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
\((3363,5049)\) → \((-1,e\left(\frac{177}{410}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{41}\right)\) | \(e\left(\frac{167}{205}\right)\) | \(e\left(\frac{169}{205}\right)\) | \(e\left(\frac{10}{41}\right)\) | \(e\left(\frac{18}{205}\right)\) | \(e\left(\frac{127}{410}\right)\) | \(e\left(\frac{192}{205}\right)\) | \(e\left(\frac{401}{410}\right)\) | \(e\left(\frac{149}{205}\right)\) | \(e\left(\frac{194}{205}\right)\) |