Basic properties
Modulus: | \(6042\) | |
Conductor: | \(159\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{159}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.bt
\(\chi_{6042}(191,\cdot)\) \(\chi_{6042}(419,\cdot)\) \(\chi_{6042}(533,\cdot)\) \(\chi_{6042}(761,\cdot)\) \(\chi_{6042}(875,\cdot)\) \(\chi_{6042}(989,\cdot)\) \(\chi_{6042}(1217,\cdot)\) \(\chi_{6042}(1445,\cdot)\) \(\chi_{6042}(1559,\cdot)\) \(\chi_{6042}(2471,\cdot)\) \(\chi_{6042}(2585,\cdot)\) \(\chi_{6042}(2927,\cdot)\) \(\chi_{6042}(3041,\cdot)\) \(\chi_{6042}(3953,\cdot)\) \(\chi_{6042}(4067,\cdot)\) \(\chi_{6042}(4295,\cdot)\) \(\chi_{6042}(4523,\cdot)\) \(\chi_{6042}(4637,\cdot)\) \(\chi_{6042}(4751,\cdot)\) \(\chi_{6042}(4979,\cdot)\) \(\chi_{6042}(5093,\cdot)\) \(\chi_{6042}(5321,\cdot)\) \(\chi_{6042}(5663,\cdot)\) \(\chi_{6042}(5891,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2015,4771,2281)\) → \((-1,1,e\left(\frac{5}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(191, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(i\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) |