Basic properties
| Modulus: | \(1444\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.x
\(\chi_{1444}(13,\cdot)\) \(\chi_{1444}(21,\cdot)\) \(\chi_{1444}(29,\cdot)\) \(\chi_{1444}(33,\cdot)\) \(\chi_{1444}(41,\cdot)\) \(\chi_{1444}(53,\cdot)\) \(\chi_{1444}(89,\cdot)\) \(\chi_{1444}(97,\cdot)\) \(\chi_{1444}(105,\cdot)\) \(\chi_{1444}(109,\cdot)\) \(\chi_{1444}(117,\cdot)\) \(\chi_{1444}(129,\cdot)\) \(\chi_{1444}(165,\cdot)\) \(\chi_{1444}(173,\cdot)\) \(\chi_{1444}(181,\cdot)\) \(\chi_{1444}(185,\cdot)\) \(\chi_{1444}(193,\cdot)\) \(\chi_{1444}(205,\cdot)\) \(\chi_{1444}(241,\cdot)\) \(\chi_{1444}(249,\cdot)\) \(\chi_{1444}(257,\cdot)\) \(\chi_{1444}(261,\cdot)\) \(\chi_{1444}(269,\cdot)\) \(\chi_{1444}(281,\cdot)\) \(\chi_{1444}(317,\cdot)\) \(\chi_{1444}(325,\cdot)\) \(\chi_{1444}(337,\cdot)\) \(\chi_{1444}(345,\cdot)\) \(\chi_{1444}(357,\cdot)\) \(\chi_{1444}(393,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((1,e\left(\frac{329}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{245}{342}\right)\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{74}{171}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{169}{342}\right)\) | \(e\left(\frac{307}{342}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{5}{342}\right)\) | \(e\left(\frac{77}{171}\right)\) |