Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1640\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1681}(317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.be
\(\chi_{6724}(13,\cdot)\) \(\chi_{6724}(17,\cdot)\) \(\chi_{6724}(29,\cdot)\) \(\chi_{6724}(53,\cdot)\) \(\chi_{6724}(65,\cdot)\) \(\chi_{6724}(69,\cdot)\) \(\chi_{6724}(89,\cdot)\) \(\chi_{6724}(93,\cdot)\) \(\chi_{6724}(97,\cdot)\) \(\chi_{6724}(101,\cdot)\) \(\chi_{6724}(117,\cdot)\) \(\chi_{6724}(129,\cdot)\) \(\chi_{6724}(145,\cdot)\) \(\chi_{6724}(149,\cdot)\) \(\chi_{6724}(153,\cdot)\) \(\chi_{6724}(157,\cdot)\) \(\chi_{6724}(177,\cdot)\) \(\chi_{6724}(181,\cdot)\) \(\chi_{6724}(193,\cdot)\) \(\chi_{6724}(217,\cdot)\) \(\chi_{6724}(229,\cdot)\) \(\chi_{6724}(233,\cdot)\) \(\chi_{6724}(253,\cdot)\) \(\chi_{6724}(257,\cdot)\) \(\chi_{6724}(261,\cdot)\) \(\chi_{6724}(265,\cdot)\) \(\chi_{6724}(281,\cdot)\) \(\chi_{6724}(293,\cdot)\) \(\chi_{6724}(309,\cdot)\) \(\chi_{6724}(317,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1640})$ |
| Fixed field: | Number field defined by a degree 1640 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((1,e\left(\frac{1503}{1640}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(317, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{328}\right)\) | \(e\left(\frac{473}{820}\right)\) | \(e\left(\frac{497}{1640}\right)\) | \(e\left(\frac{5}{164}\right)\) | \(e\left(\frac{469}{1640}\right)\) | \(e\left(\frac{1273}{1640}\right)\) | \(e\left(\frac{971}{1640}\right)\) | \(e\left(\frac{959}{1640}\right)\) | \(e\left(\frac{887}{1640}\right)\) | \(e\left(\frac{261}{820}\right)\) |