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 \(\chi_{931}(82,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ep
\(\chi_{3724}(17,\cdot)\) \(\chi_{3724}(61,\cdot)\) \(\chi_{3724}(73,\cdot)\) \(\chi_{3724}(157,\cdot)\) \(\chi_{3724}(481,\cdot)\) \(\chi_{3724}(549,\cdot)\) \(\chi_{3724}(593,\cdot)\) \(\chi_{3724}(605,\cdot)\) \(\chi_{3724}(689,\cdot)\) \(\chi_{3724}(845,\cdot)\) \(\chi_{3724}(1013,\cdot)\) \(\chi_{3724}(1081,\cdot)\) \(\chi_{3724}(1125,\cdot)\) \(\chi_{3724}(1137,\cdot)\) \(\chi_{3724}(1221,\cdot)\) \(\chi_{3724}(1377,\cdot)\) \(\chi_{3724}(1545,\cdot)\) \(\chi_{3724}(1613,\cdot)\) \(\chi_{3724}(1657,\cdot)\) \(\chi_{3724}(1669,\cdot)\) \(\chi_{3724}(1753,\cdot)\) \(\chi_{3724}(1909,\cdot)\) \(\chi_{3724}(2145,\cdot)\) \(\chi_{3724}(2189,\cdot)\) \(\chi_{3724}(2201,\cdot)\) \(\chi_{3724}(2441,\cdot)\) \(\chi_{3724}(2609,\cdot)\) \(\chi_{3724}(2721,\cdot)\) \(\chi_{3724}(2733,\cdot)\) \(\chi_{3724}(2817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{41}{42}\right),e\left(\frac{7}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(1013, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) |