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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1137.bd
\(\chi_{1137}(20,\cdot)\) \(\chi_{1137}(26,\cdot)\) \(\chi_{1137}(56,\cdot)\) \(\chi_{1137}(62,\cdot)\) \(\chi_{1137}(80,\cdot)\) \(\chi_{1137}(92,\cdot)\) \(\chi_{1137}(95,\cdot)\) \(\chi_{1137}(101,\cdot)\) \(\chi_{1137}(104,\cdot)\) \(\chi_{1137}(110,\cdot)\) \(\chi_{1137}(143,\cdot)\) \(\chi_{1137}(146,\cdot)\) \(\chi_{1137}(149,\cdot)\) \(\chi_{1137}(164,\cdot)\) \(\chi_{1137}(170,\cdot)\) \(\chi_{1137}(173,\cdot)\) \(\chi_{1137}(191,\cdot)\) \(\chi_{1137}(203,\cdot)\) \(\chi_{1137}(218,\cdot)\) \(\chi_{1137}(221,\cdot)\) \(\chi_{1137}(224,\cdot)\) \(\chi_{1137}(227,\cdot)\) \(\chi_{1137}(245,\cdot)\) \(\chi_{1137}(248,\cdot)\) \(\chi_{1137}(257,\cdot)\) \(\chi_{1137}(263,\cdot)\) \(\chi_{1137}(266,\cdot)\) \(\chi_{1137}(281,\cdot)\) \(\chi_{1137}(290,\cdot)\) \(\chi_{1137}(305,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((380,760)\) → \((-1,e\left(\frac{157}{189}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1137 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{125}{378}\right)\) | \(e\left(\frac{125}{189}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{85}{189}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{61}{189}\right)\) |