Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bv
\(\chi_{1352}(33,\cdot)\) \(\chi_{1352}(41,\cdot)\) \(\chi_{1352}(97,\cdot)\) \(\chi_{1352}(137,\cdot)\) \(\chi_{1352}(145,\cdot)\) \(\chi_{1352}(193,\cdot)\) \(\chi_{1352}(201,\cdot)\) \(\chi_{1352}(241,\cdot)\) \(\chi_{1352}(297,\cdot)\) \(\chi_{1352}(305,\cdot)\) \(\chi_{1352}(345,\cdot)\) \(\chi_{1352}(353,\cdot)\) \(\chi_{1352}(401,\cdot)\) \(\chi_{1352}(409,\cdot)\) \(\chi_{1352}(449,\cdot)\) \(\chi_{1352}(457,\cdot)\) \(\chi_{1352}(505,\cdot)\) \(\chi_{1352}(513,\cdot)\) \(\chi_{1352}(553,\cdot)\) \(\chi_{1352}(561,\cdot)\) \(\chi_{1352}(609,\cdot)\) \(\chi_{1352}(617,\cdot)\) \(\chi_{1352}(665,\cdot)\) \(\chi_{1352}(713,\cdot)\) \(\chi_{1352}(721,\cdot)\) \(\chi_{1352}(761,\cdot)\) \(\chi_{1352}(769,\cdot)\) \(\chi_{1352}(817,\cdot)\) \(\chi_{1352}(825,\cdot)\) \(\chi_{1352}(865,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1185)\) → \((1,1,e\left(\frac{71}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{1}{6}\right)\) |