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 \(\chi_{784}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2352.dn
\(\chi_{2352}(115,\cdot)\) \(\chi_{2352}(187,\cdot)\) \(\chi_{2352}(283,\cdot)\) \(\chi_{2352}(355,\cdot)\) \(\chi_{2352}(451,\cdot)\) \(\chi_{2352}(523,\cdot)\) \(\chi_{2352}(691,\cdot)\) \(\chi_{2352}(787,\cdot)\) \(\chi_{2352}(859,\cdot)\) \(\chi_{2352}(955,\cdot)\) \(\chi_{2352}(1027,\cdot)\) \(\chi_{2352}(1123,\cdot)\) \(\chi_{2352}(1291,\cdot)\) \(\chi_{2352}(1363,\cdot)\) \(\chi_{2352}(1459,\cdot)\) \(\chi_{2352}(1531,\cdot)\) \(\chi_{2352}(1627,\cdot)\) \(\chi_{2352}(1699,\cdot)\) \(\chi_{2352}(1867,\cdot)\) \(\chi_{2352}(1963,\cdot)\) \(\chi_{2352}(2035,\cdot)\) \(\chi_{2352}(2131,\cdot)\) \(\chi_{2352}(2203,\cdot)\) \(\chi_{2352}(2299,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((-1,-i,1,e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2352 }(115, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{67}{84}\right)\) |