Basic properties
Modulus: | \(3724\) | |
Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{931}(718,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ed
\(\chi_{3724}(53,\cdot)\) \(\chi_{3724}(261,\cdot)\) \(\chi_{3724}(333,\cdot)\) \(\chi_{3724}(345,\cdot)\) \(\chi_{3724}(401,\cdot)\) \(\chi_{3724}(585,\cdot)\) \(\chi_{3724}(697,\cdot)\) \(\chi_{3724}(793,\cdot)\) \(\chi_{3724}(865,\cdot)\) \(\chi_{3724}(877,\cdot)\) \(\chi_{3724}(933,\cdot)\) \(\chi_{3724}(1117,\cdot)\) \(\chi_{3724}(1229,\cdot)\) \(\chi_{3724}(1325,\cdot)\) \(\chi_{3724}(1397,\cdot)\) \(\chi_{3724}(1409,\cdot)\) \(\chi_{3724}(1465,\cdot)\) \(\chi_{3724}(1649,\cdot)\) \(\chi_{3724}(1761,\cdot)\) \(\chi_{3724}(1857,\cdot)\) \(\chi_{3724}(1997,\cdot)\) \(\chi_{3724}(2181,\cdot)\) \(\chi_{3724}(2293,\cdot)\) \(\chi_{3724}(2389,\cdot)\) \(\chi_{3724}(2461,\cdot)\) \(\chi_{3724}(2473,\cdot)\) \(\chi_{3724}(2825,\cdot)\) \(\chi_{3724}(2993,\cdot)\) \(\chi_{3724}(3005,\cdot)\) \(\chi_{3724}(3061,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{2}{21}\right),e\left(\frac{11}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(1649, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |