Basic properties
| Modulus: | \(1444\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.u
\(\chi_{1444}(5,\cdot)\) \(\chi_{1444}(9,\cdot)\) \(\chi_{1444}(17,\cdot)\) \(\chi_{1444}(25,\cdot)\) \(\chi_{1444}(61,\cdot)\) \(\chi_{1444}(73,\cdot)\) \(\chi_{1444}(81,\cdot)\) \(\chi_{1444}(85,\cdot)\) \(\chi_{1444}(93,\cdot)\) \(\chi_{1444}(101,\cdot)\) \(\chi_{1444}(137,\cdot)\) \(\chi_{1444}(149,\cdot)\) \(\chi_{1444}(157,\cdot)\) \(\chi_{1444}(161,\cdot)\) \(\chi_{1444}(169,\cdot)\) \(\chi_{1444}(177,\cdot)\) \(\chi_{1444}(213,\cdot)\) \(\chi_{1444}(225,\cdot)\) \(\chi_{1444}(233,\cdot)\) \(\chi_{1444}(237,\cdot)\) \(\chi_{1444}(253,\cdot)\) \(\chi_{1444}(289,\cdot)\) \(\chi_{1444}(301,\cdot)\) \(\chi_{1444}(309,\cdot)\) \(\chi_{1444}(313,\cdot)\) \(\chi_{1444}(321,\cdot)\) \(\chi_{1444}(329,\cdot)\) \(\chi_{1444}(365,\cdot)\) \(\chi_{1444}(377,\cdot)\) \(\chi_{1444}(385,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((1,e\left(\frac{139}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{100}{171}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{74}{171}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{121}{171}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{116}{171}\right)\) |