Basic properties
| Modulus: | \(531\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 531.k
\(\chi_{531}(10,\cdot)\) \(\chi_{531}(37,\cdot)\) \(\chi_{531}(55,\cdot)\) \(\chi_{531}(73,\cdot)\) \(\chi_{531}(82,\cdot)\) \(\chi_{531}(91,\cdot)\) \(\chi_{531}(109,\cdot)\) \(\chi_{531}(136,\cdot)\) \(\chi_{531}(172,\cdot)\) \(\chi_{531}(190,\cdot)\) \(\chi_{531}(208,\cdot)\) \(\chi_{531}(217,\cdot)\) \(\chi_{531}(244,\cdot)\) \(\chi_{531}(280,\cdot)\) \(\chi_{531}(325,\cdot)\) \(\chi_{531}(334,\cdot)\) \(\chi_{531}(388,\cdot)\) \(\chi_{531}(397,\cdot)\) \(\chi_{531}(406,\cdot)\) \(\chi_{531}(415,\cdot)\) \(\chi_{531}(424,\cdot)\) \(\chi_{531}(451,\cdot)\) \(\chi_{531}(460,\cdot)\) \(\chi_{531}(469,\cdot)\) \(\chi_{531}(478,\cdot)\) \(\chi_{531}(496,\cdot)\) \(\chi_{531}(505,\cdot)\) \(\chi_{531}(514,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,415)\) → \((1,e\left(\frac{7}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 531 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{14}{29}\right)\) |