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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1421.dt
\(\chi_{1421}(2,\cdot)\) \(\chi_{1421}(32,\cdot)\) \(\chi_{1421}(60,\cdot)\) \(\chi_{1421}(95,\cdot)\) \(\chi_{1421}(163,\cdot)\) \(\chi_{1421}(240,\cdot)\) \(\chi_{1421}(340,\cdot)\) \(\chi_{1421}(359,\cdot)\) \(\chi_{1421}(380,\cdot)\) \(\chi_{1421}(396,\cdot)\) \(\chi_{1421}(445,\cdot)\) \(\chi_{1421}(450,\cdot)\) \(\chi_{1421}(485,\cdot)\) \(\chi_{1421}(627,\cdot)\) \(\chi_{1421}(711,\cdot)\) \(\chi_{1421}(823,\cdot)\) \(\chi_{1421}(1012,\cdot)\) \(\chi_{1421}(1087,\cdot)\) \(\chi_{1421}(1129,\cdot)\) \(\chi_{1421}(1150,\cdot)\) \(\chi_{1421}(1187,\cdot)\) \(\chi_{1421}(1199,\cdot)\) \(\chi_{1421}(1348,\cdot)\) \(\chi_{1421}(1360,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{2}{21}\right),e\left(\frac{5}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1421 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) |