Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.hx
\(\chi_{6025}(12,\cdot)\) \(\chi_{6025}(238,\cdot)\) \(\chi_{6025}(402,\cdot)\) \(\chi_{6025}(423,\cdot)\) \(\chi_{6025}(1023,\cdot)\) \(\chi_{6025}(1133,\cdot)\) \(\chi_{6025}(1258,\cdot)\) \(\chi_{6025}(1417,\cdot)\) \(\chi_{6025}(1948,\cdot)\) \(\chi_{6025}(2392,\cdot)\) \(\chi_{6025}(2413,\cdot)\) \(\chi_{6025}(3088,\cdot)\) \(\chi_{6025}(3297,\cdot)\) \(\chi_{6025}(3362,\cdot)\) \(\chi_{6025}(3392,\cdot)\) \(\chi_{6025}(4047,\cdot)\) \(\chi_{6025}(4147,\cdot)\) \(\chi_{6025}(4177,\cdot)\) \(\chi_{6025}(4367,\cdot)\) \(\chi_{6025}(4387,\cdot)\) \(\chi_{6025}(4753,\cdot)\) \(\chi_{6025}(4897,\cdot)\) \(\chi_{6025}(4928,\cdot)\) \(\chi_{6025}(4953,\cdot)\) \(\chi_{6025}(5008,\cdot)\) \(\chi_{6025}(5012,\cdot)\) \(\chi_{6025}(5128,\cdot)\) \(\chi_{6025}(5133,\cdot)\) \(\chi_{6025}(5227,\cdot)\) \(\chi_{6025}(5377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{41}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{73}{120}\right)\) |