Basic properties
Modulus: | \(4056\) | |
Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1352}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cu
\(\chi_{4056}(187,\cdot)\) \(\chi_{4056}(307,\cdot)\) \(\chi_{4056}(499,\cdot)\) \(\chi_{4056}(619,\cdot)\) \(\chi_{4056}(811,\cdot)\) \(\chi_{4056}(931,\cdot)\) \(\chi_{4056}(1123,\cdot)\) \(\chi_{4056}(1243,\cdot)\) \(\chi_{4056}(1435,\cdot)\) \(\chi_{4056}(1555,\cdot)\) \(\chi_{4056}(1747,\cdot)\) \(\chi_{4056}(1867,\cdot)\) \(\chi_{4056}(2059,\cdot)\) \(\chi_{4056}(2179,\cdot)\) \(\chi_{4056}(2371,\cdot)\) \(\chi_{4056}(2491,\cdot)\) \(\chi_{4056}(2683,\cdot)\) \(\chi_{4056}(2995,\cdot)\) \(\chi_{4056}(3115,\cdot)\) \(\chi_{4056}(3307,\cdot)\) \(\chi_{4056}(3427,\cdot)\) \(\chi_{4056}(3739,\cdot)\) \(\chi_{4056}(3931,\cdot)\) \(\chi_{4056}(4051,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,-1,1,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) |