Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.bz
\(\chi_{4029}(64,\cdot)\) \(\chi_{4029}(166,\cdot)\) \(\chi_{4029}(259,\cdot)\) \(\chi_{4029}(574,\cdot)\) \(\chi_{4029}(778,\cdot)\) \(\chi_{4029}(931,\cdot)\) \(\chi_{4029}(1237,\cdot)\) \(\chi_{4029}(1381,\cdot)\) \(\chi_{4029}(1432,\cdot)\) \(\chi_{4029}(1645,\cdot)\) \(\chi_{4029}(1942,\cdot)\) \(\chi_{4029}(1993,\cdot)\) \(\chi_{4029}(2155,\cdot)\) \(\chi_{4029}(2197,\cdot)\) \(\chi_{4029}(2299,\cdot)\) \(\chi_{4029}(2707,\cdot)\) \(\chi_{4029}(2911,\cdot)\) \(\chi_{4029}(3064,\cdot)\) \(\chi_{4029}(3277,\cdot)\) \(\chi_{4029}(3328,\cdot)\) \(\chi_{4029}(3370,\cdot)\) \(\chi_{4029}(3778,\cdot)\) \(\chi_{4029}(3838,\cdot)\) \(\chi_{4029}(3889,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2687,3556,3163)\) → \((1,-i,e\left(\frac{12}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(259, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) |