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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.by
\(\chi_{4029}(38,\cdot)\) \(\chi_{4029}(89,\cdot)\) \(\chi_{4029}(302,\cdot)\) \(\chi_{4029}(599,\cdot)\) \(\chi_{4029}(650,\cdot)\) \(\chi_{4029}(812,\cdot)\) \(\chi_{4029}(854,\cdot)\) \(\chi_{4029}(956,\cdot)\) \(\chi_{4029}(1364,\cdot)\) \(\chi_{4029}(1568,\cdot)\) \(\chi_{4029}(1721,\cdot)\) \(\chi_{4029}(1934,\cdot)\) \(\chi_{4029}(1985,\cdot)\) \(\chi_{4029}(2027,\cdot)\) \(\chi_{4029}(2435,\cdot)\) \(\chi_{4029}(2495,\cdot)\) \(\chi_{4029}(2546,\cdot)\) \(\chi_{4029}(2750,\cdot)\) \(\chi_{4029}(2852,\cdot)\) \(\chi_{4029}(2945,\cdot)\) \(\chi_{4029}(3260,\cdot)\) \(\chi_{4029}(3464,\cdot)\) \(\chi_{4029}(3617,\cdot)\) \(\chi_{4029}(3923,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2687,3556,3163)\) → \((-1,-i,e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) |