Basic properties
Modulus: | \(373\) | |
Conductor: | \(373\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(31\) | 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.g
\(\chi_{373}(12,\cdot)\) \(\chi_{373}(30,\cdot)\) \(\chi_{373}(41,\cdot)\) \(\chi_{373}(49,\cdot)\) \(\chi_{373}(75,\cdot)\) \(\chi_{373}(86,\cdot)\) \(\chi_{373}(91,\cdot)\) \(\chi_{373}(109,\cdot)\) \(\chi_{373}(111,\cdot)\) \(\chi_{373}(119,\cdot)\) \(\chi_{373}(144,\cdot)\) \(\chi_{373}(154,\cdot)\) \(\chi_{373}(163,\cdot)\) \(\chi_{373}(169,\cdot)\) \(\chi_{373}(189,\cdot)\) \(\chi_{373}(213,\cdot)\) \(\chi_{373}(215,\cdot)\) \(\chi_{373}(217,\cdot)\) \(\chi_{373}(221,\cdot)\) \(\chi_{373}(236,\cdot)\) \(\chi_{373}(286,\cdot)\) \(\chi_{373}(289,\cdot)\) \(\chi_{373}(309,\cdot)\) \(\chi_{373}(318,\cdot)\) \(\chi_{373}(342,\cdot)\) \(\chi_{373}(346,\cdot)\) \(\chi_{373}(351,\cdot)\) \(\chi_{373}(356,\cdot)\) \(\chi_{373}(360,\cdot)\) \(\chi_{373}(366,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 31 polynomial |
Values on generators
\(2\) → \(e\left(\frac{9}{31}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 373 }(144, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) |