Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | 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 4029.bx
\(\chi_{4029}(140,\cdot)\) \(\chi_{4029}(191,\cdot)\) \(\chi_{4029}(251,\cdot)\) \(\chi_{4029}(659,\cdot)\) \(\chi_{4029}(701,\cdot)\) \(\chi_{4029}(752,\cdot)\) \(\chi_{4029}(965,\cdot)\) \(\chi_{4029}(1118,\cdot)\) \(\chi_{4029}(1322,\cdot)\) \(\chi_{4029}(1730,\cdot)\) \(\chi_{4029}(1832,\cdot)\) \(\chi_{4029}(1874,\cdot)\) \(\chi_{4029}(2036,\cdot)\) \(\chi_{4029}(2087,\cdot)\) \(\chi_{4029}(2384,\cdot)\) \(\chi_{4029}(2597,\cdot)\) \(\chi_{4029}(2648,\cdot)\) \(\chi_{4029}(2792,\cdot)\) \(\chi_{4029}(3098,\cdot)\) \(\chi_{4029}(3251,\cdot)\) \(\chi_{4029}(3455,\cdot)\) \(\chi_{4029}(3770,\cdot)\) \(\chi_{4029}(3863,\cdot)\) \(\chi_{4029}(3965,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2687,3556,3163)\) → \((-1,-i,e\left(\frac{17}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(3863, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) |