Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(326,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cq
\(\chi_{6042}(67,\cdot)\) \(\chi_{6042}(79,\cdot)\) \(\chi_{6042}(109,\cdot)\) \(\chi_{6042}(127,\cdot)\) \(\chi_{6042}(181,\cdot)\) \(\chi_{6042}(193,\cdot)\) \(\chi_{6042}(337,\cdot)\) \(\chi_{6042}(421,\cdot)\) \(\chi_{6042}(451,\cdot)\) \(\chi_{6042}(469,\cdot)\) \(\chi_{6042}(535,\cdot)\) \(\chi_{6042}(565,\cdot)\) \(\chi_{6042}(667,\cdot)\) \(\chi_{6042}(697,\cdot)\) \(\chi_{6042}(763,\cdot)\) \(\chi_{6042}(775,\cdot)\) \(\chi_{6042}(781,\cdot)\) \(\chi_{6042}(793,\cdot)\) \(\chi_{6042}(889,\cdot)\) \(\chi_{6042}(1009,\cdot)\) \(\chi_{6042}(1021,\cdot)\) \(\chi_{6042}(1039,\cdot)\) \(\chi_{6042}(1093,\cdot)\) \(\chi_{6042}(1105,\cdot)\) \(\chi_{6042}(1135,\cdot)\) \(\chi_{6042}(1207,\cdot)\) \(\chi_{6042}(1231,\cdot)\) \(\chi_{6042}(1237,\cdot)\) \(\chi_{6042}(1267,\cdot)\) \(\chi_{6042}(1333,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{13}{18}\right),e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(1333, a) \) | \(1\) | \(1\) | \(e\left(\frac{125}{468}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{109}{117}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{191}{468}\right)\) |