Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.be
\(\chi_{6018}(13,\cdot)\) \(\chi_{6018}(55,\cdot)\) \(\chi_{6018}(115,\cdot)\) \(\chi_{6018}(157,\cdot)\) \(\chi_{6018}(217,\cdot)\) \(\chi_{6018}(259,\cdot)\) \(\chi_{6018}(319,\cdot)\) \(\chi_{6018}(421,\cdot)\) \(\chi_{6018}(463,\cdot)\) \(\chi_{6018}(565,\cdot)\) \(\chi_{6018}(667,\cdot)\) \(\chi_{6018}(769,\cdot)\) \(\chi_{6018}(1033,\cdot)\) \(\chi_{6018}(1075,\cdot)\) \(\chi_{6018}(1135,\cdot)\) \(\chi_{6018}(1177,\cdot)\) \(\chi_{6018}(1279,\cdot)\) \(\chi_{6018}(1381,\cdot)\) \(\chi_{6018}(1483,\cdot)\) \(\chi_{6018}(1645,\cdot)\) \(\chi_{6018}(2053,\cdot)\) \(\chi_{6018}(2095,\cdot)\) \(\chi_{6018}(2155,\cdot)\) \(\chi_{6018}(2197,\cdot)\) \(\chi_{6018}(2461,\cdot)\) \(\chi_{6018}(2665,\cdot)\) \(\chi_{6018}(2707,\cdot)\) \(\chi_{6018}(2869,\cdot)\) \(\chi_{6018}(3115,\cdot)\) \(\chi_{6018}(3217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((1,i,e\left(\frac{45}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{18}{29}\right)\) |