Basic properties
| Modulus: | \(8112\) | |
| 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 \(\chi_{1352}(797,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.eu
\(\chi_{8112}(121,\cdot)\) \(\chi_{8112}(745,\cdot)\) \(\chi_{8112}(985,\cdot)\) \(\chi_{8112}(1369,\cdot)\) \(\chi_{8112}(1609,\cdot)\) \(\chi_{8112}(1993,\cdot)\) \(\chi_{8112}(2233,\cdot)\) \(\chi_{8112}(2617,\cdot)\) \(\chi_{8112}(2857,\cdot)\) \(\chi_{8112}(3241,\cdot)\) \(\chi_{8112}(3481,\cdot)\) \(\chi_{8112}(4105,\cdot)\) \(\chi_{8112}(4489,\cdot)\) \(\chi_{8112}(4729,\cdot)\) \(\chi_{8112}(5113,\cdot)\) \(\chi_{8112}(5353,\cdot)\) \(\chi_{8112}(5737,\cdot)\) \(\chi_{8112}(5977,\cdot)\) \(\chi_{8112}(6361,\cdot)\) \(\chi_{8112}(6601,\cdot)\) \(\chi_{8112}(6985,\cdot)\) \(\chi_{8112}(7225,\cdot)\) \(\chi_{8112}(7609,\cdot)\) \(\chi_{8112}(7849,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,-1,1,e\left(\frac{25}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) |