Basic properties
| Modulus: | \(3716\) | |
| Conductor: | \(3716\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | 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 3716.t
\(\chi_{3716}(95,\cdot)\) \(\chi_{3716}(115,\cdot)\) \(\chi_{3716}(123,\cdot)\) \(\chi_{3716}(131,\cdot)\) \(\chi_{3716}(167,\cdot)\) \(\chi_{3716}(287,\cdot)\) \(\chi_{3716}(319,\cdot)\) \(\chi_{3716}(327,\cdot)\) \(\chi_{3716}(351,\cdot)\) \(\chi_{3716}(367,\cdot)\) \(\chi_{3716}(459,\cdot)\) \(\chi_{3716}(479,\cdot)\) \(\chi_{3716}(487,\cdot)\) \(\chi_{3716}(495,\cdot)\) \(\chi_{3716}(515,\cdot)\) \(\chi_{3716}(543,\cdot)\) \(\chi_{3716}(587,\cdot)\) \(\chi_{3716}(591,\cdot)\) \(\chi_{3716}(631,\cdot)\) \(\chi_{3716}(639,\cdot)\) \(\chi_{3716}(691,\cdot)\) \(\chi_{3716}(703,\cdot)\) \(\chi_{3716}(743,\cdot)\) \(\chi_{3716}(747,\cdot)\) \(\chi_{3716}(763,\cdot)\) \(\chi_{3716}(787,\cdot)\) \(\chi_{3716}(819,\cdot)\) \(\chi_{3716}(827,\cdot)\) \(\chi_{3716}(831,\cdot)\) \(\chi_{3716}(851,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((1859,1861)\) → \((-1,e\left(\frac{155}{232}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 3716 }(327, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{232}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{131}{232}\right)\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{163}{232}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{7}{116}\right)\) |