Basic properties
| Modulus: | \(1137\) | |
| Conductor: | \(379\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(189\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{379}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1137.bc
\(\chi_{1137}(4,\cdot)\) \(\chi_{1137}(16,\cdot)\) \(\chi_{1137}(19,\cdot)\) \(\chi_{1137}(22,\cdot)\) \(\chi_{1137}(34,\cdot)\) \(\chi_{1137}(49,\cdot)\) \(\chi_{1137}(58,\cdot)\) \(\chi_{1137}(88,\cdot)\) \(\chi_{1137}(97,\cdot)\) \(\chi_{1137}(100,\cdot)\) \(\chi_{1137}(103,\cdot)\) \(\chi_{1137}(106,\cdot)\) \(\chi_{1137}(118,\cdot)\) \(\chi_{1137}(127,\cdot)\) \(\chi_{1137}(130,\cdot)\) \(\chi_{1137}(136,\cdot)\) \(\chi_{1137}(148,\cdot)\) \(\chi_{1137}(169,\cdot)\) \(\chi_{1137}(178,\cdot)\) \(\chi_{1137}(187,\cdot)\) \(\chi_{1137}(211,\cdot)\) \(\chi_{1137}(226,\cdot)\) \(\chi_{1137}(256,\cdot)\) \(\chi_{1137}(262,\cdot)\) \(\chi_{1137}(277,\cdot)\) \(\chi_{1137}(280,\cdot)\) \(\chi_{1137}(289,\cdot)\) \(\chi_{1137}(301,\cdot)\) \(\chi_{1137}(304,\cdot)\) \(\chi_{1137}(307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 189 polynomial (not computed) |
Values on generators
\((380,760)\) → \((1,e\left(\frac{1}{189}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1137 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{145}{189}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{124}{189}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{4}{189}\right)\) |