Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.bt
\(\chi_{1352}(37,\cdot)\) \(\chi_{1352}(45,\cdot)\) \(\chi_{1352}(85,\cdot)\) \(\chi_{1352}(93,\cdot)\) \(\chi_{1352}(141,\cdot)\) \(\chi_{1352}(149,\cdot)\) \(\chi_{1352}(189,\cdot)\) \(\chi_{1352}(197,\cdot)\) \(\chi_{1352}(245,\cdot)\) \(\chi_{1352}(253,\cdot)\) \(\chi_{1352}(293,\cdot)\) \(\chi_{1352}(301,\cdot)\) \(\chi_{1352}(349,\cdot)\) \(\chi_{1352}(397,\cdot)\) \(\chi_{1352}(405,\cdot)\) \(\chi_{1352}(453,\cdot)\) \(\chi_{1352}(461,\cdot)\) \(\chi_{1352}(501,\cdot)\) \(\chi_{1352}(509,\cdot)\) \(\chi_{1352}(557,\cdot)\) \(\chi_{1352}(565,\cdot)\) \(\chi_{1352}(605,\cdot)\) \(\chi_{1352}(613,\cdot)\) \(\chi_{1352}(661,\cdot)\) \(\chi_{1352}(669,\cdot)\) \(\chi_{1352}(709,\cdot)\) \(\chi_{1352}(717,\cdot)\) \(\chi_{1352}(773,\cdot)\) \(\chi_{1352}(813,\cdot)\) \(\chi_{1352}(821,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1185)\) → \((1,-1,e\left(\frac{151}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{5}{6}\right)\) |