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.cq
\(\chi_{8024}(43,\cdot)\) \(\chi_{8024}(83,\cdot)\) \(\chi_{8024}(155,\cdot)\) \(\chi_{8024}(179,\cdot)\) \(\chi_{8024}(195,\cdot)\) \(\chi_{8024}(219,\cdot)\) \(\chi_{8024}(291,\cdot)\) \(\chi_{8024}(427,\cdot)\) \(\chi_{8024}(451,\cdot)\) \(\chi_{8024}(467,\cdot)\) \(\chi_{8024}(563,\cdot)\) \(\chi_{8024}(587,\cdot)\) \(\chi_{8024}(603,\cdot)\) \(\chi_{8024}(627,\cdot)\) \(\chi_{8024}(699,\cdot)\) \(\chi_{8024}(739,\cdot)\) \(\chi_{8024}(763,\cdot)\) \(\chi_{8024}(859,\cdot)\) \(\chi_{8024}(899,\cdot)\) \(\chi_{8024}(1011,\cdot)\) \(\chi_{8024}(1035,\cdot)\) \(\chi_{8024}(1131,\cdot)\) \(\chi_{8024}(1171,\cdot)\) \(\chi_{8024}(1283,\cdot)\) \(\chi_{8024}(1515,\cdot)\) \(\chi_{8024}(1675,\cdot)\) \(\chi_{8024}(1691,\cdot)\) \(\chi_{8024}(1987,\cdot)\) \(\chi_{8024}(2083,\cdot)\) \(\chi_{8024}(2099,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,-1,e\left(\frac{1}{8}\right),e\left(\frac{33}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{232}\right)\) | \(e\left(\frac{125}{232}\right)\) | \(e\left(\frac{27}{232}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{23}{232}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{211}{232}\right)\) |