Basic properties
Modulus: | \(4020\) | |
Conductor: | \(1340\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1340}(683,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.dr
\(\chi_{4020}(7,\cdot)\) \(\chi_{4020}(247,\cdot)\) \(\chi_{4020}(367,\cdot)\) \(\chi_{4020}(463,\cdot)\) \(\chi_{4020}(487,\cdot)\) \(\chi_{4020}(547,\cdot)\) \(\chi_{4020}(727,\cdot)\) \(\chi_{4020}(787,\cdot)\) \(\chi_{4020}(883,\cdot)\) \(\chi_{4020}(1123,\cdot)\) \(\chi_{4020}(1183,\cdot)\) \(\chi_{4020}(1267,\cdot)\) \(\chi_{4020}(1543,\cdot)\) \(\chi_{4020}(1687,\cdot)\) \(\chi_{4020}(1723,\cdot)\) \(\chi_{4020}(1783,\cdot)\) \(\chi_{4020}(1843,\cdot)\) \(\chi_{4020}(1927,\cdot)\) \(\chi_{4020}(1963,\cdot)\) \(\chi_{4020}(1987,\cdot)\) \(\chi_{4020}(2023,\cdot)\) \(\chi_{4020}(2347,\cdot)\) \(\chi_{4020}(2443,\cdot)\) \(\chi_{4020}(2527,\cdot)\) \(\chi_{4020}(2587,\cdot)\) \(\chi_{4020}(2647,\cdot)\) \(\chi_{4020}(2743,\cdot)\) \(\chi_{4020}(2767,\cdot)\) \(\chi_{4020}(2827,\cdot)\) \(\chi_{4020}(3043,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2011,2681,3217,1141)\) → \((-1,1,-i,e\left(\frac{19}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4020 }(2023, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{66}\right)\) |