Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,22,Mod(8,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.8");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(125.764804929\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Relative dimension: | \(42\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.13 | ||
Character | \(\chi\) | \(=\) | 45.17 |
Dual form | 45.22.f.a.8.13 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −957.532 | + | 957.532i | −0.661209 | + | 0.661209i | −0.955665 | − | 0.294456i | \(-0.904861\pi\) |
0.294456 | + | 0.955665i | \(0.404861\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 263415.i | 0.125606i | ||||||||
\(5\) | −1.22450e7 | − | 1.80803e7i | −0.560758 | − | 0.827980i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.88402e8 | − | 5.88402e8i | −0.787308 | − | 0.787308i | 0.193744 | − | 0.981052i | \(-0.437937\pi\) |
−0.981052 | + | 0.193744i | \(0.937937\pi\) | |||||||
\(8\) | −2.26032e9 | − | 2.26032e9i | −0.744261 | − | 0.744261i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.90375e10 | + | 5.58742e9i | 0.918245 | + | 0.176690i | ||||
\(11\) | − | 3.48289e10i | − | 0.404870i | −0.979296 | − | 0.202435i | \(-0.935114\pi\) | ||
0.979296 | − | 0.202435i | \(-0.0648856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.12201e11 | − | 2.12201e11i | 0.426915 | − | 0.426915i | −0.460661 | − | 0.887576i | \(-0.652388\pi\) |
0.887576 | + | 0.460661i | \(0.152388\pi\) | |||||||
\(14\) | 1.12683e12 | 1.04115 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77624e12 | 0.858617 | ||||||||
\(17\) | −1.02005e13 | + | 1.02005e13i | −1.22718 | + | 1.22718i | −0.262149 | + | 0.965028i | \(0.584431\pi\) |
−0.965028 | + | 0.262149i | \(0.915569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.75067e13i | 1.02926i | 0.857412 | + | 0.514630i | \(0.172071\pi\) | ||||
−0.857412 | + | 0.514630i | \(0.827929\pi\) | |||||||
\(20\) | 4.76262e12 | − | 3.22553e12i | 0.103999 | − | 0.0704347i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.33498e13 | + | 3.33498e13i | 0.267704 | + | 0.267704i | ||||
\(23\) | 2.25988e14 | + | 2.25988e14i | 1.13748 | + | 1.13748i | 0.988901 | + | 0.148579i | \(0.0474699\pi\) |
0.148579 | + | 0.988901i | \(0.452530\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76955e14 | + | 4.42787e14i | −0.371101 | + | 0.928592i | ||||
\(26\) | 4.06378e14i | 0.564560i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.54994e14 | − | 1.54994e14i | 0.0988907 | − | 0.0988907i | ||||
\(29\) | −1.56108e15 | −0.689044 | −0.344522 | − | 0.938778i | \(-0.611959\pi\) | ||||
−0.344522 | + | 0.938778i | \(0.611959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20472e15 | 0.921381 | 0.460690 | − | 0.887561i | \(-0.347602\pi\) | ||||
0.460690 | + | 0.887561i | \(0.347602\pi\) | |||||||
\(32\) | 1.12436e15 | − | 1.12436e15i | 0.176536 | − | 0.176536i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.95346e16i | − | 1.62284i | ||||||
\(35\) | −3.43346e15 | + | 1.78435e16i | −0.210386 | + | 1.09336i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.33190e16 | + | 1.33190e16i | 0.455359 | + | 0.455359i | 0.897129 | − | 0.441769i | \(-0.145649\pi\) |
−0.441769 | + | 0.897129i | \(0.645649\pi\) | |||||||
\(38\) | −2.63385e16 | − | 2.63385e16i | −0.680556 | − | 0.680556i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.31895e16 | + | 6.85449e16i | −0.198883 | + | 1.03358i | ||||
\(41\) | 1.01890e17i | 1.18550i | 0.805388 | + | 0.592748i | \(0.201957\pi\) | ||||
−0.805388 | + | 0.592748i | \(0.798043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.64240e16 | − | 7.64240e16i | 0.539276 | − | 0.539276i | −0.384040 | − | 0.923316i | \(-0.625468\pi\) |
0.923316 | + | 0.384040i | \(0.125468\pi\) | |||||||
\(44\) | 9.17446e15 | 0.0508542 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.32782e17 | −1.50422 | ||||||||
\(47\) | 3.70927e17 | − | 3.70927e17i | 1.02863 | − | 1.02863i | 0.0290553 | − | 0.999578i | \(-0.490750\pi\) |
0.999578 | − | 0.0290553i | \(-0.00924990\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.33887e17i | 0.239707i | ||||||||
\(50\) | −2.54543e17 | − | 5.93423e17i | −0.368618 | − | 0.859369i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.58969e16 | + | 5.58969e16i | 0.0536232 | + | 0.0536232i | ||||
\(53\) | −1.12846e18 | − | 1.12846e18i | −0.886319 | − | 0.886319i | 0.107849 | − | 0.994167i | \(-0.465604\pi\) |
−0.994167 | + | 0.107849i | \(0.965604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.29715e17 | + | 4.26481e17i | −0.335225 | + | 0.227034i | ||||
\(56\) | 2.65995e18i | 1.17192i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.49479e18 | − | 1.49479e18i | 0.455602 | − | 0.455602i | ||||
\(59\) | −2.19964e17 | −0.0560280 | −0.0280140 | − | 0.999608i | \(-0.508918\pi\) | ||||
−0.0280140 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.62431e17 | 0.118899 | 0.0594494 | − | 0.998231i | \(-0.481065\pi\) | ||||
0.0594494 | + | 0.998231i | \(0.481065\pi\) | |||||||
\(62\) | −4.02616e18 | + | 4.02616e18i | −0.609225 | + | 0.609225i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00726e19i | 1.09207i | ||||||||
\(65\) | −6.43505e18 | − | 1.23824e18i | −0.592873 | − | 0.114081i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.39064e19 | + | 1.39064e19i | 0.932028 | + | 0.932028i | 0.997833 | − | 0.0658047i | \(-0.0209614\pi\) |
−0.0658047 | + | 0.997833i | \(0.520961\pi\) | |||||||
\(68\) | −2.68696e18 | − | 2.68696e18i | −0.154141 | − | 0.154141i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.37980e19 | − | 2.03733e19i | −0.583833 | − | 0.862051i | ||||
\(71\) | − | 2.64738e19i | − | 0.965169i | −0.875849 | − | 0.482585i | \(-0.839698\pi\) | ||
0.875849 | − | 0.482585i | \(-0.160302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.31833e19 | + | 4.31833e19i | −1.17605 | + | 1.17605i | −0.195307 | + | 0.980742i | \(0.562570\pi\) |
−0.980742 | + | 0.195307i | \(0.937430\pi\) | |||||||
\(74\) | −2.55068e19 | −0.602175 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.24568e18 | −0.129281 | ||||||||
\(77\) | −2.04934e19 | + | 2.04934e19i | −0.318758 | + | 0.318758i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.25073e19i | 0.623929i | 0.950094 | + | 0.311965i | \(0.100987\pi\) | ||||
−0.950094 | + | 0.311965i | \(0.899013\pi\) | |||||||
\(80\) | −4.62402e19 | − | 6.82754e19i | −0.481476 | − | 0.710918i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.75627e19 | − | 9.75627e19i | −0.783860 | − | 0.783860i | ||||
\(83\) | −1.92753e20 | − | 1.92753e20i | −1.36358 | − | 1.36358i | −0.869302 | − | 0.494282i | \(-0.835431\pi\) |
−0.494282 | − | 0.869302i | \(-0.664569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.09333e20 | + | 5.95221e19i | 1.70423 | + | 0.327929i | ||||
\(86\) | 1.46357e20i | 0.713148i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.87244e19 | + | 7.87244e19i | −0.301329 | + | 0.301329i | ||||
\(89\) | −2.42769e20 | −0.825273 | −0.412637 | − | 0.910896i | \(-0.635392\pi\) | ||||
−0.412637 | + | 0.910896i | \(0.635392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.49718e20 | −0.672227 | ||||||||
\(92\) | −5.95288e19 | + | 5.95288e19i | −0.142874 | + | 0.142874i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.10349e20i | 1.36028i | ||||||||
\(95\) | 4.97328e20 | − | 3.36820e20i | 0.852207 | − | 0.577166i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.11344e19 | − | 5.11344e19i | −0.0704060 | − | 0.0704060i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.741433 | + | 0.671027i | \(0.765853\pi\) | |||||||
\(98\) | −1.28201e20 | − | 1.28201e20i | −0.158496 | − | 0.158496i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.16637e20 | − | 4.66126e19i | −0.116637 | − | 0.0466126i | ||||
\(101\) | 1.16354e21i | 1.04811i | 0.851685 | + | 0.524054i | \(0.175581\pi\) | ||||
−0.851685 | + | 0.524054i | \(0.824419\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.23972e21 | − | 1.23972e21i | 0.908934 | − | 0.908934i | −0.0872522 | − | 0.996186i | \(-0.527809\pi\) |
0.996186 | + | 0.0872522i | \(0.0278086\pi\) | |||||||
\(104\) | −9.59282e20 | −0.635472 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.16108e21 | 1.17208 | ||||||||
\(107\) | 1.00269e21 | − | 1.00269e21i | 0.492763 | − | 0.492763i | −0.416413 | − | 0.909176i | \(-0.636713\pi\) |
0.909176 | + | 0.416413i | \(0.136713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.69875e20i | 0.351948i | 0.984395 | + | 0.175974i | \(0.0563075\pi\) | ||||
−0.984395 | + | 0.175974i | \(0.943693\pi\) | |||||||
\(110\) | 1.94603e20 | − | 1.01134e21i | 0.0715364 | − | 0.371770i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.22194e21 | − | 2.22194e21i | −0.675996 | − | 0.675996i | ||||
\(113\) | −2.06353e21 | − | 2.06353e21i | −0.571857 | − | 0.571857i | 0.360790 | − | 0.932647i | \(-0.382507\pi\) |
−0.932647 | + | 0.360790i | \(0.882507\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.31869e21 | − | 6.85316e21i | 0.303960 | − | 1.57966i | ||||
\(116\) | − | 4.11213e20i | − | 0.0865482i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.10622e20 | − | 2.10622e20i | 0.0370462 | − | 0.0370462i | ||||
\(119\) | 1.20040e22 | 1.93233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.18720e21 | 0.836080 | ||||||||
\(122\) | −6.34299e20 | + | 6.34299e20i | −0.0786169 | + | 0.0786169i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.10759e21i | 0.115731i | ||||||||
\(125\) | 1.01725e22 | − | 2.22256e21i | 0.976954 | − | 0.213451i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.70704e21 | + | 1.70704e21i | 0.138773 | + | 0.138773i | 0.773081 | − | 0.634308i | \(-0.218715\pi\) |
−0.634308 | + | 0.773081i | \(0.718715\pi\) | |||||||
\(128\) | −7.28685e21 | − | 7.28685e21i | −0.545551 | − | 0.545551i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.34742e21 | − | 4.97612e21i | 0.467444 | − | 0.316581i | ||||
\(131\) | 1.49759e22i | 0.879112i | 0.898215 | + | 0.439556i | \(0.144864\pi\) | ||||
−0.898215 | + | 0.439556i | \(0.855136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.61850e22 | − | 1.61850e22i | 0.810345 | − | 0.810345i | ||||
\(134\) | −2.66316e22 | −1.23253 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.61127e22 | 1.82668 | ||||||||
\(137\) | 1.44342e22 | − | 1.44342e22i | 0.529452 | − | 0.529452i | −0.390957 | − | 0.920409i | \(-0.627856\pi\) |
0.920409 | + | 0.390957i | \(0.127856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.80685e22i | − | 1.82930i | −0.404245 | − | 0.914651i | \(-0.632466\pi\) | ||
0.404245 | − | 0.914651i | \(-0.367534\pi\) | |||||||
\(140\) | −4.70024e21 | − | 9.04425e20i | −0.137333 | − | 0.0264258i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.53495e22 | + | 2.53495e22i | 0.638178 | + | 0.638178i | ||||
\(143\) | −7.39071e21 | − | 7.39071e21i | −0.172845 | − | 0.172845i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.91155e22 | + | 2.82248e22i | 0.386387 | + | 0.570515i | ||||
\(146\) | − | 8.26988e22i | − | 1.55523i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.50843e21 | + | 3.50843e21i | −0.0571959 | + | 0.0571959i | ||||
\(149\) | −1.09487e23 | −1.66306 | −0.831530 | − | 0.555479i | \(-0.812535\pi\) | ||||
−0.831530 | + | 0.555479i | \(0.812535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.78084e22 | −0.235162 | −0.117581 | − | 0.993063i | \(-0.537514\pi\) | ||||
−0.117581 | + | 0.993063i | \(0.537514\pi\) | |||||||
\(152\) | 6.21739e22 | − | 6.21739e22i | 0.766038 | − | 0.766038i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.92461e22i | − | 0.421531i | ||||||
\(155\) | −5.14870e22 | − | 7.60225e22i | −0.516672 | − | 0.762885i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.95180e22 | + | 6.95180e22i | 0.609749 | + | 0.609749i | 0.942880 | − | 0.333131i | \(-0.108105\pi\) |
−0.333131 | + | 0.942880i | \(0.608105\pi\) | |||||||
\(158\) | −5.02775e22 | − | 5.02775e22i | −0.412547 | − | 0.412547i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.40967e22 | − | 6.56092e21i | −0.245162 | − | 0.0471742i | ||||
\(161\) | − | 2.65944e23i | − | 1.79109i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.58264e23 | − | 1.58264e23i | 0.936296 | − | 0.936296i | −0.0617927 | − | 0.998089i | \(-0.519682\pi\) |
0.998089 | + | 0.0617927i | \(0.0196818\pi\) | |||||||
\(164\) | −2.68393e22 | −0.148906 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.69135e23 | 1.80323 | ||||||||
\(167\) | −1.79270e23 | + | 1.79270e23i | −0.822211 | + | 0.822211i | −0.986425 | − | 0.164213i | \(-0.947491\pi\) |
0.164213 | + | 0.986425i | \(0.447491\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57006e23i | 0.635487i | ||||||||
\(170\) | −3.53190e23 | + | 2.39202e23i | −1.34368 | + | 0.910020i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.01313e22 | + | 2.01313e22i | 0.0677364 | + | 0.0677364i | ||||
\(173\) | −2.96424e23 | − | 2.96424e23i | −0.938488 | − | 0.938488i | 0.0597268 | − | 0.998215i | \(-0.480977\pi\) |
−0.998215 | + | 0.0597268i | \(0.980977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.64657e23 | − | 1.56416e23i | 1.02326 | − | 0.438917i | ||||
\(176\) | − | 1.31522e23i | − | 0.347629i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.32459e23 | − | 2.32459e23i | 0.545678 | − | 0.545678i | ||||
\(179\) | 5.09775e23 | 1.12829 | 0.564146 | − | 0.825675i | \(-0.309205\pi\) | ||||
0.564146 | + | 0.825675i | \(0.309205\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.38975e23 | −0.273723 | −0.136861 | − | 0.990590i | \(-0.543702\pi\) | ||||
−0.136861 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(182\) | 2.39113e23 | − | 2.39113e23i | 0.444482 | − | 0.444482i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.02161e24i | − | 1.69316i | ||||||
\(185\) | 7.77195e22 | − | 4.03903e23i | 0.121682 | − | 0.632375i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.55271e23 | + | 3.55271e23i | 0.496847 | + | 0.496847i | ||||
\(188\) | 9.77078e22 | + | 9.77078e22i | 0.129203 | + | 0.129203i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.53691e23 | + | 7.98724e23i | −0.181860 | + | 0.945114i | ||||
\(191\) | − | 4.98751e23i | − | 0.558513i | −0.960217 | − | 0.279256i | \(-0.909912\pi\) | ||
0.960217 | − | 0.279256i | \(-0.0900879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.03988e23 | − | 5.03988e23i | 0.505905 | − | 0.505905i | −0.407362 | − | 0.913267i | \(-0.633551\pi\) |
0.913267 | + | 0.407362i | \(0.133551\pi\) | |||||||
\(194\) | 9.79257e22 | 0.0931062 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.52679e22 | −0.0301086 | ||||||||
\(197\) | −2.10363e23 | + | 2.10363e23i | −0.170245 | + | 0.170245i | −0.787087 | − | 0.616842i | \(-0.788412\pi\) |
0.616842 | + | 0.787087i | \(0.288412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.67186e23i | 0.267257i | 0.991031 | + | 0.133628i | \(0.0426629\pi\) | ||||
−0.991031 | + | 0.133628i | \(0.957337\pi\) | |||||||
\(200\) | 1.40082e24 | − | 6.00866e23i | 0.967311 | − | 0.414918i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.11413e24 | − | 1.11413e24i | −0.693018 | − | 0.693018i | ||||
\(203\) | 9.18544e23 | + | 9.18544e23i | 0.542490 | + | 0.542490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.84219e24 | − | 1.24764e24i | 0.981566 | − | 0.664776i | ||||
\(206\) | 2.37414e24i | 1.20199i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.01320e23 | − | 8.01320e23i | 0.366556 | − | 0.366556i | ||||
\(209\) | 9.58026e23 | 0.416717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.46881e24 | −0.578094 | −0.289047 | − | 0.957315i | \(-0.593338\pi\) | ||||
−0.289047 | + | 0.957315i | \(0.593338\pi\) | |||||||
\(212\) | 2.97254e23 | − | 2.97254e23i | 0.111327 | − | 0.111327i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.92022e24i | 0.651638i | ||||||||
\(215\) | −2.31758e24 | − | 4.45951e23i | −0.748913 | − | 0.144106i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.47406e24 | − | 2.47406e24i | −0.725410 | − | 0.725410i | ||||
\(218\) | −8.32933e23 | − | 8.32933e23i | −0.232711 | − | 0.232711i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.12342e23 | − | 1.65877e23i | −0.0285169 | − | 0.0421063i | ||||
\(221\) | 4.32910e24i | 1.04780i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.64239e24 | + | 5.64239e24i | −1.24240 | + | 1.24240i | −0.283400 | + | 0.959002i | \(0.591462\pi\) |
−0.959002 | + | 0.283400i | \(0.908538\pi\) | |||||||
\(224\) | −1.32316e24 | −0.277976 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.95180e24 | 0.756233 | ||||||||
\(227\) | 2.09575e24 | − | 2.09575e24i | 0.382884 | − | 0.382884i | −0.489256 | − | 0.872140i | \(-0.662732\pi\) |
0.872140 | + | 0.489256i | \(0.162732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.07052e24i | 0.678231i | 0.940745 | + | 0.339115i | \(0.110128\pi\) | ||||
−0.940745 | + | 0.339115i | \(0.889872\pi\) | |||||||
\(230\) | 5.29944e24 | + | 7.82482e24i | 0.843504 | + | 1.24547i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.52855e24 | + | 3.52855e24i | 0.512828 | + | 0.512828i | ||||
\(233\) | 5.74900e23 | + | 5.74900e23i | 0.0798647 | + | 0.0798647i | 0.745911 | − | 0.666046i | \(-0.232015\pi\) |
−0.666046 | + | 0.745911i | \(0.732015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.12485e25 | − | 2.16444e24i | −1.42850 | − | 0.274874i | ||||
\(236\) | − | 5.79418e22i | − | 0.00703746i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.14942e25 | + | 1.14942e25i | −1.27767 | + | 1.27767i | ||||
\(239\) | −6.90560e24 | −0.734554 | −0.367277 | − | 0.930112i | \(-0.619710\pi\) | ||||
−0.367277 | + | 0.930112i | \(0.619710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.85129e25 | −1.80425 | −0.902124 | − | 0.431477i | \(-0.857993\pi\) | ||||
−0.902124 | + | 0.431477i | \(0.857993\pi\) | |||||||
\(242\) | −5.92444e24 | + | 5.92444e24i | −0.552823 | + | 0.552823i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.74495e23i | 0.0149344i | ||||||||
\(245\) | 2.42072e24 | − | 1.63945e24i | 0.198472 | − | 0.134417i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.83693e24 | + | 5.83693e24i | 0.439407 | + | 0.439407i | ||||
\(248\) | −9.50401e24 | − | 9.50401e24i | −0.685748 | − | 0.685748i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.61236e24 | + | 1.18687e25i | −0.504835 | + | 0.787106i | ||||
\(251\) | 5.46480e24i | 0.347536i | 0.984787 | + | 0.173768i | \(0.0555944\pi\) | ||||
−0.984787 | + | 0.173768i | \(0.944406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.87091e24 | − | 7.87091e24i | 0.460532 | − | 0.460532i | ||||
\(254\) | −3.26909e24 | −0.183516 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.16892e24 | −0.370625 | ||||||||
\(257\) | 1.12155e25 | − | 1.12155e25i | 0.556571 | − | 0.556571i | −0.371758 | − | 0.928330i | \(-0.621245\pi\) |
0.928330 | + | 0.371758i | \(0.121245\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.56739e25i | − | 0.717016i | ||||||
\(260\) | 3.26171e23 | − | 1.69509e24i | 0.0143293 | − | 0.0744685i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.43399e25 | − | 1.43399e25i | −0.581276 | − | 0.581276i | ||||
\(263\) | 1.82457e25 | + | 1.82457e25i | 0.710601 | + | 0.710601i | 0.966661 | − | 0.256060i | \(-0.0824243\pi\) |
−0.256060 | + | 0.966661i | \(0.582424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.58482e24 | + | 3.42209e25i | −0.236844 | + | 1.23086i | ||||
\(266\) | 3.09953e25i | 1.07161i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.66315e24 | + | 3.66315e24i | −0.117068 | + | 0.117068i | ||||
\(269\) | 1.47829e25 | 0.454320 | 0.227160 | − | 0.973857i | \(-0.427056\pi\) | ||||
0.227160 | + | 0.973857i | \(0.427056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.75015e24 | −0.277226 | −0.138613 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138613 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(272\) | −3.85194e25 | + | 3.85194e25i | −1.05367 | + | 1.05367i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.76424e25i | 0.700157i | ||||||||
\(275\) | 1.54218e25 | + | 6.16314e24i | 0.375960 | + | 0.150248i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.91878e24 | + | 9.91878e24i | 0.224089 | + | 0.224089i | 0.810218 | − | 0.586129i | \(-0.199349\pi\) |
−0.586129 | + | 0.810218i | \(0.699349\pi\) | |||||||
\(278\) | 5.56025e25 | + | 5.56025e25i | 1.20955 | + | 1.20955i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.80926e25 | − | 3.25712e25i | 0.970330 | − | 0.657166i | ||||
\(281\) | − | 4.45030e25i | − | 0.864914i | −0.901655 | − | 0.432457i | \(-0.857647\pi\) | ||
0.901655 | − | 0.432457i | \(-0.142353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09235e25 | − | 1.09235e25i | 0.197062 | − | 0.197062i | −0.601677 | − | 0.798739i | \(-0.705501\pi\) |
0.798739 | + | 0.601677i | \(0.205501\pi\) | |||||||
\(284\) | 6.97360e24 | 0.121231 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.41537e25 | 0.228574 | ||||||||
\(287\) | 5.99521e25 | − | 5.99521e25i | 0.933349 | − | 0.933349i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.39008e26i | − | 2.01192i | ||||||
\(290\) | −4.53299e25 | − | 8.72242e24i | −0.632712 | − | 0.121747i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.13751e25 | − | 1.13751e25i | −0.147719 | − | 0.147719i | ||||
\(293\) | −7.61675e25 | − | 7.61675e25i | −0.954245 | − | 0.954245i | 0.0447534 | − | 0.998998i | \(-0.485750\pi\) |
−0.998998 | + | 0.0447534i | \(0.985750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.69347e24 | + | 3.97700e24i | 0.0314181 | + | 0.0463901i | ||||
\(296\) | − | 6.02105e25i | − | 0.677812i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.04838e26 | − | 1.04838e26i | 1.09963 | − | 1.09963i | ||||
\(299\) | 9.59097e25 | 0.971214 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.99360e25 | −0.849152 | ||||||||
\(302\) | 1.70522e25 | − | 1.70522e25i | 0.155491 | − | 0.155491i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.03872e26i | 0.883740i | ||||||||
\(305\) | −8.11150e24 | − | 1.19769e25i | −0.0666734 | − | 0.0984458i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.57720e25 | + | 3.57720e25i | 0.274531 | + | 0.274531i | 0.830921 | − | 0.556390i | \(-0.187814\pi\) |
−0.556390 | + | 0.830921i | \(0.687814\pi\) | |||||||
\(308\) | −5.39826e24 | − | 5.39826e24i | −0.0400379 | − | 0.0400379i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.22094e26 | + | 2.34935e25i | 0.846054 | + | 0.162798i | ||||
\(311\) | 1.80776e25i | 0.121103i | 0.998165 | + | 0.0605517i | \(0.0192860\pi\) | ||||
−0.998165 | + | 0.0605517i | \(0.980714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.33865e26 | − | 1.33865e26i | 0.838402 | − | 0.838402i | −0.150246 | − | 0.988649i | \(-0.548007\pi\) |
0.988649 | + | 0.150246i | \(0.0480066\pi\) | |||||||
\(314\) | −1.33132e26 | −0.806343 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.38312e25 | −0.0783694 | ||||||||
\(317\) | −9.10856e25 | + | 9.10856e25i | −0.499261 | + | 0.499261i | −0.911208 | − | 0.411947i | \(-0.864849\pi\) |
0.411947 | + | 0.911208i | \(0.364849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.43707e25i | 0.278974i | ||||||||
\(320\) | 1.82115e26 | − | 1.23339e26i | 0.904213 | − | 0.612387i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.54650e26 | + | 2.54650e26i | 1.18429 | + | 1.18429i | ||||
\(323\) | −2.80581e26 | − | 2.80581e26i | −1.26308 | − | 1.26308i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.64098e25 | + | 1.31510e26i | 0.238001 | + | 0.554859i | ||||
\(326\) | 3.03087e26i | 1.23817i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.30303e26 | − | 2.30303e26i | 0.882317 | − | 0.882317i | ||||
\(329\) | −4.36508e26 | −1.61970 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.04213e25 | −0.210376 | −0.105188 | − | 0.994452i | \(-0.533544\pi\) | ||||
−0.105188 | + | 0.994452i | \(0.533544\pi\) | |||||||
\(332\) | 5.07742e25 | − | 5.07742e25i | 0.171275 | − | 0.171275i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 3.43313e26i | − | 1.08731i | ||||||
\(335\) | 8.11469e25 | − | 4.21715e26i | 0.249058 | − | 1.29434i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.35119e26 | − | 1.35119e26i | −0.389585 | − | 0.389585i | 0.484954 | − | 0.874539i | \(-0.338836\pi\) |
−0.874539 | + | 0.484954i | \(0.838836\pi\) | |||||||
\(338\) | −1.50339e26 | − | 1.50339e26i | −0.420190 | − | 0.420190i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.56790e25 | + | 8.14830e25i | −0.0411899 | + | 0.214061i | ||||
\(341\) | − | 1.46446e26i | − | 0.373040i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.49870e26 | + | 2.49870e26i | −0.598585 | + | 0.598585i | ||||
\(344\) | −3.45485e26 | −0.802724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.67670e26 | 1.24107 | ||||||||
\(347\) | 4.34175e26 | − | 4.34175e26i | 0.920885 | − | 0.920885i | −0.0762066 | − | 0.997092i | \(-0.524281\pi\) |
0.997092 | + | 0.0762066i | \(0.0242809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.59635e26i | − | 0.718116i | −0.933315 | − | 0.359058i | \(-0.883098\pi\) | ||
0.933315 | − | 0.359058i | \(-0.116902\pi\) | |||||||
\(350\) | −1.99398e26 | + | 4.98945e26i | −0.386372 | + | 0.966803i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.91603e25 | − | 3.91603e25i | −0.0714741 | − | 0.0714741i | ||||
\(353\) | −3.93232e26 | − | 3.93232e26i | −0.696649 | − | 0.696649i | 0.267037 | − | 0.963686i | \(-0.413955\pi\) |
−0.963686 | + | 0.267037i | \(0.913955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.78653e26 | + | 3.24173e26i | −0.799141 | + | 0.541226i | ||||
\(356\) | − | 6.39490e25i | − | 0.103659i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.88126e26 | + | 4.88126e26i | −0.746037 | + | 0.746037i | ||||
\(359\) | 1.61743e26 | 0.240068 | 0.120034 | − | 0.992770i | \(-0.461700\pi\) | ||||
0.120034 | + | 0.992770i | \(0.461700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.24076e25 | −0.0593769 | ||||||||
\(362\) | 1.33073e26 | − | 1.33073e26i | 0.180988 | − | 0.180988i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 6.57796e25i | − | 0.0844359i | ||||||
\(365\) | 1.30955e27 | + | 2.51984e26i | 1.63322 | + | 0.314266i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.02638e26 | + | 2.02638e26i | 0.238631 | + | 0.238631i | 0.816283 | − | 0.577652i | \(-0.196031\pi\) |
−0.577652 | + | 0.816283i | \(0.696031\pi\) | |||||||
\(368\) | 8.53385e26 | + | 8.53385e26i | 0.976659 | + | 0.976659i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.12332e26 | + | 4.61170e26i | 0.337674 | + | 0.498589i | ||||
\(371\) | 1.32798e27i | 1.39561i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.30798e27 | − | 1.30798e27i | 1.29914 | − | 1.29914i | 0.370188 | − | 0.928957i | \(-0.379293\pi\) |
0.928957 | − | 0.370188i | \(-0.120707\pi\) | |||||||
\(374\) | −6.80367e26 | −0.657040 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.67683e27 | −1.53114 | ||||||||
\(377\) | −3.31263e26 | + | 3.31263e26i | −0.294163 | + | 0.294163i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.16142e26i | − | 0.349567i | −0.984607 | − | 0.174783i | \(-0.944078\pi\) | ||
0.984607 | − | 0.174783i | \(-0.0559225\pi\) | |||||||
\(380\) | 8.87237e25 | + | 1.31004e26i | 0.0724956 | + | 0.107042i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.77570e26 | + | 4.77570e26i | 0.369293 | + | 0.369293i | ||||
\(383\) | 2.17485e26 | + | 2.17485e26i | 0.163622 | + | 0.163622i | 0.784169 | − | 0.620547i | \(-0.213089\pi\) |
−0.620547 | + | 0.784169i | \(0.713089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.21467e26 | + | 1.19583e26i | 0.442671 | + | 0.0851791i | ||||
\(386\) | 9.65170e26i | 0.669017i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.34696e25 | − | 1.34696e25i | 0.00884344 | − | 0.00884344i | ||||
\(389\) | 2.15040e27 | 1.37419 | 0.687096 | − | 0.726566i | \(-0.258885\pi\) | ||||
0.687096 | + | 0.726566i | \(0.258885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.61038e27 | −2.79178 | ||||||||
\(392\) | 3.02628e26 | − | 3.02628e26i | 0.178404 | − | 0.178404i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4.02859e26i | − | 0.225135i | ||||||
\(395\) | 9.49346e26 | − | 6.42954e26i | 0.516601 | − | 0.349873i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.03518e26 | − | 2.03518e26i | −0.105028 | − | 0.105028i | 0.652640 | − | 0.757668i | \(-0.273661\pi\) |
−0.757668 | + | 0.652640i | \(0.773661\pi\) | |||||||
\(398\) | −3.51593e26 | − | 3.51593e26i | −0.176713 | − | 0.176713i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.68224e26 | + | 1.67207e27i | −0.318634 | + | 0.797305i | ||||
\(401\) | 2.73487e27i | 1.27034i | 0.772372 | + | 0.635170i | \(0.219070\pi\) | ||||
−0.772372 | + | 0.635170i | \(0.780930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.92244e26 | − | 8.92244e26i | 0.393351 | − | 0.393351i | ||||
\(404\) | −3.06494e26 | −0.131649 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.75907e27 | −0.717398 | ||||||||
\(407\) | 4.63886e26 | − | 4.63886e26i | 0.184361 | − | 0.184361i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.40855e27i | − | 0.909203i | −0.890695 | − | 0.454601i | \(-0.849782\pi\) | ||
0.890695 | − | 0.454601i | \(-0.150218\pi\) | |||||||
\(410\) | −5.69300e26 | + | 2.95862e27i | −0.209465 | + | 1.08858i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.26561e26 | + | 3.26561e26i | 0.114168 | + | 0.114168i | ||||
\(413\) | 1.29427e26 | + | 1.29427e26i | 0.0441113 | + | 0.0441113i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.12476e27 | + | 5.84530e27i | −0.364380 | + | 1.89366i | ||||
\(416\) | − | 4.77182e26i | − | 0.150731i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.17341e26 | + | 9.17341e26i | −0.275537 | + | 0.275537i | ||||
\(419\) | −2.05719e27 | −0.602596 | −0.301298 | − | 0.953530i | \(-0.597420\pi\) | ||||
−0.301298 | + | 0.953530i | \(0.597420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.41737e27 | −0.952203 | −0.476101 | − | 0.879390i | \(-0.657950\pi\) | ||||
−0.476101 | + | 0.879390i | \(0.657950\pi\) | |||||||
\(422\) | 1.40643e27 | − | 1.40643e27i | 0.382241 | − | 0.382241i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.10137e27i | 1.31930i | ||||||||
\(425\) | −2.71162e27 | − | 6.32167e27i | −0.684139 | − | 1.59495i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.89776e26 | − | 3.89776e26i | −0.0936100 | − | 0.0936100i | ||||
\(428\) | 2.64124e26 | + | 2.64124e26i | 0.0618941 | + | 0.0618941i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.64617e27 | − | 1.79215e27i | 0.590472 | − | 0.399903i | ||||
\(431\) | 4.97365e27i | 1.08309i | 0.840672 | + | 0.541544i | \(0.182160\pi\) | ||||
−0.840672 | + | 0.541544i | \(0.817840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.60856e27 | + | 2.60856e27i | −0.541099 | + | 0.541099i | −0.923851 | − | 0.382752i | \(-0.874976\pi\) |
0.382752 | + | 0.923851i | \(0.374976\pi\) | |||||||
\(434\) | 4.73799e27 | 0.959295 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.29138e26 | −0.0442069 | ||||||||
\(437\) | −6.21618e27 | + | 6.21618e27i | −1.17076 | + | 1.17076i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.62149e27i | − | 0.829668i | −0.909897 | − | 0.414834i | \(-0.863840\pi\) | ||
0.909897 | − | 0.414834i | \(-0.136160\pi\) | |||||||
\(440\) | 2.38734e27 | + | 4.59374e26i | 0.418467 | + | 0.0805218i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.14525e27 | − | 4.14525e27i | −0.692814 | − | 0.692814i | ||||
\(443\) | −4.06230e27 | − | 4.06230e27i | −0.663029 | − | 0.663029i | 0.293064 | − | 0.956093i | \(-0.405325\pi\) |
−0.956093 | + | 0.293064i | \(0.905325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.97271e27 | + | 4.38932e27i | 0.462778 | + | 0.683310i | ||||
\(446\) | − | 1.08055e28i | − | 1.64297i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.92672e27 | − | 5.92672e27i | 0.859796 | − | 0.859796i | ||||
\(449\) | −1.25782e28 | −1.78251 | −0.891253 | − | 0.453506i | \(-0.850173\pi\) | ||||
−0.891253 | + | 0.453506i | \(0.850173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.54870e27 | 0.479972 | ||||||||
\(452\) | 5.43566e26 | − | 5.43566e26i | 0.0718288 | − | 0.0718288i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.01349e27i | 0.506332i | ||||||||
\(455\) | 3.05781e27 | + | 4.51497e27i | 0.376956 | + | 0.556590i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.08104e28 | + | 1.08104e28i | 1.27269 | + | 1.27269i | 0.944673 | + | 0.328014i | \(0.106379\pi\) |
0.328014 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(458\) | −3.89766e27 | − | 3.89766e27i | −0.448452 | − | 0.448452i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.80523e27 | + | 3.47364e26i | 0.198415 | + | 0.0381792i | ||||
\(461\) | 1.61624e28i | 1.73639i | 0.496227 | + | 0.868193i | \(0.334718\pi\) | ||||
−0.496227 | + | 0.868193i | \(0.665282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.49258e27 | − | 5.49258e27i | 0.563866 | − | 0.563866i | −0.366537 | − | 0.930403i | \(-0.619457\pi\) |
0.930403 | + | 0.366537i | \(0.119457\pi\) | |||||||
\(464\) | −5.89502e27 | −0.591625 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.10097e27 | −0.105614 | ||||||||
\(467\) | 1.43777e28 | − | 1.43777e28i | 1.34853 | − | 1.34853i | 0.461278 | − | 0.887256i | \(-0.347391\pi\) |
0.887256 | − | 0.461278i | \(-0.152609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.63651e28i | − | 1.46759i | ||||||
\(470\) | 1.28433e28 | − | 8.69825e27i | 1.12629 | − | 0.762789i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.97189e26 | + | 4.97189e26i | 0.0416994 | + | 0.0416994i | ||||
\(473\) | −2.66176e27 | − | 2.66176e27i | −0.218337 | − | 0.218337i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.21796e28 | − | 4.86744e27i | −0.955763 | − | 0.381960i | ||||
\(476\) | 3.16203e27i | 0.242713i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.61234e27 | − | 6.61234e27i | 0.485693 | − | 0.485693i | ||||
\(479\) | −5.27361e27 | −0.378953 | −0.189476 | − | 0.981885i | \(-0.560679\pi\) | ||||
−0.189476 | + | 0.981885i | \(0.560679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65261e27 | 0.388799 | ||||||||
\(482\) | 1.77267e28 | − | 1.77267e28i | 1.19298 | − | 1.19298i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.62980e27i | 0.105017i | ||||||||
\(485\) | −2.98381e26 | + | 1.55067e27i | −0.0188141 | + | 0.0977755i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.38865e27 | + | 4.38865e27i | 0.265019 | + | 0.265019i | 0.827089 | − | 0.562070i | \(-0.189995\pi\) |
−0.562070 | + | 0.827089i | \(0.689995\pi\) | |||||||
\(488\) | −1.49731e27 | − | 1.49731e27i | −0.0884917 | − | 0.0884917i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.48083e26 | + | 3.88774e27i | −0.0423537 | + | 0.220109i | ||||
\(491\) | − | 1.92483e28i | − | 1.06668i | −0.845900 | − | 0.533342i | \(-0.820936\pi\) | ||
0.845900 | − | 0.533342i | \(-0.179064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.59238e28 | − | 1.59238e28i | 0.845578 | − | 0.845578i | ||||
\(494\) | −1.11781e28 | −0.581079 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.58780e28 | 0.791113 | ||||||||
\(497\) | −1.55772e28 | + | 1.55772e28i | −0.759885 | + | 0.759885i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.33022e28i | − | 1.55746i | −0.627357 | − | 0.778732i | \(-0.715863\pi\) | ||
0.627357 | − | 0.778732i | \(-0.284137\pi\) | |||||||
\(500\) | 5.85456e26 | + | 2.67960e27i | 0.0268107 | + | 0.122711i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.23272e27 | − | 5.23272e27i | −0.229794 | − | 0.229794i | ||||
\(503\) | 1.18041e27 | + | 1.18041e27i | 0.0507655 | + | 0.0507655i | 0.732034 | − | 0.681268i | \(-0.238571\pi\) |
−0.681268 | + | 0.732034i | \(0.738571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.10371e28 | − | 1.42476e28i | 0.867813 | − | 0.587735i | ||||
\(506\) | 1.50733e28i | 0.609015i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.49661e26 | + | 4.49661e26i | −0.0174307 | + | 0.0174307i | ||||
\(509\) | 3.16476e28 | 1.20172 | 0.600861 | − | 0.799354i | \(-0.294825\pi\) | ||||
0.600861 | + | 0.799354i | \(0.294825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.08182e28 | 1.85182 | ||||||||
\(512\) | 2.21461e28 | − | 2.21461e28i | 0.790611 | − | 0.790611i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.14784e28i | 0.736020i | ||||||||
\(515\) | −3.75949e28 | − | 7.23404e27i | −1.26227 | − | 0.242887i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.29190e28 | − | 1.29190e28i | −0.416463 | − | 0.416463i | ||||
\(518\) | 1.50082e28 | + | 1.50082e28i | 0.474097 | + | 0.474097i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.17465e28 | + | 1.73441e28i | 0.356346 | + | 0.526158i | ||||
\(521\) | 3.01590e28i | 0.896646i | 0.893872 | + | 0.448323i | \(0.147979\pi\) | ||||
−0.893872 | + | 0.448323i | \(0.852021\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.41287e28 | + | 2.41287e28i | −0.689074 | + | 0.689074i | −0.962027 | − | 0.272953i | \(-0.911999\pi\) |
0.272953 | + | 0.962027i | \(0.411999\pi\) | |||||||
\(524\) | −3.94488e27 | −0.110422 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.49418e28 | −0.939712 | ||||||||
\(527\) | −4.28902e28 | + | 4.28902e28i | −1.13070 | + | 1.13070i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.26698e28i | 1.58772i | ||||||||
\(530\) | −2.64625e28 | − | 3.90728e28i | −0.657255 | − | 0.970461i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.26337e27 | + | 4.26337e27i | 0.101784 | + | 0.101784i | ||||
\(533\) | 2.16211e28 | + | 2.16211e28i | 0.506106 | + | 0.506106i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.04069e28 | − | 5.85093e27i | −0.684318 | − | 0.131677i | ||||
\(536\) | − | 6.28658e28i | − | 1.38734i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.41551e28 | + | 1.41551e28i | −0.300400 | + | 0.300400i | ||||
\(539\) | 4.66314e27 | 0.0970501 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.86087e28 | −1.37344 | −0.686718 | − | 0.726924i | \(-0.740949\pi\) | ||||
−0.686718 | + | 0.726924i | \(0.740949\pi\) | |||||||
\(542\) | 9.33608e27 | − | 9.33608e27i | 0.183304 | − | 0.183304i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.29381e28i | 0.433281i | ||||||||
\(545\) | 1.57276e28 | − | 1.06517e28i | 0.291406 | − | 0.197358i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.14447e28 | − | 5.14447e28i | −0.917221 | − | 0.917221i | 0.0796058 | − | 0.996826i | \(-0.474634\pi\) |
−0.996826 | + | 0.0796058i | \(0.974634\pi\) | |||||||
\(548\) | 3.80219e27 | + | 3.80219e27i | 0.0665025 | + | 0.0665025i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.06683e28 | + | 8.86545e27i | −0.347933 | + | 0.149242i | ||||
\(551\) | − | 4.29402e28i | − | 0.709206i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.08954e28 | − | 3.08954e28i | 0.491224 | − | 0.491224i | ||||
\(554\) | −1.89951e28 | −0.296339 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.52961e28 | 0.229772 | ||||||||
\(557\) | −2.66199e28 | + | 2.66199e28i | −0.392399 | + | 0.392399i | −0.875542 | − | 0.483143i | \(-0.839495\pi\) |
0.483143 | + | 0.875542i | \(0.339495\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.24344e28i | − | 0.460450i | ||||||
\(560\) | −1.29655e28 | + | 6.73811e28i | −0.180641 | + | 0.938781i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.26131e28 | + | 4.26131e28i | 0.571889 | + | 0.571889i | ||||
\(563\) | −3.42007e28 | − | 3.42007e28i | −0.450502 | − | 0.450502i | 0.445019 | − | 0.895521i | \(-0.353197\pi\) |
−0.895521 | + | 0.445019i | \(0.853197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.20412e28 | + | 6.25772e28i | −0.152813 | + | 0.794159i | ||||
\(566\) | 2.09192e28i | 0.260598i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.98392e28 | + | 5.98392e28i | −0.718337 | + | 0.718337i | ||||
\(569\) | −2.93564e28 | −0.345958 | −0.172979 | − | 0.984925i | \(-0.555339\pi\) | ||||
−0.172979 | + | 0.984925i | \(0.555339\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.85441e28 | −0.778558 | −0.389279 | − | 0.921120i | \(-0.627276\pi\) | ||||
−0.389279 | + | 0.921120i | \(0.627276\pi\) | |||||||
\(572\) | 1.94682e27 | − | 1.94682e27i | 0.0217104 | − | 0.0217104i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.14812e29i | 1.23428i | ||||||||
\(575\) | −1.40054e29 | + | 6.00750e28i | −1.47838 | + | 0.634134i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.29375e29 | − | 1.29375e29i | −1.31675 | − | 1.31675i | −0.916332 | − | 0.400420i | \(-0.868864\pi\) |
−0.400420 | − | 0.916332i | \(-0.631136\pi\) | |||||||
\(578\) | 1.33104e29 | + | 1.33104e29i | 1.33030 | + | 1.33030i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.43484e27 | + | 5.03532e27i | −0.0716602 | + | 0.0485326i | ||||
\(581\) | 2.26833e29i | 2.14712i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.93030e28 | + | 3.93030e28i | −0.358844 | + | 0.358844i | ||||
\(584\) | 1.95216e29 | 1.75057 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.45866e29 | 1.26191 | ||||||||
\(587\) | 9.51184e28 | − | 9.51184e28i | 0.808285 | − | 0.808285i | −0.176089 | − | 0.984374i | \(-0.556345\pi\) |
0.984374 | + | 0.176089i | \(0.0563447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15658e29i | 0.948341i | ||||||||
\(590\) | −6.38719e27 | − | 1.22903e27i | −0.0514474 | − | 0.00989956i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.02958e28 | + | 5.02958e28i | 0.390979 | + | 0.390979i | ||||
\(593\) | 9.87168e28 | + | 9.87168e28i | 0.753905 | + | 0.753905i | 0.975206 | − | 0.221301i | \(-0.0710302\pi\) |
−0.221301 | + | 0.975206i | \(0.571030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46989e29 | − | 2.17035e29i | −1.08357 | − | 1.59993i | ||||
\(596\) | − | 2.88406e28i | − | 0.208891i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.18366e28 | + | 9.18366e28i | −0.642175 | + | 0.642175i | ||||
\(599\) | 1.67174e27 | 0.0114865 | 0.00574323 | − | 0.999984i | \(-0.498172\pi\) | ||||
0.00574323 | + | 0.999984i | \(0.498172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.32045e29 | 1.53954 | 0.769769 | − | 0.638322i | \(-0.220371\pi\) | ||||
0.769769 | + | 0.638322i | \(0.220371\pi\) | |||||||
\(602\) | 8.61167e28 | − | 8.61167e28i | 0.561467 | − | 0.561467i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.69102e27i | − | 0.0295379i | ||||||
\(605\) | −7.57625e28 | − | 1.11866e29i | −0.468838 | − | 0.692257i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.00869e29 | − | 2.00869e29i | −1.20069 | − | 1.20069i | −0.973956 | − | 0.226736i | \(-0.927194\pi\) |
−0.226736 | − | 0.973956i | \(-0.572806\pi\) | |||||||
\(608\) | 3.09275e28 | + | 3.09275e28i | 0.181701 | + | 0.181701i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.92353e28 | + | 3.70128e27i | 0.109178 | + | 0.0210082i | ||||
\(611\) | − | 1.57422e29i | − | 0.878278i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.87544e28 | − | 2.87544e28i | 0.155014 | − | 0.155014i | −0.625339 | − | 0.780353i | \(-0.715039\pi\) |
0.780353 | + | 0.625339i | \(0.215039\pi\) | |||||||
\(614\) | −6.85058e28 | −0.363044 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.26431e28 | 0.474477 | ||||||||
\(617\) | 6.49326e27 | − | 6.49326e27i | 0.0326940 | − | 0.0326940i | −0.690571 | − | 0.723265i | \(-0.742641\pi\) |
0.723265 | + | 0.690571i | \(0.242641\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.93542e28i | − | 0.386205i | −0.981179 | − | 0.193103i | \(-0.938145\pi\) | ||
0.981179 | − | 0.193103i | \(-0.0618550\pi\) | |||||||
\(620\) | 2.00255e28 | − | 1.35625e28i | 0.0958231 | − | 0.0648972i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.73099e28 | − | 1.73099e28i | −0.0800746 | − | 0.0800746i | ||||
\(623\) | 1.42846e29 | + | 1.42846e29i | 0.649744 | + | 0.649744i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.64748e29 | − | 1.56707e29i | −0.724567 | − | 0.689204i | ||||
\(626\) | 2.56361e29i | 1.10872i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.83121e28 | + | 1.83121e28i | −0.0765883 | + | 0.0765883i | ||||
\(629\) | −2.71721e29 | −1.11761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.23522e29 | 1.68487 | 0.842437 | − | 0.538795i | \(-0.181120\pi\) | ||||
0.842437 | + | 0.538795i | \(0.181120\pi\) | |||||||
\(632\) | 1.18683e29 | − | 1.18683e29i | 0.464366 | − | 0.464366i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.74435e29i | − | 0.660231i | ||||||
\(635\) | 9.96096e27 | − | 5.17665e28i | 0.0370832 | − | 0.192719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.84109e28 | + | 2.84109e28i | 0.102334 | + | 0.102334i | ||||
\(638\) | −5.20618e28 | − | 5.20618e28i | −0.184460 | − | 0.184460i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.25204e28 | + | 2.20976e29i | −0.145783 | + | 0.757627i | ||||
\(641\) | − | 4.02891e29i | − | 1.35887i | −0.733735 | − | 0.679435i | \(-0.762225\pi\) | ||
0.733735 | − | 0.679435i | \(-0.237775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.02727e29 | + | 2.02727e29i | −0.661753 | + | 0.661753i | −0.955793 | − | 0.294040i | \(-0.905000\pi\) |
0.294040 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(644\) | 7.00536e28 | 0.224972 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.37331e29 | 1.67032 | ||||||||
\(647\) | 5.94615e28 | − | 5.94615e28i | 0.181861 | − | 0.181861i | −0.610305 | − | 0.792167i | \(-0.708953\pi\) |
0.792167 | + | 0.610305i | \(0.208953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.66109e27i | 0.0226841i | ||||||||
\(650\) | −1.79939e29 | − | 7.19106e28i | −0.524246 | − | 0.209509i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.16893e28 | + | 4.16893e28i | 0.117605 | + | 0.117605i | ||||
\(653\) | −1.91098e29 | − | 1.91098e29i | −0.530478 | − | 0.530478i | 0.390237 | − | 0.920715i | \(-0.372393\pi\) |
−0.920715 | + | 0.390237i | \(0.872393\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.70768e29 | − | 1.83380e29i | 0.727887 | − | 0.492969i | ||||
\(656\) | 3.84760e29i | 1.01789i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.17970e29 | − | 4.17970e29i | 1.07096 | − | 1.07096i | ||||
\(659\) | −3.55396e29 | −0.896222 | −0.448111 | − | 0.893978i | \(-0.647903\pi\) | ||||
−0.448111 | + | 0.893978i | \(0.647903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.11569e29 | −1.00537 | −0.502687 | − | 0.864469i | \(-0.667655\pi\) | ||||
−0.502687 | + | 0.864469i | \(0.667655\pi\) | |||||||
\(662\) | 5.78554e28 | − | 5.78554e28i | 0.139102 | − | 0.139102i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.71368e29i | 2.02972i | ||||||||
\(665\) | −4.90814e29 | − | 9.44429e28i | −1.12536 | − | 0.216542i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.52786e29 | − | 3.52786e29i | −0.783774 | − | 0.783774i | ||||
\(668\) | −4.72223e28 | − | 4.72223e28i | −0.103275 | − | 0.103275i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.26105e29 | + | 4.81507e29i | 0.691151 | + | 1.02051i | ||||
\(671\) | − | 2.30717e28i | − | 0.0481386i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.66598e29 | − | 6.66598e29i | 1.34805 | − | 1.34805i | 0.460270 | − | 0.887779i | \(-0.347753\pi\) |
0.887779 | − | 0.460270i | \(-0.152247\pi\) | |||||||
\(674\) | 2.58762e29 | 0.515194 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.13579e28 | −0.0798211 | ||||||||
\(677\) | 2.70711e29 | − | 2.70711e29i | 0.514429 | − | 0.514429i | −0.401452 | − | 0.915880i | \(-0.631494\pi\) |
0.915880 | + | 0.401452i | \(0.131494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.01751e28i | 0.110862i | ||||||||
\(680\) | −5.64652e29 | − | 8.33730e29i | −1.02432 | − | 1.51245i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.40226e29 | + | 1.40226e29i | 0.246657 | + | 0.246657i | ||||
\(683\) | −8.65592e28 | − | 8.65592e28i | −0.149933 | − | 0.149933i | 0.628155 | − | 0.778088i | \(-0.283810\pi\) |
−0.778088 | + | 0.628155i | \(0.783810\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.37722e29 | − | 8.42268e28i | −0.735270 | − | 0.141481i | ||||
\(686\) | − | 4.78517e29i | − | 0.791579i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.88595e29 | − | 2.88595e29i | 0.463031 | − | 0.463031i | ||||
\(689\) | −4.78920e29 | −0.756766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.19365e29 | 1.25591 | 0.627954 | − | 0.778251i | \(-0.283893\pi\) | ||||
0.627954 | + | 0.778251i | \(0.283893\pi\) | |||||||
\(692\) | 7.80825e28 | − | 7.80825e28i | 0.117880 | − | 0.117880i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.31474e29i | 1.21779i | ||||||||
\(695\) | −1.04989e30 | + | 7.11051e29i | −1.51462 | + | 1.02579i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.03932e30 | − | 1.03932e30i | −1.45481 | − | 1.45481i | ||||
\(698\) | 3.44362e29 | + | 3.44362e29i | 0.474825 | + | 0.474825i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.12024e28 | + | 9.60563e28i | 0.0551307 | + | 0.128528i | ||||
\(701\) | 1.26986e29i | 0.167385i | 0.996492 | + | 0.0836923i | \(0.0266713\pi\) | ||||
−0.996492 | + | 0.0836923i | \(0.973329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.66362e29 | + | 3.66362e29i | −0.468683 | + | 0.468683i | ||||
\(704\) | 3.50816e29 | 0.442147 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.53064e29 | 0.921261 | ||||||||
\(707\) | 6.84628e29 | − | 6.84628e29i | 0.825184 | − | 0.825184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.16150e30i | − | 1.35904i | −0.733656 | − | 0.679521i | \(-0.762188\pi\) | ||
0.733656 | − | 0.679521i | \(-0.237812\pi\) | |||||||
\(710\) | 1.47920e29 | − | 7.68732e29i | 0.170535 | − | 0.886262i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.48735e29 | + | 5.48735e29i | 0.614218 | + | 0.614218i | ||||
\(713\) | 9.50217e29 | + | 9.50217e29i | 1.04805 | + | 1.04805i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.31264e28 | + | 2.24125e29i | −0.0461881 | + | 0.240037i | ||||
\(716\) | 1.34283e29i | 0.141721i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.54874e29 | + | 1.54874e29i | −0.158735 | + | 0.158735i | ||||
\(719\) | −8.03314e28 | −0.0811394 | −0.0405697 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405697 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45891e30 | −1.43122 | ||||||||
\(722\) | 4.06066e28 | − | 4.06066e28i | 0.0392605 | − | 0.0392605i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.66081e28i | − | 0.0343813i | ||||||
\(725\) | 2.76241e29 | − | 6.91228e29i | 0.255705 | − | 0.639841i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.69987e27 | − | 8.69987e27i | −0.00782351 | − | 0.00782351i | 0.703184 | − | 0.711008i | \(-0.251761\pi\) |
−0.711008 | + | 0.703184i | \(0.751761\pi\) | |||||||
\(728\) | 5.64443e29 | + | 5.64443e29i | 0.500312 | + | 0.500312i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.49522e30 | + | 1.01265e30i | −1.28770 | + | 0.872106i | ||||
\(731\) | 1.55912e30i | 1.32357i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.17633e30 | − | 1.17633e30i | 0.970367 | − | 0.970367i | −0.0292068 | − | 0.999573i | \(-0.509298\pi\) |
0.999573 | + | 0.0292068i | \(0.00929812\pi\) | |||||||
\(734\) | −3.88065e29 | −0.315570 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.08186e29 | 0.401611 | ||||||||
\(737\) | 4.84344e29 | − | 4.84344e29i | 0.377351 | − | 0.377351i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.34493e29i | − | 0.329015i | −0.986376 | − | 0.164508i | \(-0.947396\pi\) | ||
0.986376 | − | 0.164508i | \(-0.0526035\pi\) | |||||||
\(740\) | 1.06394e29 | + | 2.04725e28i | 0.0794302 | + | 0.0152840i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.27158e30 | − | 1.27158e30i | −0.922790 | − | 0.922790i | ||||
\(743\) | 1.46973e30 | + | 1.46973e30i | 1.05161 | + | 1.05161i | 0.998594 | + | 0.0530156i | \(0.0168833\pi\) |
0.0530156 | + | 0.998594i | \(0.483117\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.34068e30 | + | 1.97956e30i | 0.932574 | + | 1.37698i | ||||
\(746\) | 2.50486e30i | 1.71801i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.35838e28 | + | 9.35838e28i | −0.0624071 | + | 0.0624071i | ||||
\(749\) | −1.17997e30 | −0.775912 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.07677e30 | −0.688497 | −0.344249 | − | 0.938878i | \(-0.611866\pi\) | ||||
−0.344249 | + | 0.938878i | \(0.611866\pi\) | |||||||
\(752\) | 1.40071e30 | − | 1.40071e30i | 0.883202 | − | 0.883202i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 6.34390e29i | − | 0.389007i | ||||||
\(755\) | 2.18065e29 | + | 3.21981e29i | 0.131869 | + | 0.194710i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.35044e29 | + | 5.35044e29i | 0.314690 | + | 0.314690i | 0.846723 | − | 0.532033i | \(-0.178572\pi\) |
−0.532033 | + | 0.846723i | \(0.678572\pi\) | |||||||
\(758\) | 3.98469e29 | + | 3.98469e29i | 0.231136 | + | 0.231136i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.88544e30 | − | 3.62798e29i | −1.06383 | − | 0.204702i | ||||
\(761\) | 3.47174e30i | 1.93201i | 0.258532 | + | 0.966003i | \(0.416761\pi\) | ||||
−0.258532 | + | 0.966003i | \(0.583239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.11836e29 | − | 5.11836e29i | 0.277091 | − | 0.277091i | ||||
\(764\) | 1.31379e29 | 0.0701527 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.16498e29 | −0.216377 | ||||||||
\(767\) | −4.66765e28 | + | 4.66765e28i | −0.0239192 | + | 0.0239192i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.23557e29i | − | 0.0616084i | −0.999525 | − | 0.0308042i | \(-0.990193\pi\) | ||
0.999525 | − | 0.0308042i | \(-0.00980683\pi\) | |||||||
\(770\) | −7.09580e29 | + | 4.80570e29i | −0.349019 | + | 0.236377i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.32758e29 | + | 1.32758e29i | 0.0635447 | + | 0.0635447i | ||||
\(773\) | −2.03622e30 | − | 2.03622e30i | −0.961480 | − | 0.961480i | 0.0378049 | − | 0.999285i | \(-0.487963\pi\) |
−0.999285 | + | 0.0378049i | \(0.987963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.44046e29 | + | 1.86180e30i | −0.341926 | + | 0.855587i | ||||
\(776\) | 2.31160e29i | 0.104801i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.05907e30 | + | 2.05907e30i | −0.908628 | + | 0.908628i | ||||
\(779\) | −2.80265e30 | −1.22018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.22052e29 | −0.390768 | ||||||||
\(782\) | 4.41459e30 | − | 4.41459e30i | 1.84595 | − | 1.84595i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.05590e29i | 0.205816i | ||||||||
\(785\) | 4.05653e29 | − | 2.10816e30i | 0.162938 | − | 0.846782i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.05416e30 | − | 3.05416e30i | −1.19442 | − | 1.19442i | −0.975813 | − | 0.218608i | \(-0.929848\pi\) |
−0.218608 | − | 0.975813i | \(-0.570152\pi\) | |||||||
\(788\) | −5.54128e28 | − | 5.54128e28i | −0.0213838 | − | 0.0213838i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.93380e29 | + | 1.52468e30i | −0.110242 | + | 0.572920i | ||||
\(791\) | 2.42837e30i | 0.900455i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.40568e29 | − | 1.40568e29i | 0.0507597 | − | 0.0507597i | ||||
\(794\) | 3.89751e29 | 0.138890 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.67225e28 | −0.0335691 | ||||||||
\(797\) | 1.55837e30 | − | 1.55837e30i | 0.533776 | − | 0.533776i | −0.387918 | − | 0.921694i | \(-0.626806\pi\) |
0.921694 | + | 0.387918i | \(0.126806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.56726e30i | 2.52463i | ||||||||
\(800\) | 2.98893e29 | + | 6.96816e29i | 0.0984170 | + | 0.229442i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.61872e30 | − | 2.61872e30i | −0.839960 | − | 0.839960i | ||||
\(803\) | 1.50402e30 | + | 1.50402e30i | 0.476148 | + | 0.476148i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.80833e30 | + | 3.25649e30i | −1.48299 | + | 1.00437i | ||||
\(806\) | 1.70871e30i | 0.520175i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.62997e30 | − | 2.62997e30i | 0.780066 | − | 0.780066i | ||||
\(809\) | −6.12048e30 | −1.79195 | −0.895975 | − | 0.444105i | \(-0.853522\pi\) | ||||
−0.895975 | + | 0.444105i | \(0.853522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.15917e30 | 1.18656 | 0.593278 | − | 0.804998i | \(-0.297834\pi\) | ||||
0.593278 | + | 0.804998i | \(0.297834\pi\) | |||||||
\(812\) | −2.41959e29 | + | 2.41959e29i | −0.0681401 | + | 0.0681401i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.88372e29i | 0.243803i | ||||||||
\(815\) | −4.79942e30 | − | 9.23508e29i | −1.30027 | − | 0.250199i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10217e30 | + | 2.10217e30i | 0.555055 | + | 0.555055i | ||||
\(818\) | 2.30626e30 | + | 2.30626e30i | 0.601173 | + | 0.601173i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.28648e29 | + | 4.85262e29i | 0.0834999 | + | 0.123291i | ||||
\(821\) | 3.76196e30i | 0.943650i | 0.881692 | + | 0.471825i | \(0.156405\pi\) | ||||
−0.881692 | + | 0.471825i | \(0.843595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00221e30 | − | 4.00221e30i | 0.978592 | − | 0.978592i | −0.0211840 | − | 0.999776i | \(-0.506744\pi\) |
0.999776 | + | 0.0211840i | \(0.00674357\pi\) | |||||||
\(824\) | −5.60432e30 | −1.35297 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.47861e29 | −0.0583335 | ||||||||
\(827\) | −1.09772e30 | + | 1.09772e30i | −0.255083 | + | 0.255083i | −0.823051 | − | 0.567968i | \(-0.807730\pi\) |
0.567968 | + | 0.823051i | \(0.307730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.60657e30i | − | 1.72332i | −0.507484 | − | 0.861661i | \(-0.669424\pi\) | ||
0.507484 | − | 0.861661i | \(-0.330576\pi\) | |||||||
\(830\) | −4.52007e30 | − | 6.67406e30i | −1.01117 | − | 1.49304i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.13741e30 | + | 2.13741e30i | 0.466221 | + | 0.466221i | ||||
\(833\) | −1.36571e30 | − | 1.36571e30i | −0.294162 | − | 0.294162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.43640e30 | + | 1.04608e30i | 1.14184 | + | 0.219713i | ||||
\(836\) | 2.52359e29i | 0.0523423i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.96982e30 | − | 1.96982e30i | 0.398442 | − | 0.398442i | ||||
\(839\) | 7.81664e30 | 1.56142 | 0.780710 | − | 0.624894i | \(-0.214858\pi\) | ||||
0.780710 | + | 0.624894i | \(0.214858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.69586e30 | −0.525218 | ||||||||
\(842\) | 3.27224e30 | − | 3.27224e30i | 0.629605 | − | 0.629605i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 3.86906e29i | − | 0.0726122i | ||||||
\(845\) | 2.83872e30 | − | 1.92255e30i | 0.526171 | − | 0.356354i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.64056e30 | − | 3.64056e30i | −0.658252 | − | 0.658252i | ||||
\(848\) | −4.26134e30 | − | 4.26134e30i | −0.761008 | − | 0.761008i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.64966e30 | + | 3.45674e30i | 1.50696 | + | 0.602238i | ||||
\(851\) | 6.01988e30i | 1.03592i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.14777e30 | − | 4.14777e30i | 0.696385 | − | 0.696385i | −0.267244 | − | 0.963629i | \(-0.586113\pi\) |
0.963629 | + | 0.267244i | \(0.0861129\pi\) | |||||||
\(854\) | 7.46446e29 | 0.123791 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.53281e30 | −0.733488 | ||||||||
\(857\) | 4.90754e30 | − | 4.90754e30i | 0.784449 | − | 0.784449i | −0.196129 | − | 0.980578i | \(-0.562837\pi\) |
0.980578 | + | 0.196129i | \(0.0628371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.45720e30i | 0.383276i | 0.981466 | + | 0.191638i | \(0.0613800\pi\) | ||||
−0.981466 | + | 0.191638i | \(0.938620\pi\) | |||||||
\(860\) | 1.17470e29 | − | 6.10487e29i | 0.0181007 | − | 0.0940681i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.76243e30 | − | 4.76243e30i | −0.716148 | − | 0.716148i | ||||
\(863\) | 1.80803e30 | + | 1.80803e30i | 0.268592 | + | 0.268592i | 0.828533 | − | 0.559941i | \(-0.189176\pi\) |
−0.559941 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.72970e30 | + | 8.98914e30i | −0.250785 | + | 1.30331i | ||||
\(866\) | − | 4.99555e30i | − | 0.715559i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.51706e29 | − | 6.51706e29i | 0.0911160 | − | 0.0911160i | ||||
\(869\) | 1.82877e30 | 0.252611 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.90189e30 | 0.795793 | ||||||||
\(872\) | 1.96620e30 | − | 1.96620e30i | 0.261941 | − | 0.261941i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.19044e31i | − | 1.54824i | ||||||
\(875\) | −7.29329e30 | − | 4.67778e30i | −0.937215 | − | 0.601112i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.99001e30 | + | 1.99001e30i | 0.249666 | + | 0.249666i | 0.820834 | − | 0.571167i | \(-0.193509\pi\) |
−0.571167 | + | 0.820834i | \(0.693509\pi\) | |||||||
\(878\) | 4.42522e30 | + | 4.42522e30i | 0.548583 | + | 0.548583i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.37795e30 | + | 1.61049e30i | −0.287830 | + | 0.194935i | ||||
\(881\) | − | 3.09947e30i | − | 0.370715i | −0.982671 | − | 0.185358i | \(-0.940656\pi\) | ||
0.982671 | − | 0.185358i | \(-0.0593444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.11836e30 | − | 6.11836e30i | 0.714575 | − | 0.714575i | −0.252914 | − | 0.967489i | \(-0.581389\pi\) |
0.967489 | + | 0.252914i | \(0.0813890\pi\) | |||||||
\(884\) | −1.14035e30 | −0.131610 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.77956e30 | 0.876801 | ||||||||
\(887\) | 1.06912e31 | − | 1.06912e31i | 1.19077 | − | 1.19077i | 0.213917 | − | 0.976852i | \(-0.431378\pi\) |
0.976852 | − | 0.213917i | \(-0.0686224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.00885e30i | − | 0.218514i | ||||||
\(890\) | −7.04939e30 | − | 1.35645e30i | −0.757803 | − | 0.145817i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.48629e30 | − | 1.48629e30i | −0.156053 | − | 0.156053i | ||||
\(893\) | 1.02030e31 | + | 1.02030e31i | 1.05873 | + | 1.05873i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.24222e30 | − | 9.21687e30i | −0.632699 | − | 0.934204i | ||||
\(896\) | 8.57519e30i | 0.859033i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.20440e31 | − | 1.20440e31i | 1.17861 | − | 1.17861i | ||||
\(899\) | −6.56392e30 | −0.634872 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.30217e31 | 2.17534 | ||||||||
\(902\) | −3.39800e30 | + | 3.39800e30i | −0.317362 | + | 0.317362i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.32848e30i | 0.851221i | ||||||||
\(905\) | 1.70175e30 | + | 2.51270e30i | 0.153492 | + | 0.226637i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.06881e30 | + | 8.06881e30i | 0.711104 | + | 0.711104i | 0.966766 | − | 0.255662i | \(-0.0822935\pi\) |
−0.255662 | + | 0.966766i | \(0.582293\pi\) | |||||||
\(908\) | 5.52051e29 | + | 5.52051e29i | 0.0480926 | + | 0.0480926i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.25119e30 | − | 1.39528e30i | −0.617269 | − | 0.118776i | ||||
\(911\) | − | 1.06614e31i | − | 0.897164i | −0.893742 | − | 0.448582i | \(-0.851929\pi\) | ||
0.893742 | − | 0.448582i | \(-0.148071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.71338e30 | + | 6.71338e30i | −0.552075 | + | 0.552075i | ||||
\(914\) | −2.07026e31 | −1.68302 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.07224e30 | −0.0851900 | ||||||||
\(917\) | 8.81184e30 | − | 8.81184e30i | 0.692131 | − | 0.692131i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.83734e30i | − | 0.294590i | −0.989093 | − | 0.147295i | \(-0.952943\pi\) | ||
0.989093 | − | 0.147295i | \(-0.0470566\pi\) | |||||||
\(920\) | −1.84710e31 | + | 1.25097e31i | −1.40190 | + | 0.949454i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.54760e31 | − | 1.54760e31i | −1.14811 | − | 1.14811i | ||||
\(923\) | −5.61775e30 | − | 5.61775e30i | −0.412045 | − | 0.412045i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.25436e30 | + | 3.54063e30i | −0.591828 | + | 0.253859i | ||||
\(926\) | 1.05186e31i | 0.745666i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.75523e30 | + | 1.75523e30i | −0.121641 | + | 0.121641i | ||||
\(929\) | 1.42887e31 | 0.979102 | 0.489551 | − | 0.871975i | \(-0.337161\pi\) | ||||
0.489551 | + | 0.871975i | \(0.337161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.68279e30 | −0.246720 | ||||||||
\(932\) | −1.51437e29 | + | 1.51437e29i | −0.0100315 | + | 0.0100315i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.75342e31i | 1.78332i | ||||||||
\(935\) | 2.07309e30 | − | 1.07737e31i | 0.132769 | − | 0.689991i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.34566e30 | + | 6.34566e30i | 0.397385 | + | 0.397385i | 0.877310 | − | 0.479925i | \(-0.159336\pi\) |
−0.479925 | + | 0.877310i | \(0.659336\pi\) | |||||||
\(938\) | 1.56701e31 | + | 1.56701e31i | 0.970380 | + | 0.970380i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.70147e29 | − | 2.96302e30i | 0.0345258 | − | 0.179429i | ||||
\(941\) | 5.30410e30i | 0.317629i | 0.987308 | + | 0.158815i | \(0.0507672\pi\) | ||||
−0.987308 | + | 0.158815i | \(0.949233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.30259e31 | + | 2.30259e31i | −1.34848 | + | 1.34848i | ||||
\(944\) | −8.30635e29 | −0.0481066 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.09745e30 | 0.288732 | ||||||||
\(947\) | 6.68629e29 | − | 6.68629e29i | 0.0374551 | − | 0.0374551i | −0.688131 | − | 0.725586i | \(-0.741569\pi\) |
0.725586 | + | 0.688131i | \(0.241569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.83270e31i | 1.00415i | ||||||||
\(950\) | 1.63231e31 | − | 7.00163e30i | 0.884514 | − | 0.379404i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.71328e31 | − | 2.71328e31i | −1.43816 | − | 1.43816i | ||||
\(953\) | −5.29617e30 | − | 5.29617e30i | −0.277643 | − | 0.277643i | 0.554525 | − | 0.832167i | \(-0.312900\pi\) |
−0.832167 | + | 0.554525i | \(0.812900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.01754e30 | + | 6.10722e30i | −0.462437 | + | 0.313190i | ||||
\(956\) | − | 1.81904e30i | − | 0.0922645i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.04965e30 | − | 5.04965e30i | 0.250567 | − | 0.250567i | ||||
\(959\) | −1.69862e31 | −0.833683 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14584e30 | −0.151057 | ||||||||
\(962\) | −5.41256e30 | + | 5.41256e30i | −0.257078 | + | 0.257078i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 4.87659e30i | − | 0.226625i | ||||||
\(965\) | −1.52836e31 | − | 2.94088e30i | −0.702569 | − | 0.135189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.32785e30 | + | 1.32785e30i | 0.0597272 | + | 0.0597272i | 0.736339 | − | 0.676612i | \(-0.236553\pi\) |
−0.676612 | + | 0.736339i | \(0.736553\pi\) | |||||||
\(968\) | −1.39851e31 | − | 1.39851e31i | −0.622261 | − | 0.622261i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.19910e30 | − | 1.77052e30i | −0.0522100 | − | 0.0770900i | ||||
\(971\) | 1.58635e30i | 0.0683276i | 0.999416 | + | 0.0341638i | \(0.0108768\pi\) | ||||
−0.999416 | + | 0.0341638i | \(0.989123\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.41676e31 | + | 3.41676e31i | −1.44022 | + | 1.44022i | ||||
\(974\) | −8.40456e30 | −0.350466 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.50150e30 | 0.102089 | ||||||||
\(977\) | −1.57029e31 | + | 1.57029e31i | −0.633995 | + | 0.633995i | −0.949068 | − | 0.315073i | \(-0.897971\pi\) |
0.315073 | + | 0.949068i | \(0.397971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.45536e30i | 0.334129i | ||||||||
\(980\) | 4.31857e29 | + | 6.37653e29i | 0.0168837 | + | 0.0249293i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.84308e31 | + | 1.84308e31i | 0.705301 | + | 0.705301i | ||||
\(983\) | 9.53643e30 | + | 9.53643e30i | 0.361055 | + | 0.361055i | 0.864201 | − | 0.503146i | \(-0.167824\pi\) |
−0.503146 | + | 0.864201i | \(0.667824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.37932e30 | + | 1.22751e30i | 0.236425 | + | 0.0454932i | ||||
\(986\) | 3.04951e31i | 1.11821i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.53754e30 | + | 1.53754e30i | −0.0551922 | + | 0.0551922i | ||||
\(989\) | 3.45419e31 | 1.22683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.69150e30 | −0.0935881 | −0.0467941 | − | 0.998905i | \(-0.514900\pi\) | ||||
−0.0467941 | + | 0.998905i | \(0.514900\pi\) | |||||||
\(992\) | 4.72764e30 | − | 4.72764e30i | 0.162657 | − | 0.162657i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 2.98314e31i | − | 1.00489i | ||||||
\(995\) | 6.63882e30 | − | 4.49621e30i | 0.221283 | − | 0.149866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.96709e31 | − | 3.96709e31i | −1.29471 | − | 1.29471i | −0.931838 | − | 0.362874i | \(-0.881796\pi\) |
−0.362874 | − | 0.931838i | \(-0.618204\pi\) | |||||||
\(998\) | 3.18880e31 | + | 3.18880e31i | 1.02981 | + | 1.02981i | ||||
\(999\) | 0 | 0 |
(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 | 45.22.f.a.17.13 | yes | 84 | |
3.2 | odd | 2 | inner | 45.22.f.a.17.30 | yes | 84 | |
5.3 | odd | 4 | inner | 45.22.f.a.8.30 | yes | 84 | |
15.8 | even | 4 | inner | 45.22.f.a.8.13 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.22.f.a.8.13 | ✓ | 84 | 15.8 | even | 4 | inner | |
45.22.f.a.8.30 | yes | 84 | 5.3 | odd | 4 | inner | |
45.22.f.a.17.13 | yes | 84 | 1.1 | even | 1 | trivial | |
45.22.f.a.17.30 | yes | 84 | 3.2 | odd | 2 | inner |