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 \(\chi_{245}(137,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1960.dr
\(\chi_{1960}(137,\cdot)\) \(\chi_{1960}(193,\cdot)\) \(\chi_{1960}(233,\cdot)\) \(\chi_{1960}(417,\cdot)\) \(\chi_{1960}(457,\cdot)\) \(\chi_{1960}(473,\cdot)\) \(\chi_{1960}(513,\cdot)\) \(\chi_{1960}(697,\cdot)\) \(\chi_{1960}(737,\cdot)\) \(\chi_{1960}(793,\cdot)\) \(\chi_{1960}(977,\cdot)\) \(\chi_{1960}(1017,\cdot)\) \(\chi_{1960}(1033,\cdot)\) \(\chi_{1960}(1073,\cdot)\) \(\chi_{1960}(1257,\cdot)\) \(\chi_{1960}(1297,\cdot)\) \(\chi_{1960}(1313,\cdot)\) \(\chi_{1960}(1577,\cdot)\) \(\chi_{1960}(1593,\cdot)\) \(\chi_{1960}(1633,\cdot)\) \(\chi_{1960}(1817,\cdot)\) \(\chi_{1960}(1857,\cdot)\) \(\chi_{1960}(1873,\cdot)\) \(\chi_{1960}(1913,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((1,1,i,e\left(\frac{17}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1960 }(137, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) |