Basic properties
| Modulus: | \(6760\) | |
| Conductor: | \(6760\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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 6760.ed
\(\chi_{6760}(27,\cdot)\) \(\chi_{6760}(443,\cdot)\) \(\chi_{6760}(547,\cdot)\) \(\chi_{6760}(963,\cdot)\) \(\chi_{6760}(1067,\cdot)\) \(\chi_{6760}(1483,\cdot)\) \(\chi_{6760}(1587,\cdot)\) \(\chi_{6760}(2003,\cdot)\) \(\chi_{6760}(2107,\cdot)\) \(\chi_{6760}(2523,\cdot)\) \(\chi_{6760}(2627,\cdot)\) \(\chi_{6760}(3147,\cdot)\) \(\chi_{6760}(3563,\cdot)\) \(\chi_{6760}(3667,\cdot)\) \(\chi_{6760}(4083,\cdot)\) \(\chi_{6760}(4187,\cdot)\) \(\chi_{6760}(4603,\cdot)\) \(\chi_{6760}(4707,\cdot)\) \(\chi_{6760}(5123,\cdot)\) \(\chi_{6760}(5227,\cdot)\) \(\chi_{6760}(5643,\cdot)\) \(\chi_{6760}(6163,\cdot)\) \(\chi_{6760}(6267,\cdot)\) \(\chi_{6760}(6683,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,3381,4057,5241)\) → \((-1,-1,i,e\left(\frac{5}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6760 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(-1\) | \(e\left(\frac{9}{26}\right)\) | \(i\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) |