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.by
\(\chi_{3381}(20,\cdot)\) \(\chi_{3381}(83,\cdot)\) \(\chi_{3381}(125,\cdot)\) \(\chi_{3381}(251,\cdot)\) \(\chi_{3381}(272,\cdot)\) \(\chi_{3381}(314,\cdot)\) \(\chi_{3381}(356,\cdot)\) \(\chi_{3381}(398,\cdot)\) \(\chi_{3381}(419,\cdot)\) \(\chi_{3381}(503,\cdot)\) \(\chi_{3381}(566,\cdot)\) \(\chi_{3381}(608,\cdot)\) \(\chi_{3381}(755,\cdot)\) \(\chi_{3381}(776,\cdot)\) \(\chi_{3381}(797,\cdot)\) \(\chi_{3381}(839,\cdot)\) \(\chi_{3381}(902,\cdot)\) \(\chi_{3381}(986,\cdot)\) \(\chi_{3381}(1049,\cdot)\) \(\chi_{3381}(1091,\cdot)\) \(\chi_{3381}(1217,\cdot)\) \(\chi_{3381}(1238,\cdot)\) \(\chi_{3381}(1259,\cdot)\) \(\chi_{3381}(1280,\cdot)\) \(\chi_{3381}(1364,\cdot)\) \(\chi_{3381}(1385,\cdot)\) \(\chi_{3381}(1532,\cdot)\) \(\chi_{3381}(1574,\cdot)\) \(\chi_{3381}(1700,\cdot)\) \(\chi_{3381}(1721,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{7}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(776, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{3}{11}\right)\) |