Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(3380\) | 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 3380.bz
\(\chi_{3380}(187,\cdot)\) \(\chi_{3380}(203,\cdot)\) \(\chi_{3380}(447,\cdot)\) \(\chi_{3380}(463,\cdot)\) \(\chi_{3380}(707,\cdot)\) \(\chi_{3380}(723,\cdot)\) \(\chi_{3380}(967,\cdot)\) \(\chi_{3380}(983,\cdot)\) \(\chi_{3380}(1227,\cdot)\) \(\chi_{3380}(1243,\cdot)\) \(\chi_{3380}(1487,\cdot)\) \(\chi_{3380}(1503,\cdot)\) \(\chi_{3380}(1747,\cdot)\) \(\chi_{3380}(1763,\cdot)\) \(\chi_{3380}(2007,\cdot)\) \(\chi_{3380}(2023,\cdot)\) \(\chi_{3380}(2283,\cdot)\) \(\chi_{3380}(2527,\cdot)\) \(\chi_{3380}(2543,\cdot)\) \(\chi_{3380}(2787,\cdot)\) \(\chi_{3380}(3047,\cdot)\) \(\chi_{3380}(3063,\cdot)\) \(\chi_{3380}(3307,\cdot)\) \(\chi_{3380}(3323,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,i,e\left(\frac{15}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(2787, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(-i\) | \(e\left(\frac{33}{52}\right)\) | \(-i\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) |