Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.eu
\(\chi_{8023}(381,\cdot)\) \(\chi_{8023}(523,\cdot)\) \(\chi_{8023}(607,\cdot)\) \(\chi_{8023}(749,\cdot)\) \(\chi_{8023}(751,\cdot)\) \(\chi_{8023}(946,\cdot)\) \(\chi_{8023}(1088,\cdot)\) \(\chi_{8023}(1170,\cdot)\) \(\chi_{8023}(1517,\cdot)\) \(\chi_{8023}(1542,\cdot)\) \(\chi_{8023}(1730,\cdot)\) \(\chi_{8023}(1743,\cdot)\) \(\chi_{8023}(1956,\cdot)\) \(\chi_{8023}(2082,\cdot)\) \(\chi_{8023}(2295,\cdot)\) \(\chi_{8023}(2526,\cdot)\) \(\chi_{8023}(3016,\cdot)\) \(\chi_{8023}(3229,\cdot)\) \(\chi_{8023}(3317,\cdot)\) \(\chi_{8023}(3576,\cdot)\) \(\chi_{8023}(3802,\cdot)\) \(\chi_{8023}(4141,\cdot)\) \(\chi_{8023}(4223,\cdot)\) \(\chi_{8023}(4365,\cdot)\) \(\chi_{8023}(4372,\cdot)\) \(\chi_{8023}(4585,\cdot)\) \(\chi_{8023}(5163,\cdot)\) \(\chi_{8023}(5351,\cdot)\) \(\chi_{8023}(5359,\cdot)\) \(\chi_{8023}(5376,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(381, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{101}{112}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{112}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{75}{112}\right)\) | \(e\left(\frac{45}{56}\right)\) |