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.ci
\(\chi_{3381}(11,\cdot)\) \(\chi_{3381}(44,\cdot)\) \(\chi_{3381}(53,\cdot)\) \(\chi_{3381}(65,\cdot)\) \(\chi_{3381}(74,\cdot)\) \(\chi_{3381}(86,\cdot)\) \(\chi_{3381}(107,\cdot)\) \(\chi_{3381}(149,\cdot)\) \(\chi_{3381}(158,\cdot)\) \(\chi_{3381}(191,\cdot)\) \(\chi_{3381}(212,\cdot)\) \(\chi_{3381}(221,\cdot)\) \(\chi_{3381}(296,\cdot)\) \(\chi_{3381}(359,\cdot)\) \(\chi_{3381}(389,\cdot)\) \(\chi_{3381}(401,\cdot)\) \(\chi_{3381}(431,\cdot)\) \(\chi_{3381}(452,\cdot)\) \(\chi_{3381}(494,\cdot)\) \(\chi_{3381}(527,\cdot)\) \(\chi_{3381}(536,\cdot)\) \(\chi_{3381}(548,\cdot)\) \(\chi_{3381}(590,\cdot)\) \(\chi_{3381}(632,\cdot)\) \(\chi_{3381}(641,\cdot)\) \(\chi_{3381}(674,\cdot)\) \(\chi_{3381}(695,\cdot)\) \(\chi_{3381}(746,\cdot)\) \(\chi_{3381}(779,\cdot)\) \(\chi_{3381}(842,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,346,442)\) → \((-1,e\left(\frac{1}{21}\right),e\left(\frac{3}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3381 }(401, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{5}{231}\right)\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{47}{66}\right)\) |