Basic properties
Modulus: | \(1113\) | |
Conductor: | \(1113\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 1113.bp
\(\chi_{1113}(17,\cdot)\) \(\chi_{1113}(38,\cdot)\) \(\chi_{1113}(59,\cdot)\) \(\chi_{1113}(110,\cdot)\) \(\chi_{1113}(131,\cdot)\) \(\chi_{1113}(143,\cdot)\) \(\chi_{1113}(269,\cdot)\) \(\chi_{1113}(290,\cdot)\) \(\chi_{1113}(467,\cdot)\) \(\chi_{1113}(488,\cdot)\) \(\chi_{1113}(626,\cdot)\) \(\chi_{1113}(647,\cdot)\) \(\chi_{1113}(698,\cdot)\) \(\chi_{1113}(782,\cdot)\) \(\chi_{1113}(824,\cdot)\) \(\chi_{1113}(857,\cdot)\) \(\chi_{1113}(908,\cdot)\) \(\chi_{1113}(941,\cdot)\) \(\chi_{1113}(971,\cdot)\) \(\chi_{1113}(983,\cdot)\) \(\chi_{1113}(992,\cdot)\) \(\chi_{1113}(1013,\cdot)\) \(\chi_{1113}(1067,\cdot)\) \(\chi_{1113}(1097,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((743,955,1009)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1113 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) |