Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(520,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.by
\(\chi_{6042}(7,\cdot)\) \(\chi_{6042}(163,\cdot)\) \(\chi_{6042}(961,\cdot)\) \(\chi_{6042}(1831,\cdot)\) \(\chi_{6042}(1945,\cdot)\) \(\chi_{6042}(2743,\cdot)\) \(\chi_{6042}(2785,\cdot)\) \(\chi_{6042}(2899,\cdot)\) \(\chi_{6042}(3085,\cdot)\) \(\chi_{6042}(3541,\cdot)\) \(\chi_{6042}(3697,\cdot)\) \(\chi_{6042}(3769,\cdot)\) \(\chi_{6042}(4039,\cdot)\) \(\chi_{6042}(4225,\cdot)\) \(\chi_{6042}(4495,\cdot)\) \(\chi_{6042}(4567,\cdot)\) \(\chi_{6042}(4681,\cdot)\) \(\chi_{6042}(4723,\cdot)\) \(\chi_{6042}(4795,\cdot)\) \(\chi_{6042}(5179,\cdot)\) \(\chi_{6042}(5251,\cdot)\) \(\chi_{6042}(5521,\cdot)\) \(\chi_{6042}(5635,\cdot)\) \(\chi_{6042}(5749,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{11}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(3541, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{11}{78}\right)\) |