Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(164\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1681}(565,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.u
\(\chi_{6724}(9,\cdot)\) \(\chi_{6724}(73,\cdot)\) \(\chi_{6724}(173,\cdot)\) \(\chi_{6724}(237,\cdot)\) \(\chi_{6724}(337,\cdot)\) \(\chi_{6724}(401,\cdot)\) \(\chi_{6724}(501,\cdot)\) \(\chi_{6724}(565,\cdot)\) \(\chi_{6724}(665,\cdot)\) \(\chi_{6724}(729,\cdot)\) \(\chi_{6724}(829,\cdot)\) \(\chi_{6724}(893,\cdot)\) \(\chi_{6724}(993,\cdot)\) \(\chi_{6724}(1057,\cdot)\) \(\chi_{6724}(1157,\cdot)\) \(\chi_{6724}(1221,\cdot)\) \(\chi_{6724}(1321,\cdot)\) \(\chi_{6724}(1385,\cdot)\) \(\chi_{6724}(1485,\cdot)\) \(\chi_{6724}(1549,\cdot)\) \(\chi_{6724}(1649,\cdot)\) \(\chi_{6724}(1713,\cdot)\) \(\chi_{6724}(1813,\cdot)\) \(\chi_{6724}(1877,\cdot)\) \(\chi_{6724}(1977,\cdot)\) \(\chi_{6724}(2041,\cdot)\) \(\chi_{6724}(2141,\cdot)\) \(\chi_{6724}(2205,\cdot)\) \(\chi_{6724}(2305,\cdot)\) \(\chi_{6724}(2369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((1,e\left(\frac{153}{164}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(565, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{164}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{83}{164}\right)\) | \(e\left(\frac{5}{82}\right)\) | \(e\left(\frac{143}{164}\right)\) | \(e\left(\frac{107}{164}\right)\) | \(e\left(\frac{145}{164}\right)\) | \(e\left(\frac{77}{164}\right)\) | \(e\left(\frac{161}{164}\right)\) | \(e\left(\frac{3}{82}\right)\) |