Basic properties
| Modulus: | \(4176\) | |
| 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 \(\chi_{261}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4176.gc
\(\chi_{4176}(113,\cdot)\) \(\chi_{4176}(641,\cdot)\) \(\chi_{4176}(785,\cdot)\) \(\chi_{4176}(833,\cdot)\) \(\chi_{4176}(1121,\cdot)\) \(\chi_{4176}(1265,\cdot)\) \(\chi_{4176}(1361,\cdot)\) \(\chi_{4176}(1505,\cdot)\) \(\chi_{4176}(1697,\cdot)\) \(\chi_{4176}(1841,\cdot)\) \(\chi_{4176}(2225,\cdot)\) \(\chi_{4176}(2273,\cdot)\) \(\chi_{4176}(2417,\cdot)\) \(\chi_{4176}(2513,\cdot)\) \(\chi_{4176}(2657,\cdot)\) \(\chi_{4176}(2705,\cdot)\) \(\chi_{4176}(3089,\cdot)\) \(\chi_{4176}(3233,\cdot)\) \(\chi_{4176}(3425,\cdot)\) \(\chi_{4176}(3569,\cdot)\) \(\chi_{4176}(3665,\cdot)\) \(\chi_{4176}(3809,\cdot)\) \(\chi_{4176}(4097,\cdot)\) \(\chi_{4176}(4145,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1567,1045,929,4033)\) → \((1,1,e\left(\frac{5}{6}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(31\) | \(35\) |
| \( \chi_{ 4176 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(-i\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) |