Basic properties
Modulus: | \(1960\) | |
Conductor: | \(1960\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1960.do
\(\chi_{1960}(3,\cdot)\) \(\chi_{1960}(187,\cdot)\) \(\chi_{1960}(243,\cdot)\) \(\chi_{1960}(283,\cdot)\) \(\chi_{1960}(467,\cdot)\) \(\chi_{1960}(507,\cdot)\) \(\chi_{1960}(523,\cdot)\) \(\chi_{1960}(563,\cdot)\) \(\chi_{1960}(747,\cdot)\) \(\chi_{1960}(787,\cdot)\) \(\chi_{1960}(843,\cdot)\) \(\chi_{1960}(1027,\cdot)\) \(\chi_{1960}(1067,\cdot)\) \(\chi_{1960}(1083,\cdot)\) \(\chi_{1960}(1123,\cdot)\) \(\chi_{1960}(1307,\cdot)\) \(\chi_{1960}(1347,\cdot)\) \(\chi_{1960}(1363,\cdot)\) \(\chi_{1960}(1627,\cdot)\) \(\chi_{1960}(1643,\cdot)\) \(\chi_{1960}(1683,\cdot)\) \(\chi_{1960}(1867,\cdot)\) \(\chi_{1960}(1907,\cdot)\) \(\chi_{1960}(1923,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,981,1177,1081)\) → \((-1,-1,i,e\left(\frac{19}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 1960 }(1067, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) |