Basic properties
| Modulus: | \(1048\) | |
| Conductor: | \(524\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{524}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1048.bb
\(\chi_{1048}(23,\cdot)\) \(\chi_{1048}(31,\cdot)\) \(\chi_{1048}(87,\cdot)\) \(\chi_{1048}(95,\cdot)\) \(\chi_{1048}(103,\cdot)\) \(\chi_{1048}(111,\cdot)\) \(\chi_{1048}(119,\cdot)\) \(\chi_{1048}(127,\cdot)\) \(\chi_{1048}(207,\cdot)\) \(\chi_{1048}(247,\cdot)\) \(\chi_{1048}(255,\cdot)\) \(\chi_{1048}(279,\cdot)\) \(\chi_{1048}(319,\cdot)\) \(\chi_{1048}(359,\cdot)\) \(\chi_{1048}(399,\cdot)\) \(\chi_{1048}(407,\cdot)\) \(\chi_{1048}(415,\cdot)\) \(\chi_{1048}(423,\cdot)\) \(\chi_{1048}(447,\cdot)\) \(\chi_{1048}(503,\cdot)\) \(\chi_{1048}(511,\cdot)\) \(\chi_{1048}(519,\cdot)\) \(\chi_{1048}(591,\cdot)\) \(\chi_{1048}(607,\cdot)\) \(\chi_{1048}(639,\cdot)\) \(\chi_{1048}(663,\cdot)\) \(\chi_{1048}(695,\cdot)\) \(\chi_{1048}(711,\cdot)\) \(\chi_{1048}(727,\cdot)\) \(\chi_{1048}(743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,525,657)\) → \((-1,1,e\left(\frac{23}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1048 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{47}{65}\right)\) |