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.o
\(\chi_{265}(3,\cdot)\) \(\chi_{265}(12,\cdot)\) \(\chi_{265}(22,\cdot)\) \(\chi_{265}(27,\cdot)\) \(\chi_{265}(48,\cdot)\) \(\chi_{265}(67,\cdot)\) \(\chi_{265}(73,\cdot)\) \(\chi_{265}(87,\cdot)\) \(\chi_{265}(88,\cdot)\) \(\chi_{265}(98,\cdot)\) \(\chi_{265}(108,\cdot)\) \(\chi_{265}(127,\cdot)\) \(\chi_{265}(138,\cdot)\) \(\chi_{265}(157,\cdot)\) \(\chi_{265}(167,\cdot)\) \(\chi_{265}(177,\cdot)\) \(\chi_{265}(178,\cdot)\) \(\chi_{265}(192,\cdot)\) \(\chi_{265}(198,\cdot)\) \(\chi_{265}(217,\cdot)\) \(\chi_{265}(238,\cdot)\) \(\chi_{265}(243,\cdot)\) \(\chi_{265}(253,\cdot)\) \(\chi_{265}(262,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((-i,e\left(\frac{17}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 265 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) |