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.de
\(\chi_{8023}(91,\cdot)\) \(\chi_{8023}(400,\cdot)\) \(\chi_{8023}(529,\cdot)\) \(\chi_{8023}(534,\cdot)\) \(\chi_{8023}(616,\cdot)\) \(\chi_{8023}(1381,\cdot)\) \(\chi_{8023}(2814,\cdot)\) \(\chi_{8023}(3073,\cdot)\) \(\chi_{8023}(3286,\cdot)\) \(\chi_{8023}(3516,\cdot)\) \(\chi_{8023}(3942,\cdot)\) \(\chi_{8023}(4305,\cdot)\) \(\chi_{8023}(4787,\cdot)\) \(\chi_{8023}(5286,\cdot)\) \(\chi_{8023}(5373,\cdot)\) \(\chi_{8023}(6138,\cdot)\) \(\chi_{8023}(6278,\cdot)\) \(\chi_{8023}(6491,\cdot)\) \(\chi_{8023}(6580,\cdot)\) \(\chi_{8023}(6719,\cdot)\) \(\chi_{8023}(6924,\cdot)\) \(\chi_{8023}(7432,\cdot)\) \(\chi_{8023}(7901,\cdot)\) \(\chi_{8023}(7982,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{15}{56}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{28}\right)\) |