Basic properties
| Modulus: | \(3645\) | |
| Conductor: | \(3645\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(486\) | 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.bf
\(\chi_{3645}(14,\cdot)\) \(\chi_{3645}(29,\cdot)\) \(\chi_{3645}(59,\cdot)\) \(\chi_{3645}(74,\cdot)\) \(\chi_{3645}(104,\cdot)\) \(\chi_{3645}(119,\cdot)\) \(\chi_{3645}(149,\cdot)\) \(\chi_{3645}(164,\cdot)\) \(\chi_{3645}(194,\cdot)\) \(\chi_{3645}(209,\cdot)\) \(\chi_{3645}(239,\cdot)\) \(\chi_{3645}(254,\cdot)\) \(\chi_{3645}(284,\cdot)\) \(\chi_{3645}(299,\cdot)\) \(\chi_{3645}(329,\cdot)\) \(\chi_{3645}(344,\cdot)\) \(\chi_{3645}(374,\cdot)\) \(\chi_{3645}(389,\cdot)\) \(\chi_{3645}(419,\cdot)\) \(\chi_{3645}(434,\cdot)\) \(\chi_{3645}(464,\cdot)\) \(\chi_{3645}(479,\cdot)\) \(\chi_{3645}(509,\cdot)\) \(\chi_{3645}(524,\cdot)\) \(\chi_{3645}(554,\cdot)\) \(\chi_{3645}(569,\cdot)\) \(\chi_{3645}(599,\cdot)\) \(\chi_{3645}(614,\cdot)\) \(\chi_{3645}(644,\cdot)\) \(\chi_{3645}(659,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{243})$ |
| Fixed field: | Number field defined by a degree 486 polynomial (not computed) |
Values on generators
\((731,2917)\) → \((e\left(\frac{395}{486}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{76}{243}\right)\) | \(e\left(\frac{152}{243}\right)\) | \(e\left(\frac{353}{486}\right)\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{5}{486}\right)\) | \(e\left(\frac{163}{486}\right)\) | \(e\left(\frac{19}{486}\right)\) | \(e\left(\frac{61}{243}\right)\) | \(e\left(\frac{26}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) |