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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bh
\(\chi_{4012}(43,\cdot)\) \(\chi_{4012}(83,\cdot)\) \(\chi_{4012}(111,\cdot)\) \(\chi_{4012}(151,\cdot)\) \(\chi_{4012}(155,\cdot)\) \(\chi_{4012}(179,\cdot)\) \(\chi_{4012}(195,\cdot)\) \(\chi_{4012}(219,\cdot)\) \(\chi_{4012}(247,\cdot)\) \(\chi_{4012}(291,\cdot)\) \(\chi_{4012}(423,\cdot)\) \(\chi_{4012}(427,\cdot)\) \(\chi_{4012}(451,\cdot)\) \(\chi_{4012}(467,\cdot)\) \(\chi_{4012}(495,\cdot)\) \(\chi_{4012}(519,\cdot)\) \(\chi_{4012}(563,\cdot)\) \(\chi_{4012}(587,\cdot)\) \(\chi_{4012}(603,\cdot)\) \(\chi_{4012}(627,\cdot)\) \(\chi_{4012}(655,\cdot)\) \(\chi_{4012}(699,\cdot)\) \(\chi_{4012}(739,\cdot)\) \(\chi_{4012}(763,\cdot)\) \(\chi_{4012}(791,\cdot)\) \(\chi_{4012}(807,\cdot)\) \(\chi_{4012}(859,\cdot)\) \(\chi_{4012}(899,\cdot)\) \(\chi_{4012}(903,\cdot)\) \(\chi_{4012}(927,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{39}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(451, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{232}\right)\) | \(e\left(\frac{153}{232}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{43}{232}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{107}{232}\right)\) |