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 \(\chi_{4012}(559,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.ct
\(\chi_{8024}(15,\cdot)\) \(\chi_{8024}(87,\cdot)\) \(\chi_{8024}(127,\cdot)\) \(\chi_{8024}(223,\cdot)\) \(\chi_{8024}(263,\cdot)\) \(\chi_{8024}(287,\cdot)\) \(\chi_{8024}(359,\cdot)\) \(\chi_{8024}(383,\cdot)\) \(\chi_{8024}(399,\cdot)\) \(\chi_{8024}(535,\cdot)\) \(\chi_{8024}(559,\cdot)\) \(\chi_{8024}(631,\cdot)\) \(\chi_{8024}(671,\cdot)\) \(\chi_{8024}(695,\cdot)\) \(\chi_{8024}(831,\cdot)\) \(\chi_{8024}(1039,\cdot)\) \(\chi_{8024}(1079,\cdot)\) \(\chi_{8024}(1103,\cdot)\) \(\chi_{8024}(1199,\cdot)\) \(\chi_{8024}(1215,\cdot)\) \(\chi_{8024}(1351,\cdot)\) \(\chi_{8024}(1487,\cdot)\) \(\chi_{8024}(1511,\cdot)\) \(\chi_{8024}(1583,\cdot)\) \(\chi_{8024}(1759,\cdot)\) \(\chi_{8024}(1855,\cdot)\) \(\chi_{8024}(1895,\cdot)\) \(\chi_{8024}(2015,\cdot)\) \(\chi_{8024}(2031,\cdot)\) \(\chi_{8024}(2055,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,e\left(\frac{3}{8}\right),e\left(\frac{10}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(559, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{232}\right)\) | \(e\left(\frac{219}{232}\right)\) | \(e\left(\frac{193}{232}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{173}{232}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{69}{232}\right)\) |