Basic properties
| Modulus: | \(1113\) | |
| Conductor: | \(53\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{53}(14,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bi
\(\chi_{1113}(22,\cdot)\) \(\chi_{1113}(85,\cdot)\) \(\chi_{1113}(127,\cdot)\) \(\chi_{1113}(190,\cdot)\) \(\chi_{1113}(232,\cdot)\) \(\chi_{1113}(253,\cdot)\) \(\chi_{1113}(316,\cdot)\) \(\chi_{1113}(337,\cdot)\) \(\chi_{1113}(379,\cdot)\) \(\chi_{1113}(421,\cdot)\) \(\chi_{1113}(442,\cdot)\) \(\chi_{1113}(463,\cdot)\) \(\chi_{1113}(610,\cdot)\) \(\chi_{1113}(631,\cdot)\) \(\chi_{1113}(694,\cdot)\) \(\chi_{1113}(715,\cdot)\) \(\chi_{1113}(862,\cdot)\) \(\chi_{1113}(883,\cdot)\) \(\chi_{1113}(904,\cdot)\) \(\chi_{1113}(946,\cdot)\) \(\chi_{1113}(988,\cdot)\) \(\chi_{1113}(1009,\cdot)\) \(\chi_{1113}(1072,\cdot)\) \(\chi_{1113}(1093,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((743,955,1009)\) → \((1,1,e\left(\frac{15}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(862, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) |