Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(198\) | 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 3267.bo
\(\chi_{3267}(32,\cdot)\) \(\chi_{3267}(65,\cdot)\) \(\chi_{3267}(131,\cdot)\) \(\chi_{3267}(164,\cdot)\) \(\chi_{3267}(230,\cdot)\) \(\chi_{3267}(263,\cdot)\) \(\chi_{3267}(329,\cdot)\) \(\chi_{3267}(428,\cdot)\) \(\chi_{3267}(461,\cdot)\) \(\chi_{3267}(527,\cdot)\) \(\chi_{3267}(560,\cdot)\) \(\chi_{3267}(626,\cdot)\) \(\chi_{3267}(659,\cdot)\) \(\chi_{3267}(758,\cdot)\) \(\chi_{3267}(824,\cdot)\) \(\chi_{3267}(857,\cdot)\) \(\chi_{3267}(923,\cdot)\) \(\chi_{3267}(956,\cdot)\) \(\chi_{3267}(1022,\cdot)\) \(\chi_{3267}(1055,\cdot)\) \(\chi_{3267}(1121,\cdot)\) \(\chi_{3267}(1154,\cdot)\) \(\chi_{3267}(1220,\cdot)\) \(\chi_{3267}(1253,\cdot)\) \(\chi_{3267}(1319,\cdot)\) \(\chi_{3267}(1352,\cdot)\) \(\chi_{3267}(1418,\cdot)\) \(\chi_{3267}(1517,\cdot)\) \(\chi_{3267}(1550,\cdot)\) \(\chi_{3267}(1616,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 198 polynomial (not computed) |
Values on generators
\((3026,244)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 3267 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{99}\right)\) | \(e\left(\frac{64}{99}\right)\) | \(e\left(\frac{149}{198}\right)\) | \(e\left(\frac{151}{198}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{161}{198}\right)\) | \(e\left(\frac{17}{198}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) |