Basic properties
Modulus: | \(3381\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(596,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.cb
\(\chi_{3381}(43,\cdot)\) \(\chi_{3381}(106,\cdot)\) \(\chi_{3381}(274,\cdot)\) \(\chi_{3381}(316,\cdot)\) \(\chi_{3381}(337,\cdot)\) \(\chi_{3381}(379,\cdot)\) \(\chi_{3381}(421,\cdot)\) \(\chi_{3381}(526,\cdot)\) \(\chi_{3381}(631,\cdot)\) \(\chi_{3381}(757,\cdot)\) \(\chi_{3381}(778,\cdot)\) \(\chi_{3381}(799,\cdot)\) \(\chi_{3381}(820,\cdot)\) \(\chi_{3381}(862,\cdot)\) \(\chi_{3381}(904,\cdot)\) \(\chi_{3381}(925,\cdot)\) \(\chi_{3381}(1009,\cdot)\) \(\chi_{3381}(1072,\cdot)\) \(\chi_{3381}(1114,\cdot)\) \(\chi_{3381}(1240,\cdot)\) \(\chi_{3381}(1261,\cdot)\) \(\chi_{3381}(1282,\cdot)\) \(\chi_{3381}(1303,\cdot)\) \(\chi_{3381}(1345,\cdot)\) \(\chi_{3381}(1387,\cdot)\) \(\chi_{3381}(1408,\cdot)\) \(\chi_{3381}(1492,\cdot)\) \(\chi_{3381}(1555,\cdot)\) \(\chi_{3381}(1597,\cdot)\) \(\chi_{3381}(1723,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{6}{7}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(1723, a) \) | \(-1\) | \(1\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{19}{22}\right)\) |