Basic properties
| Modulus: | \(867\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 867.q
\(\chi_{867}(19,\cdot)\) \(\chi_{867}(25,\cdot)\) \(\chi_{867}(43,\cdot)\) \(\chi_{867}(49,\cdot)\) \(\chi_{867}(70,\cdot)\) \(\chi_{867}(76,\cdot)\) \(\chi_{867}(94,\cdot)\) \(\chi_{867}(100,\cdot)\) \(\chi_{867}(121,\cdot)\) \(\chi_{867}(127,\cdot)\) \(\chi_{867}(145,\cdot)\) \(\chi_{867}(151,\cdot)\) \(\chi_{867}(172,\cdot)\) \(\chi_{867}(178,\cdot)\) \(\chi_{867}(196,\cdot)\) \(\chi_{867}(202,\cdot)\) \(\chi_{867}(223,\cdot)\) \(\chi_{867}(229,\cdot)\) \(\chi_{867}(247,\cdot)\) \(\chi_{867}(253,\cdot)\) \(\chi_{867}(274,\cdot)\) \(\chi_{867}(280,\cdot)\) \(\chi_{867}(298,\cdot)\) \(\chi_{867}(304,\cdot)\) \(\chi_{867}(325,\cdot)\) \(\chi_{867}(331,\cdot)\) \(\chi_{867}(349,\cdot)\) \(\chi_{867}(355,\cdot)\) \(\chi_{867}(376,\cdot)\) \(\chi_{867}(382,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((290,292)\) → \((1,e\left(\frac{7}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 867 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{107}{136}\right)\) | \(e\left(\frac{133}{136}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{77}{136}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{103}{136}\right)\) | \(e\left(\frac{2}{17}\right)\) |