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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.ig
\(\chi_{6025}(196,\cdot)\) \(\chi_{6025}(741,\cdot)\) \(\chi_{6025}(1716,\cdot)\) \(\chi_{6025}(1861,\cdot)\) \(\chi_{6025}(2036,\cdot)\) \(\chi_{6025}(2061,\cdot)\) \(\chi_{6025}(2116,\cdot)\) \(\chi_{6025}(2236,\cdot)\) \(\chi_{6025}(2241,\cdot)\) \(\chi_{6025}(2631,\cdot)\) \(\chi_{6025}(2696,\cdot)\) \(\chi_{6025}(2731,\cdot)\) \(\chi_{6025}(3121,\cdot)\) \(\chi_{6025}(3371,\cdot)\) \(\chi_{6025}(3556,\cdot)\) \(\chi_{6025}(3781,\cdot)\) \(\chi_{6025}(3931,\cdot)\) \(\chi_{6025}(4146,\cdot)\) \(\chi_{6025}(4156,\cdot)\) \(\chi_{6025}(4261,\cdot)\) \(\chi_{6025}(4266,\cdot)\) \(\chi_{6025}(4391,\cdot)\) \(\chi_{6025}(4771,\cdot)\) \(\chi_{6025}(4791,\cdot)\) \(\chi_{6025}(4981,\cdot)\) \(\chi_{6025}(5011,\cdot)\) \(\chi_{6025}(5081,\cdot)\) \(\chi_{6025}(5111,\cdot)\) \(\chi_{6025}(5546,\cdot)\) \(\chi_{6025}(5766,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{113}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(5111, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) |