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.eg
\(\chi_{5796}(607,\cdot)\) \(\chi_{5796}(859,\cdot)\) \(\chi_{5796}(1363,\cdot)\) \(\chi_{5796}(1375,\cdot)\) \(\chi_{5796}(1867,\cdot)\) \(\chi_{5796}(1879,\cdot)\) \(\chi_{5796}(2119,\cdot)\) \(\chi_{5796}(2371,\cdot)\) \(\chi_{5796}(2635,\cdot)\) \(\chi_{5796}(2887,\cdot)\) \(\chi_{5796}(3643,\cdot)\) \(\chi_{5796}(3895,\cdot)\) \(\chi_{5796}(4135,\cdot)\) \(\chi_{5796}(4399,\cdot)\) \(\chi_{5796}(4639,\cdot)\) \(\chi_{5796}(4903,\cdot)\) \(\chi_{5796}(5155,\cdot)\) \(\chi_{5796}(5395,\cdot)\) \(\chi_{5796}(5407,\cdot)\) \(\chi_{5796}(5647,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{33})\) |
Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((2899,1289,829,4789)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{5}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 5796 }(607, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{41}{66}\right)\) |