Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(221,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cc
\(\chi_{6042}(221,\cdot)\) \(\chi_{6042}(335,\cdot)\) \(\chi_{6042}(449,\cdot)\) \(\chi_{6042}(749,\cdot)\) \(\chi_{6042}(905,\cdot)\) \(\chi_{6042}(1703,\cdot)\) \(\chi_{6042}(2573,\cdot)\) \(\chi_{6042}(2687,\cdot)\) \(\chi_{6042}(3485,\cdot)\) \(\chi_{6042}(3527,\cdot)\) \(\chi_{6042}(3641,\cdot)\) \(\chi_{6042}(3827,\cdot)\) \(\chi_{6042}(4283,\cdot)\) \(\chi_{6042}(4439,\cdot)\) \(\chi_{6042}(4511,\cdot)\) \(\chi_{6042}(4781,\cdot)\) \(\chi_{6042}(4967,\cdot)\) \(\chi_{6042}(5237,\cdot)\) \(\chi_{6042}(5309,\cdot)\) \(\chi_{6042}(5423,\cdot)\) \(\chi_{6042}(5465,\cdot)\) \(\chi_{6042}(5537,\cdot)\) \(\chi_{6042}(5921,\cdot)\) \(\chi_{6042}(5993,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{17}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(221, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |