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 \(\chi_{664}(355,\cdot)\) | 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
\((831,997,417)\) → \((-1,-1,e\left(\frac{30}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1328 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{41}\right)\) | \(e\left(\frac{21}{82}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{15}{41}\right)\) | \(e\left(\frac{23}{41}\right)\) | \(e\left(\frac{69}{82}\right)\) | \(e\left(\frac{77}{82}\right)\) | \(e\left(\frac{40}{41}\right)\) | \(e\left(\frac{16}{41}\right)\) | \(e\left(\frac{3}{82}\right)\) |