Basic properties
Modulus: | \(1328\) | |
Conductor: | \(664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(82\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{664}(459,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1328.p
\(\chi_{1328}(7,\cdot)\) \(\chi_{1328}(23,\cdot)\) \(\chi_{1328}(87,\cdot)\) \(\chi_{1328}(119,\cdot)\) \(\chi_{1328}(151,\cdot)\) \(\chi_{1328}(183,\cdot)\) \(\chi_{1328}(199,\cdot)\) \(\chi_{1328}(215,\cdot)\) \(\chi_{1328}(231,\cdot)\) \(\chi_{1328}(247,\cdot)\) \(\chi_{1328}(279,\cdot)\) \(\chi_{1328}(327,\cdot)\) \(\chi_{1328}(343,\cdot)\) \(\chi_{1328}(359,\cdot)\) \(\chi_{1328}(391,\cdot)\) \(\chi_{1328}(407,\cdot)\) \(\chi_{1328}(455,\cdot)\) \(\chi_{1328}(519,\cdot)\) \(\chi_{1328}(535,\cdot)\) \(\chi_{1328}(567,\cdot)\) \(\chi_{1328}(695,\cdot)\) \(\chi_{1328}(727,\cdot)\) \(\chi_{1328}(759,\cdot)\) \(\chi_{1328}(775,\cdot)\) \(\chi_{1328}(791,\cdot)\) \(\chi_{1328}(839,\cdot)\) \(\chi_{1328}(855,\cdot)\) \(\chi_{1328}(871,\cdot)\) \(\chi_{1328}(951,\cdot)\) \(\chi_{1328}(983,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{41})$ |
Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\((831,997,417)\) → \((-1,-1,e\left(\frac{13}{41}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1328 }(791, a) \) | \(-1\) | \(1\) | \(e\left(\frac{34}{41}\right)\) | \(e\left(\frac{5}{82}\right)\) | \(e\left(\frac{3}{82}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{25}{41}\right)\) | \(e\left(\frac{75}{82}\right)\) | \(e\left(\frac{73}{82}\right)\) | \(e\left(\frac{31}{41}\right)\) | \(e\left(\frac{37}{41}\right)\) | \(e\left(\frac{71}{82}\right)\) |