Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.bs
\(\chi_{6042}(49,\cdot)\) \(\chi_{6042}(121,\cdot)\) \(\chi_{6042}(505,\cdot)\) \(\chi_{6042}(577,\cdot)\) \(\chi_{6042}(619,\cdot)\) \(\chi_{6042}(733,\cdot)\) \(\chi_{6042}(805,\cdot)\) \(\chi_{6042}(1075,\cdot)\) \(\chi_{6042}(1261,\cdot)\) \(\chi_{6042}(1531,\cdot)\) \(\chi_{6042}(1603,\cdot)\) \(\chi_{6042}(1759,\cdot)\) \(\chi_{6042}(2215,\cdot)\) \(\chi_{6042}(2401,\cdot)\) \(\chi_{6042}(2515,\cdot)\) \(\chi_{6042}(2557,\cdot)\) \(\chi_{6042}(3355,\cdot)\) \(\chi_{6042}(3469,\cdot)\) \(\chi_{6042}(4339,\cdot)\) \(\chi_{6042}(5137,\cdot)\) \(\chi_{6042}(5293,\cdot)\) \(\chi_{6042}(5593,\cdot)\) \(\chi_{6042}(5707,\cdot)\) \(\chi_{6042}(5821,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{7}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) |