Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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.dc
\(\chi_{8023}(314,\cdot)\) \(\chi_{8023}(463,\cdot)\) \(\chi_{8023}(955,\cdot)\) \(\chi_{8023}(1039,\cdot)\) \(\chi_{8023}(1166,\cdot)\) \(\chi_{8023}(1252,\cdot)\) \(\chi_{8023}(1369,\cdot)\) \(\chi_{8023}(1397,\cdot)\) \(\chi_{8023}(1795,\cdot)\) \(\chi_{8023}(2877,\cdot)\) \(\chi_{8023}(2888,\cdot)\) \(\chi_{8023}(3101,\cdot)\) \(\chi_{8023}(3580,\cdot)\) \(\chi_{8023}(4432,\cdot)\) \(\chi_{8023}(4581,\cdot)\) \(\chi_{8023}(4592,\cdot)\) \(\chi_{8023}(4777,\cdot)\) \(\chi_{8023}(5712,\cdot)\) \(\chi_{8023}(5867,\cdot)\) \(\chi_{8023}(6080,\cdot)\) \(\chi_{8023}(6410,\cdot)\) \(\chi_{8023}(6919,\cdot)\) \(\chi_{8023}(6995,\cdot)\) \(\chi_{8023}(7771,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{6}{7}\right),e\left(\frac{55}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(314, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(i\) |