Basic properties
Modulus: | \(265\) | |
Conductor: | \(265\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 265.t
\(\chi_{265}(2,\cdot)\) \(\chi_{265}(8,\cdot)\) \(\chi_{265}(18,\cdot)\) \(\chi_{265}(32,\cdot)\) \(\chi_{265}(33,\cdot)\) \(\chi_{265}(58,\cdot)\) \(\chi_{265}(72,\cdot)\) \(\chi_{265}(92,\cdot)\) \(\chi_{265}(103,\cdot)\) \(\chi_{265}(118,\cdot)\) \(\chi_{265}(128,\cdot)\) \(\chi_{265}(132,\cdot)\) \(\chi_{265}(133,\cdot)\) \(\chi_{265}(137,\cdot)\) \(\chi_{265}(147,\cdot)\) \(\chi_{265}(162,\cdot)\) \(\chi_{265}(173,\cdot)\) \(\chi_{265}(193,\cdot)\) \(\chi_{265}(207,\cdot)\) \(\chi_{265}(232,\cdot)\) \(\chi_{265}(233,\cdot)\) \(\chi_{265}(247,\cdot)\) \(\chi_{265}(257,\cdot)\) \(\chi_{265}(263,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((-i,e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 265 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{33}{52}\right)\) |