Basic properties
| Modulus: | \(1421\) | |
| Conductor: | \(1421\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1421.dv
\(\chi_{1421}(61,\cdot)\) \(\chi_{1421}(73,\cdot)\) \(\chi_{1421}(222,\cdot)\) \(\chi_{1421}(234,\cdot)\) \(\chi_{1421}(271,\cdot)\) \(\chi_{1421}(292,\cdot)\) \(\chi_{1421}(334,\cdot)\) \(\chi_{1421}(409,\cdot)\) \(\chi_{1421}(598,\cdot)\) \(\chi_{1421}(710,\cdot)\) \(\chi_{1421}(794,\cdot)\) \(\chi_{1421}(936,\cdot)\) \(\chi_{1421}(971,\cdot)\) \(\chi_{1421}(976,\cdot)\) \(\chi_{1421}(1025,\cdot)\) \(\chi_{1421}(1041,\cdot)\) \(\chi_{1421}(1062,\cdot)\) \(\chi_{1421}(1081,\cdot)\) \(\chi_{1421}(1181,\cdot)\) \(\chi_{1421}(1258,\cdot)\) \(\chi_{1421}(1326,\cdot)\) \(\chi_{1421}(1361,\cdot)\) \(\chi_{1421}(1389,\cdot)\) \(\chi_{1421}(1419,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{23}{42}\right),e\left(\frac{13}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1421 }(971, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) |