Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3009}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bj
\(\chi_{6018}(53,\cdot)\) \(\chi_{6018}(257,\cdot)\) \(\chi_{6018}(263,\cdot)\) \(\chi_{6018}(281,\cdot)\) \(\chi_{6018}(287,\cdot)\) \(\chi_{6018}(359,\cdot)\) \(\chi_{6018}(383,\cdot)\) \(\chi_{6018}(389,\cdot)\) \(\chi_{6018}(461,\cdot)\) \(\chi_{6018}(491,\cdot)\) \(\chi_{6018}(593,\cdot)\) \(\chi_{6018}(665,\cdot)\) \(\chi_{6018}(671,\cdot)\) \(\chi_{6018}(695,\cdot)\) \(\chi_{6018}(875,\cdot)\) \(\chi_{6018}(971,\cdot)\) \(\chi_{6018}(995,\cdot)\) \(\chi_{6018}(1001,\cdot)\) \(\chi_{6018}(1079,\cdot)\) \(\chi_{6018}(1097,\cdot)\) \(\chi_{6018}(1103,\cdot)\) \(\chi_{6018}(1199,\cdot)\) \(\chi_{6018}(1205,\cdot)\) \(\chi_{6018}(1301,\cdot)\) \(\chi_{6018}(1307,\cdot)\) \(\chi_{6018}(1379,\cdot)\) \(\chi_{6018}(1385,\cdot)\) \(\chi_{6018}(1403,\cdot)\) \(\chi_{6018}(1487,\cdot)\) \(\chi_{6018}(1511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{25}{232}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{73}{232}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{115}{232}\right)\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{35}{58}\right)\) |