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 \(\chi_{1352}(893,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.fd
\(\chi_{8112}(217,\cdot)\) \(\chi_{8112}(601,\cdot)\) \(\chi_{8112}(841,\cdot)\) \(\chi_{8112}(1225,\cdot)\) \(\chi_{8112}(1465,\cdot)\) \(\chi_{8112}(1849,\cdot)\) \(\chi_{8112}(2089,\cdot)\) \(\chi_{8112}(2473,\cdot)\) \(\chi_{8112}(2713,\cdot)\) \(\chi_{8112}(3097,\cdot)\) \(\chi_{8112}(3337,\cdot)\) \(\chi_{8112}(3721,\cdot)\) \(\chi_{8112}(3961,\cdot)\) \(\chi_{8112}(4345,\cdot)\) \(\chi_{8112}(4969,\cdot)\) \(\chi_{8112}(5209,\cdot)\) \(\chi_{8112}(5593,\cdot)\) \(\chi_{8112}(5833,\cdot)\) \(\chi_{8112}(6217,\cdot)\) \(\chi_{8112}(6457,\cdot)\) \(\chi_{8112}(6841,\cdot)\) \(\chi_{8112}(7081,\cdot)\) \(\chi_{8112}(7465,\cdot)\) \(\chi_{8112}(7705,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,-1,1,e\left(\frac{32}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(217, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{53}{78}\right)\) |