Basic properties
| Modulus: | \(5312\) | |
| Conductor: | \(664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(82\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{664}(491,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5312.v
\(\chi_{5312}(159,\cdot)\) \(\chi_{5312}(223,\cdot)\) \(\chi_{5312}(351,\cdot)\) \(\chi_{5312}(543,\cdot)\) \(\chi_{5312}(735,\cdot)\) \(\chi_{5312}(799,\cdot)\) \(\chi_{5312}(927,\cdot)\) \(\chi_{5312}(1247,\cdot)\) \(\chi_{5312}(1311,\cdot)\) \(\chi_{5312}(1375,\cdot)\) \(\chi_{5312}(1567,\cdot)\) \(\chi_{5312}(1631,\cdot)\) \(\chi_{5312}(1695,\cdot)\) \(\chi_{5312}(1823,\cdot)\) \(\chi_{5312}(1951,\cdot)\) \(\chi_{5312}(2463,\cdot)\) \(\chi_{5312}(2591,\cdot)\) \(\chi_{5312}(2911,\cdot)\) \(\chi_{5312}(3103,\cdot)\) \(\chi_{5312}(3167,\cdot)\) \(\chi_{5312}(3295,\cdot)\) \(\chi_{5312}(3359,\cdot)\) \(\chi_{5312}(3423,\cdot)\) \(\chi_{5312}(3615,\cdot)\) \(\chi_{5312}(3743,\cdot)\) \(\chi_{5312}(3807,\cdot)\) \(\chi_{5312}(3871,\cdot)\) \(\chi_{5312}(3935,\cdot)\) \(\chi_{5312}(3999,\cdot)\) \(\chi_{5312}(4063,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\((831,3653,3073)\) → \((-1,-1,e\left(\frac{49}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(159, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{26}{41}\right)\) | \(e\left(\frac{23}{82}\right)\) | \(e\left(\frac{2}{41}\right)\) | \(e\left(\frac{14}{41}\right)\) | \(e\left(\frac{21}{41}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{19}{41}\right)\) | \(e\left(\frac{7}{82}\right)\) | \(e\left(\frac{25}{82}\right)\) |