Basic properties
Modulus: | \(338\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338.i
\(\chi_{338}(3,\cdot)\) \(\chi_{338}(9,\cdot)\) \(\chi_{338}(29,\cdot)\) \(\chi_{338}(35,\cdot)\) \(\chi_{338}(55,\cdot)\) \(\chi_{338}(61,\cdot)\) \(\chi_{338}(81,\cdot)\) \(\chi_{338}(87,\cdot)\) \(\chi_{338}(107,\cdot)\) \(\chi_{338}(113,\cdot)\) \(\chi_{338}(133,\cdot)\) \(\chi_{338}(139,\cdot)\) \(\chi_{338}(159,\cdot)\) \(\chi_{338}(165,\cdot)\) \(\chi_{338}(185,\cdot)\) \(\chi_{338}(211,\cdot)\) \(\chi_{338}(217,\cdot)\) \(\chi_{338}(237,\cdot)\) \(\chi_{338}(243,\cdot)\) \(\chi_{338}(263,\cdot)\) \(\chi_{338}(269,\cdot)\) \(\chi_{338}(289,\cdot)\) \(\chi_{338}(295,\cdot)\) \(\chi_{338}(321,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\(171\) → \(e\left(\frac{10}{39}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 338 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{3}\right)\) |