Basic properties
| Modulus: | \(6724\) | |
| Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(41\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1681}(165,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.q
\(\chi_{6724}(165,\cdot)\) \(\chi_{6724}(329,\cdot)\) \(\chi_{6724}(493,\cdot)\) \(\chi_{6724}(657,\cdot)\) \(\chi_{6724}(821,\cdot)\) \(\chi_{6724}(985,\cdot)\) \(\chi_{6724}(1149,\cdot)\) \(\chi_{6724}(1313,\cdot)\) \(\chi_{6724}(1477,\cdot)\) \(\chi_{6724}(1641,\cdot)\) \(\chi_{6724}(1805,\cdot)\) \(\chi_{6724}(1969,\cdot)\) \(\chi_{6724}(2133,\cdot)\) \(\chi_{6724}(2297,\cdot)\) \(\chi_{6724}(2461,\cdot)\) \(\chi_{6724}(2625,\cdot)\) \(\chi_{6724}(2789,\cdot)\) \(\chi_{6724}(2953,\cdot)\) \(\chi_{6724}(3117,\cdot)\) \(\chi_{6724}(3281,\cdot)\) \(\chi_{6724}(3445,\cdot)\) \(\chi_{6724}(3609,\cdot)\) \(\chi_{6724}(3773,\cdot)\) \(\chi_{6724}(3937,\cdot)\) \(\chi_{6724}(4101,\cdot)\) \(\chi_{6724}(4265,\cdot)\) \(\chi_{6724}(4429,\cdot)\) \(\chi_{6724}(4593,\cdot)\) \(\chi_{6724}(4757,\cdot)\) \(\chi_{6724}(4921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 41 polynomial |
Values on generators
\((3363,5049)\) → \((1,e\left(\frac{15}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6724 }(165, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{41}\right)\) | \(e\left(\frac{29}{41}\right)\) | \(e\left(\frac{21}{41}\right)\) | \(e\left(\frac{5}{41}\right)\) | \(e\left(\frac{10}{41}\right)\) | \(e\left(\frac{33}{41}\right)\) | \(e\left(\frac{11}{41}\right)\) | \(e\left(\frac{18}{41}\right)\) | \(e\left(\frac{19}{41}\right)\) | \(e\left(\frac{3}{41}\right)\) |