Basic properties
| Modulus: | \(3645\) | |
| Conductor: | \(3645\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(972\) | 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 3645.bi
\(\chi_{3645}(7,\cdot)\) \(\chi_{3645}(13,\cdot)\) \(\chi_{3645}(22,\cdot)\) \(\chi_{3645}(43,\cdot)\) \(\chi_{3645}(52,\cdot)\) \(\chi_{3645}(58,\cdot)\) \(\chi_{3645}(67,\cdot)\) \(\chi_{3645}(88,\cdot)\) \(\chi_{3645}(97,\cdot)\) \(\chi_{3645}(103,\cdot)\) \(\chi_{3645}(112,\cdot)\) \(\chi_{3645}(133,\cdot)\) \(\chi_{3645}(142,\cdot)\) \(\chi_{3645}(148,\cdot)\) \(\chi_{3645}(157,\cdot)\) \(\chi_{3645}(178,\cdot)\) \(\chi_{3645}(187,\cdot)\) \(\chi_{3645}(193,\cdot)\) \(\chi_{3645}(202,\cdot)\) \(\chi_{3645}(223,\cdot)\) \(\chi_{3645}(232,\cdot)\) \(\chi_{3645}(238,\cdot)\) \(\chi_{3645}(247,\cdot)\) \(\chi_{3645}(268,\cdot)\) \(\chi_{3645}(277,\cdot)\) \(\chi_{3645}(283,\cdot)\) \(\chi_{3645}(292,\cdot)\) \(\chi_{3645}(313,\cdot)\) \(\chi_{3645}(322,\cdot)\) \(\chi_{3645}(328,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{972})$ |
| Fixed field: | Number field defined by a degree 972 polynomial (not computed) |
Values on generators
\((731,2917)\) → \((e\left(\frac{197}{243}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{972}\right)\) | \(e\left(\frac{59}{486}\right)\) | \(e\left(\frac{647}{972}\right)\) | \(e\left(\frac{59}{324}\right)\) | \(e\left(\frac{104}{243}\right)\) | \(e\left(\frac{877}{972}\right)\) | \(e\left(\frac{353}{486}\right)\) | \(e\left(\frac{59}{243}\right)\) | \(e\left(\frac{1}{324}\right)\) | \(e\left(\frac{49}{162}\right)\) |