Basic properties
| Modulus: | \(1113\) | |
| Conductor: | \(1113\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bj
\(\chi_{1113}(20,\cdot)\) \(\chi_{1113}(41,\cdot)\) \(\chi_{1113}(104,\cdot)\) \(\chi_{1113}(125,\cdot)\) \(\chi_{1113}(167,\cdot)\) \(\chi_{1113}(209,\cdot)\) \(\chi_{1113}(230,\cdot)\) \(\chi_{1113}(251,\cdot)\) \(\chi_{1113}(398,\cdot)\) \(\chi_{1113}(419,\cdot)\) \(\chi_{1113}(482,\cdot)\) \(\chi_{1113}(503,\cdot)\) \(\chi_{1113}(650,\cdot)\) \(\chi_{1113}(671,\cdot)\) \(\chi_{1113}(692,\cdot)\) \(\chi_{1113}(734,\cdot)\) \(\chi_{1113}(776,\cdot)\) \(\chi_{1113}(797,\cdot)\) \(\chi_{1113}(860,\cdot)\) \(\chi_{1113}(881,\cdot)\) \(\chi_{1113}(923,\cdot)\) \(\chi_{1113}(986,\cdot)\) \(\chi_{1113}(1028,\cdot)\) \(\chi_{1113}(1091,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((743,955,1009)\) → \((-1,-1,e\left(\frac{49}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{19}{52}\right)\) |