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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 265.p
\(\chi_{265}(7,\cdot)\) \(\chi_{265}(17,\cdot)\) \(\chi_{265}(37,\cdot)\) \(\chi_{265}(38,\cdot)\) \(\chi_{265}(43,\cdot)\) \(\chi_{265}(57,\cdot)\) \(\chi_{265}(62,\cdot)\) \(\chi_{265}(78,\cdot)\) \(\chi_{265}(82,\cdot)\) \(\chi_{265}(93,\cdot)\) \(\chi_{265}(112,\cdot)\) \(\chi_{265}(113,\cdot)\) \(\chi_{265}(117,\cdot)\) \(\chi_{265}(123,\cdot)\) \(\chi_{265}(143,\cdot)\) \(\chi_{265}(163,\cdot)\) \(\chi_{265}(168,\cdot)\) \(\chi_{265}(188,\cdot)\) \(\chi_{265}(197,\cdot)\) \(\chi_{265}(202,\cdot)\) \(\chi_{265}(218,\cdot)\) \(\chi_{265}(223,\cdot)\) \(\chi_{265}(237,\cdot)\) \(\chi_{265}(252,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((i,e\left(\frac{7}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 265 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) |