Basic properties
| Modulus: | \(1421\) | |
| Conductor: | \(203\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{203}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1421.dr
\(\chi_{1421}(18,\cdot)\) \(\chi_{1421}(79,\cdot)\) \(\chi_{1421}(177,\cdot)\) \(\chi_{1421}(214,\cdot)\) \(\chi_{1421}(263,\cdot)\) \(\chi_{1421}(275,\cdot)\) \(\chi_{1421}(508,\cdot)\) \(\chi_{1421}(520,\cdot)\) \(\chi_{1421}(569,\cdot)\) \(\chi_{1421}(606,\cdot)\) \(\chi_{1421}(704,\cdot)\) \(\chi_{1421}(765,\cdot)\) \(\chi_{1421}(802,\cdot)\) \(\chi_{1421}(814,\cdot)\) \(\chi_{1421}(851,\cdot)\) \(\chi_{1421}(949,\cdot)\) \(\chi_{1421}(1047,\cdot)\) \(\chi_{1421}(1059,\cdot)\) \(\chi_{1421}(1145,\cdot)\) \(\chi_{1421}(1157,\cdot)\) \(\chi_{1421}(1255,\cdot)\) \(\chi_{1421}(1353,\cdot)\) \(\chi_{1421}(1390,\cdot)\) \(\chi_{1421}(1402,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{11}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1421 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) |