Basic properties
| Modulus: | \(1156\) | |
| Conductor: | \(1156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | 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 1156.r
\(\chi_{1156}(15,\cdot)\) \(\chi_{1156}(19,\cdot)\) \(\chi_{1156}(43,\cdot)\) \(\chi_{1156}(59,\cdot)\) \(\chi_{1156}(83,\cdot)\) \(\chi_{1156}(87,\cdot)\) \(\chi_{1156}(111,\cdot)\) \(\chi_{1156}(127,\cdot)\) \(\chi_{1156}(151,\cdot)\) \(\chi_{1156}(195,\cdot)\) \(\chi_{1156}(219,\cdot)\) \(\chi_{1156}(223,\cdot)\) \(\chi_{1156}(247,\cdot)\) \(\chi_{1156}(263,\cdot)\) \(\chi_{1156}(287,\cdot)\) \(\chi_{1156}(291,\cdot)\) \(\chi_{1156}(315,\cdot)\) \(\chi_{1156}(331,\cdot)\) \(\chi_{1156}(355,\cdot)\) \(\chi_{1156}(359,\cdot)\) \(\chi_{1156}(383,\cdot)\) \(\chi_{1156}(427,\cdot)\) \(\chi_{1156}(451,\cdot)\) \(\chi_{1156}(467,\cdot)\) \(\chi_{1156}(491,\cdot)\) \(\chi_{1156}(495,\cdot)\) \(\chi_{1156}(519,\cdot)\) \(\chi_{1156}(535,\cdot)\) \(\chi_{1156}(559,\cdot)\) \(\chi_{1156}(563,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((579,581)\) → \((-1,e\left(\frac{115}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1156 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{77}{136}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{129}{136}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{9}{136}\right)\) |