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 \(\chi_{177}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 531.l
\(\chi_{531}(17,\cdot)\) \(\chi_{531}(26,\cdot)\) \(\chi_{531}(35,\cdot)\) \(\chi_{531}(53,\cdot)\) \(\chi_{531}(62,\cdot)\) \(\chi_{531}(71,\cdot)\) \(\chi_{531}(80,\cdot)\) \(\chi_{531}(107,\cdot)\) \(\chi_{531}(116,\cdot)\) \(\chi_{531}(125,\cdot)\) \(\chi_{531}(134,\cdot)\) \(\chi_{531}(143,\cdot)\) \(\chi_{531}(197,\cdot)\) \(\chi_{531}(206,\cdot)\) \(\chi_{531}(251,\cdot)\) \(\chi_{531}(287,\cdot)\) \(\chi_{531}(314,\cdot)\) \(\chi_{531}(323,\cdot)\) \(\chi_{531}(341,\cdot)\) \(\chi_{531}(359,\cdot)\) \(\chi_{531}(395,\cdot)\) \(\chi_{531}(422,\cdot)\) \(\chi_{531}(440,\cdot)\) \(\chi_{531}(449,\cdot)\) \(\chi_{531}(458,\cdot)\) \(\chi_{531}(476,\cdot)\) \(\chi_{531}(494,\cdot)\) \(\chi_{531}(521,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,415)\) → \((-1,e\left(\frac{12}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 531 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) |