Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(409,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cp
\(\chi_{6042}(91,\cdot)\) \(\chi_{6042}(223,\cdot)\) \(\chi_{6042}(241,\cdot)\) \(\chi_{6042}(325,\cdot)\) \(\chi_{6042}(355,\cdot)\) \(\chi_{6042}(409,\cdot)\) \(\chi_{6042}(433,\cdot)\) \(\chi_{6042}(547,\cdot)\) \(\chi_{6042}(661,\cdot)\) \(\chi_{6042}(679,\cdot)\) \(\chi_{6042}(751,\cdot)\) \(\chi_{6042}(865,\cdot)\) \(\chi_{6042}(877,\cdot)\) \(\chi_{6042}(907,\cdot)\) \(\chi_{6042}(979,\cdot)\) \(\chi_{6042}(991,\cdot)\) \(\chi_{6042}(1117,\cdot)\) \(\chi_{6042}(1153,\cdot)\) \(\chi_{6042}(1363,\cdot)\) \(\chi_{6042}(1435,\cdot)\) \(\chi_{6042}(1495,\cdot)\) \(\chi_{6042}(1705,\cdot)\) \(\chi_{6042}(1789,\cdot)\) \(\chi_{6042}(1819,\cdot)\) \(\chi_{6042}(1915,\cdot)\) \(\chi_{6042}(1933,\cdot)\) \(\chi_{6042}(1951,\cdot)\) \(\chi_{6042}(2131,\cdot)\) \(\chi_{6042}(2149,\cdot)\) \(\chi_{6042}(2179,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{19}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(409, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{61}{234}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{83}{234}\right)\) |