Basic properties
| Modulus: | \(1215\) | |
| Conductor: | \(1215\) | 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 1215.bb
\(\chi_{1215}(14,\cdot)\) \(\chi_{1215}(29,\cdot)\) \(\chi_{1215}(59,\cdot)\) \(\chi_{1215}(74,\cdot)\) \(\chi_{1215}(104,\cdot)\) \(\chi_{1215}(119,\cdot)\) \(\chi_{1215}(149,\cdot)\) \(\chi_{1215}(164,\cdot)\) \(\chi_{1215}(194,\cdot)\) \(\chi_{1215}(209,\cdot)\) \(\chi_{1215}(239,\cdot)\) \(\chi_{1215}(254,\cdot)\) \(\chi_{1215}(284,\cdot)\) \(\chi_{1215}(299,\cdot)\) \(\chi_{1215}(329,\cdot)\) \(\chi_{1215}(344,\cdot)\) \(\chi_{1215}(374,\cdot)\) \(\chi_{1215}(389,\cdot)\) \(\chi_{1215}(419,\cdot)\) \(\chi_{1215}(434,\cdot)\) \(\chi_{1215}(464,\cdot)\) \(\chi_{1215}(479,\cdot)\) \(\chi_{1215}(509,\cdot)\) \(\chi_{1215}(524,\cdot)\) \(\chi_{1215}(554,\cdot)\) \(\chi_{1215}(569,\cdot)\) \(\chi_{1215}(599,\cdot)\) \(\chi_{1215}(614,\cdot)\) \(\chi_{1215}(644,\cdot)\) \(\chi_{1215}(659,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((731,487)\) → \((e\left(\frac{55}{162}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1215 }(164, a) \) | \(-1\) | \(1\) | \(e\left(\frac{68}{81}\right)\) | \(e\left(\frac{55}{81}\right)\) | \(e\left(\frac{43}{162}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{13}{162}\right)\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{17}{162}\right)\) | \(e\left(\frac{29}{81}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) |