Basic properties
| Modulus: | \(1455\) | |
| Conductor: | \(97\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{97}(76,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1455.dh
\(\chi_{1455}(76,\cdot)\) \(\chi_{1455}(136,\cdot)\) \(\chi_{1455}(181,\cdot)\) \(\chi_{1455}(211,\cdot)\) \(\chi_{1455}(286,\cdot)\) \(\chi_{1455}(301,\cdot)\) \(\chi_{1455}(331,\cdot)\) \(\chi_{1455}(511,\cdot)\) \(\chi_{1455}(526,\cdot)\) \(\chi_{1455}(541,\cdot)\) \(\chi_{1455}(556,\cdot)\) \(\chi_{1455}(736,\cdot)\) \(\chi_{1455}(766,\cdot)\) \(\chi_{1455}(781,\cdot)\) \(\chi_{1455}(856,\cdot)\) \(\chi_{1455}(886,\cdot)\) \(\chi_{1455}(931,\cdot)\) \(\chi_{1455}(991,\cdot)\) \(\chi_{1455}(1081,\cdot)\) \(\chi_{1455}(1096,\cdot)\) \(\chi_{1455}(1126,\cdot)\) \(\chi_{1455}(1141,\cdot)\) \(\chi_{1455}(1171,\cdot)\) \(\chi_{1455}(1201,\cdot)\) \(\chi_{1455}(1246,\cdot)\) \(\chi_{1455}(1276,\cdot)\) \(\chi_{1455}(1321,\cdot)\) \(\chi_{1455}(1351,\cdot)\) \(\chi_{1455}(1381,\cdot)\) \(\chi_{1455}(1396,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((971,292,781)\) → \((1,1,e\left(\frac{53}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1455 }(76, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{96}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{23}{32}\right)\) |