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.ep
\(\chi_{8023}(23,\cdot)\) \(\chi_{8023}(536,\cdot)\) \(\chi_{8023}(538,\cdot)\) \(\chi_{8023}(820,\cdot)\) \(\chi_{8023}(1177,\cdot)\) \(\chi_{8023}(1233,\cdot)\) \(\chi_{8023}(1390,\cdot)\) \(\chi_{8023}(1887,\cdot)\) \(\chi_{8023}(1897,\cdot)\) \(\chi_{8023}(2011,\cdot)\) \(\chi_{8023}(2093,\cdot)\) \(\chi_{8023}(2100,\cdot)\) \(\chi_{8023}(2153,\cdot)\) \(\chi_{8023}(2394,\cdot)\) \(\chi_{8023}(2440,\cdot)\) \(\chi_{8023}(2453,\cdot)\) \(\chi_{8023}(2465,\cdot)\) \(\chi_{8023}(2724,\cdot)\) \(\chi_{8023}(2739,\cdot)\) \(\chi_{8023}(2808,\cdot)\) \(\chi_{8023}(2863,\cdot)\) \(\chi_{8023}(2962,\cdot)\) \(\chi_{8023}(3234,\cdot)\) \(\chi_{8023}(3371,\cdot)\) \(\chi_{8023}(3726,\cdot)\) \(\chi_{8023}(3797,\cdot)\) \(\chi_{8023}(4144,\cdot)\) \(\chi_{8023}(4638,\cdot)\) \(\chi_{8023}(4783,\cdot)\) \(\chi_{8023}(4791,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{3}{14}\right),e\left(\frac{41}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{69}{112}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{41}{56}\right)\) |