Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{177}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.y
\(\chi_{6018}(443,\cdot)\) \(\chi_{6018}(545,\cdot)\) \(\chi_{6018}(1055,\cdot)\) \(\chi_{6018}(1463,\cdot)\) \(\chi_{6018}(1565,\cdot)\) \(\chi_{6018}(1871,\cdot)\) \(\chi_{6018}(2075,\cdot)\) \(\chi_{6018}(2279,\cdot)\) \(\chi_{6018}(2687,\cdot)\) \(\chi_{6018}(2993,\cdot)\) \(\chi_{6018}(3197,\cdot)\) \(\chi_{6018}(3299,\cdot)\) \(\chi_{6018}(3401,\cdot)\) \(\chi_{6018}(3605,\cdot)\) \(\chi_{6018}(3809,\cdot)\) \(\chi_{6018}(4115,\cdot)\) \(\chi_{6018}(4421,\cdot)\) \(\chi_{6018}(4523,\cdot)\) \(\chi_{6018}(4625,\cdot)\) \(\chi_{6018}(4829,\cdot)\) \(\chi_{6018}(4931,\cdot)\) \(\chi_{6018}(5033,\cdot)\) \(\chi_{6018}(5135,\cdot)\) \(\chi_{6018}(5441,\cdot)\) \(\chi_{6018}(5543,\cdot)\) \(\chi_{6018}(5645,\cdot)\) \(\chi_{6018}(5747,\cdot)\) \(\chi_{6018}(5849,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((-1,1,e\left(\frac{1}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(5135, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) |