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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.cj
\(\chi_{3381}(26,\cdot)\) \(\chi_{3381}(59,\cdot)\) \(\chi_{3381}(101,\cdot)\) \(\chi_{3381}(110,\cdot)\) \(\chi_{3381}(131,\cdot)\) \(\chi_{3381}(164,\cdot)\) \(\chi_{3381}(173,\cdot)\) \(\chi_{3381}(236,\cdot)\) \(\chi_{3381}(248,\cdot)\) \(\chi_{3381}(257,\cdot)\) \(\chi_{3381}(269,\cdot)\) \(\chi_{3381}(278,\cdot)\) \(\chi_{3381}(311,\cdot)\) \(\chi_{3381}(353,\cdot)\) \(\chi_{3381}(395,\cdot)\) \(\chi_{3381}(404,\cdot)\) \(\chi_{3381}(416,\cdot)\) \(\chi_{3381}(446,\cdot)\) \(\chi_{3381}(542,\cdot)\) \(\chi_{3381}(584,\cdot)\) \(\chi_{3381}(593,\cdot)\) \(\chi_{3381}(614,\cdot)\) \(\chi_{3381}(647,\cdot)\) \(\chi_{3381}(698,\cdot)\) \(\chi_{3381}(719,\cdot)\) \(\chi_{3381}(731,\cdot)\) \(\chi_{3381}(740,\cdot)\) \(\chi_{3381}(752,\cdot)\) \(\chi_{3381}(761,\cdot)\) \(\chi_{3381}(794,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{25}{42}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(1340, a) \) | \(1\) | \(1\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{129}{154}\right)\) | \(e\left(\frac{89}{462}\right)\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{15}{154}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{7}{66}\right)\) |