Basic properties
Modulus: | \(3724\) | |
Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 3724.eh
\(\chi_{3724}(23,\cdot)\) \(\chi_{3724}(207,\cdot)\) \(\chi_{3724}(347,\cdot)\) \(\chi_{3724}(443,\cdot)\) \(\chi_{3724}(555,\cdot)\) \(\chi_{3724}(739,\cdot)\) \(\chi_{3724}(795,\cdot)\) \(\chi_{3724}(807,\cdot)\) \(\chi_{3724}(879,\cdot)\) \(\chi_{3724}(975,\cdot)\) \(\chi_{3724}(1087,\cdot)\) \(\chi_{3724}(1271,\cdot)\) \(\chi_{3724}(1327,\cdot)\) \(\chi_{3724}(1339,\cdot)\) \(\chi_{3724}(1411,\cdot)\) \(\chi_{3724}(1507,\cdot)\) \(\chi_{3724}(1619,\cdot)\) \(\chi_{3724}(1803,\cdot)\) \(\chi_{3724}(1859,\cdot)\) \(\chi_{3724}(1871,\cdot)\) \(\chi_{3724}(1943,\cdot)\) \(\chi_{3724}(2151,\cdot)\) \(\chi_{3724}(2335,\cdot)\) \(\chi_{3724}(2391,\cdot)\) \(\chi_{3724}(2403,\cdot)\) \(\chi_{3724}(2475,\cdot)\) \(\chi_{3724}(2571,\cdot)\) \(\chi_{3724}(2683,\cdot)\) \(\chi_{3724}(2867,\cdot)\) \(\chi_{3724}(2923,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{16}{21}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(2683, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |