Basic properties
| Modulus: | \(1137\) | |
| Conductor: | \(1137\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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.ba
\(\chi_{1137}(14,\cdot)\) \(\chi_{1137}(23,\cdot)\) \(\chi_{1137}(41,\cdot)\) \(\chi_{1137}(77,\cdot)\) \(\chi_{1137}(83,\cdot)\) \(\chi_{1137}(137,\cdot)\) \(\chi_{1137}(167,\cdot)\) \(\chi_{1137}(179,\cdot)\) \(\chi_{1137}(320,\cdot)\) \(\chi_{1137}(335,\cdot)\) \(\chi_{1137}(350,\cdot)\) \(\chi_{1137}(371,\cdot)\) \(\chi_{1137}(416,\cdot)\) \(\chi_{1137}(443,\cdot)\) \(\chi_{1137}(446,\cdot)\) \(\chi_{1137}(449,\cdot)\) \(\chi_{1137}(518,\cdot)\) \(\chi_{1137}(521,\cdot)\) \(\chi_{1137}(575,\cdot)\) \(\chi_{1137}(584,\cdot)\) \(\chi_{1137}(611,\cdot)\) \(\chi_{1137}(623,\cdot)\) \(\chi_{1137}(695,\cdot)\) \(\chi_{1137}(710,\cdot)\) \(\chi_{1137}(731,\cdot)\) \(\chi_{1137}(764,\cdot)\) \(\chi_{1137}(788,\cdot)\) \(\chi_{1137}(791,\cdot)\) \(\chi_{1137}(794,\cdot)\) \(\chi_{1137}(908,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((380,760)\) → \((-1,e\left(\frac{26}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1137 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{41}{63}\right)\) |