Basic properties
| Modulus: | \(3645\) | |
| 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 \(\chi_{243}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3645.z
\(\chi_{3645}(71,\cdot)\) \(\chi_{3645}(116,\cdot)\) \(\chi_{3645}(206,\cdot)\) \(\chi_{3645}(251,\cdot)\) \(\chi_{3645}(341,\cdot)\) \(\chi_{3645}(386,\cdot)\) \(\chi_{3645}(476,\cdot)\) \(\chi_{3645}(521,\cdot)\) \(\chi_{3645}(611,\cdot)\) \(\chi_{3645}(656,\cdot)\) \(\chi_{3645}(746,\cdot)\) \(\chi_{3645}(791,\cdot)\) \(\chi_{3645}(881,\cdot)\) \(\chi_{3645}(926,\cdot)\) \(\chi_{3645}(1016,\cdot)\) \(\chi_{3645}(1061,\cdot)\) \(\chi_{3645}(1151,\cdot)\) \(\chi_{3645}(1196,\cdot)\) \(\chi_{3645}(1286,\cdot)\) \(\chi_{3645}(1331,\cdot)\) \(\chi_{3645}(1421,\cdot)\) \(\chi_{3645}(1466,\cdot)\) \(\chi_{3645}(1556,\cdot)\) \(\chi_{3645}(1601,\cdot)\) \(\chi_{3645}(1691,\cdot)\) \(\chi_{3645}(1736,\cdot)\) \(\chi_{3645}(1826,\cdot)\) \(\chi_{3645}(1871,\cdot)\) \(\chi_{3645}(1961,\cdot)\) \(\chi_{3645}(2006,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((731,2917)\) → \((e\left(\frac{17}{162}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{162}\right)\) | \(e\left(\frac{17}{81}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{113}{162}\right)\) | \(e\left(\frac{68}{81}\right)\) | \(e\left(\frac{73}{162}\right)\) | \(e\left(\frac{34}{81}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{10}{27}\right)\) |