Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(4012\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bj
\(\chi_{4012}(15,\cdot)\) \(\chi_{4012}(19,\cdot)\) \(\chi_{4012}(87,\cdot)\) \(\chi_{4012}(127,\cdot)\) \(\chi_{4012}(223,\cdot)\) \(\chi_{4012}(263,\cdot)\) \(\chi_{4012}(287,\cdot)\) \(\chi_{4012}(315,\cdot)\) \(\chi_{4012}(331,\cdot)\) \(\chi_{4012}(359,\cdot)\) \(\chi_{4012}(383,\cdot)\) \(\chi_{4012}(399,\cdot)\) \(\chi_{4012}(491,\cdot)\) \(\chi_{4012}(535,\cdot)\) \(\chi_{4012}(559,\cdot)\) \(\chi_{4012}(631,\cdot)\) \(\chi_{4012}(671,\cdot)\) \(\chi_{4012}(695,\cdot)\) \(\chi_{4012}(723,\cdot)\) \(\chi_{4012}(831,\cdot)\) \(\chi_{4012}(835,\cdot)\) \(\chi_{4012}(875,\cdot)\) \(\chi_{4012}(971,\cdot)\) \(\chi_{4012}(995,\cdot)\) \(\chi_{4012}(1039,\cdot)\) \(\chi_{4012}(1079,\cdot)\) \(\chi_{4012}(1103,\cdot)\) \(\chi_{4012}(1107,\cdot)\) \(\chi_{4012}(1147,\cdot)\) \(\chi_{4012}(1199,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{19}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{232}\right)\) | \(e\left(\frac{71}{232}\right)\) | \(e\left(\frac{213}{232}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{1}{232}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{75}{116}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{105}{232}\right)\) |