Basic properties
| Modulus: | \(5796\) | |
| Conductor: | \(1449\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(33\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1449}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5796.dv
\(\chi_{5796}(25,\cdot)\) \(\chi_{5796}(121,\cdot)\) \(\chi_{5796}(625,\cdot)\) \(\chi_{5796}(877,\cdot)\) \(\chi_{5796}(1129,\cdot)\) \(\chi_{5796}(1789,\cdot)\) \(\chi_{5796}(2293,\cdot)\) \(\chi_{5796}(2893,\cdot)\) \(\chi_{5796}(3049,\cdot)\) \(\chi_{5796}(3301,\cdot)\) \(\chi_{5796}(3397,\cdot)\) \(\chi_{5796}(4057,\cdot)\) \(\chi_{5796}(4153,\cdot)\) \(\chi_{5796}(4309,\cdot)\) \(\chi_{5796}(4405,\cdot)\) \(\chi_{5796}(4813,\cdot)\) \(\chi_{5796}(5161,\cdot)\) \(\chi_{5796}(5317,\cdot)\) \(\chi_{5796}(5413,\cdot)\) \(\chi_{5796}(5569,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{33})\) |
| Fixed field: | Number field defined by a degree 33 polynomial |
Values on generators
\((2899,1289,829,4789)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5796 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) |