Basic properties
| Modulus: | \(6018\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.ba
\(\chi_{6018}(67,\cdot)\) \(\chi_{6018}(679,\cdot)\) \(\chi_{6018}(781,\cdot)\) \(\chi_{6018}(1291,\cdot)\) \(\chi_{6018}(1699,\cdot)\) \(\chi_{6018}(1801,\cdot)\) \(\chi_{6018}(2107,\cdot)\) \(\chi_{6018}(2311,\cdot)\) \(\chi_{6018}(2515,\cdot)\) \(\chi_{6018}(2923,\cdot)\) \(\chi_{6018}(3229,\cdot)\) \(\chi_{6018}(3433,\cdot)\) \(\chi_{6018}(3535,\cdot)\) \(\chi_{6018}(3637,\cdot)\) \(\chi_{6018}(3841,\cdot)\) \(\chi_{6018}(4045,\cdot)\) \(\chi_{6018}(4351,\cdot)\) \(\chi_{6018}(4657,\cdot)\) \(\chi_{6018}(4759,\cdot)\) \(\chi_{6018}(4861,\cdot)\) \(\chi_{6018}(5065,\cdot)\) \(\chi_{6018}(5167,\cdot)\) \(\chi_{6018}(5269,\cdot)\) \(\chi_{6018}(5371,\cdot)\) \(\chi_{6018}(5677,\cdot)\) \(\chi_{6018}(5779,\cdot)\) \(\chi_{6018}(5881,\cdot)\) \(\chi_{6018}(5983,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((1,-1,e\left(\frac{3}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6018 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) |