Basic properties
| Modulus: | \(3211\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(117\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3211.cs
\(\chi_{3211}(9,\cdot)\) \(\chi_{3211}(16,\cdot)\) \(\chi_{3211}(55,\cdot)\) \(\chi_{3211}(61,\cdot)\) \(\chi_{3211}(81,\cdot)\) \(\chi_{3211}(139,\cdot)\) \(\chi_{3211}(256,\cdot)\) \(\chi_{3211}(263,\cdot)\) \(\chi_{3211}(302,\cdot)\) \(\chi_{3211}(308,\cdot)\) \(\chi_{3211}(328,\cdot)\) \(\chi_{3211}(386,\cdot)\) \(\chi_{3211}(503,\cdot)\) \(\chi_{3211}(510,\cdot)\) \(\chi_{3211}(549,\cdot)\) \(\chi_{3211}(555,\cdot)\) \(\chi_{3211}(575,\cdot)\) \(\chi_{3211}(633,\cdot)\) \(\chi_{3211}(750,\cdot)\) \(\chi_{3211}(757,\cdot)\) \(\chi_{3211}(796,\cdot)\) \(\chi_{3211}(802,\cdot)\) \(\chi_{3211}(880,\cdot)\) \(\chi_{3211}(997,\cdot)\) \(\chi_{3211}(1004,\cdot)\) \(\chi_{3211}(1043,\cdot)\) \(\chi_{3211}(1049,\cdot)\) \(\chi_{3211}(1069,\cdot)\) \(\chi_{3211}(1127,\cdot)\) \(\chi_{3211}(1244,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((1692,1522)\) → \((e\left(\frac{28}{39}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3211 }(1069, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{8}{13}\right)\) |