Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(2028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2028}(575,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.fa
\(\chi_{8112}(575,\cdot)\) \(\chi_{8112}(815,\cdot)\) \(\chi_{8112}(1199,\cdot)\) \(\chi_{8112}(1439,\cdot)\) \(\chi_{8112}(1823,\cdot)\) \(\chi_{8112}(2063,\cdot)\) \(\chi_{8112}(2447,\cdot)\) \(\chi_{8112}(2687,\cdot)\) \(\chi_{8112}(3071,\cdot)\) \(\chi_{8112}(3311,\cdot)\) \(\chi_{8112}(3935,\cdot)\) \(\chi_{8112}(4319,\cdot)\) \(\chi_{8112}(4559,\cdot)\) \(\chi_{8112}(4943,\cdot)\) \(\chi_{8112}(5183,\cdot)\) \(\chi_{8112}(5567,\cdot)\) \(\chi_{8112}(5807,\cdot)\) \(\chi_{8112}(6191,\cdot)\) \(\chi_{8112}(6431,\cdot)\) \(\chi_{8112}(6815,\cdot)\) \(\chi_{8112}(7055,\cdot)\) \(\chi_{8112}(7439,\cdot)\) \(\chi_{8112}(7679,\cdot)\) \(\chi_{8112}(8063,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,1,-1,e\left(\frac{37}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(575, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) |