Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,15,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.0554007641\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 12.4 | ||
Character | \(\chi\) | \(=\) | 29.12 |
Dual form | 29.15.c.a.17.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −157.774 | − | 157.774i | −1.23261 | − | 1.23261i | −0.962959 | − | 0.269646i | \(-0.913093\pi\) |
−0.269646 | − | 0.962959i | \(-0.586907\pi\) | |||||||
\(3\) | 3020.51 | + | 3020.51i | 1.38112 | + | 1.38112i | 0.842635 | + | 0.538484i | \(0.181003\pi\) |
0.538484 | + | 0.842635i | \(0.318997\pi\) | |||||||
\(4\) | 33401.0i | 2.03863i | ||||||||
\(5\) | 76455.0i | 0.978624i | 0.872109 | + | 0.489312i | \(0.162752\pi\) | ||||
−0.872109 | + | 0.489312i | \(0.837248\pi\) | |||||||
\(6\) | − | 953113.i | − | 3.40475i | ||||||
\(7\) | −1.19070e6 | −1.44583 | −0.722915 | − | 0.690937i | \(-0.757198\pi\) | ||||
−0.722915 | + | 0.690937i | \(0.757198\pi\) | |||||||
\(8\) | 2.68483e6 | − | 2.68483e6i | 1.28022 | − | 1.28022i | ||||
\(9\) | 1.34640e7i | 2.81498i | ||||||||
\(10\) | 1.20626e7 | − | 1.20626e7i | 1.20626 | − | 1.20626i | ||||
\(11\) | −2.59610e6 | − | 2.59610e6i | −0.133221 | − | 0.133221i | 0.637352 | − | 0.770573i | \(-0.280030\pi\) |
−0.770573 | + | 0.637352i | \(0.780030\pi\) | |||||||
\(12\) | −1.00888e8 | + | 1.00888e8i | −2.81560 | + | 2.81560i | ||||
\(13\) | 1.02359e8i | 1.63125i | 0.578579 | + | 0.815626i | \(0.303607\pi\) | ||||
−0.578579 | + | 0.815626i | \(0.696393\pi\) | |||||||
\(14\) | 1.87861e8 | + | 1.87861e8i | 1.78214 | + | 1.78214i | ||||
\(15\) | −2.30933e8 | + | 2.30933e8i | −1.35160 | + | 1.35160i | ||||
\(16\) | −2.99948e8 | −1.11739 | ||||||||
\(17\) | −1.87660e8 | − | 1.87660e8i | −0.457329 | − | 0.457329i | 0.440449 | − | 0.897778i | \(-0.354819\pi\) |
−0.897778 | + | 0.440449i | \(0.854819\pi\) | |||||||
\(18\) | 2.12426e9 | − | 2.12426e9i | 3.46977 | − | 3.46977i | ||||
\(19\) | 2.50209e8 | + | 2.50209e8i | 0.279916 | + | 0.279916i | 0.833076 | − | 0.553159i | \(-0.186578\pi\) |
−0.553159 | + | 0.833076i | \(0.686578\pi\) | |||||||
\(20\) | −2.55367e9 | −1.99506 | ||||||||
\(21\) | −3.59653e9 | − | 3.59653e9i | −1.99686 | − | 1.99686i | ||||
\(22\) | 8.19192e8i | 0.328418i | ||||||||
\(23\) | 2.66588e9 | 0.782972 | 0.391486 | − | 0.920184i | \(-0.371961\pi\) | ||||
0.391486 | + | 0.920184i | \(0.371961\pi\) | |||||||
\(24\) | 1.62191e10 | 3.53629 | ||||||||
\(25\) | 2.58146e8 | 0.0422947 | ||||||||
\(26\) | 1.61495e10 | − | 1.61495e10i | 2.01069 | − | 2.01069i | ||||
\(27\) | −2.62211e10 | + | 2.62211e10i | −2.50671 | + | 2.50671i | ||||
\(28\) | − | 3.97706e10i | − | 2.94752i | ||||||
\(29\) | −1.66443e10 | − | 4.53063e9i | −0.964892 | − | 0.262647i | ||||
\(30\) | 7.28702e10 | 3.33197 | ||||||||
\(31\) | 9.77578e9 | + | 9.77578e9i | 0.355320 | + | 0.355320i | 0.862085 | − | 0.506764i | \(-0.169159\pi\) |
−0.506764 | + | 0.862085i | \(0.669159\pi\) | |||||||
\(32\) | 3.33559e9 | + | 3.33559e9i | 0.0970784 | + | 0.0970784i | ||||
\(33\) | − | 1.56831e10i | − | 0.367988i | ||||||
\(34\) | 5.92155e10i | 1.12741i | ||||||||
\(35\) | − | 9.10352e10i | − | 1.41492i | ||||||
\(36\) | −4.49710e11 | −5.73872 | ||||||||
\(37\) | 7.28244e10 | − | 7.28244e10i | 0.767123 | − | 0.767123i | −0.210476 | − | 0.977599i | \(-0.567501\pi\) |
0.977599 | + | 0.210476i | \(0.0675014\pi\) | |||||||
\(38\) | − | 7.89528e10i | − | 0.690053i | ||||||
\(39\) | −3.09175e11 | + | 3.09175e11i | −2.25295 | + | 2.25295i | ||||
\(40\) | 2.05268e11 | + | 2.05268e11i | 1.25286 | + | 1.25286i | ||||
\(41\) | 7.53651e10 | − | 7.53651e10i | 0.386975 | − | 0.386975i | −0.486632 | − | 0.873607i | \(-0.661775\pi\) |
0.873607 | + | 0.486632i | \(0.161775\pi\) | |||||||
\(42\) | 1.13487e12i | 4.92269i | ||||||||
\(43\) | −9.89034e10 | − | 9.89034e10i | −0.363858 | − | 0.363858i | 0.501373 | − | 0.865231i | \(-0.332828\pi\) |
−0.865231 | + | 0.501373i | \(0.832828\pi\) | |||||||
\(44\) | 8.67123e10 | − | 8.67123e10i | 0.271589 | − | 0.271589i | ||||
\(45\) | −1.02939e12 | −2.75481 | ||||||||
\(46\) | −4.20606e11 | − | 4.20606e11i | −0.965096 | − | 0.965096i | ||||
\(47\) | 1.42970e11 | − | 1.42970e11i | 0.282202 | − | 0.282202i | −0.551785 | − | 0.833987i | \(-0.686053\pi\) |
0.833987 | + | 0.551785i | \(0.186053\pi\) | |||||||
\(48\) | −9.05994e11 | − | 9.05994e11i | −1.54325 | − | 1.54325i | ||||
\(49\) | 7.39551e11 | 1.09042 | ||||||||
\(50\) | −4.07287e10 | − | 4.07287e10i | −0.0521327 | − | 0.0521327i | ||||
\(51\) | − | 1.13366e12i | − | 1.26325i | ||||||
\(52\) | −3.41888e12 | −3.32552 | ||||||||
\(53\) | −2.36240e11 | −0.201105 | −0.100552 | − | 0.994932i | \(-0.532061\pi\) | ||||
−0.100552 | + | 0.994932i | \(0.532061\pi\) | |||||||
\(54\) | 8.27398e12 | 6.17957 | ||||||||
\(55\) | 1.98485e11 | − | 1.98485e11i | 0.130373 | − | 0.130373i | ||||
\(56\) | −3.19683e12 | + | 3.19683e12i | −1.85099 | + | 1.85099i | ||||
\(57\) | 1.51152e12i | 0.773196i | ||||||||
\(58\) | 1.91121e12 | + | 3.34084e12i | 0.865591 | + | 1.51307i | ||||
\(59\) | 2.90722e12 | 1.16819 | 0.584096 | − | 0.811684i | \(-0.301449\pi\) | ||||
0.584096 | + | 0.811684i | \(0.301449\pi\) | |||||||
\(60\) | −7.71339e12 | − | 7.71339e12i | −2.75541 | − | 2.75541i | ||||
\(61\) | −1.31209e12 | − | 1.31209e12i | −0.417498 | − | 0.417498i | 0.466842 | − | 0.884340i | \(-0.345392\pi\) |
−0.884340 | + | 0.466842i | \(0.845392\pi\) | |||||||
\(62\) | − | 3.08472e12i | − | 0.875939i | ||||||
\(63\) | − | 1.60316e13i | − | 4.06999i | ||||||
\(64\) | 3.86181e12i | 0.878073i | ||||||||
\(65\) | −7.82583e12 | −1.59638 | ||||||||
\(66\) | −2.47438e12 | + | 2.47438e12i | −0.453584 | + | 0.453584i | ||||
\(67\) | 7.85098e12i | 1.29539i | 0.761900 | + | 0.647695i | \(0.224267\pi\) | ||||
−0.761900 | + | 0.647695i | \(0.775733\pi\) | |||||||
\(68\) | 6.26802e12 | − | 6.26802e12i | 0.932326 | − | 0.932326i | ||||
\(69\) | 8.05232e12 | + | 8.05232e12i | 1.08138 | + | 1.08138i | ||||
\(70\) | −1.43629e13 | + | 1.43629e13i | −1.74404 | + | 1.74404i | ||||
\(71\) | − | 1.37095e13i | − | 1.50735i | −0.657248 | − | 0.753674i | \(-0.728280\pi\) | ||
0.657248 | − | 0.753674i | \(-0.271720\pi\) | |||||||
\(72\) | 3.61485e13 | + | 3.61485e13i | 3.60381 | + | 3.60381i | ||||
\(73\) | −9.07256e12 | + | 9.07256e12i | −0.821239 | + | 0.821239i | −0.986286 | − | 0.165047i | \(-0.947223\pi\) |
0.165047 | + | 0.986286i | \(0.447223\pi\) | |||||||
\(74\) | −2.29795e13 | −1.89112 | ||||||||
\(75\) | 7.79734e11 | + | 7.79734e11i | 0.0584141 | + | 0.0584141i | ||||
\(76\) | −8.35723e12 | + | 8.35723e12i | −0.570647 | + | 0.570647i | ||||
\(77\) | 3.09119e12 | + | 3.09119e12i | 0.192615 | + | 0.192615i | ||||
\(78\) | 9.75593e13 | 5.55401 | ||||||||
\(79\) | −1.07914e13 | − | 1.07914e13i | −0.561937 | − | 0.561937i | 0.367920 | − | 0.929857i | \(-0.380070\pi\) |
−0.929857 | + | 0.367920i | \(0.880070\pi\) | |||||||
\(80\) | − | 2.29325e13i | − | 1.09351i | ||||||
\(81\) | −9.40042e13 | −4.10915 | ||||||||
\(82\) | −2.37812e13 | −0.953976 | ||||||||
\(83\) | −3.82913e13 | −1.41108 | −0.705542 | − | 0.708668i | \(-0.749297\pi\) | ||||
−0.705542 | + | 0.708668i | \(0.749297\pi\) | |||||||
\(84\) | 1.20128e14 | − | 1.20128e14i | 4.07087 | − | 4.07087i | ||||
\(85\) | 1.43475e13 | − | 1.43475e13i | 0.447553 | − | 0.447553i | ||||
\(86\) | 3.12087e13i | 0.896987i | ||||||||
\(87\) | −3.65894e13 | − | 6.39590e13i | −0.969885 | − | 1.69538i | ||||
\(88\) | −1.39402e13 | −0.341106 | ||||||||
\(89\) | 3.65871e13 | + | 3.65871e13i | 0.827177 | + | 0.827177i | 0.987125 | − | 0.159948i | \(-0.0511328\pi\) |
−0.159948 | + | 0.987125i | \(0.551133\pi\) | |||||||
\(90\) | 1.62410e14 | + | 1.62410e14i | 3.39560 | + | 3.39560i | ||||
\(91\) | − | 1.21879e14i | − | 2.35851i | ||||||
\(92\) | 8.90430e13i | 1.59619i | ||||||||
\(93\) | 5.90557e13i | 0.981479i | ||||||||
\(94\) | −4.51138e13 | −0.695688 | ||||||||
\(95\) | −1.91298e13 | + | 1.91298e13i | −0.273933 | + | 0.273933i | ||||
\(96\) | 2.01503e13i | 0.268154i | ||||||||
\(97\) | 2.66553e13 | − | 2.66553e13i | 0.329899 | − | 0.329899i | −0.522649 | − | 0.852548i | \(-0.675056\pi\) |
0.852548 | + | 0.522649i | \(0.175056\pi\) | |||||||
\(98\) | −1.16682e14 | − | 1.16682e14i | −1.34406 | − | 1.34406i | ||||
\(99\) | 3.49538e13 | − | 3.49538e13i | 0.375015 | − | 0.375015i | ||||
\(100\) | 8.62234e12i | 0.0862234i | ||||||||
\(101\) | 6.93835e13 | + | 6.93835e13i | 0.647153 | + | 0.647153i | 0.952304 | − | 0.305151i | \(-0.0987070\pi\) |
−0.305151 | + | 0.952304i | \(0.598707\pi\) | |||||||
\(102\) | −1.78861e14 | + | 1.78861e14i | −1.55709 | + | 1.55709i | ||||
\(103\) | −1.35496e14 | −1.10171 | −0.550853 | − | 0.834602i | \(-0.685698\pi\) | ||||
−0.550853 | + | 0.834602i | \(0.685698\pi\) | |||||||
\(104\) | 2.74815e14 | + | 2.74815e14i | 2.08837 | + | 2.08837i | ||||
\(105\) | 2.74973e14 | − | 2.74973e14i | 1.95418 | − | 1.95418i | ||||
\(106\) | 3.72724e13 | + | 3.72724e13i | 0.247883 | + | 0.247883i | ||||
\(107\) | 1.78328e14 | 1.11053 | 0.555267 | − | 0.831672i | \(-0.312616\pi\) | ||||
0.555267 | + | 0.831672i | \(0.312616\pi\) | |||||||
\(108\) | −8.75809e14 | − | 8.75809e14i | −5.11026 | − | 5.11026i | ||||
\(109\) | 1.16221e14i | 0.635771i | 0.948129 | + | 0.317886i | \(0.102973\pi\) | ||||
−0.948129 | + | 0.317886i | \(0.897027\pi\) | |||||||
\(110\) | −6.26313e13 | −0.321398 | ||||||||
\(111\) | 4.39934e14 | 2.11898 | ||||||||
\(112\) | 3.57149e14 | 1.61556 | ||||||||
\(113\) | −2.24452e14 | + | 2.24452e14i | −0.954057 | + | 0.954057i | −0.998990 | − | 0.0449331i | \(-0.985693\pi\) |
0.0449331 | + | 0.998990i | \(0.485693\pi\) | |||||||
\(114\) | 2.38478e14 | − | 2.38478e14i | 0.953046 | − | 0.953046i | ||||
\(115\) | 2.03820e14i | 0.766235i | ||||||||
\(116\) | 1.51327e14 | − | 5.55935e14i | 0.535441 | − | 1.96706i | ||||
\(117\) | −1.37816e15 | −4.59195 | ||||||||
\(118\) | −4.58683e14 | − | 4.58683e14i | −1.43992 | − | 1.43992i | ||||
\(119\) | 2.23447e14 | + | 2.23447e14i | 0.661220 | + | 0.661220i | ||||
\(120\) | 1.24003e15i | 3.46070i | ||||||||
\(121\) | − | 3.66270e14i | − | 0.964504i | ||||||
\(122\) | 4.14026e14i | 1.02922i | ||||||||
\(123\) | 4.55282e14 | 1.06892 | ||||||||
\(124\) | −3.26521e14 | + | 3.26521e14i | −0.724367 | + | 0.724367i | ||||
\(125\) | 4.86381e14i | 1.02001i | ||||||||
\(126\) | −2.52936e15 | + | 2.52936e15i | −5.01669 | + | 5.01669i | ||||
\(127\) | −2.56286e13 | − | 2.56286e13i | −0.0480948 | − | 0.0480948i | 0.682650 | − | 0.730745i | \(-0.260827\pi\) |
−0.730745 | + | 0.682650i | \(0.760827\pi\) | |||||||
\(128\) | 6.63941e14 | − | 6.63941e14i | 1.17940 | − | 1.17940i | ||||
\(129\) | − | 5.97477e14i | − | 1.00506i | ||||||
\(130\) | 1.23471e15 | + | 1.23471e15i | 1.96771 | + | 1.96771i | ||||
\(131\) | 1.82754e14 | − | 1.82754e14i | 0.276038 | − | 0.276038i | −0.555487 | − | 0.831525i | \(-0.687468\pi\) |
0.831525 | + | 0.555487i | \(0.187468\pi\) | |||||||
\(132\) | 5.23830e14 | 0.750193 | ||||||||
\(133\) | −2.97925e14 | − | 2.97925e14i | −0.404711 | − | 0.404711i | ||||
\(134\) | 1.23868e15 | − | 1.23868e15i | 1.59670 | − | 1.59670i | ||||
\(135\) | −2.00473e15 | − | 2.00473e15i | −2.45313 | − | 2.45313i | ||||
\(136\) | −1.00767e15 | −1.17097 | ||||||||
\(137\) | 5.99325e14 | + | 5.99325e14i | 0.661635 | + | 0.661635i | 0.955765 | − | 0.294131i | \(-0.0950300\pi\) |
−0.294131 | + | 0.955765i | \(0.595030\pi\) | |||||||
\(138\) | − | 2.54089e15i | − | 2.66583i | ||||||
\(139\) | −9.68743e14 | −0.966284 | −0.483142 | − | 0.875542i | \(-0.660505\pi\) | ||||
−0.483142 | + | 0.875542i | \(0.660505\pi\) | |||||||
\(140\) | 3.04066e15 | 2.88451 | ||||||||
\(141\) | 8.63685e14 | 0.779510 | ||||||||
\(142\) | −2.16300e15 | + | 2.16300e15i | −1.85797 | + | 1.85797i | ||||
\(143\) | 2.65733e14 | − | 2.65733e14i | 0.217317 | − | 0.217317i | ||||
\(144\) | − | 4.03849e15i | − | 3.14544i | ||||||
\(145\) | 3.46389e14 | − | 1.27254e15i | 0.257033 | − | 0.944267i | ||||
\(146\) | 2.86282e15 | 2.02453 | ||||||||
\(147\) | 2.23382e15 | + | 2.23382e15i | 1.50601 | + | 1.50601i | ||||
\(148\) | 2.43241e15 | + | 2.43241e15i | 1.56388 | + | 1.56388i | ||||
\(149\) | 1.37374e15i | 0.842560i | 0.906931 | + | 0.421280i | \(0.138419\pi\) | ||||
−0.906931 | + | 0.421280i | \(0.861581\pi\) | |||||||
\(150\) | − | 2.46043e14i | − | 0.144003i | ||||||
\(151\) | 4.50562e14i | 0.251719i | 0.992048 | + | 0.125860i | \(0.0401689\pi\) | ||||
−0.992048 | + | 0.125860i | \(0.959831\pi\) | |||||||
\(152\) | 1.34354e15 | 0.716712 | ||||||||
\(153\) | 2.52665e15 | − | 2.52665e15i | 1.28737 | − | 1.28737i | ||||
\(154\) | − | 9.75414e14i | − | 0.474836i | ||||||
\(155\) | −7.47408e14 | + | 7.47408e14i | −0.347725 | + | 0.347725i | ||||
\(156\) | −1.03268e16 | − | 1.03268e16i | −4.59295 | − | 4.59295i | ||||
\(157\) | 2.25540e15 | − | 2.25540e15i | 0.959239 | − | 0.959239i | −0.0399622 | − | 0.999201i | \(-0.512724\pi\) |
0.999201 | + | 0.0399622i | \(0.0127237\pi\) | |||||||
\(158\) | 3.40519e15i | 1.38529i | ||||||||
\(159\) | −7.13565e14 | − | 7.13565e14i | −0.277750 | − | 0.277750i | ||||
\(160\) | −2.55022e14 | + | 2.55022e14i | −0.0950032 | + | 0.0950032i | ||||
\(161\) | −3.17428e15 | −1.13204 | ||||||||
\(162\) | 1.48314e16 | + | 1.48314e16i | 5.06496 | + | 5.06496i | ||||
\(163\) | 7.95427e14 | − | 7.95427e14i | 0.260188 | − | 0.260188i | −0.564942 | − | 0.825130i | \(-0.691102\pi\) |
0.825130 | + | 0.564942i | \(0.191102\pi\) | |||||||
\(164\) | 2.51727e15 | + | 2.51727e15i | 0.788901 | + | 0.788901i | ||||
\(165\) | 1.19905e15 | 0.360122 | ||||||||
\(166\) | 6.04135e15 | + | 6.04135e15i | 1.73931 | + | 1.73931i | ||||
\(167\) | − | 6.62312e14i | − | 0.182830i | −0.995813 | − | 0.0914150i | \(-0.970861\pi\) | ||
0.995813 | − | 0.0914150i | \(-0.0291390\pi\) | |||||||
\(168\) | −1.93121e16 | −5.11287 | ||||||||
\(169\) | −6.53992e15 | −1.66098 | ||||||||
\(170\) | −4.52732e15 | −1.10331 | ||||||||
\(171\) | −3.36881e15 | + | 3.36881e15i | −0.787960 | + | 0.787960i | ||||
\(172\) | 3.30347e15 | − | 3.30347e15i | 0.741773 | − | 0.741773i | ||||
\(173\) | − | 8.93103e14i | − | 0.192566i | −0.995354 | − | 0.0962828i | \(-0.969305\pi\) | ||
0.995354 | − | 0.0962828i | \(-0.0306953\pi\) | |||||||
\(174\) | −4.31820e15 | + | 1.58639e16i | −0.894248 | + | 3.28522i | ||||
\(175\) | −3.07376e14 | −0.0611510 | ||||||||
\(176\) | 7.78694e14 | + | 7.78694e14i | 0.148860 | + | 0.148860i | ||||
\(177\) | 8.78130e15 | + | 8.78130e15i | 1.61341 | + | 1.61341i | ||||
\(178\) | − | 1.15450e16i | − | 2.03917i | ||||||
\(179\) | 9.02464e14i | 0.153270i | 0.997059 | + | 0.0766352i | \(0.0244177\pi\) | ||||
−0.997059 | + | 0.0766352i | \(0.975582\pi\) | |||||||
\(180\) | − | 3.43826e16i | − | 5.61605i | ||||||
\(181\) | −7.48276e15 | −1.17574 | −0.587871 | − | 0.808955i | \(-0.700034\pi\) | ||||
−0.587871 | + | 0.808955i | \(0.700034\pi\) | |||||||
\(182\) | −1.92292e16 | + | 1.92292e16i | −2.90712 | + | 2.90712i | ||||
\(183\) | − | 7.92635e15i | − | 1.15323i | ||||||
\(184\) | 7.15743e15 | − | 7.15743e15i | 1.00238 | − | 1.00238i | ||||
\(185\) | 5.56779e15 | + | 5.56779e15i | 0.750725 | + | 0.750725i | ||||
\(186\) | 9.31742e15 | − | 9.31742e15i | 1.20978 | − | 1.20978i | ||||
\(187\) | 9.74367e14i | 0.121852i | ||||||||
\(188\) | 4.77534e15 | + | 4.77534e15i | 0.575306 | + | 0.575306i | ||||
\(189\) | 3.12215e16 | − | 3.12215e16i | 3.62428 | − | 3.62428i | ||||
\(190\) | 6.03634e15 | 0.675302 | ||||||||
\(191\) | 6.32586e14 | + | 6.32586e14i | 0.0682159 | + | 0.0682159i | 0.740392 | − | 0.672176i | \(-0.234640\pi\) |
−0.672176 | + | 0.740392i | \(0.734640\pi\) | |||||||
\(192\) | −1.16646e16 | + | 1.16646e16i | −1.21272 | + | 1.21272i | ||||
\(193\) | 3.96922e15 | + | 3.96922e15i | 0.397928 | + | 0.397928i | 0.877501 | − | 0.479574i | \(-0.159209\pi\) |
−0.479574 | + | 0.877501i | \(0.659209\pi\) | |||||||
\(194\) | −8.41100e15 | −0.813271 | ||||||||
\(195\) | −2.36380e16 | − | 2.36380e16i | −2.20480 | − | 2.20480i | ||||
\(196\) | 2.47017e16i | 2.22298i | ||||||||
\(197\) | −3.84537e15 | −0.333945 | −0.166972 | − | 0.985962i | \(-0.553399\pi\) | ||||
−0.166972 | + | 0.985962i | \(0.553399\pi\) | |||||||
\(198\) | −1.10296e16 | −0.924491 | ||||||||
\(199\) | −5.61125e15 | −0.454034 | −0.227017 | − | 0.973891i | \(-0.572897\pi\) | ||||
−0.227017 | + | 0.973891i | \(0.572897\pi\) | |||||||
\(200\) | 6.93078e14 | − | 6.93078e14i | 0.0541467 | − | 0.0541467i | ||||
\(201\) | −2.37140e16 | + | 2.37140e16i | −1.78909 | + | 1.78909i | ||||
\(202\) | − | 2.18938e16i | − | 1.59537i | ||||||
\(203\) | 1.98184e16 | + | 5.39463e15i | 1.39507 | + | 0.379743i | ||||
\(204\) | 3.78652e16 | 2.57531 | ||||||||
\(205\) | 5.76204e15 | + | 5.76204e15i | 0.378704 | + | 0.378704i | ||||
\(206\) | 2.13777e16 | + | 2.13777e16i | 1.35797 | + | 1.35797i | ||||
\(207\) | 3.58934e16i | 2.20405i | ||||||||
\(208\) | − | 3.07022e16i | − | 1.82275i | ||||||
\(209\) | − | 1.29914e15i | − | 0.0745815i | ||||||
\(210\) | −8.67668e16 | −4.81747 | ||||||||
\(211\) | 3.97702e15 | − | 3.97702e15i | 0.213590 | − | 0.213590i | −0.592201 | − | 0.805791i | \(-0.701741\pi\) |
0.805791 | + | 0.592201i | \(0.201741\pi\) | |||||||
\(212\) | − | 7.89064e15i | − | 0.409979i | ||||||
\(213\) | 4.14097e16 | − | 4.14097e16i | 2.08183 | − | 2.08183i | ||||
\(214\) | −2.81354e16 | − | 2.81354e16i | −1.36885 | − | 1.36885i | ||||
\(215\) | 7.56166e15 | − | 7.56166e15i | 0.356080 | − | 0.356080i | ||||
\(216\) | 1.40798e17i | 6.41831i | ||||||||
\(217\) | −1.16401e16 | − | 1.16401e16i | −0.513733 | − | 0.513733i | ||||
\(218\) | 1.83367e16 | − | 1.83367e16i | 0.783655 | − | 0.783655i | ||||
\(219\) | −5.48075e16 | −2.26846 | ||||||||
\(220\) | 6.62959e15 | + | 6.62959e15i | 0.265783 | + | 0.265783i | ||||
\(221\) | 1.92086e16 | − | 1.92086e16i | 0.746019 | − | 0.746019i | ||||
\(222\) | −6.94099e16 | − | 6.94099e16i | −2.61186 | − | 2.61186i | ||||
\(223\) | −2.83263e16 | −1.03289 | −0.516447 | − | 0.856319i | \(-0.672746\pi\) | ||||
−0.516447 | + | 0.856319i | \(0.672746\pi\) | |||||||
\(224\) | −3.97169e15 | − | 3.97169e15i | −0.140359 | − | 0.140359i | ||||
\(225\) | 3.47568e15i | 0.119059i | ||||||||
\(226\) | 7.08251e16 | 2.35195 | ||||||||
\(227\) | 4.23581e16 | 1.36382 | 0.681908 | − | 0.731438i | \(-0.261150\pi\) | ||||
0.681908 | + | 0.731438i | \(0.261150\pi\) | |||||||
\(228\) | −5.04862e16 | −1.57626 | ||||||||
\(229\) | −9.34763e15 | + | 9.34763e15i | −0.283043 | + | 0.283043i | −0.834322 | − | 0.551278i | \(-0.814140\pi\) |
0.551278 | + | 0.834322i | \(0.314140\pi\) | |||||||
\(230\) | 3.21574e16 | − | 3.21574e16i | 0.944466 | − | 0.944466i | ||||
\(231\) | 1.86739e16i | 0.532049i | ||||||||
\(232\) | −5.68509e16 | + | 3.25230e16i | −1.57153 | + | 0.899032i | ||||
\(233\) | 1.74563e16 | 0.468231 | 0.234116 | − | 0.972209i | \(-0.424781\pi\) | ||||
0.234116 | + | 0.972209i | \(0.424781\pi\) | |||||||
\(234\) | 2.17436e17 | + | 2.17436e17i | 5.66006 | + | 5.66006i | ||||
\(235\) | 1.09308e16 | + | 1.09308e16i | 0.276170 | + | 0.276170i | ||||
\(236\) | 9.71041e16i | 2.38152i | ||||||||
\(237\) | − | 6.51910e16i | − | 1.55220i | ||||||
\(238\) | − | 7.05081e16i | − | 1.63005i | ||||||
\(239\) | 2.03817e16 | 0.457566 | 0.228783 | − | 0.973477i | \(-0.426525\pi\) | ||||
0.228783 | + | 0.973477i | \(0.426525\pi\) | |||||||
\(240\) | 6.92678e16 | − | 6.92678e16i | 1.51026 | − | 1.51026i | ||||
\(241\) | 3.28579e16i | 0.695858i | 0.937521 | + | 0.347929i | \(0.113115\pi\) | ||||
−0.937521 | + | 0.347929i | \(0.886885\pi\) | |||||||
\(242\) | −5.77878e16 | + | 5.77878e16i | −1.18885 | + | 1.18885i | ||||
\(243\) | −1.58526e17 | − | 1.58526e17i | −3.16852 | − | 3.16852i | ||||
\(244\) | 4.38250e16 | − | 4.38250e16i | 0.851125 | − | 0.851125i | ||||
\(245\) | 5.65424e16i | 1.06712i | ||||||||
\(246\) | −7.18315e16 | − | 7.18315e16i | −1.31756 | − | 1.31756i | ||||
\(247\) | −2.56111e16 | + | 2.56111e16i | −0.456614 | + | 0.456614i | ||||
\(248\) | 5.24926e16 | 0.909779 | ||||||||
\(249\) | −1.15659e17 | − | 1.15659e17i | −1.94888 | − | 1.94888i | ||||
\(250\) | 7.67380e16 | − | 7.67380e16i | 1.25728 | − | 1.25728i | ||||
\(251\) | 2.60934e16 | + | 2.60934e16i | 0.415734 | + | 0.415734i | 0.883730 | − | 0.467997i | \(-0.155024\pi\) |
−0.467997 | + | 0.883730i | \(0.655024\pi\) | |||||||
\(252\) | 5.35471e17 | 8.29721 | ||||||||
\(253\) | −6.92090e15 | − | 6.92090e15i | −0.104308 | − | 0.104308i | ||||
\(254\) | 8.08702e15i | 0.118564i | ||||||||
\(255\) | 8.66737e16 | 1.23625 | ||||||||
\(256\) | −1.46233e17 | −2.02939 | ||||||||
\(257\) | −4.48820e16 | −0.606094 | −0.303047 | − | 0.952976i | \(-0.598004\pi\) | ||||
−0.303047 | + | 0.952976i | \(0.598004\pi\) | |||||||
\(258\) | −9.42661e16 | + | 9.42661e16i | −1.23885 | + | 1.23885i | ||||
\(259\) | −8.67123e16 | + | 8.67123e16i | −1.10913 | + | 1.10913i | ||||
\(260\) | − | 2.61390e17i | − | 3.25444i | ||||||
\(261\) | 6.10003e16 | − | 2.24098e17i | 0.739347 | − | 2.71616i | ||||
\(262\) | −5.76675e16 | −0.680491 | ||||||||
\(263\) | −5.90976e16 | − | 5.90976e16i | −0.679016 | − | 0.679016i | 0.280762 | − | 0.959778i | \(-0.409413\pi\) |
−0.959778 | + | 0.280762i | \(0.909413\pi\) | |||||||
\(264\) | −4.21064e16 | − | 4.21064e16i | −0.471108 | − | 0.471108i | ||||
\(265\) | − | 1.80617e16i | − | 0.196806i | ||||||
\(266\) | 9.40094e16i | 0.997699i | ||||||||
\(267\) | 2.21024e17i | 2.28486i | ||||||||
\(268\) | −2.62230e17 | −2.64082 | ||||||||
\(269\) | −1.15034e17 | + | 1.15034e17i | −1.12865 | + | 1.12865i | −0.138257 | + | 0.990396i | \(0.544150\pi\) |
−0.990396 | + | 0.138257i | \(0.955850\pi\) | |||||||
\(270\) | 6.32588e17i | 6.04748i | ||||||||
\(271\) | 3.35281e16 | − | 3.35281e16i | 0.312337 | − | 0.312337i | −0.533477 | − | 0.845814i | \(-0.679115\pi\) |
0.845814 | + | 0.533477i | \(0.179115\pi\) | |||||||
\(272\) | 5.62881e16 | + | 5.62881e16i | 0.511016 | + | 0.511016i | ||||
\(273\) | 3.68136e17 | − | 3.68136e17i | 3.25739 | − | 3.25739i | ||||
\(274\) | − | 1.89115e17i | − | 1.63107i | ||||||
\(275\) | −6.70174e14 | − | 6.70174e14i | −0.00563454 | − | 0.00563454i | ||||
\(276\) | −2.68955e17 | + | 2.68955e17i | −2.20453 | + | 2.20453i | ||||
\(277\) | −8.16117e16 | −0.652220 | −0.326110 | − | 0.945332i | \(-0.605738\pi\) | ||||
−0.326110 | + | 0.945332i | \(0.605738\pi\) | |||||||
\(278\) | 1.52842e17 | + | 1.52842e17i | 1.19105 | + | 1.19105i | ||||
\(279\) | −1.31621e17 | + | 1.31621e17i | −1.00022 | + | 1.00022i | ||||
\(280\) | −2.44414e17 | − | 2.44414e17i | −1.81142 | − | 1.81142i | ||||
\(281\) | 8.43870e16 | 0.610002 | 0.305001 | − | 0.952352i | \(-0.401343\pi\) | ||||
0.305001 | + | 0.952352i | \(0.401343\pi\) | |||||||
\(282\) | −1.36267e17 | − | 1.36267e17i | −0.960828 | − | 0.960828i | ||||
\(283\) | 2.68326e17i | 1.84568i | 0.385178 | + | 0.922842i | \(0.374140\pi\) | ||||
−0.385178 | + | 0.922842i | \(0.625860\pi\) | |||||||
\(284\) | 4.57911e17 | 3.07293 | ||||||||
\(285\) | −1.15563e17 | −0.756668 | ||||||||
\(286\) | −8.38514e16 | −0.535732 | ||||||||
\(287\) | −8.97375e16 | + | 8.97375e16i | −0.559501 | + | 0.559501i | ||||
\(288\) | −4.49103e16 | + | 4.49103e16i | −0.273274 | + | 0.273274i | ||||
\(289\) | − | 9.79454e16i | − | 0.581700i | ||||||
\(290\) | −2.55424e17 | + | 1.46122e17i | −1.48073 | + | 0.847089i | ||||
\(291\) | 1.61025e17 | 0.911261 | ||||||||
\(292\) | −3.03032e17 | − | 3.03032e17i | −1.67421 | − | 1.67421i | ||||
\(293\) | 5.07728e16 | + | 5.07728e16i | 0.273878 | + | 0.273878i | 0.830659 | − | 0.556781i | \(-0.187964\pi\) |
−0.556781 | + | 0.830659i | \(0.687964\pi\) | |||||||
\(294\) | − | 7.04876e17i | − | 3.71263i | ||||||
\(295\) | 2.22272e17i | 1.14322i | ||||||||
\(296\) | − | 3.91042e17i | − | 1.96418i | ||||||
\(297\) | 1.36145e17 | 0.667893 | ||||||||
\(298\) | 2.16740e17 | − | 2.16740e17i | 1.03854 | − | 1.03854i | ||||
\(299\) | 2.72876e17i | 1.27722i | ||||||||
\(300\) | −2.60439e16 | + | 2.60439e16i | −0.119085 | + | 0.119085i | ||||
\(301\) | 1.17765e17 | + | 1.17765e17i | 0.526077 | + | 0.526077i | ||||
\(302\) | 7.10868e16 | − | 7.10868e16i | 0.310270 | − | 0.310270i | ||||
\(303\) | 4.19147e17i | 1.78759i | ||||||||
\(304\) | −7.50497e16 | − | 7.50497e16i | −0.312776 | − | 0.312776i | ||||
\(305\) | 1.00316e17 | − | 1.00316e17i | 0.408574 | − | 0.408574i | ||||
\(306\) | −7.97276e17 | −3.17365 | ||||||||
\(307\) | 3.06851e16 | + | 3.06851e16i | 0.119387 | + | 0.119387i | 0.764276 | − | 0.644889i | \(-0.223096\pi\) |
−0.644889 | + | 0.764276i | \(0.723096\pi\) | |||||||
\(308\) | −1.03249e17 | + | 1.03249e17i | −0.392671 | + | 0.392671i | ||||
\(309\) | −4.09267e17 | − | 4.09267e17i | −1.52159 | − | 1.52159i | ||||
\(310\) | 2.35842e17 | 0.857215 | ||||||||
\(311\) | 9.13630e16 | + | 9.13630e16i | 0.324674 | + | 0.324674i | 0.850557 | − | 0.525883i | \(-0.176265\pi\) |
−0.525883 | + | 0.850557i | \(0.676265\pi\) | |||||||
\(312\) | 1.66016e18i | 5.76858i | ||||||||
\(313\) | −2.30790e17 | −0.784164 | −0.392082 | − | 0.919930i | \(-0.628245\pi\) | ||||
−0.392082 | + | 0.919930i | \(0.628245\pi\) | |||||||
\(314\) | −7.11686e17 | −2.36473 | ||||||||
\(315\) | 1.22570e18 | 3.98299 | ||||||||
\(316\) | 3.60443e17 | − | 3.60443e17i | 1.14558 | − | 1.14558i | ||||
\(317\) | 4.37388e17 | − | 4.37388e17i | 1.35973 | − | 1.35973i | 0.485481 | − | 0.874247i | \(-0.338645\pi\) |
0.874247 | − | 0.485481i | \(-0.161355\pi\) | |||||||
\(318\) | 2.25163e17i | 0.684712i | ||||||||
\(319\) | 3.14482e16 | + | 5.49721e16i | 0.0935538 | + | 0.163534i | ||||
\(320\) | −2.95254e17 | −0.859304 | ||||||||
\(321\) | 5.38640e17 | + | 5.38640e17i | 1.53378 | + | 1.53378i | ||||
\(322\) | 5.00817e17 | + | 5.00817e17i | 1.39536 | + | 1.39536i | ||||
\(323\) | − | 9.39085e16i | − | 0.256028i | ||||||
\(324\) | − | 3.13983e18i | − | 8.37705i | ||||||
\(325\) | 2.64235e16i | 0.0689933i | ||||||||
\(326\) | −2.50995e17 | −0.641418 | ||||||||
\(327\) | −3.51048e17 | + | 3.51048e17i | −0.878076 | + | 0.878076i | ||||
\(328\) | − | 4.04684e17i | − | 0.990831i | ||||||
\(329\) | −1.70235e17 | + | 1.70235e17i | −0.408016 | + | 0.408016i | ||||
\(330\) | −1.89178e17 | − | 1.89178e17i | −0.443889 | − | 0.443889i | ||||
\(331\) | 3.33418e17 | − | 3.33418e17i | 0.765938 | − | 0.765938i | −0.211451 | − | 0.977389i | \(-0.567819\pi\) |
0.977389 | + | 0.211451i | \(0.0678188\pi\) | |||||||
\(332\) | − | 1.27897e18i | − | 2.87668i | ||||||
\(333\) | 9.80507e17 | + | 9.80507e17i | 2.15944 | + | 2.15944i | ||||
\(334\) | −1.04495e17 | + | 1.04495e17i | −0.225357 | + | 0.225357i | ||||
\(335\) | −6.00247e17 | −1.26770 | ||||||||
\(336\) | 1.07877e18 | + | 1.07877e18i | 2.23128 | + | 2.23128i | ||||
\(337\) | −4.16676e17 | + | 4.16676e17i | −0.844091 | + | 0.844091i | −0.989388 | − | 0.145297i | \(-0.953586\pi\) |
0.145297 | + | 0.989388i | \(0.453586\pi\) | |||||||
\(338\) | 1.03183e18 | + | 1.03183e18i | 2.04734 | + | 2.04734i | ||||
\(339\) | −1.35592e18 | −2.63533 | ||||||||
\(340\) | 4.79221e17 | + | 4.79221e17i | 0.912397 | + | 0.912397i | ||||
\(341\) | − | 5.07578e16i | − | 0.0946722i | ||||||
\(342\) | 1.06302e18 | 1.94249 | ||||||||
\(343\) | −7.30237e16 | −0.130739 | ||||||||
\(344\) | −5.31077e17 | −0.931641 | ||||||||
\(345\) | −6.15640e17 | + | 6.15640e17i | −1.05826 | + | 1.05826i | ||||
\(346\) | −1.40908e17 | + | 1.40908e17i | −0.237357 | + | 0.237357i | ||||
\(347\) | − | 4.00712e15i | − | 0.00661494i | −0.999995 | − | 0.00330747i | \(-0.998947\pi\) | ||
0.999995 | − | 0.00330747i | \(-0.00105280\pi\) | |||||||
\(348\) | 2.13629e18 | − | 1.22212e18i | 3.45625 | − | 1.97724i | ||||
\(349\) | 8.89525e17 | 1.41052 | 0.705262 | − | 0.708947i | \(-0.250830\pi\) | ||||
0.705262 | + | 0.708947i | \(0.250830\pi\) | |||||||
\(350\) | 4.84958e16 | + | 4.84958e16i | 0.0753750 | + | 0.0753750i | ||||
\(351\) | −2.68395e18 | − | 2.68395e18i | −4.08908 | − | 4.08908i | ||||
\(352\) | − | 1.73190e16i | − | 0.0258658i | ||||||
\(353\) | 1.33257e18i | 1.95104i | 0.219911 | + | 0.975520i | \(0.429423\pi\) | ||||
−0.219911 | + | 0.975520i | \(0.570577\pi\) | |||||||
\(354\) | − | 2.77091e18i | − | 3.97741i | ||||||
\(355\) | 1.04816e18 | 1.47513 | ||||||||
\(356\) | −1.22205e18 | + | 1.22205e18i | −1.68631 | + | 1.68631i | ||||
\(357\) | 1.34985e18i | 1.82645i | ||||||||
\(358\) | 1.42385e17 | − | 1.42385e17i | 0.188922 | − | 0.188922i | ||||
\(359\) | −5.38417e17 | − | 5.38417e17i | −0.700580 | − | 0.700580i | 0.263955 | − | 0.964535i | \(-0.414973\pi\) |
−0.964535 | + | 0.263955i | \(0.914973\pi\) | |||||||
\(360\) | −2.76373e18 | + | 2.76373e18i | −3.52678 | + | 3.52678i | ||||
\(361\) | − | 6.73797e17i | − | 0.843294i | ||||||
\(362\) | 1.18058e18 | + | 1.18058e18i | 1.44923 | + | 1.44923i | ||||
\(363\) | 1.10632e18 | − | 1.10632e18i | 1.33210 | − | 1.33210i | ||||
\(364\) | 4.07087e18 | 4.80814 | ||||||||
\(365\) | −6.93642e17 | − | 6.93642e17i | −0.803685 | − | 0.803685i | ||||
\(366\) | −1.25057e18 | + | 1.25057e18i | −1.42148 | + | 1.42148i | ||||
\(367\) | 6.89628e17 | + | 6.89628e17i | 0.769046 | + | 0.769046i | 0.977939 | − | 0.208892i | \(-0.0669859\pi\) |
−0.208892 | + | 0.977939i | \(0.566986\pi\) | |||||||
\(368\) | −7.99625e17 | −0.874886 | ||||||||
\(369\) | 1.01471e18 | + | 1.01471e18i | 1.08933 | + | 1.08933i | ||||
\(370\) | − | 1.75690e18i | − | 1.85070i | ||||||
\(371\) | 2.81292e17 | 0.290763 | ||||||||
\(372\) | −1.97252e18 | −2.00088 | ||||||||
\(373\) | −3.83446e17 | −0.381718 | −0.190859 | − | 0.981617i | \(-0.561127\pi\) | ||||
−0.190859 | + | 0.981617i | \(0.561127\pi\) | |||||||
\(374\) | 1.53729e17 | − | 1.53729e17i | 0.150195 | − | 0.150195i | ||||
\(375\) | −1.46912e18 | + | 1.46912e18i | −1.40876 | + | 1.40876i | ||||
\(376\) | − | 7.67700e17i | − | 0.722564i | ||||||
\(377\) | 4.63749e17 | − | 1.70368e18i | 0.428443 | − | 1.57398i | ||||
\(378\) | −9.85186e18 | −8.93461 | ||||||||
\(379\) | 1.15981e18 | + | 1.15981e18i | 1.03255 | + | 1.03255i | 0.999452 | + | 0.0331025i | \(0.0105388\pi\) |
0.0331025 | + | 0.999452i | \(0.489461\pi\) | |||||||
\(380\) | −6.38952e17 | − | 6.38952e17i | −0.558449 | − | 0.558449i | ||||
\(381\) | − | 1.54823e17i | − | 0.132849i | ||||||
\(382\) | − | 1.99611e17i | − | 0.168167i | ||||||
\(383\) | 2.39487e17i | 0.198103i | 0.995082 | + | 0.0990513i | \(0.0315808\pi\) | ||||
−0.995082 | + | 0.0990513i | \(0.968419\pi\) | |||||||
\(384\) | 4.01088e18 | 3.25777 | ||||||||
\(385\) | −2.36337e17 | + | 2.36337e17i | −0.188498 | + | 0.188498i | ||||
\(386\) | − | 1.25248e18i | − | 0.980976i | ||||||
\(387\) | 1.33163e18 | − | 1.33163e18i | 1.02426 | − | 1.02426i | ||||
\(388\) | 8.90313e17 | + | 8.90313e17i | 0.672544 | + | 0.672544i | ||||
\(389\) | −6.83814e17 | + | 6.83814e17i | −0.507330 | + | 0.507330i | −0.913706 | − | 0.406376i | \(-0.866792\pi\) |
0.406376 | + | 0.913706i | \(0.366792\pi\) | |||||||
\(390\) | 7.45890e18i | 5.43529i | ||||||||
\(391\) | −5.00279e17 | − | 5.00279e17i | −0.358076 | − | 0.358076i | ||||
\(392\) | 1.98557e18 | − | 1.98557e18i | 1.39599 | − | 1.39599i | ||||
\(393\) | 1.10402e18 | 0.762482 | ||||||||
\(394\) | 6.06698e17 | + | 6.06698e17i | 0.411622 | + | 0.411622i | ||||
\(395\) | 8.25056e17 | − | 8.25056e17i | 0.549925 | − | 0.549925i | ||||
\(396\) | 1.16749e18 | + | 1.16749e18i | 0.764518 | + | 0.764518i | ||||
\(397\) | −2.67127e18 | −1.71864 | −0.859320 | − | 0.511438i | \(-0.829113\pi\) | ||||
−0.859320 | + | 0.511438i | \(0.829113\pi\) | |||||||
\(398\) | 8.85307e17 | + | 8.85307e17i | 0.559644 | + | 0.559644i | ||||
\(399\) | − | 1.79977e18i | − | 1.11791i | ||||||
\(400\) | −7.74304e16 | −0.0472598 | ||||||||
\(401\) | −1.01642e18 | −0.609624 | −0.304812 | − | 0.952413i | \(-0.598594\pi\) | ||||
−0.304812 | + | 0.952413i | \(0.598594\pi\) | |||||||
\(402\) | 7.48287e18 | 4.41048 | ||||||||
\(403\) | −1.00064e18 | + | 1.00064e18i | −0.579617 | + | 0.579617i | ||||
\(404\) | −2.31748e18 | + | 2.31748e18i | −1.31931 | + | 1.31931i | ||||
\(405\) | − | 7.18710e18i | − | 4.02132i | ||||||
\(406\) | −2.27569e18 | − | 3.97795e18i | −1.25150 | − | 2.18764i | ||||
\(407\) | −3.78119e17 | −0.204394 | ||||||||
\(408\) | −3.04367e18 | − | 3.04367e18i | −1.61725 | − | 1.61725i | ||||
\(409\) | 1.00876e18 | + | 1.00876e18i | 0.526895 | + | 0.526895i | 0.919645 | − | 0.392750i | \(-0.128476\pi\) |
−0.392750 | + | 0.919645i | \(0.628476\pi\) | |||||||
\(410\) | − | 1.81819e18i | − | 0.933584i | ||||||
\(411\) | 3.62053e18i | 1.82759i | ||||||||
\(412\) | − | 4.52570e18i | − | 2.24598i | ||||||
\(413\) | −3.46164e18 | −1.68901 | ||||||||
\(414\) | 5.66303e18 | − | 5.66303e18i | 2.71673 | − | 2.71673i | ||||
\(415\) | − | 2.92756e18i | − | 1.38092i | ||||||
\(416\) | −3.41426e17 | + | 3.41426e17i | −0.158359 | + | 0.158359i | ||||
\(417\) | −2.92610e18 | − | 2.92610e18i | −1.33455 | − | 1.33455i | ||||
\(418\) | −2.04969e17 | + | 2.04969e17i | −0.0919295 | + | 0.0919295i | ||||
\(419\) | − | 2.27186e18i | − | 1.00203i | −0.865437 | − | 0.501017i | \(-0.832959\pi\) | ||
0.865437 | − | 0.501017i | \(-0.167041\pi\) | |||||||
\(420\) | 9.18436e18 | + | 9.18436e18i | 3.98386 | + | 3.98386i | ||||
\(421\) | −2.59765e18 | + | 2.59765e18i | −1.10817 | + | 1.10817i | −0.114776 | + | 0.993391i | \(0.536615\pi\) |
−0.993391 | + | 0.114776i | \(0.963385\pi\) | |||||||
\(422\) | −1.25494e18 | −0.526544 | ||||||||
\(423\) | 1.92495e18 | + | 1.92495e18i | 0.794394 | + | 0.794394i | ||||
\(424\) | −6.34263e17 | + | 6.34263e17i | −0.257459 | + | 0.257459i | ||||
\(425\) | −4.84437e16 | − | 4.84437e16i | −0.0193426 | − | 0.0193426i | ||||
\(426\) | −1.30667e19 | −5.13215 | ||||||||
\(427\) | 1.56231e18 | + | 1.56231e18i | 0.603631 | + | 0.603631i | ||||
\(428\) | 5.95631e18i | 2.26397i | ||||||||
\(429\) | 1.60530e18 | 0.600282 | ||||||||
\(430\) | −2.38606e18 | −0.877813 | ||||||||
\(431\) | −1.99207e18 | −0.721047 | −0.360524 | − | 0.932750i | \(-0.617402\pi\) | ||||
−0.360524 | + | 0.932750i | \(0.617402\pi\) | |||||||
\(432\) | 7.86495e18 | − | 7.86495e18i | 2.80098 | − | 2.80098i | ||||
\(433\) | −2.84555e18 | + | 2.84555e18i | −0.997129 | + | 0.997129i | −0.999996 | − | 0.00286699i | \(-0.999087\pi\) |
0.00286699 | + | 0.999996i | \(0.499087\pi\) | |||||||
\(434\) | 3.67299e18i | 1.26646i | ||||||||
\(435\) | 4.88998e18 | − | 2.79744e18i | 1.65914 | − | 0.949153i | ||||
\(436\) | −3.88191e18 | −1.29610 | ||||||||
\(437\) | 6.67029e17 | + | 6.67029e17i | 0.219167 | + | 0.219167i | ||||
\(438\) | 8.64717e18 | + | 8.64717e18i | 2.79612 | + | 2.79612i | ||||
\(439\) | − | 2.46952e18i | − | 0.785888i | −0.919562 | − | 0.392944i | \(-0.871457\pi\) | ||
0.919562 | − | 0.392944i | \(-0.128543\pi\) | |||||||
\(440\) | − | 1.06579e18i | − | 0.333814i | ||||||
\(441\) | 9.95731e18i | 3.06953i | ||||||||
\(442\) | −6.06122e18 | −1.83909 | ||||||||
\(443\) | 1.19038e18 | − | 1.19038e18i | 0.355515 | − | 0.355515i | −0.506642 | − | 0.862157i | \(-0.669113\pi\) |
0.862157 | + | 0.506642i | \(0.169113\pi\) | |||||||
\(444\) | 1.46942e19i | 4.31982i | ||||||||
\(445\) | −2.79727e18 | + | 2.79727e18i | −0.809495 | + | 0.809495i | ||||
\(446\) | 4.46914e18 | + | 4.46914e18i | 1.27315 | + | 1.27315i | ||||
\(447\) | −4.14939e18 | + | 4.14939e18i | −1.16368 | + | 1.16368i | ||||
\(448\) | − | 4.59827e18i | − | 1.26954i | ||||||
\(449\) | 1.23674e18 | + | 1.23674e18i | 0.336165 | + | 0.336165i | 0.854922 | − | 0.518757i | \(-0.173605\pi\) |
−0.518757 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(450\) | 5.48370e17 | − | 5.48370e17i | 0.146753 | − | 0.146753i | ||||
\(451\) | −3.91311e17 | −0.103106 | ||||||||
\(452\) | −7.49691e18 | − | 7.49691e18i | −1.94497 | − | 1.94497i | ||||
\(453\) | −1.36093e18 | + | 1.36093e18i | −0.347654 | + | 0.347654i | ||||
\(454\) | −6.68299e18 | − | 6.68299e18i | −1.68105 | − | 1.68105i | ||||
\(455\) | 9.31824e18 | 2.30810 | ||||||||
\(456\) | 4.05817e18 | + | 4.05817e18i | 0.989865 | + | 0.989865i | ||||
\(457\) | − | 5.25704e18i | − | 1.26278i | −0.775466 | − | 0.631390i | \(-0.782485\pi\) | ||
0.775466 | − | 0.631390i | \(-0.217515\pi\) | |||||||
\(458\) | 2.94962e18 | 0.697762 | ||||||||
\(459\) | 9.84129e18 | 2.29278 | ||||||||
\(460\) | −6.80779e18 | −1.56207 | ||||||||
\(461\) | 4.36847e18 | − | 4.36847e18i | 0.987239 | − | 0.987239i | −0.0126804 | − | 0.999920i | \(-0.504036\pi\) |
0.999920 | + | 0.0126804i | \(0.00403639\pi\) | |||||||
\(462\) | 2.94625e18 | − | 2.94625e18i | 0.655806 | − | 0.655806i | ||||
\(463\) | 2.07256e18i | 0.454402i | 0.973848 | + | 0.227201i | \(0.0729574\pi\) | ||||
−0.973848 | + | 0.227201i | \(0.927043\pi\) | |||||||
\(464\) | 4.99241e18 | + | 1.35895e18i | 1.07816 | + | 0.293479i | ||||
\(465\) | −4.51510e18 | −0.960499 | ||||||||
\(466\) | −2.75414e18 | − | 2.75414e18i | −0.577144 | − | 0.577144i | ||||
\(467\) | −1.33374e18 | − | 1.33374e18i | −0.275330 | − | 0.275330i | 0.555912 | − | 0.831241i | \(-0.312369\pi\) |
−0.831241 | + | 0.555912i | \(0.812369\pi\) | |||||||
\(468\) | − | 4.60317e19i | − | 9.36130i | ||||||
\(469\) | − | 9.34819e18i | − | 1.87291i | ||||||
\(470\) | − | 3.44918e18i | − | 0.680817i | ||||||
\(471\) | 1.36249e19 | 2.64965 | ||||||||
\(472\) | 7.80539e18 | − | 7.80539e18i | 1.49555 | − | 1.49555i | ||||
\(473\) | 5.13526e17i | 0.0969471i | ||||||||
\(474\) | −1.02854e19 | + | 1.02854e19i | −1.91326 | + | 1.91326i | ||||
\(475\) | 6.45906e16 | + | 6.45906e16i | 0.0118390 | + | 0.0118390i | ||||
\(476\) | −7.46335e18 | + | 7.46335e18i | −1.34799 | + | 1.34799i | ||||
\(477\) | − | 3.18073e18i | − | 0.566106i | ||||||
\(478\) | −3.21569e18 | − | 3.21569e18i | −0.563999 | − | 0.563999i | ||||
\(479\) | 1.57289e18 | − | 1.57289e18i | 0.271862 | − | 0.271862i | −0.557987 | − | 0.829849i | \(-0.688426\pi\) |
0.829849 | + | 0.557987i | \(0.188426\pi\) | |||||||
\(480\) | −1.54059e18 | −0.262422 | ||||||||
\(481\) | 7.45421e18 | + | 7.45421e18i | 1.25137 | + | 1.25137i | ||||
\(482\) | 5.18411e18 | − | 5.18411e18i | 0.857718 | − | 0.857718i | ||||
\(483\) | −9.58793e18 | − | 9.58793e18i | −1.56349 | − | 1.56349i | ||||
\(484\) | 1.22338e19 | 1.96627 | ||||||||
\(485\) | 2.03793e18 | + | 2.03793e18i | 0.322847 | + | 0.322847i | ||||
\(486\) | 5.00224e19i | 7.81107i | ||||||||
\(487\) | 7.72652e18 | 1.18927 | 0.594636 | − | 0.803995i | \(-0.297296\pi\) | ||||
0.594636 | + | 0.803995i | \(0.297296\pi\) | |||||||
\(488\) | −7.04546e18 | −1.06898 | ||||||||
\(489\) | 4.80519e18 | 0.718702 | ||||||||
\(490\) | 8.92089e18 | − | 8.92089e18i | 1.31533 | − | 1.31533i | ||||
\(491\) | −2.22793e18 | + | 2.22793e18i | −0.323840 | + | 0.323840i | −0.850238 | − | 0.526398i | \(-0.823542\pi\) |
0.526398 | + | 0.850238i | \(0.323542\pi\) | |||||||
\(492\) | 1.52069e19i | 2.17913i | ||||||||
\(493\) | 2.27324e18 | + | 3.97368e18i | 0.321157 | + | 0.561389i | ||||
\(494\) | 8.08150e18 | 1.12565 | ||||||||
\(495\) | 2.67240e18 | + | 2.67240e18i | 0.366999 | + | 0.366999i | ||||
\(496\) | −2.93222e18 | − | 2.93222e18i | −0.397032 | − | 0.397032i | ||||
\(497\) | 1.63240e19i | 2.17937i | ||||||||
\(498\) | 3.64959e19i | 4.80439i | ||||||||
\(499\) | − | 1.31173e19i | − | 1.70271i | −0.524589 | − | 0.851356i | \(-0.675781\pi\) | ||
0.524589 | − | 0.851356i | \(-0.324219\pi\) | |||||||
\(500\) | −1.62456e19 | −2.07944 | ||||||||
\(501\) | 2.00052e18 | − | 2.00052e18i | 0.252510 | − | 0.252510i | ||||
\(502\) | − | 8.23370e18i | − | 1.02487i | ||||||
\(503\) | −9.43172e18 | + | 9.43172e18i | −1.15775 | + | 1.15775i | −0.172793 | + | 0.984958i | \(0.555279\pi\) |
−0.984958 | + | 0.172793i | \(0.944721\pi\) | |||||||
\(504\) | −4.30421e19 | − | 4.30421e19i | −5.21050 | − | 5.21050i | ||||
\(505\) | −5.30472e18 | + | 5.30472e18i | −0.633319 | + | 0.633319i | ||||
\(506\) | 2.18387e18i | 0.257142i | ||||||||
\(507\) | −1.97539e19 | − | 1.97539e19i | −2.29402 | − | 2.29402i | ||||
\(508\) | 8.56019e17 | − | 8.56019e17i | 0.0980477 | − | 0.0980477i | ||||
\(509\) | −1.54176e19 | −1.74178 | −0.870890 | − | 0.491479i | \(-0.836457\pi\) | ||||
−0.870890 | + | 0.491479i | \(0.836457\pi\) | |||||||
\(510\) | −1.36748e19 | − | 1.36748e19i | −1.52381 | − | 1.52381i | ||||
\(511\) | 1.08027e19 | − | 1.08027e19i | 1.18737 | − | 1.18737i | ||||
\(512\) | 1.21937e19 | + | 1.21937e19i | 1.32204 | + | 1.32204i | ||||
\(513\) | −1.31215e19 | −1.40334 | ||||||||
\(514\) | 7.08119e18 | + | 7.08119e18i | 0.747075 | + | 0.747075i | ||||
\(515\) | − | 1.03594e19i | − | 1.07816i | ||||||
\(516\) | 1.99563e19 | 2.04896 | ||||||||
\(517\) | −7.42329e17 | −0.0751905 | ||||||||
\(518\) | 2.73618e19 | 2.73424 | ||||||||
\(519\) | 2.69762e18 | − | 2.69762e18i | 0.265956 | − | 0.265956i | ||||
\(520\) | −2.10110e19 | + | 2.10110e19i | −2.04373 | + | 2.04373i | ||||
\(521\) | − | 1.22855e19i | − | 1.17904i | −0.807752 | − | 0.589522i | \(-0.799316\pi\) | ||
0.807752 | − | 0.589522i | \(-0.200684\pi\) | |||||||
\(522\) | −4.49810e19 | + | 2.57325e19i | −4.25927 | + | 2.43663i | ||||
\(523\) | −9.28206e18 | −0.867227 | −0.433613 | − | 0.901099i | \(-0.642762\pi\) | ||||
−0.433613 | + | 0.901099i | \(0.642762\pi\) | |||||||
\(524\) | 6.10416e18 | + | 6.10416e18i | 0.562739 | + | 0.562739i | ||||
\(525\) | −9.28431e17 | − | 9.28431e17i | −0.0844568 | − | 0.0844568i | ||||
\(526\) | 1.86481e19i | 1.67392i | ||||||||
\(527\) | − | 3.66904e18i | − | 0.324996i | ||||||
\(528\) | 4.70410e18i | 0.411187i | ||||||||
\(529\) | −4.48591e18 | −0.386955 | ||||||||
\(530\) | −2.84966e18 | + | 2.84966e18i | −0.242584 | + | 0.242584i | ||||
\(531\) | 3.91428e19i | 3.28844i | ||||||||
\(532\) | 9.95098e18 | − | 9.95098e18i | 0.825058 | − | 0.825058i | ||||
\(533\) | 7.71427e18 | + | 7.71427e18i | 0.631254 | + | 0.631254i | ||||
\(534\) | 3.48717e19 | − | 3.48717e19i | 2.81633 | − | 2.81633i | ||||
\(535\) | 1.36340e19i | 1.08680i | ||||||||
\(536\) | 2.10785e19 | + | 2.10785e19i | 1.65839 | + | 1.65839i | ||||
\(537\) | −2.72590e18 | + | 2.72590e18i | −0.211685 | + | 0.211685i | ||||
\(538\) | 3.62987e19 | 2.78237 | ||||||||
\(539\) | −1.91995e18 | − | 1.91995e18i | −0.145267 | − | 0.145267i | ||||
\(540\) | 6.69600e19 | − | 6.69600e19i | 5.00103 | − | 5.00103i | ||||
\(541\) | −1.69732e19 | − | 1.69732e19i | −1.25136 | − | 1.25136i | −0.955111 | − | 0.296248i | \(-0.904265\pi\) |
−0.296248 | − | 0.955111i | \(-0.595735\pi\) | |||||||
\(542\) | −1.05797e19 | −0.769977 | ||||||||
\(543\) | −2.26017e19 | − | 2.26017e19i | −1.62384 | − | 1.62384i | ||||
\(544\) | − | 1.25191e18i | − | 0.0887935i | ||||||
\(545\) | −8.88571e18 | −0.622181 | ||||||||
\(546\) | −1.16164e20 | −8.03015 | ||||||||
\(547\) | −9.74601e18 | −0.665144 | −0.332572 | − | 0.943078i | \(-0.607916\pi\) | ||||
−0.332572 | + | 0.943078i | \(0.607916\pi\) | |||||||
\(548\) | −2.00180e19 | + | 2.00180e19i | −1.34883 | + | 1.34883i | ||||
\(549\) | 1.76659e19 | − | 1.76659e19i | 1.17525 | − | 1.17525i | ||||
\(550\) | 2.11471e17i | 0.0138903i | ||||||||
\(551\) | −3.03095e18 | − | 5.29816e18i | −0.196570 | − | 0.343608i | ||||
\(552\) | 4.32382e19 | 2.76881 | ||||||||
\(553\) | 1.28493e19 | + | 1.28493e19i | 0.812466 | + | 0.812466i | ||||
\(554\) | 1.28762e19 | + | 1.28762e19i | 0.803930 | + | 0.803930i | ||||
\(555\) | 3.36351e19i | 2.07368i | ||||||||
\(556\) | − | 3.23569e19i | − | 1.96990i | ||||||
\(557\) | − | 1.41432e19i | − | 0.850277i | −0.905128 | − | 0.425138i | \(-0.860225\pi\) | ||
0.905128 | − | 0.425138i | \(-0.139775\pi\) | |||||||
\(558\) | 4.15326e19 | 2.46575 | ||||||||
\(559\) | 1.01236e19 | − | 1.01236e19i | 0.593544 | − | 0.593544i | ||||
\(560\) | 2.73058e19i | 1.58102i | ||||||||
\(561\) | −2.94309e18 | + | 2.94309e18i | −0.168292 | + | 0.168292i | ||||
\(562\) | −1.33140e19 | − | 1.33140e19i | −0.751892 | − | 0.751892i | ||||
\(563\) | −8.50764e18 | + | 8.50764e18i | −0.474515 | + | 0.474515i | −0.903372 | − | 0.428857i | \(-0.858916\pi\) |
0.428857 | + | 0.903372i | \(0.358916\pi\) | |||||||
\(564\) | 2.88479e19i | 1.58913i | ||||||||
\(565\) | −1.71605e19 | − | 1.71605e19i | −0.933663 | − | 0.933663i | ||||
\(566\) | 4.23347e19 | − | 4.23347e19i | 2.27500 | − | 2.27500i | ||||
\(567\) | 1.11931e20 | 5.94114 | ||||||||
\(568\) | −3.68077e19 | − | 3.68077e19i | −1.92975 | − | 1.92975i | ||||
\(569\) | −7.43352e18 | + | 7.43352e18i | −0.384954 | + | 0.384954i | −0.872883 | − | 0.487929i | \(-0.837752\pi\) |
0.487929 | + | 0.872883i | \(0.337752\pi\) | |||||||
\(570\) | 1.82328e19 | + | 1.82328e19i | 0.932674 | + | 0.932674i | ||||
\(571\) | 6.64755e18 | 0.335899 | 0.167950 | − | 0.985796i | \(-0.446285\pi\) | ||||
0.167950 | + | 0.985796i | \(0.446285\pi\) | |||||||
\(572\) | 8.87575e18 | + | 8.87575e18i | 0.443030 | + | 0.443030i | ||||
\(573\) | 3.82146e18i | 0.188429i | ||||||||
\(574\) | 2.83164e19 | 1.37929 | ||||||||
\(575\) | 6.88188e17 | 0.0331156 | ||||||||
\(576\) | −5.19953e19 | −2.47176 | ||||||||
\(577\) | −1.62688e19 | + | 1.62688e19i | −0.764057 | + | 0.764057i | −0.977053 | − | 0.212996i | \(-0.931678\pi\) |
0.212996 | + | 0.977053i | \(0.431678\pi\) | |||||||
\(578\) | −1.54532e19 | + | 1.54532e19i | −0.717007 | + | 0.717007i | ||||
\(579\) | 2.39781e19i | 1.09917i | ||||||||
\(580\) | 4.25040e19 | + | 1.15697e19i | 1.92501 | + | 0.523995i | ||||
\(581\) | 4.55935e19 | 2.04019 | ||||||||
\(582\) | −2.54055e19 | − | 2.54055e19i | −1.12323 | − | 1.12323i | ||||
\(583\) | 6.13302e17 | + | 6.13302e17i | 0.0267914 | + | 0.0267914i | ||||
\(584\) | 4.87165e19i | 2.10274i | ||||||||
\(585\) | − | 1.05367e20i | − | 4.49379i | ||||||
\(586\) | − | 1.60212e19i | − | 0.675168i | ||||||
\(587\) | −1.38598e19 | −0.577152 | −0.288576 | − | 0.957457i | \(-0.593182\pi\) | ||||
−0.288576 | + | 0.957457i | \(0.593182\pi\) | |||||||
\(588\) | −7.46118e19 | + | 7.46118e19i | −3.07020 | + | 3.07020i | ||||
\(589\) | 4.89198e18i | 0.198920i | ||||||||
\(590\) | 3.50686e19 | − | 3.50686e19i | 1.40914 | − | 1.40914i | ||||
\(591\) | −1.16150e19 | − | 1.16150e19i | −0.461218 | − | 0.461218i | ||||
\(592\) | −2.18435e19 | + | 2.18435e19i | −0.857177 | + | 0.857177i | ||||
\(593\) | 1.38884e19i | 0.538604i | 0.963056 | + | 0.269302i | \(0.0867929\pi\) | ||||
−0.963056 | + | 0.269302i | \(0.913207\pi\) | |||||||
\(594\) | −2.14801e19 | − | 2.14801e19i | −0.823249 | − | 0.823249i | ||||
\(595\) | −1.70837e19 | + | 1.70837e19i | −0.647086 | + | 0.647086i | ||||
\(596\) | −4.58842e19 | −1.71767 | ||||||||
\(597\) | −1.69488e19 | − | 1.69488e19i | −0.627075 | − | 0.627075i | ||||
\(598\) | 4.30526e19 | − | 4.30526e19i | 1.57431 | − | 1.57431i | ||||
\(599\) | 1.86538e19 | + | 1.86538e19i | 0.674184 | + | 0.674184i | 0.958678 | − | 0.284494i | \(-0.0918255\pi\) |
−0.284494 | + | 0.958678i | \(0.591825\pi\) | |||||||
\(600\) | 4.18690e18 | 0.149566 | ||||||||
\(601\) | 2.41617e19 | + | 2.41617e19i | 0.853111 | + | 0.853111i | 0.990515 | − | 0.137404i | \(-0.0438760\pi\) |
−0.137404 | + | 0.990515i | \(0.543876\pi\) | |||||||
\(602\) | − | 3.71603e19i | − | 1.29689i | ||||||
\(603\) | −1.05705e20 | −3.64650 | ||||||||
\(604\) | −1.50492e19 | −0.513163 | ||||||||
\(605\) | 2.80032e19 | 0.943887 | ||||||||
\(606\) | 6.61303e19 | − | 6.61303e19i | 2.20339 | − | 2.20339i | ||||
\(607\) | −3.46077e19 | + | 3.46077e19i | −1.13986 | + | 1.13986i | −0.151387 | + | 0.988475i | \(0.548374\pi\) |
−0.988475 | + | 0.151387i | \(0.951626\pi\) | |||||||
\(608\) | 1.66919e18i | 0.0543476i | ||||||||
\(609\) | 4.35671e19 | + | 7.61562e19i | 1.40229 | + | 2.45123i | ||||
\(610\) | −3.16543e19 | −1.00722 | ||||||||
\(611\) | 1.46342e19 | + | 1.46342e19i | 0.460343 | + | 0.460343i | ||||
\(612\) | 8.43925e19 | + | 8.43925e19i | 2.62448 | + | 2.62448i | ||||
\(613\) | − | 5.20342e19i | − | 1.59980i | −0.600134 | − | 0.799899i | \(-0.704886\pi\) | ||
0.600134 | − | 0.799899i | \(-0.295114\pi\) | |||||||
\(614\) | − | 9.68258e18i | − | 0.294315i | ||||||
\(615\) | 3.48086e19i | 1.04607i | ||||||||
\(616\) | 1.65986e19 | 0.493181 | ||||||||
\(617\) | 2.12039e19 | − | 2.12039e19i | 0.622903 | − | 0.622903i | −0.323370 | − | 0.946273i | \(-0.604816\pi\) |
0.946273 | + | 0.323370i | \(0.104816\pi\) | |||||||
\(618\) | 1.29143e20i | 3.75104i | ||||||||
\(619\) | −6.16135e18 | + | 6.16135e18i | −0.176946 | + | 0.176946i | −0.790023 | − | 0.613077i | \(-0.789932\pi\) |
0.613077 | + | 0.790023i | \(0.289932\pi\) | |||||||
\(620\) | −2.49641e19 | − | 2.49641e19i | −0.708883 | − | 0.708883i | ||||
\(621\) | −6.99023e19 | + | 6.99023e19i | −1.96268 | + | 1.96268i | ||||
\(622\) | − | 2.88293e19i | − | 0.800390i | ||||||
\(623\) | −4.35644e19 | − | 4.35644e19i | −1.19596 | − | 1.19596i | ||||
\(624\) | 9.27364e19 | − | 9.27364e19i | 2.51743 | − | 2.51743i | ||||
\(625\) | −3.56107e19 | −0.955916 | ||||||||
\(626\) | 3.64126e19 | + | 3.64126e19i | 0.966564 | + | 0.966564i | ||||
\(627\) | 3.92405e18 | − | 3.92405e18i | 0.103006 | − | 0.103006i | ||||
\(628\) | 7.53327e19 | + | 7.53327e19i | 1.95554 | + | 1.95554i | ||||
\(629\) | −2.73324e19 | −0.701655 | ||||||||
\(630\) | −1.93383e20 | − | 1.93383e20i | −4.90946 | − | 4.90946i | ||||
\(631\) | − | 1.91579e19i | − | 0.480998i | −0.970649 | − | 0.240499i | \(-0.922689\pi\) | ||
0.970649 | − | 0.240499i | \(-0.0773111\pi\) | |||||||
\(632\) | −5.79460e19 | −1.43881 | ||||||||
\(633\) | 2.40253e19 | 0.589987 | ||||||||
\(634\) | −1.38016e20 | −3.35202 | ||||||||
\(635\) | 1.95943e18 | − | 1.95943e18i | 0.0470667 | − | 0.0470667i | ||||
\(636\) | 2.38338e19 | − | 2.38338e19i | 0.566230 | − | 0.566230i | ||||
\(637\) | 7.56995e19i | 1.77876i | ||||||||
\(638\) | 3.71145e18 | − | 1.36348e19i | 0.0862579 | − | 0.316888i | ||||
\(639\) | 1.84585e20 | 4.24316 | ||||||||
\(640\) | 5.07616e19 | + | 5.07616e19i | 1.15419 | + | 1.15419i | ||||
\(641\) | 4.71022e19 | + | 4.71022e19i | 1.05934 | + | 1.05934i | 0.998125 | + | 0.0612149i | \(0.0194975\pi\) |
0.0612149 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(642\) | − | 1.69966e20i | − | 3.78109i | ||||||
\(643\) | 5.44255e19i | 1.19764i | 0.800884 | + | 0.598819i | \(0.204363\pi\) | ||||
−0.800884 | + | 0.598819i | \(0.795637\pi\) | |||||||
\(644\) | − | 1.06024e20i | − | 2.30782i | ||||||
\(645\) | 4.56801e19 | 0.983580 | ||||||||
\(646\) | −1.48163e19 | + | 1.48163e19i | −0.315581 | + | 0.315581i | ||||
\(647\) | 3.86217e19i | 0.813770i | 0.913479 | + | 0.406885i | \(0.133385\pi\) | ||||
−0.913479 | + | 0.406885i | \(0.866615\pi\) | |||||||
\(648\) | −2.52385e20 | + | 2.52385e20i | −5.26064 | + | 5.26064i | ||||
\(649\) | −7.54744e18 | − | 7.54744e18i | −0.155628 | − | 0.155628i | ||||
\(650\) | 4.16893e18 | − | 4.16893e18i | 0.0850416 | − | 0.0850416i | ||||
\(651\) | − | 7.03178e19i | − | 1.41905i | ||||||
\(652\) | 2.65680e19 | + | 2.65680e19i | 0.530428 | + | 0.530428i | ||||
\(653\) | −4.74041e18 | + | 4.74041e18i | −0.0936318 | + | 0.0936318i | −0.752371 | − | 0.658739i | \(-0.771090\pi\) |
0.658739 | + | 0.752371i | \(0.271090\pi\) | |||||||
\(654\) | 1.10772e20 | 2.16464 | ||||||||
\(655\) | 1.39725e19 | + | 1.39725e19i | 0.270137 | + | 0.270137i | ||||
\(656\) | −2.26056e19 | + | 2.26056e19i | −0.432403 | + | 0.432403i | ||||
\(657\) | −1.22153e20 | − | 1.22153e20i | −2.31178 | − | 2.31178i | ||||
\(658\) | 5.37171e19 | 1.00585 | ||||||||
\(659\) | 2.43433e18 | + | 2.43433e18i | 0.0451005 | + | 0.0451005i | 0.729297 | − | 0.684197i | \(-0.239847\pi\) |
−0.684197 | + | 0.729297i | \(0.739847\pi\) | |||||||
\(660\) | 4.00495e19i | 0.734157i | ||||||||
\(661\) | −8.37299e19 | −1.51869 | −0.759347 | − | 0.650686i | \(-0.774481\pi\) | ||||
−0.759347 | + | 0.650686i | \(0.774481\pi\) | |||||||
\(662\) | −1.05209e20 | −1.88820 | ||||||||
\(663\) | 1.16040e20 | 2.06068 | ||||||||
\(664\) | −1.02805e20 | + | 1.02805e20i | −1.80651 | + | 1.80651i | ||||
\(665\) | 2.27779e19 | − | 2.27779e19i | 0.396060 | − | 0.396060i | ||||
\(666\) | − | 3.09396e20i | − | 5.32347i | ||||||
\(667\) | −4.43717e19 | − | 1.20781e19i | −0.755483 | − | 0.205645i | ||||
\(668\) | 2.21219e19 | 0.372723 | ||||||||
\(669\) | −8.55599e19 | − | 8.55599e19i | −1.42655 | − | 1.42655i | ||||
\(670\) | 9.47031e19 | + | 9.47031e19i | 1.56257 | + | 1.56257i | ||||
\(671\) | 6.81263e18i | 0.111239i | ||||||||
\(672\) | − | 2.39931e19i | − | 0.387705i | ||||||
\(673\) | − | 1.97363e19i | − | 0.315617i | −0.987470 | − | 0.157808i | \(-0.949557\pi\) | ||
0.987470 | − | 0.157808i | \(-0.0504428\pi\) | |||||||
\(674\) | 1.31481e20 | 2.08086 | ||||||||
\(675\) | −6.76888e18 | + | 6.76888e18i | −0.106021 | + | 0.106021i | ||||
\(676\) | − | 2.18439e20i | − | 3.38613i | ||||||
\(677\) | −3.19634e19 | + | 3.19634e19i | −0.490380 | + | 0.490380i | −0.908426 | − | 0.418046i | \(-0.862715\pi\) |
0.418046 | + | 0.908426i | \(0.362715\pi\) | |||||||
\(678\) | 2.13928e20 | + | 2.13928e20i | 3.24833 | + | 3.24833i | ||||
\(679\) | −3.17385e19 | + | 3.17385e19i | −0.476978 | + | 0.476978i | ||||
\(680\) | − | 7.70413e19i | − | 1.14594i | ||||||
\(681\) | 1.27943e20 | + | 1.27943e20i | 1.88359 | + | 1.88359i | ||||
\(682\) | −8.00824e18 | + | 8.00824e18i | −0.116693 | + | 0.116693i | ||||
\(683\) | 1.67871e19 | 0.242120 | 0.121060 | − | 0.992645i | \(-0.461371\pi\) | ||||
0.121060 | + | 0.992645i | \(0.461371\pi\) | |||||||
\(684\) | −1.12522e20 | − | 1.12522e20i | −1.60636 | − | 1.60636i | ||||
\(685\) | −4.58214e19 | + | 4.58214e19i | −0.647492 | + | 0.647492i | ||||
\(686\) | 1.15212e19 | + | 1.15212e19i | 0.161150 | + | 0.161150i | ||||
\(687\) | −5.64692e19 | −0.781834 | ||||||||
\(688\) | 2.96658e19 | + | 2.96658e19i | 0.406572 | + | 0.406572i | ||||
\(689\) | − | 2.41812e19i | − | 0.328052i | ||||||
\(690\) | 1.94264e20 | 2.60884 | ||||||||
\(691\) | 1.03822e20 | 1.38021 | 0.690105 | − | 0.723710i | \(-0.257564\pi\) | ||||
0.690105 | + | 0.723710i | \(0.257564\pi\) | |||||||
\(692\) | 2.98305e19 | 0.392571 | ||||||||
\(693\) | −4.16197e19 | + | 4.16197e19i | −0.542208 | + | 0.542208i | ||||
\(694\) | −6.32217e17 | + | 6.32217e17i | −0.00815361 | + | 0.00815361i | ||||
\(695\) | − | 7.40652e19i | − | 0.945629i | ||||||
\(696\) | −2.69955e20 | − | 7.34826e19i | −3.41214 | − | 0.928795i | ||||
\(697\) | −2.82860e19 | −0.353950 | ||||||||
\(698\) | −1.40344e20 | − | 1.40344e20i | −1.73862 | − | 1.73862i | ||||
\(699\) | 5.27269e19 | + | 5.27269e19i | 0.646683 | + | 0.646683i | ||||
\(700\) | − | 1.02666e19i | − | 0.124664i | ||||||
\(701\) | − | 5.68503e18i | − | 0.0683450i | −0.999416 | − | 0.0341725i | \(-0.989120\pi\) | ||
0.999416 | − | 0.0341725i | \(-0.0108796\pi\) | |||||||
\(702\) | 8.46914e20i | 10.0804i | ||||||||
\(703\) | 3.64427e19 | 0.429460 | ||||||||
\(704\) | 1.00256e19 | − | 1.00256e19i | 0.116978 | − | 0.116978i | ||||
\(705\) | 6.60330e19i | 0.762847i | ||||||||
\(706\) | 2.10244e20 | − | 2.10244e20i | 2.40486 | − | 2.40486i | ||||
\(707\) | −8.26152e19 | − | 8.26152e19i | −0.935673 | − | 0.935673i | ||||
\(708\) | −2.93304e20 | + | 2.93304e20i | −3.28916 | + | 3.28916i | ||||
\(709\) | − | 1.02470e19i | − | 0.113782i | −0.998380 | − | 0.0568909i | \(-0.981881\pi\) | ||
0.998380 | − | 0.0568909i | \(-0.0181187\pi\) | |||||||
\(710\) | −1.65372e20 | − | 1.65372e20i | −1.81825 | − | 1.81825i | ||||
\(711\) | 1.45295e20 | − | 1.45295e20i | 1.58184 | − | 1.58184i | ||||
\(712\) | 1.96460e20 | 2.11795 | ||||||||
\(713\) | 2.60611e19 | + | 2.60611e19i | 0.278206 | + | 0.278206i | ||||
\(714\) | 2.12970e20 | − | 2.12970e20i | 2.25129 | − | 2.25129i | ||||
\(715\) | 2.03166e19 | + | 2.03166e19i | 0.212672 | + | 0.212672i | ||||
\(716\) | −3.01432e19 | −0.312462 | ||||||||
\(717\) | 6.15630e19 | + | 6.15630e19i | 0.631954 | + | 0.631954i | ||||
\(718\) | 1.69896e20i | 1.72708i | ||||||||
\(719\) | 1.77767e20 | 1.78957 | 0.894784 | − | 0.446499i | \(-0.147330\pi\) | ||||
0.894784 | + | 0.446499i | \(0.147330\pi\) | |||||||
\(720\) | 3.08763e20 | 3.07820 | ||||||||
\(721\) | 1.61336e20 | 1.59288 | ||||||||
\(722\) | −1.06307e20 | + | 1.06307e20i | −1.03945 | + | 1.03945i | ||||
\(723\) | −9.92476e19 | + | 9.92476e19i | −0.961063 | + | 0.961063i | ||||
\(724\) | − | 2.49931e20i | − | 2.39691i | ||||||
\(725\) | −4.29666e18 | − | 1.16956e18i | −0.0408098 | − | 0.0111086i | ||||
\(726\) | −3.49097e20 | −3.28390 | ||||||||
\(727\) | 1.93395e19 | + | 1.93395e19i | 0.180179 | + | 0.180179i | 0.791434 | − | 0.611255i | \(-0.209335\pi\) |
−0.611255 | + | 0.791434i | \(0.709335\pi\) | |||||||
\(728\) | −3.27223e20 | − | 3.27223e20i | −3.01943 | − | 3.01943i | ||||
\(729\) | − | 5.08039e20i | − | 4.64306i | ||||||
\(730\) | 2.18877e20i | 1.98125i | ||||||||
\(731\) | 3.71204e19i | 0.332806i | ||||||||
\(732\) | 2.64748e20 | 2.35101 | ||||||||
\(733\) | −8.62359e18 | + | 8.62359e18i | −0.0758508 | + | 0.0758508i | −0.744014 | − | 0.668164i | \(-0.767081\pi\) |
0.668164 | + | 0.744014i | \(0.267081\pi\) | |||||||
\(734\) | − | 2.17610e20i | − | 1.89586i | ||||||
\(735\) | −1.70787e20 | + | 1.70787e20i | −1.47382 | + | 1.47382i | ||||
\(736\) | 8.89228e18 | + | 8.89228e18i | 0.0760096 | + | 0.0760096i | ||||
\(737\) | 2.03819e19 | − | 2.03819e19i | 0.172573 | − | 0.172573i | ||||
\(738\) | − | 3.20190e20i | − | 2.68543i | ||||||
\(739\) | 1.07904e20 | + | 1.07904e20i | 0.896453 | + | 0.896453i | 0.995120 | − | 0.0986674i | \(-0.0314580\pi\) |
−0.0986674 | + | 0.995120i | \(0.531458\pi\) | |||||||
\(740\) | −1.85970e20 | + | 1.85970e20i | −1.53045 | + | 1.53045i | ||||
\(741\) | −1.54717e20 | −1.26128 | ||||||||
\(742\) | −4.43804e19 | − | 4.43804e19i | −0.358396 | − | 0.358396i | ||||
\(743\) | −8.86207e19 | + | 8.86207e19i | −0.708947 | + | 0.708947i | −0.966314 | − | 0.257367i | \(-0.917145\pi\) |
0.257367 | + | 0.966314i | \(0.417145\pi\) | |||||||
\(744\) | 1.58554e20 | + | 1.58554e20i | 1.25651 | + | 1.25651i | ||||
\(745\) | −1.05029e20 | −0.824549 | ||||||||
\(746\) | 6.04977e19 | + | 6.04977e19i | 0.470508 | + | 0.470508i | ||||
\(747\) | − | 5.15553e20i | − | 3.97218i | ||||||
\(748\) | −3.25448e19 | −0.248411 | ||||||||
\(749\) | −2.12335e20 | −1.60564 | ||||||||
\(750\) | 4.63576e20 | 3.47290 | ||||||||
\(751\) | −1.62288e20 | + | 1.62288e20i | −1.20450 | + | 1.20450i | −0.231716 | + | 0.972783i | \(0.574434\pi\) |
−0.972783 | + | 0.231716i | \(0.925566\pi\) | |||||||
\(752\) | −4.28835e19 | + | 4.28835e19i | −0.315330 | + | 0.315330i | ||||
\(753\) | 1.57631e20i | 1.14836i | ||||||||
\(754\) | −3.41964e20 | + | 1.95629e20i | −2.46820 | + | 1.41200i | ||||
\(755\) | −3.44477e19 | −0.246338 | ||||||||
\(756\) | 1.04283e21 | + | 1.04283e21i | 7.38857 | + | 7.38857i | ||||
\(757\) | 8.05193e19 | + | 8.05193e19i | 0.565235 | + | 0.565235i | 0.930790 | − | 0.365555i | \(-0.119121\pi\) |
−0.365555 | + | 0.930790i | \(0.619121\pi\) | |||||||
\(758\) | − | 3.65975e20i | − | 2.54546i | ||||||
\(759\) | − | 4.18093e19i | − | 0.288125i | ||||||
\(760\) | 1.02720e20i | 0.701391i | ||||||||
\(761\) | −8.87783e19 | −0.600640 | −0.300320 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300320 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(762\) | −2.44269e19 | + | 2.44269e19i | −0.163751 | + | 0.163751i | ||||
\(763\) | − | 1.38385e20i | − | 0.919217i | ||||||
\(764\) | −2.11290e19 | + | 2.11290e19i | −0.139067 | + | 0.139067i | ||||
\(765\) | 1.93175e20 | + | 1.93175e20i | 1.25986 | + | 1.25986i | ||||
\(766\) | 3.77847e19 | − | 3.77847e19i | 0.244182 | − | 0.244182i | ||||
\(767\) | 2.97579e20i | 1.90562i | ||||||||
\(768\) | −4.41697e20 | − | 4.41697e20i | −2.80283 | − | 2.80283i | ||||
\(769\) | 3.28745e19 | − | 3.28745e19i | 0.206716 | − | 0.206716i | −0.596154 | − | 0.802870i | \(-0.703305\pi\) |
0.802870 | + | 0.596154i | \(0.203305\pi\) | |||||||
\(770\) | 7.45753e19 | 0.464686 | ||||||||
\(771\) | −1.35566e20 | − | 1.35566e20i | −0.837089 | − | 0.837089i | ||||
\(772\) | −1.32576e20 | + | 1.32576e20i | −0.811228 | + | 0.811228i | ||||
\(773\) | −1.19644e20 | − | 1.19644e20i | −0.725493 | − | 0.725493i | 0.244226 | − | 0.969718i | \(-0.421466\pi\) |
−0.969718 | + | 0.244226i | \(0.921466\pi\) | |||||||
\(774\) | −4.20193e20 | −2.52501 | ||||||||
\(775\) | 2.52358e18 | + | 2.52358e18i | 0.0150282 | + | 0.0150282i | ||||
\(776\) | − | 1.43130e20i | − | 0.844691i | ||||||
\(777\) | −5.23830e20 | −3.06368 | ||||||||
\(778\) | 2.15775e20 | 1.25068 | ||||||||
\(779\) | 3.77141e19 | 0.216641 | ||||||||
\(780\) | 7.89532e20 | − | 7.89532e20i | 4.49477 | − | 4.49477i | ||||
\(781\) | −3.55913e19 | + | 3.55913e19i | −0.200810 | + | 0.200810i | ||||
\(782\) | 1.57862e20i | 0.882732i | ||||||||
\(783\) | 5.55229e20 | − | 3.17633e20i | 3.07709 | − | 1.76033i | ||||
\(784\) | −2.21827e20 | −1.21843 | ||||||||
\(785\) | 1.72437e20 | + | 1.72437e20i | 0.938734 | + | 0.938734i | ||||
\(786\) | −1.74185e20 | − | 1.74185e20i | −0.939840 | − | 0.939840i | ||||
\(787\) | 6.88760e19i | 0.368336i | 0.982895 | + | 0.184168i | \(0.0589591\pi\) | ||||
−0.982895 | + | 0.184168i | \(0.941041\pi\) | |||||||
\(788\) | − | 1.28439e20i | − | 0.680791i | ||||||
\(789\) | − | 3.57010e20i | − | 1.87560i | ||||||
\(790\) | −2.60344e20 | −1.35568 | ||||||||
\(791\) | 2.67256e20 | − | 2.67256e20i | 1.37940 | − | 1.37940i | ||||
\(792\) | − | 1.87690e20i | − | 0.960207i | ||||||
\(793\) | 1.34304e20 | − | 1.34304e20i | 0.681044 | − | 0.681044i | ||||
\(794\) | 4.21456e20 | + | 4.21456e20i | 2.11841 | + | 2.11841i | ||||
\(795\) | 5.45556e19 | − | 5.45556e19i | 0.271813 | − | 0.271813i | ||||
\(796\) | − | 1.87421e20i | − | 0.925608i | ||||||
\(797\) | −1.75093e20 | − | 1.75093e20i | −0.857159 | − | 0.857159i | 0.133843 | − | 0.991003i | \(-0.457268\pi\) |
−0.991003 | + | 0.133843i | \(0.957268\pi\) | |||||||
\(798\) | −2.83956e20 | + | 2.83956e20i | −1.37794 | + | 1.37794i | ||||
\(799\) | −5.36595e19 | −0.258118 | ||||||||
\(800\) | 8.61070e17 | + | 8.61070e17i | 0.00410590 | + | 0.00410590i | ||||
\(801\) | −4.92609e20 | + | 4.92609e20i | −2.32849 | + | 2.32849i | ||||
\(802\) | 1.60364e20 | + | 1.60364e20i | 0.751426 | + | 0.751426i | ||||
\(803\) | 4.71065e19 | 0.218813 | ||||||||
\(804\) | −7.92069e20 | − | 7.92069e20i | −3.64729 | − | 3.64729i | ||||
\(805\) | − | 2.42689e20i | − | 1.10785i | ||||||
\(806\) | 3.15748e20 | 1.42888 | ||||||||
\(807\) | −6.94923e20 | −3.11761 | ||||||||
\(808\) | 3.72565e20 | 1.65700 | ||||||||
\(809\) | 1.16998e20 | − | 1.16998e20i | 0.515866 | − | 0.515866i | −0.400452 | − | 0.916318i | \(-0.631147\pi\) |
0.916318 | + | 0.400452i | \(0.131147\pi\) | |||||||
\(810\) | −1.13393e21 | + | 1.13393e21i | −4.95670 | + | 4.95670i | ||||
\(811\) | 3.14845e20i | 1.36443i | 0.731152 | + | 0.682215i | \(0.238983\pi\) | ||||
−0.731152 | + | 0.682215i | \(0.761017\pi\) | |||||||
\(812\) | −1.80186e20 | + | 6.61953e20i | −0.774156 | + | 2.84404i | ||||
\(813\) | 2.02544e20 | 0.862750 | ||||||||
\(814\) | 5.96572e19 | + | 5.96572e19i | 0.251937 | + | 0.251937i | ||||
\(815\) | 6.08144e19 | + | 6.08144e19i | 0.254626 | + | 0.254626i | ||||
\(816\) | 3.40037e20i | 1.41155i | ||||||||
\(817\) | − | 4.94931e19i | − | 0.203700i | ||||||
\(818\) | − | 3.18311e20i | − | 1.29891i | ||||||
\(819\) | 1.64097e21 | 6.63918 | ||||||||
\(820\) | −1.92458e20 | + | 1.92458e20i | −0.772037 | + | 0.772037i | ||||
\(821\) | 2.34347e20i | 0.932087i | 0.884762 | + | 0.466044i | \(0.154321\pi\) | ||||
−0.884762 | + | 0.466044i | \(0.845679\pi\) | |||||||
\(822\) | 5.71224e20 | − | 5.71224e20i | 2.25270 | − | 2.25270i | ||||
\(823\) | −2.09677e20 | − | 2.09677e20i | −0.819884 | − | 0.819884i | 0.166207 | − | 0.986091i | \(-0.446848\pi\) |
−0.986091 | + | 0.166207i | \(0.946848\pi\) | |||||||
\(824\) | −3.63783e20 | + | 3.63783e20i | −1.41043 | + | 1.41043i | ||||
\(825\) | − | 4.04853e18i | − | 0.0155640i | ||||||
\(826\) | 5.46155e20 | + | 5.46155e20i | 2.08188 | + | 2.08188i | ||||
\(827\) | −1.23026e20 | + | 1.23026e20i | −0.465005 | + | 0.465005i | −0.900292 | − | 0.435287i | \(-0.856647\pi\) |
0.435287 | + | 0.900292i | \(0.356647\pi\) | |||||||
\(828\) | −1.19887e21 | −4.49326 | ||||||||
\(829\) | −1.77462e20 | − | 1.77462e20i | −0.659513 | − | 0.659513i | 0.295752 | − | 0.955265i | \(-0.404430\pi\) |
−0.955265 | + | 0.295752i | \(0.904430\pi\) | |||||||
\(830\) | −4.61891e20 | + | 4.61891e20i | −1.70213 | + | 1.70213i | ||||
\(831\) | −2.46509e20 | − | 2.46509e20i | −0.900794 | − | 0.900794i | ||||
\(832\) | −3.95289e20 | −1.43236 | ||||||||
\(833\) | −1.38784e20 | − | 1.38784e20i | −0.498683 | − | 0.498683i | ||||
\(834\) | 9.23321e20i | 3.28996i | ||||||||
\(835\) | 5.06371e19 | 0.178922 | ||||||||
\(836\) | 4.33924e19 | 0.152044 | ||||||||
\(837\) | −5.12663e20 | −1.78137 | ||||||||
\(838\) | −3.58439e20 | + | 3.58439e20i | −1.23511 | + | 1.23511i | ||||
\(839\) | 4.05696e20 | − | 4.05696e20i | 1.38633 | − | 1.38633i | 0.553449 | − | 0.832883i | \(-0.313311\pi\) |
0.832883 | − | 0.553449i | \(-0.186689\pi\) | |||||||
\(840\) | − | 1.47651e21i | − | 5.00358i | ||||||
\(841\) | 2.56505e20 | + | 1.50818e20i | 0.862033 | + | 0.506852i | ||||
\(842\) | 8.19680e20 | 2.73187 | ||||||||
\(843\) | 2.54892e20 | + | 2.54892e20i | 0.842486 | + | 0.842486i | ||||
\(844\) | 1.32836e20 | + | 1.32836e20i | 0.435432 | + | 0.435432i | ||||
\(845\) | − | 5.00009e20i | − | 1.62548i | ||||||
\(846\) | − | 6.07411e20i | − | 1.95835i | ||||||
\(847\) | 4.36119e20i | 1.39451i | ||||||||
\(848\) | 7.08596e19 | 0.224713 | ||||||||
\(849\) | −8.10481e20 | + | 8.10481e20i | −2.54911 | + | 2.54911i | ||||
\(850\) | 1.52863e19i | 0.0476836i | ||||||||
\(851\) | 1.94141e20 | − | 1.94141e20i | 0.600636 | − | 0.600636i | ||||
\(852\) | 1.38312e21 | + | 1.38312e21i | 4.24409 | + | 4.24409i | ||||
\(853\) | 2.63227e20 | − | 2.63227e20i | 0.801099 | − | 0.801099i | −0.182168 | − | 0.983267i | \(-0.558311\pi\) |
0.983267 | + | 0.182168i | \(0.0583115\pi\) | |||||||
\(854\) | − | 4.92982e20i | − | 1.48808i | ||||||
\(855\) | −2.57563e20 | − | 2.57563e20i | −0.771117 | − | 0.771117i | ||||
\(856\) | 4.78779e20 | − | 4.78779e20i | 1.42173 | − | 1.42173i | ||||
\(857\) | 4.60408e20 | 1.35606 | 0.678028 | − | 0.735036i | \(-0.262835\pi\) | ||||
0.678028 | + | 0.735036i | \(0.262835\pi\) | |||||||
\(858\) | −2.53274e20 | − | 2.53274e20i | −0.739911 | − | 0.739911i | ||||
\(859\) | 1.93894e20 | − | 1.93894e20i | 0.561838 | − | 0.561838i | −0.367991 | − | 0.929829i | \(-0.619954\pi\) |
0.929829 | + | 0.367991i | \(0.119954\pi\) | |||||||
\(860\) | 2.52567e20 | + | 2.52567e20i | 0.725917 | + | 0.725917i | ||||
\(861\) | −5.42106e20 | −1.54548 | ||||||||
\(862\) | 3.14296e20 | + | 3.14296e20i | 0.888767 | + | 0.888767i | ||||
\(863\) | − | 3.85219e20i | − | 1.08052i | −0.841499 | − | 0.540259i | \(-0.818326\pi\) | ||
0.841499 | − | 0.540259i | \(-0.181674\pi\) | |||||||
\(864\) | −1.74925e20 | −0.486695 | ||||||||
\(865\) | 6.82822e19 | 0.188449 | ||||||||
\(866\) | 8.97906e20 | 2.45813 | ||||||||
\(867\) | 2.95845e20 | − | 2.95845e20i | 0.803398 | − | 0.803398i | ||||
\(868\) | 3.88789e20 | − | 3.88789e20i | 1.04731 | − | 1.04731i | ||||
\(869\) | 5.60311e19i | 0.149724i | ||||||||
\(870\) | −1.21287e21 | − | 3.30148e20i | −3.21499 | − | 0.875132i | ||||
\(871\) | −8.03616e20 | −2.11311 | ||||||||
\(872\) | 3.12034e20 | + | 3.12034e20i | 0.813930 | + | 0.813930i | ||||
\(873\) | 3.58886e20 | + | 3.58886e20i | 0.928661 | + | 0.928661i | ||||
\(874\) | − | 2.10479e20i | − | 0.540292i | ||||||
\(875\) | − | 5.79135e20i | − | 1.47477i | ||||||
\(876\) | − | 1.83062e21i | − | 4.62456i | ||||||
\(877\) | −1.55216e20 | −0.388992 | −0.194496 | − | 0.980903i | \(-0.562307\pi\) | ||||
−0.194496 | + | 0.980903i | \(0.562307\pi\) | |||||||
\(878\) | −3.89625e20 | + | 3.89625e20i | −0.968690 | + | 0.968690i | ||||
\(879\) | 3.06719e20i | 0.756517i | ||||||||
\(880\) | −5.95351e19 | + | 5.95351e19i | −0.145678 | + | 0.145678i | ||||
\(881\) | −3.53503e20 | − | 3.53503e20i | −0.858147 | − | 0.858147i | 0.132973 | − | 0.991120i | \(-0.457548\pi\) |
−0.991120 | + | 0.132973i | \(0.957548\pi\) | |||||||
\(882\) | 1.57100e21 | − | 1.57100e21i | 3.78352 | − | 3.78352i | ||||
\(883\) | 7.88527e20i | 1.88405i | 0.335547 | + | 0.942023i | \(0.391079\pi\) | ||||
−0.335547 | + | 0.942023i | \(0.608921\pi\) | |||||||
\(884\) | 6.41586e20 | + | 6.41586e20i | 1.52086 | + | 1.52086i | ||||
\(885\) | −6.71374e20 | + | 6.71374e20i | −1.57893 | + | 1.57893i | ||||
\(886\) | −3.75619e20 | −0.876419 | ||||||||
\(887\) | 3.16198e20 | + | 3.16198e20i | 0.731970 | + | 0.731970i | 0.971010 | − | 0.239039i | \(-0.0768325\pi\) |
−0.239039 | + | 0.971010i | \(0.576833\pi\) | |||||||
\(888\) | 1.18115e21 | − | 1.18115e21i | 2.71277 | − | 2.71277i | ||||
\(889\) | 3.05160e19 | + | 3.05160e19i | 0.0695369 | + | 0.0695369i | ||||
\(890\) | 8.82670e20 | 1.99558 | ||||||||
\(891\) | 2.44044e20 | + | 2.44044e20i | 0.547425 | + | 0.547425i | ||||
\(892\) | − | 9.46126e20i | − | 2.10569i | ||||||
\(893\) | 7.15449e19 | 0.157986 | ||||||||
\(894\) | 1.30933e21 | 2.86871 | ||||||||
\(895\) | −6.89979e19 | −0.149994 | ||||||||
\(896\) | −7.90557e20 | + | 7.90557e20i | −1.70521 | + | 1.70521i | ||||
\(897\) | −8.24225e20 | + | 8.24225e20i | −1.76400 | + | 1.76400i | ||||
\(898\) | − | 3.90248e20i | − | 0.828718i | ||||||
\(899\) | −1.18420e20 | − | 2.07001e20i | −0.249522 | − | 0.436169i | ||||
\(900\) | −1.16091e20 | −0.242717 | ||||||||
\(901\) | 4.43327e19 | + | 4.43327e19i | 0.0919710 | + | 0.0919710i | ||||
\(902\) | 6.17385e19 | + | 6.17385e19i | 0.127090 | + | 0.127090i | ||||
\(903\) | 7.11418e20i | 1.45315i | ||||||||
\(904\) | 1.20523e21i | 2.44281i | ||||||||
\(905\) | − | 5.72095e20i | − | 1.15061i | ||||||
\(906\) | 4.29437e20 | 0.857041 | ||||||||
\(907\) | 1.05727e20 | − | 1.05727e20i | 0.209380 | − | 0.209380i | −0.594624 | − | 0.804004i | \(-0.702699\pi\) |
0.804004 | + | 0.594624i | \(0.202699\pi\) | |||||||
\(908\) | 1.41480e21i | 2.78032i | ||||||||
\(909\) | −9.34178e20 | + | 9.34178e20i | −1.82172 | + | 1.82172i | ||||
\(910\) | −1.47017e21 | − | 1.47017e21i | −2.84497 | − | 2.84497i | ||||
\(911\) | 3.51751e20 | − | 3.51751e20i | 0.675470 | − | 0.675470i | −0.283501 | − | 0.958972i | \(-0.591496\pi\) |
0.958972 | + | 0.283501i | \(0.0914961\pi\) | |||||||
\(912\) | − | 4.53376e20i | − | 0.863963i | ||||||
\(913\) | 9.94080e19 | + | 9.94080e19i | 0.187986 | + | 0.187986i | ||||
\(914\) | −8.29421e20 | + | 8.29421e20i | −1.55651 | + | 1.55651i | ||||
\(915\) | 6.06009e20 | 1.12858 | ||||||||
\(916\) | −3.12220e20 | − | 3.12220e20i | −0.577022 | − | 0.577022i | ||||
\(917\) | −2.17606e20 | + | 2.17606e20i | −0.399103 | + | 0.399103i | ||||
\(918\) | −1.55269e21 | − | 1.55269e21i | −2.82610 | − | 2.82610i | ||||
\(919\) | −1.32924e19 | −0.0240101 | −0.0120050 | − | 0.999928i | \(-0.503821\pi\) | ||||
−0.0120050 | + | 0.999928i | \(0.503821\pi\) | |||||||
\(920\) | 5.47222e20 | + | 5.47222e20i | 0.980953 | + | 0.980953i | ||||
\(921\) | 1.85369e20i | 0.329777i | ||||||||
\(922\) | −1.37846e21 | −2.43375 | ||||||||
\(923\) | 1.40329e21 | 2.45887 | ||||||||
\(924\) | −6.23726e20 | −1.08465 | ||||||||
\(925\) | 1.87994e19 | − | 1.87994e19i | 0.0324452 | − | 0.0324452i | ||||
\(926\) | 3.26995e20 | − | 3.26995e20i | 0.560098 | − | 0.560098i | ||||
\(927\) | − | 1.82432e21i | − | 3.10129i | ||||||
\(928\) | −4.04061e19 | − | 7.06307e19i | −0.0681728 | − | 0.119167i | ||||
\(929\) | 1.09234e21 | 1.82915 | 0.914575 | − | 0.404417i | \(-0.132525\pi\) | ||||
0.914575 | + | 0.404417i | \(0.132525\pi\) | |||||||
\(930\) | 7.12364e20 | + | 7.12364e20i | 1.18392 | + | 1.18392i | ||||
\(931\) | 1.85043e20 | + | 1.85043e20i | 0.305228 | + | 0.305228i | ||||
\(932\) | 5.83057e20i | 0.954551i | ||||||||
\(933\) | 5.51925e20i | 0.896827i | ||||||||
\(934\) | 4.20858e20i | 0.678746i | ||||||||
\(935\) | −7.44953e19 | −0.119247 | ||||||||
\(936\) | −3.70011e21 | + | 3.70011e21i | −5.87873 | + | 5.87873i | ||||
\(937\) | 6.08601e20i | 0.959745i | 0.877338 | + | 0.479872i | \(0.159317\pi\) | ||||
−0.877338 | + | 0.479872i | \(0.840683\pi\) | |||||||
\(938\) | −1.47490e21 | + | 1.47490e21i | −2.30856 | + | 2.30856i | ||||
\(939\) | −6.97103e20 | − | 6.97103e20i | −1.08302 | − | 1.08302i | ||||
\(940\) | −3.65099e20 | + | 3.65099e20i | −0.563009 | + | 0.563009i | ||||
\(941\) | − | 2.91262e20i | − | 0.445817i | −0.974839 | − | 0.222908i | \(-0.928445\pi\) | ||
0.974839 | − | 0.222908i | \(-0.0715551\pi\) | |||||||
\(942\) | −2.14965e21 | − | 2.14965e21i | −3.26597 | − | 3.26597i | ||||
\(943\) | 2.00915e20 | − | 2.00915e20i | 0.302991 | − | 0.302991i | ||||
\(944\) | −8.72015e20 | −1.30533 | ||||||||
\(945\) | 2.38704e21 | + | 2.38704e21i | 3.54681 | + | 3.54681i | ||||
\(946\) | 8.10209e19 | − | 8.10209e19i | 0.119498 | − | 0.119498i | ||||
\(947\) | −4.45783e20 | − | 4.45783e20i | −0.652640 | − | 0.652640i | 0.300988 | − | 0.953628i | \(-0.402684\pi\) |
−0.953628 | + | 0.300988i | \(0.902684\pi\) | |||||||
\(948\) | 2.17744e21 | 3.16438 | ||||||||
\(949\) | −9.28655e20 | − | 9.28655e20i | −1.33965 | − | 1.33965i | ||||
\(950\) | − | 2.03814e19i | − | 0.0291856i | ||||||
\(951\) | 2.64227e21 | 3.75590 | ||||||||
\(952\) | 1.19983e21 | 1.69302 | ||||||||
\(953\) | 3.90772e20 | 0.547359 | 0.273680 | − | 0.961821i | \(-0.411759\pi\) | ||||
0.273680 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(954\) | −5.01835e20 | + | 5.01835e20i | −0.697786 | + | 0.697786i | ||||
\(955\) | −4.83643e19 | + | 4.83643e19i | −0.0667578 | + | 0.0667578i | ||||
\(956\) | 6.80767e20i | 0.932810i | ||||||||
\(957\) | −7.10542e19 | + | 2.61034e20i | −0.0966510 | + | 0.355069i | ||||
\(958\) | −4.96319e20 | −0.670197 | ||||||||
\(959\) | −7.13618e20 | − | 7.13618e20i | −0.956611 | − | 0.956611i | ||||
\(960\) | −8.91819e20 | − | 8.91819e20i | −1.18680 | − | 1.18680i | ||||
\(961\) | − | 5.65812e20i | − | 0.747495i | ||||||
\(962\) | − | 2.35215e21i | − | 3.08489i | ||||||
\(963\) | 2.40100e21i | 3.12614i | ||||||||
\(964\) | −1.09749e21 | −1.41860 | ||||||||
\(965\) | −3.03467e20 | + | 3.03467e20i | −0.389422 | + | 0.389422i | ||||
\(966\) | 3.02544e21i | 3.85433i | ||||||||
\(967\) | −4.08574e20 | + | 4.08574e20i | −0.516756 | + | 0.516756i | −0.916588 | − | 0.399832i | \(-0.869068\pi\) |
0.399832 | + | 0.916588i | \(0.369068\pi\) | |||||||
\(968\) | −9.83372e20 | − | 9.83372e20i | −1.23478 | − | 1.23478i | ||||
\(969\) | 2.83651e20 | − | 2.83651e20i | 0.353605 | − | 0.353605i | ||||
\(970\) | − | 6.43063e20i | − | 0.795887i | ||||||
\(971\) | −1.57578e20 | − | 1.57578e20i | −0.193625 | − | 0.193625i | 0.603636 | − | 0.797260i | \(-0.293718\pi\) |
−0.797260 | + | 0.603636i | \(0.793718\pi\) | |||||||
\(972\) | 5.29492e21 | − | 5.29492e21i | 6.45945 | − | 6.45945i | ||||
\(973\) | 1.15349e21 | 1.39708 | ||||||||
\(974\) | −1.21904e21 | − | 1.21904e21i | −1.46590 | − | 1.46590i | ||||
\(975\) | −7.98125e19 | + | 7.98125e19i | −0.0952881 | + | 0.0952881i | ||||
\(976\) | 3.93558e20 | + | 3.93558e20i | 0.466509 | + | 0.466509i | ||||
\(977\) | 7.88439e20 | 0.927910 | 0.463955 | − | 0.885859i | \(-0.346430\pi\) | ||||
0.463955 | + | 0.885859i | \(0.346430\pi\) | |||||||
\(978\) | −7.58132e20 | − | 7.58132e20i | −0.885876 | − | 0.885876i | ||||
\(979\) | − | 1.89968e20i | − | 0.220395i | ||||||
\(980\) | −1.88857e21 | −2.17546 | ||||||||
\(981\) | −1.56480e21 | −1.78969 | ||||||||
\(982\) | 7.03016e20 | 0.798335 | ||||||||
\(983\) | −9.82330e20 | + | 9.82330e20i | −1.10760 | + | 1.10760i | −0.114134 | + | 0.993465i | \(0.536409\pi\) |
−0.993465 | + | 0.114134i | \(0.963591\pi\) | |||||||
\(984\) | 1.22235e21 | − | 1.22235e21i | 1.36846 | − | 1.36846i | ||||
\(985\) | − | 2.93998e20i | − | 0.326807i | ||||||
\(986\) | 2.68283e20 | − | 9.85599e20i | 0.296111 | − | 1.08783i | ||||
\(987\) | −1.02839e21 | −1.12704 | ||||||||
\(988\) | −8.55435e20 | − | 8.55435e20i | −0.930869 | − | 0.930869i | ||||
\(989\) | −2.63665e20 | − | 2.63665e20i | −0.284891 | − | 0.284891i | ||||
\(990\) | − | 8.43267e20i | − | 0.904729i | ||||||
\(991\) | − | 6.01434e20i | − | 0.640727i | −0.947295 | − | 0.320363i | \(-0.896195\pi\) | ||
0.947295 | − | 0.320363i | \(-0.103805\pi\) | |||||||
\(992\) | 6.52160e19i | 0.0689878i | ||||||||
\(993\) | 2.01419e21 | 2.11570 | ||||||||
\(994\) | 2.57549e21 | − | 2.57549e21i | 2.68630 | − | 2.68630i | ||||
\(995\) | − | 4.29008e20i | − | 0.444328i | ||||||
\(996\) | 3.86313e21 | − | 3.86313e21i | 3.97305 | − | 3.97305i | ||||
\(997\) | −1.53152e20 | − | 1.53152e20i | −0.156407 | − | 0.156407i | 0.624565 | − | 0.780972i | \(-0.285276\pi\) |
−0.780972 | + | 0.624565i | \(0.785276\pi\) | |||||||
\(998\) | −2.06956e21 | + | 2.06956e21i | −2.09877 | + | 2.09877i | ||||
\(999\) | 3.81907e21i | 3.84591i |
(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 | 29.15.c.a.12.4 | ✓ | 68 | |
29.17 | odd | 4 | inner | 29.15.c.a.17.4 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.15.c.a.12.4 | ✓ | 68 | 1.1 | even | 1 | trivial | |
29.15.c.a.17.4 | yes | 68 | 29.17 | odd | 4 | inner |