Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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.be
\(\chi_{4012}(47,\cdot)\) \(\chi_{4012}(55,\cdot)\) \(\chi_{4012}(115,\cdot)\) \(\chi_{4012}(183,\cdot)\) \(\chi_{4012}(191,\cdot)\) \(\chi_{4012}(259,\cdot)\) \(\chi_{4012}(319,\cdot)\) \(\chi_{4012}(327,\cdot)\) \(\chi_{4012}(387,\cdot)\) \(\chi_{4012}(455,\cdot)\) \(\chi_{4012}(463,\cdot)\) \(\chi_{4012}(659,\cdot)\) \(\chi_{4012}(667,\cdot)\) \(\chi_{4012}(863,\cdot)\) \(\chi_{4012}(939,\cdot)\) \(\chi_{4012}(999,\cdot)\) \(\chi_{4012}(1075,\cdot)\) \(\chi_{4012}(1135,\cdot)\) \(\chi_{4012}(1203,\cdot)\) \(\chi_{4012}(1211,\cdot)\) \(\chi_{4012}(1271,\cdot)\) \(\chi_{4012}(1279,\cdot)\) \(\chi_{4012}(1407,\cdot)\) \(\chi_{4012}(1483,\cdot)\) \(\chi_{4012}(1611,\cdot)\) \(\chi_{4012}(1755,\cdot)\) \(\chi_{4012}(1883,\cdot)\) \(\chi_{4012}(2019,\cdot)\) \(\chi_{4012}(2095,\cdot)\) \(\chi_{4012}(2155,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,i,e\left(\frac{23}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{116}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{19}{116}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{23}{116}\right)\) |