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 \(\chi_{2028}(1427,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ev
\(\chi_{8112}(95,\cdot)\) \(\chi_{8112}(335,\cdot)\) \(\chi_{8112}(719,\cdot)\) \(\chi_{8112}(959,\cdot)\) \(\chi_{8112}(1343,\cdot)\) \(\chi_{8112}(1583,\cdot)\) \(\chi_{8112}(1967,\cdot)\) \(\chi_{8112}(2207,\cdot)\) \(\chi_{8112}(2591,\cdot)\) \(\chi_{8112}(2831,\cdot)\) \(\chi_{8112}(3215,\cdot)\) \(\chi_{8112}(3455,\cdot)\) \(\chi_{8112}(3839,\cdot)\) \(\chi_{8112}(4463,\cdot)\) \(\chi_{8112}(4703,\cdot)\) \(\chi_{8112}(5087,\cdot)\) \(\chi_{8112}(5327,\cdot)\) \(\chi_{8112}(5711,\cdot)\) \(\chi_{8112}(5951,\cdot)\) \(\chi_{8112}(6335,\cdot)\) \(\chi_{8112}(6575,\cdot)\) \(\chi_{8112}(6959,\cdot)\) \(\chi_{8112}(7199,\cdot)\) \(\chi_{8112}(7823,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,1,-1,e\left(\frac{71}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(3455, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) |