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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bm
\(\chi_{1352}(69,\cdot)\) \(\chi_{1352}(101,\cdot)\) \(\chi_{1352}(173,\cdot)\) \(\chi_{1352}(205,\cdot)\) \(\chi_{1352}(277,\cdot)\) \(\chi_{1352}(309,\cdot)\) \(\chi_{1352}(381,\cdot)\) \(\chi_{1352}(413,\cdot)\) \(\chi_{1352}(517,\cdot)\) \(\chi_{1352}(589,\cdot)\) \(\chi_{1352}(621,\cdot)\) \(\chi_{1352}(693,\cdot)\) \(\chi_{1352}(725,\cdot)\) \(\chi_{1352}(797,\cdot)\) \(\chi_{1352}(829,\cdot)\) \(\chi_{1352}(901,\cdot)\) \(\chi_{1352}(933,\cdot)\) \(\chi_{1352}(1005,\cdot)\) \(\chi_{1352}(1109,\cdot)\) \(\chi_{1352}(1141,\cdot)\) \(\chi_{1352}(1213,\cdot)\) \(\chi_{1352}(1245,\cdot)\) \(\chi_{1352}(1317,\cdot)\) \(\chi_{1352}(1349,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1185)\) → \((1,-1,e\left(\frac{49}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 1352 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) |