Basic properties
| Modulus: | \(531\) | |
| Conductor: | \(531\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(174\) | 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 531.n
\(\chi_{531}(5,\cdot)\) \(\chi_{531}(20,\cdot)\) \(\chi_{531}(29,\cdot)\) \(\chi_{531}(41,\cdot)\) \(\chi_{531}(68,\cdot)\) \(\chi_{531}(74,\cdot)\) \(\chi_{531}(86,\cdot)\) \(\chi_{531}(95,\cdot)\) \(\chi_{531}(104,\cdot)\) \(\chi_{531}(110,\cdot)\) \(\chi_{531}(122,\cdot)\) \(\chi_{531}(137,\cdot)\) \(\chi_{531}(140,\cdot)\) \(\chi_{531}(146,\cdot)\) \(\chi_{531}(164,\cdot)\) \(\chi_{531}(167,\cdot)\) \(\chi_{531}(182,\cdot)\) \(\chi_{531}(194,\cdot)\) \(\chi_{531}(203,\cdot)\) \(\chi_{531}(212,\cdot)\) \(\chi_{531}(218,\cdot)\) \(\chi_{531}(230,\cdot)\) \(\chi_{531}(239,\cdot)\) \(\chi_{531}(245,\cdot)\) \(\chi_{531}(248,\cdot)\) \(\chi_{531}(257,\cdot)\) \(\chi_{531}(263,\cdot)\) \(\chi_{531}(272,\cdot)\) \(\chi_{531}(281,\cdot)\) \(\chi_{531}(284,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{87})$ |
| Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((119,415)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{4}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 531 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{174}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{115}{174}\right)\) | \(e\left(\frac{13}{87}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{107}{174}\right)\) | \(e\left(\frac{47}{87}\right)\) | \(e\left(\frac{79}{174}\right)\) | \(e\left(\frac{19}{87}\right)\) |