Basic properties
Modulus: | \(265\) | |
Conductor: | \(53\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{53}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 265.s
\(\chi_{265}(21,\cdot)\) \(\chi_{265}(26,\cdot)\) \(\chi_{265}(31,\cdot)\) \(\chi_{265}(41,\cdot)\) \(\chi_{265}(51,\cdot)\) \(\chi_{265}(56,\cdot)\) \(\chi_{265}(61,\cdot)\) \(\chi_{265}(71,\cdot)\) \(\chi_{265}(86,\cdot)\) \(\chi_{265}(101,\cdot)\) \(\chi_{265}(111,\cdot)\) \(\chi_{265}(126,\cdot)\) \(\chi_{265}(141,\cdot)\) \(\chi_{265}(151,\cdot)\) \(\chi_{265}(156,\cdot)\) \(\chi_{265}(161,\cdot)\) \(\chi_{265}(171,\cdot)\) \(\chi_{265}(181,\cdot)\) \(\chi_{265}(186,\cdot)\) \(\chi_{265}(191,\cdot)\) \(\chi_{265}(226,\cdot)\) \(\chi_{265}(231,\cdot)\) \(\chi_{265}(246,\cdot)\) \(\chi_{265}(251,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((107,161)\) → \((1,e\left(\frac{25}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 265 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) |