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.r
\(\chi_{265}(14,\cdot)\) \(\chi_{265}(19,\cdot)\) \(\chi_{265}(34,\cdot)\) \(\chi_{265}(39,\cdot)\) \(\chi_{265}(74,\cdot)\) \(\chi_{265}(79,\cdot)\) \(\chi_{265}(84,\cdot)\) \(\chi_{265}(94,\cdot)\) \(\chi_{265}(104,\cdot)\) \(\chi_{265}(109,\cdot)\) \(\chi_{265}(114,\cdot)\) \(\chi_{265}(124,\cdot)\) \(\chi_{265}(139,\cdot)\) \(\chi_{265}(154,\cdot)\) \(\chi_{265}(164,\cdot)\) \(\chi_{265}(179,\cdot)\) \(\chi_{265}(194,\cdot)\) \(\chi_{265}(204,\cdot)\) \(\chi_{265}(209,\cdot)\) \(\chi_{265}(214,\cdot)\) \(\chi_{265}(224,\cdot)\) \(\chi_{265}(234,\cdot)\) \(\chi_{265}(239,\cdot)\) \(\chi_{265}(244,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((-1,e\left(\frac{17}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 265 }(109, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) |