Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(1363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(161\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1363}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.ci
\(\chi_{6815}(16,\cdot)\) \(\chi_{6815}(36,\cdot)\) \(\chi_{6815}(81,\cdot)\) \(\chi_{6815}(111,\cdot)\) \(\chi_{6815}(136,\cdot)\) \(\chi_{6815}(256,\cdot)\) \(\chi_{6815}(286,\cdot)\) \(\chi_{6815}(306,\cdot)\) \(\chi_{6815}(371,\cdot)\) \(\chi_{6815}(401,\cdot)\) \(\chi_{6815}(426,\cdot)\) \(\chi_{6815}(431,\cdot)\) \(\chi_{6815}(451,\cdot)\) \(\chi_{6815}(571,\cdot)\) \(\chi_{6815}(576,\cdot)\) \(\chi_{6815}(596,\cdot)\) \(\chi_{6815}(661,\cdot)\) \(\chi_{6815}(721,\cdot)\) \(\chi_{6815}(741,\cdot)\) \(\chi_{6815}(761,\cdot)\) \(\chi_{6815}(806,\cdot)\) \(\chi_{6815}(836,\cdot)\) \(\chi_{6815}(1011,\cdot)\) \(\chi_{6815}(1051,\cdot)\) \(\chi_{6815}(1156,\cdot)\) \(\chi_{6815}(1196,\cdot)\) \(\chi_{6815}(1271,\cdot)\) \(\chi_{6815}(1296,\cdot)\) \(\chi_{6815}(1301,\cdot)\) \(\chi_{6815}(1341,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 161 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((1,e\left(\frac{1}{7}\right),e\left(\frac{13}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{161}\right)\) | \(e\left(\frac{3}{161}\right)\) | \(e\left(\frac{102}{161}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{129}{161}\right)\) | \(e\left(\frac{153}{161}\right)\) | \(e\left(\frac{6}{161}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{127}{161}\right)\) |