Basic properties
| Modulus: | \(6042\) | |
| Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3021}(2285,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cj
\(\chi_{6042}(17,\cdot)\) \(\chi_{6042}(131,\cdot)\) \(\chi_{6042}(149,\cdot)\) \(\chi_{6042}(329,\cdot)\) \(\chi_{6042}(347,\cdot)\) \(\chi_{6042}(377,\cdot)\) \(\chi_{6042}(461,\cdot)\) \(\chi_{6042}(587,\cdot)\) \(\chi_{6042}(785,\cdot)\) \(\chi_{6042}(833,\cdot)\) \(\chi_{6042}(1013,\cdot)\) \(\chi_{6042}(1175,\cdot)\) \(\chi_{6042}(1259,\cdot)\) \(\chi_{6042}(1289,\cdot)\) \(\chi_{6042}(1301,\cdot)\) \(\chi_{6042}(1385,\cdot)\) \(\chi_{6042}(1403,\cdot)\) \(\chi_{6042}(1415,\cdot)\) \(\chi_{6042}(1469,\cdot)\) \(\chi_{6042}(1601,\cdot)\) \(\chi_{6042}(1619,\cdot)\) \(\chi_{6042}(1733,\cdot)\) \(\chi_{6042}(1811,\cdot)\) \(\chi_{6042}(1859,\cdot)\) \(\chi_{6042}(1925,\cdot)\) \(\chi_{6042}(2039,\cdot)\) \(\chi_{6042}(2057,\cdot)\) \(\chi_{6042}(2213,\cdot)\) \(\chi_{6042}(2285,\cdot)\) \(\chi_{6042}(2495,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{9}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6042 }(2285, a) \) | \(-1\) | \(1\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{20}{117}\right)\) |