Basic properties
| Modulus: | \(6498\) | |
| Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3249}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.bm
\(\chi_{6498}(7,\cdot)\) \(\chi_{6498}(49,\cdot)\) \(\chi_{6498}(349,\cdot)\) \(\chi_{6498}(391,\cdot)\) \(\chi_{6498}(691,\cdot)\) \(\chi_{6498}(733,\cdot)\) \(\chi_{6498}(1033,\cdot)\) \(\chi_{6498}(1075,\cdot)\) \(\chi_{6498}(1417,\cdot)\) \(\chi_{6498}(1717,\cdot)\) \(\chi_{6498}(1759,\cdot)\) \(\chi_{6498}(2059,\cdot)\) \(\chi_{6498}(2101,\cdot)\) \(\chi_{6498}(2401,\cdot)\) \(\chi_{6498}(2443,\cdot)\) \(\chi_{6498}(2743,\cdot)\) \(\chi_{6498}(2785,\cdot)\) \(\chi_{6498}(3085,\cdot)\) \(\chi_{6498}(3127,\cdot)\) \(\chi_{6498}(3427,\cdot)\) \(\chi_{6498}(3469,\cdot)\) \(\chi_{6498}(3769,\cdot)\) \(\chi_{6498}(3811,\cdot)\) \(\chi_{6498}(4111,\cdot)\) \(\chi_{6498}(4153,\cdot)\) \(\chi_{6498}(4453,\cdot)\) \(\chi_{6498}(4495,\cdot)\) \(\chi_{6498}(4795,\cdot)\) \(\chi_{6498}(4837,\cdot)\) \(\chi_{6498}(5137,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((3611,6139)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6498 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) |