Basic properties
Modulus: | \(4020\) | |
Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{335}(117,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.dl
\(\chi_{4020}(13,\cdot)\) \(\chi_{4020}(337,\cdot)\) \(\chi_{4020}(433,\cdot)\) \(\chi_{4020}(517,\cdot)\) \(\chi_{4020}(577,\cdot)\) \(\chi_{4020}(637,\cdot)\) \(\chi_{4020}(733,\cdot)\) \(\chi_{4020}(757,\cdot)\) \(\chi_{4020}(817,\cdot)\) \(\chi_{4020}(1033,\cdot)\) \(\chi_{4020}(1213,\cdot)\) \(\chi_{4020}(1237,\cdot)\) \(\chi_{4020}(1453,\cdot)\) \(\chi_{4020}(1537,\cdot)\) \(\chi_{4020}(1573,\cdot)\) \(\chi_{4020}(1693,\cdot)\) \(\chi_{4020}(1753,\cdot)\) \(\chi_{4020}(1837,\cdot)\) \(\chi_{4020}(1933,\cdot)\) \(\chi_{4020}(1993,\cdot)\) \(\chi_{4020}(2017,\cdot)\) \(\chi_{4020}(2257,\cdot)\) \(\chi_{4020}(2377,\cdot)\) \(\chi_{4020}(2473,\cdot)\) \(\chi_{4020}(2497,\cdot)\) \(\chi_{4020}(2557,\cdot)\) \(\chi_{4020}(2737,\cdot)\) \(\chi_{4020}(2797,\cdot)\) \(\chi_{4020}(2893,\cdot)\) \(\chi_{4020}(3133,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2011,2681,3217,1141)\) → \((1,1,i,e\left(\frac{31}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4020 }(2797, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{119}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{66}\right)\) |