Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bo
\(\chi_{1352}(95,\cdot)\) \(\chi_{1352}(127,\cdot)\) \(\chi_{1352}(199,\cdot)\) \(\chi_{1352}(231,\cdot)\) \(\chi_{1352}(303,\cdot)\) \(\chi_{1352}(335,\cdot)\) \(\chi_{1352}(407,\cdot)\) \(\chi_{1352}(439,\cdot)\) \(\chi_{1352}(511,\cdot)\) \(\chi_{1352}(543,\cdot)\) \(\chi_{1352}(615,\cdot)\) \(\chi_{1352}(647,\cdot)\) \(\chi_{1352}(719,\cdot)\) \(\chi_{1352}(751,\cdot)\) \(\chi_{1352}(855,\cdot)\) \(\chi_{1352}(927,\cdot)\) \(\chi_{1352}(959,\cdot)\) \(\chi_{1352}(1031,\cdot)\) \(\chi_{1352}(1063,\cdot)\) \(\chi_{1352}(1135,\cdot)\) \(\chi_{1352}(1167,\cdot)\) \(\chi_{1352}(1239,\cdot)\) \(\chi_{1352}(1271,\cdot)\) \(\chi_{1352}(1343,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1185)\) → \((-1,1,e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) |