Basic properties
| Modulus: | \(3645\) | |
| Conductor: | \(729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(486\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{729}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3645.bg
\(\chi_{3645}(11,\cdot)\) \(\chi_{3645}(41,\cdot)\) \(\chi_{3645}(56,\cdot)\) \(\chi_{3645}(86,\cdot)\) \(\chi_{3645}(101,\cdot)\) \(\chi_{3645}(131,\cdot)\) \(\chi_{3645}(146,\cdot)\) \(\chi_{3645}(176,\cdot)\) \(\chi_{3645}(191,\cdot)\) \(\chi_{3645}(221,\cdot)\) \(\chi_{3645}(236,\cdot)\) \(\chi_{3645}(266,\cdot)\) \(\chi_{3645}(281,\cdot)\) \(\chi_{3645}(311,\cdot)\) \(\chi_{3645}(326,\cdot)\) \(\chi_{3645}(356,\cdot)\) \(\chi_{3645}(371,\cdot)\) \(\chi_{3645}(401,\cdot)\) \(\chi_{3645}(416,\cdot)\) \(\chi_{3645}(446,\cdot)\) \(\chi_{3645}(461,\cdot)\) \(\chi_{3645}(491,\cdot)\) \(\chi_{3645}(506,\cdot)\) \(\chi_{3645}(536,\cdot)\) \(\chi_{3645}(551,\cdot)\) \(\chi_{3645}(581,\cdot)\) \(\chi_{3645}(596,\cdot)\) \(\chi_{3645}(626,\cdot)\) \(\chi_{3645}(641,\cdot)\) \(\chi_{3645}(671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{243})$ |
| Fixed field: | Number field defined by a degree 486 polynomial (not computed) |
Values on generators
\((731,2917)\) → \((e\left(\frac{283}{486}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{283}{486}\right)\) | \(e\left(\frac{40}{243}\right)\) | \(e\left(\frac{104}{243}\right)\) | \(e\left(\frac{121}{162}\right)\) | \(e\left(\frac{385}{486}\right)\) | \(e\left(\frac{79}{243}\right)\) | \(e\left(\frac{5}{486}\right)\) | \(e\left(\frac{80}{243}\right)\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{14}{81}\right)\) |