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.et
\(\chi_{8023}(70,\cdot)\) \(\chi_{8023}(425,\cdot)\) \(\chi_{8023}(993,\cdot)\) \(\chi_{8023}(1064,\cdot)\) \(\chi_{8023}(1135,\cdot)\) \(\chi_{8023}(1206,\cdot)\) \(\chi_{8023}(1277,\cdot)\) \(\chi_{8023}(1490,\cdot)\) \(\chi_{8023}(1561,\cdot)\) \(\chi_{8023}(1774,\cdot)\) \(\chi_{8023}(1845,\cdot)\) \(\chi_{8023}(1916,\cdot)\) \(\chi_{8023}(1987,\cdot)\) \(\chi_{8023}(2058,\cdot)\) \(\chi_{8023}(2626,\cdot)\) \(\chi_{8023}(2981,\cdot)\) \(\chi_{8023}(3265,\cdot)\) \(\chi_{8023}(3336,\cdot)\) \(\chi_{8023}(3407,\cdot)\) \(\chi_{8023}(3549,\cdot)\) \(\chi_{8023}(3691,\cdot)\) \(\chi_{8023}(3762,\cdot)\) \(\chi_{8023}(3975,\cdot)\) \(\chi_{8023}(4401,\cdot)\) \(\chi_{8023}(4543,\cdot)\) \(\chi_{8023}(4614,\cdot)\) \(\chi_{8023}(4756,\cdot)\) \(\chi_{8023}(4898,\cdot)\) \(\chi_{8023}(4969,\cdot)\) \(\chi_{8023}(5040,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((-1,e\left(\frac{103}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(70, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{103}{112}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{37}{112}\right)\) | \(e\left(\frac{107}{112}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{41}{112}\right)\) | \(e\left(\frac{31}{56}\right)\) |