Basic properties
Modulus: | \(833\) | |
Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 833.bf
\(\chi_{833}(8,\cdot)\) \(\chi_{833}(15,\cdot)\) \(\chi_{833}(36,\cdot)\) \(\chi_{833}(43,\cdot)\) \(\chi_{833}(127,\cdot)\) \(\chi_{833}(134,\cdot)\) \(\chi_{833}(155,\cdot)\) \(\chi_{833}(162,\cdot)\) \(\chi_{833}(253,\cdot)\) \(\chi_{833}(274,\cdot)\) \(\chi_{833}(281,\cdot)\) \(\chi_{833}(365,\cdot)\) \(\chi_{833}(372,\cdot)\) \(\chi_{833}(400,\cdot)\) \(\chi_{833}(484,\cdot)\) \(\chi_{833}(512,\cdot)\) \(\chi_{833}(519,\cdot)\) \(\chi_{833}(603,\cdot)\) \(\chi_{833}(610,\cdot)\) \(\chi_{833}(631,\cdot)\) \(\chi_{833}(722,\cdot)\) \(\chi_{833}(729,\cdot)\) \(\chi_{833}(750,\cdot)\) \(\chi_{833}(757,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((52,785)\) → \((e\left(\frac{6}{7}\right),e\left(\frac{5}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 833 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) |