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.bx
\(\chi_{3380}(359,\cdot)\) \(\chi_{3380}(499,\cdot)\) \(\chi_{3380}(619,\cdot)\) \(\chi_{3380}(759,\cdot)\) \(\chi_{3380}(879,\cdot)\) \(\chi_{3380}(1019,\cdot)\) \(\chi_{3380}(1139,\cdot)\) \(\chi_{3380}(1279,\cdot)\) \(\chi_{3380}(1399,\cdot)\) \(\chi_{3380}(1539,\cdot)\) \(\chi_{3380}(1659,\cdot)\) \(\chi_{3380}(1799,\cdot)\) \(\chi_{3380}(1919,\cdot)\) \(\chi_{3380}(2059,\cdot)\) \(\chi_{3380}(2179,\cdot)\) \(\chi_{3380}(2319,\cdot)\) \(\chi_{3380}(2439,\cdot)\) \(\chi_{3380}(2579,\cdot)\) \(\chi_{3380}(2699,\cdot)\) \(\chi_{3380}(2839,\cdot)\) \(\chi_{3380}(2959,\cdot)\) \(\chi_{3380}(3099,\cdot)\) \(\chi_{3380}(3219,\cdot)\) \(\chi_{3380}(3359,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,-1,e\left(\frac{25}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(359, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(-i\) | \(e\left(\frac{3}{52}\right)\) | \(-1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) |