Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,24,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(214.530583901\) |
Analytic rank: | \(0\) |
Dimension: | \(90\) |
Relative dimension: | \(45\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.45 | ||
Character | \(\chi\) | \(=\) | 64.49 |
Dual form | 64.24.e.a.17.45 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 413460. | − | 413460.i | 1.34753 | − | 1.34753i | 0.459199 | − | 0.888333i | \(-0.348136\pi\) |
0.888333 | − | 0.459199i | \(-0.151864\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.88787e6 | − | 3.88787e6i | −0.0356088 | − | 0.0356088i | 0.689078 | − | 0.724687i | \(-0.258016\pi\) |
−0.724687 | + | 0.689078i | \(0.758016\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.12996e9i | − | 1.36289i | −0.731871 | − | 0.681443i | \(-0.761353\pi\) | ||
0.731871 | − | 0.681443i | \(-0.238647\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.47755e11i | − | 2.63169i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.30508e11 | − | 5.30508e11i | −0.560630 | − | 0.560630i | 0.368857 | − | 0.929486i | \(-0.379749\pi\) |
−0.929486 | + | 0.368857i | \(0.879749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.16422e12 | − | 2.16422e12i | 0.334929 | − | 0.334929i | −0.519526 | − | 0.854455i | \(-0.673891\pi\) |
0.854455 | + | 0.519526i | \(0.173891\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.21496e12 | −0.0959680 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.09838e14 | 0.777305 | 0.388653 | − | 0.921384i | \(-0.372941\pi\) | ||||
0.388653 | + | 0.921384i | \(0.372941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.54544e14 | + | 5.54544e14i | −1.09212 | + | 1.09212i | −0.0968162 | + | 0.995302i | \(0.530866\pi\) |
−0.995302 | + | 0.0968162i | \(0.969134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.94795e15 | − | 2.94795e15i | −1.83653 | − | 1.83653i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.03696e15i | 0.664613i | 0.943171 | + | 0.332307i | \(0.107827\pi\) | ||||
−0.943171 | + | 0.332307i | \(0.892173\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.18907e16i | − | 0.997464i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.35126e16 | − | 6.35126e16i | −2.19875 | − | 2.19875i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.21568e16 | + | 3.21568e16i | −0.489435 | + | 0.489435i | −0.908128 | − | 0.418693i | \(-0.862488\pi\) |
0.418693 | + | 0.908128i | \(0.362488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.25797e17 | −0.889225 | −0.444613 | − | 0.895723i | \(-0.646659\pi\) | ||||
−0.444613 | + | 0.895723i | \(0.646659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.38688e17 | −1.51093 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.77204e16 | + | 2.77204e16i | −0.0485307 | + | 0.0485307i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16722e18 | − | 1.16722e18i | −1.07853 | − | 1.07853i | −0.996642 | − | 0.0818857i | \(-0.973906\pi\) |
−0.0818857 | − | 0.996642i | \(-0.526094\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.78964e18i | − | 0.902655i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.75070e18i | 0.780601i | 0.920688 | + | 0.390300i | \(0.127629\pi\) | ||||
−0.920688 | + | 0.390300i | \(0.872371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.78659e18 | + | 6.78659e18i | 1.11369 | + | 1.11369i | 0.992647 | + | 0.121042i | \(0.0386236\pi\) |
0.121042 | + | 0.992647i | \(0.461376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.63242e17 | + | 9.63242e17i | −0.0937112 | + | 0.0937112i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.15595e18 | 0.481226 | 0.240613 | − | 0.970621i | \(-0.422652\pi\) | ||||
0.240613 | + | 0.970621i | \(0.422652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.34675e19 | −0.857457 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.54138e19 | − | 4.54138e19i | 1.04744 | − | 1.04744i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.87678e19 | − | 5.87678e19i | −0.870897 | − | 0.870897i | 0.121673 | − | 0.992570i | \(-0.461174\pi\) |
−0.992570 | + | 0.121673i | \(0.961174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.12510e18i | 0.0399267i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.58564e20i | 2.94333i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.38468e19 | − | 2.38468e19i | −0.102951 | − | 0.102951i | 0.653755 | − | 0.756706i | \(-0.273193\pi\) |
−0.756706 | + | 0.653755i | \(0.773193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.83019e20 | − | 3.83019e20i | 1.12701 | − | 1.12701i | 0.136349 | − | 0.990661i | \(-0.456463\pi\) |
0.990661 | − | 0.136349i | \(-0.0435369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.76649e21 | −3.58669 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.68284e19 | −0.0238528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.83073e20 | − | 5.83073e20i | 0.583261 | − | 0.583261i | −0.352537 | − | 0.935798i | \(-0.614681\pi\) |
0.935798 | + | 0.352537i | \(0.114681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.25566e21 | + | 1.25566e21i | 0.895588 | + | 0.895588i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.63662e21i | 0.840384i | 0.907435 | + | 0.420192i | \(0.138037\pi\) | ||||
−0.907435 | + | 0.420192i | \(0.861963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.55178e21i | 0.578918i | 0.957190 | + | 0.289459i | \(0.0934754\pi\) | ||||
−0.957190 | + | 0.289459i | \(0.906525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.91633e21 | − | 4.91633e21i | −1.34412 | − | 1.34412i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.78250e21 | + | 3.78250e21i | −0.764074 | + | 0.764074i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.07753e21 | −0.162076 | −0.0810381 | − | 0.996711i | \(-0.525824\pi\) | ||||
−0.0810381 | + | 0.996711i | \(0.525824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.91954e22 | −3.29409 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.13427e22 | + | 1.13427e22i | −0.966762 | + | 0.966762i | −0.999465 | − | 0.0327035i | \(-0.989588\pi\) |
0.0327035 | + | 0.999465i | \(0.489588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.27038e20 | − | 4.27038e20i | −0.0276789 | − | 0.0276789i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.65911e22i | 1.31906i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.95437e22i | − | 1.12844i | −0.825624 | − | 0.564221i | \(-0.809177\pi\) | ||
0.825624 | − | 0.564221i | \(-0.190823\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.54308e22 | − | 1.54308e22i | −0.456470 | − | 0.456470i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.20122e22 | + | 5.20122e22i | −1.19826 | + | 1.19826i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.31200e21 | 0.0777780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.92555e22 | 0.699164 | 0.349582 | − | 0.936906i | \(-0.386324\pi\) | ||||
0.349582 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.31436e23 | + | 1.31436e23i | −1.47540 | + | 1.47540i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.44883e22 | − | 4.44883e22i | −0.396780 | − | 0.396780i | 0.480315 | − | 0.877096i | \(-0.340522\pi\) |
−0.877096 | + | 0.480315i | \(0.840522\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.67866e22i | 0.404220i | 0.979363 | + | 0.202110i | \(0.0647799\pi\) | ||||
−0.979363 | + | 0.202110i | \(0.935220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.29225e22i | 0.130793i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.07572e23 | + | 1.07572e23i | 0.494066 | + | 0.494066i | 0.909585 | − | 0.415518i | \(-0.136400\pi\) |
−0.415518 | + | 0.909585i | \(0.636400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.12098e23 | − | 2.12098e23i | 0.787286 | − | 0.787286i | −0.193762 | − | 0.981049i | \(-0.562069\pi\) |
0.981049 | + | 0.193762i | \(0.0620690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.65194e23 | −2.90670 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.40518e23 | 0.344611 | 0.172306 | − | 0.985044i | \(-0.444878\pi\) | ||||
0.172306 | + | 0.985044i | \(0.444878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.18073e22 | − | 1.18073e22i | 0.0236661 | − | 0.0236661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.36197e23 | − | 5.36197e23i | −0.881428 | − | 0.881428i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.83143e23i | − | 1.05938i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.32553e23i | − | 0.371389i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.13730e24 | + | 1.13730e24i | 1.05188 | + | 1.05188i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.25766e22 | + | 9.25766e22i | −0.0711273 | + | 0.0711273i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.98723e24 | 1.27205 | 0.636027 | − | 0.771667i | \(-0.280577\pi\) | ||||
0.636027 | + | 0.771667i | \(0.280577\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.61197e24 | 3.00147 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.09241e24 | − | 1.09241e24i | 0.489516 | − | 0.489516i | −0.418638 | − | 0.908153i | \(-0.637492\pi\) |
0.908153 | + | 0.418638i | \(0.137492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.95388e24 | + | 3.95388e24i | 1.48843 | + | 1.48843i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.93858e23i | 0.156590i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.63782e24i | − | 1.50947i | −0.656029 | − | 0.754735i | \(-0.727765\pi\) | ||
0.656029 | − | 0.754735i | \(-0.272235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80248e23 | + | 2.80248e23i | 0.0635145 | + | 0.0635145i | 0.738151 | − | 0.674636i | \(-0.235699\pi\) |
−0.674636 | + | 0.738151i | \(0.735699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.37216e24 | − | 3.37216e24i | 0.648468 | − | 0.648468i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.29627e24 | −0.375542 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50043e23 | 0.0348564 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.70289e24 | + | 9.70289e24i | −1.15545 | + | 1.15545i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.46325e24 | − | 2.46325e24i | −0.251111 | − | 0.251111i | 0.570315 | − | 0.821426i | \(-0.306821\pi\) |
−0.821426 | + | 0.570315i | \(0.806821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.64216e24i | − | 0.405962i | −0.979183 | − | 0.202981i | \(-0.934937\pi\) | ||
0.979183 | − | 0.202981i | \(-0.0650629\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.72131e25i | − | 2.04563i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.89084e23 | + | 4.89084e23i | 0.0316642 | + | 0.0316642i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.23932e25 | + | 2.23932e25i | −1.25104 | + | 1.25104i | −0.295784 | + | 0.955255i | \(0.595581\pi\) |
−0.955255 | + | 0.295784i | \(0.904419\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.85963e25 | −2.34712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.16534e25 | 0.905792 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.79549e24 | − | 8.79549e24i | 0.319229 | − | 0.319229i | −0.529242 | − | 0.848471i | \(-0.677524\pi\) |
0.848471 | + | 0.529242i | \(0.177524\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.70556e24 | + | 1.70556e24i | 0.0538025 | + | 0.0538025i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.44337e25i | 0.671042i | 0.942033 | + | 0.335521i | \(0.108912\pi\) | ||||
−0.942033 | + | 0.335521i | \(0.891088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.23862e25i | 0.775645i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.37391e26 | + | 1.37391e26i | 2.87412 | + | 2.87412i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.63426e25 | + | 4.63426e25i | −0.848107 | + | 0.848107i | −0.989897 | − | 0.141790i | \(-0.954714\pi\) |
0.141790 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.47801e25 | −1.35943 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.97194e25 | −0.277461 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.10789e25 | + | 5.10789e25i | −0.631584 | + | 0.631584i | −0.948465 | − | 0.316881i | \(-0.897364\pi\) |
0.316881 | + | 0.948465i | \(0.397364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.20766e26 | − | 1.20766e26i | −1.31414 | − | 1.31414i | −0.918333 | − | 0.395808i | \(-0.870465\pi\) |
−0.395808 | − | 0.918333i | \(-0.629535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.16727e26i | − | 3.03737i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.07597e24i | 0.0768101i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.82702e25 | − | 5.82702e25i | −0.435780 | − | 0.435780i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.52842e26 | + | 4.52842e26i | −2.99665 | + | 2.99665i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.75233e26 | −1.02738 | −0.513692 | − | 0.857975i | \(-0.671723\pi\) | ||||
−0.513692 | + | 0.857975i | \(0.671723\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.30198e26 | 1.19727 | 0.598635 | − | 0.801022i | \(-0.295710\pi\) | ||||
0.598635 | + | 0.801022i | \(0.295710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.95788e24 | + | 6.95788e24i | −0.0321424 | + | 0.0321424i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.73927e26 | + | 2.73927e26i | 1.12531 | + | 1.12531i | 0.990930 | + | 0.134382i | \(0.0429051\pi\) |
0.134382 | + | 0.990930i | \(0.457095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.70318e25i | − | 0.0622946i | −0.999515 | − | 0.0311473i | \(-0.990084\pi\) | ||
0.999515 | − | 0.0311473i | \(-0.00991610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.82155e26i | − | 1.57193i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.29276e26 | + | 2.29276e26i | 0.667044 | + | 0.667044i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.06944e25 | − | 1.06944e25i | 0.0277962 | − | 0.0277962i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.52424e26 | 1.74905 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.88380e26 | 1.22455 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.66989e25 | − | 9.66989e25i | 0.180374 | − | 0.180374i | −0.611145 | − | 0.791519i | \(-0.709291\pi\) |
0.791519 | + | 0.611145i | \(0.209291\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.76679e26 | + | 6.76679e26i | 1.13245 | + | 1.13245i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5.27708e25i | − | 0.0793143i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.96929e26i | 1.21191i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.41599e26 | + | 6.41599e26i | 0.780111 | + | 0.780111i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.37714e26 | − | 2.37714e26i | 0.260342 | − | 0.260342i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.41282e26 | −0.435723 | −0.217862 | − | 0.975980i | \(-0.569908\pi\) | ||||
−0.217862 | + | 0.975980i | \(0.569908\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.94599e27 | −2.62501 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.62600e27 | − | 1.62600e27i | 1.30865 | − | 1.30865i | 0.386256 | − | 0.922392i | \(-0.373768\pi\) |
0.922392 | − | 0.386256i | \(-0.126232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.75095e27 | − | 1.75095e27i | −1.27399 | − | 1.27399i | −0.943976 | − | 0.330014i | \(-0.892947\pi\) |
−0.330014 | − | 0.943976i | \(-0.607053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.12783e27i | 2.05923i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.92833e26i | 0.174593i | 0.996182 | + | 0.0872965i | \(0.0278227\pi\) | ||||
−0.996182 | + | 0.0872965i | \(0.972177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.17093e25 | − | 3.17093e25i | −0.0171359 | − | 0.0171359i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.45517e26 | + | 4.45517e26i | −0.218403 | + | 0.218403i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.46769e27 | −1.09829 | −0.549143 | − | 0.835728i | \(-0.685046\pi\) | ||||
−0.549143 | + | 0.835728i | \(0.685046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.28956e27 | 0.925883 | 0.462942 | − | 0.886389i | \(-0.346794\pi\) | ||||
0.462942 | + | 0.886389i | \(0.346794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.09184e27 | + | 6.09184e27i | −2.24015 | + | 2.24015i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.12388e25 | + | 9.12388e25i | 0.0305330 | + | 0.0305330i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.40031e27i | 0.731564i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.37953e27i | 2.60549i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.04026e27 | − | 3.04026e27i | −0.770306 | − | 0.770306i | 0.207854 | − | 0.978160i | \(-0.433352\pi\) |
−0.978160 | + | 0.207854i | \(0.933352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61113e27 | − | 1.61113e27i | 0.372602 | − | 0.372602i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.53126e26 | −0.0745964 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.09902e27 | −0.984591 | −0.492296 | − | 0.870428i | \(-0.663842\pi\) | ||||
−0.492296 | + | 0.870428i | \(0.663842\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.32219e27 | + | 8.32219e27i | −1.46991 | + | 1.46991i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.96701e27 | + | 7.96701e27i | 1.28804 | + | 1.28804i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.26287e27i | 1.07552i | 0.843099 | + | 0.537758i | \(0.180729\pi\) | ||||
−0.843099 | + | 0.537758i | \(0.819271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.56963e26i | 0.0620232i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.22151e28 | − | 1.22151e28i | −1.52061 | − | 1.52061i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.75395e27 | + | 5.75395e27i | −0.657377 | + | 0.657377i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.297382 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.18370e27 | 0.334030 | 0.167015 | − | 0.985954i | \(-0.446587\pi\) | ||||
0.167015 | + | 0.985954i | \(0.446587\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.27600e28 | −1.23022 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.30811e27 | + | 6.30811e27i | −0.559208 | + | 0.559208i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.93363e27 | − | 6.93363e27i | −0.565514 | − | 0.565514i | 0.365355 | − | 0.930868i | \(-0.380948\pi\) |
−0.930868 | + | 0.365355i | \(0.880948\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.11670e28i | 2.34016i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.31290e27i | 0.229132i | 0.993416 | + | 0.114566i | \(0.0365477\pi\) | ||||
−0.993416 | + | 0.114566i | \(0.963452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09607e28 | + | 1.09607e28i | 0.698706 | + | 0.698706i | 0.964131 | − | 0.265425i | \(-0.0855124\pi\) |
−0.265425 | + | 0.964131i | \(0.585512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.78284e27 | − | 1.78284e27i | 0.104808 | − | 0.104808i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.96124e28 | 1.06387 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.90309e27 | −0.395796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.03652e28 | − | 2.03652e28i | 0.942147 | − | 0.942147i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.77690e26 | + | 5.77690e26i | 0.0247012 | + | 0.0247012i | 0.719349 | − | 0.694648i | \(-0.244440\pi\) |
−0.694648 | + | 0.719349i | \(0.744440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.85427e26i | 0.00733196i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.73879e28i | 2.46537i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.57264e27 | + | 6.57264e27i | 0.222598 | + | 0.222598i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83881e28 | − | 4.83881e28i | 1.51783 | − | 1.51783i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.67883e28 | −1.06935 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.97826e27 | −0.0802629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.02178e28 | − | 2.02178e28i | 0.505409 | − | 0.505409i | −0.407705 | − | 0.913114i | \(-0.633671\pi\) |
0.913114 | + | 0.407705i | \(0.133671\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.34790e28 | + | 2.34790e28i | 0.544700 | + | 0.544700i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.08054e28i | 0.878968i | 0.898250 | + | 0.439484i | \(0.144839\pi\) | ||||
−0.898250 | + | 0.439484i | \(0.855161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.04282e28i | − | 0.808955i | −0.914548 | − | 0.404477i | \(-0.867453\pi\) | ||
0.914548 | − | 0.404477i | \(-0.132547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.86788e27 | + | 6.86788e27i | 0.127718 | + | 0.127718i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.36363e28 | + | 6.36363e28i | −1.10033 | + | 1.10033i | −0.105961 | + | 0.994370i | \(0.533792\pi\) |
−0.994370 | + | 0.105961i | \(0.966208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.41188e28 | 0.548784 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.89534e28 | 1.33154 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.09103e28 | + | 6.09103e28i | −0.848909 | + | 0.848909i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.57341e28 | − | 2.57341e28i | −0.334079 | − | 0.334079i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.75389e29i | − | 2.12179i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.81516e28i | − | 0.655856i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.76430e28 | + | 3.76430e28i | 0.395970 | + | 0.395970i | 0.876809 | − | 0.480839i | \(-0.159668\pi\) |
−0.480839 | + | 0.876809i | \(0.659668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.89184e29 | + | 2.89184e29i | −2.83835 | + | 2.83835i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.53383e27 | −0.0415384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.33695e28 | −0.371057 | −0.185528 | − | 0.982639i | \(-0.559400\pi\) | ||||
−0.185528 | + | 0.982639i | \(0.559400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.80985e28 | − | 5.80985e28i | 0.464375 | − | 0.464375i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.67365e28 | + | 6.67365e28i | 0.498526 | + | 0.498526i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.78156e28i | − | 0.194270i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 9.76371e27i | − | 0.0637816i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.04551e29 | + | 1.04551e29i | 0.639054 | + | 0.639054i | 0.950322 | − | 0.311268i | \(-0.100754\pi\) |
−0.311268 | + | 0.950322i | \(0.600754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.01381e28 | + | 5.01381e28i | −0.286864 | + | 0.286864i | −0.835839 | − | 0.548975i | \(-0.815018\pi\) |
0.548975 | + | 0.835839i | \(0.315018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.74910e29 | −1.47285 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.69372e28 | 0.185376 | 0.0926882 | − | 0.995695i | \(-0.470454\pi\) | ||||
0.0926882 | + | 0.995695i | \(0.470454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.36299e27 | − | 6.36299e27i | 0.0299251 | − | 0.0299251i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.23798e29 | − | 3.23798e29i | −1.42755 | − | 1.42755i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.60781e28i | − | 0.397227i | −0.980078 | − | 0.198613i | \(-0.936356\pi\) | ||
0.980078 | − | 0.198613i | \(-0.0636438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.57209e29i | − | 1.38545i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.37497e29 | − | 1.37497e29i | −0.500459 | − | 0.500459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.03313e27 | − | 6.03313e27i | 0.0206146 | − | 0.0206146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.53567e29 | −0.492762 | −0.246381 | − | 0.969173i | \(-0.579241\pi\) | ||||
−0.246381 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.81501e29 | 2.05430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.19012e29 | + | 4.19012e29i | −1.18693 | + | 1.18693i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.58794e28 | + | 7.58794e28i | 0.202056 | + | 0.202056i | 0.800881 | − | 0.598824i | \(-0.204365\pi\) |
−0.598824 | + | 0.800881i | \(0.704365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.65535e28i | 0.191693i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.39188e29i | 0.327852i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.12000e29 | + | 2.12000e29i | 0.469878 | + | 0.469878i | 0.901875 | − | 0.431997i | \(-0.142191\pi\) |
−0.431997 | + | 0.901875i | \(0.642191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.21641e29 | − | 8.21641e29i | 1.71413 | − | 1.71413i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.91961e29 | −1.55567 | −0.777836 | − | 0.628467i | \(-0.783683\pi\) | ||||
−0.777836 | + | 0.628467i | \(0.783683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.94118e28 | 0.0544155 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.68141e30 | − | 1.68141e30i | 2.93088 | − | 2.93088i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.37999e29 | − | 1.37999e29i | −0.226702 | − | 0.226702i | 0.584612 | − | 0.811313i | \(-0.301247\pi\) |
−0.811313 | + | 0.584612i | \(0.801247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.33575e29i | 0.516607i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.03338e29i | − | 1.31928i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.18932e27 | + | 4.18932e27i | 0.00577134 | + | 0.00577134i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.14687e29 | − | 9.14687e29i | 1.18900 | − | 1.18900i | 0.211655 | − | 0.977344i | \(-0.432115\pi\) |
0.977344 | − | 0.211655i | \(-0.0678854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.26954e30 | 4.01142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.13962e29 | 0.711183 | 0.355592 | − | 0.934641i | \(-0.384279\pi\) | ||||
0.355592 | + | 0.934641i | \(0.384279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.72253e29 | + | 2.72253e29i | −0.297827 | + | 0.297827i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.13508e29 | + | 1.13508e29i | 0.117299 | + | 0.117299i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.23843e30i | 1.20931i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.58802e28i | − | 0.0700342i | −0.999387 | − | 0.0350171i | \(-0.988851\pi\) | ||
0.999387 | − | 0.0350171i | \(-0.0111486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.33101e30 | − | 2.33101e30i | −2.03406 | − | 2.03406i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.70027e29 | + | 1.70027e29i | −0.140311 | + | 0.140311i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.81982e28 | 0.0688504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.31743e29 | 0.171176 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.29670e29 | − | 6.29670e29i | 0.440201 | − | 0.440201i | −0.451878 | − | 0.892080i | \(-0.649246\pi\) |
0.892080 | + | 0.451878i | \(0.149246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.48107e29 | − | 2.48107e29i | −0.164208 | − | 0.164208i | 0.620220 | − | 0.784428i | \(-0.287043\pi\) |
−0.784428 | + | 0.620220i | \(0.787043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.02068e30i | − | 1.26644i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.30606e30i | − | 0.775334i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.73091e30 | − | 2.73091e30i | −1.53599 | − | 1.53599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.49416e29 | + | 9.49416e29i | −0.506055 | + | 0.506055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.39038e29 | 0.373403 | 0.186702 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186702 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.70039e29 | −0.320988 | −0.160494 | − | 0.987037i | \(-0.551309\pi\) | ||||
−0.160494 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.03383e29 | − | 1.03383e29i | 0.0469701 | − | 0.0469701i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.68413e30 | − | 1.68413e30i | −0.725836 | − | 0.725836i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.81983e30i | 1.15314i | 0.817048 | + | 0.576569i | \(0.195609\pi\) | ||||
−0.817048 | + | 0.576569i | \(0.804391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.81421e30i | 2.25656i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.35646e30 | + | 3.35646e30i | 1.23663 | + | 1.23663i | 0.961371 | + | 0.275256i | \(0.0887625\pi\) |
0.275256 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.14862e29 | + | 1.14862e29i | −0.0401825 | + | 0.0401825i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.03691e30 | −0.676760 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.31342e30 | 0.414543 | 0.207271 | − | 0.978283i | \(-0.433542\pi\) | ||||
0.207271 | + | 0.978283i | \(0.433542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.45927e30 | − | 1.45927e30i | 0.437628 | − | 0.437628i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.91935e30 | − | 1.91935e30i | −0.547047 | − | 0.547047i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.19986e29i | 0.0325087i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.10645e30i | 1.57309i | 0.617536 | + | 0.786543i | \(0.288131\pi\) | ||||
−0.617536 | + | 0.786543i | \(0.711869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.97612e30 | − | 6.97612e30i | −1.70910 | − | 1.70910i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.64152e30 | − | 2.64152e30i | 0.615593 | − | 0.615593i | −0.328805 | − | 0.944398i | \(-0.606646\pi\) |
0.944398 | + | 0.328805i | \(0.106646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.83079e30 | 0.627663 | 0.313832 | − | 0.949479i | \(-0.398387\pi\) | ||||
0.313832 | + | 0.949479i | \(0.398387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.04434e29 | 0.0853372 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.04608e29 | − | 8.04608e29i | 0.161600 | − | 0.161600i | −0.621675 | − | 0.783275i | \(-0.713548\pi\) |
0.783275 | + | 0.621675i | \(0.213548\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.15728e30 | − | 4.15728e30i | −0.794918 | − | 0.794918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.85174e31i | 3.37163i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.20068e30i | − | 1.24873i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.59392e30 | + | 6.59392e30i | 1.08935 | + | 1.08935i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.45600e31 | + | 1.45600e31i | −2.29193 | + | 2.29193i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.62313e30 | −1.29362 | −0.646810 | − | 0.762651i | \(-0.723897\pi\) | ||||
−0.646810 | + | 0.762651i | \(0.723897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.05222e30 | −0.722460 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.95282e30 | − | 8.95282e30i | 1.22058 | − | 1.22058i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.91499e29 | − | 1.91499e29i | −0.0248964 | − | 0.0248964i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.64386e30i | − | 1.07183i | −0.844273 | − | 0.535913i | \(-0.819967\pi\) | ||
0.844273 | − | 0.535913i | \(-0.180033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.27317e30i | − | 0.860344i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.42191e30 | − | 8.42191e30i | −0.950546 | − | 0.950546i | 0.0482871 | − | 0.998833i | \(-0.484624\pi\) |
−0.998833 | + | 0.0482871i | \(0.984624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.53205e30 | + | 3.53205e30i | −0.380441 | + | 0.380441i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.02202e30 | 0.105075 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.16691e31 | 1.14535 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.24291e30 | + | 7.24291e30i | −0.678824 | + | 0.678824i | −0.959734 | − | 0.280910i | \(-0.909364\pi\) |
0.280910 | + | 0.959734i | \(0.409364\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.01024e31 | + | 1.01024e31i | 0.904251 | + | 0.904251i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.76960e29i | 0.0322302i | 0.999870 | + | 0.0161151i | \(0.00512982\pi\) | ||||
−0.999870 | + | 0.0161151i | \(0.994870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.45930e29i | 0.0282577i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.33904e31 | + | 1.33904e31i | 1.04521 | + | 1.04521i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.75535e29 | + | 2.75535e29i | −0.0205552 | + | 0.0205552i | −0.717310 | − | 0.696754i | \(-0.754627\pi\) |
0.696754 | + | 0.717310i | \(0.254627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.10641e31 | 0.788999 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.04411e31 | 4.80260 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.20779e29 | − | 2.20779e29i | 0.0143938 | − | 0.0143938i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.32680e30 | − | 4.32680e30i | −0.269790 | − | 0.269790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.83217e31i | 2.28570i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.81840e31i | − | 1.03766i | −0.854878 | − | 0.518830i | \(-0.826368\pi\) | ||
0.854878 | − | 0.518830i | \(-0.173632\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.60811e30 | − | 7.60811e30i | −0.415439 | − | 0.415439i | 0.468189 | − | 0.883628i | \(-0.344907\pi\) |
−0.883628 | + | 0.468189i | \(0.844907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.50532e31 | + | 3.50532e31i | −1.83188 | + | 1.83188i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.38174e31 | −0.691199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.16573e31 | 0.558289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.90819e30 | + | 5.90819e30i | −0.270936 | + | 0.270936i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.95311e30 | + | 5.95311e30i | 0.261446 | + | 0.261446i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.36452e29i | − | 0.0351862i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.22382e31i | 1.70216i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.24497e31 | + | 1.24497e31i | 0.480716 | + | 0.480716i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.33778e31 | + | 1.33778e31i | −0.495014 | + | 0.495014i | −0.909882 | − | 0.414868i | \(-0.863828\pi\) |
0.414868 | + | 0.909882i | \(0.363828\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.98641e31 | −3.54170 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.64922e30 | −0.0560686 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.09839e30 | − | 4.09839e30i | 0.133585 | − | 0.133585i | −0.637153 | − | 0.770738i | \(-0.719888\pi\) |
0.770738 | + | 0.637153i | \(0.219888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.48952e31 | − | 9.48952e31i | −2.96594 | − | 2.96594i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.56647e31i | − | 1.06904i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.68277e30i | 0.220891i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.75255e30 | + | 3.75255e30i | 0.103504 | + | 0.103504i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.75875e30 | − | 6.75875e30i | 0.178868 | − | 0.178868i | −0.611994 | − | 0.790862i | \(-0.709633\pi\) |
0.790862 | + | 0.611994i | \(0.209633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.93753e31 | 0.746013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.81848e31 | −1.17446 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.29263e31 | + | 1.29263e31i | −0.302431 | + | 0.302431i | −0.841964 | − | 0.539533i | \(-0.818601\pi\) |
0.539533 | + | 0.841964i | \(0.318601\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.46316e29 | − | 5.46316e29i | −0.0122712 | − | 0.0122712i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.08162e32i | 4.48947i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.86683e30i | − | 0.0386646i | −0.999813 | − | 0.0193323i | \(-0.993846\pi\) | ||
0.999813 | − | 0.0193323i | \(-0.00615405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.64962e31 | − | 5.64962e31i | −1.12384 | − | 1.12384i | −0.991159 | − | 0.132679i | \(-0.957642\pi\) |
−0.132679 | − | 0.991159i | \(-0.542358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.24520e31 | + | 7.24520e31i | −1.38443 | + | 1.38443i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.61116e31 | 0.662928 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.06780e28 | 0.000541134 | 0.000270567 | − | 1.00000i | \(-0.499914\pi\) | ||||
0.000270567 | 1.00000i | \(0.499914\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.51776e31 | − | 9.51776e31i | 1.61336 | − | 1.61336i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.08731e31 | + | 8.08731e31i | 1.31759 | + | 1.31759i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.23535e31i | 0.976501i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.16933e30i | 0.0627732i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.34622e31 | − | 8.34622e31i | −1.20824 | − | 1.20824i | −0.971598 | − | 0.236638i | \(-0.923954\pi\) |
−0.236638 | − | 0.971598i | \(-0.576046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.97601e31 | − | 6.97601e31i | 0.971139 | − | 0.971139i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.26516e32 | 3.03279 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.38215e31 | −0.178003 | −0.0890015 | − | 0.996031i | \(-0.528368\pi\) | ||||
−0.0890015 | + | 0.996031i | \(0.528368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.04476e30 | + | 3.04476e30i | −0.0377232 | + | 0.0377232i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.04197e30 | − | 7.04197e30i | −0.0839440 | − | 0.0839440i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.68323e31i | − | 0.996031i | −0.867168 | − | 0.498016i | \(-0.834062\pi\) | ||
0.867168 | − | 0.498016i | \(-0.165938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.78480e31i | 0.528211i | 0.964494 | + | 0.264106i | \(0.0850768\pi\) | ||||
−0.964494 | + | 0.264106i | \(0.914923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.44460e32 | − | 1.44460e32i | −1.53496 | − | 1.53496i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.29292e30 | + | 1.29292e30i | −0.0132247 | + | 0.0132247i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.43435e31 | 0.239725 | 0.119863 | − | 0.992790i | \(-0.461755\pi\) | ||||
0.119863 | + | 0.992790i | \(0.461755\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.89593e32 | 1.79773 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.76513e31 | − | 1.76513e31i | 0.161176 | − | 0.161176i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.69111e31 | − | 5.69111e31i | −0.500497 | − | 0.500497i | 0.411095 | − | 0.911592i | \(-0.365146\pi\) |
−0.911592 | + | 0.411095i | \(0.865146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 8.84340e30i | − | 0.0749127i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.91058e31i | 0.237520i | 0.992923 | + | 0.118760i | \(0.0378919\pi\) | ||||
−0.992923 | + | 0.118760i | \(0.962108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.20195e31 | − | 2.20195e31i | −0.173127 | − | 0.173127i | 0.615225 | − | 0.788352i | \(-0.289065\pi\) |
−0.788352 | + | 0.615225i | \(0.789065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92885e32 | − | 1.92885e32i | 1.46132 | − | 1.46132i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.10645e32 | −1.53794 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.41028e32 | −0.992399 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.43272e32 | − | 2.43272e32i | 1.65012 | − | 1.65012i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.28205e32 | − | 1.28205e32i | −0.838345 | − | 0.838345i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.80137e32i | − | 1.13570i | −0.823130 | − | 0.567852i | \(-0.807774\pi\) | ||
0.823130 | − | 0.567852i | \(-0.192226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 7.99623e31i | − | 0.486119i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.72611e30 | − | 7.72611e30i | −0.0452963 | − | 0.0452963i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.07888e31 | + | 5.07888e31i | −0.287187 | + | 0.287187i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.05483e32 | 2.21163 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.46958e32 | 1.29944 | 0.649720 | − | 0.760173i | \(-0.274886\pi\) | ||||
0.649720 | + | 0.760173i | \(0.274886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.26113e32 | − | 1.26113e32i | 0.640224 | − | 0.640224i | −0.310386 | − | 0.950611i | \(-0.600458\pi\) |
0.950611 | + | 0.310386i | \(0.100458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.18186e31 | − | 2.18186e31i | −0.106879 | − | 0.106879i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.33543e32i | 1.57671i | 0.615218 | + | 0.788357i | \(0.289068\pi\) | ||||
−0.615218 | + | 0.788357i | \(0.710932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.53019e31i | 0.115435i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.70844e32 | + | 3.70844e32i | 1.63309 | + | 1.63309i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.09727e32 | − | 1.09727e32i | 0.466459 | − | 0.466459i | −0.434307 | − | 0.900765i | \(-0.643007\pi\) |
0.900765 | + | 0.434307i | \(0.143007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.49432e30 | −0.0348621 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.84462e32 | 1.52353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.20437e32 | − | 1.20437e32i | 0.460868 | − | 0.460868i | −0.438072 | − | 0.898940i | \(-0.644339\pi\) |
0.898940 | + | 0.438072i | \(0.144339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.64234e32 | − | 1.64234e32i | −0.606941 | − | 0.606941i | 0.335205 | − | 0.942145i | \(-0.391195\pi\) |
−0.942145 | + | 0.335205i | \(0.891195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.96571e32i | − | 0.701638i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.07443e31i | − | 0.106003i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.76588e31 | − | 9.76588e31i | −0.325285 | − | 0.325285i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.82453e32 | + | 1.82453e32i | −0.587151 | + | 0.587151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.06390e32 | −1.26367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.43606e32 | −0.431520 | −0.215760 | − | 0.976446i | \(-0.569223\pi\) | ||||
−0.215760 | + | 0.976446i | \(0.569223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.55209e32 | + | 7.55209e32i | −2.19318 | + | 2.19318i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.47612e31 | − | 7.47612e31i | −0.209849 | − | 0.209849i | 0.594354 | − | 0.804203i | \(-0.297408\pi\) |
−0.804203 | + | 0.594354i | \(0.797408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.51189e32i | − | 0.952881i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.34457e33i | − | 3.52689i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.03984e32 | − | 2.03984e32i | −0.517318 | − | 0.517318i | 0.399441 | − | 0.916759i | \(-0.369204\pi\) |
−0.916759 | + | 0.399441i | \(0.869204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.19191e31 | + | 2.19191e31i | −0.0537504 | + | 0.0537504i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.44790e33 | −3.43349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.54373e32 | −0.583377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79869e32 | + | 1.79869e32i | −0.398987 | + | 0.398987i | −0.877875 | − | 0.478889i | \(-0.841040\pi\) |
0.478889 | + | 0.877875i | \(0.341040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.37135e32 | + | 9.37135e32i | 2.01080 | + | 2.01080i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.17914e30i | − | 0.00452335i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.02132e32i | 0.606765i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.21075e32 | + | 1.21075e32i | 0.235270 | + | 0.235270i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.11377e32 | + | 2.11377e32i | −0.397466 | + | 0.397466i | −0.877338 | − | 0.479872i | \(-0.840683\pi\) |
0.479872 | + | 0.877338i | \(0.340683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.29455e33 | 2.35576 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.62211e31 | −0.0461823 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.17200e32 | + | 3.17200e32i | −0.540766 | + | 0.540766i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.71195e32 | − | 7.71195e32i | −1.27272 | − | 1.27272i | −0.944656 | − | 0.328064i | \(-0.893604\pi\) |
−0.328064 | − | 0.944656i | \(-0.606396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.66965e32i | 0.426534i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.82041e32i | − | 0.590991i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.92761e30 | + | 8.92761e30i | 0.0133726 | + | 0.0133726i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.02029e33 | + | 1.02029e33i | −1.47998 | + | 1.47998i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.98038e32 | −0.278206 | −0.139103 | − | 0.990278i | \(-0.544422\pi\) | ||||
−0.139103 | + | 0.990278i | \(0.544422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.04886e32 | 0.550906 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.46642e32 | − | 9.46642e32i | 1.24766 | − | 1.24766i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.82366e32 | + | 3.82366e32i | 0.488194 | + | 0.488194i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.06311e33i | − | 1.31502i | −0.753447 | − | 0.657509i | \(-0.771610\pi\) | ||
0.753447 | − | 0.657509i | \(-0.228390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.28892e33i | 2.74325i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.45428e32 | + | 7.45428e32i | 0.865677 | + | 0.865677i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.33473e32 | − | 9.33473e32i | 1.05052 | − | 1.05052i | 0.0518702 | − | 0.998654i | \(-0.483482\pi\) |
0.998654 | − | 0.0518702i | \(-0.0165182\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.54472e31 | 0.0822884 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.18650e32 | −0.653986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.05364e32 | − | 2.05364e32i | 0.210433 | − | 0.210433i | −0.594019 | − | 0.804451i | \(-0.702459\pi\) |
0.804451 | + | 0.594019i | \(0.202459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.92432e32 | + | 9.92432e32i | 0.985806 | + | 0.985806i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.38126e32i | − | 0.518218i | −0.965848 | − | 0.259109i | \(-0.916571\pi\) | ||
0.965848 | − | 0.259109i | \(-0.0834288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.91536e31i | 0.0178835i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.81022e33 | + | 2.81022e33i | 2.54422 | + | 2.54422i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.66983e32 | − | 7.66983e32i | 0.673356 | − | 0.673356i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.79917e32 | −0.578891 | −0.289445 | − | 0.957195i | \(-0.593471\pi\) | ||||
−0.289445 | + | 0.957195i | \(0.593471\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.51406e33 | −2.07603 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.80481e31 | + | 1.80481e31i | −0.0144558 | + | 0.0144558i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.56844e32 | − | 4.56844e32i | −0.354948 | − | 0.354948i | 0.506999 | − | 0.861947i | \(-0.330755\pi\) |
−0.861947 | + | 0.506999i | \(0.830755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.33228e33i | − | 1.00419i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.31413e33i | − | 1.69225i | −0.532987 | − | 0.846124i | \(-0.678930\pi\) | ||
0.532987 | − | 0.846124i | \(-0.321070\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.51225e33 | − | 1.51225e33i | −1.07298 | − | 1.07298i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.05801e32 | + | 1.05801e32i | −0.0728422 | + | 0.0728422i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.03220e32 | −0.0689628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.56779e32 | 0.620381 | 0.310191 | − | 0.950674i | \(-0.399607\pi\) | ||||
0.310191 | + | 0.950674i | \(0.399607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.10824e33 | + | 2.10824e33i | −1.32677 | + | 1.32677i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.78234e31 | − | 7.78234e31i | −0.0475385 | − | 0.0475385i | 0.682938 | − | 0.730476i | \(-0.260702\pi\) |
−0.730476 | + | 0.682938i | \(0.760702\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.49582e33i | 0.886970i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.88179e33i | 3.96150i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.52538e33 | − | 1.52538e33i | −0.852508 | − | 0.852508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.68242e32 | − | 8.68242e32i | 0.471144 | − | 0.471144i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.08472e33 | 2.15229 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.74124e32 | 0.0890960 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.59201e33 | + | 2.59201e33i | −1.28803 | + | 1.28803i | −0.352053 | + | 0.935980i | \(0.614516\pi\) |
−0.935980 | + | 0.352053i | \(0.885484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00291e33 | + | 3.00291e33i | 1.44929 | + | 1.44929i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.00189e33i | − | 0.469665i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.65788e33i | − | 0.754936i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.88936e32 | + | 1.88936e32i | 0.0835782 | + | 0.0835782i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.28553e32 | + | 3.28553e32i | −0.141200 | + | 0.141200i | −0.774174 | − | 0.632973i | \(-0.781834\pi\) |
0.632973 | + | 0.774174i | \(0.281834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.95836e32 | 0.374060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.31960e33 | −2.96971 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.23232e32 | − | 8.23232e32i | 0.324559 | − | 0.324559i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.41857e31 | − | 8.41857e31i | −0.0322541 | − | 0.0322541i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.75806e33i | 1.77167i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.77070e33i | − | 1.36463i | −0.731059 | − | 0.682314i | \(-0.760974\pi\) | ||
0.731059 | − | 0.682314i | \(-0.239026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.69185e32 | − | 6.69185e32i | −0.235400 | − | 0.235400i | 0.579542 | − | 0.814942i | \(-0.303231\pi\) |
−0.814942 | + | 0.579542i | \(0.803231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.31634e33 | − | 1.31634e33i | 0.450117 | − | 0.450117i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.83916e31 | −0.0227347 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.52692e33 | −2.43256 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.82306e33 | + | 3.82306e33i | −1.20129 | + | 1.20129i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.91011e33 | − | 2.91011e33i | −0.889125 | − | 0.889125i | 0.105314 | − | 0.994439i | \(-0.466415\pi\) |
−0.994439 | + | 0.105314i | \(0.966415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12876e33i | 0.335355i | 0.985842 | + | 0.167678i | \(0.0536268\pi\) | ||||
−0.985842 | + | 0.167678i | \(0.946373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.21630e33i | 1.50710i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.55227e32 | − | 8.55227e32i | −0.240308 | − | 0.240308i | 0.576670 | − | 0.816977i | \(-0.304352\pi\) |
−0.816977 | + | 0.576670i | \(0.804352\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.79886e33 | − | 1.79886e33i | 0.491610 | − | 0.491610i | −0.417203 | − | 0.908813i | \(-0.636990\pi\) |
0.908813 | + | 0.417203i | \(0.136990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.73356e33 | −1.52410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.57764e33 | −0.666506 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.49951e31 | − | 9.49951e31i | 0.0238950 | − | 0.0238950i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.98971e33 | + | 7.98971e33i | 1.95519 | + | 1.95519i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.84419e33i | − | 1.86761i | −0.357787 | − | 0.933803i | \(-0.616468\pi\) | ||
0.357787 | − | 0.933803i | \(-0.383532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.24861e33i | 0.520906i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.36975e33 | + | 1.36975e33i | 0.308763 | + | 0.308763i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.25914e32 | − | 1.25914e32i | 0.0276198 | − | 0.0276198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.37109e33 | −0.506161 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.06363e33 | 1.88306 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.54479e33 | − | 3.54479e33i | 0.716804 | − | 0.716804i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.45092e33 | − | 3.45092e33i | −0.679237 | − | 0.679237i | 0.280591 | − | 0.959827i | \(-0.409470\pi\) |
−0.959827 | + | 0.280591i | \(0.909470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.06832e33i | − | 0.204688i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.59169e32i | 0.0669914i | 0.999439 | + | 0.0334957i | \(0.0106640\pi\) | ||||
−0.999439 | + | 0.0334957i | \(0.989336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.50352e33 | + | 2.50352e33i | 0.454599 | + | 0.454599i | 0.896878 | − | 0.442278i | \(-0.145830\pi\) |
−0.442278 | + | 0.896878i | \(0.645830\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.10893e33 | − | 8.10893e33i | 1.43360 | − | 1.43360i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.96771e33 | −0.338716 | −0.169358 | − | 0.985555i | \(-0.554169\pi\) | ||||
−0.169358 | + | 0.985555i | \(0.554169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.60349e32 | 0.0604001 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.26761e33 | + | 3.26761e33i | −0.533349 | + | 0.533349i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.71640e32 | + | 5.71640e32i | 0.0908648 | + | 0.0908648i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.52379e33i | − | 0.390702i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.22033e34i | − | 1.83998i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.60067e32 | + | 6.60067e32i | 0.0969383 | + | 0.0969383i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.66848e33 | − | 2.66848e33i | 0.381740 | − | 0.381740i | −0.489989 | − | 0.871729i | \(-0.662999\pi\) |
0.871729 | + | 0.489989i | \(0.162999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.77704e32 | 0.0665712 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.22905e34 | 1.66858 | 0.834288 | − | 0.551329i | \(-0.185879\pi\) | ||||
0.834288 | + | 0.551329i | \(0.185879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.73943e33 | − | 2.73943e33i | 0.362336 | − | 0.362336i | −0.502336 | − | 0.864672i | \(-0.667526\pi\) |
0.864672 | + | 0.502336i | \(0.167526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.66667e31 | + | 7.66667e31i | 0.00988005 | + | 0.00988005i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.48329e33i | − | 0.562957i | −0.959567 | − | 0.281479i | \(-0.909175\pi\) | ||
0.959567 | − | 0.281479i | \(-0.0908249\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.41689e34i | − | 1.73366i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.54884e34 | + | 1.54884e34i | 1.84677 | + | 1.84677i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.52283e33 | + | 4.52283e33i | −0.525556 | + | 0.525556i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.97176e32 | 0.0449799 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.43505e33 | 0.599916 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.04523e33 | − | 4.04523e33i | 0.435218 | − | 0.435218i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.45496e33 | − | 6.45496e33i | −0.676953 | − | 0.676953i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.00131e34i | − | 4.09065i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.39048e32i | 0.0935899i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.37928e33 | − | 2.37928e33i | −0.231186 | − | 0.231186i | 0.582001 | − | 0.813188i | \(-0.302270\pi\) |
−0.813188 | + | 0.582001i | \(0.802270\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.10222e34 | + | 1.10222e34i | −1.04420 | + | 1.04420i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.71172e34 | 1.58114 | 0.790572 | − | 0.612370i | \(-0.209784\pi\) | ||||
0.790572 | + | 0.612370i | \(0.209784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.20348e34 | 1.08399 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.23139e33 | + | 1.23139e33i | −0.108157 | + | 0.108157i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.78885e33 | − | 7.78885e33i | −0.667154 | − | 0.667154i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.04227e34i | 0.870669i | 0.900269 | + | 0.435334i | \(0.143370\pi\) | ||||
−0.900269 | + | 0.435334i | \(0.856630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.67185e34i | − | 1.36211i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.54201e33 | + | 3.54201e33i | 0.281469 | + | 0.281469i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.38790e34 | + | 1.38790e34i | −1.07579 | + | 1.07579i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.40692e34 | 1.06378 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.07870e34 | −1.53324 | −0.766622 | − | 0.642099i | \(-0.778064\pi\) | ||||
−0.766622 | + | 0.642099i | \(0.778064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.30138e34 | − | 1.30138e34i | 0.936445 | − | 0.936445i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.68714e34 | + | 1.68714e34i | 1.18444 | + | 1.18444i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.53094e32i | 0.0310352i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.07866e34i | − | 0.720906i | −0.932777 | − | 0.360453i | \(-0.882622\pi\) | ||
0.932777 | − | 0.360453i | \(-0.117378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.67154e34 | − | 1.67154e34i | −1.09009 | − | 1.09009i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.78205e33 | − | 3.78205e33i | 0.240684 | − | 0.240684i | −0.576449 | − | 0.817133i | \(-0.695562\pi\) |
0.817133 | + | 0.576449i | \(0.195562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.35377e33 | −0.518797 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.52118e33 | 0.213414 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.91394e33 | + | 3.91394e33i | −0.231520 | + | 0.231520i | −0.813327 | − | 0.581807i | \(-0.802346\pi\) |
0.581807 | + | 0.813327i | \(0.302346\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.35839e33 | + | 3.35839e33i | 0.193896 | + | 0.193896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.26222e34i | 2.96546i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.86566e34i | 1.57637i | 0.615441 | + | 0.788183i | \(0.288978\pi\) | ||||
−0.615441 | + | 0.788183i | \(0.711022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.81285e32 | + | 6.81285e32i | 0.0365839 | + | 0.0365839i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.41068e34 | − | 1.41068e34i | 0.739504 | − | 0.739504i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.01974e34 | −2.05724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.18836e33 | −0.209279 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.66515e34 | − | 2.66515e34i | 1.30023 | − | 1.30023i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.94980e32 | − | 8.94980e32i | −0.0426333 | − | 0.0426333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.95827e34i | − | 1.37605i | −0.725687 | − | 0.688025i | \(-0.758478\pi\) | ||
0.725687 | − | 0.688025i | \(-0.241522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.03679e34i | 2.28787i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.76308e34 | − | 1.76308e34i | −0.782078 | − | 0.782078i | 0.198103 | − | 0.980181i | \(-0.436522\pi\) |
−0.980181 | + | 0.198103i | \(0.936522\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.99816e33 | − | 1.99816e33i | 0.0865629 | − | 0.0865629i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.12800e34 | −0.900366 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.50377e34 | −1.03468 | −0.517341 | − | 0.855779i | \(-0.673078\pi\) | ||||
−0.517341 | + | 0.855779i | \(0.673078\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.56731e34 | + | 1.56731e34i | −0.632638 | + | 0.632638i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.25486e34 | − | 5.25486e34i | −2.07189 | − | 2.07189i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.46494e34i | − | 0.949383i | −0.880152 | − | 0.474691i | \(-0.842560\pi\) | ||
0.880152 | − | 0.474691i | \(-0.157440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.12999e33i | − | 0.0801420i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.40434e34 | − | 2.40434e34i | −0.883787 | − | 0.883787i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.06106e34 | + | 2.06106e34i | −0.740173 | + | 0.740173i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.64245e33 | −0.268155 | −0.134077 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134077 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.11278e34 | 1.06717 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.62175e31 | + | 6.62175e31i | −0.00221823 | + | 0.00221823i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.50250e33 | + | 5.50250e33i | 0.180122 | + | 0.180122i | 0.791409 | − | 0.611287i | \(-0.209348\pi\) |
−0.611287 | + | 0.791409i | \(0.709348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.48266e35i | 4.74283i |
(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 | 64.24.e.a.49.45 | 90 | ||
4.3 | odd | 2 | 16.24.e.a.5.30 | ✓ | 90 | ||
16.3 | odd | 4 | 16.24.e.a.13.30 | yes | 90 | ||
16.13 | even | 4 | inner | 64.24.e.a.17.45 | 90 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.24.e.a.5.30 | ✓ | 90 | 4.3 | odd | 2 | ||
16.24.e.a.13.30 | yes | 90 | 16.3 | odd | 4 | ||
64.24.e.a.17.45 | 90 | 16.13 | even | 4 | inner | ||
64.24.e.a.49.45 | 90 | 1.1 | even | 1 | trivial |