Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | 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 8024.cn
\(\chi_{8024}(53,\cdot)\) \(\chi_{8024}(189,\cdot)\) \(\chi_{8024}(213,\cdot)\) \(\chi_{8024}(253,\cdot)\) \(\chi_{8024}(389,\cdot)\) \(\chi_{8024}(461,\cdot)\) \(\chi_{8024}(501,\cdot)\) \(\chi_{8024}(525,\cdot)\) \(\chi_{8024}(597,\cdot)\) \(\chi_{8024}(661,\cdot)\) \(\chi_{8024}(733,\cdot)\) \(\chi_{8024}(757,\cdot)\) \(\chi_{8024}(933,\cdot)\) \(\chi_{8024}(1029,\cdot)\) \(\chi_{8024}(1069,\cdot)\) \(\chi_{8024}(1141,\cdot)\) \(\chi_{8024}(1205,\cdot)\) \(\chi_{8024}(1301,\cdot)\) \(\chi_{8024}(1317,\cdot)\) \(\chi_{8024}(1437,\cdot)\) \(\chi_{8024}(1549,\cdot)\) \(\chi_{8024}(1613,\cdot)\) \(\chi_{8024}(1709,\cdot)\) \(\chi_{8024}(1821,\cdot)\) \(\chi_{8024}(1845,\cdot)\) \(\chi_{8024}(2021,\cdot)\) \(\chi_{8024}(2093,\cdot)\) \(\chi_{8024}(2133,\cdot)\) \(\chi_{8024}(2229,\cdot)\) \(\chi_{8024}(2269,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{232}\right)\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{25}{232}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{189}{232}\right)\) |