Basic properties
| Modulus: | \(6760\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6760.eu
\(\chi_{6760}(101,\cdot)\) \(\chi_{6760}(381,\cdot)\) \(\chi_{6760}(621,\cdot)\) \(\chi_{6760}(901,\cdot)\) \(\chi_{6760}(1141,\cdot)\) \(\chi_{6760}(1421,\cdot)\) \(\chi_{6760}(1661,\cdot)\) \(\chi_{6760}(1941,\cdot)\) \(\chi_{6760}(2181,\cdot)\) \(\chi_{6760}(2461,\cdot)\) \(\chi_{6760}(2701,\cdot)\) \(\chi_{6760}(2981,\cdot)\) \(\chi_{6760}(3221,\cdot)\) \(\chi_{6760}(3501,\cdot)\) \(\chi_{6760}(4021,\cdot)\) \(\chi_{6760}(4261,\cdot)\) \(\chi_{6760}(4781,\cdot)\) \(\chi_{6760}(5061,\cdot)\) \(\chi_{6760}(5301,\cdot)\) \(\chi_{6760}(5581,\cdot)\) \(\chi_{6760}(5821,\cdot)\) \(\chi_{6760}(6101,\cdot)\) \(\chi_{6760}(6341,\cdot)\) \(\chi_{6760}(6621,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,3381,4057,5241)\) → \((1,-1,1,e\left(\frac{35}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6760 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{35}{78}\right)\) |