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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bu
\(\chi_{1352}(11,\cdot)\) \(\chi_{1352}(59,\cdot)\) \(\chi_{1352}(67,\cdot)\) \(\chi_{1352}(115,\cdot)\) \(\chi_{1352}(123,\cdot)\) \(\chi_{1352}(163,\cdot)\) \(\chi_{1352}(171,\cdot)\) \(\chi_{1352}(219,\cdot)\) \(\chi_{1352}(227,\cdot)\) \(\chi_{1352}(267,\cdot)\) \(\chi_{1352}(275,\cdot)\) \(\chi_{1352}(323,\cdot)\) \(\chi_{1352}(331,\cdot)\) \(\chi_{1352}(371,\cdot)\) \(\chi_{1352}(379,\cdot)\) \(\chi_{1352}(435,\cdot)\) \(\chi_{1352}(475,\cdot)\) \(\chi_{1352}(483,\cdot)\) \(\chi_{1352}(531,\cdot)\) \(\chi_{1352}(539,\cdot)\) \(\chi_{1352}(579,\cdot)\) \(\chi_{1352}(635,\cdot)\) \(\chi_{1352}(643,\cdot)\) \(\chi_{1352}(683,\cdot)\) \(\chi_{1352}(691,\cdot)\) \(\chi_{1352}(739,\cdot)\) \(\chi_{1352}(747,\cdot)\) \(\chi_{1352}(787,\cdot)\) \(\chi_{1352}(795,\cdot)\) \(\chi_{1352}(843,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1185)\) → \((-1,-1,e\left(\frac{149}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(643, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{2}{3}\right)\) |