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 \(\chi_{784}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2352.dq
\(\chi_{2352}(163,\cdot)\) \(\chi_{2352}(235,\cdot)\) \(\chi_{2352}(331,\cdot)\) \(\chi_{2352}(403,\cdot)\) \(\chi_{2352}(499,\cdot)\) \(\chi_{2352}(571,\cdot)\) \(\chi_{2352}(739,\cdot)\) \(\chi_{2352}(835,\cdot)\) \(\chi_{2352}(907,\cdot)\) \(\chi_{2352}(1003,\cdot)\) \(\chi_{2352}(1075,\cdot)\) \(\chi_{2352}(1171,\cdot)\) \(\chi_{2352}(1339,\cdot)\) \(\chi_{2352}(1411,\cdot)\) \(\chi_{2352}(1507,\cdot)\) \(\chi_{2352}(1579,\cdot)\) \(\chi_{2352}(1675,\cdot)\) \(\chi_{2352}(1747,\cdot)\) \(\chi_{2352}(1915,\cdot)\) \(\chi_{2352}(2011,\cdot)\) \(\chi_{2352}(2083,\cdot)\) \(\chi_{2352}(2179,\cdot)\) \(\chi_{2352}(2251,\cdot)\) \(\chi_{2352}(2347,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,785,2257)\) → \((-1,-i,1,e\left(\frac{10}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 2352 }(163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{83}{84}\right)\) |