Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(3380\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.co
\(\chi_{3380}(179,\cdot)\) \(\chi_{3380}(199,\cdot)\) \(\chi_{3380}(439,\cdot)\) \(\chi_{3380}(459,\cdot)\) \(\chi_{3380}(719,\cdot)\) \(\chi_{3380}(959,\cdot)\) \(\chi_{3380}(979,\cdot)\) \(\chi_{3380}(1219,\cdot)\) \(\chi_{3380}(1239,\cdot)\) \(\chi_{3380}(1479,\cdot)\) \(\chi_{3380}(1739,\cdot)\) \(\chi_{3380}(1759,\cdot)\) \(\chi_{3380}(1999,\cdot)\) \(\chi_{3380}(2019,\cdot)\) \(\chi_{3380}(2259,\cdot)\) \(\chi_{3380}(2279,\cdot)\) \(\chi_{3380}(2519,\cdot)\) \(\chi_{3380}(2539,\cdot)\) \(\chi_{3380}(2779,\cdot)\) \(\chi_{3380}(2799,\cdot)\) \(\chi_{3380}(3039,\cdot)\) \(\chi_{3380}(3059,\cdot)\) \(\chi_{3380}(3299,\cdot)\) \(\chi_{3380}(3319,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,-1,e\left(\frac{71}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(2779, a) \) | \(-1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) |