Basic properties
| Modulus: | \(2656\) | |
| 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 \(\chi_{664}(379,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2656.r
\(\chi_{2656}(15,\cdot)\) \(\chi_{2656}(47,\cdot)\) \(\chi_{2656}(79,\cdot)\) \(\chi_{2656}(143,\cdot)\) \(\chi_{2656}(239,\cdot)\) \(\chi_{2656}(271,\cdot)\) \(\chi_{2656}(303,\cdot)\) \(\chi_{2656}(367,\cdot)\) \(\chi_{2656}(399,\cdot)\) \(\chi_{2656}(495,\cdot)\) \(\chi_{2656}(623,\cdot)\) \(\chi_{2656}(655,\cdot)\) \(\chi_{2656}(719,\cdot)\) \(\chi_{2656}(975,\cdot)\) \(\chi_{2656}(1039,\cdot)\) \(\chi_{2656}(1103,\cdot)\) \(\chi_{2656}(1135,\cdot)\) \(\chi_{2656}(1167,\cdot)\) \(\chi_{2656}(1263,\cdot)\) \(\chi_{2656}(1295,\cdot)\) \(\chi_{2656}(1487,\cdot)\) \(\chi_{2656}(1551,\cdot)\) \(\chi_{2656}(1583,\cdot)\) \(\chi_{2656}(1679,\cdot)\) \(\chi_{2656}(1775,\cdot)\) \(\chi_{2656}(1839,\cdot)\) \(\chi_{2656}(1871,\cdot)\) \(\chi_{2656}(1967,\cdot)\) \(\chi_{2656}(2031,\cdot)\) \(\chi_{2656}(2063,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{41})$ |
| Fixed field: | Number field defined by a degree 82 polynomial |
Values on generators
\((831,997,417)\) → \((-1,-1,e\left(\frac{23}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2656 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{41}\right)\) | \(e\left(\frac{3}{41}\right)\) | \(e\left(\frac{61}{82}\right)\) | \(e\left(\frac{16}{41}\right)\) | \(e\left(\frac{30}{41}\right)\) | \(e\left(\frac{4}{41}\right)\) | \(e\left(\frac{11}{41}\right)\) | \(e\left(\frac{29}{41}\right)\) | \(e\left(\frac{15}{82}\right)\) | \(e\left(\frac{77}{82}\right)\) |