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 \(\chi_{524}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1048.bc
\(\chi_{1048}(7,\cdot)\) \(\chi_{1048}(15,\cdot)\) \(\chi_{1048}(55,\cdot)\) \(\chi_{1048}(135,\cdot)\) \(\chi_{1048}(143,\cdot)\) \(\chi_{1048}(151,\cdot)\) \(\chi_{1048}(159,\cdot)\) \(\chi_{1048}(167,\cdot)\) \(\chi_{1048}(175,\cdot)\) \(\chi_{1048}(231,\cdot)\) \(\chi_{1048}(239,\cdot)\) \(\chi_{1048}(271,\cdot)\) \(\chi_{1048}(287,\cdot)\) \(\chi_{1048}(295,\cdot)\) \(\chi_{1048}(303,\cdot)\) \(\chi_{1048}(311,\cdot)\) \(\chi_{1048}(327,\cdot)\) \(\chi_{1048}(343,\cdot)\) \(\chi_{1048}(367,\cdot)\) \(\chi_{1048}(383,\cdot)\) \(\chi_{1048}(391,\cdot)\) \(\chi_{1048}(431,\cdot)\) \(\chi_{1048}(439,\cdot)\) \(\chi_{1048}(487,\cdot)\) \(\chi_{1048}(495,\cdot)\) \(\chi_{1048}(527,\cdot)\) \(\chi_{1048}(535,\cdot)\) \(\chi_{1048}(551,\cdot)\) \(\chi_{1048}(559,\cdot)\) \(\chi_{1048}(567,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,525,657)\) → \((-1,1,e\left(\frac{51}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1048 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{53}{65}\right)\) |