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.cg
\(\chi_{3380}(47,\cdot)\) \(\chi_{3380}(83,\cdot)\) \(\chi_{3380}(307,\cdot)\) \(\chi_{3380}(343,\cdot)\) \(\chi_{3380}(567,\cdot)\) \(\chi_{3380}(603,\cdot)\) \(\chi_{3380}(827,\cdot)\) \(\chi_{3380}(863,\cdot)\) \(\chi_{3380}(1087,\cdot)\) \(\chi_{3380}(1123,\cdot)\) \(\chi_{3380}(1347,\cdot)\) \(\chi_{3380}(1383,\cdot)\) \(\chi_{3380}(1607,\cdot)\) \(\chi_{3380}(1643,\cdot)\) \(\chi_{3380}(1867,\cdot)\) \(\chi_{3380}(1903,\cdot)\) \(\chi_{3380}(2163,\cdot)\) \(\chi_{3380}(2387,\cdot)\) \(\chi_{3380}(2423,\cdot)\) \(\chi_{3380}(2647,\cdot)\) \(\chi_{3380}(2683,\cdot)\) \(\chi_{3380}(2907,\cdot)\) \(\chi_{3380}(3167,\cdot)\) \(\chi_{3380}(3203,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,677,1861)\) → \((-1,i,e\left(\frac{49}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3380 }(2907, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(i\) | \(e\left(\frac{35}{52}\right)\) | \(-i\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) |