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.hz
\(\chi_{6025}(3,\cdot)\) \(\chi_{6025}(77,\cdot)\) \(\chi_{6025}(188,\cdot)\) \(\chi_{6025}(212,\cdot)\) \(\chi_{6025}(313,\cdot)\) \(\chi_{6025}(678,\cdot)\) \(\chi_{6025}(772,\cdot)\) \(\chi_{6025}(1187,\cdot)\) \(\chi_{6025}(1397,\cdot)\) \(\chi_{6025}(1767,\cdot)\) \(\chi_{6025}(1908,\cdot)\) \(\chi_{6025}(2187,\cdot)\) \(\chi_{6025}(2338,\cdot)\) \(\chi_{6025}(2422,\cdot)\) \(\chi_{6025}(2463,\cdot)\) \(\chi_{6025}(2817,\cdot)\) \(\chi_{6025}(2833,\cdot)\) \(\chi_{6025}(2967,\cdot)\) \(\chi_{6025}(3162,\cdot)\) \(\chi_{6025}(3178,\cdot)\) \(\chi_{6025}(3433,\cdot)\) \(\chi_{6025}(3548,\cdot)\) \(\chi_{6025}(3723,\cdot)\) \(\chi_{6025}(3748,\cdot)\) \(\chi_{6025}(3853,\cdot)\) \(\chi_{6025}(3923,\cdot)\) \(\chi_{6025}(4017,\cdot)\) \(\chi_{6025}(4358,\cdot)\) \(\chi_{6025}(4502,\cdot)\) \(\chi_{6025}(5252,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{91}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) |