Basic properties
Modulus: | \(313\) | |
Conductor: | \(313\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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 313.k
\(\chi_{313}(3,\cdot)\) \(\chi_{313}(9,\cdot)\) \(\chi_{313}(16,\cdot)\) \(\chi_{313}(26,\cdot)\) \(\chi_{313}(50,\cdot)\) \(\chi_{313}(76,\cdot)\) \(\chi_{313}(78,\cdot)\) \(\chi_{313}(81,\cdot)\) \(\chi_{313}(83,\cdot)\) \(\chi_{313}(119,\cdot)\) \(\chi_{313}(121,\cdot)\) \(\chi_{313}(132,\cdot)\) \(\chi_{313}(137,\cdot)\) \(\chi_{313}(142,\cdot)\) \(\chi_{313}(144,\cdot)\) \(\chi_{313}(174,\cdot)\) \(\chi_{313}(205,\cdot)\) \(\chi_{313}(209,\cdot)\) \(\chi_{313}(228,\cdot)\) \(\chi_{313}(243,\cdot)\) \(\chi_{313}(256,\cdot)\) \(\chi_{313}(301,\cdot)\) \(\chi_{313}(302,\cdot)\) \(\chi_{313}(309,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\(10\) → \(e\left(\frac{32}{39}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 313 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) |