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Input interpretation:

1 -12i -7j -1k


Unit quaternion:

1\/sqrt(195) - 4 sqrt(3\/65)i - 7\/sqrt(195)j - 1\/sqrt(195)k


Conjugate:

1 + 12i + 7j + 1k


Inverse:

1\/195 + 4\/65i + 7\/195j + 1\/195k


Primality:

1 - 12i - 7j - 1k is not prime.


Matrix representation of corresponding 3D rotation:

(19\/39 | 34\/39 | 2\/39\n166\/195 | -19\/39 | 38\/195\n38\/195 | -2\/39 | -191\/195)


Axis/angle of corresponding 3D rotation:

axis: (-4 sqrt(3\/65), -7\/sqrt(195), -1\/sqrt(195))  |   angle: 2 cos^(-1)(1\/sqrt(195))

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