Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | 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 731.be
\(\chi_{731}(59,\cdot)\) \(\chi_{731}(121,\cdot)\) \(\chi_{731}(127,\cdot)\) \(\chi_{731}(145,\cdot)\) \(\chi_{731}(213,\cdot)\) \(\chi_{731}(219,\cdot)\) \(\chi_{731}(236,\cdot)\) \(\chi_{731}(274,\cdot)\) \(\chi_{731}(342,\cdot)\) \(\chi_{731}(348,\cdot)\) \(\chi_{731}(355,\cdot)\) \(\chi_{731}(365,\cdot)\) \(\chi_{731}(434,\cdot)\) \(\chi_{731}(451,\cdot)\) \(\chi_{731}(484,\cdot)\) \(\chi_{731}(508,\cdot)\) \(\chi_{731}(563,\cdot)\) \(\chi_{731}(570,\cdot)\) \(\chi_{731}(580,\cdot)\) \(\chi_{731}(637,\cdot)\) \(\chi_{731}(661,\cdot)\) \(\chi_{731}(699,\cdot)\) \(\chi_{731}(723,\cdot)\) \(\chi_{731}(729,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((173,562)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(342, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{23}{56}\right)\) |