Basic properties
| Modulus: | \(261\) | |
| Conductor: | \(261\) | 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 261.w
\(\chi_{261}(31,\cdot)\) \(\chi_{261}(40,\cdot)\) \(\chi_{261}(43,\cdot)\) \(\chi_{261}(61,\cdot)\) \(\chi_{261}(76,\cdot)\) \(\chi_{261}(79,\cdot)\) \(\chi_{261}(85,\cdot)\) \(\chi_{261}(97,\cdot)\) \(\chi_{261}(106,\cdot)\) \(\chi_{261}(124,\cdot)\) \(\chi_{261}(130,\cdot)\) \(\chi_{261}(142,\cdot)\) \(\chi_{261}(148,\cdot)\) \(\chi_{261}(160,\cdot)\) \(\chi_{261}(166,\cdot)\) \(\chi_{261}(184,\cdot)\) \(\chi_{261}(193,\cdot)\) \(\chi_{261}(205,\cdot)\) \(\chi_{261}(211,\cdot)\) \(\chi_{261}(214,\cdot)\) \(\chi_{261}(229,\cdot)\) \(\chi_{261}(247,\cdot)\) \(\chi_{261}(250,\cdot)\) \(\chi_{261}(259,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((146,118)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 261 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{10}{21}\right)\) |