Basic properties
Modulus: | \(4176\) | |
Conductor: | \(4176\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 4176.fz
\(\chi_{4176}(619,\cdot)\) \(\chi_{4176}(859,\cdot)\) \(\chi_{4176}(907,\cdot)\) \(\chi_{4176}(931,\cdot)\) \(\chi_{4176}(1075,\cdot)\) \(\chi_{4176}(1123,\cdot)\) \(\chi_{4176}(1291,\cdot)\) \(\chi_{4176}(1411,\cdot)\) \(\chi_{4176}(2011,\cdot)\) \(\chi_{4176}(2131,\cdot)\) \(\chi_{4176}(2299,\cdot)\) \(\chi_{4176}(2347,\cdot)\) \(\chi_{4176}(2491,\cdot)\) \(\chi_{4176}(2515,\cdot)\) \(\chi_{4176}(2563,\cdot)\) \(\chi_{4176}(2803,\cdot)\) \(\chi_{4176}(3523,\cdot)\) \(\chi_{4176}(3643,\cdot)\) \(\chi_{4176}(3715,\cdot)\) \(\chi_{4176}(3739,\cdot)\) \(\chi_{4176}(3859,\cdot)\) \(\chi_{4176}(3883,\cdot)\) \(\chi_{4176}(3955,\cdot)\) \(\chi_{4176}(4075,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1567,1045,929,4033)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{23}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(31\) | \(35\) |
\( \chi_{ 4176 }(619, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(i\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) |