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.er
\(\chi_{8023}(183,\cdot)\) \(\chi_{8023}(602,\cdot)\) \(\chi_{8023}(619,\cdot)\) \(\chi_{8023}(733,\cdot)\) \(\chi_{8023}(1091,\cdot)\) \(\chi_{8023}(1301,\cdot)\) \(\chi_{8023}(1672,\cdot)\) \(\chi_{8023}(1814,\cdot)\) \(\chi_{8023}(2014,\cdot)\) \(\chi_{8023}(2022,\cdot)\) \(\chi_{8023}(2306,\cdot)\) \(\chi_{8023}(2524,\cdot)\) \(\chi_{8023}(3094,\cdot)\) \(\chi_{8023}(3513,\cdot)\) \(\chi_{8023}(3520,\cdot)\) \(\chi_{8023}(3875,\cdot)\) \(\chi_{8023}(3928,\cdot)\) \(\chi_{8023}(3931,\cdot)\) \(\chi_{8023}(4240,\cdot)\) \(\chi_{8023}(4299,\cdot)\) \(\chi_{8023}(4428,\cdot)\) \(\chi_{8023}(4499,\cdot)\) \(\chi_{8023}(4567,\cdot)\) \(\chi_{8023}(4780,\cdot)\) \(\chi_{8023}(4996,\cdot)\) \(\chi_{8023}(5075,\cdot)\) \(\chi_{8023}(5080,\cdot)\) \(\chi_{8023}(5277,\cdot)\) \(\chi_{8023}(5490,\cdot)\) \(\chi_{8023}(5508,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{103}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{23}{112}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{37}{112}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{1}{8}\right)\) |