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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.v
\(\chi_{1444}(23,\cdot)\) \(\chi_{1444}(35,\cdot)\) \(\chi_{1444}(43,\cdot)\) \(\chi_{1444}(47,\cdot)\) \(\chi_{1444}(55,\cdot)\) \(\chi_{1444}(63,\cdot)\) \(\chi_{1444}(111,\cdot)\) \(\chi_{1444}(119,\cdot)\) \(\chi_{1444}(123,\cdot)\) \(\chi_{1444}(131,\cdot)\) \(\chi_{1444}(139,\cdot)\) \(\chi_{1444}(175,\cdot)\) \(\chi_{1444}(187,\cdot)\) \(\chi_{1444}(195,\cdot)\) \(\chi_{1444}(199,\cdot)\) \(\chi_{1444}(207,\cdot)\) \(\chi_{1444}(215,\cdot)\) \(\chi_{1444}(251,\cdot)\) \(\chi_{1444}(263,\cdot)\) \(\chi_{1444}(271,\cdot)\) \(\chi_{1444}(275,\cdot)\) \(\chi_{1444}(283,\cdot)\) \(\chi_{1444}(291,\cdot)\) \(\chi_{1444}(327,\cdot)\) \(\chi_{1444}(339,\cdot)\) \(\chi_{1444}(347,\cdot)\) \(\chi_{1444}(351,\cdot)\) \(\chi_{1444}(359,\cdot)\) \(\chi_{1444}(367,\cdot)\) \(\chi_{1444}(403,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((-1,e\left(\frac{73}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{287}{342}\right)\) | \(e\left(\frac{7}{171}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{116}{171}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{301}{342}\right)\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{64}{171}\right)\) | \(e\left(\frac{283}{342}\right)\) |