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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.em
\(\chi_{3724}(51,\cdot)\) \(\chi_{3724}(219,\cdot)\) \(\chi_{3724}(375,\cdot)\) \(\chi_{3724}(515,\cdot)\) \(\chi_{3724}(583,\cdot)\) \(\chi_{3724}(751,\cdot)\) \(\chi_{3724}(907,\cdot)\) \(\chi_{3724}(991,\cdot)\) \(\chi_{3724}(1003,\cdot)\) \(\chi_{3724}(1115,\cdot)\) \(\chi_{3724}(1283,\cdot)\) \(\chi_{3724}(1523,\cdot)\) \(\chi_{3724}(1535,\cdot)\) \(\chi_{3724}(1579,\cdot)\) \(\chi_{3724}(1815,\cdot)\) \(\chi_{3724}(1971,\cdot)\) \(\chi_{3724}(2055,\cdot)\) \(\chi_{3724}(2067,\cdot)\) \(\chi_{3724}(2111,\cdot)\) \(\chi_{3724}(2179,\cdot)\) \(\chi_{3724}(2347,\cdot)\) \(\chi_{3724}(2503,\cdot)\) \(\chi_{3724}(2587,\cdot)\) \(\chi_{3724}(2599,\cdot)\) \(\chi_{3724}(2643,\cdot)\) \(\chi_{3724}(2711,\cdot)\) \(\chi_{3724}(2879,\cdot)\) \(\chi_{3724}(3035,\cdot)\) \(\chi_{3724}(3119,\cdot)\) \(\chi_{3724}(3131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(1971, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) |