Basic properties
| Modulus: | \(1734\) | |
| 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 1734.o
\(\chi_{1734}(13,\cdot)\) \(\chi_{1734}(55,\cdot)\) \(\chi_{1734}(115,\cdot)\) \(\chi_{1734}(157,\cdot)\) \(\chi_{1734}(217,\cdot)\) \(\chi_{1734}(259,\cdot)\) \(\chi_{1734}(319,\cdot)\) \(\chi_{1734}(361,\cdot)\) \(\chi_{1734}(421,\cdot)\) \(\chi_{1734}(463,\cdot)\) \(\chi_{1734}(523,\cdot)\) \(\chi_{1734}(565,\cdot)\) \(\chi_{1734}(625,\cdot)\) \(\chi_{1734}(667,\cdot)\) \(\chi_{1734}(727,\cdot)\) \(\chi_{1734}(769,\cdot)\) \(\chi_{1734}(871,\cdot)\) \(\chi_{1734}(931,\cdot)\) \(\chi_{1734}(973,\cdot)\) \(\chi_{1734}(1033,\cdot)\) \(\chi_{1734}(1075,\cdot)\) \(\chi_{1734}(1135,\cdot)\) \(\chi_{1734}(1177,\cdot)\) \(\chi_{1734}(1237,\cdot)\) \(\chi_{1734}(1279,\cdot)\) \(\chi_{1734}(1339,\cdot)\) \(\chi_{1734}(1381,\cdot)\) \(\chi_{1734}(1441,\cdot)\) \(\chi_{1734}(1543,\cdot)\) \(\chi_{1734}(1585,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((1157,1159)\) → \((1,e\left(\frac{49}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{12}{17}\right)\) |