Basic properties
Modulus: | \(4020\) | |
Conductor: | \(1340\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1340}(583,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.dn
\(\chi_{4020}(103,\cdot)\) \(\chi_{4020}(127,\cdot)\) \(\chi_{4020}(307,\cdot)\) \(\chi_{4020}(523,\cdot)\) \(\chi_{4020}(583,\cdot)\) \(\chi_{4020}(607,\cdot)\) \(\chi_{4020}(703,\cdot)\) \(\chi_{4020}(763,\cdot)\) \(\chi_{4020}(823,\cdot)\) \(\chi_{4020}(907,\cdot)\) \(\chi_{4020}(1003,\cdot)\) \(\chi_{4020}(1327,\cdot)\) \(\chi_{4020}(1363,\cdot)\) \(\chi_{4020}(1387,\cdot)\) \(\chi_{4020}(1423,\cdot)\) \(\chi_{4020}(1507,\cdot)\) \(\chi_{4020}(1567,\cdot)\) \(\chi_{4020}(1627,\cdot)\) \(\chi_{4020}(1663,\cdot)\) \(\chi_{4020}(1807,\cdot)\) \(\chi_{4020}(2083,\cdot)\) \(\chi_{4020}(2167,\cdot)\) \(\chi_{4020}(2227,\cdot)\) \(\chi_{4020}(2467,\cdot)\) \(\chi_{4020}(2563,\cdot)\) \(\chi_{4020}(2623,\cdot)\) \(\chi_{4020}(2803,\cdot)\) \(\chi_{4020}(2863,\cdot)\) \(\chi_{4020}(2887,\cdot)\) \(\chi_{4020}(2983,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2011,2681,3217,1141)\) → \((-1,1,-i,e\left(\frac{25}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4020 }(583, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{33}\right)\) |