Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{241}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.in
\(\chi_{6025}(651,\cdot)\) \(\chi_{6025}(726,\cdot)\) \(\chi_{6025}(776,\cdot)\) \(\chi_{6025}(976,\cdot)\) \(\chi_{6025}(1176,\cdot)\) \(\chi_{6025}(1401,\cdot)\) \(\chi_{6025}(1426,\cdot)\) \(\chi_{6025}(1526,\cdot)\) \(\chi_{6025}(1851,\cdot)\) \(\chi_{6025}(2151,\cdot)\) \(\chi_{6025}(2351,\cdot)\) \(\chi_{6025}(2576,\cdot)\) \(\chi_{6025}(2601,\cdot)\) \(\chi_{6025}(2701,\cdot)\) \(\chi_{6025}(2726,\cdot)\) \(\chi_{6025}(2951,\cdot)\) \(\chi_{6025}(3151,\cdot)\) \(\chi_{6025}(3451,\cdot)\) \(\chi_{6025}(3776,\cdot)\) \(\chi_{6025}(3876,\cdot)\) \(\chi_{6025}(3901,\cdot)\) \(\chi_{6025}(4126,\cdot)\) \(\chi_{6025}(4326,\cdot)\) \(\chi_{6025}(4526,\cdot)\) \(\chi_{6025}(4576,\cdot)\) \(\chi_{6025}(4651,\cdot)\) \(\chi_{6025}(5351,\cdot)\) \(\chi_{6025}(5476,\cdot)\) \(\chi_{6025}(5651,\cdot)\) \(\chi_{6025}(5676,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((1,e\left(\frac{37}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(3151, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(-i\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) |