Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 731.bh
\(\chi_{731}(13,\cdot)\) \(\chi_{731}(38,\cdot)\) \(\chi_{731}(81,\cdot)\) \(\chi_{731}(225,\cdot)\) \(\chi_{731}(268,\cdot)\) \(\chi_{731}(310,\cdot)\) \(\chi_{731}(353,\cdot)\) \(\chi_{731}(361,\cdot)\) \(\chi_{731}(404,\cdot)\) \(\chi_{731}(412,\cdot)\) \(\chi_{731}(455,\cdot)\) \(\chi_{731}(497,\cdot)\) \(\chi_{731}(531,\cdot)\) \(\chi_{731}(540,\cdot)\) \(\chi_{731}(574,\cdot)\) \(\chi_{731}(582,\cdot)\) \(\chi_{731}(599,\cdot)\) \(\chi_{731}(616,\cdot)\) \(\chi_{731}(625,\cdot)\) \(\chi_{731}(633,\cdot)\) \(\chi_{731}(642,\cdot)\) \(\chi_{731}(659,\cdot)\) \(\chi_{731}(676,\cdot)\) \(\chi_{731}(701,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((173,562)\) → \((i,e\left(\frac{2}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) |