Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(1363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1363}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.cc
\(\chi_{6815}(41,\cdot)\) \(\chi_{6815}(186,\cdot)\) \(\chi_{6815}(481,\cdot)\) \(\chi_{6815}(621,\cdot)\) \(\chi_{6815}(626,\cdot)\) \(\chi_{6815}(771,\cdot)\) \(\chi_{6815}(916,\cdot)\) \(\chi_{6815}(1056,\cdot)\) \(\chi_{6815}(1201,\cdot)\) \(\chi_{6815}(1206,\cdot)\) \(\chi_{6815}(1346,\cdot)\) \(\chi_{6815}(1351,\cdot)\) \(\chi_{6815}(1496,\cdot)\) \(\chi_{6815}(1636,\cdot)\) \(\chi_{6815}(1641,\cdot)\) \(\chi_{6815}(2361,\cdot)\) \(\chi_{6815}(2506,\cdot)\) \(\chi_{6815}(2511,\cdot)\) \(\chi_{6815}(2651,\cdot)\) \(\chi_{6815}(2796,\cdot)\) \(\chi_{6815}(3086,\cdot)\) \(\chi_{6815}(3231,\cdot)\) \(\chi_{6815}(3236,\cdot)\) \(\chi_{6815}(3376,\cdot)\) \(\chi_{6815}(3381,\cdot)\) \(\chi_{6815}(3521,\cdot)\) \(\chi_{6815}(3671,\cdot)\) \(\chi_{6815}(3961,\cdot)\) \(\chi_{6815}(4391,\cdot)\) \(\chi_{6815}(4541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{92})$ |
| Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2727,2351,146)\) → \((1,i,e\left(\frac{15}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{92}\right)\) | \(e\left(\frac{71}{92}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{2}{23}\right)\) |