Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(44,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.v
\(\chi_{6018}(103,\cdot)\) \(\chi_{6018}(409,\cdot)\) \(\chi_{6018}(511,\cdot)\) \(\chi_{6018}(613,\cdot)\) \(\chi_{6018}(817,\cdot)\) \(\chi_{6018}(919,\cdot)\) \(\chi_{6018}(1021,\cdot)\) \(\chi_{6018}(1123,\cdot)\) \(\chi_{6018}(1429,\cdot)\) \(\chi_{6018}(1531,\cdot)\) \(\chi_{6018}(1633,\cdot)\) \(\chi_{6018}(1735,\cdot)\) \(\chi_{6018}(1837,\cdot)\) \(\chi_{6018}(2449,\cdot)\) \(\chi_{6018}(2551,\cdot)\) \(\chi_{6018}(3061,\cdot)\) \(\chi_{6018}(3469,\cdot)\) \(\chi_{6018}(3571,\cdot)\) \(\chi_{6018}(3877,\cdot)\) \(\chi_{6018}(4081,\cdot)\) \(\chi_{6018}(4285,\cdot)\) \(\chi_{6018}(4693,\cdot)\) \(\chi_{6018}(4999,\cdot)\) \(\chi_{6018}(5203,\cdot)\) \(\chi_{6018}(5305,\cdot)\) \(\chi_{6018}(5407,\cdot)\) \(\chi_{6018}(5611,\cdot)\) \(\chi_{6018}(5815,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((1,1,e\left(\frac{27}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(103, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) |