Basic properties
| Modulus: | \(972\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{243}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 972.s
\(\chi_{972}(5,\cdot)\) \(\chi_{972}(29,\cdot)\) \(\chi_{972}(41,\cdot)\) \(\chi_{972}(65,\cdot)\) \(\chi_{972}(77,\cdot)\) \(\chi_{972}(101,\cdot)\) \(\chi_{972}(113,\cdot)\) \(\chi_{972}(137,\cdot)\) \(\chi_{972}(149,\cdot)\) \(\chi_{972}(173,\cdot)\) \(\chi_{972}(185,\cdot)\) \(\chi_{972}(209,\cdot)\) \(\chi_{972}(221,\cdot)\) \(\chi_{972}(245,\cdot)\) \(\chi_{972}(257,\cdot)\) \(\chi_{972}(281,\cdot)\) \(\chi_{972}(293,\cdot)\) \(\chi_{972}(317,\cdot)\) \(\chi_{972}(329,\cdot)\) \(\chi_{972}(353,\cdot)\) \(\chi_{972}(365,\cdot)\) \(\chi_{972}(389,\cdot)\) \(\chi_{972}(401,\cdot)\) \(\chi_{972}(425,\cdot)\) \(\chi_{972}(437,\cdot)\) \(\chi_{972}(461,\cdot)\) \(\chi_{972}(473,\cdot)\) \(\chi_{972}(497,\cdot)\) \(\chi_{972}(509,\cdot)\) \(\chi_{972}(533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,245)\) → \((1,e\left(\frac{23}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 972 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{162}\right)\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{29}{162}\right)\) | \(e\left(\frac{11}{81}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{43}{81}\right)\) | \(e\left(\frac{41}{162}\right)\) | \(e\left(\frac{68}{81}\right)\) |