Basic properties
| Modulus: | \(6498\) | |
| Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3249}(335,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.bu
\(\chi_{6498}(335,\cdot)\) \(\chi_{6498}(635,\cdot)\) \(\chi_{6498}(677,\cdot)\) \(\chi_{6498}(977,\cdot)\) \(\chi_{6498}(1019,\cdot)\) \(\chi_{6498}(1319,\cdot)\) \(\chi_{6498}(1361,\cdot)\) \(\chi_{6498}(1661,\cdot)\) \(\chi_{6498}(1703,\cdot)\) \(\chi_{6498}(2003,\cdot)\) \(\chi_{6498}(2045,\cdot)\) \(\chi_{6498}(2345,\cdot)\) \(\chi_{6498}(2387,\cdot)\) \(\chi_{6498}(2687,\cdot)\) \(\chi_{6498}(2729,\cdot)\) \(\chi_{6498}(3029,\cdot)\) \(\chi_{6498}(3071,\cdot)\) \(\chi_{6498}(3371,\cdot)\) \(\chi_{6498}(3413,\cdot)\) \(\chi_{6498}(3713,\cdot)\) \(\chi_{6498}(3755,\cdot)\) \(\chi_{6498}(4055,\cdot)\) \(\chi_{6498}(4097,\cdot)\) \(\chi_{6498}(4397,\cdot)\) \(\chi_{6498}(4439,\cdot)\) \(\chi_{6498}(4739,\cdot)\) \(\chi_{6498}(4781,\cdot)\) \(\chi_{6498}(5081,\cdot)\) \(\chi_{6498}(5423,\cdot)\) \(\chi_{6498}(5465,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3611,6139)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{53}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6498 }(335, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{11}{114}\right)\) |