Basic properties
| Modulus: | \(1171\) | |
| Conductor: | \(1171\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 1171.u
\(\chi_{1171}(3,\cdot)\) \(\chi_{1171}(7,\cdot)\) \(\chi_{1171}(29,\cdot)\) \(\chi_{1171}(32,\cdot)\) \(\chi_{1171}(60,\cdot)\) \(\chi_{1171}(63,\cdot)\) \(\chi_{1171}(89,\cdot)\) \(\chi_{1171}(130,\cdot)\) \(\chi_{1171}(140,\cdot)\) \(\chi_{1171}(142,\cdot)\) \(\chi_{1171}(147,\cdot)\) \(\chi_{1171}(152,\cdot)\) \(\chi_{1171}(176,\cdot)\) \(\chi_{1171}(183,\cdot)\) \(\chi_{1171}(243,\cdot)\) \(\chi_{1171}(248,\cdot)\) \(\chi_{1171}(250,\cdot)\) \(\chi_{1171}(258,\cdot)\) \(\chi_{1171}(276,\cdot)\) \(\chi_{1171}(285,\cdot)\) \(\chi_{1171}(307,\cdot)\) \(\chi_{1171}(316,\cdot)\) \(\chi_{1171}(326,\cdot)\) \(\chi_{1171}(330,\cdot)\) \(\chi_{1171}(397,\cdot)\) \(\chi_{1171}(410,\cdot)\) \(\chi_{1171}(413,\cdot)\) \(\chi_{1171}(419,\cdot)\) \(\chi_{1171}(422,\cdot)\) \(\chi_{1171}(458,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{175}{234}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1171 }(258, a) \) | \(-1\) | \(1\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{98}{117}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{25}{78}\right)\) |