Basic properties
| Modulus: | \(1444\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.w
\(\chi_{1444}(3,\cdot)\) \(\chi_{1444}(15,\cdot)\) \(\chi_{1444}(51,\cdot)\) \(\chi_{1444}(59,\cdot)\) \(\chi_{1444}(67,\cdot)\) \(\chi_{1444}(71,\cdot)\) \(\chi_{1444}(79,\cdot)\) \(\chi_{1444}(91,\cdot)\) \(\chi_{1444}(135,\cdot)\) \(\chi_{1444}(143,\cdot)\) \(\chi_{1444}(147,\cdot)\) \(\chi_{1444}(155,\cdot)\) \(\chi_{1444}(167,\cdot)\) \(\chi_{1444}(203,\cdot)\) \(\chi_{1444}(211,\cdot)\) \(\chi_{1444}(219,\cdot)\) \(\chi_{1444}(223,\cdot)\) \(\chi_{1444}(231,\cdot)\) \(\chi_{1444}(243,\cdot)\) \(\chi_{1444}(279,\cdot)\) \(\chi_{1444}(287,\cdot)\) \(\chi_{1444}(295,\cdot)\) \(\chi_{1444}(319,\cdot)\) \(\chi_{1444}(355,\cdot)\) \(\chi_{1444}(363,\cdot)\) \(\chi_{1444}(371,\cdot)\) \(\chi_{1444}(375,\cdot)\) \(\chi_{1444}(383,\cdot)\) \(\chi_{1444}(395,\cdot)\) \(\chi_{1444}(431,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((-1,e\left(\frac{269}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{142}{171}\right)\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{113}{171}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{107}{342}\right)\) | \(e\left(\frac{115}{342}\right)\) |