Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(6724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1640\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.bf
\(\chi_{6724}(7,\cdot)\) \(\chi_{6724}(11,\cdot)\) \(\chi_{6724}(15,\cdot)\) \(\chi_{6724}(19,\cdot)\) \(\chi_{6724}(35,\cdot)\) \(\chi_{6724}(47,\cdot)\) \(\chi_{6724}(63,\cdot)\) \(\chi_{6724}(67,\cdot)\) \(\chi_{6724}(71,\cdot)\) \(\chi_{6724}(75,\cdot)\) \(\chi_{6724}(95,\cdot)\) \(\chi_{6724}(99,\cdot)\) \(\chi_{6724}(111,\cdot)\) \(\chi_{6724}(135,\cdot)\) \(\chi_{6724}(147,\cdot)\) \(\chi_{6724}(151,\cdot)\) \(\chi_{6724}(171,\cdot)\) \(\chi_{6724}(175,\cdot)\) \(\chi_{6724}(179,\cdot)\) \(\chi_{6724}(183,\cdot)\) \(\chi_{6724}(199,\cdot)\) \(\chi_{6724}(211,\cdot)\) \(\chi_{6724}(227,\cdot)\) \(\chi_{6724}(231,\cdot)\) \(\chi_{6724}(235,\cdot)\) \(\chi_{6724}(239,\cdot)\) \(\chi_{6724}(259,\cdot)\) \(\chi_{6724}(263,\cdot)\) \(\chi_{6724}(275,\cdot)\) \(\chi_{6724}(299,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1640})$ |
| Fixed field: | Number field defined by a degree 1640 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((-1,e\left(\frac{559}{1640}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{225}{328}\right)\) | \(e\left(\frac{129}{820}\right)\) | \(e\left(\frac{61}{1640}\right)\) | \(e\left(\frac{61}{164}\right)\) | \(e\left(\frac{1097}{1640}\right)\) | \(e\left(\frac{49}{1640}\right)\) | \(e\left(\frac{1383}{1640}\right)\) | \(e\left(\frac{1007}{1640}\right)\) | \(e\left(\frac{1211}{1640}\right)\) | \(e\left(\frac{593}{820}\right)\) |