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 \(\chi_{1003}(361,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bc
\(\chi_{6018}(361,\cdot)\) \(\chi_{6018}(523,\cdot)\) \(\chi_{6018}(625,\cdot)\) \(\chi_{6018}(727,\cdot)\) \(\chi_{6018}(829,\cdot)\) \(\chi_{6018}(871,\cdot)\) \(\chi_{6018}(931,\cdot)\) \(\chi_{6018}(973,\cdot)\) \(\chi_{6018}(1237,\cdot)\) \(\chi_{6018}(1339,\cdot)\) \(\chi_{6018}(1441,\cdot)\) \(\chi_{6018}(1543,\cdot)\) \(\chi_{6018}(1585,\cdot)\) \(\chi_{6018}(1687,\cdot)\) \(\chi_{6018}(1747,\cdot)\) \(\chi_{6018}(1789,\cdot)\) \(\chi_{6018}(1849,\cdot)\) \(\chi_{6018}(1891,\cdot)\) \(\chi_{6018}(1951,\cdot)\) \(\chi_{6018}(1993,\cdot)\) \(\chi_{6018}(2257,\cdot)\) \(\chi_{6018}(2299,\cdot)\) \(\chi_{6018}(2401,\cdot)\) \(\chi_{6018}(2503,\cdot)\) \(\chi_{6018}(2563,\cdot)\) \(\chi_{6018}(2605,\cdot)\) \(\chi_{6018}(2767,\cdot)\) \(\chi_{6018}(2809,\cdot)\) \(\chi_{6018}(2911,\cdot)\) \(\chi_{6018}(2971,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((1,-i,e\left(\frac{9}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(361, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{51}{116}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{13}{29}\right)\) |