Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(47\) | 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 5077.k
\(\chi_{5077}(321,\cdot)\) \(\chi_{5077}(340,\cdot)\) \(\chi_{5077}(381,\cdot)\) \(\chi_{5077}(451,\cdot)\) \(\chi_{5077}(453,\cdot)\) \(\chi_{5077}(594,\cdot)\) \(\chi_{5077}(625,\cdot)\) \(\chi_{5077}(626,\cdot)\) \(\chi_{5077}(629,\cdot)\) \(\chi_{5077}(947,\cdot)\) \(\chi_{5077}(1030,\cdot)\) \(\chi_{5077}(1223,\cdot)\) \(\chi_{5077}(1501,\cdot)\) \(\chi_{5077}(1654,\cdot)\) \(\chi_{5077}(1710,\cdot)\) \(\chi_{5077}(2129,\cdot)\) \(\chi_{5077}(2196,\cdot)\) \(\chi_{5077}(2523,\cdot)\) \(\chi_{5077}(2580,\cdot)\) \(\chi_{5077}(2615,\cdot)\) \(\chi_{5077}(2622,\cdot)\) \(\chi_{5077}(2640,\cdot)\) \(\chi_{5077}(2825,\cdot)\) \(\chi_{5077}(2926,\cdot)\) \(\chi_{5077}(2943,\cdot)\) \(\chi_{5077}(3005,\cdot)\) \(\chi_{5077}(3091,\cdot)\) \(\chi_{5077}(3119,\cdot)\) \(\chi_{5077}(3257,\cdot)\) \(\chi_{5077}(3890,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{47})$ |
Fixed field: | Number field defined by a degree 47 polynomial |
Values on generators
\(2\) → \(e\left(\frac{14}{47}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(321, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{47}\right)\) | \(e\left(\frac{15}{47}\right)\) | \(e\left(\frac{28}{47}\right)\) | \(e\left(\frac{22}{47}\right)\) | \(e\left(\frac{29}{47}\right)\) | \(e\left(\frac{32}{47}\right)\) | \(e\left(\frac{42}{47}\right)\) | \(e\left(\frac{30}{47}\right)\) | \(e\left(\frac{36}{47}\right)\) | \(e\left(\frac{4}{47}\right)\) |