Basic properties
| Modulus: | \(531\) | |
| Conductor: | \(177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{177}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 531.j
\(\chi_{531}(8,\cdot)\) \(\chi_{531}(44,\cdot)\) \(\chi_{531}(89,\cdot)\) \(\chi_{531}(98,\cdot)\) \(\chi_{531}(152,\cdot)\) \(\chi_{531}(161,\cdot)\) \(\chi_{531}(170,\cdot)\) \(\chi_{531}(179,\cdot)\) \(\chi_{531}(188,\cdot)\) \(\chi_{531}(215,\cdot)\) \(\chi_{531}(224,\cdot)\) \(\chi_{531}(233,\cdot)\) \(\chi_{531}(242,\cdot)\) \(\chi_{531}(260,\cdot)\) \(\chi_{531}(269,\cdot)\) \(\chi_{531}(278,\cdot)\) \(\chi_{531}(305,\cdot)\) \(\chi_{531}(332,\cdot)\) \(\chi_{531}(350,\cdot)\) \(\chi_{531}(368,\cdot)\) \(\chi_{531}(377,\cdot)\) \(\chi_{531}(386,\cdot)\) \(\chi_{531}(404,\cdot)\) \(\chi_{531}(431,\cdot)\) \(\chi_{531}(467,\cdot)\) \(\chi_{531}(485,\cdot)\) \(\chi_{531}(503,\cdot)\) \(\chi_{531}(512,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,415)\) → \((-1,e\left(\frac{3}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 531 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |