Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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.fq
\(\chi_{8023}(121,\cdot)\) \(\chi_{8023}(240,\cdot)\) \(\chi_{8023}(371,\cdot)\) \(\chi_{8023}(450,\cdot)\) \(\chi_{8023}(505,\cdot)\) \(\chi_{8023}(783,\cdot)\) \(\chi_{8023}(890,\cdot)\) \(\chi_{8023}(1138,\cdot)\) \(\chi_{8023}(1342,\cdot)\) \(\chi_{8023}(1580,\cdot)\) \(\chi_{8023}(2149,\cdot)\) \(\chi_{8023}(2204,\cdot)\) \(\chi_{8023}(2207,\cdot)\) \(\chi_{8023}(2429,\cdot)\) \(\chi_{8023}(2656,\cdot)\) \(\chi_{8023}(3111,\cdot)\) \(\chi_{8023}(3517,\cdot)\) \(\chi_{8023}(3556,\cdot)\) \(\chi_{8023}(3941,\cdot)\) \(\chi_{8023}(3969,\cdot)\) \(\chi_{8023}(4036,\cdot)\) \(\chi_{8023}(4066,\cdot)\) \(\chi_{8023}(4460,\cdot)\) \(\chi_{8023}(4522,\cdot)\) \(\chi_{8023}(4625,\cdot)\) \(\chi_{8023}(4689,\cdot)\) \(\chi_{8023}(4690,\cdot)\) \(\chi_{8023}(4980,\cdot)\) \(\chi_{8023}(5053,\cdot)\) \(\chi_{8023}(5141,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{31}{35}\right),e\left(\frac{9}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{70}\right)\) |