Basic properties
Modulus: | \(6003\) | |
Conductor: | \(6003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | 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 6003.dk
\(\chi_{6003}(4,\cdot)\) \(\chi_{6003}(13,\cdot)\) \(\chi_{6003}(121,\cdot)\) \(\chi_{6003}(151,\cdot)\) \(\chi_{6003}(187,\cdot)\) \(\chi_{6003}(196,\cdot)\) \(\chi_{6003}(238,\cdot)\) \(\chi_{6003}(265,\cdot)\) \(\chi_{6003}(328,\cdot)\) \(\chi_{6003}(439,\cdot)\) \(\chi_{6003}(499,\cdot)\) \(\chi_{6003}(535,\cdot)\) \(\chi_{6003}(556,\cdot)\) \(\chi_{6003}(673,\cdot)\) \(\chi_{6003}(763,\cdot)\) \(\chi_{6003}(817,\cdot)\) \(\chi_{6003}(961,\cdot)\) \(\chi_{6003}(970,\cdot)\) \(\chi_{6003}(979,\cdot)\) \(\chi_{6003}(1021,\cdot)\) \(\chi_{6003}(1024,\cdot)\) \(\chi_{6003}(1048,\cdot)\) \(\chi_{6003}(1066,\cdot)\) \(\chi_{6003}(1222,\cdot)\) \(\chi_{6003}(1231,\cdot)\) \(\chi_{6003}(1327,\cdot)\) \(\chi_{6003}(1501,\cdot)\) \(\chi_{6003}(1543,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{11}\right),e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(1021, a) \) | \(1\) | \(1\) | \(e\left(\frac{211}{462}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{461}{462}\right)\) | \(e\left(\frac{191}{231}\right)\) |