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
\((487,245)\) → \((-1,e\left(\frac{49}{81}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 972 }(391, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{81}\right)\) | \(e\left(\frac{137}{162}\right)\) | \(e\left(\frac{113}{162}\right)\) | \(e\left(\frac{68}{81}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{133}{162}\right)\) | \(e\left(\frac{67}{81}\right)\) | \(e\left(\frac{31}{81}\right)\) | \(e\left(\frac{97}{162}\right)\) |