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.ck
\(\chi_{3381}(5,\cdot)\) \(\chi_{3381}(17,\cdot)\) \(\chi_{3381}(38,\cdot)\) \(\chi_{3381}(89,\cdot)\) \(\chi_{3381}(122,\cdot)\) \(\chi_{3381}(143,\cdot)\) \(\chi_{3381}(152,\cdot)\) \(\chi_{3381}(194,\cdot)\) \(\chi_{3381}(290,\cdot)\) \(\chi_{3381}(320,\cdot)\) \(\chi_{3381}(332,\cdot)\) \(\chi_{3381}(341,\cdot)\) \(\chi_{3381}(383,\cdot)\) \(\chi_{3381}(425,\cdot)\) \(\chi_{3381}(458,\cdot)\) \(\chi_{3381}(467,\cdot)\) \(\chi_{3381}(479,\cdot)\) \(\chi_{3381}(488,\cdot)\) \(\chi_{3381}(500,\cdot)\) \(\chi_{3381}(563,\cdot)\) \(\chi_{3381}(572,\cdot)\) \(\chi_{3381}(605,\cdot)\) \(\chi_{3381}(626,\cdot)\) \(\chi_{3381}(635,\cdot)\) \(\chi_{3381}(677,\cdot)\) \(\chi_{3381}(710,\cdot)\) \(\chi_{3381}(773,\cdot)\) \(\chi_{3381}(824,\cdot)\) \(\chi_{3381}(845,\cdot)\) \(\chi_{3381}(866,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{17}{42}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(320, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{95}{231}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{95}{154}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{1}{33}\right)\) |