Basic properties
Modulus: | \(338\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338.k
\(\chi_{338}(17,\cdot)\) \(\chi_{338}(43,\cdot)\) \(\chi_{338}(49,\cdot)\) \(\chi_{338}(69,\cdot)\) \(\chi_{338}(75,\cdot)\) \(\chi_{338}(95,\cdot)\) \(\chi_{338}(101,\cdot)\) \(\chi_{338}(121,\cdot)\) \(\chi_{338}(127,\cdot)\) \(\chi_{338}(153,\cdot)\) \(\chi_{338}(173,\cdot)\) \(\chi_{338}(179,\cdot)\) \(\chi_{338}(199,\cdot)\) \(\chi_{338}(205,\cdot)\) \(\chi_{338}(225,\cdot)\) \(\chi_{338}(231,\cdot)\) \(\chi_{338}(251,\cdot)\) \(\chi_{338}(257,\cdot)\) \(\chi_{338}(277,\cdot)\) \(\chi_{338}(283,\cdot)\) \(\chi_{338}(303,\cdot)\) \(\chi_{338}(309,\cdot)\) \(\chi_{338}(329,\cdot)\) \(\chi_{338}(335,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\(171\) → \(e\left(\frac{73}{78}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 338 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{2}{3}\right)\) |