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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1215.ba
\(\chi_{1215}(4,\cdot)\) \(\chi_{1215}(34,\cdot)\) \(\chi_{1215}(49,\cdot)\) \(\chi_{1215}(79,\cdot)\) \(\chi_{1215}(94,\cdot)\) \(\chi_{1215}(124,\cdot)\) \(\chi_{1215}(139,\cdot)\) \(\chi_{1215}(169,\cdot)\) \(\chi_{1215}(184,\cdot)\) \(\chi_{1215}(214,\cdot)\) \(\chi_{1215}(229,\cdot)\) \(\chi_{1215}(259,\cdot)\) \(\chi_{1215}(274,\cdot)\) \(\chi_{1215}(304,\cdot)\) \(\chi_{1215}(319,\cdot)\) \(\chi_{1215}(349,\cdot)\) \(\chi_{1215}(364,\cdot)\) \(\chi_{1215}(394,\cdot)\) \(\chi_{1215}(409,\cdot)\) \(\chi_{1215}(439,\cdot)\) \(\chi_{1215}(454,\cdot)\) \(\chi_{1215}(484,\cdot)\) \(\chi_{1215}(499,\cdot)\) \(\chi_{1215}(529,\cdot)\) \(\chi_{1215}(544,\cdot)\) \(\chi_{1215}(574,\cdot)\) \(\chi_{1215}(589,\cdot)\) \(\chi_{1215}(619,\cdot)\) \(\chi_{1215}(634,\cdot)\) \(\chi_{1215}(664,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((731,487)\) → \((e\left(\frac{70}{81}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1215 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{162}\right)\) | \(e\left(\frac{59}{81}\right)\) | \(e\left(\frac{161}{162}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{67}{162}\right)\) | \(e\left(\frac{29}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) |