Basic properties
Modulus: | \(8024\) | |
Conductor: | \(236\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{236}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.by
\(\chi_{8024}(103,\cdot)\) \(\chi_{8024}(511,\cdot)\) \(\chi_{8024}(919,\cdot)\) \(\chi_{8024}(1055,\cdot)\) \(\chi_{8024}(1191,\cdot)\) \(\chi_{8024}(1463,\cdot)\) \(\chi_{8024}(1599,\cdot)\) \(\chi_{8024}(1735,\cdot)\) \(\chi_{8024}(1871,\cdot)\) \(\chi_{8024}(2279,\cdot)\) \(\chi_{8024}(2415,\cdot)\) \(\chi_{8024}(2551,\cdot)\) \(\chi_{8024}(2687,\cdot)\) \(\chi_{8024}(2823,\cdot)\) \(\chi_{8024}(3639,\cdot)\) \(\chi_{8024}(4455,\cdot)\) \(\chi_{8024}(4999,\cdot)\) \(\chi_{8024}(5135,\cdot)\) \(\chi_{8024}(5407,\cdot)\) \(\chi_{8024}(5543,\cdot)\) \(\chi_{8024}(5815,\cdot)\) \(\chi_{8024}(6087,\cdot)\) \(\chi_{8024}(6631,\cdot)\) \(\chi_{8024}(7039,\cdot)\) \(\chi_{8024}(7311,\cdot)\) \(\chi_{8024}(7447,\cdot)\) \(\chi_{8024}(7583,\cdot)\) \(\chi_{8024}(7855,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,1,e\left(\frac{27}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 8024 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) |