Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,10,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (of order \(2\), degree \(1\), not 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: | \(41.2028668931\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(2.87724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.10.c.c.49.3 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 37.6407i | − | 0.268294i | −0.990961 | − | 0.134147i | \(-0.957170\pi\) | ||
0.990961 | − | 0.134147i | \(-0.0428295\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1138.29 | − | 810.818i | 0.814492 | − | 0.580174i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5315.22i | 0.836719i | 0.908281 | + | 0.418360i | \(0.137395\pi\) | ||||
−0.908281 | + | 0.418360i | \(0.862605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 18266.2 | 0.928018 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10426.2 | −0.214714 | −0.107357 | − | 0.994221i | \(-0.534239\pi\) | ||||
−0.107357 | + | 0.994221i | \(0.534239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 79655.1i | 0.773515i | 0.922181 | + | 0.386758i | \(0.126405\pi\) | ||||
−0.922181 | + | 0.386758i | \(0.873595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30519.7 | − | 42845.9i | −0.155658 | − | 0.218524i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 313750.i | 0.911095i | 0.890212 | + | 0.455547i | \(0.150556\pi\) | ||||
−0.890212 | + | 0.455547i | \(0.849444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −246945. | −0.434719 | −0.217360 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217360 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 200068. | 0.224487 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 721761.i | 0.537797i | 0.963169 | + | 0.268898i | \(0.0866595\pi\) | ||||
−0.963169 | + | 0.268898i | \(0.913340\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 638273. | − | 1.84589e6i | 0.326796 | − | 0.945095i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.42843e6i | − | 0.517277i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.56903e6 | −0.674493 | −0.337247 | − | 0.941416i | \(-0.609496\pi\) | ||||
−0.337247 | + | 0.941416i | \(0.609496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.29543e6 | 0.640891 | 0.320445 | − | 0.947267i | \(-0.396167\pi\) | ||||
0.320445 | + | 0.947267i | \(0.396167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 392451.i | 0.0576066i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.30967e6 | + | 6.05025e6i | 0.485443 | + | 0.681502i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40463e7i | 1.23212i | 0.787699 | + | 0.616060i | \(0.211272\pi\) | ||||
−0.787699 | + | 0.616060i | \(0.788728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.99827e6 | 0.207530 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70412e7 | 0.941830 | 0.470915 | − | 0.882178i | \(-0.343924\pi\) | ||||
0.470915 | + | 0.882178i | \(0.343924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.92261e7i | 1.30365i | 0.758368 | + | 0.651827i | \(0.225997\pi\) | ||||
−0.758368 | + | 0.651827i | \(0.774003\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.07922e7 | − | 1.48105e7i | 0.755864 | − | 0.538412i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.10316e7i | − | 1.22653i | −0.789878 | − | 0.613264i | \(-0.789856\pi\) | ||
0.789878 | − | 0.613264i | \(-0.210144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.21021e7 | 0.299901 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.18098e7 | 0.244442 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.67230e7i | 0.987456i | 0.869616 | + | 0.493728i | \(0.164366\pi\) | ||||
−0.869616 | + | 0.493728i | \(0.835634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18681e7 | + | 8.45379e6i | −0.174883 | + | 0.124572i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.29518e6i | 0.116633i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.60408e8 | 1.72342 | 0.861710 | − | 0.507402i | \(-0.169394\pi\) | ||||
0.861710 | + | 0.507402i | \(0.169394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.33033e7 | 0.492912 | 0.246456 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246456 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.70887e7i | 0.776491i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.45858e7 | + | 9.06705e7i | 0.448773 | + | 0.630022i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.80916e8i | 1.70310i | 0.524276 | + | 0.851548i | \(0.324336\pi\) | ||||
−0.524276 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.71676e7 | 0.144288 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.97228e7 | 0.419025 | 0.209513 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209513 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.60225e7i | 0.313321i | 0.987653 | + | 0.156660i | \(0.0500728\pi\) | ||||
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.94805e7 | − | 2.40250e7i | −0.253564 | − | 0.0876775i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.54178e7i | − | 0.179656i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.10672e8 | 1.18624 | 0.593120 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593120 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.05766e8 | 0.789236 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.21969e8i | − | 1.20724i | −0.797272 | − | 0.603620i | \(-0.793724\pi\) | ||
0.797272 | − | 0.603620i | \(-0.206276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.54394e8 | + | 3.57138e8i | 0.528594 | + | 0.742080i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.66999e7i | 0.180963i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.37312e8 | −0.400926 | −0.200463 | − | 0.979701i | \(-0.564245\pi\) | ||||
−0.200463 | + | 0.979701i | \(0.564245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.23384e8 | −0.647215 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.24042e8i | − | 0.171947i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.81094e8 | + | 2.00227e8i | −0.354076 | + | 0.252213i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.03778e8i | − | 0.692476i | −0.938147 | − | 0.346238i | \(-0.887459\pi\) | ||
0.938147 | − | 0.346238i | \(-0.112541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.90448e8 | −0.199259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.03606e8 | −0.194690 | −0.0973451 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973451 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.15893e8i | 0.801821i | 0.916117 | + | 0.400910i | \(0.131306\pi\) | ||||
−0.916117 | + | 0.400910i | \(0.868694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.27735e8 | − | 1.62219e8i | 0.182843 | − | 0.130242i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.66237e9i | − | 1.22603i | −0.790072 | − | 0.613014i | \(-0.789957\pi\) | ||
0.790072 | − | 0.613014i | \(-0.210043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73161e9 | −1.17498 | −0.587491 | − | 0.809231i | \(-0.699884\pi\) | ||||
−0.587491 | + | 0.809231i | \(0.699884\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.28711e8 | 0.330571 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.30956e8i | − | 0.364038i | −0.983295 | − | 0.182019i | \(-0.941737\pi\) | ||
0.983295 | − | 0.182019i | \(-0.0582632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.85217e8 | + | 8.21571e8i | 0.312016 | + | 0.438031i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.45500e9i | 0.717836i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.66765e9 | −0.762331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.24924e9 | −0.953898 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 6.41442e8i | − | 0.252688i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.70141e8 | − | 2.61868e9i | −0.282147 | − | 0.959371i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.12104e9i | − | 0.723490i | −0.932277 | − | 0.361745i | \(-0.882181\pi\) | ||
0.932277 | − | 0.361745i | \(-0.117819\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.10009e9 | 0.349763 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.57686e9 | −1.65451 | −0.827254 | − | 0.561828i | \(-0.810098\pi\) | ||||
−0.827254 | + | 0.561828i | \(0.810098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.31257e9i | − | 0.363738i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.15820e9 | − | 1.62597e9i | −0.300111 | − | 0.421318i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.57317e9i | − | 0.624059i | −0.950072 | − | 0.312029i | \(-0.898991\pi\) | ||
0.950072 | − | 0.312029i | \(-0.101009\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.62297e9 | −0.368761 | −0.184380 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184380 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.54446e9 | −0.329071 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.30504e8i | − | 0.166085i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.92429e9 | + | 2.08301e9i | −0.549370 | + | 0.391324i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 4.55530e8i | − | 0.0804617i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.98422e9 | 0.994647 | 0.497324 | − | 0.867565i | \(-0.334316\pi\) | ||||
0.497324 | + | 0.867565i | \(0.334316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.95089e9 | 0.931505 | 0.465753 | − | 0.884915i | \(-0.345784\pi\) | ||||
0.465753 | + | 0.884915i | \(0.345784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.73101e9i | 0.845513i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.75114e9 | − | 2.67199e9i | 0.522001 | − | 0.371828i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.94325e9i | − | 0.386615i | −0.981138 | − | 0.193308i | \(-0.938078\pi\) | ||
0.981138 | − | 0.193308i | \(-0.0619215\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.13509e9 | 0.264929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.83632e9 | −0.449985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.69823e9i | 0.299389i | 0.988732 | + | 0.149694i | \(0.0478290\pi\) | ||||
−0.988732 | + | 0.149694i | \(0.952171\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.18206e8 | + | 4.46722e8i | 0.0334219 | + | 0.0469202i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.47132e10i | 1.46380i | 0.681410 | + | 0.731902i | \(0.261367\pi\) | ||||
−0.681410 | + | 0.731902i | \(0.738633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.25956e9 | 0.401675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.51074e9 | −0.403427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.56605e8i | 0.0132923i | 0.999978 | + | 0.00664613i | \(0.00211555\pi\) | ||||
−0.999978 | + | 0.00664613i | \(0.997884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.81130e9 | + | 3.39256e9i | 0.790779 | + | 0.273436i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.03785e9i | − | 0.462384i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.35516e9 | −0.389883 | −0.194941 | − | 0.980815i | \(-0.562452\pi\) | ||||
−0.194941 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.52107e9 | −0.105341 | −0.0526704 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526704 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.00637e9i | − | 0.132246i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.13890e10 | + | 1.59887e10i | 0.714845 | + | 1.00355i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.27123e9i | − | 0.195625i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.59243e9 | 0.432815 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.28266e9 | 0.504687 | 0.252344 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252344 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.94351e9i | − | 0.360223i | −0.983646 | − | 0.180111i | \(-0.942354\pi\) | ||
0.983646 | − | 0.180111i | \(-0.0576458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.41290e9 | − | 2.43105e9i | 0.169031 | − | 0.120403i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.60722e10i | 1.70637i | 0.521606 | + | 0.853187i | \(0.325333\pi\) | ||||
−0.521606 | + | 0.853187i | \(0.674667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.25173e10 | 1.01784 | 0.508918 | − | 0.860815i | \(-0.330045\pi\) | ||||
0.508918 | + | 0.860815i | \(0.330045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.05739e10 | 0.456931 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.36549e10i | − | 0.564362i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.93978e10 | − | 1.38173e10i | 0.767114 | − | 0.546426i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.31838e10i | 0.499085i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.57471e9 | 0.0933404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.62300e10 | −1.25834 | −0.629169 | − | 0.777268i | \(-0.716605\pi\) | ||||
−0.629169 | + | 0.777268i | \(0.716605\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.37723e9i | − | 0.112422i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.36970e10 | + | 3.32677e10i | 0.756346 | + | 1.06182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.75159e10i | 0.536246i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.86154e9 | 0.0840623 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.49918e10 | −0.704746 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.93834e10i | 1.33724i | 0.743605 | + | 0.668619i | \(0.233114\pi\) | ||||
−0.743605 | + | 0.668619i | \(0.766886\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.16588e10 | − | 3.37173e10i | 0.303272 | − | 0.877065i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.27710e10i | − | 0.819169i | −0.912272 | − | 0.409585i | \(-0.865674\pi\) | ||
0.912272 | − | 0.409585i | \(-0.134326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.35586e10 | −0.325803 | −0.162902 | − | 0.986642i | \(-0.552085\pi\) | ||||
−0.162902 | + | 0.986642i | \(0.552085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.08596e9 | −0.0482006 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.99837e9i | 0.177787i | 0.996041 | + | 0.0888935i | \(0.0283331\pi\) | ||||
−0.996041 | + | 0.0888935i | \(0.971667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.32691e10 | − | 4.67057e10i | −0.711600 | − | 0.998998i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.54580e10i | − | 0.318262i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.30208e10 | 1.64587 | 0.822937 | − | 0.568133i | \(-0.192334\pi\) | ||||
0.822937 | + | 0.568133i | \(0.192334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.04789e10 | −1.15485 | −0.577427 | − | 0.816442i | \(-0.695943\pi\) | ||||
−0.577427 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.96251e10i | − | 0.729024i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.37756e10 | − | 9.81258e9i | 0.244267 | − | 0.173995i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.96704e10i | − | 0.336262i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.96473e10 | −0.323896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.04682e11 | −1.66471 | −0.832354 | − | 0.554244i | \(-0.813007\pi\) | ||||
−0.832354 | + | 0.554244i | \(0.813007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.52525e9i | − | 0.115473i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.34429e10 | − | 9.57557e9i | 0.199096 | − | 0.141819i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.92751e10i | − | 1.13354i | −0.823875 | − | 0.566771i | \(-0.808192\pi\) | ||
0.823875 | − | 0.566771i | \(-0.191808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.46590e10 | −1.03094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.69263e10 | −0.625942 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.04629e8i | − | 0.00134850i | −1.00000 | 0.000674250i | \(-0.999785\pi\) | |||
1.00000 | 0.000674250i | \(-0.000214620\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.59920e10 | + | 6.45671e10i | 0.572897 | + | 0.804275i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.93258e9i | 0.107566i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.38735e9 | 0.0860208 | 0.0430104 | − | 0.999075i | \(-0.486305\pi\) | ||||
0.0430104 | + | 0.999075i | \(0.486305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.27706e11 | −1.43831 | −0.719153 | − | 0.694852i | \(-0.755470\pi\) | ||||
−0.719153 | + | 0.694852i | \(0.755470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.59365e10i | 0.173644i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.65479e9 | + | 1.92457e10i | −0.0701677 | + | 0.202925i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.16563e10i | − | 0.323074i | −0.986867 | − | 0.161537i | \(-0.948355\pi\) | ||
0.986867 | − | 0.161537i | \(-0.0516451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.01949e10 | 0.594758 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50309e10 | −0.909257 | −0.454628 | − | 0.890681i | \(-0.650228\pi\) | ||||
−0.454628 | + | 0.890681i | \(0.650228\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.91862e10i | − | 0.455832i | −0.973681 | − | 0.227916i | \(-0.926809\pi\) | ||
0.973681 | − | 0.227916i | \(-0.0731911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.53670e9 | + | 1.05806e10i | 0.0676673 | + | 0.0949965i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.05777e10i | 0.788048i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.01488e10 | 0.169906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.27266e10 | −0.185787 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.53889e10i | 0.280519i | 0.990115 | + | 0.140260i | \(0.0447937\pi\) | ||||
−0.990115 | + | 0.140260i | \(0.955206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.82590e11 | − | 1.30061e11i | 1.40371 | − | 0.999883i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.48932e10i | 0.111067i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.74920e10 | −0.415994 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.55343e11 | −1.09079 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.66386e9i | 0.0522343i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.06745e10 | − | 4.32193e10i | 0.401473 | − | 0.285975i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.30301e10i | − | 0.533474i | −0.963769 | − | 0.266737i | \(-0.914055\pi\) | ||
0.963769 | − | 0.266737i | \(-0.0859455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.44748e10 | 0.215124 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.13935e10 | −0.129676 | −0.0648382 | − | 0.997896i | \(-0.520653\pi\) | ||||
−0.0648382 | + | 0.997896i | \(0.520653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.56558e11i | − | 1.51090i | −0.655204 | − | 0.755452i | \(-0.727418\pi\) | ||
0.655204 | − | 0.755452i | \(-0.272582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.87213e10 | + | 1.10515e11i | 0.450500 | + | 0.632446i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.26112e11i | − | 0.701436i | −0.936481 | − | 0.350718i | \(-0.885938\pi\) | ||
0.936481 | − | 0.350718i | \(-0.114062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.67853e10 | 0.144823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.25727e10 | −0.328936 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.74790e10i | − | 0.396071i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.47035e11 | + | 5.08417e10i | 0.731045 | + | 0.252781i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.51790e10i | 0.315241i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.18092e11 | 1.02626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.71300e11 | −0.784389 | −0.392194 | − | 0.919882i | \(-0.628284\pi\) | ||||
−0.392194 | + | 0.919882i | \(0.628284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.56572e11i | 1.14343i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.27771e11 | + | 3.19763e11i | 0.988093 | + | 1.38716i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70320e11i | 1.98637i | 0.116569 | + | 0.993183i | \(0.462810\pi\) | ||||
−0.116569 | + | 0.993183i | \(0.537190\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.37496e10 | −0.0976693 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.43589e10 | −0.137608 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.78813e11i | 1.08765i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.09245e10 | − | 2.20279e10i | 0.117521 | − | 0.0837121i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.86642e11i | − | 1.06135i | −0.847576 | − | 0.530674i | \(-0.821939\pi\) | ||
0.847576 | − | 0.530674i | \(-0.178061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.54310e11 | 1.27841 | 0.639203 | − | 0.769038i | \(-0.279264\pi\) | ||||
0.639203 | + | 0.769038i | \(0.279264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.13782e11 | 0.400121 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.09491e11i | 0.718092i | 0.933320 | + | 0.359046i | \(0.116898\pi\) | ||||
−0.933320 | + | 0.359046i | \(0.883102\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.02130e11 | − | 7.27489e10i | 0.341293 | − | 0.243108i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.27715e10i | 0.204529i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.88081e11 | 0.915355 | 0.457678 | − | 0.889118i | \(-0.348681\pi\) | ||||
0.457678 | + | 0.889118i | \(0.348681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.61706e11 | −0.811019 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.46630e10i | 0.255926i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.16404e10 | + | 8.65355e10i | 0.181781 | + | 0.255197i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.33587e10i | − | 0.0384387i | −0.999815 | − | 0.0192193i | \(-0.993882\pi\) | ||
0.999815 | − | 0.0192193i | \(-0.00611808\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.11278e11 | 0.874036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.01495e11 | −0.826224 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.17763e11i | − | 1.11748i | −0.829342 | − | 0.558741i | \(-0.811284\pi\) | ||
0.829342 | − | 0.558741i | \(-0.188716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.85687e10 | + | 2.89886e10i | −0.257394 | + | 0.0756985i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.04636e11i | − | 0.521731i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.63110e11 | 0.655031 | 0.327515 | − | 0.944846i | \(-0.393789\pi\) | ||||
0.327515 | + | 0.944846i | \(0.393789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.98374e10 | −0.194108 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.84146e10i | − | 0.186210i | −0.995656 | − | 0.0931049i | \(-0.970321\pi\) | ||
0.995656 | − | 0.0931049i | \(-0.0296792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.49337e10 | − | 6.30814e10i | −0.104232 | − | 0.146328i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.33849e11i | 1.20981i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.66007e11 | −0.367581 | −0.183791 | − | 0.982965i | \(-0.558837\pi\) | ||||
−0.183791 | + | 0.982965i | \(0.558837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.26452e11 | −0.489984 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.09917e11i | 0.443896i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.67462e11 | − | 3.32980e11i | 0.966184 | − | 0.688226i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.09536e11i | − | 0.827437i | −0.910405 | − | 0.413719i | \(-0.864230\pi\) | ||
0.910405 | − | 0.413719i | \(-0.135770\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.94059e10 | −0.0975889 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.92645e10 | −0.153084 | −0.0765419 | − | 0.997066i | \(-0.524388\pi\) | ||||
−0.0765419 | + | 0.997066i | \(0.524388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.62498e11i | 0.495739i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.48050e11 | − | 2.47921e11i | 0.642826 | − | 0.457894i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.46450e11i | − | 0.264554i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.85827e11 | −1.21188 | −0.605940 | − | 0.795510i | \(-0.707203\pi\) | ||||
−0.605940 | + | 0.795510i | \(0.707203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.68557e10 | −0.167431 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.52601e11i | 1.44202i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.23222e11 | − | 5.94151e11i | −0.700410 | − | 0.983288i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.10898e10i | 0.0989365i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.31879e11 | 0.526037 | 0.263018 | − | 0.964791i | \(-0.415282\pi\) | ||||
0.263018 | + | 0.964791i | \(0.415282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.30694e11 | −0.978475 | −0.489237 | − | 0.872151i | \(-0.662725\pi\) | ||||
−0.489237 | + | 0.872151i | \(0.662725\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7.49490e11i | − | 1.13824i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.79148e11 | + | 2.00258e11i | 0.861071 | + | 0.297742i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.83319e11i | 0.412429i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.12607e10 | −0.0445596 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.70903e11 | −1.07610 | −0.538049 | − | 0.842913i | \(-0.680839\pi\) | ||||
−0.538049 | + | 0.842913i | \(0.680839\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.07829e12i | − | 1.47415i | −0.675811 | − | 0.737075i | \(-0.736206\pi\) | ||
0.675811 | − | 0.737075i | \(-0.263794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.84060e10 | + | 1.10072e11i | 0.104990 | + | 0.147393i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.78235e11i | − | 0.233791i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.56419e11 | −1.22902 | −0.614508 | − | 0.788910i | \(-0.710646\pi\) | ||||
−0.614508 | + | 0.788910i | \(0.710646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.21059e11 | 0.278313 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.06392e11i | 0.254611i | 0.991864 | + | 0.127305i | \(0.0406328\pi\) | ||||
−0.991864 | + | 0.127305i | \(0.959367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.70129e11 | + | 1.92417e11i | −0.326551 | + | 0.232607i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.25250e11i | − | 0.266858i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75939e11 | −0.204293 | −0.102147 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102147 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.77676e11 | −0.202224 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.23995e11i | − | 0.249918i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.81933e11 | + | 3.43288e11i | −0.527152 | + | 0.375497i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.98819e11i | − | 0.320469i | −0.987079 | − | 0.160234i | \(-0.948775\pi\) | ||
0.987079 | − | 0.160234i | \(-0.0512250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.48171e11 | 0.471288 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.39422e11 | 0.453135 | 0.226567 | − | 0.973995i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973995i | \(0.427250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.16254e12i | − | 1.17569i | −0.808973 | − | 0.587846i | \(-0.799976\pi\) | ||
0.808973 | − | 0.587846i | \(-0.200024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00576e11 | − | 1.41196e11i | −0.0997595 | − | 0.140050i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.65923e11i | 0.161429i | 0.996737 | + | 0.0807144i | \(0.0257202\pi\) | ||||
−0.996737 | + | 0.0807144i | \(0.974280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.49313e12 | −1.42501 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10786e11 | −0.103727 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.04718e11i | − | 0.279913i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57618e11 | + | 4.55833e11i | −0.142064 | + | 0.410851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.03611e12i | 0.916377i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.33180e11 | 0.115592 | 0.0577960 | − | 0.998328i | \(-0.481593\pi\) | ||||
0.0577960 | + | 0.998328i | \(0.481593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.11886e12 | −0.953064 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.44401e11i | 0.120728i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.89554e11 | − | 6.87273e11i | −0.401756 | − | 0.564016i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.43276e12i | − | 1.15423i | −0.816662 | − | 0.577116i | \(-0.804178\pi\) | ||
0.816662 | − | 0.577116i | \(-0.195822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.01563e11 | 0.0803243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05688e12 | 0.820655 | 0.410327 | − | 0.911938i | \(-0.365414\pi\) | ||||
0.410327 | + | 0.911938i | \(0.365414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.06032e11i | − | 0.614527i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.16784e11 | + | 1.54418e11i | −0.162295 | + | 0.115605i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.76896e11i | 0.350607i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.77897e11 | 0.128445 | 0.0642223 | − | 0.997936i | \(-0.479543\pi\) | ||||
0.0642223 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.53814e11 | 0.392730 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.58467e12i | 1.10378i | 0.833917 | + | 0.551889i | \(0.186093\pi\) | ||||
−0.833917 | + | 0.551889i | \(0.813907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.31762e11 | + | 1.65087e11i | −0.158574 | + | 0.112954i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.60333e11i | − | 0.107767i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.93674e12 | 1.27891 | 0.639456 | − | 0.768827i | \(-0.279159\pi\) | ||||
0.639456 | + | 0.768827i | \(0.279159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.04076e11 | −0.262162 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.52744e11i | 0.224870i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.42623e11 | + | 1.04255e12i | 0.465196 | + | 0.653077i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.27805e11i | 0.263353i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.89473e9 | 0.00356624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.72419e12 | 1.61982 | 0.809912 | − | 0.586552i | \(-0.199515\pi\) | ||||
0.809912 | + | 0.586552i | \(0.199515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.86784e11i | 0.284497i | 0.989831 | + | 0.142249i | \(0.0454333\pi\) | ||||
−0.989831 | + | 0.142249i | \(0.954567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.27698e11 | − | 3.69304e11i | 0.0733615 | − | 0.212162i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03394e12i | 0.583912i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28021e12 | 0.710775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.93003e12 | 1.59936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.35742e12i | 0.728520i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.34788e12 | − | 1.89225e12i | −0.711309 | − | 0.998590i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.01572e11i | 0.104603i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.26179e11 | −0.0643929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.98233e11 | 0.0994920 | 0.0497460 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497460 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.72543e10i | 0.0282624i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97107e12 | + | 1.40402e12i | −0.957014 | + | 0.681694i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.79532e11i | 0.229021i | 0.993422 | + | 0.114510i | \(0.0365299\pi\) | ||||
−0.993422 | + | 0.114510i | \(0.963470\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.73647e11 | 0.457432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34408e11 | 0.293215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.18281e12i | 0.992550i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.01825e11 | − | 4.28688e11i | 0.269248 | − | 0.191789i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.20856e11i | 0.0532011i | 0.999646 | + | 0.0266006i | \(0.00846822\pi\) | ||||
−0.999646 | + | 0.0266006i | \(0.991532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.32801e12 | −1.00840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23131e11 | −0.0524851 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.01468e12i | − | 0.425637i | −0.977092 | − | 0.212818i | \(-0.931736\pi\) | ||
0.977092 | − | 0.212818i | \(-0.0682643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.11591e11 | − | 7.18210e11i | −0.211205 | − | 0.296506i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.62521e12i | 0.660369i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.12630e12 | −0.450454 | −0.225227 | − | 0.974306i | \(-0.572312\pi\) | ||||
−0.225227 | + | 0.974306i | \(0.572312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.75478e12 | 1.08449 | 0.542243 | − | 0.840221i | \(-0.317575\pi\) | ||||
0.542243 | + | 0.840221i | \(0.317575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.49405e11i | − | 0.135405i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.33229e12 | + | 4.60680e11i | 0.508269 | + | 0.175750i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.14763e12i | − | 1.55779i | −0.627155 | − | 0.778895i | \(-0.715781\pi\) | ||
0.627155 | − | 0.778895i | \(-0.284219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.61358e11 | −0.0966458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.77438e12 | 1.01012 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.91408e11i | − | 0.212021i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.17974e12 | + | 1.65620e12i | 0.416470 | + | 0.584672i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.38017e12i | 0.479800i | 0.970798 | + | 0.239900i | \(0.0771147\pi\) | ||||
−0.970798 | + | 0.239900i | \(0.922885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.13789e11 | −0.278608 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.35778e12 | 0.457811 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.90406e11i | − | 0.229276i | −0.993407 | − | 0.114638i | \(-0.963429\pi\) | ||
0.993407 | − | 0.114638i | \(-0.0365708\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.89827e12 | + | 1.35216e12i | −0.620913 | + | 0.442285i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.47568e11i | − | 0.273080i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.24239e12 | 0.394309 | 0.197155 | − | 0.980372i | \(-0.436830\pi\) | ||||
0.197155 | + | 0.980372i | \(0.436830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.01140e12 | 0.628873 | 0.314437 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314437 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.13126e12i | 1.58050i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.56028e12 | + | 1.82373e12i | −0.776943 | + | 0.553427i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.73579e12i | − | 0.817963i | −0.912543 | − | 0.408981i | \(-0.865884\pi\) | ||
0.912543 | − | 0.408981i | \(-0.134116\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.13981e11 | −0.151415 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.26838e12 | 0.948738 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.63707e12i | 0.468269i | 0.972204 | + | 0.234135i | \(0.0752257\pi\) | ||||
−0.972204 | + | 0.234135i | \(0.924774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.20093e11 | − | 7.30146e11i | −0.146603 | − | 0.205812i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.22267e12i | 0.339646i | 0.985475 | + | 0.169823i | \(0.0543197\pi\) | ||||
−0.985475 | + | 0.169823i | \(0.945680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.78784e12 | −1.58456 | −0.792280 | − | 0.610158i | \(-0.791106\pi\) | ||||
−0.792280 | + | 0.610158i | \(0.791106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.03099e12 | 0.278190 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.26136e12i | − | 0.335463i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.99991e12 | − | 2.35636e12i | −0.786409 | − | 0.617706i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 9.69138e10i | − | 0.0250427i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.40702e12 | −1.12258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00341e12 | −0.503081 | −0.251540 | − | 0.967847i | \(-0.580937\pi\) | ||||
−0.251540 | + | 0.967847i | \(0.580937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.36372e12i | 0.337605i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.71978e12 | − | 2.41435e12i | −0.419750 | − | 0.589277i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.63992e11i | 0.231978i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.63889e12 | 0.388863 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.75478e12 | 0.644505 | 0.322253 | − | 0.946654i | \(-0.395560\pi\) | ||||
0.322253 | + | 0.946654i | \(0.395560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.38857e12i | − | 1.70455i | −0.523091 | − | 0.852277i | \(-0.675221\pi\) | ||
0.523091 | − | 0.852277i | \(-0.324779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.25222e12 | − | 8.91972e11i | 0.284879 | − | 0.202924i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.12045e12i | − | 0.924432i | −0.886767 | − | 0.462216i | \(-0.847054\pi\) | ||
0.886767 | − | 0.462216i | \(-0.152946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.67245e12 | −0.370043 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.59311e11 | 0.143872 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 6.51407e12i | − | 1.40198i | −0.713170 | − | 0.700992i | \(-0.752741\pi\) | ||
0.713170 | − | 0.700992i | \(-0.247259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.34807e12 | + | 4.52182e12i | −1.34758 | + | 0.959903i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.38864e12i | 0.290767i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.74145e12 | −0.359688 | −0.179844 | − | 0.983695i | \(-0.557559\pi\) | ||||
−0.179844 | + | 0.983695i | \(0.557559\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39849e12 | −0.284939 | −0.142469 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142469 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.40708e11i | 0.189079i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.06425e12 | − | 1.49408e12i | −0.211031 | − | 0.296262i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.85422e12i | − | 0.362740i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.85882e12 | 0.358774 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.55753e11 | −0.105835 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 7.23077e12i | − | 1.35868i | −0.733824 | − | 0.679340i | \(-0.762266\pi\) | ||
0.733824 | − | 0.679340i | \(-0.237734\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.63673e12 | − | 9.11730e11i | −0.488876 | − | 0.169044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.09854e12i | 0.200986i | 0.994938 | + | 0.100493i | \(0.0320419\pi\) | ||||
−0.994938 | + | 0.100493i | \(0.967958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.20921e12 | 0.579408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23352e12 | −0.219779 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.51781e12i | 0.266885i | 0.991057 | + | 0.133442i | \(0.0426031\pi\) | ||||
−0.991057 | + | 0.133442i | \(0.957397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.08637e12 | − | 2.92900e12i | −0.362063 | − | 0.508291i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.10355e11i | 0.0874112i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.51828e12 | −0.763812 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.51489e12 | −0.252772 | −0.126386 | − | 0.991981i | \(-0.540338\pi\) | ||||
−0.126386 | + | 0.991981i | \(0.540338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.01227e12i | − | 0.166724i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.84741e12 | + | 1.31594e12i | −0.300353 | + | 0.213946i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.34668e12i | 0.858097i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.01064e11 | 0.0476993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.62368e12 | 1.19243 | 0.596216 | − | 0.802824i | \(-0.296670\pi\) | ||||
0.596216 | + | 0.802824i | \(0.296670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.46866e12i | − | 0.535627i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.75804e12 | + | 1.25227e12i | −0.268026 | + | 0.190918i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.08221e12i | − | 0.162901i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00657e13 | −1.49602 | −0.748010 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748010 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.50140e12 | 1.10085 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.37851e12i | 0.344669i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.73388e11 | − | 9.45353e11i | −0.0963580 | − | 0.135275i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.12496e12i | − | 0.441579i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.94464e12 | 1.24820 | 0.624098 | − | 0.781346i | \(-0.285466\pi\) | ||||
0.624098 | + | 0.781346i | \(0.285466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.86817e12 | −0.670899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.27647e12i | 0.309841i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.63974e12 | + | 4.74214e12i | −0.220422 | + | 0.637460i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.22168e13i | 1.62201i | 0.585038 | + | 0.811006i | \(0.301079\pi\) | ||||
−0.585038 | + | 0.811006i | \(0.698921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.52688e12 | 0.593642 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.16968e12 | −1.18775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.44452e13i | 1.84823i | 0.382118 | + | 0.924114i | \(0.375195\pi\) | ||||
−0.382118 | + | 0.924114i | \(0.624805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.69352e11 | − | 5.18524e11i | −0.0466818 | − | 0.0655354i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.92889e12i | − | 0.365679i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11591e13 | −1.37635 | −0.688175 | − | 0.725545i | \(-0.741588\pi\) | ||||
−0.688175 | + | 0.725545i | \(0.741588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.40409e11 | −0.0902172 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.35882e12i | 1.12660i | 0.826251 | + | 0.563302i | \(0.190469\pi\) | ||||
−0.826251 | + | 0.563302i | \(0.809531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.81176e12 | − | 4.85211e12i | 0.810133 | − | 0.577069i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9.53439e12i | − | 1.12034i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.83585e12 | 1.02584 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.28609e13 | 1.47533 | 0.737667 | − | 0.675165i | \(-0.235928\pi\) | ||||
0.737667 | + | 0.675165i | \(0.235928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.94028e12i | 0.446632i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.77382e12 | − | 4.82509e12i | 0.758704 | − | 0.540435i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.42250e13i | − | 1.57442i | −0.616684 | − | 0.787211i | \(-0.711524\pi\) | ||
0.616684 | − | 0.787211i | \(-0.288476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.83256e11 | −0.0309807 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.65722e13 | 1.79122 | 0.895610 | − | 0.444841i | \(-0.146740\pi\) | ||||
0.895610 | + | 0.444841i | \(0.146740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9.20389e12i | − | 0.983130i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.64681e12 | + | 6.52354e12i | 0.490545 | + | 0.688664i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.27773e13i | 1.33309i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.81269e12 | −0.290037 | −0.145019 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145019 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.98397e12 | −0.304123 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.57982e12i | − | 0.864311i | −0.901799 | − | 0.432156i | \(-0.857753\pi\) | ||
0.901799 | − | 0.432156i | \(-0.142247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.10338e12 | − | 6.08299e12i | 0.209440 | − | 0.605703i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.81021e12i | 0.276595i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.20824e12 | −0.409432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.35472e11 | −0.0899707 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.66968e12i | 0.348900i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.38644e12 | − | 3.35027e12i | −0.224304 | − | 0.314895i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.75771e12i | − | 0.163328i | −0.996660 | − | 0.0816642i | \(-0.973976\pi\) | ||
0.996660 | − | 0.0816642i | \(-0.0260235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.93830e9 | −0.000361795 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.35367e12 | 0.304597 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.24588e12i | 0.381275i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.43035e12 | − | 1.73117e12i | 0.215783 | − | 0.153705i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.27115e13i | 1.99381i | 0.0786130 | + | 0.996905i | \(0.474951\pi\) | ||||
−0.0786130 | + | 0.996905i | \(0.525049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.28737e13 | 1.11748 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.33478e12 | −0.372067 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 7.92629e11i | − | 0.0672744i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.36683e12 | + | 3.11055e12i | −0.366509 | + | 0.261070i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.78065e11i | − | 0.0230789i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.95176e12 | 0.816829 | 0.408415 | − | 0.912796i | \(-0.366082\pi\) | ||||
0.408415 | + | 0.912796i | \(0.366082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.01292e12 | 0.569253 | 0.284626 | − | 0.958639i | \(-0.408130\pi\) | ||||
0.284626 | + | 0.958639i | \(0.408130\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.80696e12i | 0.385889i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.18778e12 | + | 3.07137e12i | 0.173698 | + | 0.243850i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.21723e12i | − | 0.566724i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.73362e12 | −0.600627 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20992e13 | −0.929420 | −0.464710 | − | 0.885463i | \(-0.653841\pi\) | ||||
−0.464710 | + | 0.885463i | \(0.653841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.21261e13i | 0.921346i | 0.887570 | + | 0.460673i | \(0.152392\pi\) | ||||
−0.887570 | + | 0.460673i | \(0.847608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.24421e11 | + | 2.50491e11i | 0.0544438 | + | 0.0188256i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.32495e13i | 0.984973i | 0.870320 | + | 0.492486i | \(0.163912\pi\) | ||||
−0.870320 | + | 0.492486i | \(0.836088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.87106e13 | 1.37592 | 0.687960 | − | 0.725749i | \(-0.258507\pi\) | ||||
0.687960 | + | 0.725749i | \(0.258507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.19157e12 | −0.0866789 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.79702e12i | 0.273238i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.19297e13 | + | 1.67478e13i | 0.849261 | + | 1.19226i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.70730e12i | − | 0.331518i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.21346e13 | 0.845469 | 0.422734 | − | 0.906254i | \(-0.361070\pi\) | ||||
0.422734 | + | 0.906254i | \(0.361070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90725e12 | −0.545059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.57703e12i | 0.243949i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.84860e12 | − | 3.45373e12i | 0.327161 | − | 0.233041i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.19552e13i | − | 0.798145i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.85140e12 | −0.122297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.01380e13 | −0.662630 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.34098e13i | − | 1.51401i | −0.653411 | − | 0.757004i | \(-0.726663\pi\) | ||
0.653411 | − | 0.757004i | \(-0.273337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.13452e12 | + | 3.65739e12i | −0.328589 | + | 0.234058i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.61008e13i | 1.01961i | 0.860290 | + | 0.509805i | \(0.170282\pi\) | ||||
−0.860290 | + | 0.509805i | \(0.829718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.34163e13 | −0.840745 | −0.420373 | − | 0.907352i | \(-0.638101\pi\) | ||||
−0.420373 | + | 0.907352i | \(0.638101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.40940e12 | 0.211429 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.03784e13i | − | 1.25061i | −0.780381 | − | 0.625304i | \(-0.784975\pi\) | ||
0.780381 | − | 0.625304i | \(-0.215025\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.26978e11 | + | 1.78262e11i | 0.00771183 | + | 0.0108264i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 7.58415e11i | − | 0.0455849i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.28176e12 | −0.254703 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.23764e13 | −1.31737 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.10287e13i | − | 0.642630i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.39188e13 | − | 4.09347e12i | 0.802725 | − | 0.236078i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.55027e12i | 0.202658i | 0.994853 | + | 0.101329i | \(0.0323094\pi\) | ||||
−0.994853 | + | 0.101329i | \(0.967691\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.33206e12 | 0.0752617 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.33443e13 | −1.30554 | −0.652769 | − | 0.757557i | \(-0.726393\pi\) | ||||
−0.652769 | + | 0.757557i | \(0.726393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.70030e12i | − | 0.481627i | −0.970571 | − | 0.240814i | \(-0.922586\pi\) | ||
0.970571 | − | 0.240814i | \(-0.0774142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.89560e12 | − | 6.87281e12i | −0.268263 | − | 0.376608i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.98568e13i | − | 1.61952i | −0.586760 | − | 0.809761i | \(-0.699597\pi\) | ||
0.586760 | − | 0.809761i | \(-0.300403\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12738e13 | 0.605358 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.18799e12 | −0.169460 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.01325e13i | 0.533196i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.09572e12 | + | 4.34206e12i | −0.317557 | + | 0.226200i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.16404e12i | 0.111609i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.46604e12 | −0.432277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77968e13 | −0.899666 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.84721e12i | 0.292654i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.73142e12 | + | 1.23331e12i | −0.0857993 | + | 0.0611160i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.14293e13i | − | 1.05142i | −0.850664 | − | 0.525709i | \(-0.823800\pi\) | ||
0.850664 | − | 0.525709i | \(-0.176200\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.71910e12 | −0.180676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.43474e13 | −1.65219 | −0.826097 | − | 0.563529i | \(-0.809443\pi\) | ||||
−0.826097 | + | 0.563529i | \(0.809443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.44218e12i | 0.259212i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.62680e12 | − | 2.28383e12i | −0.0767255 | − | 0.107713i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.96422e13i | − | 1.38436i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.05847e13 | 0.951975 | 0.475987 | − | 0.879452i | \(-0.342091\pi\) | ||||
0.475987 | + | 0.879452i | \(0.342091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.12531e12 | −0.143128 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.14688e12i | 0.324122i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.59278e13 | + | 8.96535e12i | 1.16447 | + | 0.402652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.67299e13i | 0.744104i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.78605e13 | −0.786726 | −0.393363 | − | 0.919383i | \(-0.628688\pi\) | ||||
−0.393363 | + | 0.919383i | \(0.628688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.98855e12 | −0.130373 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.05267e11i | 0.0347915i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.65238e12 | − | 3.72361e12i | −0.113497 | − | 0.159335i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.00969e13i | − | 0.427917i | −0.976843 | − | 0.213959i | \(-0.931364\pi\) | ||
0.976843 | − | 0.213959i | \(-0.0686358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.65703e12 | −0.405367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.40159e12 | −0.0998496 | −0.0499248 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499248 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22997e13i | 0.506513i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.64237e12 | − | 6.15608e12i | 0.352525 | − | 0.251108i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.09609e13i | 0.846907i | 0.905918 | + | 0.423453i | \(0.139182\pi\) | ||||
−0.905918 | + | 0.423453i | \(0.860818\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.05558e12 | −0.242358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.74692e12 | −0.188191 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.23636e12i | 0.0485543i | 0.999705 | + | 0.0242771i | \(0.00772841\pi\) | ||||
−0.999705 | + | 0.0242771i | \(0.992272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.05663e13 | − | 7.52655e12i | 0.411064 | − | 0.292806i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.00822e12i | − | 0.0388553i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.36769e13 | 0.522162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.55798e13 | −0.589259 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3.03651e13i | − | 1.13778i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.62992e12 | − | 7.90371e12i | −0.208992 | − | 0.293399i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.93044e13i | 0.709966i | 0.934873 | + | 0.354983i | \(0.115513\pi\) | ||||
−0.934873 | + | 0.354983i | \(0.884487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.91636e12 | −0.106264 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.95198e12 | 0.106568 | 0.0532840 | − | 0.998579i | \(-0.483031\pi\) | ||||
0.0532840 | + | 0.998579i | \(0.483031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.62646e12i | − | 0.308549i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.91372e12 | − | 5.53448e12i | 0.0678199 | − | 0.196135i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.39705e13i | − | 1.89509i | −0.319617 | − | 0.947547i | \(-0.603554\pi\) | ||
0.319617 | − | 0.947547i | \(-0.396446\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47427e12 | 0.0860845 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.16299e13 | −1.09040 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.52782e13i | − | 0.863487i | −0.901996 | − | 0.431743i | \(-0.857899\pi\) | ||
0.901996 | − | 0.431743i | \(-0.142101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.92480e13 | + | 4.10605e13i | 0.989994 | + | 1.38983i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 8.20912e12i | − | 0.275340i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.10942e13 | −0.701101 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.62973e13 | −1.19548 | −0.597741 | − | 0.801689i | \(-0.703935\pi\) | ||||
−0.597741 | + | 0.801689i | \(0.703935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.44785e12i | 0.210447i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.56312e13 | − | 1.82575e13i | 0.829020 | − | 0.590523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.75313e13i | 1.84406i | 0.387114 | + | 0.922032i | \(0.373472\pi\) | ||||
−0.387114 | + | 0.922032i | \(0.626528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 80.10.c.c.49.2 | 4 | ||
4.3 | odd | 2 | 5.10.b.a.4.1 | ✓ | 4 | ||
5.2 | odd | 4 | 400.10.a.ba.1.2 | 4 | |||
5.3 | odd | 4 | 400.10.a.ba.1.3 | 4 | |||
5.4 | even | 2 | inner | 80.10.c.c.49.3 | 4 | ||
12.11 | even | 2 | 45.10.b.b.19.4 | 4 | |||
20.3 | even | 4 | 25.10.a.e.1.1 | 4 | |||
20.7 | even | 4 | 25.10.a.e.1.4 | 4 | |||
20.19 | odd | 2 | 5.10.b.a.4.4 | yes | 4 | ||
60.23 | odd | 4 | 225.10.a.s.1.4 | 4 | |||
60.47 | odd | 4 | 225.10.a.s.1.1 | 4 | |||
60.59 | even | 2 | 45.10.b.b.19.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.b.a.4.1 | ✓ | 4 | 4.3 | odd | 2 | ||
5.10.b.a.4.4 | yes | 4 | 20.19 | odd | 2 | ||
25.10.a.e.1.1 | 4 | 20.3 | even | 4 | |||
25.10.a.e.1.4 | 4 | 20.7 | even | 4 | |||
45.10.b.b.19.1 | 4 | 60.59 | even | 2 | |||
45.10.b.b.19.4 | 4 | 12.11 | even | 2 | |||
80.10.c.c.49.2 | 4 | 1.1 | even | 1 | trivial | ||
80.10.c.c.49.3 | 4 | 5.4 | even | 2 | inner | ||
225.10.a.s.1.1 | 4 | 60.47 | odd | 4 | |||
225.10.a.s.1.4 | 4 | 60.23 | odd | 4 | |||
400.10.a.ba.1.2 | 4 | 5.2 | odd | 4 | |||
400.10.a.ba.1.3 | 4 | 5.3 | odd | 4 |