Basic properties
Modulus: | \(4029\) | |
Conductor: | \(79\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{79}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.bs
\(\chi_{4029}(256,\cdot)\) \(\chi_{4029}(358,\cdot)\) \(\chi_{4029}(562,\cdot)\) \(\chi_{4029}(664,\cdot)\) \(\chi_{4029}(715,\cdot)\) \(\chi_{4029}(919,\cdot)\) \(\chi_{4029}(1021,\cdot)\) \(\chi_{4029}(1072,\cdot)\) \(\chi_{4029}(1225,\cdot)\) \(\chi_{4029}(1582,\cdot)\) \(\chi_{4029}(1684,\cdot)\) \(\chi_{4029}(1735,\cdot)\) \(\chi_{4029}(1837,\cdot)\) \(\chi_{4029}(2296,\cdot)\) \(\chi_{4029}(2500,\cdot)\) \(\chi_{4029}(2857,\cdot)\) \(\chi_{4029}(2959,\cdot)\) \(\chi_{4029}(3112,\cdot)\) \(\chi_{4029}(3265,\cdot)\) \(\chi_{4029}(3367,\cdot)\) \(\chi_{4029}(3469,\cdot)\) \(\chi_{4029}(3520,\cdot)\) \(\chi_{4029}(3571,\cdot)\) \(\chi_{4029}(3724,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((2687,3556,3163)\) → \((1,1,e\left(\frac{32}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(1072, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) |