Basic properties
Modulus: | \(1856\) | |
Conductor: | \(928\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{928}(253,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1856.cg
\(\chi_{1856}(137,\cdot)\) \(\chi_{1856}(153,\cdot)\) \(\chi_{1856}(345,\cdot)\) \(\chi_{1856}(425,\cdot)\) \(\chi_{1856}(537,\cdot)\) \(\chi_{1856}(553,\cdot)\) \(\chi_{1856}(569,\cdot)\) \(\chi_{1856}(649,\cdot)\) \(\chi_{1856}(665,\cdot)\) \(\chi_{1856}(681,\cdot)\) \(\chi_{1856}(793,\cdot)\) \(\chi_{1856}(873,\cdot)\) \(\chi_{1856}(1065,\cdot)\) \(\chi_{1856}(1081,\cdot)\) \(\chi_{1856}(1273,\cdot)\) \(\chi_{1856}(1353,\cdot)\) \(\chi_{1856}(1465,\cdot)\) \(\chi_{1856}(1481,\cdot)\) \(\chi_{1856}(1497,\cdot)\) \(\chi_{1856}(1577,\cdot)\) \(\chi_{1856}(1593,\cdot)\) \(\chi_{1856}(1609,\cdot)\) \(\chi_{1856}(1721,\cdot)\) \(\chi_{1856}(1801,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((639,581,321)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{17}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1856 }(137, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(i\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) |