Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(8112\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.dz
\(\chi_{8112}(131,\cdot)\) \(\chi_{8112}(443,\cdot)\) \(\chi_{8112}(755,\cdot)\) \(\chi_{8112}(1067,\cdot)\) \(\chi_{8112}(1379,\cdot)\) \(\chi_{8112}(2003,\cdot)\) \(\chi_{8112}(2315,\cdot)\) \(\chi_{8112}(2627,\cdot)\) \(\chi_{8112}(2939,\cdot)\) \(\chi_{8112}(3251,\cdot)\) \(\chi_{8112}(3563,\cdot)\) \(\chi_{8112}(3875,\cdot)\) \(\chi_{8112}(4187,\cdot)\) \(\chi_{8112}(4499,\cdot)\) \(\chi_{8112}(4811,\cdot)\) \(\chi_{8112}(5123,\cdot)\) \(\chi_{8112}(5435,\cdot)\) \(\chi_{8112}(6059,\cdot)\) \(\chi_{8112}(6371,\cdot)\) \(\chi_{8112}(6683,\cdot)\) \(\chi_{8112}(6995,\cdot)\) \(\chi_{8112}(7307,\cdot)\) \(\chi_{8112}(7619,\cdot)\) \(\chi_{8112}(7931,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,-i,-1,e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{17}{52}\right)\) |