Basic properties
Modulus: | \(3381\) | |
Conductor: | \(3381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.cl
\(\chi_{3381}(2,\cdot)\) \(\chi_{3381}(32,\cdot)\) \(\chi_{3381}(95,\cdot)\) \(\chi_{3381}(170,\cdot)\) \(\chi_{3381}(179,\cdot)\) \(\chi_{3381}(200,\cdot)\) \(\chi_{3381}(233,\cdot)\) \(\chi_{3381}(242,\cdot)\) \(\chi_{3381}(284,\cdot)\) \(\chi_{3381}(305,\cdot)\) \(\chi_{3381}(317,\cdot)\) \(\chi_{3381}(326,\cdot)\) \(\chi_{3381}(338,\cdot)\) \(\chi_{3381}(347,\cdot)\) \(\chi_{3381}(380,\cdot)\) \(\chi_{3381}(443,\cdot)\) \(\chi_{3381}(464,\cdot)\) \(\chi_{3381}(473,\cdot)\) \(\chi_{3381}(485,\cdot)\) \(\chi_{3381}(515,\cdot)\) \(\chi_{3381}(578,\cdot)\) \(\chi_{3381}(611,\cdot)\) \(\chi_{3381}(653,\cdot)\) \(\chi_{3381}(662,\cdot)\) \(\chi_{3381}(683,\cdot)\) \(\chi_{3381}(725,\cdot)\) \(\chi_{3381}(767,\cdot)\) \(\chi_{3381}(788,\cdot)\) \(\chi_{3381}(800,\cdot)\) \(\chi_{3381}(809,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{17}{21}\right),e\left(\frac{3}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(284, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{115}{462}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{299}{462}\right)\) | \(e\left(\frac{14}{33}\right)\) |