Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1276\) | 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 8027.bq
\(\chi_{8027}(10,\cdot)\) \(\chi_{8027}(11,\cdot)\) \(\chi_{8027}(21,\cdot)\) \(\chi_{8027}(28,\cdot)\) \(\chi_{8027}(38,\cdot)\) \(\chi_{8027}(53,\cdot)\) \(\chi_{8027}(61,\cdot)\) \(\chi_{8027}(65,\cdot)\) \(\chi_{8027}(79,\cdot)\) \(\chi_{8027}(102,\cdot)\) \(\chi_{8027}(103,\cdot)\) \(\chi_{8027}(182,\cdot)\) \(\chi_{8027}(203,\cdot)\) \(\chi_{8027}(218,\cdot)\) \(\chi_{8027}(222,\cdot)\) \(\chi_{8027}(247,\cdot)\) \(\chi_{8027}(251,\cdot)\) \(\chi_{8027}(270,\cdot)\) \(\chi_{8027}(291,\cdot)\) \(\chi_{8027}(296,\cdot)\) \(\chi_{8027}(297,\cdot)\) \(\chi_{8027}(310,\cdot)\) \(\chi_{8027}(314,\cdot)\) \(\chi_{8027}(339,\cdot)\) \(\chi_{8027}(341,\cdot)\) \(\chi_{8027}(343,\cdot)\) \(\chi_{8027}(355,\cdot)\) \(\chi_{8027}(359,\cdot)\) \(\chi_{8027}(360,\cdot)\) \(\chi_{8027}(387,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1276})$ |
Fixed field: | Number field defined by a degree 1276 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{15}{22}\right),e\left(\frac{71}{116}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{1245}{1276}\right)\) | \(e\left(\frac{525}{638}\right)\) | \(e\left(\frac{607}{638}\right)\) | \(e\left(\frac{278}{319}\right)\) | \(e\left(\frac{1019}{1276}\right)\) | \(e\left(\frac{1229}{1276}\right)\) | \(e\left(\frac{1183}{1276}\right)\) | \(e\left(\frac{206}{319}\right)\) | \(e\left(\frac{1081}{1276}\right)\) | \(e\left(\frac{1263}{1276}\right)\) |