Basic properties
Modulus: | \(311\) | |
Conductor: | \(311\) | 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 311.e
\(\chi_{311}(7,\cdot)\) \(\chi_{311}(13,\cdot)\) \(\chi_{311}(15,\cdot)\) \(\chi_{311}(18,\cdot)\) \(\chi_{311}(20,\cdot)\) \(\chi_{311}(24,\cdot)\) \(\chi_{311}(32,\cdot)\) \(\chi_{311}(47,\cdot)\) \(\chi_{311}(49,\cdot)\) \(\chi_{311}(83,\cdot)\) \(\chi_{311}(89,\cdot)\) \(\chi_{311}(91,\cdot)\) \(\chi_{311}(105,\cdot)\) \(\chi_{311}(113,\cdot)\) \(\chi_{311}(121,\cdot)\) \(\chi_{311}(126,\cdot)\) \(\chi_{311}(140,\cdot)\) \(\chi_{311}(146,\cdot)\) \(\chi_{311}(168,\cdot)\) \(\chi_{311}(169,\cdot)\) \(\chi_{311}(195,\cdot)\) \(\chi_{311}(224,\cdot)\) \(\chi_{311}(225,\cdot)\) \(\chi_{311}(234,\cdot)\) \(\chi_{311}(243,\cdot)\) \(\chi_{311}(250,\cdot)\) \(\chi_{311}(260,\cdot)\) \(\chi_{311}(265,\cdot)\) \(\chi_{311}(270,\cdot)\) \(\chi_{311}(300,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 31 polynomial |
Values on generators
\(17\) → \(e\left(\frac{17}{31}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 311 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{1}{31}\right)\) |