Basic properties
Modulus: | \(961\) | |
Conductor: | \(961\) | 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 961.i
\(\chi_{961}(32,\cdot)\) \(\chi_{961}(63,\cdot)\) \(\chi_{961}(94,\cdot)\) \(\chi_{961}(125,\cdot)\) \(\chi_{961}(156,\cdot)\) \(\chi_{961}(187,\cdot)\) \(\chi_{961}(218,\cdot)\) \(\chi_{961}(249,\cdot)\) \(\chi_{961}(280,\cdot)\) \(\chi_{961}(311,\cdot)\) \(\chi_{961}(342,\cdot)\) \(\chi_{961}(373,\cdot)\) \(\chi_{961}(404,\cdot)\) \(\chi_{961}(435,\cdot)\) \(\chi_{961}(466,\cdot)\) \(\chi_{961}(497,\cdot)\) \(\chi_{961}(528,\cdot)\) \(\chi_{961}(559,\cdot)\) \(\chi_{961}(590,\cdot)\) \(\chi_{961}(621,\cdot)\) \(\chi_{961}(652,\cdot)\) \(\chi_{961}(683,\cdot)\) \(\chi_{961}(714,\cdot)\) \(\chi_{961}(745,\cdot)\) \(\chi_{961}(776,\cdot)\) \(\chi_{961}(807,\cdot)\) \(\chi_{961}(838,\cdot)\) \(\chi_{961}(869,\cdot)\) \(\chi_{961}(900,\cdot)\) \(\chi_{961}(931,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | 31.31.303180754947920226773910663600827932461415650100367091342054488471568688197420529491484801.1 |
Values on generators
\(3\) → \(e\left(\frac{11}{31}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 961 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{19}{31}\right)\) |