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.en
\(\chi_{6760}(499,\cdot)\) \(\chi_{6760}(619,\cdot)\) \(\chi_{6760}(1019,\cdot)\) \(\chi_{6760}(1139,\cdot)\) \(\chi_{6760}(1539,\cdot)\) \(\chi_{6760}(1659,\cdot)\) \(\chi_{6760}(2059,\cdot)\) \(\chi_{6760}(2179,\cdot)\) \(\chi_{6760}(2579,\cdot)\) \(\chi_{6760}(2699,\cdot)\) \(\chi_{6760}(3099,\cdot)\) \(\chi_{6760}(3219,\cdot)\) \(\chi_{6760}(3739,\cdot)\) \(\chi_{6760}(4139,\cdot)\) \(\chi_{6760}(4259,\cdot)\) \(\chi_{6760}(4659,\cdot)\) \(\chi_{6760}(4779,\cdot)\) \(\chi_{6760}(5179,\cdot)\) \(\chi_{6760}(5299,\cdot)\) \(\chi_{6760}(5699,\cdot)\) \(\chi_{6760}(5819,\cdot)\) \(\chi_{6760}(6219,\cdot)\) \(\chi_{6760}(6339,\cdot)\) \(\chi_{6760}(6739,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,3381,4057,5241)\) → \((-1,-1,-1,e\left(\frac{27}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6760 }(499, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(-i\) | \(e\left(\frac{23}{52}\right)\) | \(-1\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) |