Basic properties
| Modulus: | \(1734\) | |
| Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{867}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1734.t
\(\chi_{1734}(5,\cdot)\) \(\chi_{1734}(11,\cdot)\) \(\chi_{1734}(23,\cdot)\) \(\chi_{1734}(29,\cdot)\) \(\chi_{1734}(41,\cdot)\) \(\chi_{1734}(71,\cdot)\) \(\chi_{1734}(95,\cdot)\) \(\chi_{1734}(107,\cdot)\) \(\chi_{1734}(113,\cdot)\) \(\chi_{1734}(125,\cdot)\) \(\chi_{1734}(143,\cdot)\) \(\chi_{1734}(167,\cdot)\) \(\chi_{1734}(173,\cdot)\) \(\chi_{1734}(197,\cdot)\) \(\chi_{1734}(209,\cdot)\) \(\chi_{1734}(215,\cdot)\) \(\chi_{1734}(227,\cdot)\) \(\chi_{1734}(233,\cdot)\) \(\chi_{1734}(245,\cdot)\) \(\chi_{1734}(269,\cdot)\) \(\chi_{1734}(275,\cdot)\) \(\chi_{1734}(299,\cdot)\) \(\chi_{1734}(311,\cdot)\) \(\chi_{1734}(317,\cdot)\) \(\chi_{1734}(335,\cdot)\) \(\chi_{1734}(347,\cdot)\) \(\chi_{1734}(371,\cdot)\) \(\chi_{1734}(377,\cdot)\) \(\chi_{1734}(401,\cdot)\) \(\chi_{1734}(413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((1157,1159)\) → \((-1,e\left(\frac{229}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1734 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{272}\right)\) | \(e\left(\frac{135}{272}\right)\) | \(e\left(\frac{235}{272}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{107}{136}\right)\) | \(e\left(\frac{67}{272}\right)\) | \(e\left(\frac{81}{136}\right)\) | \(e\left(\frac{201}{272}\right)\) | \(e\left(\frac{157}{272}\right)\) | \(e\left(\frac{27}{34}\right)\) |