Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.eh
\(\chi_{8112}(31,\cdot)\) \(\chi_{8112}(463,\cdot)\) \(\chi_{8112}(655,\cdot)\) \(\chi_{8112}(1087,\cdot)\) \(\chi_{8112}(1279,\cdot)\) \(\chi_{8112}(1711,\cdot)\) \(\chi_{8112}(1903,\cdot)\) \(\chi_{8112}(2335,\cdot)\) \(\chi_{8112}(2527,\cdot)\) \(\chi_{8112}(2959,\cdot)\) \(\chi_{8112}(3151,\cdot)\) \(\chi_{8112}(3583,\cdot)\) \(\chi_{8112}(3775,\cdot)\) \(\chi_{8112}(4207,\cdot)\) \(\chi_{8112}(4399,\cdot)\) \(\chi_{8112}(5023,\cdot)\) \(\chi_{8112}(5455,\cdot)\) \(\chi_{8112}(6079,\cdot)\) \(\chi_{8112}(6271,\cdot)\) \(\chi_{8112}(6703,\cdot)\) \(\chi_{8112}(6895,\cdot)\) \(\chi_{8112}(7327,\cdot)\) \(\chi_{8112}(7519,\cdot)\) \(\chi_{8112}(7951,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,1,1,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(i\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) |