Basic properties
Modulus: | \(6003\) | |
Conductor: | \(261\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{261}(182,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.cq
\(\chi_{6003}(47,\cdot)\) \(\chi_{6003}(185,\cdot)\) \(\chi_{6003}(392,\cdot)\) \(\chi_{6003}(461,\cdot)\) \(\chi_{6003}(599,\cdot)\) \(\chi_{6003}(1013,\cdot)\) \(\chi_{6003}(1220,\cdot)\) \(\chi_{6003}(1634,\cdot)\) \(\chi_{6003}(1703,\cdot)\) \(\chi_{6003}(1841,\cdot)\) \(\chi_{6003}(2048,\cdot)\) \(\chi_{6003}(2462,\cdot)\) \(\chi_{6003}(2531,\cdot)\) \(\chi_{6003}(3704,\cdot)\) \(\chi_{6003}(3773,\cdot)\) \(\chi_{6003}(4187,\cdot)\) \(\chi_{6003}(4394,\cdot)\) \(\chi_{6003}(4532,\cdot)\) \(\chi_{6003}(4601,\cdot)\) \(\chi_{6003}(5015,\cdot)\) \(\chi_{6003}(5222,\cdot)\) \(\chi_{6003}(5636,\cdot)\) \(\chi_{6003}(5774,\cdot)\) \(\chi_{6003}(5843,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((668,3133,4555)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{3}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(2531, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) |