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 \(\chi_{1449}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5796.ff
\(\chi_{5796}(101,\cdot)\) \(\chi_{5796}(257,\cdot)\) \(\chi_{5796}(353,\cdot)\) \(\chi_{5796}(509,\cdot)\) \(\chi_{5796}(761,\cdot)\) \(\chi_{5796}(857,\cdot)\) \(\chi_{5796}(1361,\cdot)\) \(\chi_{5796}(1613,\cdot)\) \(\chi_{5796}(1865,\cdot)\) \(\chi_{5796}(2525,\cdot)\) \(\chi_{5796}(3029,\cdot)\) \(\chi_{5796}(3629,\cdot)\) \(\chi_{5796}(3785,\cdot)\) \(\chi_{5796}(4037,\cdot)\) \(\chi_{5796}(4133,\cdot)\) \(\chi_{5796}(4793,\cdot)\) \(\chi_{5796}(4889,\cdot)\) \(\chi_{5796}(5045,\cdot)\) \(\chi_{5796}(5141,\cdot)\) \(\chi_{5796}(5549,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{33})\) |
| Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((2899,1289,829,4789)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{6}\right),e\left(\frac{5}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5796 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) |