Basic properties
| Modulus: | \(1137\) | |
| Conductor: | \(1137\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | 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 1137.be
\(\chi_{1137}(2,\cdot)\) \(\chi_{1137}(17,\cdot)\) \(\chi_{1137}(32,\cdot)\) \(\chi_{1137}(35,\cdot)\) \(\chi_{1137}(38,\cdot)\) \(\chi_{1137}(47,\cdot)\) \(\chi_{1137}(50,\cdot)\) \(\chi_{1137}(53,\cdot)\) \(\chi_{1137}(65,\cdot)\) \(\chi_{1137}(71,\cdot)\) \(\chi_{1137}(74,\cdot)\) \(\chi_{1137}(89,\cdot)\) \(\chi_{1137}(98,\cdot)\) \(\chi_{1137}(113,\cdot)\) \(\chi_{1137}(116,\cdot)\) \(\chi_{1137}(122,\cdot)\) \(\chi_{1137}(131,\cdot)\) \(\chi_{1137}(134,\cdot)\) \(\chi_{1137}(152,\cdot)\) \(\chi_{1137}(155,\cdot)\) \(\chi_{1137}(158,\cdot)\) \(\chi_{1137}(161,\cdot)\) \(\chi_{1137}(176,\cdot)\) \(\chi_{1137}(188,\cdot)\) \(\chi_{1137}(206,\cdot)\) \(\chi_{1137}(209,\cdot)\) \(\chi_{1137}(215,\cdot)\) \(\chi_{1137}(230,\cdot)\) \(\chi_{1137}(233,\cdot)\) \(\chi_{1137}(236,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((380,760)\) → \((-1,e\left(\frac{115}{378}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1137 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{115}{189}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{43}{378}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{85}{378}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{41}{189}\right)\) |