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.fo
\(\chi_{8023}(145,\cdot)\) \(\chi_{8023}(166,\cdot)\) \(\chi_{8023}(466,\cdot)\) \(\chi_{8023}(557,\cdot)\) \(\chi_{8023}(597,\cdot)\) \(\chi_{8023}(912,\cdot)\) \(\chi_{8023}(1144,\cdot)\) \(\chi_{8023}(1186,\cdot)\) \(\chi_{8023}(1211,\cdot)\) \(\chi_{8023}(1245,\cdot)\) \(\chi_{8023}(1296,\cdot)\) \(\chi_{8023}(1568,\cdot)\) \(\chi_{8023}(1574,\cdot)\) \(\chi_{8023}(1697,\cdot)\) \(\chi_{8023}(1929,\cdot)\) \(\chi_{8023}(2139,\cdot)\) \(\chi_{8023}(2203,\cdot)\) \(\chi_{8023}(2433,\cdot)\) \(\chi_{8023}(2472,\cdot)\) \(\chi_{8023}(2494,\cdot)\) \(\chi_{8023}(2631,\cdot)\) \(\chi_{8023}(3162,\cdot)\) \(\chi_{8023}(3495,\cdot)\) \(\chi_{8023}(3560,\cdot)\) \(\chi_{8023}(3614,\cdot)\) \(\chi_{8023}(3782,\cdot)\) \(\chi_{8023}(3850,\cdot)\) \(\chi_{8023}(4195,\cdot)\) \(\chi_{8023}(4296,\cdot)\) \(\chi_{8023}(4488,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{13}{35}\right),e\left(\frac{15}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) |