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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.cc
\(\chi_{3380}(103,\cdot)\) \(\chi_{3380}(207,\cdot)\) \(\chi_{3380}(363,\cdot)\) \(\chi_{3380}(467,\cdot)\) \(\chi_{3380}(623,\cdot)\) \(\chi_{3380}(727,\cdot)\) \(\chi_{3380}(883,\cdot)\) \(\chi_{3380}(987,\cdot)\) \(\chi_{3380}(1143,\cdot)\) \(\chi_{3380}(1247,\cdot)\) \(\chi_{3380}(1403,\cdot)\) \(\chi_{3380}(1507,\cdot)\) \(\chi_{3380}(1663,\cdot)\) \(\chi_{3380}(1767,\cdot)\) \(\chi_{3380}(1923,\cdot)\) \(\chi_{3380}(2183,\cdot)\) \(\chi_{3380}(2287,\cdot)\) \(\chi_{3380}(2443,\cdot)\) \(\chi_{3380}(2547,\cdot)\) \(\chi_{3380}(2807,\cdot)\) \(\chi_{3380}(2963,\cdot)\) \(\chi_{3380}(3067,\cdot)\) \(\chi_{3380}(3223,\cdot)\) \(\chi_{3380}(3327,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,-i,e\left(\frac{23}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(1663, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(-1\) | \(e\left(\frac{9}{26}\right)\) | \(-i\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) |