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 \(\chi_{177}(32,\cdot)\) | 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
\((4013,1771,1123)\) → \((-1,1,e\left(\frac{5}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(2687, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{33}{58}\right)\) |