Basic properties
| Modulus: | \(2842\) | |
| 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 \(\chi_{203}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2842.dx
\(\chi_{2842}(19,\cdot)\) \(\chi_{2842}(31,\cdot)\) \(\chi_{2842}(607,\cdot)\) \(\chi_{2842}(619,\cdot)\) \(\chi_{2842}(717,\cdot)\) \(\chi_{2842}(815,\cdot)\) \(\chi_{2842}(901,\cdot)\) \(\chi_{2842}(913,\cdot)\) \(\chi_{2842}(1207,\cdot)\) \(\chi_{2842}(1403,\cdot)\) \(\chi_{2842}(1489,\cdot)\) \(\chi_{2842}(1587,\cdot)\) \(\chi_{2842}(1685,\cdot)\) \(\chi_{2842}(1697,\cdot)\) \(\chi_{2842}(1783,\cdot)\) \(\chi_{2842}(1795,\cdot)\) \(\chi_{2842}(1893,\cdot)\) \(\chi_{2842}(1991,\cdot)\) \(\chi_{2842}(2077,\cdot)\) \(\chi_{2842}(2273,\cdot)\) \(\chi_{2842}(2567,\cdot)\) \(\chi_{2842}(2579,\cdot)\) \(\chi_{2842}(2665,\cdot)\) \(\chi_{2842}(2763,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1277,785)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 2842 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) |