Basic properties
Modulus: | \(311\) | |
Conductor: | \(311\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(62\) | 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 311.f
\(\chi_{311}(11,\cdot)\) \(\chi_{311}(41,\cdot)\) \(\chi_{311}(46,\cdot)\) \(\chi_{311}(51,\cdot)\) \(\chi_{311}(61,\cdot)\) \(\chi_{311}(68,\cdot)\) \(\chi_{311}(77,\cdot)\) \(\chi_{311}(86,\cdot)\) \(\chi_{311}(87,\cdot)\) \(\chi_{311}(116,\cdot)\) \(\chi_{311}(142,\cdot)\) \(\chi_{311}(143,\cdot)\) \(\chi_{311}(165,\cdot)\) \(\chi_{311}(171,\cdot)\) \(\chi_{311}(185,\cdot)\) \(\chi_{311}(190,\cdot)\) \(\chi_{311}(198,\cdot)\) \(\chi_{311}(206,\cdot)\) \(\chi_{311}(220,\cdot)\) \(\chi_{311}(222,\cdot)\) \(\chi_{311}(228,\cdot)\) \(\chi_{311}(262,\cdot)\) \(\chi_{311}(264,\cdot)\) \(\chi_{311}(279,\cdot)\) \(\chi_{311}(287,\cdot)\) \(\chi_{311}(291,\cdot)\) \(\chi_{311}(293,\cdot)\) \(\chi_{311}(296,\cdot)\) \(\chi_{311}(298,\cdot)\) \(\chi_{311}(304,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 62 polynomial |
Values on generators
\(17\) → \(e\left(\frac{11}{62}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 311 }(264, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(1\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{59}{62}\right)\) |