Basic properties
| Modulus: | \(1156\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1156.p
\(\chi_{1156}(13,\cdot)\) \(\chi_{1156}(21,\cdot)\) \(\chi_{1156}(81,\cdot)\) \(\chi_{1156}(89,\cdot)\) \(\chi_{1156}(149,\cdot)\) \(\chi_{1156}(157,\cdot)\) \(\chi_{1156}(217,\cdot)\) \(\chi_{1156}(225,\cdot)\) \(\chi_{1156}(285,\cdot)\) \(\chi_{1156}(293,\cdot)\) \(\chi_{1156}(353,\cdot)\) \(\chi_{1156}(361,\cdot)\) \(\chi_{1156}(421,\cdot)\) \(\chi_{1156}(429,\cdot)\) \(\chi_{1156}(489,\cdot)\) \(\chi_{1156}(497,\cdot)\) \(\chi_{1156}(557,\cdot)\) \(\chi_{1156}(565,\cdot)\) \(\chi_{1156}(625,\cdot)\) \(\chi_{1156}(633,\cdot)\) \(\chi_{1156}(693,\cdot)\) \(\chi_{1156}(701,\cdot)\) \(\chi_{1156}(761,\cdot)\) \(\chi_{1156}(769,\cdot)\) \(\chi_{1156}(837,\cdot)\) \(\chi_{1156}(897,\cdot)\) \(\chi_{1156}(965,\cdot)\) \(\chi_{1156}(973,\cdot)\) \(\chi_{1156}(1033,\cdot)\) \(\chi_{1156}(1041,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((579,581)\) → \((1,e\left(\frac{49}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1156 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{47}{68}\right)\) |