Basic properties
| Modulus: | \(1156\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1156.s
\(\chi_{1156}(5,\cdot)\) \(\chi_{1156}(29,\cdot)\) \(\chi_{1156}(37,\cdot)\) \(\chi_{1156}(41,\cdot)\) \(\chi_{1156}(45,\cdot)\) \(\chi_{1156}(57,\cdot)\) \(\chi_{1156}(61,\cdot)\) \(\chi_{1156}(73,\cdot)\) \(\chi_{1156}(97,\cdot)\) \(\chi_{1156}(105,\cdot)\) \(\chi_{1156}(109,\cdot)\) \(\chi_{1156}(113,\cdot)\) \(\chi_{1156}(125,\cdot)\) \(\chi_{1156}(129,\cdot)\) \(\chi_{1156}(133,\cdot)\) \(\chi_{1156}(141,\cdot)\) \(\chi_{1156}(165,\cdot)\) \(\chi_{1156}(173,\cdot)\) \(\chi_{1156}(177,\cdot)\) \(\chi_{1156}(181,\cdot)\) \(\chi_{1156}(193,\cdot)\) \(\chi_{1156}(197,\cdot)\) \(\chi_{1156}(201,\cdot)\) \(\chi_{1156}(209,\cdot)\) \(\chi_{1156}(233,\cdot)\) \(\chi_{1156}(241,\cdot)\) \(\chi_{1156}(245,\cdot)\) \(\chi_{1156}(261,\cdot)\) \(\chi_{1156}(265,\cdot)\) \(\chi_{1156}(269,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((579,581)\) → \((1,e\left(\frac{129}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1156 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{272}\right)\) | \(e\left(\frac{165}{272}\right)\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{129}{136}\right)\) | \(e\left(\frac{247}{272}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{11}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{207}{272}\right)\) |