Basic properties
Modulus: | \(2365\) | |
Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 2365.db
\(\chi_{2365}(142,\cdot)\) \(\chi_{2365}(153,\cdot)\) \(\chi_{2365}(197,\cdot)\) \(\chi_{2365}(318,\cdot)\) \(\chi_{2365}(483,\cdot)\) \(\chi_{2365}(582,\cdot)\) \(\chi_{2365}(703,\cdot)\) \(\chi_{2365}(857,\cdot)\) \(\chi_{2365}(912,\cdot)\) \(\chi_{2365}(1088,\cdot)\) \(\chi_{2365}(1132,\cdot)\) \(\chi_{2365}(1143,\cdot)\) \(\chi_{2365}(1242,\cdot)\) \(\chi_{2365}(1407,\cdot)\) \(\chi_{2365}(1528,\cdot)\) \(\chi_{2365}(1572,\cdot)\) \(\chi_{2365}(1737,\cdot)\) \(\chi_{2365}(1803,\cdot)\) \(\chi_{2365}(1858,\cdot)\) \(\chi_{2365}(1902,\cdot)\) \(\chi_{2365}(2078,\cdot)\) \(\chi_{2365}(2122,\cdot)\) \(\chi_{2365}(2188,\cdot)\) \(\chi_{2365}(2353,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((947,431,1981)\) → \((-i,-1,e\left(\frac{20}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 2365 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) |