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 \(\chi_{1127}(430,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.cg
\(\chi_{3381}(52,\cdot)\) \(\chi_{3381}(73,\cdot)\) \(\chi_{3381}(82,\cdot)\) \(\chi_{3381}(94,\cdot)\) \(\chi_{3381}(124,\cdot)\) \(\chi_{3381}(187,\cdot)\) \(\chi_{3381}(220,\cdot)\) \(\chi_{3381}(262,\cdot)\) \(\chi_{3381}(271,\cdot)\) \(\chi_{3381}(292,\cdot)\) \(\chi_{3381}(334,\cdot)\) \(\chi_{3381}(376,\cdot)\) \(\chi_{3381}(397,\cdot)\) \(\chi_{3381}(409,\cdot)\) \(\chi_{3381}(418,\cdot)\) \(\chi_{3381}(430,\cdot)\) \(\chi_{3381}(439,\cdot)\) \(\chi_{3381}(514,\cdot)\) \(\chi_{3381}(535,\cdot)\) \(\chi_{3381}(556,\cdot)\) \(\chi_{3381}(565,\cdot)\) \(\chi_{3381}(577,\cdot)\) \(\chi_{3381}(670,\cdot)\) \(\chi_{3381}(703,\cdot)\) \(\chi_{3381}(745,\cdot)\) \(\chi_{3381}(775,\cdot)\) \(\chi_{3381}(808,\cdot)\) \(\chi_{3381}(817,\cdot)\) \(\chi_{3381}(859,\cdot)\) \(\chi_{3381}(880,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{19}{42}\right),e\left(\frac{4}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(430, a) \) | \(-1\) | \(1\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{223}{462}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{395}{462}\right)\) | \(e\left(\frac{19}{66}\right)\) |