Basic properties
Modulus: | \(683\) | |
Conductor: | \(683\) | 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 683.e
\(\chi_{683}(3,\cdot)\) \(\chi_{683}(9,\cdot)\) \(\chi_{683}(27,\cdot)\) \(\chi_{683}(46,\cdot)\) \(\chi_{683}(67,\cdot)\) \(\chi_{683}(76,\cdot)\) \(\chi_{683}(81,\cdot)\) \(\chi_{683}(104,\cdot)\) \(\chi_{683}(138,\cdot)\) \(\chi_{683}(201,\cdot)\) \(\chi_{683}(228,\cdot)\) \(\chi_{683}(243,\cdot)\) \(\chi_{683}(250,\cdot)\) \(\chi_{683}(253,\cdot)\) \(\chi_{683}(311,\cdot)\) \(\chi_{683}(312,\cdot)\) \(\chi_{683}(347,\cdot)\) \(\chi_{683}(350,\cdot)\) \(\chi_{683}(358,\cdot)\) \(\chi_{683}(367,\cdot)\) \(\chi_{683}(391,\cdot)\) \(\chi_{683}(414,\cdot)\) \(\chi_{683}(418,\cdot)\) \(\chi_{683}(443,\cdot)\) \(\chi_{683}(490,\cdot)\) \(\chi_{683}(559,\cdot)\) \(\chi_{683}(571,\cdot)\) \(\chi_{683}(572,\cdot)\) \(\chi_{683}(603,\cdot)\) \(\chi_{683}(646,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 31 polynomial |
Values on generators
\(5\) → \(e\left(\frac{9}{31}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 683 }(201, a) \) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{25}{31}\right)\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(1\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{23}{31}\right)\) |