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.ev
\(\chi_{3724}(123,\cdot)\) \(\chi_{3724}(291,\cdot)\) \(\chi_{3724}(359,\cdot)\) \(\chi_{3724}(403,\cdot)\) \(\chi_{3724}(415,\cdot)\) \(\chi_{3724}(499,\cdot)\) \(\chi_{3724}(823,\cdot)\) \(\chi_{3724}(891,\cdot)\) \(\chi_{3724}(935,\cdot)\) \(\chi_{3724}(947,\cdot)\) \(\chi_{3724}(1031,\cdot)\) \(\chi_{3724}(1187,\cdot)\) \(\chi_{3724}(1355,\cdot)\) \(\chi_{3724}(1423,\cdot)\) \(\chi_{3724}(1467,\cdot)\) \(\chi_{3724}(1479,\cdot)\) \(\chi_{3724}(1563,\cdot)\) \(\chi_{3724}(1719,\cdot)\) \(\chi_{3724}(1887,\cdot)\) \(\chi_{3724}(1955,\cdot)\) \(\chi_{3724}(1999,\cdot)\) \(\chi_{3724}(2011,\cdot)\) \(\chi_{3724}(2095,\cdot)\) \(\chi_{3724}(2251,\cdot)\) \(\chi_{3724}(2487,\cdot)\) \(\chi_{3724}(2531,\cdot)\) \(\chi_{3724}(2543,\cdot)\) \(\chi_{3724}(2783,\cdot)\) \(\chi_{3724}(2951,\cdot)\) \(\chi_{3724}(3063,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{4}{21}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(1955, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) |