Basic properties
| Modulus: | \(4020\) | |
| Conductor: | \(1005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1005}(827,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.dk
\(\chi_{4020}(17,\cdot)\) \(\chi_{4020}(77,\cdot)\) \(\chi_{4020}(173,\cdot)\) \(\chi_{4020}(257,\cdot)\) \(\chi_{4020}(317,\cdot)\) \(\chi_{4020}(437,\cdot)\) \(\chi_{4020}(473,\cdot)\) \(\chi_{4020}(557,\cdot)\) \(\chi_{4020}(773,\cdot)\) \(\chi_{4020}(797,\cdot)\) \(\chi_{4020}(977,\cdot)\) \(\chi_{4020}(1193,\cdot)\) \(\chi_{4020}(1253,\cdot)\) \(\chi_{4020}(1277,\cdot)\) \(\chi_{4020}(1373,\cdot)\) \(\chi_{4020}(1433,\cdot)\) \(\chi_{4020}(1493,\cdot)\) \(\chi_{4020}(1577,\cdot)\) \(\chi_{4020}(1673,\cdot)\) \(\chi_{4020}(1997,\cdot)\) \(\chi_{4020}(2033,\cdot)\) \(\chi_{4020}(2057,\cdot)\) \(\chi_{4020}(2093,\cdot)\) \(\chi_{4020}(2177,\cdot)\) \(\chi_{4020}(2237,\cdot)\) \(\chi_{4020}(2297,\cdot)\) \(\chi_{4020}(2333,\cdot)\) \(\chi_{4020}(2477,\cdot)\) \(\chi_{4020}(2753,\cdot)\) \(\chi_{4020}(2837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2011,2681,3217,1141)\) → \((1,-1,i,e\left(\frac{14}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4020 }(2837, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{119}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{65}{66}\right)\) |