Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3009}(2702,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.x
\(\chi_{6018}(101,\cdot)\) \(\chi_{6018}(305,\cdot)\) \(\chi_{6018}(509,\cdot)\) \(\chi_{6018}(917,\cdot)\) \(\chi_{6018}(1223,\cdot)\) \(\chi_{6018}(1427,\cdot)\) \(\chi_{6018}(1529,\cdot)\) \(\chi_{6018}(1631,\cdot)\) \(\chi_{6018}(1835,\cdot)\) \(\chi_{6018}(2039,\cdot)\) \(\chi_{6018}(2345,\cdot)\) \(\chi_{6018}(2651,\cdot)\) \(\chi_{6018}(2753,\cdot)\) \(\chi_{6018}(2855,\cdot)\) \(\chi_{6018}(3059,\cdot)\) \(\chi_{6018}(3161,\cdot)\) \(\chi_{6018}(3263,\cdot)\) \(\chi_{6018}(3365,\cdot)\) \(\chi_{6018}(3671,\cdot)\) \(\chi_{6018}(3773,\cdot)\) \(\chi_{6018}(3875,\cdot)\) \(\chi_{6018}(3977,\cdot)\) \(\chi_{6018}(4079,\cdot)\) \(\chi_{6018}(4691,\cdot)\) \(\chi_{6018}(4793,\cdot)\) \(\chi_{6018}(5303,\cdot)\) \(\chi_{6018}(5711,\cdot)\) \(\chi_{6018}(5813,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((-1,-1,e\left(\frac{23}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(5711, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) |