Basic properties
| Modulus: | \(2019\) | |
| Conductor: | \(2019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2019.bn
\(\chi_{2019}(146,\cdot)\) \(\chi_{2019}(194,\cdot)\) \(\chi_{2019}(257,\cdot)\) \(\chi_{2019}(263,\cdot)\) \(\chi_{2019}(281,\cdot)\) \(\chi_{2019}(296,\cdot)\) \(\chi_{2019}(302,\cdot)\) \(\chi_{2019}(335,\cdot)\) \(\chi_{2019}(338,\cdot)\) \(\chi_{2019}(371,\cdot)\) \(\chi_{2019}(377,\cdot)\) \(\chi_{2019}(392,\cdot)\) \(\chi_{2019}(410,\cdot)\) \(\chi_{2019}(416,\cdot)\) \(\chi_{2019}(479,\cdot)\) \(\chi_{2019}(527,\cdot)\) \(\chi_{2019}(680,\cdot)\) \(\chi_{2019}(773,\cdot)\) \(\chi_{2019}(857,\cdot)\) \(\chi_{2019}(860,\cdot)\) \(\chi_{2019}(932,\cdot)\) \(\chi_{2019}(1016,\cdot)\) \(\chi_{2019}(1037,\cdot)\) \(\chi_{2019}(1079,\cdot)\) \(\chi_{2019}(1097,\cdot)\) \(\chi_{2019}(1121,\cdot)\) \(\chi_{2019}(1130,\cdot)\) \(\chi_{2019}(1157,\cdot)\) \(\chi_{2019}(1250,\cdot)\) \(\chi_{2019}(1259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((674,1351)\) → \((-1,e\left(\frac{1}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2019 }(146, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{71}{112}\right)\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(-1\) |