Basic properties
| Modulus: | \(2940\) | |
| Conductor: | \(2940\) | 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 2940.dq
\(\chi_{2940}(47,\cdot)\) \(\chi_{2940}(143,\cdot)\) \(\chi_{2940}(383,\cdot)\) \(\chi_{2940}(467,\cdot)\) \(\chi_{2940}(563,\cdot)\) \(\chi_{2940}(647,\cdot)\) \(\chi_{2940}(887,\cdot)\) \(\chi_{2940}(983,\cdot)\) \(\chi_{2940}(1067,\cdot)\) \(\chi_{2940}(1223,\cdot)\) \(\chi_{2940}(1307,\cdot)\) \(\chi_{2940}(1487,\cdot)\) \(\chi_{2940}(1643,\cdot)\) \(\chi_{2940}(1727,\cdot)\) \(\chi_{2940}(1823,\cdot)\) \(\chi_{2940}(1907,\cdot)\) \(\chi_{2940}(2063,\cdot)\) \(\chi_{2940}(2147,\cdot)\) \(\chi_{2940}(2243,\cdot)\) \(\chi_{2940}(2327,\cdot)\) \(\chi_{2940}(2483,\cdot)\) \(\chi_{2940}(2663,\cdot)\) \(\chi_{2940}(2747,\cdot)\) \(\chi_{2940}(2903,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1961,1177,1081)\) → \((-1,-1,i,e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2940 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{27}{28}\right)\) |