Basic properties
| Modulus: | \(2352\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{784}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2352.dp
\(\chi_{2352}(37,\cdot)\) \(\chi_{2352}(109,\cdot)\) \(\chi_{2352}(205,\cdot)\) \(\chi_{2352}(277,\cdot)\) \(\chi_{2352}(445,\cdot)\) \(\chi_{2352}(541,\cdot)\) \(\chi_{2352}(613,\cdot)\) \(\chi_{2352}(709,\cdot)\) \(\chi_{2352}(781,\cdot)\) \(\chi_{2352}(877,\cdot)\) \(\chi_{2352}(1045,\cdot)\) \(\chi_{2352}(1117,\cdot)\) \(\chi_{2352}(1213,\cdot)\) \(\chi_{2352}(1285,\cdot)\) \(\chi_{2352}(1381,\cdot)\) \(\chi_{2352}(1453,\cdot)\) \(\chi_{2352}(1621,\cdot)\) \(\chi_{2352}(1717,\cdot)\) \(\chi_{2352}(1789,\cdot)\) \(\chi_{2352}(1885,\cdot)\) \(\chi_{2352}(1957,\cdot)\) \(\chi_{2352}(2053,\cdot)\) \(\chi_{2352}(2221,\cdot)\) \(\chi_{2352}(2293,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((1,-i,1,e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2352 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{84}\right)\) |