Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,17,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
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("3.2");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.86973631570\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3814x^{2} + 2981440 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Root | \(33.1293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.17.b.a.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 198.776i | 0.776468i | 0.921561 | + | 0.388234i | \(0.126915\pi\) | ||||
−0.921561 | + | 0.388234i | \(0.873085\pi\) | |||||||
\(3\) | 4343.70 | − | 4917.21i | 0.662048 | − | 0.749461i | ||||
\(4\) | 26024.2 | 0.397098 | ||||||||
\(5\) | 482304.i | 1.23470i | 0.786689 | + | 0.617350i | \(0.211794\pi\) | ||||
−0.786689 | + | 0.617350i | \(0.788206\pi\) | |||||||
\(6\) | 977423. | + | 863422.i | 0.581933 | + | 0.514059i | ||||
\(7\) | 5.53804e6 | 0.960664 | 0.480332 | − | 0.877087i | \(-0.340516\pi\) | ||||
0.480332 | + | 0.877087i | \(0.340516\pi\) | |||||||
\(8\) | 1.81999e7i | 1.08480i | ||||||||
\(9\) | −5.31128e6 | − | 4.27178e7i | −0.123384 | − | 0.992359i | ||||
\(10\) | −9.58704e7 | −0.958704 | ||||||||
\(11\) | − | 1.03813e8i | − | 0.484293i | −0.970240 | − | 0.242147i | \(-0.922148\pi\) | ||
0.970240 | − | 0.242147i | \(-0.0778515\pi\) | |||||||
\(12\) | 1.13041e8 | − | 1.27967e8i | 0.262898 | − | 0.297609i | ||||
\(13\) | −7.54564e7 | −0.0925016 | −0.0462508 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462508 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(14\) | 1.10083e9i | 0.745925i | ||||||||
\(15\) | 2.37159e9 | + | 2.09499e9i | 0.925359 | + | 0.817431i | ||||
\(16\) | −1.91219e9 | −0.445216 | ||||||||
\(17\) | − | 7.90639e9i | − | 1.13341i | −0.823921 | − | 0.566705i | \(-0.808218\pi\) | ||
0.823921 | − | 0.566705i | \(-0.191782\pi\) | |||||||
\(18\) | 8.49126e9 | − | 1.05575e9i | 0.770535 | − | 0.0958038i | ||||
\(19\) | −3.27620e10 | −1.92904 | −0.964521 | − | 0.264004i | \(-0.914957\pi\) | ||||
−0.964521 | + | 0.264004i | \(0.914957\pi\) | |||||||
\(20\) | 1.25516e10i | 0.490296i | ||||||||
\(21\) | 2.40556e10 | − | 2.72317e10i | 0.636006 | − | 0.719980i | ||||
\(22\) | 2.06354e10 | 0.376038 | ||||||||
\(23\) | 4.02817e10i | 0.514381i | 0.966361 | + | 0.257191i | \(0.0827968\pi\) | ||||
−0.966361 | + | 0.257191i | \(0.917203\pi\) | |||||||
\(24\) | 8.94931e10 | + | 7.90551e10i | 0.813017 | + | 0.718191i | ||||
\(25\) | −8.00297e10 | −0.524483 | ||||||||
\(26\) | − | 1.49989e10i | − | 0.0718245i | ||||||
\(27\) | −2.33123e11 | − | 1.59437e11i | −0.825421 | − | 0.564518i | ||||
\(28\) | 1.44123e11 | 0.381477 | ||||||||
\(29\) | − | 6.12299e11i | − | 1.22400i | −0.790859 | − | 0.611998i | \(-0.790366\pi\) | ||
0.790859 | − | 0.611998i | \(-0.209634\pi\) | |||||||
\(30\) | −4.16432e11 | + | 4.71416e11i | −0.634709 | + | 0.718512i | ||||
\(31\) | 5.76962e11 | 0.676477 | 0.338239 | − | 0.941060i | \(-0.390169\pi\) | ||||
0.338239 | + | 0.941060i | \(0.390169\pi\) | |||||||
\(32\) | 8.12655e11i | 0.739106i | ||||||||
\(33\) | −5.10469e11 | − | 4.50931e11i | −0.362959 | − | 0.320626i | ||||
\(34\) | 1.57160e12 | 0.880056 | ||||||||
\(35\) | 2.67102e12i | 1.18613i | ||||||||
\(36\) | −1.38222e11 | − | 1.11170e12i | −0.0489955 | − | 0.394063i | ||||
\(37\) | −2.03746e11 | −0.0580063 | −0.0290032 | − | 0.999579i | \(-0.509233\pi\) | ||||
−0.0290032 | + | 0.999579i | \(0.509233\pi\) | |||||||
\(38\) | − | 6.51230e12i | − | 1.49784i | ||||||
\(39\) | −3.27760e11 | + | 3.71035e11i | −0.0612405 | + | 0.0693264i | ||||
\(40\) | −8.77792e12 | −1.33940 | ||||||||
\(41\) | 2.51630e12i | 0.315131i | 0.987509 | + | 0.157566i | \(0.0503646\pi\) | ||||
−0.987509 | + | 0.157566i | \(0.949635\pi\) | |||||||
\(42\) | 5.41300e12 | + | 4.78166e12i | 0.559042 | + | 0.493838i | ||||
\(43\) | 2.81005e12 | 0.240418 | 0.120209 | − | 0.992749i | \(-0.461644\pi\) | ||||
0.120209 | + | 0.992749i | \(0.461644\pi\) | |||||||
\(44\) | − | 2.70164e12i | − | 0.192312i | ||||||
\(45\) | 2.06030e13 | − | 2.56165e12i | 1.22527 | − | 0.152342i | ||||
\(46\) | −8.00702e12 | −0.399400 | ||||||||
\(47\) | 1.80566e13i | 0.758320i | 0.925331 | + | 0.379160i | \(0.123787\pi\) | ||||
−0.925331 | + | 0.379160i | \(0.876213\pi\) | |||||||
\(48\) | −8.30597e12 | + | 9.40263e12i | −0.294754 | + | 0.333672i | ||||
\(49\) | −2.56309e12 | −0.0771250 | ||||||||
\(50\) | − | 1.59080e13i | − | 0.407244i | ||||||
\(51\) | −3.88774e13 | − | 3.43430e13i | −0.849447 | − | 0.750372i | ||||
\(52\) | −1.96369e12 | −0.0367322 | ||||||||
\(53\) | − | 2.59324e13i | − | 0.416519i | −0.978074 | − | 0.208260i | \(-0.933220\pi\) | ||
0.978074 | − | 0.208260i | \(-0.0667799\pi\) | |||||||
\(54\) | 3.16921e13 | − | 4.63392e13i | 0.438330 | − | 0.640913i | ||||
\(55\) | 5.00693e13 | 0.597957 | ||||||||
\(56\) | 1.00792e14i | 1.04213i | ||||||||
\(57\) | −1.42308e14 | + | 1.61098e14i | −1.27712 | + | 1.44574i | ||||
\(58\) | 1.21710e14 | 0.950393 | ||||||||
\(59\) | − | 1.63379e14i | − | 1.11270i | −0.830947 | − | 0.556352i | \(-0.812201\pi\) | ||
0.830947 | − | 0.556352i | \(-0.187799\pi\) | |||||||
\(60\) | 6.17188e13 | + | 5.45203e13i | 0.367458 | + | 0.324600i | ||||
\(61\) | 7.04936e13 | 0.367715 | 0.183857 | − | 0.982953i | \(-0.441142\pi\) | ||||
0.183857 | + | 0.982953i | \(0.441142\pi\) | |||||||
\(62\) | 1.14686e14i | 0.525263i | ||||||||
\(63\) | −2.94141e13 | − | 2.36573e14i | −0.118531 | − | 0.953323i | ||||
\(64\) | −2.86853e14 | −1.01911 | ||||||||
\(65\) | − | 3.63930e13i | − | 0.114212i | ||||||
\(66\) | 8.96341e13 | − | 1.01469e14i | 0.248955 | − | 0.281826i | ||||
\(67\) | −1.75368e14 | −0.431869 | −0.215934 | − | 0.976408i | \(-0.569280\pi\) | ||||
−0.215934 | + | 0.976408i | \(0.569280\pi\) | |||||||
\(68\) | − | 2.05757e14i | − | 0.450074i | ||||||
\(69\) | 1.98074e14 | + | 1.74972e14i | 0.385509 | + | 0.340545i | ||||
\(70\) | −5.30934e14 | −0.920993 | ||||||||
\(71\) | 6.72953e14i | 1.04212i | 0.853520 | + | 0.521060i | \(0.174463\pi\) | ||||
−0.853520 | + | 0.521060i | \(0.825537\pi\) | |||||||
\(72\) | 7.77462e14 | − | 9.66650e13i | 1.07651 | − | 0.133847i | ||||
\(73\) | 1.04423e15 | 1.29483 | 0.647416 | − | 0.762137i | \(-0.275850\pi\) | ||||
0.647416 | + | 0.762137i | \(0.275850\pi\) | |||||||
\(74\) | − | 4.04998e13i | − | 0.0450401i | ||||||
\(75\) | −3.47625e14 | + | 3.93523e14i | −0.347233 | + | 0.393079i | ||||
\(76\) | −8.52605e14 | −0.766018 | ||||||||
\(77\) | − | 5.74918e14i | − | 0.465243i | ||||||
\(78\) | −7.37528e13 | − | 6.51507e13i | −0.0538297 | − | 0.0475513i | ||||
\(79\) | 4.55899e13 | 0.0300505 | 0.0150252 | − | 0.999887i | \(-0.495217\pi\) | ||||
0.0150252 | + | 0.999887i | \(0.495217\pi\) | |||||||
\(80\) | − | 9.22256e14i | − | 0.549708i | ||||||
\(81\) | −1.79660e15 | + | 4.53772e14i | −0.969553 | + | 0.244883i | ||||
\(82\) | −5.00180e14 | −0.244689 | ||||||||
\(83\) | − | 3.65326e14i | − | 0.162202i | −0.996706 | − | 0.0811009i | \(-0.974156\pi\) | ||
0.996706 | − | 0.0811009i | \(-0.0258436\pi\) | |||||||
\(84\) | 6.26027e14 | − | 7.08683e14i | 0.252556 | − | 0.285902i | ||||
\(85\) | 3.81329e15 | 1.39942 | ||||||||
\(86\) | 5.58570e14i | 0.186677i | ||||||||
\(87\) | −3.01081e15 | − | 2.65964e15i | −0.917337 | − | 0.810344i | ||||
\(88\) | 1.88938e15 | 0.525362 | ||||||||
\(89\) | 6.68789e15i | 1.69891i | 0.527665 | + | 0.849453i | \(0.323068\pi\) | ||||
−0.527665 | + | 0.849453i | \(0.676932\pi\) | |||||||
\(90\) | 5.09195e14 | + | 4.09537e15i | 0.118289 | + | 0.951379i | ||||
\(91\) | −4.17880e14 | −0.0888630 | ||||||||
\(92\) | 1.04830e15i | 0.204260i | ||||||||
\(93\) | 2.50615e15 | − | 2.83704e15i | 0.447861 | − | 0.506994i | ||||
\(94\) | −3.58921e15 | −0.588811 | ||||||||
\(95\) | − | 1.58013e16i | − | 2.38179i | ||||||
\(96\) | 3.99600e15 | + | 3.52993e15i | 0.553931 | + | 0.489324i | ||||
\(97\) | −5.40349e15 | −0.689446 | −0.344723 | − | 0.938704i | \(-0.612027\pi\) | ||||
−0.344723 | + | 0.938704i | \(0.612027\pi\) | |||||||
\(98\) | − | 5.09480e14i | − | 0.0598851i | ||||||
\(99\) | −4.43465e15 | + | 5.51378e14i | −0.480593 | + | 0.0597541i | ||||
\(100\) | −2.08271e15 | −0.208271 | ||||||||
\(101\) | 1.22011e16i | 1.12675i | 0.826202 | + | 0.563374i | \(0.190497\pi\) | ||||
−0.826202 | + | 0.563374i | \(0.809503\pi\) | |||||||
\(102\) | 6.82655e15 | − | 7.72789e15i | 0.582640 | − | 0.659568i | ||||
\(103\) | −9.05312e15 | −0.714662 | −0.357331 | − | 0.933978i | \(-0.616313\pi\) | ||||
−0.357331 | + | 0.933978i | \(0.616313\pi\) | |||||||
\(104\) | − | 1.37330e15i | − | 0.100346i | ||||||
\(105\) | 1.31340e16 | + | 1.16021e16i | 0.888959 | + | 0.785276i | ||||
\(106\) | 5.15473e15 | 0.323414 | ||||||||
\(107\) | − | 6.69296e14i | − | 0.0389537i | −0.999810 | − | 0.0194768i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194768i | \(-0.00620006\pi\) | |||||||
\(108\) | −6.06684e15 | − | 4.14921e15i | −0.327773 | − | 0.224169i | ||||
\(109\) | 2.32335e16 | 1.16601 | 0.583004 | − | 0.812469i | \(-0.301877\pi\) | ||||
0.583004 | + | 0.812469i | \(0.301877\pi\) | |||||||
\(110\) | 9.95256e15i | 0.464294i | ||||||||
\(111\) | −8.85012e14 | + | 1.00186e15i | −0.0384030 | + | 0.0434735i | ||||
\(112\) | −1.05898e16 | −0.427703 | ||||||||
\(113\) | 7.46562e15i | 0.280827i | 0.990093 | + | 0.140413i | \(0.0448431\pi\) | ||||
−0.990093 | + | 0.140413i | \(0.955157\pi\) | |||||||
\(114\) | −3.20224e16 | − | 2.82875e16i | −1.12257 | − | 0.991642i | ||||
\(115\) | −1.94280e16 | −0.635106 | ||||||||
\(116\) | − | 1.59346e16i | − | 0.486046i | ||||||
\(117\) | 4.00770e14 | + | 3.22333e15i | 0.0114132 | + | 0.0917948i | ||||
\(118\) | 3.24757e16 | 0.863979 | ||||||||
\(119\) | − | 4.37859e16i | − | 1.08883i | ||||||
\(120\) | −3.81286e16 | + | 4.31629e16i | −0.886750 | + | 1.00383i | ||||
\(121\) | 3.51727e16 | 0.765460 | ||||||||
\(122\) | 1.40124e16i | 0.285519i | ||||||||
\(123\) | 1.23732e16 | + | 1.09301e16i | 0.236179 | + | 0.208632i | ||||
\(124\) | 1.50150e16 | 0.268628 | ||||||||
\(125\) | 3.49951e16i | 0.587121i | ||||||||
\(126\) | 4.70249e16 | − | 5.84680e15i | 0.740225 | − | 0.0920352i | ||||
\(127\) | −3.26265e16 | −0.482104 | −0.241052 | − | 0.970512i | \(-0.577492\pi\) | ||||
−0.241052 | + | 0.970512i | \(0.577492\pi\) | |||||||
\(128\) | − | 3.76130e15i | − | 0.0521986i | ||||||
\(129\) | 1.22060e16 | − | 1.38176e16i | 0.159168 | − | 0.180184i | ||||
\(130\) | 7.23404e15 | 0.0886817 | ||||||||
\(131\) | 8.12417e16i | 0.936717i | 0.883538 | + | 0.468359i | \(0.155154\pi\) | ||||
−0.883538 | + | 0.468359i | \(0.844846\pi\) | |||||||
\(132\) | −1.32845e16 | − | 1.17351e16i | −0.144130 | − | 0.127320i | ||||
\(133\) | −1.81437e17 | −1.85316 | ||||||||
\(134\) | − | 3.48589e16i | − | 0.335332i | ||||||
\(135\) | 7.68970e16 | − | 1.12436e17i | 0.697010 | − | 1.01915i | ||||
\(136\) | 1.43896e17 | 1.22952 | ||||||||
\(137\) | − | 1.67072e17i | − | 1.34629i | −0.739511 | − | 0.673145i | \(-0.764943\pi\) | ||
0.739511 | − | 0.673145i | \(-0.235057\pi\) | |||||||
\(138\) | −3.47801e16 | + | 3.93723e16i | −0.264422 | + | 0.299335i | ||||
\(139\) | −1.60035e17 | −1.14841 | −0.574203 | − | 0.818713i | \(-0.694688\pi\) | ||||
−0.574203 | + | 0.818713i | \(0.694688\pi\) | |||||||
\(140\) | 6.95111e16i | 0.471010i | ||||||||
\(141\) | 8.87881e16 | + | 7.84324e16i | 0.568332 | + | 0.502045i | ||||
\(142\) | −1.33767e17 | −0.809173 | ||||||||
\(143\) | 7.83332e15i | 0.0447979i | ||||||||
\(144\) | 1.01562e16 | + | 8.16844e16i | 0.0549325 | + | 0.441814i | ||||
\(145\) | 2.95315e17 | 1.51127 | ||||||||
\(146\) | 2.07568e17i | 1.00540i | ||||||||
\(147\) | −1.11333e16 | + | 1.26033e16i | −0.0510604 | + | 0.0578022i | ||||
\(148\) | −5.30233e15 | −0.0230342 | ||||||||
\(149\) | 5.03915e16i | 0.207428i | 0.994607 | + | 0.103714i | \(0.0330726\pi\) | ||||
−0.994607 | + | 0.103714i | \(0.966927\pi\) | |||||||
\(150\) | −7.82229e16 | − | 6.90994e16i | −0.305214 | − | 0.269615i | ||||
\(151\) | 2.76836e17 | 1.02425 | 0.512127 | − | 0.858910i | \(-0.328858\pi\) | ||||
0.512127 | + | 0.858910i | \(0.328858\pi\) | |||||||
\(152\) | − | 5.96267e17i | − | 2.09263i | ||||||
\(153\) | −3.37744e17 | + | 4.19931e16i | −1.12475 | + | 0.139845i | ||||
\(154\) | 1.14280e17 | 0.361246 | ||||||||
\(155\) | 2.78271e17i | 0.835246i | ||||||||
\(156\) | −8.52969e15 | + | 9.65590e15i | −0.0243185 | + | 0.0275293i | ||||
\(157\) | −3.20791e17 | −0.869011 | −0.434506 | − | 0.900669i | \(-0.643077\pi\) | ||||
−0.434506 | + | 0.900669i | \(0.643077\pi\) | |||||||
\(158\) | 9.06216e15i | 0.0233332i | ||||||||
\(159\) | −1.27515e17 | − | 1.12642e17i | −0.312165 | − | 0.275756i | ||||
\(160\) | −3.91947e17 | −0.912573 | ||||||||
\(161\) | 2.23081e17i | 0.494147i | ||||||||
\(162\) | −9.01990e16 | − | 3.57121e17i | −0.190144 | − | 0.752827i | ||||
\(163\) | 8.96440e17 | 1.79895 | 0.899477 | − | 0.436967i | \(-0.143947\pi\) | ||||
0.899477 | + | 0.436967i | \(0.143947\pi\) | |||||||
\(164\) | 6.54847e16i | 0.125138i | ||||||||
\(165\) | 2.17486e17 | − | 2.46201e17i | 0.395876 | − | 0.448145i | ||||
\(166\) | 7.26179e16 | 0.125945 | ||||||||
\(167\) | − | 1.19275e17i | − | 0.197159i | −0.995129 | − | 0.0985795i | \(-0.968570\pi\) | ||
0.995129 | − | 0.0985795i | \(-0.0314299\pi\) | |||||||
\(168\) | 4.95616e17 | + | 4.37810e17i | 0.781036 | + | 0.689940i | ||||
\(169\) | −6.59723e17 | −0.991443 | ||||||||
\(170\) | 7.57989e17i | 1.08660i | ||||||||
\(171\) | 1.74008e17 | + | 1.39952e18i | 0.238013 | + | 1.91430i | ||||
\(172\) | 7.31292e16 | 0.0954693 | ||||||||
\(173\) | − | 1.37077e18i | − | 1.70843i | −0.519922 | − | 0.854214i | \(-0.674039\pi\) | ||
0.519922 | − | 0.854214i | \(-0.325961\pi\) | |||||||
\(174\) | 5.28673e17 | − | 5.98476e17i | 0.629206 | − | 0.712283i | ||||
\(175\) | −4.43207e17 | −0.503852 | ||||||||
\(176\) | 1.98509e17i | 0.215615i | ||||||||
\(177\) | −8.03369e17 | − | 7.09668e17i | −0.833928 | − | 0.736664i | ||||
\(178\) | −1.32939e18 | −1.31915 | ||||||||
\(179\) | − | 1.29943e17i | − | 0.123290i | −0.998098 | − | 0.0616451i | \(-0.980365\pi\) | ||
0.998098 | − | 0.0616451i | \(-0.0196347\pi\) | |||||||
\(180\) | 5.36176e17 | − | 6.66650e16i | 0.486550 | − | 0.0604948i | ||||
\(181\) | 1.06449e18 | 0.924090 | 0.462045 | − | 0.886857i | \(-0.347116\pi\) | ||||
0.462045 | + | 0.886857i | \(0.347116\pi\) | |||||||
\(182\) | − | 8.30645e16i | − | 0.0689992i | ||||||
\(183\) | 3.06203e17 | − | 3.46632e17i | 0.243445 | − | 0.275588i | ||||
\(184\) | −7.33125e17 | −0.558001 | ||||||||
\(185\) | − | 9.82676e16i | − | 0.0716204i | ||||||
\(186\) | 5.63936e17 | + | 4.98161e17i | 0.393664 | + | 0.347749i | ||||
\(187\) | −8.20783e17 | −0.548903 | ||||||||
\(188\) | 4.69908e17i | 0.301127i | ||||||||
\(189\) | −1.29104e18 | − | 8.82965e17i | −0.792952 | − | 0.542312i | ||||
\(190\) | 3.14091e18 | 1.84938 | ||||||||
\(191\) | 2.28288e18i | 1.28889i | 0.764649 | + | 0.644447i | \(0.222912\pi\) | ||||
−0.764649 | + | 0.644447i | \(0.777088\pi\) | |||||||
\(192\) | −1.24600e18 | + | 1.41052e18i | −0.674698 | + | 0.763782i | ||||
\(193\) | 1.20324e18 | 0.625019 | 0.312509 | − | 0.949915i | \(-0.398830\pi\) | ||||
0.312509 | + | 0.949915i | \(0.398830\pi\) | |||||||
\(194\) | − | 1.07408e18i | − | 0.535332i | ||||||
\(195\) | −1.78952e17 | − | 1.58080e17i | −0.0855972 | − | 0.0756137i | ||||
\(196\) | −6.67023e16 | −0.0306261 | ||||||||
\(197\) | 1.11597e18i | 0.491951i | 0.969276 | + | 0.245976i | \(0.0791083\pi\) | ||||
−0.969276 | + | 0.245976i | \(0.920892\pi\) | |||||||
\(198\) | −1.09601e17 | − | 8.81500e17i | −0.0463971 | − | 0.373165i | ||||
\(199\) | 1.79444e18 | 0.729632 | 0.364816 | − | 0.931080i | \(-0.381132\pi\) | ||||
0.364816 | + | 0.931080i | \(0.381132\pi\) | |||||||
\(200\) | − | 1.45654e18i | − | 0.568960i | ||||||
\(201\) | −7.61746e17 | + | 8.62322e17i | −0.285918 | + | 0.323669i | ||||
\(202\) | −2.42528e18 | −0.874884 | ||||||||
\(203\) | − | 3.39094e18i | − | 1.17585i | ||||||
\(204\) | −1.01175e18 | − | 8.93748e17i | −0.337313 | − | 0.297971i | ||||
\(205\) | −1.21362e18 | −0.389093 | ||||||||
\(206\) | − | 1.79954e18i | − | 0.554912i | ||||||
\(207\) | 1.72075e18 | − | 2.13947e17i | 0.510451 | − | 0.0634664i | ||||
\(208\) | 1.44287e17 | 0.0411832 | ||||||||
\(209\) | 3.40111e18i | 0.934223i | ||||||||
\(210\) | −2.30622e18 | + | 2.61072e18i | −0.609742 | + | 0.690248i | ||||
\(211\) | −1.86500e18 | −0.474699 | −0.237350 | − | 0.971424i | \(-0.576279\pi\) | ||||
−0.237350 | + | 0.971424i | \(0.576279\pi\) | |||||||
\(212\) | − | 6.74869e17i | − | 0.165399i | ||||||
\(213\) | 3.30905e18 | + | 2.92311e18i | 0.781029 | + | 0.689934i | ||||
\(214\) | 1.33040e17 | 0.0302463 | ||||||||
\(215\) | 1.35530e18i | 0.296843i | ||||||||
\(216\) | 2.90174e18 | − | 4.24283e18i | 0.612390 | − | 0.895418i | ||||
\(217\) | 3.19523e18 | 0.649867 | ||||||||
\(218\) | 4.61825e18i | 0.905368i | ||||||||
\(219\) | 4.53582e18 | − | 5.13470e18i | 0.857241 | − | 0.970426i | ||||
\(220\) | 1.30301e18 | 0.237447 | ||||||||
\(221\) | 5.96588e17i | 0.104842i | ||||||||
\(222\) | −1.99146e17 | − | 1.75919e17i | −0.0337558 | − | 0.0298187i | ||||
\(223\) | −1.06591e19 | −1.74293 | −0.871465 | − | 0.490458i | \(-0.836829\pi\) | ||||
−0.871465 | + | 0.490458i | \(0.836829\pi\) | |||||||
\(224\) | 4.50051e18i | 0.710032i | ||||||||
\(225\) | 4.25060e17 | + | 3.41869e18i | 0.0647128 | + | 0.520475i | ||||
\(226\) | −1.48398e18 | −0.218053 | ||||||||
\(227\) | − | 8.51142e18i | − | 1.20724i | −0.797271 | − | 0.603622i | \(-0.793724\pi\) | ||
0.797271 | − | 0.603622i | \(-0.206276\pi\) | |||||||
\(228\) | −3.70346e18 | + | 4.19244e18i | −0.507141 | + | 0.574101i | ||||
\(229\) | −2.44574e18 | −0.323390 | −0.161695 | − | 0.986841i | \(-0.551696\pi\) | ||||
−0.161695 | + | 0.986841i | \(0.551696\pi\) | |||||||
\(230\) | − | 3.86182e18i | − | 0.493139i | ||||||
\(231\) | −2.82699e18 | − | 2.49727e18i | −0.348682 | − | 0.308013i | ||||
\(232\) | 1.11438e19 | 1.32779 | ||||||||
\(233\) | − | 8.15863e18i | − | 0.939226i | −0.882872 | − | 0.469613i | \(-0.844393\pi\) | ||
0.882872 | − | 0.469613i | \(-0.155607\pi\) | |||||||
\(234\) | −6.40720e17 | + | 7.96634e16i | −0.0712757 | + | 0.00886200i | ||||
\(235\) | −8.70877e18 | −0.936298 | ||||||||
\(236\) | − | 4.25180e18i | − | 0.441852i | ||||||
\(237\) | 1.98029e17 | − | 2.24175e17i | 0.0198949 | − | 0.0225217i | ||||
\(238\) | 8.70357e18 | 0.845438 | ||||||||
\(239\) | 1.59803e19i | 1.50107i | 0.660828 | + | 0.750537i | \(0.270205\pi\) | ||||
−0.660828 | + | 0.750537i | \(0.729795\pi\) | |||||||
\(240\) | −4.53493e18 | − | 4.00600e18i | −0.411985 | − | 0.363933i | ||||
\(241\) | 1.54187e19 | 1.35491 | 0.677456 | − | 0.735564i | \(-0.263083\pi\) | ||||
0.677456 | + | 0.735564i | \(0.263083\pi\) | |||||||
\(242\) | 6.99148e18i | 0.594355i | ||||||||
\(243\) | −5.57260e18 | + | 1.08053e19i | −0.458361 | + | 0.888766i | ||||
\(244\) | 1.83454e18 | 0.146019 | ||||||||
\(245\) | − | 1.23619e18i | − | 0.0952261i | ||||||
\(246\) | −2.17263e18 | + | 2.45949e18i | −0.161996 | + | 0.183385i | ||||
\(247\) | 2.47210e18 | 0.178440 | ||||||||
\(248\) | 1.05007e19i | 0.733844i | ||||||||
\(249\) | −1.79639e18 | − | 1.58687e18i | −0.121564 | − | 0.107385i | ||||
\(250\) | −6.95618e18 | −0.455880 | ||||||||
\(251\) | − | 2.32208e19i | − | 1.47396i | −0.675912 | − | 0.736982i | \(-0.736250\pi\) | ||
0.675912 | − | 0.736982i | \(-0.263750\pi\) | |||||||
\(252\) | −7.65477e17 | − | 6.15661e18i | −0.0470682 | − | 0.378563i | ||||
\(253\) | 4.18175e18 | 0.249111 | ||||||||
\(254\) | − | 6.48536e18i | − | 0.374338i | ||||||
\(255\) | 1.65638e19 | − | 1.87508e19i | 0.926484 | − | 1.04881i | ||||
\(256\) | −1.80516e19 | −0.978577 | ||||||||
\(257\) | 2.25664e19i | 1.18576i | 0.805290 | + | 0.592881i | \(0.202010\pi\) | ||||
−0.805290 | + | 0.592881i | \(0.797990\pi\) | |||||||
\(258\) | 2.74661e18 | + | 2.42626e18i | 0.139907 | + | 0.123589i | ||||
\(259\) | −1.12835e18 | −0.0557246 | ||||||||
\(260\) | − | 9.47097e17i | − | 0.0453532i | ||||||
\(261\) | −2.61561e19 | + | 3.25209e18i | −1.21464 | + | 0.151022i | ||||
\(262\) | −1.61489e19 | −0.727331 | ||||||||
\(263\) | − | 2.26673e18i | − | 0.0990272i | −0.998773 | − | 0.0495136i | \(-0.984233\pi\) | ||
0.998773 | − | 0.0495136i | \(-0.0157671\pi\) | |||||||
\(264\) | 8.20691e18 | − | 9.29050e18i | 0.347815 | − | 0.393739i | ||||
\(265\) | 1.25073e19 | 0.514276 | ||||||||
\(266\) | − | 3.60653e19i | − | 1.43892i | ||||||
\(267\) | 3.28858e19 | + | 2.90502e19i | 1.27326 | + | 1.12476i | ||||
\(268\) | −4.56381e18 | −0.171494 | ||||||||
\(269\) | 2.50953e19i | 0.915323i | 0.889126 | + | 0.457662i | \(0.151313\pi\) | ||||
−0.889126 | + | 0.457662i | \(0.848687\pi\) | |||||||
\(270\) | 2.23496e19 | + | 1.52853e19i | 0.791335 | + | 0.541206i | ||||
\(271\) | −4.19713e19 | −1.44277 | −0.721387 | − | 0.692532i | \(-0.756495\pi\) | ||||
−0.721387 | + | 0.692532i | \(0.756495\pi\) | |||||||
\(272\) | 1.51185e19i | 0.504612i | ||||||||
\(273\) | −1.81515e18 | + | 2.05481e18i | −0.0588316 | + | 0.0665993i | ||||
\(274\) | 3.32098e19 | 1.04535 | ||||||||
\(275\) | 8.30809e18i | 0.254004i | ||||||||
\(276\) | 5.15471e18 | + | 4.55349e18i | 0.153085 | + | 0.135230i | ||||
\(277\) | 4.25589e19 | 1.22787 | 0.613934 | − | 0.789357i | \(-0.289586\pi\) | ||||
0.613934 | + | 0.789357i | \(0.289586\pi\) | |||||||
\(278\) | − | 3.18110e19i | − | 0.891700i | ||||||
\(279\) | −3.06440e18 | − | 2.46465e19i | −0.0834666 | − | 0.671308i | ||||
\(280\) | −4.86124e19 | −1.28672 | ||||||||
\(281\) | − | 1.12360e19i | − | 0.289041i | −0.989502 | − | 0.144520i | \(-0.953836\pi\) | ||
0.989502 | − | 0.144520i | \(-0.0461639\pi\) | |||||||
\(282\) | −1.55905e19 | + | 1.76489e19i | −0.389822 | + | 0.441291i | ||||
\(283\) | 1.09842e19 | 0.266978 | 0.133489 | − | 0.991050i | \(-0.457382\pi\) | ||||
0.133489 | + | 0.991050i | \(0.457382\pi\) | |||||||
\(284\) | 1.75131e19i | 0.413824i | ||||||||
\(285\) | −7.76982e19 | − | 6.86360e19i | −1.78506 | − | 1.57686i | ||||
\(286\) | −1.55708e18 | −0.0347841 | ||||||||
\(287\) | 1.39354e19i | 0.302735i | ||||||||
\(288\) | 3.47148e19 | − | 4.31624e18i | 0.733458 | − | 0.0911939i | ||||
\(289\) | −1.38498e19 | −0.284618 | ||||||||
\(290\) | 5.87014e19i | 1.17345i | ||||||||
\(291\) | −2.34711e19 | + | 2.65701e19i | −0.456446 | + | 0.516713i | ||||
\(292\) | 2.71752e19 | 0.514175 | ||||||||
\(293\) | − | 9.07495e19i | − | 1.67072i | −0.549704 | − | 0.835359i | \(-0.685260\pi\) | ||
0.549704 | − | 0.835359i | \(-0.314740\pi\) | |||||||
\(294\) | −2.50522e18 | − | 2.21303e18i | −0.0448815 | − | 0.0396468i | ||||
\(295\) | 7.87983e19 | 1.37385 | ||||||||
\(296\) | − | 3.70817e18i | − | 0.0629254i | ||||||
\(297\) | −1.65515e19 | + | 2.42011e19i | −0.273392 | + | 0.399746i | ||||
\(298\) | −1.00166e19 | −0.161061 | ||||||||
\(299\) | − | 3.03951e18i | − | 0.0475811i | ||||||
\(300\) | −9.04666e18 | + | 1.02411e19i | −0.137885 | + | 0.156091i | ||||
\(301\) | 1.55622e19 | 0.230960 | ||||||||
\(302\) | 5.50283e19i | 0.795300i | ||||||||
\(303\) | 5.99953e19 | + | 5.29978e19i | 0.844454 | + | 0.745962i | ||||
\(304\) | 6.26471e19 | 0.858840 | ||||||||
\(305\) | 3.39994e19i | 0.454017i | ||||||||
\(306\) | −8.34720e18 | − | 6.71353e19i | −0.108585 | − | 0.873332i | ||||
\(307\) | −9.03091e19 | −1.14452 | −0.572262 | − | 0.820071i | \(-0.693934\pi\) | ||||
−0.572262 | + | 0.820071i | \(0.693934\pi\) | |||||||
\(308\) | − | 1.49618e19i | − | 0.184747i | ||||||
\(309\) | −3.93240e19 | + | 4.45161e19i | −0.473141 | + | 0.535611i | ||||
\(310\) | −5.53136e19 | −0.648542 | ||||||||
\(311\) | 2.45372e19i | 0.280377i | 0.990125 | + | 0.140188i | \(0.0447708\pi\) | ||||
−0.990125 | + | 0.140188i | \(0.955229\pi\) | |||||||
\(312\) | −6.75282e18 | − | 5.96521e18i | −0.0752053 | − | 0.0664338i | ||||
\(313\) | −3.08699e19 | −0.335104 | −0.167552 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167552 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(314\) | − | 6.37655e19i | − | 0.674759i | ||||||
\(315\) | 1.14100e20 | − | 1.41865e19i | 1.17707 | − | 0.146350i | ||||
\(316\) | 1.18644e18 | 0.0119330 | ||||||||
\(317\) | − | 1.73419e20i | − | 1.70068i | −0.526235 | − | 0.850339i | \(-0.676397\pi\) | ||
0.526235 | − | 0.850339i | \(-0.323603\pi\) | |||||||
\(318\) | 2.23906e19 | − | 2.53469e19i | 0.214116 | − | 0.242386i | ||||
\(319\) | −6.35644e19 | −0.592773 | ||||||||
\(320\) | − | 1.38351e20i | − | 1.25829i | ||||||
\(321\) | −3.29107e18 | − | 2.90722e18i | −0.0291942 | − | 0.0257892i | ||||
\(322\) | −4.43432e19 | −0.383690 | ||||||||
\(323\) | 2.59029e20i | 2.18640i | ||||||||
\(324\) | −4.67551e19 | + | 1.18091e19i | −0.385007 | + | 0.0972423i | ||||
\(325\) | 6.03876e18 | 0.0485155 | ||||||||
\(326\) | 1.78190e20i | 1.39683i | ||||||||
\(327\) | 1.00919e20 | − | 1.14244e20i | 0.771954 | − | 0.873878i | ||||
\(328\) | −4.57965e19 | −0.341855 | ||||||||
\(329\) | 9.99980e19i | 0.728491i | ||||||||
\(330\) | 4.89389e19 | + | 4.32309e19i | 0.347970 | + | 0.307385i | ||||
\(331\) | 2.49632e19 | 0.173251 | 0.0866256 | − | 0.996241i | \(-0.472392\pi\) | ||||
0.0866256 | + | 0.996241i | \(0.472392\pi\) | |||||||
\(332\) | − | 9.50731e18i | − | 0.0644100i | ||||||
\(333\) | 1.08215e18 | + | 8.70358e18i | 0.00715706 | + | 0.0575631i | ||||
\(334\) | 2.37089e19 | 0.153088 | ||||||||
\(335\) | − | 8.45808e19i | − | 0.533228i | ||||||
\(336\) | −4.59987e19 | + | 5.20721e19i | −0.283160 | + | 0.320547i | ||||
\(337\) | 2.29644e20 | 1.38043 | 0.690217 | − | 0.723602i | \(-0.257515\pi\) | ||||
0.690217 | + | 0.723602i | \(0.257515\pi\) | |||||||
\(338\) | − | 1.31137e20i | − | 0.769824i | ||||||
\(339\) | 3.67100e19 | + | 3.24284e19i | 0.210469 | + | 0.185921i | ||||
\(340\) | 9.92377e19 | 0.555707 | ||||||||
\(341\) | − | 5.98959e19i | − | 0.327614i | ||||||
\(342\) | −2.78191e20 | + | 3.45886e19i | −1.48639 | + | 0.184810i | ||||
\(343\) | −1.98240e20 | −1.03476 | ||||||||
\(344\) | 5.11427e19i | 0.260805i | ||||||||
\(345\) | −8.43896e19 | + | 9.55318e19i | −0.420471 | + | 0.475987i | ||||
\(346\) | 2.72476e20 | 1.32654 | ||||||||
\(347\) | − | 2.23524e20i | − | 1.06338i | −0.846939 | − | 0.531690i | \(-0.821557\pi\) | ||
0.846939 | − | 0.531690i | \(-0.178443\pi\) | |||||||
\(348\) | −7.83539e19 | − | 6.92151e19i | −0.364273 | − | 0.321786i | ||||
\(349\) | −2.27023e20 | −1.03149 | −0.515747 | − | 0.856741i | \(-0.672486\pi\) | ||||
−0.515747 | + | 0.856741i | \(0.672486\pi\) | |||||||
\(350\) | − | 8.80989e19i | − | 0.391225i | ||||||
\(351\) | 1.75906e19 | + | 1.20305e19i | 0.0763528 | + | 0.0522188i | ||||
\(352\) | 8.43638e19 | 0.357944 | ||||||||
\(353\) | 2.03750e20i | 0.845085i | 0.906343 | + | 0.422543i | \(0.138862\pi\) | ||||
−0.906343 | + | 0.422543i | \(0.861138\pi\) | |||||||
\(354\) | 1.41065e20 | − | 1.59690e20i | 0.571996 | − | 0.647519i | ||||
\(355\) | −3.24568e20 | −1.28671 | ||||||||
\(356\) | 1.74047e20i | 0.674631i | ||||||||
\(357\) | −2.15305e20 | − | 1.90193e20i | −0.816033 | − | 0.720855i | ||||
\(358\) | 2.58295e19 | 0.0957309 | ||||||||
\(359\) | − | 3.04784e20i | − | 1.10468i | −0.833619 | − | 0.552341i | \(-0.813735\pi\) | ||
0.833619 | − | 0.552341i | \(-0.186265\pi\) | |||||||
\(360\) | 4.66220e19 | + | 3.74973e20i | 0.165261 | + | 1.32917i | ||||
\(361\) | 7.84909e20 | 2.72121 | ||||||||
\(362\) | 2.11595e20i | 0.717526i | ||||||||
\(363\) | 1.52780e20 | − | 1.72952e20i | 0.506771 | − | 0.573683i | ||||
\(364\) | −1.08750e19 | −0.0352873 | ||||||||
\(365\) | 5.03637e20i | 1.59873i | ||||||||
\(366\) | 6.89021e19 | + | 6.08657e19i | 0.213985 | + | 0.189027i | ||||
\(367\) | −3.27286e20 | −0.994486 | −0.497243 | − | 0.867611i | \(-0.665654\pi\) | ||||
−0.497243 | + | 0.867611i | \(0.665654\pi\) | |||||||
\(368\) | − | 7.70261e19i | − | 0.229011i | ||||||
\(369\) | 1.07491e20 | − | 1.33648e19i | 0.312723 | − | 0.0388822i | ||||
\(370\) | 1.95332e19 | 0.0556109 | ||||||||
\(371\) | − | 1.43614e20i | − | 0.400135i | ||||||
\(372\) | 6.52205e19 | − | 7.38318e19i | 0.177844 | − | 0.201326i | ||||
\(373\) | −4.63340e20 | −1.23660 | −0.618300 | − | 0.785942i | \(-0.712178\pi\) | ||||
−0.618300 | + | 0.785942i | \(0.712178\pi\) | |||||||
\(374\) | − | 1.63152e20i | − | 0.426205i | ||||||
\(375\) | 1.72079e20 | + | 1.52008e20i | 0.440024 | + | 0.388702i | ||||
\(376\) | −3.28629e20 | −0.822627 | ||||||||
\(377\) | 4.62019e19i | 0.113222i | ||||||||
\(378\) | 1.75512e20 | − | 2.56628e20i | 0.421088 | − | 0.615702i | ||||
\(379\) | 9.70265e19 | 0.227917 | 0.113959 | − | 0.993486i | \(-0.463647\pi\) | ||||
0.113959 | + | 0.993486i | \(0.463647\pi\) | |||||||
\(380\) | − | 4.11215e20i | − | 0.945803i | ||||||
\(381\) | −1.41720e20 | + | 1.60432e20i | −0.319176 | + | 0.361318i | ||||
\(382\) | −4.53782e20 | −1.00078 | ||||||||
\(383\) | 1.93222e20i | 0.417317i | 0.977989 | + | 0.208659i | \(0.0669098\pi\) | ||||
−0.977989 | + | 0.208659i | \(0.933090\pi\) | |||||||
\(384\) | −1.84951e19 | − | 1.63380e19i | −0.0391208 | − | 0.0345580i | ||||
\(385\) | 2.77285e20 | 0.574435 | ||||||||
\(386\) | 2.39175e20i | 0.485307i | ||||||||
\(387\) | −1.49250e19 | − | 1.20039e20i | −0.0296637 | − | 0.238581i | ||||
\(388\) | −1.40621e20 | −0.273777 | ||||||||
\(389\) | − | 8.17463e20i | − | 1.55909i | −0.626346 | − | 0.779545i | \(-0.715450\pi\) | ||
0.626346 | − | 0.779545i | \(-0.284550\pi\) | |||||||
\(390\) | 3.14225e19 | − | 3.55713e19i | 0.0587116 | − | 0.0664635i | ||||
\(391\) | 3.18483e20 | 0.583005 | ||||||||
\(392\) | − | 4.66481e19i | − | 0.0836653i | ||||||
\(393\) | 3.99483e20 | + | 3.52889e20i | 0.702033 | + | 0.620152i | ||||
\(394\) | −2.21828e20 | −0.381984 | ||||||||
\(395\) | 2.19882e19i | 0.0371033i | ||||||||
\(396\) | −1.15408e20 | + | 1.43492e19i | −0.190842 | + | 0.0237282i | ||||
\(397\) | 7.89790e20 | 1.27993 | 0.639967 | − | 0.768402i | \(-0.278948\pi\) | ||||
0.639967 | + | 0.768402i | \(0.278948\pi\) | |||||||
\(398\) | 3.56691e20i | 0.566536i | ||||||||
\(399\) | −7.88109e20 | + | 8.92166e20i | −1.22688 | + | 1.38887i | ||||
\(400\) | 1.53032e20 | 0.233508 | ||||||||
\(401\) | 1.03439e21i | 1.54713i | 0.633714 | + | 0.773567i | \(0.281530\pi\) | ||||
−0.633714 | + | 0.773567i | \(0.718470\pi\) | |||||||
\(402\) | −1.71409e20 | − | 1.51417e20i | −0.251319 | − | 0.222006i | ||||
\(403\) | −4.35354e19 | −0.0625752 | ||||||||
\(404\) | 3.17523e20i | 0.447429i | ||||||||
\(405\) | −2.18857e20 | − | 8.66509e20i | −0.302356 | − | 1.19711i | ||||
\(406\) | 6.74036e20 | 0.913009 | ||||||||
\(407\) | 2.11514e19i | 0.0280921i | ||||||||
\(408\) | 6.25040e20 | − | 7.07567e20i | 0.814005 | − | 0.921481i | ||||
\(409\) | 1.88705e20 | 0.240989 | 0.120495 | − | 0.992714i | \(-0.461552\pi\) | ||||
0.120495 | + | 0.992714i | \(0.461552\pi\) | |||||||
\(410\) | − | 2.41239e20i | − | 0.302118i | ||||||
\(411\) | −8.21528e20 | − | 7.25710e20i | −1.00899 | − | 0.891309i | ||||
\(412\) | −2.35600e20 | −0.283790 | ||||||||
\(413\) | − | 9.04798e20i | − | 1.06893i | ||||||
\(414\) | 4.25276e19 | + | 3.42042e20i | 0.0492797 | + | 0.396349i | ||||
\(415\) | 1.76198e20 | 0.200271 | ||||||||
\(416\) | − | 6.13200e19i | − | 0.0683685i | ||||||
\(417\) | −6.95142e20 | + | 7.86924e20i | −0.760300 | + | 0.860686i | ||||
\(418\) | −6.76058e20 | −0.725394 | ||||||||
\(419\) | − | 4.80232e20i | − | 0.505520i | −0.967529 | − | 0.252760i | \(-0.918662\pi\) | ||
0.967529 | − | 0.252760i | \(-0.0813384\pi\) | |||||||
\(420\) | 3.41801e20 | + | 3.01935e20i | 0.353004 | + | 0.311831i | ||||
\(421\) | −9.58853e20 | −0.971617 | −0.485809 | − | 0.874065i | \(-0.661475\pi\) | ||||
−0.485809 | + | 0.874065i | \(0.661475\pi\) | |||||||
\(422\) | − | 3.70716e20i | − | 0.368589i | ||||||
\(423\) | 7.71338e20 | − | 9.59036e19i | 0.752526 | − | 0.0935647i | ||||
\(424\) | 4.71968e20 | 0.451841 | ||||||||
\(425\) | 6.32746e20i | 0.594454i | ||||||||
\(426\) | −5.81042e20 | + | 6.57760e20i | −0.535712 | + | 0.606444i | ||||
\(427\) | 3.90396e20 | 0.353250 | ||||||||
\(428\) | − | 1.74179e19i | − | 0.0154684i | ||||||
\(429\) | 3.85181e19 | + | 3.40256e19i | 0.0335743 | + | 0.0296584i | ||||
\(430\) | −2.69401e20 | −0.230489 | ||||||||
\(431\) | 3.66306e20i | 0.307628i | 0.988100 | + | 0.153814i | \(0.0491556\pi\) | ||||
−0.988100 | + | 0.153814i | \(0.950844\pi\) | |||||||
\(432\) | 4.45775e20 | + | 3.04873e20i | 0.367490 | + | 0.251332i | ||||
\(433\) | −1.35950e20 | −0.110021 | −0.0550107 | − | 0.998486i | \(-0.517519\pi\) | ||||
−0.0550107 | + | 0.998486i | \(0.517519\pi\) | |||||||
\(434\) | 6.35135e20i | 0.504601i | ||||||||
\(435\) | 1.28276e21 | − | 1.45213e21i | 1.00053 | − | 1.13264i | ||||
\(436\) | 6.04632e20 | 0.463019 | ||||||||
\(437\) | − | 1.31971e21i | − | 0.992263i | ||||||
\(438\) | 1.02065e21 | + | 9.01611e20i | 0.753505 | + | 0.665620i | ||||
\(439\) | 4.40467e20 | 0.319299 | 0.159649 | − | 0.987174i | \(-0.448964\pi\) | ||||
0.159649 | + | 0.987174i | \(0.448964\pi\) | |||||||
\(440\) | 9.11258e20i | 0.648664i | ||||||||
\(441\) | 1.36133e19 | + | 1.09490e20i | 0.00951599 | + | 0.0765356i | ||||
\(442\) | −1.18587e20 | −0.0814066 | ||||||||
\(443\) | 1.63123e21i | 1.09973i | 0.835254 | + | 0.549865i | \(0.185321\pi\) | ||||
−0.835254 | + | 0.549865i | \(0.814679\pi\) | |||||||
\(444\) | −2.30317e19 | + | 2.60727e19i | −0.0152497 | + | 0.0172632i | ||||
\(445\) | −3.22560e21 | −2.09764 | ||||||||
\(446\) | − | 2.11876e21i | − | 1.35333i | ||||||
\(447\) | 2.47786e20 | + | 2.18886e20i | 0.155459 | + | 0.137327i | ||||
\(448\) | −1.58860e21 | −0.979020 | ||||||||
\(449\) | 2.11301e20i | 0.127918i | 0.997953 | + | 0.0639588i | \(0.0203726\pi\) | ||||
−0.997953 | + | 0.0639588i | \(0.979627\pi\) | |||||||
\(450\) | −6.79553e20 | + | 8.44917e19i | −0.404132 | + | 0.0502474i | ||||
\(451\) | 2.61224e20 | 0.152616 | ||||||||
\(452\) | 1.94287e20i | 0.111516i | ||||||||
\(453\) | 1.20249e21 | − | 1.36126e21i | 0.678105 | − | 0.767638i | ||||
\(454\) | 1.69186e21 | 0.937386 | ||||||||
\(455\) | − | 2.01546e20i | − | 0.109719i | ||||||
\(456\) | −2.93197e21 | − | 2.59000e21i | −1.56834 | − | 1.38542i | ||||
\(457\) | 1.57273e21 | 0.826657 | 0.413329 | − | 0.910582i | \(-0.364366\pi\) | ||||
0.413329 | + | 0.910582i | \(0.364366\pi\) | |||||||
\(458\) | − | 4.86154e20i | − | 0.251102i | ||||||
\(459\) | −1.26057e21 | + | 1.84316e21i | −0.639830 | + | 0.935540i | ||||
\(460\) | −5.05599e20 | −0.252199 | ||||||||
\(461\) | − | 1.48905e21i | − | 0.729963i | −0.931015 | − | 0.364981i | \(-0.881075\pi\) | ||
0.931015 | − | 0.364981i | \(-0.118925\pi\) | |||||||
\(462\) | 4.96397e20 | − | 5.61938e20i | 0.239163 | − | 0.270740i | ||||
\(463\) | 5.50698e20 | 0.260775 | 0.130387 | − | 0.991463i | \(-0.458378\pi\) | ||||
0.130387 | + | 0.991463i | \(0.458378\pi\) | |||||||
\(464\) | 1.17083e21i | 0.544942i | ||||||||
\(465\) | 1.36832e21 | + | 1.20873e21i | 0.625985 | + | 0.552973i | ||||
\(466\) | 1.62174e21 | 0.729279 | ||||||||
\(467\) | 4.29729e21i | 1.89959i | 0.312878 | + | 0.949793i | \(0.398707\pi\) | ||||
−0.312878 | + | 0.949793i | \(0.601293\pi\) | |||||||
\(468\) | 1.04297e19 | + | 8.38846e19i | 0.00453217 | + | 0.0364515i | ||||
\(469\) | −9.71194e20 | −0.414881 | ||||||||
\(470\) | − | 1.73109e21i | − | 0.727005i | ||||||
\(471\) | −1.39342e21 | + | 1.57740e21i | −0.575327 | + | 0.651290i | ||||
\(472\) | 2.97349e21 | 1.20706 | ||||||||
\(473\) | − | 2.91718e20i | − | 0.116433i | ||||||
\(474\) | 4.45606e19 | + | 3.93633e19i | 0.0174874 | + | 0.0154477i | ||||
\(475\) | 2.62194e21 | 1.01175 | ||||||||
\(476\) | − | 1.13949e21i | − | 0.432370i | ||||||
\(477\) | −1.10777e21 | + | 1.37734e20i | −0.413337 | + | 0.0513919i | ||||
\(478\) | −3.17650e21 | −1.16554 | ||||||||
\(479\) | − | 2.49777e21i | − | 0.901297i | −0.892702 | − | 0.450648i | \(-0.851193\pi\) | ||
0.892702 | − | 0.450648i | \(-0.148807\pi\) | |||||||
\(480\) | −1.70250e21 | + | 1.92729e21i | −0.604168 | + | 0.683938i | ||||
\(481\) | 1.53739e19 | 0.00536568 | ||||||||
\(482\) | 3.06486e21i | 1.05205i | ||||||||
\(483\) | 1.09694e21 | + | 9.68999e20i | 0.370344 | + | 0.327149i | ||||
\(484\) | 9.15341e20 | 0.303962 | ||||||||
\(485\) | − | 2.60613e21i | − | 0.851258i | ||||||
\(486\) | −2.14784e21 | − | 1.10770e21i | −0.690098 | − | 0.355902i | ||||
\(487\) | −6.06848e20 | −0.191800 | −0.0958999 | − | 0.995391i | \(-0.530573\pi\) | ||||
−0.0958999 | + | 0.995391i | \(0.530573\pi\) | |||||||
\(488\) | 1.28298e21i | 0.398897i | ||||||||
\(489\) | 3.89386e21 | − | 4.40799e21i | 1.19099 | − | 1.34825i | ||||
\(490\) | 2.45724e20 | 0.0739400 | ||||||||
\(491\) | − | 3.25851e21i | − | 0.964645i | −0.875994 | − | 0.482322i | \(-0.839793\pi\) | ||
0.875994 | − | 0.482322i | \(-0.160207\pi\) | |||||||
\(492\) | 3.22002e20 | + | 2.84446e20i | 0.0937860 | + | 0.0828474i | ||||
\(493\) | −4.84108e21 | −1.38729 | ||||||||
\(494\) | 4.91394e20i | 0.138553i | ||||||||
\(495\) | −2.65932e20 | − | 2.13885e21i | −0.0737784 | − | 0.593388i | ||||
\(496\) | −1.10326e21 | −0.301178 | ||||||||
\(497\) | 3.72684e21i | 1.00113i | ||||||||
\(498\) | 3.15430e20 | − | 3.57078e20i | 0.0833814 | − | 0.0943905i | ||||
\(499\) | −1.08927e21 | −0.283355 | −0.141678 | − | 0.989913i | \(-0.545250\pi\) | ||||
−0.141678 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(500\) | 9.10720e20i | 0.233144i | ||||||||
\(501\) | −5.86499e20 | − | 5.18094e20i | −0.147763 | − | 0.130529i | ||||
\(502\) | 4.61573e21 | 1.14449 | ||||||||
\(503\) | − | 3.04610e20i | − | 0.0743361i | −0.999309 | − | 0.0371680i | \(-0.988166\pi\) | ||
0.999309 | − | 0.0371680i | \(-0.0118337\pi\) | |||||||
\(504\) | 4.30561e21 | − | 5.35334e20i | 1.03417 | − | 0.128582i | ||||
\(505\) | −5.88463e21 | −1.39120 | ||||||||
\(506\) | 8.31230e20i | 0.193427i | ||||||||
\(507\) | −2.86564e21 | + | 3.24400e21i | −0.656383 | + | 0.743048i | ||||
\(508\) | −8.49079e20 | −0.191442 | ||||||||
\(509\) | 5.82783e21i | 1.29350i | 0.762704 | + | 0.646748i | \(0.223871\pi\) | ||||
−0.762704 | + | 0.646748i | \(0.776129\pi\) | |||||||
\(510\) | 3.72720e21 | + | 3.29248e21i | 0.814368 | + | 0.719385i | ||||
\(511\) | 5.78298e21 | 1.24390 | ||||||||
\(512\) | − | 3.83471e21i | − | 0.812032i | ||||||
\(513\) | 7.63759e21 | + | 5.22346e21i | 1.59227 | + | 1.08898i | ||||
\(514\) | −4.48566e21 | −0.920706 | ||||||||
\(515\) | − | 4.36636e21i | − | 0.882392i | ||||||
\(516\) | 3.17651e20 | − | 3.59592e20i | 0.0632053 | − | 0.0715505i | ||||
\(517\) | 1.87450e21 | 0.367250 | ||||||||
\(518\) | − | 2.24289e20i | − | 0.0432684i | ||||||
\(519\) | −6.74038e21 | − | 5.95422e21i | −1.28040 | − | 1.13106i | ||||
\(520\) | 6.62350e20 | 0.123897 | ||||||||
\(521\) | − | 8.10069e20i | − | 0.149218i | −0.997213 | − | 0.0746088i | \(-0.976229\pi\) | ||
0.997213 | − | 0.0746088i | \(-0.0237708\pi\) | |||||||
\(522\) | −6.46438e20 | − | 5.19920e21i | −0.117263 | − | 0.943131i | ||||
\(523\) | −1.43005e21 | −0.255468 | −0.127734 | − | 0.991808i | \(-0.540770\pi\) | ||||
−0.127734 | + | 0.991808i | \(0.540770\pi\) | |||||||
\(524\) | 2.11425e21i | 0.371968i | ||||||||
\(525\) | −1.92516e21 | + | 2.17935e21i | −0.333574 | + | 0.377617i | ||||
\(526\) | 4.50572e20 | 0.0768914 | ||||||||
\(527\) | − | 4.56168e21i | − | 0.766726i | ||||||
\(528\) | 9.76112e20 | + | 8.62264e20i | 0.161595 | + | 0.142748i | ||||
\(529\) | 4.51000e21 | 0.735412 | ||||||||
\(530\) | 2.48615e21i | 0.399319i | ||||||||
\(531\) | −6.97918e21 | + | 8.67751e20i | −1.10420 | + | 0.137290i | ||||
\(532\) | −4.72176e21 | −0.735886 | ||||||||
\(533\) | − | 1.89871e20i | − | 0.0291502i | ||||||
\(534\) | −5.77447e21 | + | 6.53690e21i | −0.873338 | + | 0.988648i | ||||
\(535\) | 3.22805e20 | 0.0480961 | ||||||||
\(536\) | − | 3.19169e21i | − | 0.468492i | ||||||
\(537\) | −6.38957e20 | − | 5.64433e20i | −0.0924012 | − | 0.0816241i | ||||
\(538\) | −4.98834e21 | −0.710719 | ||||||||
\(539\) | 2.66081e20i | 0.0373511i | ||||||||
\(540\) | 2.00118e21 | − | 2.92607e21i | 0.276781 | − | 0.404701i | ||||
\(541\) | 1.23948e22 | 1.68913 | 0.844563 | − | 0.535456i | \(-0.179860\pi\) | ||||
0.844563 | + | 0.535456i | \(0.179860\pi\) | |||||||
\(542\) | − | 8.34288e21i | − | 1.12027i | ||||||
\(543\) | 4.62384e21 | − | 5.23434e21i | 0.611792 | − | 0.692570i | ||||
\(544\) | 6.42517e21 | 0.837710 | ||||||||
\(545\) | 1.12056e22i | 1.43967i | ||||||||
\(546\) | −4.08446e20 | − | 3.60807e20i | −0.0517122 | − | 0.0456808i | ||||
\(547\) | 3.91673e21 | 0.488680 | 0.244340 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244340 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(548\) | − | 4.34791e21i | − | 0.534609i | ||||||
\(549\) | −3.74411e20 | − | 3.01133e21i | −0.0453702 | − | 0.364905i | ||||
\(550\) | −1.65145e21 | −0.197226 | ||||||||
\(551\) | 2.00602e22i | 2.36114i | ||||||||
\(552\) | −3.18447e21 | + | 3.60493e21i | −0.369424 | + | 0.418200i | ||||
\(553\) | 2.52478e20 | 0.0288684 | ||||||||
\(554\) | 8.45967e21i | 0.953401i | ||||||||
\(555\) | −4.83203e20 | − | 4.26845e20i | −0.0536767 | − | 0.0474162i | ||||
\(556\) | −4.16477e21 | −0.456029 | ||||||||
\(557\) | − | 4.96525e21i | − | 0.535919i | −0.963430 | − | 0.267960i | \(-0.913651\pi\) | ||
0.963430 | − | 0.267960i | \(-0.0863494\pi\) | |||||||
\(558\) | 4.89913e21 | − | 6.09129e20i | 0.521249 | − | 0.0648091i | ||||
\(559\) | −2.12036e20 | −0.0222390 | ||||||||
\(560\) | − | 5.10749e21i | − | 0.528084i | ||||||
\(561\) | −3.56523e21 | + | 4.03597e21i | −0.363400 | + | 0.411381i | ||||
\(562\) | 2.23343e21 | 0.224431 | ||||||||
\(563\) | − | 1.04818e22i | − | 1.03841i | −0.854650 | − | 0.519205i | \(-0.826228\pi\) | ||
0.854650 | − | 0.519205i | \(-0.173772\pi\) | |||||||
\(564\) | 2.31064e21 | + | 2.04114e21i | 0.225683 | + | 0.199361i | ||||
\(565\) | −3.60070e21 | −0.346736 | ||||||||
\(566\) | 2.18338e21i | 0.207300i | ||||||||
\(567\) | −9.94964e21 | + | 2.51301e21i | −0.931414 | + | 0.235250i | ||||
\(568\) | −1.22477e22 | −1.13049 | ||||||||
\(569\) | − | 1.83294e22i | − | 1.66821i | −0.551606 | − | 0.834105i | \(-0.685985\pi\) | ||
0.551606 | − | 0.834105i | \(-0.314015\pi\) | |||||||
\(570\) | 1.36432e22 | − | 1.54445e22i | 1.22438 | − | 1.38604i | ||||
\(571\) | −5.87637e21 | −0.520020 | −0.260010 | − | 0.965606i | \(-0.583726\pi\) | ||||
−0.260010 | + | 0.965606i | \(0.583726\pi\) | |||||||
\(572\) | 2.03856e20i | 0.0177891i | ||||||||
\(573\) | 1.12254e22 | + | 9.91616e21i | 0.965976 | + | 0.853310i | ||||
\(574\) | −2.77001e21 | −0.235064 | ||||||||
\(575\) | − | 3.22373e21i | − | 0.269784i | ||||||
\(576\) | 1.52356e21 | + | 1.22537e22i | 0.125742 | + | 1.01132i | ||||
\(577\) | −1.18497e22 | −0.964496 | −0.482248 | − | 0.876035i | \(-0.660180\pi\) | ||||
−0.482248 | + | 0.876035i | \(0.660180\pi\) | |||||||
\(578\) | − | 2.75301e21i | − | 0.220996i | ||||||
\(579\) | 5.22650e21 | − | 5.91658e21i | 0.413793 | − | 0.468427i | ||||
\(580\) | 7.68533e21 | 0.600121 | ||||||||
\(581\) | − | 2.02319e21i | − | 0.155821i | ||||||
\(582\) | −5.28149e21 | − | 4.66549e21i | −0.401211 | − | 0.354416i | ||||
\(583\) | −2.69211e21 | −0.201718 | ||||||||
\(584\) | 1.90049e22i | 1.40464i | ||||||||
\(585\) | −1.55463e21 | + | 1.93293e20i | −0.113339 | + | 0.0140919i | ||||
\(586\) | 1.80388e22 | 1.29726 | ||||||||
\(587\) | 3.83504e21i | 0.272060i | 0.990705 | + | 0.136030i | \(0.0434344\pi\) | ||||
−0.990705 | + | 0.136030i | \(0.956566\pi\) | |||||||
\(588\) | −2.89735e20 | + | 3.27990e20i | −0.0202760 | + | 0.0229531i | ||||
\(589\) | −1.89024e22 | −1.30495 | ||||||||
\(590\) | 1.56632e22i | 1.06675i | ||||||||
\(591\) | 5.48746e21 | + | 4.84743e21i | 0.368698 | + | 0.325696i | ||||
\(592\) | 3.89601e20 | 0.0258253 | ||||||||
\(593\) | 1.40261e21i | 0.0917274i | 0.998948 | + | 0.0458637i | \(0.0146040\pi\) | ||||
−0.998948 | + | 0.0458637i | \(0.985396\pi\) | |||||||
\(594\) | −4.81060e21 | − | 3.29004e21i | −0.310390 | − | 0.212280i | ||||
\(595\) | 2.11181e22 | 1.34437 | ||||||||
\(596\) | 1.31140e21i | 0.0823691i | ||||||||
\(597\) | 7.79450e21 | − | 8.82364e21i | 0.483052 | − | 0.546831i | ||||
\(598\) | 6.04181e20 | 0.0369452 | ||||||||
\(599\) | − | 1.21866e22i | − | 0.735306i | −0.929963 | − | 0.367653i | \(-0.880161\pi\) | ||
0.929963 | − | 0.367653i | \(-0.119839\pi\) | |||||||
\(600\) | −7.16210e21 | − | 6.32676e21i | −0.426413 | − | 0.376679i | ||||
\(601\) | 7.79610e21 | 0.458017 | 0.229009 | − | 0.973424i | \(-0.426452\pi\) | ||||
0.229009 | + | 0.973424i | \(0.426452\pi\) | |||||||
\(602\) | 3.09338e21i | 0.179333i | ||||||||
\(603\) | 9.31429e20 | + | 7.49134e21i | 0.0532858 | + | 0.428569i | ||||
\(604\) | 7.20444e21 | 0.406729 | ||||||||
\(605\) | 1.69639e22i | 0.945113i | ||||||||
\(606\) | −1.05347e22 | + | 1.19256e22i | −0.579215 | + | 0.655691i | ||||
\(607\) | −1.39324e22 | −0.755991 | −0.377995 | − | 0.925807i | \(-0.623387\pi\) | ||||
−0.377995 | + | 0.925807i | \(0.623387\pi\) | |||||||
\(608\) | − | 2.66242e22i | − | 1.42577i | ||||||
\(609\) | −1.66740e22 | − | 1.47292e22i | −0.881253 | − | 0.778468i | ||||
\(610\) | −6.75825e21 | −0.352530 | ||||||||
\(611\) | − | 1.36248e21i | − | 0.0701459i | ||||||
\(612\) | −8.78951e21 | + | 1.09284e21i | −0.446635 | + | 0.0555320i | ||||
\(613\) | 2.18069e22 | 1.09373 | 0.546866 | − | 0.837220i | \(-0.315821\pi\) | ||||
0.546866 | + | 0.837220i | \(0.315821\pi\) | |||||||
\(614\) | − | 1.79513e22i | − | 0.888686i | ||||||
\(615\) | −5.27161e21 | + | 5.96764e21i | −0.257598 | + | 0.291610i | ||||
\(616\) | 1.04635e22 | 0.504696 | ||||||||
\(617\) | − | 1.41464e22i | − | 0.673540i | −0.941587 | − | 0.336770i | \(-0.890666\pi\) | ||
0.941587 | − | 0.336770i | \(-0.109334\pi\) | |||||||
\(618\) | −8.84873e21 | − | 7.81666e21i | −0.415885 | − | 0.367378i | ||||
\(619\) | −1.06168e22 | −0.492571 | −0.246285 | − | 0.969197i | \(-0.579210\pi\) | ||||
−0.246285 | + | 0.969197i | \(0.579210\pi\) | |||||||
\(620\) | 7.24178e21i | 0.331674i | ||||||||
\(621\) | 6.42237e21 | − | 9.39060e21i | 0.290377 | − | 0.424581i | ||||
\(622\) | −4.87740e21 | −0.217703 | ||||||||
\(623\) | 3.70378e22i | 1.63208i | ||||||||
\(624\) | 6.26738e20 | − | 7.09489e20i | 0.0272653 | − | 0.0308652i | ||||
\(625\) | −2.90899e22 | −1.24940 | ||||||||
\(626\) | − | 6.13618e21i | − | 0.260198i | ||||||
\(627\) | 1.67240e22 | + | 1.47734e22i | 0.700164 | + | 0.618501i | ||||
\(628\) | −8.34833e21 | −0.345082 | ||||||||
\(629\) | 1.61090e21i | 0.0657450i | ||||||||
\(630\) | 2.81994e21 | + | 2.26803e22i | 0.113636 | + | 0.913955i | ||||
\(631\) | 4.92516e22 | 1.95968 | 0.979841 | − | 0.199781i | \(-0.0640232\pi\) | ||||
0.979841 | + | 0.199781i | \(0.0640232\pi\) | |||||||
\(632\) | 8.29733e20i | 0.0325988i | ||||||||
\(633\) | −8.10099e21 | + | 9.17059e21i | −0.314274 | + | 0.355769i | ||||
\(634\) | 3.44715e22 | 1.32052 | ||||||||
\(635\) | − | 1.57359e22i | − | 0.595254i | ||||||
\(636\) | −3.31847e21 | − | 2.93143e21i | −0.123960 | − | 0.109502i | ||||
\(637\) | 1.93401e20 | 0.00713418 | ||||||||
\(638\) | − | 1.26351e22i | − | 0.460269i | ||||||
\(639\) | 2.87471e22 | − | 3.57424e21i | 1.03416 | − | 0.128581i | ||||
\(640\) | 1.81409e21 | 0.0644495 | ||||||||
\(641\) | 5.24245e21i | 0.183937i | 0.995762 | + | 0.0919686i | \(0.0293160\pi\) | ||||
−0.995762 | + | 0.0919686i | \(0.970684\pi\) | |||||||
\(642\) | 5.77885e20 | − | 6.54186e20i | 0.0200245 | − | 0.0226684i | ||||
\(643\) | −3.35417e22 | −1.14788 | −0.573941 | − | 0.818897i | \(-0.694586\pi\) | ||||
−0.573941 | + | 0.818897i | \(0.694586\pi\) | |||||||
\(644\) | 5.80551e21i | 0.196225i | ||||||||
\(645\) | 6.66430e21 | + | 5.88701e21i | 0.222473 | + | 0.196525i | ||||
\(646\) | −5.14888e22 | −1.69767 | ||||||||
\(647\) | 1.65630e22i | 0.539393i | 0.962945 | + | 0.269697i | \(0.0869235\pi\) | ||||
−0.962945 | + | 0.269697i | \(0.913077\pi\) | |||||||
\(648\) | −8.25864e21 | − | 3.26980e22i | −0.265649 | − | 1.05177i | ||||
\(649\) | −1.69608e22 | −0.538875 | ||||||||
\(650\) | 1.20036e21i | 0.0376707i | ||||||||
\(651\) | 1.38791e22 | − | 1.57116e22i | 0.430244 | − | 0.487050i | ||||
\(652\) | 2.33291e22 | 0.714361 | ||||||||
\(653\) | 4.29848e22i | 1.30020i | 0.759849 | + | 0.650099i | \(0.225273\pi\) | ||||
−0.759849 | + | 0.650099i | \(0.774727\pi\) | |||||||
\(654\) | 2.27089e22 | + | 2.00603e22i | 0.678539 | + | 0.599398i | ||||
\(655\) | −3.91832e22 | −1.15656 | ||||||||
\(656\) | − | 4.81164e21i | − | 0.140301i | ||||||
\(657\) | −5.54620e21 | − | 4.46072e22i | −0.159762 | − | 1.28494i | ||||
\(658\) | −1.98772e22 | −0.565650 | ||||||||
\(659\) | − | 1.66575e22i | − | 0.468303i | −0.972200 | − | 0.234151i | \(-0.924769\pi\) | ||
0.972200 | − | 0.234151i | \(-0.0752312\pi\) | |||||||
\(660\) | 5.65989e21 | − | 6.40719e21i | 0.157202 | − | 0.177957i | ||||
\(661\) | −6.24453e21 | −0.171352 | −0.0856758 | − | 0.996323i | \(-0.527305\pi\) | ||||
−0.0856758 | + | 0.996323i | \(0.527305\pi\) | |||||||
\(662\) | 4.96208e21i | 0.134524i | ||||||||
\(663\) | 2.93355e21 | + | 2.59140e21i | 0.0785752 | + | 0.0694106i | ||||
\(664\) | 6.64891e21 | 0.175957 | ||||||||
\(665\) | − | 8.75080e22i | − | 2.28810i | ||||||
\(666\) | −1.73006e21 | + | 2.15106e20i | −0.0446959 | + | 0.00555723i | ||||
\(667\) | 2.46645e22 | 0.629600 | ||||||||
\(668\) | − | 3.10403e21i | − | 0.0782914i | ||||||
\(669\) | −4.62997e22 | + | 5.24129e22i | −1.15390 | + | 1.30626i | ||||
\(670\) | 1.68126e22 | 0.414035 | ||||||||
\(671\) | − | 7.31812e21i | − | 0.178082i | ||||||
\(672\) | 2.21300e22 | + | 1.95489e22i | 0.532142 | + | 0.470076i | ||||
\(673\) | 6.40128e22 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(674\) | 4.56477e22i | 1.07186i | ||||||||
\(675\) | 1.86568e22 | + | 1.27597e22i | 0.432919 | + | 0.296080i | ||||
\(676\) | −1.71688e22 | −0.393700 | ||||||||
\(677\) | − | 2.51675e22i | − | 0.570336i | −0.958478 | − | 0.285168i | \(-0.907951\pi\) | ||
0.958478 | − | 0.285168i | \(-0.0920494\pi\) | |||||||
\(678\) | −6.44598e21 | + | 7.29707e21i | −0.144361 | + | 0.163422i | ||||
\(679\) | −2.99247e22 | −0.662326 | ||||||||
\(680\) | 6.94016e22i | 1.51809i | ||||||||
\(681\) | −4.18525e22 | − | 3.69710e22i | −0.904782 | − | 0.799254i | ||||
\(682\) | 1.19058e22 | 0.254381 | ||||||||
\(683\) | 6.35355e22i | 1.34169i | 0.741599 | + | 0.670843i | \(0.234068\pi\) | ||||
−0.741599 | + | 0.670843i | \(0.765932\pi\) | |||||||
\(684\) | 4.52843e21 | + | 3.64214e22i | 0.0945145 | + | 0.760165i | ||||
\(685\) | 8.05795e22 | 1.66226 | ||||||||
\(686\) | − | 3.94052e22i | − | 0.803454i | ||||||
\(687\) | −1.06236e22 | + | 1.20262e22i | −0.214100 | + | 0.242368i | ||||
\(688\) | −5.37334e21 | −0.107038 | ||||||||
\(689\) | 1.95676e21i | 0.0385287i | ||||||||
\(690\) | −1.89894e22 | − | 1.67746e22i | −0.369589 | − | 0.326482i | ||||
\(691\) | −5.74302e22 | −1.10488 | −0.552441 | − | 0.833552i | \(-0.686303\pi\) | ||||
−0.552441 | + | 0.833552i | \(0.686303\pi\) | |||||||
\(692\) | − | 3.56732e22i | − | 0.678413i | ||||||
\(693\) | −2.45592e22 | + | 3.05355e21i | −0.461688 | + | 0.0574036i | ||||
\(694\) | 4.44312e22 | 0.825681 | ||||||||
\(695\) | − | 7.71854e22i | − | 1.41794i | ||||||
\(696\) | 4.84054e22 | − | 5.47965e22i | 0.879063 | − | 0.995129i | ||||
\(697\) | 1.98949e22 | 0.357173 | ||||||||
\(698\) | − | 4.51267e22i | − | 0.800922i | ||||||
\(699\) | −4.01178e22 | − | 3.54386e22i | −0.703913 | − | 0.621813i | ||||
\(700\) | −1.15341e22 | −0.200078 | ||||||||
\(701\) | 5.88811e22i | 1.00979i | 0.863180 | + | 0.504896i | \(0.168469\pi\) | ||||
−0.863180 | + | 0.504896i | \(0.831531\pi\) | |||||||
\(702\) | −2.39137e21 | + | 3.49659e21i | −0.0405462 | + | 0.0592855i | ||||
\(703\) | 6.67513e21 | 0.111897 | ||||||||
\(704\) | 2.97790e22i | 0.493547i | ||||||||
\(705\) | −3.78283e22 | + | 4.28229e22i | −0.619874 | + | 0.701719i | ||||
\(706\) | −4.05006e22 | −0.656182 | ||||||||
\(707\) | 6.75700e22i | 1.08243i | ||||||||
\(708\) | −2.09070e22 | − | 1.84685e22i | −0.331151 | − | 0.292527i | ||||
\(709\) | 5.30257e22 | 0.830456 | 0.415228 | − | 0.909717i | \(-0.363702\pi\) | ||||
0.415228 | + | 0.909717i | \(0.363702\pi\) | |||||||
\(710\) | − | 6.45163e22i | − | 0.999086i | ||||||
\(711\) | −2.42141e20 | − | 1.94750e21i | −0.00370775 | − | 0.0298209i | ||||
\(712\) | −1.21719e23 | −1.84297 | ||||||||
\(713\) | 2.32410e22i | 0.347967i | ||||||||
\(714\) | 3.78057e22 | − | 4.27973e22i | 0.559721 | − | 0.633623i | ||||
\(715\) | −3.77805e21 | −0.0553120 | ||||||||
\(716\) | − | 3.38166e21i | − | 0.0489582i | ||||||
\(717\) | 7.85787e22 | + | 6.94137e22i | 1.12500 | + | 0.993784i | ||||
\(718\) | 6.05837e22 | 0.857749 | ||||||||
\(719\) | − | 1.00941e23i | − | 1.41330i | −0.707562 | − | 0.706651i | \(-0.750205\pi\) | ||
0.707562 | − | 0.706651i | \(-0.249795\pi\) | |||||||
\(720\) | −3.93968e22 | + | 4.89836e21i | −0.545507 | + | 0.0678252i | ||||
\(721\) | −5.01365e22 | −0.686550 | ||||||||
\(722\) | 1.56021e23i | 2.11293i | ||||||||
\(723\) | 6.69741e22 | − | 7.58170e22i | 0.897017 | − | 1.01545i | ||||
\(724\) | 2.77026e22 | 0.366954 | ||||||||
\(725\) | 4.90022e22i | 0.641965i | ||||||||
\(726\) | 3.43786e22 | + | 3.03689e22i | 0.445446 | + | 0.393492i | ||||
\(727\) | 7.22307e22 | 0.925649 | 0.462824 | − | 0.886450i | \(-0.346836\pi\) | ||||
0.462824 | + | 0.886450i | \(0.346836\pi\) | |||||||
\(728\) | − | 7.60540e21i | − | 0.0963987i | ||||||
\(729\) | 2.89264e22 | + | 7.43367e22i | 0.362639 | + | 0.931930i | ||||
\(730\) | −1.00111e23 | −1.24136 | ||||||||
\(731\) | − | 2.22173e22i | − | 0.272492i | ||||||
\(732\) | 7.96869e21 | − | 9.02082e21i | 0.0966714 | − | 0.109435i | ||||
\(733\) | 6.69461e22 | 0.803329 | 0.401664 | − | 0.915787i | \(-0.368432\pi\) | ||||
0.401664 | + | 0.915787i | \(0.368432\pi\) | |||||||
\(734\) | − | 6.50565e22i | − | 0.772186i | ||||||
\(735\) | −6.07861e21 | − | 5.36963e21i | −0.0713683 | − | 0.0630443i | ||||
\(736\) | −3.27351e22 | −0.380182 | ||||||||
\(737\) | 1.82054e22i | 0.209151i | ||||||||
\(738\) | 2.65659e21 | + | 2.13666e22i | 0.0301908 | + | 0.242820i | ||||
\(739\) | −1.18482e23 | −1.33197 | −0.665986 | − | 0.745964i | \(-0.731989\pi\) | ||||
−0.665986 | + | 0.745964i | \(0.731989\pi\) | |||||||
\(740\) | − | 2.55734e21i | − | 0.0284403i | ||||||
\(741\) | 1.07381e22 | − | 1.21559e22i | 0.118136 | − | 0.133734i | ||||
\(742\) | 2.85471e22 | 0.310692 | ||||||||
\(743\) | − | 9.49194e22i | − | 1.02199i | −0.859585 | − | 0.510993i | \(-0.829278\pi\) | ||
0.859585 | − | 0.510993i | \(-0.170722\pi\) | |||||||
\(744\) | 5.16340e22 | + | 4.56117e22i | 0.549987 | + | 0.485840i | ||||
\(745\) | −2.43040e22 | −0.256111 | ||||||||
\(746\) | − | 9.21007e22i | − | 0.960180i | ||||||
\(747\) | −1.56059e22 | + | 1.94035e21i | −0.160962 | + | 0.0200131i | ||||
\(748\) | −2.13602e22 | −0.217968 | ||||||||
\(749\) | − | 3.70659e21i | − | 0.0374214i | ||||||
\(750\) | −3.02156e22 | + | 3.42050e22i | −0.301815 | + | 0.341665i | ||||
\(751\) | −1.45353e23 | −1.43649 | −0.718246 | − | 0.695789i | \(-0.755055\pi\) | ||||
−0.718246 | + | 0.695789i | \(0.755055\pi\) | |||||||
\(752\) | − | 3.45276e22i | − | 0.337616i | ||||||
\(753\) | −1.14182e23 | − | 1.00864e23i | −1.10468 | − | 0.975836i | ||||
\(754\) | −9.18382e21 | −0.0879129 | ||||||||
\(755\) | 1.33519e23i | 1.26464i | ||||||||
\(756\) | −3.35984e22 | − | 2.29785e22i | −0.314879 | − | 0.215351i | ||||
\(757\) | 6.76777e22 | 0.627594 | 0.313797 | − | 0.949490i | \(-0.398399\pi\) | ||||
0.313797 | + | 0.949490i | \(0.398399\pi\) | |||||||
\(758\) | 1.92865e22i | 0.176970i | ||||||||
\(759\) | 1.81642e22 | − | 2.05625e22i | 0.164924 | − | 0.186699i | ||||
\(760\) | 2.87582e23 | 2.58377 | ||||||||
\(761\) | 4.27404e22i | 0.379981i | 0.981786 | + | 0.189990i | \(0.0608456\pi\) | ||||
−0.981786 | + | 0.189990i | \(0.939154\pi\) | |||||||
\(762\) | −3.18899e22 | − | 2.81705e22i | −0.280552 | − | 0.247830i | ||||
\(763\) | 1.28668e23 | 1.12014 | ||||||||
\(764\) | 5.94102e22i | 0.511817i | ||||||||
\(765\) | −2.02534e22 | − | 1.62895e23i | −0.172666 | − | 1.38873i | ||||
\(766\) | −3.84079e22 | −0.324034 | ||||||||
\(767\) | 1.23280e22i | 0.102927i | ||||||||
\(768\) | −7.84105e22 | + | 8.87634e22i | −0.647865 | + | 0.733406i | ||||
\(769\) | −8.99380e22 | −0.735415 | −0.367708 | − | 0.929941i | \(-0.619857\pi\) | ||||
−0.367708 | + | 0.929941i | \(0.619857\pi\) | |||||||
\(770\) | 5.51176e22i | 0.446031i | ||||||||
\(771\) | 1.10964e23 | + | 9.80217e22i | 0.888683 | + | 0.785032i | ||||
\(772\) | 3.13133e22 | 0.248193 | ||||||||
\(773\) | 9.93303e22i | 0.779194i | 0.920985 | + | 0.389597i | \(0.127386\pi\) | ||||
−0.920985 | + | 0.389597i | \(0.872614\pi\) | |||||||
\(774\) | 2.38609e22 | − | 2.96672e21i | 0.185250 | − | 0.0230329i | ||||
\(775\) | −4.61741e22 | −0.354801 | ||||||||
\(776\) | − | 9.83432e22i | − | 0.747912i | ||||||
\(777\) | −4.90123e21 | + | 5.54835e21i | −0.0368924 | + | 0.0417634i | ||||
\(778\) | 1.62492e23 | 1.21058 | ||||||||
\(779\) | − | 8.24391e22i | − | 0.607902i | ||||||
\(780\) | −4.65708e21 | − | 4.11391e21i | −0.0339905 | − | 0.0300260i | ||||
\(781\) | 6.98610e22 | 0.504692 | ||||||||
\(782\) | 6.33067e22i | 0.452684i | ||||||||
\(783\) | −9.76229e22 | + | 1.42741e23i | −0.690968 | + | 1.01031i | ||||
\(784\) | 4.90110e21 | 0.0343372 | ||||||||
\(785\) | − | 1.54719e23i | − | 1.07297i | ||||||
\(786\) | −7.01458e22 | + | 7.94075e22i | −0.481528 | + | 0.545106i | ||||
\(787\) | −2.04674e23 | −1.39080 | −0.695402 | − | 0.718621i | \(-0.744774\pi\) | ||||
−0.695402 | + | 0.718621i | \(0.744774\pi\) | |||||||
\(788\) | 2.90422e22i | 0.195353i | ||||||||
\(789\) | −1.11460e22 | − | 9.84600e21i | −0.0742170 | − | 0.0655608i | ||||
\(790\) | −4.37072e21 | −0.0288095 | ||||||||
\(791\) | 4.13449e22i | 0.269780i | ||||||||
\(792\) | −1.00350e22 | − | 8.07103e22i | −0.0648213 | − | 0.521348i | ||||
\(793\) | −5.31919e21 | −0.0340142 | ||||||||
\(794\) | 1.56991e23i | 0.993828i | ||||||||
\(795\) | 5.43279e22 | − | 6.15011e22i | 0.340476 | − | 0.385430i | ||||
\(796\) | 4.66988e22 | 0.289735 | ||||||||
\(797\) | − | 2.95415e23i | − | 1.81454i | −0.420550 | − | 0.907270i | \(-0.638163\pi\) | ||
0.420550 | − | 0.907270i | \(-0.361837\pi\) | |||||||
\(798\) | −1.77341e23 | − | 1.56657e23i | −1.07842 | − | 0.952635i | ||||
\(799\) | 1.42762e23 | 0.859488 | ||||||||
\(800\) | − | 6.50366e22i | − | 0.387648i | ||||||
\(801\) | 2.85692e23 | − | 3.55213e22i | 1.68592 | − | 0.209618i | ||||
\(802\) | −2.05611e23 | −1.20130 | ||||||||
\(803\) | − | 1.08404e23i | − | 0.627078i | ||||||
\(804\) | −1.98238e22 | + | 2.24412e22i | −0.113537 | + | 0.128528i | ||||
\(805\) | −1.07593e23 | −0.610123 | ||||||||
\(806\) | − | 8.65379e21i | − | 0.0485877i | ||||||
\(807\) | 1.23399e23 | + | 1.09007e23i | 0.685999 | + | 0.605988i | ||||
\(808\) | −2.22059e23 | −1.22230 | ||||||||
\(809\) | 2.17183e22i | 0.118369i | 0.998247 | + | 0.0591845i | \(0.0188500\pi\) | ||||
−0.998247 | + | 0.0591845i | \(0.981150\pi\) | |||||||
\(810\) | 1.72241e23 | − | 4.35034e22i | 0.929515 | − | 0.234770i | ||||
\(811\) | 4.93494e22 | 0.263703 | 0.131852 | − | 0.991269i | \(-0.457908\pi\) | ||||
0.131852 | + | 0.991269i | \(0.457908\pi\) | |||||||
\(812\) | − | 8.82464e22i | − | 0.466927i | ||||||
\(813\) | −1.82311e23 | + | 2.06382e23i | −0.955186 | + | 1.08130i | ||||
\(814\) | −4.20439e21 | −0.0218126 | ||||||||
\(815\) | 4.32357e23i | 2.22117i | ||||||||
\(816\) | 7.43409e22 | + | 6.56702e22i | 0.378187 | + | 0.334077i | ||||
\(817\) | −9.20629e22 | −0.463776 | ||||||||
\(818\) | 3.75101e22i | 0.187120i | ||||||||
\(819\) | 2.21948e21 | + | 1.78509e22i | 0.0109643 | + | 0.0881840i | ||||
\(820\) | −3.15836e22 | −0.154508 | ||||||||
\(821\) | 3.24453e23i | 1.57184i | 0.618331 | + | 0.785918i | \(0.287809\pi\) | ||||
−0.618331 | + | 0.785918i | \(0.712191\pi\) | |||||||
\(822\) | 1.44253e23 | − | 1.63300e23i | 0.692073 | − | 0.783450i | ||||
\(823\) | 2.49116e23 | 1.18359 | 0.591797 | − | 0.806087i | \(-0.298419\pi\) | ||||
0.591797 | + | 0.806087i | \(0.298419\pi\) | |||||||
\(824\) | − | 1.64766e23i | − | 0.775266i | ||||||
\(825\) | 4.08527e22 | + | 3.60879e22i | 0.190366 | + | 0.168163i | ||||
\(826\) | 1.79852e23 | 0.829993 | ||||||||
\(827\) | − | 1.87497e23i | − | 0.856939i | −0.903556 | − | 0.428469i | \(-0.859053\pi\) | ||
0.903556 | − | 0.428469i | \(-0.140947\pi\) | |||||||
\(828\) | 4.47810e22 | − | 5.56781e21i | 0.202699 | − | 0.0252024i | ||||
\(829\) | −2.57644e23 | −1.15501 | −0.577503 | − | 0.816389i | \(-0.695973\pi\) | ||||
−0.577503 | + | 0.816389i | \(0.695973\pi\) | |||||||
\(830\) | 3.50240e22i | 0.155504i | ||||||||
\(831\) | 1.84863e23 | − | 2.09271e23i | 0.812909 | − | 0.920240i | ||||
\(832\) | 2.16449e22 | 0.0942691 | ||||||||
\(833\) | 2.02648e22i | 0.0874142i | ||||||||
\(834\) | −1.56422e23 | − | 1.38177e23i | −0.668295 | − | 0.590349i | ||||
\(835\) | 5.75267e22 | 0.243432 | ||||||||
\(836\) | 8.85111e22i | 0.370978i | ||||||||
\(837\) | −1.34503e23 | − | 9.19888e22i | −0.558378 | − | 0.381884i | ||||
\(838\) | 9.54584e22 | 0.392520 | ||||||||
\(839\) | 1.20740e23i | 0.491764i | 0.969300 | + | 0.245882i | \(0.0790776\pi\) | ||||
−0.969300 | + | 0.245882i | \(0.920922\pi\) | |||||||
\(840\) | −2.11158e23 | + | 2.39038e23i | −0.851869 | + | 0.964344i | ||||
\(841\) | −1.24664e23 | −0.498166 | ||||||||
\(842\) | − | 1.90597e23i | − | 0.754430i | ||||||
\(843\) | −5.52496e22 | − | 4.88056e22i | −0.216625 | − | 0.191359i | ||||
\(844\) | −4.85350e22 | −0.188502 | ||||||||
\(845\) | − | 3.18187e23i | − | 1.22413i | ||||||
\(846\) | 1.90633e22 | + | 1.53323e23i | 0.0726500 | + | 0.584312i | ||||
\(847\) | 1.94788e23 | 0.735350 | ||||||||
\(848\) | 4.95875e22i | 0.185441i | ||||||||
\(849\) | 4.77118e22 | − | 5.40114e22i | 0.176752 | − | 0.200089i | ||||
\(850\) | −1.25775e23 | −0.461574 | ||||||||
\(851\) | − | 8.20724e21i | − | 0.0298374i | ||||||
\(852\) | 8.61155e22 | + | 7.60715e22i | 0.310145 | + | 0.273971i | ||||
\(853\) | −1.07020e23 | −0.381831 | −0.190915 | − | 0.981606i | \(-0.561146\pi\) | ||||
−0.190915 | + | 0.981606i | \(0.561146\pi\) | |||||||
\(854\) | 7.76013e22i | 0.274287i | ||||||||
\(855\) | −6.74996e23 | + | 8.39250e22i | −2.36359 | + | 0.293875i | ||||
\(856\) | 1.21812e22 | 0.0422570 | ||||||||
\(857\) | − | 2.75774e23i | − | 0.947779i | −0.880584 | − | 0.473890i | \(-0.842850\pi\) | ||
0.880584 | − | 0.473890i | \(-0.157150\pi\) | |||||||
\(858\) | −6.76347e21 | + | 7.65647e21i | −0.0230288 | + | 0.0260694i | ||||
\(859\) | 1.57950e23 | 0.532814 | 0.266407 | − | 0.963861i | \(-0.414164\pi\) | ||||
0.266407 | + | 0.963861i | \(0.414164\pi\) | |||||||
\(860\) | 3.52706e22i | 0.117876i | ||||||||
\(861\) | 6.85232e22 | + | 6.05310e22i | 0.226888 | + | 0.200425i | ||||
\(862\) | −7.28127e22 | −0.238863 | ||||||||
\(863\) | − | 1.49755e23i | − | 0.486737i | −0.969934 | − | 0.243369i | \(-0.921748\pi\) | ||
0.969934 | − | 0.243369i | \(-0.0782525\pi\) | |||||||
\(864\) | 1.29567e23 | − | 1.89449e23i | 0.417238 | − | 0.610073i | ||||
\(865\) | 6.61130e23 | 2.10939 | ||||||||
\(866\) | − | 2.70236e22i | − | 0.0854281i | ||||||
\(867\) | −6.01595e22 | + | 6.81026e22i | −0.188431 | + | 0.213310i | ||||
\(868\) | 8.31534e22 | 0.258061 | ||||||||
\(869\) | − | 4.73280e21i | − | 0.0145532i | ||||||
\(870\) | 2.88648e23 | + | 2.54981e23i | 0.879455 | + | 0.776881i | ||||
\(871\) | 1.32326e22 | 0.0399486 | ||||||||
\(872\) | 4.22848e23i | 1.26489i | ||||||||
\(873\) | 2.86994e22 | + | 2.30825e23i | 0.0850666 | + | 0.684178i | ||||
\(874\) | 2.62326e23 | 0.770461 | ||||||||
\(875\) | 1.93804e23i | 0.564026i | ||||||||
\(876\) | 1.18041e23 | − | 1.33627e23i | 0.340408 | − | 0.385354i | ||||
\(877\) | −4.27669e23 | −1.22211 | −0.611057 | − | 0.791587i | \(-0.709255\pi\) | ||||
−0.611057 | + | 0.791587i | \(0.709255\pi\) | |||||||
\(878\) | 8.75542e22i | 0.247925i | ||||||||
\(879\) | −4.46235e23 | − | 3.94189e23i | −1.25214 | − | 1.10610i | ||||
\(880\) | −9.57418e22 | −0.266220 | ||||||||
\(881\) | 3.24349e23i | 0.893729i | 0.894602 | + | 0.446865i | \(0.147459\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(882\) | −2.17639e22 | + | 2.70599e21i | −0.0594275 | + | 0.00738886i | ||||
\(883\) | 2.72976e23 | 0.738651 | 0.369326 | − | 0.929300i | \(-0.379589\pi\) | ||||
0.369326 | + | 0.929300i | \(0.379589\pi\) | |||||||
\(884\) | 1.55257e22i | 0.0416326i | ||||||||
\(885\) | 3.42276e23 | − | 3.87468e23i | 0.909558 | − | 1.02965i | ||||
\(886\) | −3.24249e23 | −0.853905 | ||||||||
\(887\) | 5.11773e23i | 1.33564i | 0.744324 | + | 0.667819i | \(0.232772\pi\) | ||||
−0.744324 | + | 0.667819i | \(0.767228\pi\) | |||||||
\(888\) | −1.82339e22 | − | 1.61072e22i | −0.0471601 | − | 0.0416596i | ||||
\(889\) | −1.80687e23 | −0.463140 | ||||||||
\(890\) | − | 6.41171e23i | − | 1.62875i | ||||||
\(891\) | 4.71073e22 | + | 1.86510e23i | 0.118595 | + | 0.469548i | ||||
\(892\) | −2.77393e23 | −0.692113 | ||||||||
\(893\) | − | 5.91570e23i | − | 1.46283i | ||||||
\(894\) | −4.35091e22 | + | 4.92538e22i | −0.106630 | + | 0.120709i | ||||
\(895\) | 6.26721e22 | 0.152226 | ||||||||
\(896\) | − | 2.08302e22i | − | 0.0501453i | ||||||
\(897\) | −1.49459e22 | − | 1.32027e22i | −0.0356602 | − | 0.0315010i | ||||
\(898\) | −4.20015e22 | −0.0993239 | ||||||||
\(899\) | − | 3.53273e23i | − | 0.828005i | ||||||
\(900\) | 1.10619e22 | + | 8.89687e22i | 0.0256973 | + | 0.206679i | ||||
\(901\) | −2.05031e23 | −0.472087 | ||||||||
\(902\) | 5.19249e22i | 0.118501i | ||||||||
\(903\) | 6.75973e22 | − | 7.65224e22i | 0.152907 | − | 0.173096i | ||||
\(904\) | −1.35874e23 | −0.304641 | ||||||||
\(905\) | 5.13410e23i | 1.14097i | ||||||||
\(906\) | 2.70586e23 | + | 2.39026e23i | 0.596046 | + | 0.526527i | ||||
\(907\) | −5.81091e23 | −1.26878 | −0.634389 | − | 0.773014i | \(-0.718748\pi\) | ||||
−0.634389 | + | 0.773014i | \(0.718748\pi\) | |||||||
\(908\) | − | 2.21503e23i | − | 0.479394i | ||||||
\(909\) | 5.21203e23 | − | 6.48033e22i | 1.11814 | − | 0.139023i | ||||
\(910\) | 4.00624e22 | 0.0851933 | ||||||||
\(911\) | − | 3.99461e23i | − | 0.842030i | −0.907054 | − | 0.421015i | \(-0.861674\pi\) | ||
0.907054 | − | 0.421015i | \(-0.138326\pi\) | |||||||
\(912\) | 2.72120e23 | − | 3.08049e23i | 0.568594 | − | 0.643667i | ||||
\(913\) | −3.79254e22 | −0.0785533 | ||||||||
\(914\) | 3.12621e23i | 0.641873i | ||||||||
\(915\) | 1.67182e23 | + | 1.47683e23i | 0.340268 | + | 0.300581i | ||||
\(916\) | −6.36484e22 | −0.128417 | ||||||||
\(917\) | 4.49919e23i | 0.899870i | ||||||||
\(918\) | −3.66376e23 | − | 2.50570e23i | −0.726417 | − | 0.496808i | ||||
\(919\) | 5.27094e23 | 1.03601 | 0.518005 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518005 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(920\) | − | 3.53589e23i | − | 0.688964i | ||||||
\(921\) | −3.92276e23 | + | 4.44069e23i | −0.757730 | + | 0.857776i | ||||
\(922\) | 2.95986e23 | 0.566793 | ||||||||
\(923\) | − | 5.07786e22i | − | 0.0963978i | ||||||
\(924\) | −7.35702e22 | − | 6.49894e22i | −0.138461 | − | 0.122311i | ||||
\(925\) | 1.63057e22 | 0.0304233 | ||||||||
\(926\) | 1.09465e23i | 0.202483i | ||||||||
\(927\) | 4.80837e22 | + | 3.86729e23i | 0.0881779 | + | 0.709201i | ||||
\(928\) | 4.97588e23 | 0.904662 | ||||||||
\(929\) | 1.10076e24i | 1.98412i | 0.125765 | + | 0.992060i | \(0.459861\pi\) | ||||
−0.125765 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(930\) | −2.40265e23 | + | 2.71989e23i | −0.429366 | + | 0.486057i | ||||
\(931\) | 8.39720e22 | 0.148777 | ||||||||
\(932\) | − | 2.12322e23i | − | 0.372964i | ||||||
\(933\) | 1.20655e23 | + | 1.06582e23i | 0.210131 | + | 0.185623i | ||||
\(934\) | −8.54196e23 | −1.47497 | ||||||||
\(935\) | − | 3.95867e23i | − | 0.677730i | ||||||
\(936\) | −5.86645e22 | + | 7.29400e21i | −0.0995791 | + | 0.0123811i | ||||
\(937\) | 1.08089e24 | 1.81914 | 0.909570 | − | 0.415550i | \(-0.136411\pi\) | ||||
0.909570 | + | 0.415550i | \(0.136411\pi\) | |||||||
\(938\) | − | 1.93050e23i | − | 0.322142i | ||||||
\(939\) | −1.34089e23 | + | 1.51794e23i | −0.221855 | + | 0.251148i | ||||
\(940\) | −2.26639e23 | −0.371802 | ||||||||
\(941\) | − | 1.11484e24i | − | 1.81341i | −0.421768 | − | 0.906704i | \(-0.638590\pi\) | ||
0.421768 | − | 0.906704i | \(-0.361410\pi\) | |||||||
\(942\) | −3.13549e23 | − | 2.76978e23i | −0.505706 | − | 0.446723i | ||||
\(943\) | −1.01361e23 | −0.162098 | ||||||||
\(944\) | 3.12411e23i | 0.495393i | ||||||||
\(945\) | 4.25858e23 | − | 6.22677e23i | 0.669592 | − | 0.979057i | ||||
\(946\) | 5.79866e22 | 0.0904062 | ||||||||
\(947\) | − | 2.98102e23i | − | 0.460855i | −0.973089 | − | 0.230428i | \(-0.925987\pi\) | ||
0.973089 | − | 0.230428i | \(-0.0740125\pi\) | |||||||
\(948\) | 5.15353e21 | − | 5.83398e21i | 0.00790021 | − | 0.00894330i | ||||
\(949\) | −7.87939e22 | −0.119774 | ||||||||
\(950\) | 5.21177e23i | 0.785591i | ||||||||
\(951\) | −8.52738e23 | − | 7.53279e23i | −1.27459 | − | 1.12593i | ||||
\(952\) | 7.96901e23 | 1.18116 | ||||||||
\(953\) | 6.23008e23i | 0.915694i | 0.889031 | + | 0.457847i | \(0.151379\pi\) | ||||
−0.889031 | + | 0.457847i | \(0.848621\pi\) | |||||||
\(954\) | −2.73782e22 | − | 2.20199e23i | −0.0399041 | − | 0.320943i | ||||
\(955\) | −1.10105e24 | −1.59140 | ||||||||
\(956\) | 4.15875e23i | 0.596073i | ||||||||
\(957\) | −2.76105e23 | + | 3.12560e23i | −0.392444 | + | 0.444260i | ||||
\(958\) | 4.96496e23 | 0.699828 | ||||||||
\(959\) | − | 9.25250e23i | − | 1.29333i | ||||||
\(960\) | −6.80300e23 | − | 6.00953e23i | −0.943041 | − | 0.833050i | ||||
\(961\) | −3.94539e23 | −0.542378 | ||||||||
\(962\) | 3.05597e21i | 0.00416628i | ||||||||
\(963\) | −2.85909e22 | + | 3.55482e21i | −0.0386560 | + | 0.00480626i | ||||
\(964\) | 4.01259e23 | 0.538032 | ||||||||
\(965\) | 5.80327e23i | 0.771710i | ||||||||
\(966\) | −1.92613e23 | + | 2.18045e23i | −0.254021 | + | 0.287560i | ||||
\(967\) | 2.93621e23 | 0.384039 | 0.192019 | − | 0.981391i | \(-0.438496\pi\) | ||||
0.192019 | + | 0.981391i | \(0.438496\pi\) | |||||||
\(968\) | 6.40141e23i | 0.830372i | ||||||||
\(969\) | 1.27370e24 | + | 1.12515e24i | 1.63862 | + | 1.44750i | ||||
\(970\) | 5.18035e23 | 0.660975 | ||||||||
\(971\) | 8.47517e21i | 0.0107249i | 0.999986 | + | 0.00536247i | \(0.00170693\pi\) | ||||
−0.999986 | + | 0.00536247i | \(0.998293\pi\) | |||||||
\(972\) | −1.45022e23 | + | 2.81200e23i | −0.182014 | + | 0.352927i | ||||
\(973\) | −8.86277e23 | −1.10323 | ||||||||
\(974\) | − | 1.20627e23i | − | 0.148926i | ||||||
\(975\) | 2.62305e22 | − | 2.96939e22i | 0.0321196 | − | 0.0363605i | ||||
\(976\) | −1.34797e23 | −0.163712 | ||||||||
\(977\) | − | 1.02852e24i | − | 1.23896i | −0.785013 | − | 0.619479i | \(-0.787344\pi\) | ||
0.785013 | − | 0.619479i | \(-0.212656\pi\) | |||||||
\(978\) | 8.76201e23 | + | 7.74006e23i | 1.04687 | + | 0.924769i | ||||
\(979\) | 6.94287e23 | 0.822769 | ||||||||
\(980\) | − | 3.21708e22i | − | 0.0378141i | ||||||
\(981\) | −1.23399e23 | − | 9.92482e23i | −0.143867 | − | 1.15710i | ||||
\(982\) | 6.47713e23 | 0.749016 | ||||||||
\(983\) | 2.43073e23i | 0.278811i | 0.990235 | + | 0.139405i | \(0.0445191\pi\) | ||||
−0.990235 | + | 0.139405i | \(0.955481\pi\) | |||||||
\(984\) | −1.98926e23 | + | 2.25191e23i | −0.226324 | + | 0.256207i | ||||
\(985\) | −5.38237e23 | −0.607412 | ||||||||
\(986\) | − | 9.62289e23i | − | 1.07719i | ||||||
\(987\) | 4.91712e23 | + | 4.34361e23i | 0.545976 | + | 0.482296i | ||||
\(988\) | 6.43345e22 | 0.0708579 | ||||||||
\(989\) | 1.13194e23i | 0.123666i | ||||||||
\(990\) | 4.25151e23 | − | 5.28608e22i | 0.460747 | − | 0.0572865i | ||||
\(991\) | −2.01271e23 | −0.216368 | −0.108184 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108184 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(992\) | 4.68871e23i | 0.499988i | ||||||||
\(993\) | 1.08433e23 | − | 1.22749e23i | 0.114701 | − | 0.129845i | ||||
\(994\) | −7.40805e23 | −0.777343 | ||||||||
\(995\) | 8.65466e23i | 0.900877i | ||||||||
\(996\) | −4.67495e22 | − | 4.12969e22i | −0.0482728 | − | 0.0426425i | ||||
\(997\) | −8.40325e23 | −0.860768 | −0.430384 | − | 0.902646i | \(-0.641622\pi\) | ||||
−0.430384 | + | 0.902646i | \(0.641622\pi\) | |||||||
\(998\) | − | 2.16520e23i | − | 0.220016i | ||||||
\(999\) | 4.74979e22 | + | 3.24846e22i | 0.0478796 | + | 0.0327456i |
(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 | 3.17.b.a.2.3 | yes | 4 | |
3.2 | odd | 2 | inner | 3.17.b.a.2.2 | ✓ | 4 | |
4.3 | odd | 2 | 48.17.e.b.17.2 | 4 | |||
5.2 | odd | 4 | 75.17.d.b.74.3 | 8 | |||
5.3 | odd | 4 | 75.17.d.b.74.6 | 8 | |||
5.4 | even | 2 | 75.17.c.d.26.2 | 4 | |||
12.11 | even | 2 | 48.17.e.b.17.1 | 4 | |||
15.2 | even | 4 | 75.17.d.b.74.5 | 8 | |||
15.8 | even | 4 | 75.17.d.b.74.4 | 8 | |||
15.14 | odd | 2 | 75.17.c.d.26.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.17.b.a.2.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
3.17.b.a.2.3 | yes | 4 | 1.1 | even | 1 | trivial | |
48.17.e.b.17.1 | 4 | 12.11 | even | 2 | |||
48.17.e.b.17.2 | 4 | 4.3 | odd | 2 | |||
75.17.c.d.26.2 | 4 | 5.4 | even | 2 | |||
75.17.c.d.26.3 | 4 | 15.14 | odd | 2 | |||
75.17.d.b.74.3 | 8 | 5.2 | odd | 4 | |||
75.17.d.b.74.4 | 8 | 15.8 | even | 4 | |||
75.17.d.b.74.5 | 8 | 15.2 | even | 4 | |||
75.17.d.b.74.6 | 8 | 5.3 | odd | 4 |