Basic properties
| Modulus: | \(1960\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1960.dp
\(\chi_{1960}(17,\cdot)\) \(\chi_{1960}(33,\cdot)\) \(\chi_{1960}(73,\cdot)\) \(\chi_{1960}(257,\cdot)\) \(\chi_{1960}(297,\cdot)\) \(\chi_{1960}(353,\cdot)\) \(\chi_{1960}(537,\cdot)\) \(\chi_{1960}(577,\cdot)\) \(\chi_{1960}(593,\cdot)\) \(\chi_{1960}(633,\cdot)\) \(\chi_{1960}(817,\cdot)\) \(\chi_{1960}(857,\cdot)\) \(\chi_{1960}(873,\cdot)\) \(\chi_{1960}(1137,\cdot)\) \(\chi_{1960}(1153,\cdot)\) \(\chi_{1960}(1193,\cdot)\) \(\chi_{1960}(1377,\cdot)\) \(\chi_{1960}(1417,\cdot)\) \(\chi_{1960}(1433,\cdot)\) \(\chi_{1960}(1473,\cdot)\) \(\chi_{1960}(1657,\cdot)\) \(\chi_{1960}(1713,\cdot)\) \(\chi_{1960}(1753,\cdot)\) \(\chi_{1960}(1937,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((1,1,i,e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1960 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) |