Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(820\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1681}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.bd
\(\chi_{6724}(5,\cdot)\) \(\chi_{6724}(21,\cdot)\) \(\chi_{6724}(33,\cdot)\) \(\chi_{6724}(49,\cdot)\) \(\chi_{6724}(61,\cdot)\) \(\chi_{6724}(77,\cdot)\) \(\chi_{6724}(121,\cdot)\) \(\chi_{6724}(125,\cdot)\) \(\chi_{6724}(169,\cdot)\) \(\chi_{6724}(185,\cdot)\) \(\chi_{6724}(197,\cdot)\) \(\chi_{6724}(213,\cdot)\) \(\chi_{6724}(225,\cdot)\) \(\chi_{6724}(241,\cdot)\) \(\chi_{6724}(285,\cdot)\) \(\chi_{6724}(289,\cdot)\) \(\chi_{6724}(333,\cdot)\) \(\chi_{6724}(349,\cdot)\) \(\chi_{6724}(361,\cdot)\) \(\chi_{6724}(377,\cdot)\) \(\chi_{6724}(389,\cdot)\) \(\chi_{6724}(405,\cdot)\) \(\chi_{6724}(449,\cdot)\) \(\chi_{6724}(453,\cdot)\) \(\chi_{6724}(497,\cdot)\) \(\chi_{6724}(513,\cdot)\) \(\chi_{6724}(525,\cdot)\) \(\chi_{6724}(541,\cdot)\) \(\chi_{6724}(553,\cdot)\) \(\chi_{6724}(569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{820})$ |
| Fixed field: | Number field defined by a degree 820 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((1,e\left(\frac{489}{820}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{164}\right)\) | \(e\left(\frac{239}{410}\right)\) | \(e\left(\frac{291}{820}\right)\) | \(e\left(\frac{45}{82}\right)\) | \(e\left(\frac{367}{820}\right)\) | \(e\left(\frac{59}{820}\right)\) | \(e\left(\frac{293}{820}\right)\) | \(e\left(\frac{677}{820}\right)\) | \(e\left(\frac{521}{820}\right)\) | \(e\left(\frac{53}{410}\right)\) |