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 \(\chi_{931}(477,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 3724.er
\(\chi_{3724}(29,\cdot)\) \(\chi_{3724}(281,\cdot)\) \(\chi_{3724}(337,\cdot)\) \(\chi_{3724}(421,\cdot)\) \(\chi_{3724}(477,\cdot)\) \(\chi_{3724}(561,\cdot)\) \(\chi_{3724}(813,\cdot)\) \(\chi_{3724}(869,\cdot)\) \(\chi_{3724}(925,\cdot)\) \(\chi_{3724}(953,\cdot)\) \(\chi_{3724}(1009,\cdot)\) \(\chi_{3724}(1093,\cdot)\) \(\chi_{3724}(1345,\cdot)\) \(\chi_{3724}(1401,\cdot)\) \(\chi_{3724}(1457,\cdot)\) \(\chi_{3724}(1485,\cdot)\) \(\chi_{3724}(1541,\cdot)\) \(\chi_{3724}(1625,\cdot)\) \(\chi_{3724}(1877,\cdot)\) \(\chi_{3724}(1933,\cdot)\) \(\chi_{3724}(1989,\cdot)\) \(\chi_{3724}(2017,\cdot)\) \(\chi_{3724}(2073,\cdot)\) \(\chi_{3724}(2409,\cdot)\) \(\chi_{3724}(2465,\cdot)\) \(\chi_{3724}(2521,\cdot)\) \(\chi_{3724}(2605,\cdot)\) \(\chi_{3724}(2689,\cdot)\) \(\chi_{3724}(2997,\cdot)\) \(\chi_{3724}(3053,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{2}{7}\right),e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(477, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) |