Basic properties
Modulus: | \(4704\) | |
Conductor: | \(2352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2352}(611,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4704.ej
\(\chi_{4704}(23,\cdot)\) \(\chi_{4704}(359,\cdot)\) \(\chi_{4704}(599,\cdot)\) \(\chi_{4704}(695,\cdot)\) \(\chi_{4704}(935,\cdot)\) \(\chi_{4704}(1031,\cdot)\) \(\chi_{4704}(1271,\cdot)\) \(\chi_{4704}(1367,\cdot)\) \(\chi_{4704}(1607,\cdot)\) \(\chi_{4704}(1703,\cdot)\) \(\chi_{4704}(1943,\cdot)\) \(\chi_{4704}(2279,\cdot)\) \(\chi_{4704}(2375,\cdot)\) \(\chi_{4704}(2711,\cdot)\) \(\chi_{4704}(2951,\cdot)\) \(\chi_{4704}(3047,\cdot)\) \(\chi_{4704}(3287,\cdot)\) \(\chi_{4704}(3383,\cdot)\) \(\chi_{4704}(3623,\cdot)\) \(\chi_{4704}(3719,\cdot)\) \(\chi_{4704}(3959,\cdot)\) \(\chi_{4704}(4055,\cdot)\) \(\chi_{4704}(4295,\cdot)\) \(\chi_{4704}(4631,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1765,3137,4609)\) → \((-1,-i,-1,e\left(\frac{19}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 4704 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{59}{84}\right)\) |