Basic properties
| Modulus: | \(531\) | |
| Conductor: | \(531\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(87\) | 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 531.m
\(\chi_{531}(4,\cdot)\) \(\chi_{531}(7,\cdot)\) \(\chi_{531}(16,\cdot)\) \(\chi_{531}(22,\cdot)\) \(\chi_{531}(25,\cdot)\) \(\chi_{531}(49,\cdot)\) \(\chi_{531}(76,\cdot)\) \(\chi_{531}(79,\cdot)\) \(\chi_{531}(85,\cdot)\) \(\chi_{531}(88,\cdot)\) \(\chi_{531}(94,\cdot)\) \(\chi_{531}(112,\cdot)\) \(\chi_{531}(121,\cdot)\) \(\chi_{531}(130,\cdot)\) \(\chi_{531}(133,\cdot)\) \(\chi_{531}(139,\cdot)\) \(\chi_{531}(166,\cdot)\) \(\chi_{531}(169,\cdot)\) \(\chi_{531}(175,\cdot)\) \(\chi_{531}(184,\cdot)\) \(\chi_{531}(193,\cdot)\) \(\chi_{531}(196,\cdot)\) \(\chi_{531}(202,\cdot)\) \(\chi_{531}(205,\cdot)\) \(\chi_{531}(223,\cdot)\) \(\chi_{531}(241,\cdot)\) \(\chi_{531}(256,\cdot)\) \(\chi_{531}(265,\cdot)\) \(\chi_{531}(277,\cdot)\) \(\chi_{531}(304,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{87})$ |
| Fixed field: | Number field defined by a degree 87 polynomial |
Values on generators
\((119,415)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 531 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{87}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{76}{87}\right)\) | \(e\left(\frac{83}{87}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{19}{87}\right)\) | \(e\left(\frac{28}{87}\right)\) | \(e\left(\frac{41}{87}\right)\) |