Basic properties
| Modulus: | \(1137\) | |
| Conductor: | \(379\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{379}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1137.bf
\(\chi_{1137}(7,\cdot)\) \(\chi_{1137}(10,\cdot)\) \(\chi_{1137}(13,\cdot)\) \(\chi_{1137}(28,\cdot)\) \(\chi_{1137}(31,\cdot)\) \(\chi_{1137}(43,\cdot)\) \(\chi_{1137}(46,\cdot)\) \(\chi_{1137}(55,\cdot)\) \(\chi_{1137}(82,\cdot)\) \(\chi_{1137}(109,\cdot)\) \(\chi_{1137}(154,\cdot)\) \(\chi_{1137}(160,\cdot)\) \(\chi_{1137}(172,\cdot)\) \(\chi_{1137}(175,\cdot)\) \(\chi_{1137}(190,\cdot)\) \(\chi_{1137}(208,\cdot)\) \(\chi_{1137}(223,\cdot)\) \(\chi_{1137}(235,\cdot)\) \(\chi_{1137}(238,\cdot)\) \(\chi_{1137}(247,\cdot)\) \(\chi_{1137}(250,\cdot)\) \(\chi_{1137}(253,\cdot)\) \(\chi_{1137}(259,\cdot)\) \(\chi_{1137}(265,\cdot)\) \(\chi_{1137}(274,\cdot)\) \(\chi_{1137}(283,\cdot)\) \(\chi_{1137}(298,\cdot)\) \(\chi_{1137}(325,\cdot)\) \(\chi_{1137}(334,\cdot)\) \(\chi_{1137}(358,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((380,760)\) → \((1,e\left(\frac{205}{378}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1137 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{205}{378}\right)\) | \(e\left(\frac{16}{189}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{23}{378}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{241}{378}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{283}{378}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{32}{189}\right)\) |