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.dv
\(\chi_{8112}(317,\cdot)\) \(\chi_{8112}(941,\cdot)\) \(\chi_{8112}(1061,\cdot)\) \(\chi_{8112}(1565,\cdot)\) \(\chi_{8112}(1685,\cdot)\) \(\chi_{8112}(2189,\cdot)\) \(\chi_{8112}(2309,\cdot)\) \(\chi_{8112}(2813,\cdot)\) \(\chi_{8112}(2933,\cdot)\) \(\chi_{8112}(3437,\cdot)\) \(\chi_{8112}(3557,\cdot)\) \(\chi_{8112}(4061,\cdot)\) \(\chi_{8112}(4181,\cdot)\) \(\chi_{8112}(4685,\cdot)\) \(\chi_{8112}(4805,\cdot)\) \(\chi_{8112}(5429,\cdot)\) \(\chi_{8112}(5933,\cdot)\) \(\chi_{8112}(6053,\cdot)\) \(\chi_{8112}(6557,\cdot)\) \(\chi_{8112}(6677,\cdot)\) \(\chi_{8112}(7181,\cdot)\) \(\chi_{8112}(7301,\cdot)\) \(\chi_{8112}(7805,\cdot)\) \(\chi_{8112}(7925,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((1,-i,-1,e\left(\frac{51}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(317, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) |