Basic properties
Modulus: | \(3381\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(481,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3381.cf
\(\chi_{3381}(10,\cdot)\) \(\chi_{3381}(40,\cdot)\) \(\chi_{3381}(61,\cdot)\) \(\chi_{3381}(103,\cdot)\) \(\chi_{3381}(136,\cdot)\) \(\chi_{3381}(145,\cdot)\) \(\chi_{3381}(157,\cdot)\) \(\chi_{3381}(199,\cdot)\) \(\chi_{3381}(241,\cdot)\) \(\chi_{3381}(250,\cdot)\) \(\chi_{3381}(283,\cdot)\) \(\chi_{3381}(304,\cdot)\) \(\chi_{3381}(355,\cdot)\) \(\chi_{3381}(388,\cdot)\) \(\chi_{3381}(451,\cdot)\) \(\chi_{3381}(481,\cdot)\) \(\chi_{3381}(493,\cdot)\) \(\chi_{3381}(502,\cdot)\) \(\chi_{3381}(523,\cdot)\) \(\chi_{3381}(544,\cdot)\) \(\chi_{3381}(586,\cdot)\) \(\chi_{3381}(628,\cdot)\) \(\chi_{3381}(640,\cdot)\) \(\chi_{3381}(649,\cdot)\) \(\chi_{3381}(661,\cdot)\) \(\chi_{3381}(682,\cdot)\) \(\chi_{3381}(724,\cdot)\) \(\chi_{3381}(733,\cdot)\) \(\chi_{3381}(787,\cdot)\) \(\chi_{3381}(796,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((1,e\left(\frac{23}{42}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(481, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{20}{77}\right)\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{1}{33}\right)\) |