Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(6724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(410\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.bb
\(\chi_{6724}(59,\cdot)\) \(\chi_{6724}(119,\cdot)\) \(\chi_{6724}(139,\cdot)\) \(\chi_{6724}(215,\cdot)\) \(\chi_{6724}(223,\cdot)\) \(\chi_{6724}(283,\cdot)\) \(\chi_{6724}(303,\cdot)\) \(\chi_{6724}(379,\cdot)\) \(\chi_{6724}(387,\cdot)\) \(\chi_{6724}(447,\cdot)\) \(\chi_{6724}(467,\cdot)\) \(\chi_{6724}(543,\cdot)\) \(\chi_{6724}(551,\cdot)\) \(\chi_{6724}(611,\cdot)\) \(\chi_{6724}(631,\cdot)\) \(\chi_{6724}(707,\cdot)\) \(\chi_{6724}(715,\cdot)\) \(\chi_{6724}(775,\cdot)\) \(\chi_{6724}(795,\cdot)\) \(\chi_{6724}(871,\cdot)\) \(\chi_{6724}(879,\cdot)\) \(\chi_{6724}(939,\cdot)\) \(\chi_{6724}(959,\cdot)\) \(\chi_{6724}(1035,\cdot)\) \(\chi_{6724}(1043,\cdot)\) \(\chi_{6724}(1103,\cdot)\) \(\chi_{6724}(1123,\cdot)\) \(\chi_{6724}(1199,\cdot)\) \(\chi_{6724}(1207,\cdot)\) \(\chi_{6724}(1267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{205})$ |
| Fixed field: | Number field defined by a degree 410 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((-1,e\left(\frac{137}{205}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{82}\right)\) | \(e\left(\frac{79}{205}\right)\) | \(e\left(\frac{31}{410}\right)\) | \(e\left(\frac{31}{41}\right)\) | \(e\left(\frac{87}{410}\right)\) | \(e\left(\frac{162}{205}\right)\) | \(e\left(\frac{313}{410}\right)\) | \(e\left(\frac{66}{205}\right)\) | \(e\left(\frac{71}{410}\right)\) | \(e\left(\frac{93}{205}\right)\) |