Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,10,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(2.57517918082\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.49740556.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 45x^{2} + 304 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.4 | ||
Root | \(2.87724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.10.b.a.4.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 41.3193i | 1.82607i | 0.407877 | + | 0.913037i | \(0.366269\pi\) | ||||
−0.407877 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(3\) | − | 37.6407i | − | 0.268294i | −0.990961 | − | 0.134147i | \(-0.957170\pi\) | ||
0.990961 | − | 0.134147i | \(-0.0428295\pi\) | |||||||
\(4\) | −1195.29 | −2.33455 | ||||||||
\(5\) | 1138.29 | + | 810.818i | 0.814492 | + | 0.580174i | ||||
\(6\) | 1555.29 | 0.489926 | ||||||||
\(7\) | 5315.22i | 0.836719i | 0.908281 | + | 0.418360i | \(0.137395\pi\) | ||||
−0.908281 | + | 0.418360i | \(0.862605\pi\) | |||||||
\(8\) | − | 28233.0i | − | 2.43698i | ||||||
\(9\) | 18266.2 | 0.928018 | ||||||||
\(10\) | −33502.5 | + | 47033.3i | −1.05944 | + | 1.48732i | ||||
\(11\) | 10426.2 | 0.214714 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(12\) | 44991.4i | 0.626346i | ||||||||
\(13\) | − | 79655.1i | − | 0.773515i | −0.922181 | − | 0.386758i | \(-0.873595\pi\) | ||
0.922181 | − | 0.386758i | \(-0.126405\pi\) | |||||||
\(14\) | −219621. | −1.52791 | ||||||||
\(15\) | 30519.7 | − | 42845.9i | 0.155658 | − | 0.218524i | ||||
\(16\) | 554581. | 2.11556 | ||||||||
\(17\) | − | 313750.i | − | 0.911095i | −0.890212 | − | 0.455547i | \(-0.849444\pi\) | ||
0.890212 | − | 0.455547i | \(-0.150556\pi\) | |||||||
\(18\) | 754746.i | 1.69463i | ||||||||
\(19\) | 246945. | 0.434719 | 0.217360 | − | 0.976092i | \(-0.430256\pi\) | ||||
0.217360 | + | 0.976092i | \(0.430256\pi\) | |||||||
\(20\) | −1.36058e6 | − | 969161.i | −1.90147 | − | 1.35444i | ||||
\(21\) | 200068. | 0.224487 | ||||||||
\(22\) | 430806.i | 0.392084i | ||||||||
\(23\) | 721761.i | 0.537797i | 0.963169 | + | 0.268898i | \(0.0866595\pi\) | ||||
−0.963169 | + | 0.268898i | \(0.913340\pi\) | |||||||
\(24\) | −1.06271e6 | −0.653828 | ||||||||
\(25\) | 638273. | + | 1.84589e6i | 0.326796 | + | 0.945095i | ||||
\(26\) | 3.29130e6 | 1.41250 | ||||||||
\(27\) | − | 1.42843e6i | − | 0.517277i | ||||||
\(28\) | − | 6.35321e6i | − | 1.95336i | ||||||
\(29\) | −2.56903e6 | −0.674493 | −0.337247 | − | 0.941416i | \(-0.609496\pi\) | ||||
−0.337247 | + | 0.941416i | \(0.609496\pi\) | |||||||
\(30\) | 1.77037e6 | + | 1.26106e6i | 0.399041 | + | 0.284242i | ||||
\(31\) | −3.29543e6 | −0.640891 | −0.320445 | − | 0.947267i | \(-0.603833\pi\) | ||||
−0.320445 | + | 0.947267i | \(0.603833\pi\) | |||||||
\(32\) | 8.45965e6i | 1.42619i | ||||||||
\(33\) | − | 392451.i | − | 0.0576066i | ||||||
\(34\) | 1.29639e7 | 1.66373 | ||||||||
\(35\) | −4.30967e6 | + | 6.05025e6i | −0.485443 | + | 0.681502i | ||||
\(36\) | −2.18333e7 | −2.16650 | ||||||||
\(37\) | − | 1.40463e7i | − | 1.23212i | −0.787699 | − | 0.616060i | \(-0.788728\pi\) | ||
0.787699 | − | 0.616060i | \(-0.211272\pi\) | |||||||
\(38\) | 1.02036e7i | 0.793830i | ||||||||
\(39\) | −2.99827e6 | −0.207530 | ||||||||
\(40\) | 2.28918e7 | − | 3.21373e7i | 1.41387 | − | 1.98490i | ||||
\(41\) | 1.70412e7 | 0.941830 | 0.470915 | − | 0.882178i | \(-0.343924\pi\) | ||||
0.470915 | + | 0.882178i | \(0.343924\pi\) | |||||||
\(42\) | 8.26669e6i | 0.409930i | ||||||||
\(43\) | 2.92261e7i | 1.30365i | 0.758368 | + | 0.651827i | \(0.225997\pi\) | ||||
−0.758368 | + | 0.651827i | \(0.774003\pi\) | |||||||
\(44\) | −1.24624e7 | −0.501260 | ||||||||
\(45\) | 2.07922e7 | + | 1.48105e7i | 0.755864 | + | 0.538412i | ||||
\(46\) | −2.98227e7 | −0.982056 | ||||||||
\(47\) | − | 4.10316e7i | − | 1.22653i | −0.789878 | − | 0.613264i | \(-0.789856\pi\) | ||
0.789878 | − | 0.613264i | \(-0.210144\pi\) | |||||||
\(48\) | − | 2.08748e7i | − | 0.567593i | ||||||
\(49\) | 1.21021e7 | 0.299901 | ||||||||
\(50\) | −7.62709e7 | + | 2.63730e7i | −1.72581 | + | 0.596753i | ||||
\(51\) | −1.18098e7 | −0.244442 | ||||||||
\(52\) | 9.52108e7i | 1.80581i | ||||||||
\(53\) | − | 5.67230e7i | − | 0.987456i | −0.869616 | − | 0.493728i | \(-0.835634\pi\) | ||
0.869616 | − | 0.493728i | \(-0.164366\pi\) | |||||||
\(54\) | 5.90219e7 | 0.944585 | ||||||||
\(55\) | 1.18681e7 | + | 8.45379e6i | 0.174883 | + | 0.124572i | ||||
\(56\) | 1.50065e8 | 2.03907 | ||||||||
\(57\) | − | 9.29518e6i | − | 0.116633i | ||||||
\(58\) | − | 1.06150e8i | − | 1.23167i | ||||||
\(59\) | −1.60408e8 | −1.72342 | −0.861710 | − | 0.507402i | \(-0.830606\pi\) | ||||
−0.861710 | + | 0.507402i | \(0.830606\pi\) | |||||||
\(60\) | −3.64799e7 | + | 5.12132e7i | −0.363390 | + | 0.510154i | ||||
\(61\) | 5.33033e7 | 0.492912 | 0.246456 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246456 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(62\) | − | 1.36165e8i | − | 1.17031i | ||||||
\(63\) | 9.70887e7i | 0.776491i | ||||||||
\(64\) | −6.56012e7 | −0.488767 | ||||||||
\(65\) | 6.45858e7 | − | 9.06705e7i | 0.448773 | − | 0.630022i | ||||
\(66\) | 1.62158e7 | 0.105194 | ||||||||
\(67\) | 2.80916e8i | 1.70310i | 0.524276 | + | 0.851548i | \(0.324336\pi\) | ||||
−0.524276 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(68\) | 3.75022e8i | 2.12699i | ||||||||
\(69\) | 2.71676e7 | 0.144288 | ||||||||
\(70\) | −2.49992e8 | − | 1.78073e8i | −1.24447 | − | 0.886455i | ||||
\(71\) | −8.97228e7 | −0.419025 | −0.209513 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209513 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(72\) | − | 5.15709e8i | − | 2.26156i | ||||||
\(73\) | − | 7.60225e7i | − | 0.313321i | −0.987653 | − | 0.156660i | \(-0.949927\pi\) | ||
0.987653 | − | 0.156660i | \(-0.0500728\pi\) | |||||||
\(74\) | 5.80383e8 | 2.24994 | ||||||||
\(75\) | 6.94805e7 | − | 2.40250e7i | 0.253564 | − | 0.0876775i | ||||
\(76\) | −2.95170e8 | −1.01487 | ||||||||
\(77\) | 5.54178e7i | 0.179656i | ||||||||
\(78\) | − | 1.23887e8i | − | 0.378965i | ||||||
\(79\) | −4.10672e8 | −1.18624 | −0.593120 | − | 0.805114i | \(-0.702104\pi\) | ||||
−0.593120 | + | 0.805114i | \(0.702104\pi\) | |||||||
\(80\) | 6.31273e8 | + | 4.49665e8i | 1.72311 | + | 1.22739i | ||||
\(81\) | 3.05766e8 | 0.789236 | ||||||||
\(82\) | 7.04131e8i | 1.71985i | ||||||||
\(83\) | − | 5.21969e8i | − | 1.20724i | −0.797272 | − | 0.603620i | \(-0.793724\pi\) | ||
0.797272 | − | 0.603620i | \(-0.206276\pi\) | |||||||
\(84\) | −2.39139e8 | −0.524076 | ||||||||
\(85\) | 2.54394e8 | − | 3.57138e8i | 0.528594 | − | 0.742080i | ||||
\(86\) | −1.20760e9 | −2.38057 | ||||||||
\(87\) | 9.66999e7i | 0.180963i | ||||||||
\(88\) | − | 2.94364e8i | − | 0.523254i | ||||||
\(89\) | −2.37312e8 | −0.400926 | −0.200463 | − | 0.979701i | \(-0.564245\pi\) | ||||
−0.200463 | + | 0.979701i | \(0.564245\pi\) | |||||||
\(90\) | −6.11962e8 | + | 8.59119e8i | −0.983180 | + | 1.38026i | ||||
\(91\) | 4.23384e8 | 0.647215 | ||||||||
\(92\) | − | 8.62712e8i | − | 1.25551i | ||||||
\(93\) | 1.24042e8i | 0.171947i | ||||||||
\(94\) | 1.69540e9 | 2.23973 | ||||||||
\(95\) | 2.81094e8 | + | 2.00227e8i | 0.354076 | + | 0.252213i | ||||
\(96\) | 3.18427e8 | 0.382639 | ||||||||
\(97\) | 6.03778e8i | 0.692476i | 0.938147 | + | 0.346238i | \(0.112541\pi\) | ||||
−0.938147 | + | 0.346238i | \(0.887459\pi\) | |||||||
\(98\) | 5.00050e8i | 0.547641i | ||||||||
\(99\) | 1.90448e8 | 0.199259 | ||||||||
\(100\) | −7.62920e8 | − | 2.20637e9i | −0.762920 | − | 2.20637i | ||||
\(101\) | −2.03606e8 | −0.194690 | −0.0973451 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973451 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(102\) | − | 4.87972e8i | − | 0.446369i | ||||||
\(103\) | 9.15893e8i | 0.801821i | 0.916117 | + | 0.400910i | \(0.131306\pi\) | ||||
−0.916117 | + | 0.400910i | \(0.868694\pi\) | |||||||
\(104\) | −2.24890e9 | −1.88504 | ||||||||
\(105\) | 2.27735e8 | + | 1.62219e8i | 0.182843 | + | 0.130242i | ||||
\(106\) | 2.34376e9 | 1.80317 | ||||||||
\(107\) | − | 1.66237e9i | − | 1.22603i | −0.790072 | − | 0.613014i | \(-0.789957\pi\) | ||
0.790072 | − | 0.613014i | \(-0.210043\pi\) | |||||||
\(108\) | 1.70739e9i | 1.20761i | ||||||||
\(109\) | −1.73161e9 | −1.17498 | −0.587491 | − | 0.809231i | \(-0.699884\pi\) | ||||
−0.587491 | + | 0.809231i | \(0.699884\pi\) | |||||||
\(110\) | −3.49305e8 | + | 4.90381e8i | −0.227477 | + | 0.319350i | ||||
\(111\) | −5.28711e8 | −0.330571 | ||||||||
\(112\) | 2.94772e9i | 1.77013i | ||||||||
\(113\) | 6.30956e8i | 0.364038i | 0.983295 | + | 0.182019i | \(0.0582632\pi\) | ||||
−0.983295 | + | 0.182019i | \(0.941737\pi\) | |||||||
\(114\) | 3.84070e8 | 0.212980 | ||||||||
\(115\) | −5.85217e8 | + | 8.21571e8i | −0.312016 | + | 0.438031i | ||||
\(116\) | 3.07073e9 | 1.57464 | ||||||||
\(117\) | − | 1.45500e9i | − | 0.717836i | ||||||
\(118\) | − | 6.62794e9i | − | 3.14709i | ||||||
\(119\) | 1.66765e9 | 0.762331 | ||||||||
\(120\) | −1.20967e9 | − | 8.61664e8i | −0.532538 | − | 0.379334i | ||||
\(121\) | −2.24924e9 | −0.953898 | ||||||||
\(122\) | 2.20246e9i | 0.900094i | ||||||||
\(123\) | − | 6.41442e8i | − | 0.252688i | ||||||
\(124\) | 3.93898e9 | 1.49619 | ||||||||
\(125\) | −7.70141e8 | + | 2.61868e9i | −0.282147 | + | 0.959371i | ||||
\(126\) | −4.01164e9 | −1.41793 | ||||||||
\(127\) | − | 2.12104e9i | − | 0.723490i | −0.932277 | − | 0.361745i | \(-0.882181\pi\) | ||
0.932277 | − | 0.361745i | \(-0.117819\pi\) | |||||||
\(128\) | 1.62074e9i | 0.533664i | ||||||||
\(129\) | 1.10009e9 | 0.349763 | ||||||||
\(130\) | 3.74644e9 | + | 2.66864e9i | 1.15047 | + | 0.819494i | ||||
\(131\) | 5.57686e9 | 1.65451 | 0.827254 | − | 0.561828i | \(-0.189902\pi\) | ||||
0.827254 | + | 0.561828i | \(0.189902\pi\) | |||||||
\(132\) | 4.69092e8i | 0.134485i | ||||||||
\(133\) | 1.31257e9i | 0.363738i | ||||||||
\(134\) | −1.16072e10 | −3.10998 | ||||||||
\(135\) | 1.15820e9 | − | 1.62597e9i | 0.300111 | − | 0.421318i | ||||
\(136\) | −8.85810e9 | −2.22032 | ||||||||
\(137\) | 2.57317e9i | 0.624059i | 0.950072 | + | 0.312029i | \(0.101009\pi\) | ||||
−0.950072 | + | 0.312029i | \(0.898991\pi\) | |||||||
\(138\) | 1.12255e9i | 0.263480i | ||||||||
\(139\) | 1.62297e9 | 0.368761 | 0.184380 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(140\) | 5.15130e9 | − | 7.23179e9i | 1.13329 | − | 1.59100i | ||||
\(141\) | −1.54446e9 | −0.329071 | ||||||||
\(142\) | − | 3.70729e9i | − | 0.765171i | ||||||
\(143\) | − | 8.30504e8i | − | 0.166085i | ||||||
\(144\) | 1.01301e10 | 1.96328 | ||||||||
\(145\) | −2.92429e9 | − | 2.08301e9i | −0.549370 | − | 0.391324i | ||||
\(146\) | 3.14120e9 | 0.572147 | ||||||||
\(147\) | − | 4.55530e8i | − | 0.0804617i | ||||||
\(148\) | 1.67893e10i | 2.87644i | ||||||||
\(149\) | 5.98422e9 | 0.994647 | 0.497324 | − | 0.867565i | \(-0.334316\pi\) | ||||
0.497324 | + | 0.867565i | \(0.334316\pi\) | |||||||
\(150\) | 9.92698e8 | + | 2.87089e9i | 0.160106 | + | 0.463026i | ||||
\(151\) | −5.95089e9 | −0.931505 | −0.465753 | − | 0.884915i | \(-0.654216\pi\) | ||||
−0.465753 | + | 0.884915i | \(0.654216\pi\) | |||||||
\(152\) | − | 6.97200e9i | − | 1.05940i | ||||||
\(153\) | − | 5.73101e9i | − | 0.845513i | ||||||
\(154\) | −2.28983e9 | −0.328064 | ||||||||
\(155\) | −3.75114e9 | − | 2.67199e9i | −0.522001 | − | 0.371828i | ||||
\(156\) | 3.58380e9 | 0.484488 | ||||||||
\(157\) | 2.94325e9i | 0.386615i | 0.981138 | + | 0.193308i | \(0.0619215\pi\) | ||||
−0.981138 | + | 0.193308i | \(0.938078\pi\) | |||||||
\(158\) | − | 1.69687e10i | − | 2.16616i | ||||||
\(159\) | −2.13509e9 | −0.264929 | ||||||||
\(160\) | −6.85923e9 | + | 9.62951e9i | −0.827438 | + | 1.16162i | ||||
\(161\) | −3.83632e9 | −0.449985 | ||||||||
\(162\) | 1.26341e10i | 1.44120i | ||||||||
\(163\) | 2.69823e9i | 0.299389i | 0.988732 | + | 0.149694i | \(0.0478290\pi\) | ||||
−0.988732 | + | 0.149694i | \(0.952171\pi\) | |||||||
\(164\) | −2.03691e10 | −2.19875 | ||||||||
\(165\) | 3.18206e8 | − | 4.46722e8i | 0.0334219 | − | 0.0469202i | ||||
\(166\) | 2.15674e10 | 2.20451 | ||||||||
\(167\) | 1.47132e10i | 1.46380i | 0.681410 | + | 0.731902i | \(0.261367\pi\) | ||||
−0.681410 | + | 0.731902i | \(0.738633\pi\) | |||||||
\(168\) | − | 5.64853e9i | − | 0.547071i | ||||||
\(169\) | 4.25956e9 | 0.401675 | ||||||||
\(170\) | 1.47567e10 | + | 1.05114e10i | 1.35509 | + | 0.965251i | ||||
\(171\) | 4.51074e9 | 0.403427 | ||||||||
\(172\) | − | 3.49336e10i | − | 3.04344i | ||||||
\(173\) | − | 1.56605e8i | − | 0.0132923i | −0.999978 | − | 0.00664613i | \(-0.997884\pi\) | ||
0.999978 | − | 0.00664613i | \(-0.00211555\pi\) | |||||||
\(174\) | −3.99558e9 | −0.330452 | ||||||||
\(175\) | −9.81130e9 | + | 3.39256e9i | −0.790779 | + | 0.273436i | ||||
\(176\) | 5.78220e9 | 0.454241 | ||||||||
\(177\) | 6.03785e9i | 0.462384i | ||||||||
\(178\) | − | 9.80557e9i | − | 0.732121i | ||||||
\(179\) | 5.35516e9 | 0.389883 | 0.194941 | − | 0.980815i | \(-0.437548\pi\) | ||||
0.194941 | + | 0.980815i | \(0.437548\pi\) | |||||||
\(180\) | −2.48526e10 | − | 1.77029e10i | −1.76460 | − | 1.25695i | ||||
\(181\) | −1.52107e9 | −0.105341 | −0.0526704 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526704 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(182\) | 1.74940e10i | 1.18186i | ||||||||
\(183\) | − | 2.00637e9i | − | 0.132246i | ||||||
\(184\) | 2.03775e10 | 1.31060 | ||||||||
\(185\) | 1.13890e10 | − | 1.59887e10i | 0.714845 | − | 1.00355i | ||||
\(186\) | −5.12534e9 | −0.313989 | ||||||||
\(187\) | − | 3.27123e9i | − | 0.195625i | ||||||
\(188\) | 4.90445e10i | 2.86339i | ||||||||
\(189\) | 7.59243e9 | 0.432815 | ||||||||
\(190\) | −8.27327e9 | + | 1.16146e10i | −0.460560 | + | 0.646568i | ||||
\(191\) | −9.28266e9 | −0.504687 | −0.252344 | − | 0.967638i | \(-0.581201\pi\) | ||||
−0.252344 | + | 0.967638i | \(0.581201\pi\) | |||||||
\(192\) | 2.46927e9i | 0.131134i | ||||||||
\(193\) | 6.94351e9i | 0.360223i | 0.983646 | + | 0.180111i | \(0.0576458\pi\) | ||||
−0.983646 | + | 0.180111i | \(0.942354\pi\) | |||||||
\(194\) | −2.49477e10 | −1.26451 | ||||||||
\(195\) | −3.41290e9 | − | 2.43105e9i | −0.169031 | − | 0.120403i | ||||
\(196\) | −1.44655e10 | −0.700132 | ||||||||
\(197\) | − | 3.60722e10i | − | 1.70637i | −0.521606 | − | 0.853187i | \(-0.674667\pi\) | ||
0.521606 | − | 0.853187i | \(-0.325333\pi\) | |||||||
\(198\) | 7.86917e9i | 0.363861i | ||||||||
\(199\) | −2.25173e10 | −1.01784 | −0.508918 | − | 0.860815i | \(-0.669955\pi\) | ||||
−0.508918 | + | 0.860815i | \(0.669955\pi\) | |||||||
\(200\) | 5.21150e10 | − | 1.80204e10i | 2.30318 | − | 0.796395i | ||||
\(201\) | 1.05739e10 | 0.456931 | ||||||||
\(202\) | − | 8.41286e9i | − | 0.355519i | ||||||
\(203\) | − | 1.36549e10i | − | 0.564362i | ||||||
\(204\) | 1.41161e10 | 0.570661 | ||||||||
\(205\) | 1.93978e10 | + | 1.38173e10i | 0.767114 | + | 0.546426i | ||||
\(206\) | −3.78441e10 | −1.46418 | ||||||||
\(207\) | 1.31838e10i | 0.499085i | ||||||||
\(208\) | − | 4.41753e10i | − | 1.63642i | ||||||
\(209\) | 2.57471e9 | 0.0933404 | ||||||||
\(210\) | −6.70278e9 | + | 9.40988e9i | −0.237831 | + | 0.333885i | ||||
\(211\) | 3.62300e10 | 1.25834 | 0.629169 | − | 0.777268i | \(-0.283395\pi\) | ||||
0.629169 | + | 0.777268i | \(0.283395\pi\) | |||||||
\(212\) | 6.78003e10i | 2.30526i | ||||||||
\(213\) | 3.37723e9i | 0.112422i | ||||||||
\(214\) | 6.86879e10 | 2.23882 | ||||||||
\(215\) | −2.36970e10 | + | 3.32677e10i | −0.756346 | + | 1.06182i | ||||
\(216\) | −4.03289e10 | −1.26059 | ||||||||
\(217\) | − | 1.75159e10i | − | 0.536246i | ||||||
\(218\) | − | 7.15490e10i | − | 2.14560i | ||||||
\(219\) | −2.86154e9 | −0.0840623 | ||||||||
\(220\) | −1.41858e10 | − | 1.01047e10i | −0.408273 | − | 0.290818i | ||||
\(221\) | −2.49918e10 | −0.704746 | ||||||||
\(222\) | − | 2.18460e10i | − | 0.603647i | ||||||
\(223\) | 4.93834e10i | 1.33724i | 0.743605 | + | 0.668619i | \(0.233114\pi\) | ||||
−0.743605 | + | 0.668619i | \(0.766886\pi\) | |||||||
\(224\) | −4.49649e10 | −1.19332 | ||||||||
\(225\) | 1.16588e10 | + | 3.37173e10i | 0.303272 | + | 0.877065i | ||||
\(226\) | −2.60707e10 | −0.664760 | ||||||||
\(227\) | − | 3.27710e10i | − | 0.819169i | −0.912272 | − | 0.409585i | \(-0.865674\pi\) | ||
0.912272 | − | 0.409585i | \(-0.134326\pi\) | |||||||
\(228\) | 1.11104e10i | 0.272285i | ||||||||
\(229\) | −1.35586e10 | −0.325803 | −0.162902 | − | 0.986642i | \(-0.552085\pi\) | ||||
−0.162902 | + | 0.986642i | \(0.552085\pi\) | |||||||
\(230\) | −3.39468e10 | − | 2.41808e10i | −0.799877 | − | 0.569764i | ||||
\(231\) | 2.08596e9 | 0.0482006 | ||||||||
\(232\) | 7.25313e10i | 1.64373i | ||||||||
\(233\) | − | 7.99837e9i | − | 0.177787i | −0.996041 | − | 0.0888935i | \(-0.971667\pi\) | ||
0.996041 | − | 0.0888935i | \(-0.0283331\pi\) | |||||||
\(234\) | 6.01194e10 | 1.31082 | ||||||||
\(235\) | 3.32691e10 | − | 4.67057e10i | 0.711600 | − | 0.998998i | ||||
\(236\) | 1.91733e11 | 4.02340 | ||||||||
\(237\) | 1.54580e10i | 0.318262i | ||||||||
\(238\) | 6.89062e10i | 1.39207i | ||||||||
\(239\) | −8.30208e10 | −1.64587 | −0.822937 | − | 0.568133i | \(-0.807666\pi\) | ||||
−0.822937 | + | 0.568133i | \(0.807666\pi\) | |||||||
\(240\) | 1.69257e10 | − | 2.37616e10i | 0.329303 | − | 0.462300i | ||||
\(241\) | −6.04789e10 | −1.15485 | −0.577427 | − | 0.816442i | \(-0.695943\pi\) | ||||
−0.577427 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(242\) | − | 9.29372e10i | − | 1.74189i | ||||||
\(243\) | − | 3.96251e10i | − | 0.729024i | ||||||
\(244\) | −6.37128e10 | −1.15073 | ||||||||
\(245\) | 1.37756e10 | + | 9.81258e9i | 0.244267 | + | 0.173995i | ||||
\(246\) | 2.65040e10 | 0.461427 | ||||||||
\(247\) | − | 1.96704e10i | − | 0.336262i | ||||||
\(248\) | 9.30398e10i | 1.56184i | ||||||||
\(249\) | −1.96473e10 | −0.323896 | ||||||||
\(250\) | −1.08202e11 | − | 3.18217e10i | −1.75188 | − | 0.515221i | ||||
\(251\) | 1.04682e11 | 1.66471 | 0.832354 | − | 0.554244i | \(-0.186993\pi\) | ||||
0.832354 | + | 0.554244i | \(0.186993\pi\) | |||||||
\(252\) | − | 1.16049e11i | − | 1.81275i | ||||||
\(253\) | 7.52525e9i | 0.115473i | ||||||||
\(254\) | 8.76400e10 | 1.32115 | ||||||||
\(255\) | −1.34429e10 | − | 9.57557e9i | −0.199096 | − | 0.141819i | ||||
\(256\) | −1.00556e11 | −1.46328 | ||||||||
\(257\) | 7.92751e10i | 1.13354i | 0.823875 | + | 0.566771i | \(0.191808\pi\) | ||||
−0.823875 | + | 0.566771i | \(0.808192\pi\) | |||||||
\(258\) | 4.54549e10i | 0.638693i | ||||||||
\(259\) | 7.46590e10 | 1.03094 | ||||||||
\(260\) | −7.71987e10 | + | 1.08377e11i | −1.04768 | + | 1.47082i | ||||
\(261\) | −4.69263e10 | −0.625942 | ||||||||
\(262\) | 2.30432e11i | 3.02126i | ||||||||
\(263\) | − | 1.04629e8i | − | 0.00134850i | −1.00000 | 0.000674250i | \(-0.999785\pi\) | |||
1.00000 | 0.000674250i | \(-0.000214620\pi\) | ||||||||
\(264\) | −1.10801e10 | −0.140386 | ||||||||
\(265\) | 4.59920e10 | − | 6.45671e10i | 0.572897 | − | 0.804275i | ||||
\(266\) | −5.42344e10 | −0.664213 | ||||||||
\(267\) | 8.93258e9i | 0.107566i | ||||||||
\(268\) | − | 3.35775e11i | − | 3.97596i | ||||||
\(269\) | 7.38735e9 | 0.0860208 | 0.0430104 | − | 0.999075i | \(-0.486305\pi\) | ||||
0.0430104 | + | 0.999075i | \(0.486305\pi\) | |||||||
\(270\) | 6.71839e10 | + | 4.78560e10i | 0.769358 | + | 0.548024i | ||||
\(271\) | 1.27706e11 | 1.43831 | 0.719153 | − | 0.694852i | \(-0.244530\pi\) | ||||
0.719153 | + | 0.694852i | \(0.244530\pi\) | |||||||
\(272\) | − | 1.74000e11i | − | 1.92748i | ||||||
\(273\) | − | 1.59365e10i | − | 0.173644i | ||||||
\(274\) | −1.06322e11 | −1.13958 | ||||||||
\(275\) | 6.65479e9 | + | 1.92457e10i | 0.0701677 | + | 0.202925i | ||||
\(276\) | −3.24731e10 | −0.336847 | ||||||||
\(277\) | 3.16563e10i | 0.323074i | 0.986867 | + | 0.161537i | \(0.0516451\pi\) | ||||
−0.986867 | + | 0.161537i | \(0.948355\pi\) | |||||||
\(278\) | 6.70602e10i | 0.673385i | ||||||||
\(279\) | −6.01949e10 | −0.594758 | ||||||||
\(280\) | 1.70817e11 | + | 1.21675e11i | 1.66081 | + | 1.18302i | ||||
\(281\) | −9.50309e10 | −0.909257 | −0.454628 | − | 0.890681i | \(-0.650228\pi\) | ||||
−0.454628 | + | 0.890681i | \(0.650228\pi\) | |||||||
\(282\) | − | 6.38159e10i | − | 0.600908i | ||||||
\(283\) | − | 4.91862e10i | − | 0.455832i | −0.973681 | − | 0.227916i | \(-0.926809\pi\) | ||
0.973681 | − | 0.227916i | \(-0.0731911\pi\) | |||||||
\(284\) | 1.07245e11 | 0.978234 | ||||||||
\(285\) | 7.53670e9 | − | 1.05806e10i | 0.0676673 | − | 0.0949965i | ||||
\(286\) | 3.43159e10 | 0.303283 | ||||||||
\(287\) | 9.05777e10i | 0.788048i | ||||||||
\(288\) | 1.54525e11i | 1.32353i | ||||||||
\(289\) | 2.01488e10 | 0.169906 | ||||||||
\(290\) | 8.60687e10 | − | 1.20830e11i | 0.714586 | − | 1.00319i | ||||
\(291\) | 2.27266e10 | 0.185787 | ||||||||
\(292\) | 9.08688e10i | 0.731462i | ||||||||
\(293\) | − | 3.53889e10i | − | 0.280519i | −0.990115 | − | 0.140260i | \(-0.955206\pi\) | ||
0.990115 | − | 0.140260i | \(-0.0447937\pi\) | |||||||
\(294\) | 1.88222e10 | 0.146929 | ||||||||
\(295\) | −1.82590e11 | − | 1.30061e11i | −1.40371 | − | 0.999883i | ||||
\(296\) | −3.96568e11 | −3.00265 | ||||||||
\(297\) | − | 1.48932e10i | − | 0.111067i | ||||||
\(298\) | 2.47264e11i | 1.81630i | ||||||||
\(299\) | 5.74920e10 | 0.415994 | ||||||||
\(300\) | −8.30492e10 | + | 2.87168e10i | −0.591956 | + | 0.204687i | ||||
\(301\) | −1.55343e11 | −1.09079 | ||||||||
\(302\) | − | 2.45887e11i | − | 1.70100i | ||||||
\(303\) | 7.66386e9i | 0.0522343i | ||||||||
\(304\) | 1.36951e11 | 0.919675 | ||||||||
\(305\) | 6.06745e10 | + | 4.32193e10i | 0.401473 | + | 0.285975i | ||||
\(306\) | 2.36802e11 | 1.54397 | ||||||||
\(307\) | − | 8.30301e10i | − | 0.533474i | −0.963769 | − | 0.266737i | \(-0.914055\pi\) | ||
0.963769 | − | 0.266737i | \(-0.0859455\pi\) | |||||||
\(308\) | − | 6.62402e10i | − | 0.419414i | ||||||
\(309\) | 3.44748e10 | 0.215124 | ||||||||
\(310\) | 1.10405e11 | − | 1.54995e11i | 0.678986 | − | 0.953212i | ||||
\(311\) | 2.13935e10 | 0.129676 | 0.0648382 | − | 0.997896i | \(-0.479347\pi\) | ||||
0.0648382 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(312\) | 8.46502e10i | 0.505746i | ||||||||
\(313\) | 2.56558e11i | 1.51090i | 0.655204 | + | 0.755452i | \(0.272582\pi\) | ||||
−0.655204 | + | 0.755452i | \(0.727418\pi\) | |||||||
\(314\) | −1.21613e11 | −0.705988 | ||||||||
\(315\) | −7.87213e10 | + | 1.10515e11i | −0.450500 | + | 0.632446i | ||||
\(316\) | 4.90871e11 | 2.76933 | ||||||||
\(317\) | 1.26112e11i | 0.701436i | 0.936481 | + | 0.350718i | \(0.114062\pi\) | ||||
−0.936481 | + | 0.350718i | \(0.885938\pi\) | |||||||
\(318\) | − | 8.82206e10i | − | 0.483780i | ||||||
\(319\) | −2.67853e10 | −0.144823 | ||||||||
\(320\) | −7.46731e10 | − | 5.31907e10i | −0.398097 | − | 0.283570i | ||||
\(321\) | −6.25727e10 | −0.328936 | ||||||||
\(322\) | − | 1.58514e11i | − | 0.821706i | ||||||
\(323\) | − | 7.74790e10i | − | 0.396071i | ||||||
\(324\) | −3.65478e11 | −1.84251 | ||||||||
\(325\) | 1.47035e11 | − | 5.08417e10i | 0.731045 | − | 0.252781i | ||||
\(326\) | −1.11489e11 | −0.546706 | ||||||||
\(327\) | 6.51790e10i | 0.315241i | ||||||||
\(328\) | − | 4.81124e11i | − | 2.29522i | ||||||
\(329\) | 2.18092e11 | 1.02626 | ||||||||
\(330\) | 1.84583e10 | + | 1.31481e10i | 0.0856797 | + | 0.0610308i | ||||
\(331\) | 1.71300e11 | 0.784389 | 0.392194 | − | 0.919882i | \(-0.371716\pi\) | ||||
0.392194 | + | 0.919882i | \(0.371716\pi\) | |||||||
\(332\) | 6.23904e11i | 2.81836i | ||||||||
\(333\) | − | 2.56572e11i | − | 1.14343i | ||||||
\(334\) | −6.07939e11 | −2.67301 | ||||||||
\(335\) | −2.27771e11 | + | 3.19763e11i | −0.988093 | + | 1.38716i | ||||
\(336\) | 1.10954e11 | 0.474916 | ||||||||
\(337\) | − | 4.70320e11i | − | 1.98637i | −0.116569 | − | 0.993183i | \(-0.537190\pi\) | ||
0.116569 | − | 0.993183i | \(-0.462810\pi\) | |||||||
\(338\) | 1.76002e11i | 0.733487i | ||||||||
\(339\) | 2.37496e10 | 0.0976693 | ||||||||
\(340\) | −3.04074e11 | + | 4.26882e11i | −1.23403 | + | 1.73242i | ||||
\(341\) | −3.43589e10 | −0.137608 | ||||||||
\(342\) | 1.86381e11i | 0.736688i | ||||||||
\(343\) | 2.78813e11i | 1.08765i | ||||||||
\(344\) | 8.25140e11 | 3.17698 | ||||||||
\(345\) | 3.09245e10 | + | 2.20279e10i | 0.117521 | + | 0.0837121i | ||||
\(346\) | 6.47083e9 | 0.0242727 | ||||||||
\(347\) | − | 2.86642e11i | − | 1.06135i | −0.847576 | − | 0.530674i | \(-0.821939\pi\) | ||
0.847576 | − | 0.530674i | \(-0.178061\pi\) | |||||||
\(348\) | − | 1.15584e11i | − | 0.422466i | ||||||
\(349\) | 3.54310e11 | 1.27841 | 0.639203 | − | 0.769038i | \(-0.279264\pi\) | ||||
0.639203 | + | 0.769038i | \(0.279264\pi\) | |||||||
\(350\) | −1.40178e11 | − | 4.05396e11i | −0.499315 | − | 1.44402i | ||||
\(351\) | −1.13782e11 | −0.400121 | ||||||||
\(352\) | 8.82023e10i | 0.306223i | ||||||||
\(353\) | − | 2.09491e11i | − | 0.718092i | −0.933320 | − | 0.359046i | \(-0.883102\pi\) | ||
0.933320 | − | 0.359046i | \(-0.116898\pi\) | |||||||
\(354\) | −2.49480e11 | −0.844347 | ||||||||
\(355\) | −1.02130e11 | − | 7.27489e10i | −0.341293 | − | 0.243108i | ||||
\(356\) | 2.83656e11 | 0.935981 | ||||||||
\(357\) | − | 6.27715e10i | − | 0.204529i | ||||||
\(358\) | 2.21272e11i | 0.711955i | ||||||||
\(359\) | −2.88081e11 | −0.915355 | −0.457678 | − | 0.889118i | \(-0.651319\pi\) | ||||
−0.457678 | + | 0.889118i | \(0.651319\pi\) | |||||||
\(360\) | 4.18146e11 | − | 5.87025e11i | 1.31210 | − | 1.84203i | ||||
\(361\) | −2.61706e11 | −0.811019 | ||||||||
\(362\) | − | 6.28498e10i | − | 0.192360i | ||||||
\(363\) | 8.46630e10i | 0.255926i | ||||||||
\(364\) | −5.06066e11 | −1.51095 | ||||||||
\(365\) | 6.16404e10 | − | 8.65355e10i | 0.181781 | − | 0.255197i | ||||
\(366\) | 8.29019e10 | 0.241490 | ||||||||
\(367\) | − | 1.33587e10i | − | 0.0384387i | −0.999815 | − | 0.0192193i | \(-0.993882\pi\) | ||
0.999815 | − | 0.0192193i | \(-0.00611808\pi\) | |||||||
\(368\) | 4.00275e11i | 1.13774i | ||||||||
\(369\) | 3.11278e11 | 0.874036 | ||||||||
\(370\) | 6.60642e11 | + | 4.70585e11i | 1.83256 | + | 1.30536i | ||||
\(371\) | 3.01495e11 | 0.826224 | ||||||||
\(372\) | − | 1.48266e11i | − | 0.401419i | ||||||
\(373\) | 4.17763e11i | 1.11748i | 0.829342 | + | 0.558741i | \(0.188716\pi\) | ||||
−0.829342 | + | 0.558741i | \(0.811284\pi\) | |||||||
\(374\) | 1.35165e11 | 0.357226 | ||||||||
\(375\) | 9.85687e10 | + | 2.89886e10i | 0.257394 | + | 0.0756985i | ||||
\(376\) | −1.15844e12 | −2.98903 | ||||||||
\(377\) | 2.04636e11i | 0.521731i | ||||||||
\(378\) | 3.13714e11i | 0.790353i | ||||||||
\(379\) | −2.63110e11 | −0.655031 | −0.327515 | − | 0.944846i | \(-0.606211\pi\) | ||||
−0.327515 | + | 0.944846i | \(0.606211\pi\) | |||||||
\(380\) | −3.35989e11 | − | 2.39329e11i | −0.826606 | − | 0.588803i | ||||
\(381\) | −7.98374e10 | −0.194108 | ||||||||
\(382\) | − | 3.83553e11i | − | 0.921596i | ||||||
\(383\) | − | 7.84146e10i | − | 0.186210i | −0.995656 | − | 0.0931049i | \(-0.970321\pi\) | ||
0.995656 | − | 0.0931049i | \(-0.0296792\pi\) | |||||||
\(384\) | 6.10057e10 | 0.143179 | ||||||||
\(385\) | −4.49337e10 | + | 6.30814e10i | −0.104232 | + | 0.146328i | ||||
\(386\) | −2.86901e11 | −0.657793 | ||||||||
\(387\) | 5.33849e11i | 1.20981i | ||||||||
\(388\) | − | 7.21688e11i | − | 1.61662i | ||||||
\(389\) | −1.66007e11 | −0.367581 | −0.183791 | − | 0.982965i | \(-0.558837\pi\) | ||||
−0.183791 | + | 0.982965i | \(0.558837\pi\) | |||||||
\(390\) | 1.00450e11 | − | 1.41019e11i | 0.219866 | − | 0.308664i | ||||
\(391\) | 2.26452e11 | 0.489984 | ||||||||
\(392\) | − | 3.41678e11i | − | 0.730852i | ||||||
\(393\) | − | 2.09917e11i | − | 0.443896i | ||||||
\(394\) | 1.49048e12 | 3.11596 | ||||||||
\(395\) | −4.67462e11 | − | 3.32980e11i | −0.966184 | − | 0.688226i | ||||
\(396\) | −2.27640e11 | −0.465179 | ||||||||
\(397\) | 4.09536e11i | 0.827437i | 0.910405 | + | 0.413719i | \(0.135770\pi\) | ||||
−0.910405 | + | 0.413719i | \(0.864230\pi\) | |||||||
\(398\) | − | 9.30402e11i | − | 1.85865i | ||||||
\(399\) | 4.94059e10 | 0.0975889 | ||||||||
\(400\) | 3.53974e11 | + | 1.02370e12i | 0.691356 | + | 1.99941i | ||||
\(401\) | −7.92645e10 | −0.153084 | −0.0765419 | − | 0.997066i | \(-0.524388\pi\) | ||||
−0.0765419 | + | 0.997066i | \(0.524388\pi\) | |||||||
\(402\) | 4.36905e11i | 0.834391i | ||||||||
\(403\) | 2.62498e11i | 0.495739i | ||||||||
\(404\) | 2.43367e11 | 0.454513 | ||||||||
\(405\) | 3.48050e11 | + | 2.47921e11i | 0.642826 | + | 0.457894i | ||||
\(406\) | 5.64213e11 | 1.03057 | ||||||||
\(407\) | − | 1.46450e11i | − | 0.264554i | ||||||
\(408\) | 3.33425e11i | 0.595700i | ||||||||
\(409\) | −6.85827e11 | −1.21188 | −0.605940 | − | 0.795510i | \(-0.707203\pi\) | ||||
−0.605940 | + | 0.795510i | \(0.707203\pi\) | |||||||
\(410\) | −5.70922e11 | + | 8.01504e11i | −0.997814 | + | 1.40081i | ||||
\(411\) | 9.68557e10 | 0.167431 | ||||||||
\(412\) | − | 1.09476e12i | − | 1.87189i | ||||||
\(413\) | − | 8.52601e11i | − | 1.44202i | ||||||
\(414\) | −5.44746e11 | −0.911366 | ||||||||
\(415\) | 4.23222e11 | − | 5.94151e11i | 0.700410 | − | 0.983288i | ||||
\(416\) | 6.73854e11 | 1.10318 | ||||||||
\(417\) | − | 6.10898e10i | − | 0.0989365i | ||||||
\(418\) | 1.06385e11i | 0.170447i | ||||||||
\(419\) | −3.31879e11 | −0.526037 | −0.263018 | − | 0.964791i | \(-0.584718\pi\) | ||||
−0.263018 | + | 0.964791i | \(0.584718\pi\) | |||||||
\(420\) | −2.72209e11 | − | 1.93898e11i | −0.426856 | − | 0.304055i | ||||
\(421\) | −6.30694e11 | −0.978475 | −0.489237 | − | 0.872151i | \(-0.662725\pi\) | ||||
−0.489237 | + | 0.872151i | \(0.662725\pi\) | |||||||
\(422\) | 1.49700e12i | 2.29782i | ||||||||
\(423\) | − | 7.49490e11i | − | 1.13824i | ||||||
\(424\) | −1.60146e12 | −2.40641 | ||||||||
\(425\) | 5.79148e11 | − | 2.00258e11i | 0.861071 | − | 0.297742i | ||||
\(426\) | −1.39545e11 | −0.205291 | ||||||||
\(427\) | 2.83319e11i | 0.412429i | ||||||||
\(428\) | 1.98701e12i | 2.86222i | ||||||||
\(429\) | −3.12607e10 | −0.0445596 | ||||||||
\(430\) | −1.37460e12 | − | 9.79145e11i | −1.93896 | − | 1.38114i | ||||
\(431\) | 7.70903e11 | 1.07610 | 0.538049 | − | 0.842913i | \(-0.319161\pi\) | ||||
0.538049 | + | 0.842913i | \(0.319161\pi\) | |||||||
\(432\) | − | 7.92182e11i | − | 1.09433i | ||||||
\(433\) | 1.07829e12i | 1.47415i | 0.675811 | + | 0.737075i | \(0.263794\pi\) | ||||
−0.675811 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(434\) | 7.23746e11 | 0.979225 | ||||||||
\(435\) | −7.84060e10 | + | 1.10072e11i | −0.104990 | + | 0.147393i | ||||
\(436\) | 2.06977e12 | 2.74305 | ||||||||
\(437\) | 1.78235e11i | 0.233791i | ||||||||
\(438\) | − | 1.18237e11i | − | 0.153504i | ||||||
\(439\) | 9.56419e11 | 1.22902 | 0.614508 | − | 0.788910i | \(-0.289354\pi\) | ||||
0.614508 | + | 0.788910i | \(0.289354\pi\) | |||||||
\(440\) | 2.38676e11 | − | 3.35071e11i | 0.303579 | − | 0.426187i | ||||
\(441\) | 2.21059e11 | 0.278313 | ||||||||
\(442\) | − | 1.03264e12i | − | 1.28692i | ||||||
\(443\) | 2.06392e11i | 0.254611i | 0.991864 | + | 0.127305i | \(0.0406328\pi\) | ||||
−0.991864 | + | 0.127305i | \(0.959367\pi\) | |||||||
\(444\) | 6.31962e11 | 0.771734 | ||||||||
\(445\) | −2.70129e11 | − | 1.92417e11i | −0.326551 | − | 0.232607i | ||||
\(446\) | −2.04049e12 | −2.44190 | ||||||||
\(447\) | − | 2.25250e11i | − | 0.266858i | ||||||
\(448\) | − | 3.48685e11i | − | 0.408961i | ||||||
\(449\) | −1.75939e11 | −0.204293 | −0.102147 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102147 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(450\) | −1.39318e12 | + | 4.81734e11i | −1.60159 | + | 0.553798i | ||||
\(451\) | 1.77676e11 | 0.202224 | ||||||||
\(452\) | − | 7.54174e11i | − | 0.849863i | ||||||
\(453\) | 2.23995e11i | 0.249918i | ||||||||
\(454\) | 1.35408e12 | 1.49586 | ||||||||
\(455\) | 4.81933e11 | + | 3.43288e11i | 0.527152 | + | 0.375497i | ||||
\(456\) | −2.62431e11 | −0.284232 | ||||||||
\(457\) | 2.98819e11i | 0.320469i | 0.987079 | + | 0.160234i | \(0.0512250\pi\) | ||||
−0.987079 | + | 0.160234i | \(0.948775\pi\) | |||||||
\(458\) | − | 5.60233e11i | − | 0.594941i | ||||||
\(459\) | −4.48171e11 | −0.471288 | ||||||||
\(460\) | 6.99502e11 | − | 9.82014e11i | 0.728415 | − | 1.02260i | ||||
\(461\) | 4.39422e11 | 0.453135 | 0.226567 | − | 0.973995i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973995i | \(0.427250\pi\) | |||||||
\(462\) | 8.61906e10i | 0.0880179i | ||||||||
\(463\) | − | 1.16254e12i | − | 1.17569i | −0.808973 | − | 0.587846i | \(-0.799976\pi\) | ||
0.808973 | − | 0.587846i | \(-0.200024\pi\) | |||||||
\(464\) | −1.42473e12 | −1.42693 | ||||||||
\(465\) | −1.00576e11 | + | 1.41196e11i | −0.0997595 | + | 0.140050i | ||||
\(466\) | 3.30487e11 | 0.324652 | ||||||||
\(467\) | 1.65923e11i | 0.161429i | 0.996737 | + | 0.0807144i | \(0.0257202\pi\) | ||||
−0.996737 | + | 0.0807144i | \(0.974280\pi\) | |||||||
\(468\) | 1.73914e12i | 1.67582i | ||||||||
\(469\) | −1.49313e12 | −1.42501 | ||||||||
\(470\) | 1.92985e12 | + | 1.37466e12i | 1.82425 | + | 1.29944i | ||||
\(471\) | 1.10786e11 | 0.103727 | ||||||||
\(472\) | 4.52879e12i | 4.19994i | ||||||||
\(473\) | 3.04718e11i | 0.279913i | ||||||||
\(474\) | −6.38712e11 | −0.581169 | ||||||||
\(475\) | 1.57618e11 | + | 4.55833e11i | 0.142064 | + | 0.410851i | ||||
\(476\) | −1.99332e12 | −1.77970 | ||||||||
\(477\) | − | 1.03611e12i | − | 0.916377i | ||||||
\(478\) | − | 3.43036e12i | − | 3.00549i | ||||||
\(479\) | −1.33180e11 | −0.115592 | −0.0577960 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577960 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(480\) | 3.62461e11 | + | 2.58186e11i | 0.311656 | + | 0.221997i | ||||
\(481\) | −1.11886e12 | −0.953064 | ||||||||
\(482\) | − | 2.49895e12i | − | 2.10885i | ||||||
\(483\) | 1.44401e11i | 0.120728i | ||||||||
\(484\) | 2.68849e12 | 2.22692 | ||||||||
\(485\) | −4.89554e11 | + | 6.87273e11i | −0.401756 | + | 0.564016i | ||||
\(486\) | 1.63728e12 | 1.33125 | ||||||||
\(487\) | − | 1.43276e12i | − | 1.15423i | −0.816662 | − | 0.577116i | \(-0.804178\pi\) | ||
0.816662 | − | 0.577116i | \(-0.195822\pi\) | |||||||
\(488\) | − | 1.50491e12i | − | 1.20122i | ||||||
\(489\) | 1.01563e11 | 0.0803243 | ||||||||
\(490\) | −4.05449e11 | + | 5.69200e11i | −0.317727 | + | 0.446049i | ||||
\(491\) | −1.05688e12 | −0.820655 | −0.410327 | − | 0.911938i | \(-0.634586\pi\) | ||||
−0.410327 | + | 0.911938i | \(0.634586\pi\) | |||||||
\(492\) | 7.66708e11i | 0.589912i | ||||||||
\(493\) | 8.06032e11i | 0.614527i | ||||||||
\(494\) | 8.12769e11 | 0.614039 | ||||||||
\(495\) | 2.16784e11 | + | 1.54418e11i | 0.162295 | + | 0.115605i | ||||
\(496\) | −1.82758e12 | −1.35584 | ||||||||
\(497\) | − | 4.76896e11i | − | 0.350607i | ||||||
\(498\) | − | 8.11813e11i | − | 0.591458i | ||||||
\(499\) | −1.77897e11 | −0.128445 | −0.0642223 | − | 0.997936i | \(-0.520457\pi\) | ||||
−0.0642223 | + | 0.997936i | \(0.520457\pi\) | |||||||
\(500\) | 9.20541e11 | − | 3.13007e12i | 0.658685 | − | 2.23970i | ||||
\(501\) | 5.53814e11 | 0.392730 | ||||||||
\(502\) | 4.32537e12i | 3.03988i | ||||||||
\(503\) | 1.58467e12i | 1.10378i | 0.833917 | + | 0.551889i | \(0.186093\pi\) | ||||
−0.833917 | + | 0.551889i | \(0.813907\pi\) | |||||||
\(504\) | 2.74111e12 | 1.89229 | ||||||||
\(505\) | −2.31762e11 | − | 1.65087e11i | −0.158574 | − | 0.112954i | ||||
\(506\) | −3.10939e11 | −0.210861 | ||||||||
\(507\) | − | 1.60333e11i | − | 0.107767i | ||||||
\(508\) | 2.53525e12i | 1.68902i | ||||||||
\(509\) | 1.93674e12 | 1.27891 | 0.639456 | − | 0.768827i | \(-0.279159\pi\) | ||||
0.639456 | + | 0.768827i | \(0.279159\pi\) | |||||||
\(510\) | 3.95656e11 | − | 5.55452e11i | 0.258972 | − | 0.363564i | ||||
\(511\) | 4.04076e11 | 0.262162 | ||||||||
\(512\) | − | 3.32508e12i | − | 2.13839i | ||||||
\(513\) | − | 3.52744e11i | − | 0.224870i | ||||||
\(514\) | −3.27560e12 | −2.06993 | ||||||||
\(515\) | −7.42623e11 | + | 1.04255e12i | −0.465196 | + | 0.653077i | ||||
\(516\) | −1.31492e12 | −0.816538 | ||||||||
\(517\) | − | 4.27805e11i | − | 0.263353i | ||||||
\(518\) | 3.08486e12i | 1.88257i | ||||||||
\(519\) | −5.89473e9 | −0.00356624 | ||||||||
\(520\) | −2.55990e12 | − | 1.82345e12i | −1.53535 | − | 1.09365i | ||||
\(521\) | 2.72419e12 | 1.61982 | 0.809912 | − | 0.586552i | \(-0.199515\pi\) | ||||
0.809912 | + | 0.586552i | \(0.199515\pi\) | |||||||
\(522\) | − | 1.93896e12i | − | 1.14302i | ||||||
\(523\) | 4.86784e11i | 0.284497i | 0.989831 | + | 0.142249i | \(0.0454333\pi\) | ||||
−0.989831 | + | 0.142249i | \(0.954567\pi\) | |||||||
\(524\) | −6.66596e12 | −3.86253 | ||||||||
\(525\) | 1.27698e11 | + | 3.69304e11i | 0.0733615 | + | 0.212162i | ||||
\(526\) | 4.32320e9 | 0.00246246 | ||||||||
\(527\) | 1.03394e12i | 0.583912i | ||||||||
\(528\) | − | 2.17646e11i | − | 0.121870i | ||||||
\(529\) | 1.28021e12 | 0.710775 | ||||||||
\(530\) | 2.66787e12 | + | 1.90036e12i | 1.46867 | + | 1.04615i | ||||
\(531\) | −2.93003e12 | −1.59936 | ||||||||
\(532\) | − | 1.56889e12i | − | 0.849164i | ||||||
\(533\) | − | 1.35742e12i | − | 0.728520i | ||||||
\(534\) | −3.69088e11 | −0.196424 | ||||||||
\(535\) | 1.34788e12 | − | 1.89225e12i | 0.711309 | − | 0.998590i | ||||
\(536\) | 7.93109e12 | 4.15041 | ||||||||
\(537\) | − | 2.01572e11i | − | 0.104603i | ||||||
\(538\) | 3.05240e11i | 0.157080i | ||||||||
\(539\) | 1.26179e11 | 0.0643929 | ||||||||
\(540\) | −1.38438e12 | + | 1.94350e12i | −0.700622 | + | 0.983586i | ||||
\(541\) | 1.98233e11 | 0.0994920 | 0.0497460 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497460 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(542\) | 5.27675e12i | 2.62645i | ||||||||
\(543\) | 5.72543e10i | 0.0282624i | ||||||||
\(544\) | 2.65421e12 | 1.29939 | ||||||||
\(545\) | −1.97107e12 | − | 1.40402e12i | −0.957014 | − | 0.681694i | ||||
\(546\) | 6.58485e11 | 0.317087 | ||||||||
\(547\) | 4.79532e11i | 0.229021i | 0.993422 | + | 0.114510i | \(0.0365299\pi\) | ||||
−0.993422 | + | 0.114510i | \(0.963470\pi\) | |||||||
\(548\) | − | 3.07567e12i | − | 1.45689i | ||||||
\(549\) | 9.73647e11 | 0.457432 | ||||||||
\(550\) | −7.95219e11 | + | 2.74972e11i | −0.370557 | + | 0.128131i | ||||
\(551\) | −6.34408e11 | −0.293215 | ||||||||
\(552\) | − | 7.67022e11i | − | 0.351627i | ||||||
\(553\) | − | 2.18281e12i | − | 0.992550i | ||||||
\(554\) | −1.30802e12 | −0.589957 | ||||||||
\(555\) | −6.01825e11 | − | 4.28688e11i | −0.269248 | − | 0.191789i | ||||
\(556\) | −1.93992e12 | −0.860889 | ||||||||
\(557\) | − | 1.20856e11i | − | 0.0532011i | −0.999646 | − | 0.0266006i | \(-0.991532\pi\) | ||
0.999646 | − | 0.0266006i | \(-0.00846822\pi\) | |||||||
\(558\) | − | 2.48721e12i | − | 1.08607i | ||||||
\(559\) | 2.32801e12 | 1.00840 | ||||||||
\(560\) | −2.39007e12 | + | 3.35536e12i | −1.02698 | + | 1.44176i | ||||
\(561\) | −1.23131e11 | −0.0524851 | ||||||||
\(562\) | − | 3.92662e12i | − | 1.66037i | ||||||
\(563\) | − | 1.01468e12i | − | 0.425637i | −0.977092 | − | 0.212818i | \(-0.931736\pi\) | ||
0.977092 | − | 0.212818i | \(-0.0682643\pi\) | |||||||
\(564\) | 1.84607e12 | 0.768231 | ||||||||
\(565\) | −5.11591e11 | + | 7.18210e11i | −0.211205 | + | 0.296506i | ||||
\(566\) | 2.03234e12 | 0.832382 | ||||||||
\(567\) | 1.62521e12i | 0.660369i | ||||||||
\(568\) | 2.53314e12i | 1.02116i | ||||||||
\(569\) | −1.12630e12 | −0.450454 | −0.225227 | − | 0.974306i | \(-0.572312\pi\) | ||||
−0.225227 | + | 0.974306i | \(0.572312\pi\) | |||||||
\(570\) | 4.37183e11 | + | 3.11411e11i | 0.173471 | + | 0.123566i | ||||
\(571\) | −2.75478e12 | −1.08449 | −0.542243 | − | 0.840221i | \(-0.682425\pi\) | ||||
−0.542243 | + | 0.840221i | \(0.682425\pi\) | |||||||
\(572\) | 9.92691e11i | 0.387732i | ||||||||
\(573\) | 3.49405e11i | 0.135405i | ||||||||
\(574\) | −3.74261e12 | −1.43903 | ||||||||
\(575\) | −1.33229e12 | + | 4.60680e11i | −0.508269 | + | 0.175750i | ||||
\(576\) | −1.19828e12 | −0.453585 | ||||||||
\(577\) | 4.14763e12i | 1.55779i | 0.627155 | + | 0.778895i | \(0.284219\pi\) | ||||
−0.627155 | + | 0.778895i | \(0.715781\pi\) | |||||||
\(578\) | 8.32535e11i | 0.310261i | ||||||||
\(579\) | 2.61358e11 | 0.0966458 | ||||||||
\(580\) | 3.49537e12 | + | 2.48980e12i | 1.28253 | + | 0.913563i | ||||
\(581\) | 2.77438e12 | 1.01012 | ||||||||
\(582\) | 9.39049e11i | 0.339262i | ||||||||
\(583\) | − | 5.91408e11i | − | 0.212021i | ||||||
\(584\) | −2.14634e12 | −0.763557 | ||||||||
\(585\) | 1.17974e12 | − | 1.65620e12i | 0.416470 | − | 0.584672i | ||||
\(586\) | 1.46224e12 | 0.512248 | ||||||||
\(587\) | 1.38017e12i | 0.479800i | 0.970798 | + | 0.239900i | \(0.0771147\pi\) | ||||
−0.970798 | + | 0.239900i | \(0.922885\pi\) | |||||||
\(588\) | 5.44490e11i | 0.187842i | ||||||||
\(589\) | −8.13789e11 | −0.278608 | ||||||||
\(590\) | 5.37405e12 | − | 7.54450e12i | 1.82586 | − | 2.56328i | ||||
\(591\) | −1.35778e12 | −0.457811 | ||||||||
\(592\) | − | 7.78980e12i | − | 2.60663i | ||||||
\(593\) | 6.90406e11i | 0.229276i | 0.993407 | + | 0.114638i | \(0.0365708\pi\) | ||||
−0.993407 | + | 0.114638i | \(0.963429\pi\) | |||||||
\(594\) | 6.15377e11 | 0.202816 | ||||||||
\(595\) | 1.89827e12 | + | 1.35216e12i | 0.620913 | + | 0.442285i | ||||
\(596\) | −7.15286e12 | −2.32205 | ||||||||
\(597\) | 8.47568e11i | 0.273080i | ||||||||
\(598\) | 2.37553e12i | 0.759635i | ||||||||
\(599\) | −1.24239e12 | −0.394309 | −0.197155 | − | 0.980372i | \(-0.563170\pi\) | ||||
−0.197155 | + | 0.980372i | \(0.563170\pi\) | |||||||
\(600\) | −6.78299e11 | − | 1.96164e12i | −0.213668 | − | 0.617930i | ||||
\(601\) | 2.01140e12 | 0.628873 | 0.314437 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314437 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(602\) | − | 6.41867e12i | − | 1.99187i | ||||||
\(603\) | 5.13126e12i | 1.58050i | ||||||||
\(604\) | 7.11302e12 | 2.17464 | ||||||||
\(605\) | −2.56028e12 | − | 1.82373e12i | −0.776943 | − | 0.553427i | ||||
\(606\) | −3.16666e11 | −0.0953837 | ||||||||
\(607\) | − | 2.73579e12i | − | 0.817963i | −0.912543 | − | 0.408981i | \(-0.865884\pi\) | ||
0.912543 | − | 0.408981i | \(-0.134116\pi\) | |||||||
\(608\) | 2.08907e12i | 0.619992i | ||||||||
\(609\) | −5.13981e11 | −0.151415 | ||||||||
\(610\) | −1.78579e12 | + | 2.50703e12i | −0.522211 | + | 0.733120i | ||||
\(611\) | −3.26838e12 | −0.948738 | ||||||||
\(612\) | 6.85021e12i | 1.97389i | ||||||||
\(613\) | − | 1.63707e12i | − | 0.468269i | −0.972204 | − | 0.234135i | \(-0.924774\pi\) | ||
0.972204 | − | 0.234135i | \(-0.0752257\pi\) | |||||||
\(614\) | 3.43075e12 | 0.974162 | ||||||||
\(615\) | 5.20093e11 | − | 7.30146e11i | 0.146603 | − | 0.205812i | ||||
\(616\) | 1.56461e12 | 0.437817 | ||||||||
\(617\) | − | 1.22267e12i | − | 0.339646i | −0.985475 | − | 0.169823i | \(-0.945680\pi\) | ||
0.985475 | − | 0.169823i | \(-0.0543197\pi\) | |||||||
\(618\) | 1.42448e12i | 0.392832i | ||||||||
\(619\) | 5.78784e12 | 1.58456 | 0.792280 | − | 0.610158i | \(-0.208894\pi\) | ||||
0.792280 | + | 0.610158i | \(0.208894\pi\) | |||||||
\(620\) | 4.48370e12 | + | 3.19380e12i | 1.21863 | + | 0.868050i | ||||
\(621\) | 1.03099e12 | 0.278190 | ||||||||
\(622\) | 8.83967e11i | 0.236799i | ||||||||
\(623\) | − | 1.26136e12i | − | 0.335463i | ||||||
\(624\) | −1.66279e12 | −0.439042 | ||||||||
\(625\) | −2.99991e12 | + | 2.35636e12i | −0.786409 | + | 0.617706i | ||||
\(626\) | −1.06008e13 | −2.75902 | ||||||||
\(627\) | − | 9.69138e10i | − | 0.0250427i | ||||||
\(628\) | − | 3.51803e12i | − | 0.902571i | ||||||
\(629\) | −4.40702e12 | −1.12258 | ||||||||
\(630\) | −4.56640e12 | − | 3.25271e12i | −1.15489 | − | 0.822646i | ||||
\(631\) | 2.00341e12 | 0.503081 | 0.251540 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251540 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(632\) | 1.15945e13i | 2.89084i | ||||||||
\(633\) | − | 1.36372e12i | − | 0.337605i | ||||||
\(634\) | −5.21084e12 | −1.28087 | ||||||||
\(635\) | 1.71978e12 | − | 2.41435e12i | 0.419750 | − | 0.589277i | ||||
\(636\) | 2.55205e12 | 0.618489 | ||||||||
\(637\) | − | 9.63992e11i | − | 0.231978i | ||||||
\(638\) | − | 1.10675e12i | − | 0.264458i | ||||||
\(639\) | −1.63889e12 | −0.388863 | ||||||||
\(640\) | −1.31412e12 | + | 1.84487e12i | −0.309618 | + | 0.434666i | ||||
\(641\) | 2.75478e12 | 0.644505 | 0.322253 | − | 0.946654i | \(-0.395560\pi\) | ||||
0.322253 | + | 0.946654i | \(0.395560\pi\) | |||||||
\(642\) | − | 2.58546e12i | − | 0.600662i | ||||||
\(643\) | − | 7.38857e12i | − | 1.70455i | −0.523091 | − | 0.852277i | \(-0.675221\pi\) | ||
0.523091 | − | 0.852277i | \(-0.324779\pi\) | |||||||
\(644\) | 4.58550e12 | 1.05051 | ||||||||
\(645\) | 1.25222e12 | + | 8.91972e11i | 0.284879 | + | 0.202924i | ||||
\(646\) | 3.20138e12 | 0.723254 | ||||||||
\(647\) | − | 4.12045e12i | − | 0.924432i | −0.886767 | − | 0.462216i | \(-0.847054\pi\) | ||
0.886767 | − | 0.462216i | \(-0.152946\pi\) | |||||||
\(648\) | − | 8.63269e12i | − | 1.92335i | ||||||
\(649\) | −1.67245e12 | −0.370043 | ||||||||
\(650\) | 2.10075e12 | + | 6.07537e12i | 0.461598 | + | 1.33494i | ||||
\(651\) | −6.59311e11 | −0.143872 | ||||||||
\(652\) | − | 3.22517e12i | − | 0.698937i | ||||||
\(653\) | 6.51407e12i | 1.40198i | 0.713170 | + | 0.700992i | \(0.247259\pi\) | ||||
−0.713170 | + | 0.700992i | \(0.752741\pi\) | |||||||
\(654\) | −2.69315e12 | −0.575654 | ||||||||
\(655\) | 6.34807e12 | + | 4.52182e12i | 1.34758 | + | 0.959903i | ||||
\(656\) | 9.45073e12 | 1.99250 | ||||||||
\(657\) | − | 1.38864e12i | − | 0.290767i | ||||||
\(658\) | 9.01141e12i | 1.87403i | ||||||||
\(659\) | 1.74145e12 | 0.359688 | 0.179844 | − | 0.983695i | \(-0.442441\pi\) | ||||
0.179844 | + | 0.983695i | \(0.442441\pi\) | |||||||
\(660\) | −3.80348e11 | + | 5.33961e11i | −0.0780250 | + | 0.109537i | ||||
\(661\) | −1.39849e12 | −0.284939 | −0.142469 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142469 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(662\) | 7.07800e12i | 1.43235i | ||||||||
\(663\) | 9.40708e11i | 0.189079i | ||||||||
\(664\) | −1.47368e13 | −2.94202 | ||||||||
\(665\) | −1.06425e12 | + | 1.49408e12i | −0.211031 | + | 0.296262i | ||||
\(666\) | 1.06014e13 | 2.08799 | ||||||||
\(667\) | − | 1.85422e12i | − | 0.362740i | ||||||
\(668\) | − | 1.75865e13i | − | 3.41732i | ||||||
\(669\) | 1.85882e12 | 0.358774 | ||||||||
\(670\) | −1.32124e13 | − | 9.41137e12i | −2.53306 | − | 1.80433i | ||||
\(671\) | 5.55753e11 | 0.105835 | ||||||||
\(672\) | 1.69251e12i | 0.320161i | ||||||||
\(673\) | 7.23077e12i | 1.35868i | 0.733824 | + | 0.679340i | \(0.237734\pi\) | ||||
−0.733824 | + | 0.679340i | \(0.762266\pi\) | |||||||
\(674\) | 1.94333e13 | 3.62725 | ||||||||
\(675\) | 2.63673e12 | − | 9.11730e11i | 0.488876 | − | 0.169044i | ||||
\(676\) | −5.09140e12 | −0.937728 | ||||||||
\(677\) | − | 1.09854e12i | − | 0.200986i | −0.994938 | − | 0.100493i | \(-0.967958\pi\) | ||
0.994938 | − | 0.100493i | \(-0.0320419\pi\) | |||||||
\(678\) | 9.81319e11i | 0.178351i | ||||||||
\(679\) | −3.20921e12 | −0.579408 | ||||||||
\(680\) | −1.00831e13 | − | 7.18231e12i | −1.80843 | − | 1.28817i | ||||
\(681\) | −1.23352e12 | −0.219779 | ||||||||
\(682\) | − | 1.41969e12i | − | 0.251283i | ||||||
\(683\) | 1.51781e12i | 0.266885i | 0.991057 | + | 0.133442i | \(0.0426031\pi\) | ||||
−0.991057 | + | 0.133442i | \(0.957397\pi\) | |||||||
\(684\) | −5.39163e12 | −0.941820 | ||||||||
\(685\) | −2.08637e12 | + | 2.92900e12i | −0.362063 | + | 0.508291i | ||||
\(686\) | −1.15204e13 | −1.98613 | ||||||||
\(687\) | 5.10355e11i | 0.0874112i | ||||||||
\(688\) | 1.62082e13i | 2.75796i | ||||||||
\(689\) | −4.51828e12 | −0.763812 | ||||||||
\(690\) | −9.10180e11 | + | 1.27778e12i | −0.152864 | + | 0.214603i | ||||
\(691\) | 1.51489e12 | 0.252772 | 0.126386 | − | 0.991981i | \(-0.459662\pi\) | ||||
0.126386 | + | 0.991981i | \(0.459662\pi\) | |||||||
\(692\) | 1.87188e11i | 0.0310314i | ||||||||
\(693\) | 1.01227e12i | 0.166724i | ||||||||
\(694\) | 1.18439e13 | 1.93810 | ||||||||
\(695\) | 1.84741e12 | + | 1.31594e12i | 0.300353 | + | 0.213946i | ||||
\(696\) | 2.73013e12 | 0.441003 | ||||||||
\(697\) | − | 5.34668e12i | − | 0.858097i | ||||||
\(698\) | 1.46398e13i | 2.33446i | ||||||||
\(699\) | −3.01064e11 | −0.0476993 | ||||||||
\(700\) | 1.17273e13 | − | 4.05509e12i | 1.84611 | − | 0.638350i | ||||
\(701\) | 7.62368e12 | 1.19243 | 0.596216 | − | 0.802824i | \(-0.296670\pi\) | ||||
0.596216 | + | 0.802824i | \(0.296670\pi\) | |||||||
\(702\) | − | 4.70140e12i | − | 0.730651i | ||||||
\(703\) | − | 3.46866e12i | − | 0.535627i | ||||||
\(704\) | −6.83975e11 | −0.104945 | ||||||||
\(705\) | −1.75804e12 | − | 1.25227e12i | −0.268026 | − | 0.190918i | ||||
\(706\) | 8.65605e12 | 1.31129 | ||||||||
\(707\) | − | 1.08221e12i | − | 0.162901i | ||||||
\(708\) | − | 7.21697e12i | − | 1.07946i | ||||||
\(709\) | −1.00657e13 | −1.49602 | −0.748010 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748010 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(710\) | 3.00594e12 | − | 4.21996e12i | 0.443933 | − | 0.623226i | ||||
\(711\) | −7.50140e12 | −1.10085 | ||||||||
\(712\) | 6.70002e12i | 0.977049i | ||||||||
\(713\) | − | 2.37851e12i | − | 0.344669i | ||||||
\(714\) | 2.59367e12 | 0.373485 | ||||||||
\(715\) | 6.73388e11 | − | 9.45353e11i | 0.0963580 | − | 0.135275i | ||||
\(716\) | −6.40096e12 | −0.910199 | ||||||||
\(717\) | 3.12496e12i | 0.441579i | ||||||||
\(718\) | − | 1.19033e13i | − | 1.67151i | ||||||
\(719\) | −8.94464e12 | −1.24820 | −0.624098 | − | 0.781346i | \(-0.714534\pi\) | ||||
−0.624098 | + | 0.781346i | \(0.714534\pi\) | |||||||
\(720\) | 1.15310e13 | + | 8.21366e12i | 1.59908 | + | 1.13904i | ||||
\(721\) | −4.86817e12 | −0.670899 | ||||||||
\(722\) | − | 1.08135e13i | − | 1.48098i | ||||||
\(723\) | 2.27647e12i | 0.309841i | ||||||||
\(724\) | 1.81812e12 | 0.245923 | ||||||||
\(725\) | −1.63974e12 | − | 4.74214e12i | −0.220422 | − | 0.637460i | ||||
\(726\) | −3.49822e12 | −0.467339 | ||||||||
\(727\) | 1.22168e13i | 1.62201i | 0.585038 | + | 0.811006i | \(0.301079\pi\) | ||||
−0.585038 | + | 0.811006i | \(0.698921\pi\) | |||||||
\(728\) | − | 1.19534e13i | − | 1.57725i | ||||||
\(729\) | 4.52688e12 | 0.593642 | ||||||||
\(730\) | 3.57559e12 | + | 2.54694e12i | 0.466009 | + | 0.331945i | ||||
\(731\) | 9.16968e12 | 1.18775 | ||||||||
\(732\) | 2.39819e12i | 0.308734i | ||||||||
\(733\) | − | 1.44452e13i | − | 1.84823i | −0.382118 | − | 0.924114i | \(-0.624805\pi\) | ||
0.382118 | − | 0.924114i | \(-0.375195\pi\) | |||||||
\(734\) | 5.51974e11 | 0.0701919 | ||||||||
\(735\) | 3.69352e11 | − | 5.18524e11i | 0.0466818 | − | 0.0655354i | ||||
\(736\) | −6.10584e12 | −0.767000 | ||||||||
\(737\) | 2.92889e12i | 0.365679i | ||||||||
\(738\) | 1.28618e13i | 1.59605i | ||||||||
\(739\) | 1.11591e13 | 1.37635 | 0.688175 | − | 0.725545i | \(-0.258412\pi\) | ||||
0.688175 | + | 0.725545i | \(0.258412\pi\) | |||||||
\(740\) | −1.36131e13 | + | 1.91111e13i | −1.66884 | + | 2.34284i | ||||
\(741\) | −7.40409e11 | −0.0902172 | ||||||||
\(742\) | 1.24576e13i | 1.50875i | ||||||||
\(743\) | 9.35882e12i | 1.12660i | 0.826251 | + | 0.563302i | \(0.190469\pi\) | ||||
−0.826251 | + | 0.563302i | \(0.809531\pi\) | |||||||
\(744\) | 3.50208e12 | 0.419033 | ||||||||
\(745\) | 6.81176e12 | + | 4.85211e12i | 0.810133 | + | 0.577069i | ||||
\(746\) | −1.72617e13 | −2.04061 | ||||||||
\(747\) | − | 9.53439e12i | − | 1.12034i | ||||||
\(748\) | 3.91007e12i | 0.456696i | ||||||||
\(749\) | 8.83585e12 | 1.02584 | ||||||||
\(750\) | −1.19779e12 | + | 4.07279e12i | −0.138231 | + | 0.470020i | ||||
\(751\) | −1.28609e13 | −1.47533 | −0.737667 | − | 0.675165i | \(-0.764072\pi\) | ||||
−0.737667 | + | 0.675165i | \(0.764072\pi\) | |||||||
\(752\) | − | 2.27553e13i | − | 2.59480i | ||||||
\(753\) | − | 3.94028e12i | − | 0.446632i | ||||||
\(754\) | −8.45543e12 | −0.952719 | ||||||||
\(755\) | −6.77382e12 | − | 4.82509e12i | −0.758704 | − | 0.540435i | ||||
\(756\) | −9.07514e12 | −1.01043 | ||||||||
\(757\) | 1.42250e13i | 1.57442i | 0.616684 | + | 0.787211i | \(0.288476\pi\) | ||||
−0.616684 | + | 0.787211i | \(0.711524\pi\) | |||||||
\(758\) | − | 1.08716e13i | − | 1.19613i | ||||||
\(759\) | 2.83256e11 | 0.0309807 | ||||||||
\(760\) | 5.65302e12 | − | 7.93614e12i | 0.614638 | − | 0.862875i | ||||
\(761\) | 1.65722e13 | 1.79122 | 0.895610 | − | 0.444841i | \(-0.146740\pi\) | ||||
0.895610 | + | 0.444841i | \(0.146740\pi\) | |||||||
\(762\) | − | 3.29883e12i | − | 0.354456i | ||||||
\(763\) | − | 9.20389e12i | − | 0.983130i | ||||||
\(764\) | 1.10954e13 | 1.17822 | ||||||||
\(765\) | 4.64681e12 | − | 6.52354e12i | 0.490545 | − | 0.688664i | ||||
\(766\) | 3.24004e12 | 0.340033 | ||||||||
\(767\) | 1.27773e13i | 1.33309i | ||||||||
\(768\) | 3.78498e12i | 0.392589i | ||||||||
\(769\) | −2.81269e12 | −0.290037 | −0.145019 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145019 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(770\) | −2.60648e12 | − | 1.85663e12i | −0.267206 | − | 0.190334i | ||||
\(771\) | 2.98397e12 | 0.304123 | ||||||||
\(772\) | − | 8.29949e12i | − | 0.840957i | ||||||
\(773\) | 8.57982e12i | 0.864311i | 0.901799 | + | 0.432156i | \(0.142247\pi\) | ||||
−0.901799 | + | 0.432156i | \(0.857753\pi\) | |||||||
\(774\) | −2.20583e13 | −2.20921 | ||||||||
\(775\) | −2.10338e12 | − | 6.08299e12i | −0.209440 | − | 0.605703i | ||||
\(776\) | 1.70465e13 | 1.68755 | ||||||||
\(777\) | − | 2.81021e12i | − | 0.276595i | ||||||
\(778\) | − | 6.85930e12i | − | 0.671230i | ||||||
\(779\) | 4.20824e12 | 0.409432 | ||||||||
\(780\) | 4.07940e12 | + | 2.90581e12i | 0.394612 | + | 0.281087i | ||||
\(781\) | −9.35472e11 | −0.0899707 | ||||||||
\(782\) | 9.35687e12i | 0.894746i | ||||||||
\(783\) | 3.66968e12i | 0.348900i | ||||||||
\(784\) | 6.71158e12 | 0.634458 | ||||||||
\(785\) | −2.38644e12 | + | 3.35027e12i | −0.224304 | + | 0.314895i | ||||
\(786\) | 8.67363e12 | 0.810586 | ||||||||
\(787\) | − | 1.75771e12i | − | 0.163328i | −0.996660 | − | 0.0816642i | \(-0.973976\pi\) | ||
0.996660 | − | 0.0816642i | \(-0.0260235\pi\) | |||||||
\(788\) | 4.31166e13i | 3.98361i | ||||||||
\(789\) | −3.93830e9 | −0.000361795 | ||||||||
\(790\) | 1.37585e13 | − | 1.93152e13i | 1.25675 | − | 1.76432i | ||||
\(791\) | −3.35367e12 | −0.304597 | ||||||||
\(792\) | − | 5.37691e12i | − | 0.485590i | ||||||
\(793\) | − | 4.24588e12i | − | 0.381275i | ||||||
\(794\) | −1.69218e13 | −1.51096 | ||||||||
\(795\) | −2.43035e12 | − | 1.73117e12i | −0.215783 | − | 0.153705i | ||||
\(796\) | 2.69147e13 | 2.37619 | ||||||||
\(797\) | − | 2.27115e13i | − | 1.99381i | −0.0786130 | − | 0.996905i | \(-0.525049\pi\) | ||
0.0786130 | − | 0.996905i | \(-0.474951\pi\) | |||||||
\(798\) | 2.04142e12i | 0.178205i | ||||||||
\(799\) | −1.28737e13 | −1.11748 | ||||||||
\(800\) | −1.56156e13 | + | 5.39956e12i | −1.34788 | + | 0.466073i | ||||
\(801\) | −4.33478e12 | −0.372067 | ||||||||
\(802\) | − | 3.27516e12i | − | 0.279542i | ||||||
\(803\) | − | 7.92629e11i | − | 0.0672744i | ||||||
\(804\) | −1.26388e13 | −1.06673 | ||||||||
\(805\) | −4.36683e12 | − | 3.11055e12i | −0.366509 | − | 0.261070i | ||||
\(806\) | −1.08462e13 | −0.905255 | ||||||||
\(807\) | − | 2.78065e11i | − | 0.0230789i | ||||||
\(808\) | 5.74840e12i | 0.474456i | ||||||||
\(809\) | 9.95176e12 | 0.816829 | 0.408415 | − | 0.912796i | \(-0.366082\pi\) | ||||
0.408415 | + | 0.912796i | \(0.366082\pi\) | |||||||
\(810\) | −1.02439e13 | + | 1.43812e13i | −0.836149 | + | 1.17385i | ||||
\(811\) | −7.01292e12 | −0.569253 | −0.284626 | − | 0.958639i | \(-0.591870\pi\) | ||||
−0.284626 | + | 0.958639i | \(0.591870\pi\) | |||||||
\(812\) | 1.63216e13i | 1.31753i | ||||||||
\(813\) | − | 4.80696e12i | − | 0.385889i | ||||||
\(814\) | 6.05121e12 | 0.483095 | ||||||||
\(815\) | −2.18778e12 | + | 3.07137e12i | −0.173698 | + | 0.243850i | ||||
\(816\) | −6.54948e12 | −0.517131 | ||||||||
\(817\) | 7.21723e12i | 0.566724i | ||||||||
\(818\) | − | 2.83379e13i | − | 2.21298i | ||||||
\(819\) | 7.73362e12 | 0.600627 | ||||||||
\(820\) | −2.31859e13 | − | 1.65157e13i | −1.79086 | − | 1.27566i | ||||
\(821\) | −1.20992e13 | −0.929420 | −0.464710 | − | 0.885463i | \(-0.653841\pi\) | ||||
−0.464710 | + | 0.885463i | \(0.653841\pi\) | |||||||
\(822\) | 4.00202e12i | 0.305742i | ||||||||
\(823\) | 1.21261e13i | 0.921346i | 0.887570 | + | 0.460673i | \(0.152392\pi\) | ||||
−0.887570 | + | 0.460673i | \(0.847608\pi\) | |||||||
\(824\) | 2.58584e13 | 1.95402 | ||||||||
\(825\) | 7.24421e11 | − | 2.50491e11i | 0.0544438 | − | 0.0188256i | ||||
\(826\) | 3.52289e13 | 2.63323 | ||||||||
\(827\) | 1.32495e13i | 0.984973i | 0.870320 | + | 0.492486i | \(0.163912\pi\) | ||||
−0.870320 | + | 0.492486i | \(0.836088\pi\) | |||||||
\(828\) | − | 1.57584e13i | − | 1.16514i | ||||||
\(829\) | 1.87106e13 | 1.37592 | 0.687960 | − | 0.725749i | \(-0.258507\pi\) | ||||
0.687960 | + | 0.725749i | \(0.258507\pi\) | |||||||
\(830\) | 2.45499e13 | + | 1.74873e13i | 1.79556 | + | 1.27900i | ||||
\(831\) | 1.19157e12 | 0.0866789 | ||||||||
\(832\) | 5.22548e12i | 0.378069i | ||||||||
\(833\) | − | 3.79702e12i | − | 0.273238i | ||||||
\(834\) | 2.52419e12 | 0.180665 | ||||||||
\(835\) | −1.19297e13 | + | 1.67478e13i | −0.849261 | + | 1.19226i | ||||
\(836\) | −3.07752e12 | −0.217908 | ||||||||
\(837\) | 4.70730e12i | 0.331518i | ||||||||
\(838\) | − | 1.37130e13i | − | 0.960582i | ||||||
\(839\) | −1.21346e13 | −0.845469 | −0.422734 | − | 0.906254i | \(-0.638930\pi\) | ||||
−0.422734 | + | 0.906254i | \(0.638930\pi\) | |||||||
\(840\) | 4.57993e12 | − | 6.42965e12i | 0.317396 | − | 0.445585i | ||||
\(841\) | −7.90725e12 | −0.545059 | ||||||||
\(842\) | − | 2.60599e13i | − | 1.78677i | ||||||
\(843\) | 3.57703e12i | 0.243949i | ||||||||
\(844\) | −4.33053e13 | −2.93765 | ||||||||
\(845\) | 4.84860e12 | + | 3.45373e12i | 0.327161 | + | 0.233041i | ||||
\(846\) | 3.09684e13 | 2.07851 | ||||||||
\(847\) | − | 1.19552e13i | − | 0.798145i | ||||||
\(848\) | − | 3.14575e13i | − | 2.08902i | ||||||
\(849\) | −1.85140e12 | −0.122297 | ||||||||
\(850\) | 8.27454e12 | + | 2.39300e13i | 0.543699 | + | 1.57238i | ||||
\(851\) | 1.01380e13 | 0.662630 | ||||||||
\(852\) | − | 4.03676e12i | − | 0.262455i | ||||||
\(853\) | 2.34098e13i | 1.51401i | 0.653411 | + | 0.757004i | \(0.273337\pi\) | ||||
−0.653411 | + | 0.757004i | \(0.726663\pi\) | |||||||
\(854\) | −1.17065e13 | −0.753126 | ||||||||
\(855\) | 5.13452e12 | + | 3.65739e12i | 0.328589 | + | 0.234058i | ||||
\(856\) | −4.69336e13 | −2.98780 | ||||||||
\(857\) | − | 1.61008e13i | − | 1.01961i | −0.860290 | − | 0.509805i | \(-0.829718\pi\) | ||
0.860290 | − | 0.509805i | \(-0.170282\pi\) | |||||||
\(858\) | − | 1.29167e12i | − | 0.0813691i | ||||||
\(859\) | 1.34163e13 | 0.840745 | 0.420373 | − | 0.907352i | \(-0.361899\pi\) | ||||
0.420373 | + | 0.907352i | \(0.361899\pi\) | |||||||
\(860\) | 2.83248e13 | − | 3.97644e13i | 1.76573 | − | 2.47886i | ||||
\(861\) | 3.40940e12 | 0.211429 | ||||||||
\(862\) | 3.18532e13i | 1.96504i | ||||||||
\(863\) | − | 2.03784e13i | − | 1.25061i | −0.780381 | − | 0.625304i | \(-0.784975\pi\) | ||
0.780381 | − | 0.625304i | \(-0.215025\pi\) | |||||||
\(864\) | 1.20840e13 | 0.737735 | ||||||||
\(865\) | 1.26978e11 | − | 1.78262e11i | 0.00771183 | − | 0.0108264i | ||||
\(866\) | −4.45544e13 | −2.69191 | ||||||||
\(867\) | − | 7.58415e11i | − | 0.0455849i | ||||||
\(868\) | 2.09366e13i | 1.25189i | ||||||||
\(869\) | −4.28176e12 | −0.254703 | ||||||||
\(870\) | −4.54811e12 | − | 3.23969e12i | −0.269150 | − | 0.191719i | ||||
\(871\) | 2.23764e13 | 1.31737 | ||||||||
\(872\) | 4.88886e13i | 2.86341i | ||||||||
\(873\) | 1.10287e13i | 0.642630i | ||||||||
\(874\) | −7.36456e12 | −0.426919 | ||||||||
\(875\) | −1.39188e13 | − | 4.09347e12i | −0.802725 | − | 0.236078i | ||||
\(876\) | 3.42036e12 | 0.196247 | ||||||||
\(877\) | − | 3.55027e12i | − | 0.202658i | −0.994853 | − | 0.101329i | \(-0.967691\pi\) | ||
0.994853 | − | 0.101329i | \(-0.0323094\pi\) | |||||||
\(878\) | 3.95186e13i | 2.24428i | ||||||||
\(879\) | −1.33206e12 | −0.0752617 | ||||||||
\(880\) | 6.58181e12 | + | 4.68831e12i | 0.369976 | + | 0.263539i | ||||
\(881\) | −2.33443e13 | −1.30554 | −0.652769 | − | 0.757557i | \(-0.726393\pi\) | ||||
−0.652769 | + | 0.757557i | \(0.726393\pi\) | |||||||
\(882\) | 9.13399e12i | 0.508220i | ||||||||
\(883\) | − | 8.70030e12i | − | 0.481627i | −0.970571 | − | 0.240814i | \(-0.922586\pi\) | ||
0.970571 | − | 0.240814i | \(-0.0774142\pi\) | |||||||
\(884\) | 2.98724e13 | 1.64526 | ||||||||
\(885\) | −4.89560e12 | + | 6.87281e12i | −0.268263 | + | 0.376608i | ||||
\(886\) | −8.52799e12 | −0.464938 | ||||||||
\(887\) | − | 2.98568e13i | − | 1.61952i | −0.586760 | − | 0.809761i | \(-0.699597\pi\) | ||
0.586760 | − | 0.809761i | \(-0.300403\pi\) | |||||||
\(888\) | 1.49271e13i | 0.805596i | ||||||||
\(889\) | 1.12738e13 | 0.605358 | ||||||||
\(890\) | 7.95053e12 | − | 1.11616e13i | 0.424758 | − | 0.596307i | ||||
\(891\) | 3.18799e12 | 0.169460 | ||||||||
\(892\) | − | 5.90273e13i | − | 3.12184i | ||||||
\(893\) | − | 1.01325e13i | − | 0.533196i | ||||||
\(894\) | 9.30718e12 | 0.487303 | ||||||||
\(895\) | 6.09572e12 | + | 4.34206e12i | 0.317557 | + | 0.226200i | ||||
\(896\) | −8.61458e12 | −0.446527 | ||||||||
\(897\) | − | 2.16404e12i | − | 0.111609i | ||||||
\(898\) | − | 7.26969e12i | − | 0.373055i | ||||||
\(899\) | 8.46604e12 | 0.432277 | ||||||||
\(900\) | −1.39356e13 | − | 4.03019e13i | −0.708004 | − | 2.04755i | ||||
\(901\) | −1.77968e13 | −0.899666 | ||||||||
\(902\) | 7.34144e12i | 0.369277i | ||||||||
\(903\) | 5.84721e12i | 0.292654i | ||||||||
\(904\) | 1.78138e13 | 0.887153 | ||||||||
\(905\) | −1.73142e12 | − | 1.23331e12i | −0.0857993 | − | 0.0611160i | ||||
\(906\) | −9.25534e12 | −0.456368 | ||||||||
\(907\) | − | 2.14293e13i | − | 1.05142i | −0.850664 | − | 0.525709i | \(-0.823800\pi\) | ||
0.850664 | − | 0.525709i | \(-0.176200\pi\) | |||||||
\(908\) | 3.91708e13i | 1.91239i | ||||||||
\(909\) | −3.71910e12 | −0.180676 | ||||||||
\(910\) | −1.41844e13 | + | 1.99132e13i | −0.685686 | + | 0.962618i | ||||
\(911\) | 3.43474e13 | 1.65219 | 0.826097 | − | 0.563529i | \(-0.190557\pi\) | ||||
0.826097 | + | 0.563529i | \(0.190557\pi\) | |||||||
\(912\) | − | 5.15493e12i | − | 0.246744i | ||||||
\(913\) | − | 5.44218e12i | − | 0.259212i | ||||||
\(914\) | −1.23470e13 | −0.585200 | ||||||||
\(915\) | 1.62680e12 | − | 2.28383e12i | 0.0767255 | − | 0.107713i | ||||
\(916\) | 1.62064e13 | 0.760603 | ||||||||
\(917\) | 2.96422e13i | 1.38436i | ||||||||
\(918\) | − | 1.85181e13i | − | 0.860607i | ||||||
\(919\) | −2.05847e13 | −0.951975 | −0.475987 | − | 0.879452i | \(-0.657909\pi\) | ||||
−0.475987 | + | 0.879452i | \(0.657909\pi\) | |||||||
\(920\) | 2.31954e13 | + | 1.65224e13i | 1.06747 | + | 0.760376i | ||||
\(921\) | −3.12531e12 | −0.143128 | ||||||||
\(922\) | 1.81566e13i | 0.827458i | ||||||||
\(923\) | 7.14688e12i | 0.324122i | ||||||||
\(924\) | −2.49332e12 | −0.112527 | ||||||||
\(925\) | 2.59278e13 | − | 8.96535e12i | 1.16447 | − | 0.402652i | ||||
\(926\) | 4.80354e13 | 2.14690 | ||||||||
\(927\) | 1.67299e13i | 0.744104i | ||||||||
\(928\) | − | 2.17331e13i | − | 0.961955i | ||||||
\(929\) | −1.78605e13 | −0.786726 | −0.393363 | − | 0.919383i | \(-0.628688\pi\) | ||||
−0.393363 | + | 0.919383i | \(0.628688\pi\) | |||||||
\(930\) | −5.83411e12 | − | 4.15572e12i | −0.255741 | − | 0.182168i | ||||
\(931\) | 2.98855e12 | 0.130373 | ||||||||
\(932\) | 9.56035e12i | 0.415052i | ||||||||
\(933\) | − | 8.05267e11i | − | 0.0347915i | ||||||
\(934\) | −6.85583e12 | −0.294781 | ||||||||
\(935\) | 2.65238e12 | − | 3.72361e12i | 0.113497 | − | 0.159335i | ||||
\(936\) | −4.10789e13 | −1.74935 | ||||||||
\(937\) | 1.00969e13i | 0.427917i | 0.976843 | + | 0.213959i | \(0.0686358\pi\) | ||||
−0.976843 | + | 0.213959i | \(0.931364\pi\) | |||||||
\(938\) | − | 6.16950e13i | − | 2.60218i | ||||||
\(939\) | 9.65703e12 | 0.405367 | ||||||||
\(940\) | −3.97662e13 | + | 5.58268e13i | −1.66126 | + | 2.33221i | ||||
\(941\) | −2.40159e12 | −0.0998496 | −0.0499248 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499248 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(942\) | 4.57760e12i | 0.189413i | ||||||||
\(943\) | 1.22997e13i | 0.506513i | ||||||||
\(944\) | −8.89591e13 | −3.64600 | ||||||||
\(945\) | 8.64237e12 | + | 6.15608e12i | 0.352525 | + | 0.251108i | ||||
\(946\) | −1.25908e13 | −0.511142 | ||||||||
\(947\) | 2.09609e13i | 0.846907i | 0.905918 | + | 0.423453i | \(0.139182\pi\) | ||||
−0.905918 | + | 0.423453i | \(0.860818\pi\) | |||||||
\(948\) | − | 1.84767e13i | − | 0.742997i | ||||||
\(949\) | −6.05558e12 | −0.242358 | ||||||||
\(950\) | −1.88347e13 | + | 6.51268e12i | −0.750245 | + | 0.259420i | ||||
\(951\) | 4.74692e12 | 0.188191 | ||||||||
\(952\) | − | 4.70827e13i | − | 1.85779i | ||||||
\(953\) | − | 1.23636e12i | − | 0.0485543i | −0.999705 | − | 0.0242771i | \(-0.992272\pi\) | ||
0.999705 | − | 0.0242771i | \(-0.00772841\pi\) | |||||||
\(954\) | 4.28115e13 | 1.67337 | ||||||||
\(955\) | −1.05663e13 | − | 7.52655e12i | −0.411064 | − | 0.292806i | ||||
\(956\) | 9.92338e13 | 3.84237 | ||||||||
\(957\) | 1.00822e12i | 0.0388553i | ||||||||
\(958\) | − | 5.50289e12i | − | 0.211080i | ||||||
\(959\) | −1.36769e13 | −0.522162 | ||||||||
\(960\) | −2.00213e12 | + | 2.81075e12i | −0.0760803 | + | 0.106807i | ||||
\(961\) | −1.55798e13 | −0.589259 | ||||||||
\(962\) | − | 4.62305e13i | − | 1.74037i | ||||||
\(963\) | − | 3.03651e13i | − | 1.13778i | ||||||
\(964\) | 7.22897e13 | 2.69606 | ||||||||
\(965\) | −5.62992e12 | + | 7.90371e12i | −0.208992 | + | 0.293399i | ||||
\(966\) | −5.96657e12 | −0.220459 | ||||||||
\(967\) | 1.93044e13i | 0.709966i | 0.934873 | + | 0.354983i | \(0.115513\pi\) | ||||
−0.934873 | + | 0.354983i | \(0.884487\pi\) | |||||||
\(968\) | 6.35028e13i | 2.32463i | ||||||||
\(969\) | −2.91636e12 | −0.106264 | ||||||||
\(970\) | −2.83977e13 | − | 2.02281e13i | −1.02994 | − | 0.733637i | ||||
\(971\) | −2.95198e12 | −0.106568 | −0.0532840 | − | 0.998579i | \(-0.516969\pi\) | ||||
−0.0532840 | + | 0.998579i | \(0.516969\pi\) | |||||||
\(972\) | 4.73634e13i | 1.70194i | ||||||||
\(973\) | 8.62646e12i | 0.308549i | ||||||||
\(974\) | 5.92007e13 | 2.10771 | ||||||||
\(975\) | −1.91372e12 | − | 5.53448e12i | −0.0678199 | − | 0.196135i | ||||
\(976\) | 2.95610e13 | 1.04279 | ||||||||
\(977\) | 5.39705e13i | 1.89509i | 0.319617 | + | 0.947547i | \(0.396446\pi\) | ||||
−0.319617 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(978\) | 4.19653e12i | 0.146678i | ||||||||
\(979\) | −2.47427e12 | −0.0860845 | ||||||||
\(980\) | −1.64659e13 | − | 1.17289e13i | −0.570252 | − | 0.406198i | ||||
\(981\) | −3.16299e13 | −1.09040 | ||||||||
\(982\) | − | 4.36697e13i | − | 1.49858i | ||||||
\(983\) | − | 2.52782e13i | − | 0.863487i | −0.901996 | − | 0.431743i | \(-0.857899\pi\) | ||
0.901996 | − | 0.431743i | \(-0.142101\pi\) | |||||||
\(984\) | −1.81098e13 | −0.615795 | ||||||||
\(985\) | 2.92480e13 | − | 4.10605e13i | 0.989994 | − | 1.38983i | ||||
\(986\) | −3.33047e13 | −1.12217 | ||||||||
\(987\) | − | 8.20912e12i | − | 0.275340i | ||||||
\(988\) | 2.35118e13i | 0.785019i | ||||||||
\(989\) | −2.10942e13 | −0.701101 | ||||||||
\(990\) | −6.38047e12 | + | 8.95738e12i | −0.211103 | + | 0.296362i | ||||
\(991\) | 3.62973e13 | 1.19548 | 0.597741 | − | 0.801689i | \(-0.296065\pi\) | ||||
0.597741 | + | 0.801689i | \(0.296065\pi\) | |||||||
\(992\) | − | 2.78781e13i | − | 0.914032i | ||||||
\(993\) | − | 6.44785e12i | − | 0.210447i | ||||||
\(994\) | 1.97050e13 | 0.640234 | ||||||||
\(995\) | −2.56312e13 | − | 1.82575e13i | −0.829020 | − | 0.590523i | ||||
\(996\) | 2.34842e13 | 0.756150 | ||||||||
\(997\) | − | 5.75313e13i | − | 1.84406i | −0.387114 | − | 0.922032i | \(-0.626528\pi\) | ||
0.387114 | − | 0.922032i | \(-0.373472\pi\) | |||||||
\(998\) | − | 7.35058e12i | − | 0.234549i | ||||||
\(999\) | −2.00642e13 | −0.637347 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.10.b.a.4.4 | yes | 4 | |
3.2 | odd | 2 | 45.10.b.b.19.1 | 4 | |||
4.3 | odd | 2 | 80.10.c.c.49.3 | 4 | |||
5.2 | odd | 4 | 25.10.a.e.1.1 | 4 | |||
5.3 | odd | 4 | 25.10.a.e.1.4 | 4 | |||
5.4 | even | 2 | inner | 5.10.b.a.4.1 | ✓ | 4 | |
15.2 | even | 4 | 225.10.a.s.1.4 | 4 | |||
15.8 | even | 4 | 225.10.a.s.1.1 | 4 | |||
15.14 | odd | 2 | 45.10.b.b.19.4 | 4 | |||
20.3 | even | 4 | 400.10.a.ba.1.2 | 4 | |||
20.7 | even | 4 | 400.10.a.ba.1.3 | 4 | |||
20.19 | odd | 2 | 80.10.c.c.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.b.a.4.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
5.10.b.a.4.4 | yes | 4 | 1.1 | even | 1 | trivial | |
25.10.a.e.1.1 | 4 | 5.2 | odd | 4 | |||
25.10.a.e.1.4 | 4 | 5.3 | odd | 4 | |||
45.10.b.b.19.1 | 4 | 3.2 | odd | 2 | |||
45.10.b.b.19.4 | 4 | 15.14 | odd | 2 | |||
80.10.c.c.49.2 | 4 | 20.19 | odd | 2 | |||
80.10.c.c.49.3 | 4 | 4.3 | odd | 2 | |||
225.10.a.s.1.1 | 4 | 15.8 | even | 4 | |||
225.10.a.s.1.4 | 4 | 15.2 | even | 4 | |||
400.10.a.ba.1.2 | 4 | 20.3 | even | 4 | |||
400.10.a.ba.1.3 | 4 | 20.7 | even | 4 |