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.do
\(\chi_{1421}(26,\cdot)\) \(\chi_{1421}(89,\cdot)\) \(\chi_{1421}(108,\cdot)\) \(\chi_{1421}(164,\cdot)\) \(\chi_{1421}(213,\cdot)\) \(\chi_{1421}(250,\cdot)\) \(\chi_{1421}(327,\cdot)\) \(\chi_{1421}(395,\cdot)\) \(\chi_{1421}(446,\cdot)\) \(\chi_{1421}(467,\cdot)\) \(\chi_{1421}(479,\cdot)\) \(\chi_{1421}(537,\cdot)\) \(\chi_{1421}(572,\cdot)\) \(\chi_{1421}(591,\cdot)\) \(\chi_{1421}(780,\cdot)\) \(\chi_{1421}(955,\cdot)\) \(\chi_{1421}(1116,\cdot)\) \(\chi_{1421}(1174,\cdot)\) \(\chi_{1421}(1216,\cdot)\) \(\chi_{1421}(1221,\cdot)\) \(\chi_{1421}(1237,\cdot)\) \(\chi_{1421}(1249,\cdot)\) \(\chi_{1421}(1284,\cdot)\) \(\chi_{1421}(1286,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{17}{42}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1421 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) |