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.z
\(\chi_{6724}(23,\cdot)\) \(\chi_{6724}(31,\cdot)\) \(\chi_{6724}(107,\cdot)\) \(\chi_{6724}(127,\cdot)\) \(\chi_{6724}(187,\cdot)\) \(\chi_{6724}(195,\cdot)\) \(\chi_{6724}(271,\cdot)\) \(\chi_{6724}(291,\cdot)\) \(\chi_{6724}(351,\cdot)\) \(\chi_{6724}(359,\cdot)\) \(\chi_{6724}(435,\cdot)\) \(\chi_{6724}(455,\cdot)\) \(\chi_{6724}(515,\cdot)\) \(\chi_{6724}(523,\cdot)\) \(\chi_{6724}(599,\cdot)\) \(\chi_{6724}(619,\cdot)\) \(\chi_{6724}(679,\cdot)\) \(\chi_{6724}(687,\cdot)\) \(\chi_{6724}(763,\cdot)\) \(\chi_{6724}(783,\cdot)\) \(\chi_{6724}(843,\cdot)\) \(\chi_{6724}(851,\cdot)\) \(\chi_{6724}(927,\cdot)\) \(\chi_{6724}(947,\cdot)\) \(\chi_{6724}(1007,\cdot)\) \(\chi_{6724}(1015,\cdot)\) \(\chi_{6724}(1091,\cdot)\) \(\chi_{6724}(1111,\cdot)\) \(\chi_{6724}(1171,\cdot)\) \(\chi_{6724}(1179,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{205})$ |
Fixed field: | Number field defined by a degree 410 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((-1,e\left(\frac{143}{410}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6724 }(127, a) \) | \(-1\) | \(1\) | \(e\left(\frac{14}{41}\right)\) | \(e\left(\frac{33}{205}\right)\) | \(e\left(\frac{96}{205}\right)\) | \(e\left(\frac{28}{41}\right)\) | \(e\left(\frac{157}{205}\right)\) | \(e\left(\frac{3}{410}\right)\) | \(e\left(\frac{103}{205}\right)\) | \(e\left(\frac{229}{410}\right)\) | \(e\left(\frac{81}{205}\right)\) | \(e\left(\frac{166}{205}\right)\) |