Basic properties
| Modulus: | \(5796\) | |
| Conductor: | \(5796\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(66\) | 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 5796.fz
\(\chi_{5796}(67,\cdot)\) \(\chi_{5796}(79,\cdot)\) \(\chi_{5796}(319,\cdot)\) \(\chi_{5796}(571,\cdot)\) \(\chi_{5796}(835,\cdot)\) \(\chi_{5796}(1075,\cdot)\) \(\chi_{5796}(1339,\cdot)\) \(\chi_{5796}(1579,\cdot)\) \(\chi_{5796}(1831,\cdot)\) \(\chi_{5796}(2587,\cdot)\) \(\chi_{5796}(2839,\cdot)\) \(\chi_{5796}(3103,\cdot)\) \(\chi_{5796}(3355,\cdot)\) \(\chi_{5796}(3595,\cdot)\) \(\chi_{5796}(3607,\cdot)\) \(\chi_{5796}(4099,\cdot)\) \(\chi_{5796}(4111,\cdot)\) \(\chi_{5796}(4615,\cdot)\) \(\chi_{5796}(4867,\cdot)\) \(\chi_{5796}(5623,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{33})\) |
| Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((2899,1289,829,4789)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5796 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) |