Basic properties
Modulus: | \(1352\) | |
Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bp
\(\chi_{1352}(43,\cdot)\) \(\chi_{1352}(75,\cdot)\) \(\chi_{1352}(179,\cdot)\) \(\chi_{1352}(251,\cdot)\) \(\chi_{1352}(283,\cdot)\) \(\chi_{1352}(355,\cdot)\) \(\chi_{1352}(387,\cdot)\) \(\chi_{1352}(459,\cdot)\) \(\chi_{1352}(491,\cdot)\) \(\chi_{1352}(563,\cdot)\) \(\chi_{1352}(595,\cdot)\) \(\chi_{1352}(667,\cdot)\) \(\chi_{1352}(771,\cdot)\) \(\chi_{1352}(803,\cdot)\) \(\chi_{1352}(875,\cdot)\) \(\chi_{1352}(907,\cdot)\) \(\chi_{1352}(979,\cdot)\) \(\chi_{1352}(1011,\cdot)\) \(\chi_{1352}(1083,\cdot)\) \(\chi_{1352}(1115,\cdot)\) \(\chi_{1352}(1187,\cdot)\) \(\chi_{1352}(1219,\cdot)\) \(\chi_{1352}(1291,\cdot)\) \(\chi_{1352}(1323,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1185)\) → \((-1,-1,e\left(\frac{61}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1352 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) |