Basic properties
Modulus: | \(373\) | |
Conductor: | \(373\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 373.h
\(\chi_{373}(7,\cdot)\) \(\chi_{373}(13,\cdot)\) \(\chi_{373}(17,\cdot)\) \(\chi_{373}(22,\cdot)\) \(\chi_{373}(27,\cdot)\) \(\chi_{373}(31,\cdot)\) \(\chi_{373}(55,\cdot)\) \(\chi_{373}(64,\cdot)\) \(\chi_{373}(84,\cdot)\) \(\chi_{373}(87,\cdot)\) \(\chi_{373}(137,\cdot)\) \(\chi_{373}(152,\cdot)\) \(\chi_{373}(156,\cdot)\) \(\chi_{373}(158,\cdot)\) \(\chi_{373}(160,\cdot)\) \(\chi_{373}(184,\cdot)\) \(\chi_{373}(204,\cdot)\) \(\chi_{373}(210,\cdot)\) \(\chi_{373}(219,\cdot)\) \(\chi_{373}(229,\cdot)\) \(\chi_{373}(254,\cdot)\) \(\chi_{373}(262,\cdot)\) \(\chi_{373}(264,\cdot)\) \(\chi_{373}(282,\cdot)\) \(\chi_{373}(287,\cdot)\) \(\chi_{373}(298,\cdot)\) \(\chi_{373}(324,\cdot)\) \(\chi_{373}(332,\cdot)\) \(\chi_{373}(343,\cdot)\) \(\chi_{373}(361,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 62 polynomial |
Values on generators
\(2\) → \(e\left(\frac{55}{62}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 373 }(156, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{62}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{57}{62}\right)\) | \(e\left(\frac{1}{62}\right)\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{41}{62}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{21}{62}\right)\) |