Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4012}(111,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.cp
\(\chi_{8024}(111,\cdot)\) \(\chi_{8024}(151,\cdot)\) \(\chi_{8024}(247,\cdot)\) \(\chi_{8024}(423,\cdot)\) \(\chi_{8024}(495,\cdot)\) \(\chi_{8024}(519,\cdot)\) \(\chi_{8024}(655,\cdot)\) \(\chi_{8024}(791,\cdot)\) \(\chi_{8024}(807,\cdot)\) \(\chi_{8024}(903,\cdot)\) \(\chi_{8024}(927,\cdot)\) \(\chi_{8024}(967,\cdot)\) \(\chi_{8024}(1175,\cdot)\) \(\chi_{8024}(1311,\cdot)\) \(\chi_{8024}(1335,\cdot)\) \(\chi_{8024}(1375,\cdot)\) \(\chi_{8024}(1447,\cdot)\) \(\chi_{8024}(1471,\cdot)\) \(\chi_{8024}(1607,\cdot)\) \(\chi_{8024}(1623,\cdot)\) \(\chi_{8024}(1647,\cdot)\) \(\chi_{8024}(1719,\cdot)\) \(\chi_{8024}(1743,\cdot)\) \(\chi_{8024}(1783,\cdot)\) \(\chi_{8024}(1879,\cdot)\) \(\chi_{8024}(1919,\cdot)\) \(\chi_{8024}(1991,\cdot)\) \(\chi_{8024}(2167,\cdot)\) \(\chi_{8024}(2191,\cdot)\) \(\chi_{8024}(2303,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,e\left(\frac{1}{8}\right),e\left(\frac{47}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{232}\right)\) | \(e\left(\frac{113}{232}\right)\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{147}{232}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{123}{232}\right)\) |