Basic properties
| Modulus: | \(5796\) | |
| Conductor: | \(1449\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(66\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1449}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5796.dy
\(\chi_{5796}(65,\cdot)\) \(\chi_{5796}(221,\cdot)\) \(\chi_{5796}(569,\cdot)\) \(\chi_{5796}(977,\cdot)\) \(\chi_{5796}(1073,\cdot)\) \(\chi_{5796}(1229,\cdot)\) \(\chi_{5796}(1325,\cdot)\) \(\chi_{5796}(1985,\cdot)\) \(\chi_{5796}(2081,\cdot)\) \(\chi_{5796}(2333,\cdot)\) \(\chi_{5796}(2489,\cdot)\) \(\chi_{5796}(3089,\cdot)\) \(\chi_{5796}(3593,\cdot)\) \(\chi_{5796}(4253,\cdot)\) \(\chi_{5796}(4505,\cdot)\) \(\chi_{5796}(4757,\cdot)\) \(\chi_{5796}(5261,\cdot)\) \(\chi_{5796}(5357,\cdot)\) \(\chi_{5796}(5609,\cdot)\) \(\chi_{5796}(5765,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{33})\) |
| Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((2899,1289,829,4789)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5796 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) |