Basic properties
| Modulus: | \(2656\) | |
| Conductor: | \(1328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(164\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1328}(123,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2656.z
\(\chi_{2656}(7,\cdot)\) \(\chi_{2656}(23,\cdot)\) \(\chi_{2656}(87,\cdot)\) \(\chi_{2656}(119,\cdot)\) \(\chi_{2656}(151,\cdot)\) \(\chi_{2656}(183,\cdot)\) \(\chi_{2656}(199,\cdot)\) \(\chi_{2656}(215,\cdot)\) \(\chi_{2656}(231,\cdot)\) \(\chi_{2656}(247,\cdot)\) \(\chi_{2656}(279,\cdot)\) \(\chi_{2656}(327,\cdot)\) \(\chi_{2656}(343,\cdot)\) \(\chi_{2656}(359,\cdot)\) \(\chi_{2656}(391,\cdot)\) \(\chi_{2656}(407,\cdot)\) \(\chi_{2656}(455,\cdot)\) \(\chi_{2656}(519,\cdot)\) \(\chi_{2656}(535,\cdot)\) \(\chi_{2656}(567,\cdot)\) \(\chi_{2656}(695,\cdot)\) \(\chi_{2656}(727,\cdot)\) \(\chi_{2656}(759,\cdot)\) \(\chi_{2656}(775,\cdot)\) \(\chi_{2656}(791,\cdot)\) \(\chi_{2656}(839,\cdot)\) \(\chi_{2656}(855,\cdot)\) \(\chi_{2656}(871,\cdot)\) \(\chi_{2656}(951,\cdot)\) \(\chi_{2656}(983,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((831,997,417)\) → \((-1,i,e\left(\frac{15}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2656 }(455, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{164}\right)\) | \(e\left(\frac{21}{164}\right)\) | \(e\left(\frac{38}{41}\right)\) | \(e\left(\frac{15}{82}\right)\) | \(e\left(\frac{87}{164}\right)\) | \(e\left(\frac{151}{164}\right)\) | \(e\left(\frac{59}{82}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{73}{164}\right)\) | \(e\left(\frac{85}{164}\right)\) |