Basic properties
| Modulus: | \(3381\) | |
| Conductor: | \(3381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.bx
\(\chi_{3381}(8,\cdot)\) \(\chi_{3381}(29,\cdot)\) \(\chi_{3381}(71,\cdot)\) \(\chi_{3381}(239,\cdot)\) \(\chi_{3381}(302,\cdot)\) \(\chi_{3381}(386,\cdot)\) \(\chi_{3381}(407,\cdot)\) \(\chi_{3381}(449,\cdot)\) \(\chi_{3381}(512,\cdot)\) \(\chi_{3381}(533,\cdot)\) \(\chi_{3381}(554,\cdot)\) \(\chi_{3381}(680,\cdot)\) \(\chi_{3381}(722,\cdot)\) \(\chi_{3381}(869,\cdot)\) \(\chi_{3381}(890,\cdot)\) \(\chi_{3381}(974,\cdot)\) \(\chi_{3381}(995,\cdot)\) \(\chi_{3381}(1016,\cdot)\) \(\chi_{3381}(1037,\cdot)\) \(\chi_{3381}(1163,\cdot)\) \(\chi_{3381}(1205,\cdot)\) \(\chi_{3381}(1268,\cdot)\) \(\chi_{3381}(1352,\cdot)\) \(\chi_{3381}(1415,\cdot)\) \(\chi_{3381}(1457,\cdot)\) \(\chi_{3381}(1478,\cdot)\) \(\chi_{3381}(1499,\cdot)\) \(\chi_{3381}(1646,\cdot)\) \(\chi_{3381}(1688,\cdot)\) \(\chi_{3381}(1751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{1}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3381 }(1037, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{4}{11}\right)\) |