Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bs
\(\chi_{1352}(7,\cdot)\) \(\chi_{1352}(15,\cdot)\) \(\chi_{1352}(63,\cdot)\) \(\chi_{1352}(71,\cdot)\) \(\chi_{1352}(111,\cdot)\) \(\chi_{1352}(119,\cdot)\) \(\chi_{1352}(167,\cdot)\) \(\chi_{1352}(175,\cdot)\) \(\chi_{1352}(215,\cdot)\) \(\chi_{1352}(223,\cdot)\) \(\chi_{1352}(271,\cdot)\) \(\chi_{1352}(279,\cdot)\) \(\chi_{1352}(327,\cdot)\) \(\chi_{1352}(375,\cdot)\) \(\chi_{1352}(383,\cdot)\) \(\chi_{1352}(423,\cdot)\) \(\chi_{1352}(431,\cdot)\) \(\chi_{1352}(479,\cdot)\) \(\chi_{1352}(487,\cdot)\) \(\chi_{1352}(527,\cdot)\) \(\chi_{1352}(535,\cdot)\) \(\chi_{1352}(583,\cdot)\) \(\chi_{1352}(591,\cdot)\) \(\chi_{1352}(631,\cdot)\) \(\chi_{1352}(639,\cdot)\) \(\chi_{1352}(687,\cdot)\) \(\chi_{1352}(735,\cdot)\) \(\chi_{1352}(743,\cdot)\) \(\chi_{1352}(791,\cdot)\) \(\chi_{1352}(799,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1185)\) → \((-1,1,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{2}{3}\right)\) |