Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bi
\(\chi_{4012}(9,\cdot)\) \(\chi_{4012}(25,\cdot)\) \(\chi_{4012}(49,\cdot)\) \(\chi_{4012}(53,\cdot)\) \(\chi_{4012}(121,\cdot)\) \(\chi_{4012}(145,\cdot)\) \(\chi_{4012}(189,\cdot)\) \(\chi_{4012}(213,\cdot)\) \(\chi_{4012}(253,\cdot)\) \(\chi_{4012}(257,\cdot)\) \(\chi_{4012}(281,\cdot)\) \(\chi_{4012}(321,\cdot)\) \(\chi_{4012}(389,\cdot)\) \(\chi_{4012}(417,\cdot)\) \(\chi_{4012}(433,\cdot)\) \(\chi_{4012}(461,\cdot)\) \(\chi_{4012}(501,\cdot)\) \(\chi_{4012}(525,\cdot)\) \(\chi_{4012}(529,\cdot)\) \(\chi_{4012}(553,\cdot)\) \(\chi_{4012}(593,\cdot)\) \(\chi_{4012}(597,\cdot)\) \(\chi_{4012}(661,\cdot)\) \(\chi_{4012}(665,\cdot)\) \(\chi_{4012}(729,\cdot)\) \(\chi_{4012}(733,\cdot)\) \(\chi_{4012}(757,\cdot)\) \(\chi_{4012}(841,\cdot)\) \(\chi_{4012}(933,\cdot)\) \(\chi_{4012}(961,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{21}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{225}{232}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{171}{232}\right)\) |