Basic properties
Modulus: | \(1113\) | |
Conductor: | \(159\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{159}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bh
\(\chi_{1113}(8,\cdot)\) \(\chi_{1113}(50,\cdot)\) \(\chi_{1113}(71,\cdot)\) \(\chi_{1113}(92,\cdot)\) \(\chi_{1113}(239,\cdot)\) \(\chi_{1113}(260,\cdot)\) \(\chi_{1113}(323,\cdot)\) \(\chi_{1113}(344,\cdot)\) \(\chi_{1113}(491,\cdot)\) \(\chi_{1113}(512,\cdot)\) \(\chi_{1113}(533,\cdot)\) \(\chi_{1113}(575,\cdot)\) \(\chi_{1113}(617,\cdot)\) \(\chi_{1113}(638,\cdot)\) \(\chi_{1113}(701,\cdot)\) \(\chi_{1113}(722,\cdot)\) \(\chi_{1113}(764,\cdot)\) \(\chi_{1113}(827,\cdot)\) \(\chi_{1113}(869,\cdot)\) \(\chi_{1113}(932,\cdot)\) \(\chi_{1113}(974,\cdot)\) \(\chi_{1113}(995,\cdot)\) \(\chi_{1113}(1058,\cdot)\) \(\chi_{1113}(1079,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((743,955,1009)\) → \((-1,1,e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1113 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{52}\right)\) |