Basic properties
| Modulus: | \(1734\) | |
| 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 \(\chi_{289}(138,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1734.q
\(\chi_{1734}(19,\cdot)\) \(\chi_{1734}(25,\cdot)\) \(\chi_{1734}(43,\cdot)\) \(\chi_{1734}(49,\cdot)\) \(\chi_{1734}(121,\cdot)\) \(\chi_{1734}(127,\cdot)\) \(\chi_{1734}(145,\cdot)\) \(\chi_{1734}(151,\cdot)\) \(\chi_{1734}(223,\cdot)\) \(\chi_{1734}(229,\cdot)\) \(\chi_{1734}(247,\cdot)\) \(\chi_{1734}(253,\cdot)\) \(\chi_{1734}(325,\cdot)\) \(\chi_{1734}(331,\cdot)\) \(\chi_{1734}(349,\cdot)\) \(\chi_{1734}(355,\cdot)\) \(\chi_{1734}(427,\cdot)\) \(\chi_{1734}(433,\cdot)\) \(\chi_{1734}(451,\cdot)\) \(\chi_{1734}(457,\cdot)\) \(\chi_{1734}(529,\cdot)\) \(\chi_{1734}(535,\cdot)\) \(\chi_{1734}(553,\cdot)\) \(\chi_{1734}(559,\cdot)\) \(\chi_{1734}(631,\cdot)\) \(\chi_{1734}(637,\cdot)\) \(\chi_{1734}(655,\cdot)\) \(\chi_{1734}(661,\cdot)\) \(\chi_{1734}(739,\cdot)\) \(\chi_{1734}(763,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((1157,1159)\) → \((1,e\left(\frac{71}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(427, a) \) | \(1\) | \(1\) | \(e\left(\frac{75}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{35}{136}\right)\) | \(e\left(\frac{95}{136}\right)\) | \(e\left(\frac{8}{17}\right)\) |