Basic properties
| Modulus: | \(972\) | |
| Conductor: | \(972\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | 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 972.r
\(\chi_{972}(7,\cdot)\) \(\chi_{972}(31,\cdot)\) \(\chi_{972}(43,\cdot)\) \(\chi_{972}(67,\cdot)\) \(\chi_{972}(79,\cdot)\) \(\chi_{972}(103,\cdot)\) \(\chi_{972}(115,\cdot)\) \(\chi_{972}(139,\cdot)\) \(\chi_{972}(151,\cdot)\) \(\chi_{972}(175,\cdot)\) \(\chi_{972}(187,\cdot)\) \(\chi_{972}(211,\cdot)\) \(\chi_{972}(223,\cdot)\) \(\chi_{972}(247,\cdot)\) \(\chi_{972}(259,\cdot)\) \(\chi_{972}(283,\cdot)\) \(\chi_{972}(295,\cdot)\) \(\chi_{972}(319,\cdot)\) \(\chi_{972}(331,\cdot)\) \(\chi_{972}(355,\cdot)\) \(\chi_{972}(367,\cdot)\) \(\chi_{972}(391,\cdot)\) \(\chi_{972}(403,\cdot)\) \(\chi_{972}(427,\cdot)\) \(\chi_{972}(439,\cdot)\) \(\chi_{972}(463,\cdot)\) \(\chi_{972}(475,\cdot)\) \(\chi_{972}(499,\cdot)\) \(\chi_{972}(511,\cdot)\) \(\chi_{972}(535,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,245)\) → \((-1,e\left(\frac{35}{81}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 972 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{121}{162}\right)\) | \(e\left(\frac{127}{162}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{95}{162}\right)\) | \(e\left(\frac{71}{81}\right)\) | \(e\left(\frac{80}{81}\right)\) | \(e\left(\frac{23}{162}\right)\) |