Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(6724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(328\) | 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 6724.x
\(\chi_{6724}(3,\cdot)\) \(\chi_{6724}(27,\cdot)\) \(\chi_{6724}(55,\cdot)\) \(\chi_{6724}(79,\cdot)\) \(\chi_{6724}(167,\cdot)\) \(\chi_{6724}(191,\cdot)\) \(\chi_{6724}(219,\cdot)\) \(\chi_{6724}(243,\cdot)\) \(\chi_{6724}(331,\cdot)\) \(\chi_{6724}(355,\cdot)\) \(\chi_{6724}(383,\cdot)\) \(\chi_{6724}(407,\cdot)\) \(\chi_{6724}(495,\cdot)\) \(\chi_{6724}(519,\cdot)\) \(\chi_{6724}(547,\cdot)\) \(\chi_{6724}(571,\cdot)\) \(\chi_{6724}(659,\cdot)\) \(\chi_{6724}(683,\cdot)\) \(\chi_{6724}(711,\cdot)\) \(\chi_{6724}(735,\cdot)\) \(\chi_{6724}(823,\cdot)\) \(\chi_{6724}(875,\cdot)\) \(\chi_{6724}(899,\cdot)\) \(\chi_{6724}(987,\cdot)\) \(\chi_{6724}(1011,\cdot)\) \(\chi_{6724}(1039,\cdot)\) \(\chi_{6724}(1063,\cdot)\) \(\chi_{6724}(1151,\cdot)\) \(\chi_{6724}(1175,\cdot)\) \(\chi_{6724}(1203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{328})$ |
| Fixed field: | Number field defined by a degree 328 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((-1,e\left(\frac{67}{328}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{305}{328}\right)\) | \(e\left(\frac{129}{164}\right)\) | \(e\left(\frac{225}{328}\right)\) | \(e\left(\frac{141}{164}\right)\) | \(e\left(\frac{277}{328}\right)\) | \(e\left(\frac{213}{328}\right)\) | \(e\left(\frac{235}{328}\right)\) | \(e\left(\frac{187}{328}\right)\) | \(e\left(\frac{63}{328}\right)\) | \(e\left(\frac{101}{164}\right)\) |