Basic properties
| Modulus: | \(1352\) | |
| 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 \(\chi_{169}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bq
\(\chi_{1352}(17,\cdot)\) \(\chi_{1352}(49,\cdot)\) \(\chi_{1352}(121,\cdot)\) \(\chi_{1352}(153,\cdot)\) \(\chi_{1352}(225,\cdot)\) \(\chi_{1352}(257,\cdot)\) \(\chi_{1352}(329,\cdot)\) \(\chi_{1352}(433,\cdot)\) \(\chi_{1352}(465,\cdot)\) \(\chi_{1352}(537,\cdot)\) \(\chi_{1352}(569,\cdot)\) \(\chi_{1352}(641,\cdot)\) \(\chi_{1352}(673,\cdot)\) \(\chi_{1352}(745,\cdot)\) \(\chi_{1352}(777,\cdot)\) \(\chi_{1352}(849,\cdot)\) \(\chi_{1352}(881,\cdot)\) \(\chi_{1352}(953,\cdot)\) \(\chi_{1352}(985,\cdot)\) \(\chi_{1352}(1057,\cdot)\) \(\chi_{1352}(1089,\cdot)\) \(\chi_{1352}(1193,\cdot)\) \(\chi_{1352}(1265,\cdot)\) \(\chi_{1352}(1297,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1185)\) → \((1,1,e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) |