Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(6815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.cg
\(\chi_{6815}(12,\cdot)\) \(\chi_{6815}(157,\cdot)\) \(\chi_{6815}(447,\cdot)\) \(\chi_{6815}(568,\cdot)\) \(\chi_{6815}(592,\cdot)\) \(\chi_{6815}(713,\cdot)\) \(\chi_{6815}(737,\cdot)\) \(\chi_{6815}(858,\cdot)\) \(\chi_{6815}(882,\cdot)\) \(\chi_{6815}(1003,\cdot)\) \(\chi_{6815}(1293,\cdot)\) \(\chi_{6815}(1438,\cdot)\) \(\chi_{6815}(1583,\cdot)\) \(\chi_{6815}(1607,\cdot)\) \(\chi_{6815}(1728,\cdot)\) \(\chi_{6815}(1897,\cdot)\) \(\chi_{6815}(2042,\cdot)\) \(\chi_{6815}(2187,\cdot)\) \(\chi_{6815}(2453,\cdot)\) \(\chi_{6815}(2622,\cdot)\) \(\chi_{6815}(2743,\cdot)\) \(\chi_{6815}(2888,\cdot)\) \(\chi_{6815}(3033,\cdot)\) \(\chi_{6815}(3057,\cdot)\) \(\chi_{6815}(3202,\cdot)\) \(\chi_{6815}(3468,\cdot)\) \(\chi_{6815}(3492,\cdot)\) \(\chi_{6815}(3637,\cdot)\) \(\chi_{6815}(3903,\cdot)\) \(\chi_{6815}(4048,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{92})$ |
| Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2727,2351,146)\) → \((i,i,e\left(\frac{5}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{59}{92}\right)\) |