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.eg
\(\chi_{3724}(3,\cdot)\) \(\chi_{3724}(59,\cdot)\) \(\chi_{3724}(243,\cdot)\) \(\chi_{3724}(355,\cdot)\) \(\chi_{3724}(451,\cdot)\) \(\chi_{3724}(523,\cdot)\) \(\chi_{3724}(535,\cdot)\) \(\chi_{3724}(591,\cdot)\) \(\chi_{3724}(775,\cdot)\) \(\chi_{3724}(887,\cdot)\) \(\chi_{3724}(983,\cdot)\) \(\chi_{3724}(1055,\cdot)\) \(\chi_{3724}(1067,\cdot)\) \(\chi_{3724}(1123,\cdot)\) \(\chi_{3724}(1307,\cdot)\) \(\chi_{3724}(1419,\cdot)\) \(\chi_{3724}(1515,\cdot)\) \(\chi_{3724}(1655,\cdot)\) \(\chi_{3724}(1839,\cdot)\) \(\chi_{3724}(1951,\cdot)\) \(\chi_{3724}(2047,\cdot)\) \(\chi_{3724}(2119,\cdot)\) \(\chi_{3724}(2131,\cdot)\) \(\chi_{3724}(2483,\cdot)\) \(\chi_{3724}(2651,\cdot)\) \(\chi_{3724}(2663,\cdot)\) \(\chi_{3724}(2719,\cdot)\) \(\chi_{3724}(2903,\cdot)\) \(\chi_{3724}(3015,\cdot)\) \(\chi_{3724}(3111,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{37}{42}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(3111, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) |