Basic properties
| Modulus: | \(6498\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.cc
\(\chi_{6498}(55,\cdot)\) \(\chi_{6498}(73,\cdot)\) \(\chi_{6498}(199,\cdot)\) \(\chi_{6498}(253,\cdot)\) \(\chi_{6498}(271,\cdot)\) \(\chi_{6498}(289,\cdot)\) \(\chi_{6498}(397,\cdot)\) \(\chi_{6498}(541,\cdot)\) \(\chi_{6498}(613,\cdot)\) \(\chi_{6498}(631,\cdot)\) \(\chi_{6498}(739,\cdot)\) \(\chi_{6498}(757,\cdot)\) \(\chi_{6498}(883,\cdot)\) \(\chi_{6498}(937,\cdot)\) \(\chi_{6498}(955,\cdot)\) \(\chi_{6498}(973,\cdot)\) \(\chi_{6498}(1081,\cdot)\) \(\chi_{6498}(1099,\cdot)\) \(\chi_{6498}(1225,\cdot)\) \(\chi_{6498}(1279,\cdot)\) \(\chi_{6498}(1297,\cdot)\) \(\chi_{6498}(1315,\cdot)\) \(\chi_{6498}(1423,\cdot)\) \(\chi_{6498}(1441,\cdot)\) \(\chi_{6498}(1567,\cdot)\) \(\chi_{6498}(1621,\cdot)\) \(\chi_{6498}(1639,\cdot)\) \(\chi_{6498}(1657,\cdot)\) \(\chi_{6498}(1765,\cdot)\) \(\chi_{6498}(1783,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((3611,6139)\) → \((1,e\left(\frac{167}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6498 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{100}{171}\right)\) | \(e\left(\frac{25}{171}\right)\) | \(e\left(\frac{103}{171}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{11}{171}\right)\) |