | 0.185165i | ||||
\(653\) | −4.85301e13 | + | 4.85301e13i | −0.408738 | + | 0.408738i | −0.881298 | − | 0.472560i | \(-0.843330\pi\) |
0.472560 | + | 0.881298i | \(0.343330\pi\) | |||||||
\(654\) | 6.60521e12i | 0.0552075i | ||||||||
\(655\) | 6.09494e13 | − | 1.78878e13i | 0.505549 | − | 0.148371i | ||||
\(656\) | −2.13042e13 | −0.175366 | ||||||||
\(657\) | 3.23700e13 | + | 3.23700e13i | 0.264433 | + | 0.264433i | ||||
\(658\) | 1.52205e13 | − | 1.52205e13i | 0.123395 | − | 0.123395i | ||||
\(659\) | − | 1.36281e14i | − | 1.09650i | −0.836316 | − | 0.548248i | \(-0.815295\pi\) | ||
0.836316 | − | 0.548248i | \(-0.184705\pi\) | |||||||
\(660\) | −2.42271e13 | − | 1.32331e13i | −0.193456 | − | 0.105668i | ||||
\(661\) | −1.44495e14 | −1.14510 | −0.572551 | − | 0.819869i | \(-0.694046\pi\) | ||||
−0.572551 | + | 0.819869i | \(0.694046\pi\) | |||||||
\(662\) | −1.23538e14 | − | 1.23538e14i | −0.971655 | − | 0.971655i | ||||
\(663\) | −7.94151e13 | + | 7.94151e13i | −0.619920 | + | 0.619920i | ||||
\(664\) | 1.16669e14i | 0.903892i | ||||||||
\(665\) | 2.14323e12 | − | 3.92381e12i | 0.0164801 | − | 0.0301717i | ||||
\(666\) | −6.79049e13 | −0.518239 | ||||||||
\(667\) | 4.06606e13 | + | 4.06606e13i | 0.307996 | + | 0.307996i | ||||
\(668\) | −3.86152e12 | + | 3.86152e12i | −0.0290319 | + | 0.0290319i | ||||
\(669\) | 9.13333e13i | 0.681551i | ||||||||
\(670\) | 3.48250e12 | + | 1.18660e13i | 0.0257939 | + | 0.0878883i | ||||
\(671\) | 2.10185e14 | 1.54522 | ||||||||
\(672\) | −7.62833e12 | − | 7.62833e12i | −0.0556651 | − | 0.0556651i | ||||
\(673\) | 1.27146e14 | − | 1.27146e14i | 0.920932 | − | 0.920932i | −0.0761637 | − | 0.997095i | \(-0.524267\pi\) |
0.997095 | + | 0.0761637i | \(0.0242672\pi\) | |||||||
\(674\) | − | 1.78330e12i | − | 0.0128211i | ||||||
\(675\) | 2.63495e13 | + | 5.73915e12i | 0.188041 | + | 0.0409571i | ||||
\(676\) | −7.56762e12 | −0.0536075 | ||||||||
\(677\) | 7.64265e13 | + | 7.64265e13i | 0.537404 | + | 0.537404i | 0.922766 | − | 0.385362i | \(-0.125923\pi\) |
−0.385362 | + | 0.922766i | \(0.625923\pi\) | |||||||
\(678\) | 4.06211e13 | − | 4.06211e13i | 0.283533 | − | 0.283533i | ||||
\(679\) | 6.08695e12i | 0.0421746i | ||||||||
\(680\) | 2.09698e14 | − | 6.15432e13i | 1.44228 | − | 0.423288i | ||||
\(681\) | 4.54054e13 | 0.310007 | ||||||||
\(682\) | 1.74197e13 | + | 1.74197e13i | 0.118065 | + | 0.118065i | ||||
\(683\) | 1.74091e14 | − | 1.74091e14i | 1.17132 | − | 1.17132i | 0.189420 | − | 0.981896i | \(-0.439339\pi\) |
0.981896 | − | 0.189420i | \(-0.0606606\pi\) | |||||||
\(684\) | − | 1.73988e12i | − | 0.0116208i | ||||||
\(685\) | 1.94824e14 | + | 1.06415e14i | 1.29178 | + | 0.705584i | ||||
\(686\) | −6.61016e13 | −0.435102 | ||||||||
\(687\) | 5.50229e13 | + | 5.50229e13i | 0.359551 | + | 0.359551i | ||||
\(688\) | 4.15964e13 | − | 4.15964e13i | 0.269844 | − | 0.269844i | ||||
\(689\) | 1.37392e14i | 0.884840i | ||||||||
\(690\) | 5.92856e13 | − | 1.08540e14i | 0.379057 | − | 0.693976i | ||||
\(691\) | −1.59952e14 | −1.01531 | −0.507656 | − | 0.861560i | \(-0.669488\pi\) | ||||
−0.507656 | + | 0.861560i | \(0.669488\pi\) | |||||||
\(692\) | 3.33326e13 | + | 3.33326e13i | 0.210058 | + | 0.210058i | ||||
\(693\) | 1.41842e13 | − | 1.41842e13i | 0.0887437 | − | 0.0887437i | ||||
\(694\) | 3.20225e13i | 0.198911i | ||||||||
\(695\) | −8.48606e13 | − | 2.89147e14i | −0.523338 | − | 1.78318i | ||||
\(696\) | −2.78516e13 | −0.170531 | ||||||||
\(697\) | −4.27067e13 | − | 4.27067e13i | −0.259616 | − | 0.259616i | ||||
\(698\) | −1.65430e14 | + | 1.65430e14i | −0.998473 | + | 0.998473i | ||||
\(699\) | 2.89274e13i | 0.173350i | ||||||||
\(700\) | 2.51273e12 | − | 1.15364e13i | 0.0149505 | − | 0.0686405i | ||||
\(701\) | −5.32572e13 | −0.314622 | −0.157311 | − | 0.987549i | \(-0.550282\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550282\pi\) | |||||||
\(702\) | −2.17678e13 | − | 2.17678e13i | −0.127682 | − | 0.127682i | ||||
\(703\) | −2.87963e13 | + | 2.87963e13i | −0.167711 | + | 0.167711i | ||||
\(704\) | − | 2.73446e14i | − | 1.58128i | ||||||
\(705\) | 7.47112e13 | − | 2.19267e13i | 0.428983 | − | 0.125900i | ||||
\(706\) | 5.44547e13 | 0.310464 | ||||||||
\(707\) | −1.82647e13 | − | 1.82647e13i | −0.103399 | − | 0.103399i | ||||
\(708\) | −4.14784e12 | + | 4.14784e12i | −0.0233161 | + | 0.0233161i | ||||
\(709\) | − | 1.45905e14i | − | 0.814403i | −0.913338 | − | 0.407201i | \(-0.866505\pi\) | ||
0.913338 | − | 0.407201i | \(-0.133495\pi\) | |||||||
\(710\) | 2.41768e14 | + | 1.32056e14i | 1.34000 | + | 0.731924i | ||||
\(711\) | 9.57211e13 | 0.526817 | ||||||||
\(712\) | 1.82916e14 | + | 1.82916e14i | 0.999656 | + | 0.999656i | ||||
\(713\) | 2.84134e13 | − | 2.84134e13i | 0.154197 | − | 0.154197i | ||||
\(714\) | 3.34556e13i | 0.180292i | ||||||||
\(715\) | −1.40418e14 | + | 2.57077e14i | −0.751436 | + | 1.37573i | ||||
\(716\) | −2.47491e13 | −0.131521 | ||||||||
\(717\) | −9.87308e13 | − | 9.87308e13i | −0.521023 | − | 0.521023i | ||||
\(718\) | −1.66555e14 | + | 1.66555e14i | −0.872839 | + | 0.872839i | ||||
\(719\) | 2.00526e14i | 1.04358i | 0.853073 | + | 0.521791i | \(0.174736\pi\) | ||||
−0.853073 | + | 0.521791i | \(0.825264\pi\) | |||||||
\(720\) | 1.20213e13 | + | 4.09605e13i | 0.0621282 | + | 0.211691i | ||||
\(721\) | 1.64366e13 | 0.0843600 | ||||||||
\(722\) | −1.16756e14 | − | 1.16756e14i | −0.595103 | − | 0.595103i | ||||
\(723\) | 5.86571e13 | − | 5.86571e13i | 0.296913 | − | 0.296913i | ||||
\(724\) | 9.89381e13i | 0.497360i | ||||||||
\(725\) | −2.94756e13 | − | 4.58912e13i | −0.147154 | − | 0.229108i | ||||
\(726\) | 1.04317e14 | 0.517214 | ||||||||
\(727\) | −1.43344e14 | − | 1.43344e14i | −0.705841 | − | 0.705841i | 0.259817 | − | 0.965658i | \(-0.416338\pi\) |
−0.965658 | + | 0.259817i | \(0.916338\pi\) | |||||||
\(728\) | −4.52378e13 | + | 4.52378e13i | −0.221230 | + | 0.221230i | ||||
\(729\) | 7.62560e12i | 0.0370370i | ||||||||
\(730\) | −1.91076e14 | + | 5.60779e13i | −0.921703 | + | 0.270506i | ||||
\(731\) | 1.66769e14 | 0.798969 | ||||||||
\(732\) | 2.47366e13 | + | 2.47366e13i | 0.117702 | + | 0.117702i | ||||
\(733\) | −1.53239e14 | + | 1.53239e14i | −0.724183 | + | 0.724183i | −0.969454 | − | 0.245271i | \(-0.921123\pi\) |
0.245271 | + | 0.969454i | \(0.421123\pi\) | |||||||
\(734\) | − | 1.55083e13i | − | 0.0727918i | ||||||
\(735\) | −1.01158e14 | − | 5.52537e13i | −0.471591 | − | 0.257588i | ||||
\(736\) | −1.78969e14 | −0.828682 | ||||||||
\(737\) | 2.35287e13 | + | 2.35287e13i | 0.108208 | + | 0.108208i | ||||
\(738\) | 1.17059e13 | − | 1.17059e13i | 0.0534717 | − | 0.0534717i | ||||
\(739\) | − | 1.18250e14i | − | 0.536510i | −0.963348 | − | 0.268255i | \(-0.913553\pi\) | ||
0.963348 | − | 0.268255i | \(-0.0864470\pi\) | |||||||
\(740\) | −5.15524e13 | + | 9.43819e13i | −0.232322 | + | 0.425334i | ||||
\(741\) | −1.84620e13 | −0.0826396 | ||||||||
\(742\) | 2.89398e13 | + | 2.89398e13i | 0.128670 | + | 0.128670i | ||||
\(743\) | 7.93545e13 | − | 7.93545e13i | 0.350451 | − | 0.350451i | −0.509826 | − | 0.860277i | \(-0.670290\pi\) |
0.860277 | + | 0.509826i | \(0.170290\pi\) | |||||||
\(744\) | 1.94625e13i | 0.0853757i | ||||||||
\(745\) | −9.85912e13 | − | 3.35932e14i | −0.429593 | − | 1.46376i | ||||
\(746\) | −1.15083e13 | −0.0498102 | ||||||||
\(747\) | −4.56835e13 | − | 4.56835e13i | −0.196407 | − | 0.196407i | ||||
\(748\) | 8.75986e13 | − | 8.75986e13i | 0.374101 | − | 0.374101i | ||||
\(749\) | 6.04777e12i | 0.0256558i | ||||||||
\(750\) | −7.68547e13 | + | 8.86252e13i | −0.323865 | + | 0.373466i | ||||
\(751\) | −3.34618e13 | −0.140072 | −0.0700358 | − | 0.997544i | \(-0.522311\pi\) | ||||
−0.0700358 | + | 0.997544i | \(0.522311\pi\) | |||||||
\(752\) | 8.71530e13 | + | 8.71530e13i | 0.362404 | + | 0.362404i | ||||
\(753\) | 2.13317e13 | − | 2.13317e13i | 0.0881152 | − | 0.0881152i | ||||
\(754\) | 6.22618e13i | 0.255485i | ||||||||
\(755\) | −1.86020e14 | + | 5.45941e13i | −0.758271 | + | 0.222542i | ||||
\(756\) | 3.33866e12 | 0.0135196 | ||||||||
\(757\) | −8.70456e13 | − | 8.70456e13i | −0.350161 | − | 0.350161i | 0.510009 | − | 0.860169i | \(-0.329642\pi\) |
−0.860169 | + | 0.510009i | \(0.829642\pi\) | |||||||
\(758\) | 2.23360e13 | − | 2.23360e13i | 0.0892607 | − | 0.0892607i | ||||
\(759\) | − | 3.32775e14i | − | 1.32112i | ||||||
\(760\) | 3.15284e13 | + | 1.72211e13i | 0.124346 | + | 0.0679193i | ||||
\(761\) | −1.71905e14 | −0.673542 | −0.336771 | − | 0.941587i | \(-0.609335\pi\) | ||||
−0.336771 | + | 0.941587i | \(0.609335\pi\) | |||||||
\(762\) | −5.31839e13 | − | 5.31839e13i | −0.207017 | − | 0.207017i | ||||
\(763\) | −5.37497e12 | + | 5.37497e12i | −0.0207852 | + | 0.0207852i | ||||
\(764\) | − | 1.30501e14i | − | 0.501357i | ||||||
\(765\) | −5.80119e13 | + | 1.06208e14i | −0.221416 | + | 0.405369i | ||||
\(766\) | 4.93525e13 | 0.187139 | ||||||||
\(767\) | 4.40132e13 | + | 4.40132e13i | 0.165808 | + | 0.165808i | ||||
\(768\) | 8.05633e13 | − | 8.05633e13i | 0.301530 | − | 0.301530i | ||||
\(769\) | 1.68570e14i | 0.626828i | 0.949617 | + | 0.313414i | \(0.101473\pi\) | ||||
−0.949617 | + | 0.313414i | \(0.898527\pi\) | |||||||
\(770\) | 2.45727e13 | + | 8.37272e13i | 0.0907819 | + | 0.309323i | ||||
\(771\) | 2.56078e14 | 0.939942 | ||||||||
\(772\) | −6.80348e12 | − | 6.80348e12i | −0.0248110 | − | 0.0248110i | ||||
\(773\) | −6.52829e12 | + | 6.52829e12i | −0.0236538 | + | 0.0236538i | −0.718835 | − | 0.695181i | \(-0.755324\pi\) |
0.695181 | + | 0.718835i | \(0.255324\pi\) | |||||||
\(774\) | 4.57117e13i | 0.164559i | ||||||||
\(775\) | −3.20685e13 | + | 2.05974e13i | −0.114702 | + | 0.0736723i | ||||
\(776\) | −4.89094e13 | −0.173814 | ||||||||
\(777\) | −5.52575e13 | − | 5.52575e13i | −0.195113 | − | 0.195113i | ||||
\(778\) | 6.26755e13 | − | 6.26755e13i | 0.219887 | − | 0.219887i | ||||
\(779\) | − | 9.92823e12i | − | 0.0346086i | ||||||
\(780\) | −4.67810e13 | + | 1.37295e13i | −0.162030 | + | 0.0475536i | ||||
\(781\) | 7.41240e14 | 2.55096 | ||||||||
\(782\) | 3.92451e14 | + | 3.92451e14i | 1.34200 | + | 1.34200i | ||||
\(783\) | 1.09057e13 | − | 1.09057e13i | 0.0370547 | − | 0.0370547i | ||||
\(784\) | − | 1.82460e14i | − | 0.616008i | ||||||
\(785\) | −4.33331e14 | − | 2.36690e14i | −1.45369 | − | 0.794019i | ||||
\(786\) | −7.81335e13 | −0.260450 | ||||||||
\(787\) | −1.24436e14 | − | 1.24436e14i | −0.412167 | − | 0.412167i | 0.470326 | − | 0.882493i | \(-0.344136\pi\) |
−0.882493 | + | 0.470326i | \(0.844136\pi\) | |||||||
\(788\) | −8.91122e13 | + | 8.91122e13i | −0.293296 | + | 0.293296i | ||||
\(789\) | 1.72053e14i | 0.562700i | ||||||||
\(790\) | −1.99600e14 | + | 3.65428e14i | −0.648673 | + | 1.18759i | ||||
\(791\) | 6.61106e13 | 0.213496 | ||||||||
\(792\) | 1.13972e14 | + | 1.13972e14i | 0.365739 | + | 0.365739i | ||||
\(793\) | 2.62483e14 | − | 2.62483e14i | 0.837019 | − | 0.837019i | ||||
\(794\) | − | 3.29283e14i | − | 1.04344i | ||||||
\(795\) | 4.16908e13 | + | 1.42054e14i | 0.131282 | + | 0.447320i | ||||
\(796\) | −3.68512e13 | −0.115315 | ||||||||
\(797\) | 1.74781e14 | + | 1.74781e14i | 0.543503 | + | 0.543503i | 0.924554 | − | 0.381051i | \(-0.124438\pi\) |
−0.381051 | + | 0.924554i | \(0.624438\pi\) | |||||||
\(798\) | −3.88879e12 | + | 3.88879e12i | −0.0120171 | + | 0.0120171i | ||||
\(799\) | 3.49416e14i | 1.07302i | ||||||||
\(800\) | 1.65864e14 | + | 3.61267e13i | 0.506178 | + | 0.110250i | ||||
\(801\) | −1.43246e14 | −0.434430 | ||||||||
\(802\) | 5.01369e13 | + | 5.01369e13i | 0.151107 | + | 0.151107i | ||||
\(803\) | −3.78877e14 | + | 3.78877e14i | −1.13480 | + | 1.13480i | ||||
\(804\) | 5.53817e12i | 0.0164849i | ||||||||
\(805\) | 1.36568e14 | − | 4.00806e13i | 0.403988 | − | 0.118565i | ||||
\(806\) | 4.35082e13 | 0.127907 | ||||||||
\(807\) | 6.92643e13 | + | 6.92643e13i | 0.202368 | + | 0.202368i | ||||
\(808\) | 1.46759e14 | − | 1.46759e14i | 0.426136 | − | 0.426136i | ||||
\(809\) | − | 2.76524e14i | − | 0.797977i | −0.916956 | − | 0.398988i | \(-0.869361\pi\) | ||
0.916956 | − | 0.398988i | \(-0.130639\pi\) | |||||||
\(810\) | −2.91117e13 | − | 1.59011e13i | −0.0834916 | − | 0.0456040i | ||||
\(811\) | 4.11773e14 | 1.17369 | 0.586845 | − | 0.809700i | \(-0.300370\pi\) | ||||
0.586845 | + | 0.809700i | \(0.300370\pi\) | |||||||
\(812\) | −4.77475e12 | − | 4.77475e12i | −0.0135260 | − | 0.0135260i | ||||
\(813\) | −1.40960e14 | + | 1.40960e14i | −0.396865 | + | 0.396865i | ||||
\(814\) | − | 7.94798e14i | − | 2.22400i | ||||||
\(815\) | 1.69111e14 | − | 3.09609e14i | 0.470311 | − | 0.861044i | ||||
\(816\) | −1.91568e14 | −0.529507 | ||||||||
\(817\) | 1.93849e13 | + | 1.93849e13i | 0.0532540 | + | 0.0532540i | ||||
\(818\) | −8.03131e13 | + | 8.03131e13i | −0.219291 | + | 0.219291i | ||||
\(819\) | − | 3.54269e13i | − | 0.0961421i | ||||||
\(820\) | −7.38327e12 | − | 2.51572e13i | −0.0199150 | − | 0.0678567i | ||||
\(821\) | −1.22882e14 | −0.329438 | −0.164719 | − | 0.986341i | \(-0.552672\pi\) | ||||
−0.164719 | + | 0.986341i | \(0.552672\pi\) | |||||||
\(822\) | −1.93085e14 | − | 1.93085e14i | −0.514504 | − | 0.514504i | ||||
\(823\) | −2.83711e14 | + | 2.83711e14i | −0.751409 | + | 0.751409i | −0.974742 | − | 0.223333i | \(-0.928306\pi\) |
0.223333 | + | 0.974742i | \(0.428306\pi\) | |||||||
\(824\) | 1.32071e14i | 0.347672i | ||||||||
\(825\) | −6.71743e13 | + | 3.08409e14i | −0.175765 | + | 0.806971i | ||||
\(826\) | 1.85416e13 | 0.0482223 | ||||||||
\(827\) | 2.76194e14 | + | 2.76194e14i | 0.713980 | + | 0.713980i | 0.967365 | − | 0.253385i | \(-0.0815440\pi\) |
−0.253385 | + | 0.967365i | \(0.581544\pi\) | |||||||
\(828\) | 3.91642e13 | − | 3.91642e13i | 0.100632 | − | 0.100632i | ||||
\(829\) | 5.06104e14i | 1.29261i | 0.763080 | + | 0.646304i | \(0.223686\pi\) | ||||
−0.763080 | + | 0.646304i | \(0.776314\pi\) | |||||||
\(830\) | 2.69663e14 | − | 7.91422e13i | 0.684591 | − | 0.200917i | ||||
\(831\) | 1.74393e14 | 0.440072 | ||||||||
\(832\) | −3.41485e14 | − | 3.41485e14i | −0.856554 | − | 0.856554i | ||||
\(833\) | 3.65761e14 | − | 3.65761e14i | 0.911953 | − | 0.911953i | ||||
\(834\) | 3.70670e14i | 0.918665i | ||||||||
\(835\) | 5.47991e13 | + | 2.99318e13i | 0.135002 | + | 0.0737396i | ||||
\(836\) | 2.03645e13 | 0.0498703 | ||||||||
\(837\) | −7.62081e12 | − | 7.62081e12i | −0.0185513 | − | 0.0185513i | ||||
\(838\) | 1.16449e14 | − | 1.16449e14i | 0.281783 | − | 0.281783i | ||||
\(839\) | − | 6.76549e14i | − | 1.62738i | −0.581298 | − | 0.813691i | \(-0.697455\pi\) | ||
0.581298 | − | 0.813691i | \(-0.302545\pi\) | |||||||
\(840\) | −3.30457e13 | + | 6.05000e13i | −0.0790167 | + | 0.144664i | ||||
\(841\) | 3.89514e14 | 0.925855 | ||||||||
\(842\) | −1.30222e14 | − | 1.30222e14i | −0.307698 | − | 0.307698i | ||||
\(843\) | −1.49704e14 | + | 1.49704e14i | −0.351639 | + | 0.351639i | ||||
\(844\) | − | 1.82102e14i | − | 0.425209i | ||||||
\(845\) | 2.43669e13 | + | 8.30258e13i | 0.0565609 | + | 0.192721i | ||||
\(846\) | −9.57753e13 | −0.221005 | ||||||||
\(847\) | 8.48874e13 | + | 8.48874e13i | 0.194727 | + | 0.194727i | ||||
\(848\) | −1.65710e14 | + | 1.65710e14i | −0.377895 | + | 0.377895i | ||||
\(849\) | − | 3.00769e14i | − | 0.681860i | ||||||
\(850\) | −2.84495e14 | − | 4.42936e14i | −0.641181 | − | 0.998267i | ||||
\(851\) | −1.29640e15 | −2.90463 | ||||||||
\(852\) | 8.72364e13 | + | 8.72364e13i | 0.194312 | + | 0.194312i | ||||
\(853\) | −2.87513e14 | + | 2.87513e14i | −0.636668 | + | 0.636668i | −0.949732 | − | 0.313064i | \(-0.898645\pi\) |
0.313064 | + | 0.949732i | \(0.398645\pi\) | |||||||
\(854\) | − | 1.10578e14i | − | 0.243432i | ||||||
\(855\) | −1.90885e13 | + | 5.60220e12i | −0.0417774 | + | 0.0122611i | ||||
\(856\) | −4.85946e13 | −0.105735 | ||||||||
\(857\) | 1.42114e14 | + | 1.42114e14i | 0.307421 | + | 0.307421i | 0.843908 | − | 0.536488i | \(-0.180249\pi\) |
−0.536488 | + | 0.843908i | \(0.680249\pi\) | |||||||
\(858\) | 2.54782e14 | − | 2.54782e14i | 0.547939 | − | 0.547939i | ||||
\(859\) | 7.62838e12i | 0.0163105i | 0.999967 | + | 0.00815523i | \(0.00259592\pi\) | ||||
−0.999967 | + | 0.00815523i | \(0.997404\pi\) | |||||||
\(860\) | 6.35353e13 | + | 3.47036e13i | 0.135059 | + | 0.0737704i | ||||
\(861\) | 1.90514e13 | 0.0402634 | ||||||||
\(862\) | 1.29640e14 | + | 1.29640e14i | 0.272397 | + | 0.272397i | ||||
\(863\) | −5.51158e14 | + | 5.51158e14i | −1.15139 | + | 1.15139i | −0.165114 | + | 0.986274i | \(0.552799\pi\) |
−0.986274 | + | 0.165114i | \(0.947201\pi\) | |||||||
\(864\) | 4.80015e13i | 0.0996980i | ||||||||
\(865\) | 2.58372e14 | − | 4.73026e14i | 0.533537 | − | 0.976798i | ||||
\(866\) | −3.39754e14 | −0.697550 | ||||||||
\(867\) | −1.84024e14 | − | 1.84024e14i | −0.375646 | − | 0.375646i | ||||
\(868\) | −3.33657e12 | + | 3.33657e12i | −0.00677175 | + | 0.00677175i | ||||
\(869\) | 1.12037e15i | 2.26081i | ||||||||
\(870\) | 1.88930e13 | + | 6.43746e13i | 0.0379057 | + | 0.129157i | ||||
\(871\) | 5.87662e13 | 0.117229 | ||||||||
\(872\) | −4.31886e13 | − | 4.31886e13i | −0.0856618 | − | 0.0856618i | ||||
\(873\) | 1.91512e13 | − | 1.91512e13i | 0.0377680 | − | 0.0377680i | ||||
\(874\) | 9.12351e13i | 0.178898i | ||||||||
\(875\) | −1.34659e14 | + | 9.57824e12i | −0.262540 | + | 0.0186743i | ||||
\(876\) | −8.91798e13 | −0.172880 | ||||||||
\(877\) | 2.02513e14 | + | 2.02513e14i | 0.390351 | + | 0.390351i | 0.874813 | − | 0.484461i | \(-0.160984\pi\) |
−0.484461 | + | 0.874813i | \(0.660984\pi\) | |||||||
\(878\) | 2.48726e14 | − | 2.48726e14i | 0.476704 | − | 0.476704i | ||||
\(879\) | − | 3.21596e14i | − | 0.612867i | ||||||
\(880\) | −4.79424e14 | + | 1.40704e14i | −0.908462 | + | 0.266620i | ||||
\(881\) | 4.41083e14 | 0.831076 | 0.415538 | − | 0.909576i | \(-0.363593\pi\) | ||||
0.415538 | + | 0.909576i | \(0.363593\pi\) | |||||||
\(882\) | 1.00256e14 | + | 1.00256e14i | 0.187830 | + | 0.187830i | ||||
\(883\) | −5.16406e14 | + | 5.16406e14i | −0.962028 | + | 0.962028i | −0.999305 | − | 0.0372771i | \(-0.988132\pi\) |
0.0372771 | + | 0.999305i | \(0.488132\pi\) | |||||||
\(884\) | − | 2.18790e14i | − | 0.405290i | ||||||
\(885\) | 5.88623e13 | + | 3.21512e13i | 0.108423 | + | 0.0592216i | ||||
\(886\) | −1.21220e14 | −0.222028 | ||||||||
\(887\) | 7.68826e13 | + | 7.68826e13i | 0.140026 | + | 0.140026i | 0.773645 | − | 0.633619i | \(-0.218431\pi\) |
−0.633619 | + | 0.773645i | \(0.718431\pi\) | |||||||
\(888\) | 4.44001e14 | − | 4.44001e14i | 0.804117 | − | 0.804117i | ||||
\(889\) | − | 8.65565e13i | − | 0.155880i | ||||||
\(890\) | 2.98701e14 | − | 5.46861e14i | 0.534917 | − | 0.979325i | ||||
\(891\) | −8.92543e13 | −0.158943 | ||||||||
\(892\) | −1.25812e14 | − | 1.25812e14i | −0.222792 | − | 0.222792i | ||||
\(893\) | −4.06153e13 | + | 4.06153e13i | −0.0715207 | + | 0.0715207i | ||||
\(894\) | 4.30645e14i | 0.754105i | ||||||||
\(895\) | 7.96892e13 | + | 2.71527e14i | 0.138766 | + | 0.472822i | ||||
\(896\) | −6.51182e13 | −0.112762 | ||||||||
\(897\) | −4.15576e14 | − | 4.15576e14i | −0.715630 | − | 0.715630i | ||||
\(898\) | 3.34997e14 | − | 3.34997e14i | 0.573667 | − | 0.573667i | ||||
\(899\) | 2.17976e13i | 0.0371202i | ||||||||
\(900\) | −4.42023e13 | + | 2.83909e13i | −0.0748570 | + | 0.0480802i | ||||
\(901\) | −6.64371e14 | −1.11889 | ||||||||
\(902\) | 1.37013e14 | + | 1.37013e14i | 0.229471 | + | 0.229471i | ||||
\(903\) | −3.71978e13 | + | 3.71978e13i | −0.0619553 | + | 0.0619553i | ||||
\(904\) | 5.31208e14i | 0.879878i | ||||||||
\(905\) | 1.08547e15 | − | 3.18569e14i | 1.78803 | − | 0.524760i | ||||
\(906\) | 2.38466e14 | 0.390648 | ||||||||
\(907\) | −4.66630e14 | − | 4.66630e14i | −0.760215 | − | 0.760215i | 0.216146 | − | 0.976361i | \(-0.430651\pi\) |
−0.976361 | + | 0.216146i | \(0.930651\pi\) | |||||||
\(908\) | −6.25462e13 | + | 6.25462e13i | −0.101338 | + | 0.101338i | ||||
\(909\) | 1.14931e14i | 0.185190i | ||||||||
\(910\) | 1.35247e14 | + | 7.38732e13i | 0.216731 | + | 0.118380i | ||||
\(911\) | 6.14213e14 | 0.978874 | 0.489437 | − | 0.872039i | \(-0.337202\pi\) | ||||
0.489437 | + | 0.872039i | \(0.337202\pi\) | |||||||
\(912\) | −2.22673e13 | − | 2.22673e13i | −0.0352935 | − | 0.0352935i | ||||
\(913\) | 5.34705e14 | − | 5.34705e14i | 0.842870 | − | 0.842870i | ||||
\(914\) | 3.09103e14i | 0.484588i | ||||||||
\(915\) | 1.91741e14 | − | 3.51039e14i | 0.298958 | − | 0.547332i | ||||
\(916\) | −1.51589e14 | −0.235066 | ||||||||
\(917\) | −6.35809e13 | − | 6.35809e13i | −0.0980574 | − | 0.0980574i | ||||
\(918\) | 1.05260e14 | − | 1.05260e14i | 0.161455 | − | 0.161455i | ||||
\(919\) | 5.29233e14i | 0.807364i | 0.914899 | + | 0.403682i | \(0.132270\pi\) | ||||
−0.914899 | + | 0.403682i | \(0.867730\pi\) | |||||||
\(920\) | 3.22053e14 | + | 1.09734e15i | 0.488640 | + | 1.66495i | ||||
\(921\) | 5.34307e14 | 0.806293 | ||||||||
\(922\) | 1.98739e14 | + | 1.98739e14i | 0.298283 | + | 0.298283i | ||||
\(923\) | 9.25675e14 | − | 9.25675e14i | 1.38182 | − | 1.38182i | ||||
\(924\) | 3.90776e13i | 0.0580187i | ||||||||
\(925\) | 1.20148e15 | + | 2.61692e14i | 1.77421 | + | 0.386440i | ||||
\(926\) | −1.05250e14 | −0.154585 | ||||||||
\(927\) | −5.17140e13 | − | 5.17140e13i | −0.0755457 | − | 0.0755457i | ||||
\(928\) | 6.86488e13 | − | 6.86488e13i | 0.0997454 | − | 0.0997454i | ||||
\(929\) | − | 4.26804e14i | − | 0.616808i | −0.951256 | − | 0.308404i | \(-0.900205\pi\) | ||
0.951256 | − | 0.308404i | \(-0.0997948\pi\) | |||||||
\(930\) | 4.49846e13 | − | 1.32023e13i | 0.0646620 | − | 0.0189773i | ||||
\(931\) | 8.50303e13 | 0.121570 | ||||||||
\(932\) | −3.98477e13 | − | 3.98477e13i | −0.0566661 | − | 0.0566661i | ||||
\(933\) | 3.23009e13 | − | 3.23009e13i | 0.0456884 | − | 0.0456884i | ||||
\(934\) | 8.53650e14i | 1.20101i | ||||||||
\(935\) | −1.24312e15 | − | 6.79004e14i | −1.73962 | − | 0.950198i | ||||
\(936\) | 2.84660e14 | 0.396230 | ||||||||
\(937\) | −7.69391e14 | − | 7.69391e14i | −1.06524 | − | 1.06524i | −0.997717 | − | 0.0675269i | \(-0.978489\pi\) |
−0.0675269 | − | 0.997717i | \(-0.521511\pi\) | |||||||
\(938\) | 1.23783e13 | − | 1.23783e13i | 0.0170470 | − | 0.0170470i | ||||
\(939\) | − | 1.23977e14i | − | 0.169829i | ||||||
\(940\) | −7.27111e13 | + | 1.33119e14i | −0.0990744 | + | 0.181385i | ||||
\(941\) | −4.47671e14 | −0.606751 | −0.303376 | − | 0.952871i | \(-0.598114\pi\) | ||||
−0.303376 | + | 0.952871i | \(0.598114\pi\) | |||||||
\(942\) | 4.29463e14 | + | 4.29463e14i | 0.578990 | + | 0.578990i | ||||
\(943\) | 2.23482e14 | − | 2.23482e14i | 0.299699 | − | 0.299699i | ||||
\(944\) | 1.06170e14i | 0.141626i | ||||||||
\(945\) | −1.07501e13 | − | 3.66291e13i | −0.0142644 | − | 0.0486035i | ||||
\(946\) | −5.35035e14 | −0.706198 | ||||||||
\(947\) | 4.56644e14 | + | 4.56644e14i | 0.599553 | + | 0.599553i | 0.940194 | − | 0.340640i | \(-0.110644\pi\) |
−0.340640 | + | 0.940194i | \(0.610644\pi\) | |||||||
\(948\) | −1.31856e14 | + | 1.31856e14i | −0.172211 | + | 0.172211i | ||||
\(949\) | 9.46297e14i | 1.22941i | ||||||||
\(950\) | 1.84168e13 | − | 8.45548e13i | 0.0238010 | − | 0.109275i | ||||
\(951\) | −5.29282e14 | −0.680432 | ||||||||
\(952\) | −2.18752e14 | − | 2.18752e14i | −0.279748 | − | 0.279748i | ||||
\(953\) | 1.31748e14 | − | 1.31748e14i | 0.167602 | − | 0.167602i | −0.618323 | − | 0.785924i | \(-0.712188\pi\) |
0.785924 | + | 0.618323i | \(0.212188\pi\) | |||||||
\(954\) | − | 1.82105e14i | − | 0.230452i | ||||||
\(955\) | −1.43175e15 | + | 4.20198e14i | −1.80240 | + | 0.528978i | ||||
\(956\) | 2.72005e14 | 0.340633 | ||||||||
\(957\) | 1.27646e14 | + | 1.27646e14i | 0.159018 | + | 0.159018i | ||||
\(958\) | −7.20308e13 | + | 7.20308e13i | −0.0892670 | + | 0.0892670i | ||||
\(959\) | − | 3.14245e14i | − | 0.387414i | ||||||
\(960\) | −4.56694e14 | − | 2.49451e14i | −0.560105 | − | 0.305935i | ||||
\(961\) | −8.04396e14 | −0.981416 | ||||||||
\(962\) | −9.92559e14 | − | 9.92559e14i | −1.20471 | − | 1.20471i | ||||
\(963\) | 1.90279e13 | − | 1.90279e13i | 0.0229752 | − | 0.0229752i | ||||
\(964\) | 1.61601e14i | 0.194115i | ||||||||
\(965\) | −5.27359e13 | + | 9.65487e13i | −0.0630187 | + | 0.115374i | ||||
\(966\) | −1.75072e14 | −0.208128 | ||||||||
\(967\) | −8.05270e13 | − | 8.05270e13i | −0.0952378 | − | 0.0952378i | 0.657883 | − | 0.753120i | \(-0.271452\pi\) |
−0.753120 | + | 0.657883i | \(0.771452\pi\) | |||||||
\(968\) | −6.82081e14 | + | 6.82081e14i | −0.802527 | + | 0.802527i | ||||
\(969\) | − | 8.92749e13i | − | 0.104499i | ||||||
\(970\) | 3.31775e13 | + | 1.13047e14i | 0.0386354 | + | 0.131643i | ||||
\(971\) | 6.04346e14 | 0.700148 | 0.350074 | − | 0.936722i | \(-0.386156\pi\) | ||||
0.350074 | + | 0.936722i | \(0.386156\pi\) | |||||||
\(972\) | −1.05043e13 | − | 1.05043e13i | −0.0121070 | − | 0.0121070i | ||||
\(973\) | −3.01632e14 | + | 3.01632e14i | −0.345870 | + | 0.345870i | ||||
\(974\) | 3.00908e14i | 0.343273i | ||||||||
\(975\) | 3.01259e14 | + | 4.69036e14i | 0.341914 | + | 0.532333i | ||||
\(976\) | 6.33170e14 | 0.714943 | ||||||||
\(977\) | −1.18795e15 | − | 1.18795e15i | −1.33452 | − | 1.33452i | −0.901280 | − | 0.433237i | \(-0.857371\pi\) |
−0.433237 | − | 0.901280i | \(-0.642629\pi\) | |||||||
\(978\) | −3.06845e14 | + | 3.06845e14i | −0.342946 | + | 0.342946i | ||||
\(979\) | − | 1.67663e15i | − | 1.86434i | ||||||
\(980\) | 2.15459e14 | − | 6.32340e13i | 0.238360 | − | 0.0699553i | ||||
\(981\) | 3.38222e13 | 0.0372269 | ||||||||
\(982\) | 5.44665e14 | + | 5.44665e14i | 0.596447 | + | 0.596447i | ||||
\(983\) | −3.11566e13 | + | 3.11566e13i | −0.0339455 | + | 0.0339455i | −0.723876 | − | 0.689930i | \(-0.757641\pi\) |
0.689930 | + | 0.723876i | \(0.257641\pi\) | |||||||
\(984\) | 1.53080e14i | 0.165937i | ||||||||
\(985\) | 1.26460e15 | + | 6.90736e14i | 1.36387 | + | 0.744957i | ||||
\(986\) | −3.01073e14 | −0.323063 | ||||||||
\(987\) | −7.79370e13 | − | 7.79370e13i | −0.0832066 | − | 0.0832066i | ||||
\(988\) | 2.54316e13 | − | 2.54316e13i | 0.0270140 | − | 0.0270140i | ||||
\(989\) | 8.72698e14i | 0.922322i | ||||||||
\(990\) | 1.86116e14 | − | 3.40740e14i | 0.195707 | − | 0.358300i | ||||
\(991\) | 2.03999e14 | 0.213432 | 0.106716 | − | 0.994290i | \(-0.465966\pi\) | ||||
0.106716 | + | 0.994290i | \(0.465966\pi\) | |||||||
\(992\) | −4.79714e13 | − | 4.79714e13i | −0.0499372 | − | 0.0499372i | ||||
\(993\) | −6.32582e14 | + | 6.32582e14i | −0.655195 | + | 0.655195i | ||||
\(994\) | − | 3.89963e14i | − | 0.401876i | ||||||
\(995\) | 1.18656e14 | + | 4.04301e14i | 0.121668 | + | 0.414562i | ||||
\(996\) | 1.25859e14 | 0.128406 | ||||||||
\(997\) | 3.47182e14 | + | 3.47182e14i | 0.352437 | + | 0.352437i | 0.861016 | − | 0.508579i | \(-0.169829\pi\) |
−0.508579 | + | 0.861016i | \(0.669829\pi\) | |||||||
\(998\) | −6.17426e13 | + | 6.17426e13i | −0.0623637 | + | 0.0623637i | ||||
\(999\) | 3.47709e14i | 0.349453i |
(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 | 15.11.f.a.7.4 | ✓ | 20 | |
3.2 | odd | 2 | 45.11.g.c.37.7 | 20 | |||
5.2 | odd | 4 | 75.11.f.d.43.7 | 20 | |||
5.3 | odd | 4 | inner | 15.11.f.a.13.4 | yes | 20 | |
5.4 | even | 2 | 75.11.f.d.7.7 | 20 | |||
15.8 | even | 4 | 45.11.g.c.28.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.f.a.7.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
15.11.f.a.13.4 | yes | 20 | 5.3 | odd | 4 | inner | |
45.11.g.c.28.7 | 20 | 15.8 | even | 4 | |||
45.11.g.c.37.7 | 20 | 3.2 | odd | 2 | |||
75.11.f.d.7.7 | 20 | 5.4 | even | 2 | |||
75.11.f.d.43.7 | 20 | 5.2 | odd | 4 |