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 \(\chi_{676}(659,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bl
\(\chi_{1352}(55,\cdot)\) \(\chi_{1352}(87,\cdot)\) \(\chi_{1352}(159,\cdot)\) \(\chi_{1352}(263,\cdot)\) \(\chi_{1352}(295,\cdot)\) \(\chi_{1352}(367,\cdot)\) \(\chi_{1352}(399,\cdot)\) \(\chi_{1352}(471,\cdot)\) \(\chi_{1352}(503,\cdot)\) \(\chi_{1352}(575,\cdot)\) \(\chi_{1352}(607,\cdot)\) \(\chi_{1352}(679,\cdot)\) \(\chi_{1352}(711,\cdot)\) \(\chi_{1352}(783,\cdot)\) \(\chi_{1352}(815,\cdot)\) \(\chi_{1352}(887,\cdot)\) \(\chi_{1352}(919,\cdot)\) \(\chi_{1352}(1023,\cdot)\) \(\chi_{1352}(1095,\cdot)\) \(\chi_{1352}(1127,\cdot)\) \(\chi_{1352}(1199,\cdot)\) \(\chi_{1352}(1231,\cdot)\) \(\chi_{1352}(1303,\cdot)\) \(\chi_{1352}(1335,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1185)\) → \((-1,1,e\left(\frac{17}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(1335, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) |