Basic properties
Modulus: | \(3381\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(592,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.ch
\(\chi_{3381}(37,\cdot)\) \(\chi_{3381}(88,\cdot)\) \(\chi_{3381}(109,\cdot)\) \(\chi_{3381}(130,\cdot)\) \(\chi_{3381}(172,\cdot)\) \(\chi_{3381}(205,\cdot)\) \(\chi_{3381}(235,\cdot)\) \(\chi_{3381}(247,\cdot)\) \(\chi_{3381}(268,\cdot)\) \(\chi_{3381}(310,\cdot)\) \(\chi_{3381}(319,\cdot)\) \(\chi_{3381}(352,\cdot)\) \(\chi_{3381}(382,\cdot)\) \(\chi_{3381}(424,\cdot)\) \(\chi_{3381}(457,\cdot)\) \(\chi_{3381}(550,\cdot)\) \(\chi_{3381}(562,\cdot)\) \(\chi_{3381}(571,\cdot)\) \(\chi_{3381}(592,\cdot)\) \(\chi_{3381}(613,\cdot)\) \(\chi_{3381}(688,\cdot)\) \(\chi_{3381}(697,\cdot)\) \(\chi_{3381}(709,\cdot)\) \(\chi_{3381}(718,\cdot)\) \(\chi_{3381}(730,\cdot)\) \(\chi_{3381}(751,\cdot)\) \(\chi_{3381}(793,\cdot)\) \(\chi_{3381}(835,\cdot)\) \(\chi_{3381}(856,\cdot)\) \(\chi_{3381}(865,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{5}{21}\right),e\left(\frac{7}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(592, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{179}{462}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{83}{462}\right)\) | \(e\left(\frac{7}{66}\right)\) |