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 \(\chi_{335}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4020.dp
\(\chi_{4020}(73,\cdot)\) \(\chi_{4020}(157,\cdot)\) \(\chi_{4020}(217,\cdot)\) \(\chi_{4020}(457,\cdot)\) \(\chi_{4020}(553,\cdot)\) \(\chi_{4020}(613,\cdot)\) \(\chi_{4020}(793,\cdot)\) \(\chi_{4020}(853,\cdot)\) \(\chi_{4020}(877,\cdot)\) \(\chi_{4020}(973,\cdot)\) \(\chi_{4020}(1093,\cdot)\) \(\chi_{4020}(1333,\cdot)\) \(\chi_{4020}(1357,\cdot)\) \(\chi_{4020}(1417,\cdot)\) \(\chi_{4020}(1513,\cdot)\) \(\chi_{4020}(1597,\cdot)\) \(\chi_{4020}(1657,\cdot)\) \(\chi_{4020}(1777,\cdot)\) \(\chi_{4020}(1813,\cdot)\) \(\chi_{4020}(1897,\cdot)\) \(\chi_{4020}(2113,\cdot)\) \(\chi_{4020}(2137,\cdot)\) \(\chi_{4020}(2317,\cdot)\) \(\chi_{4020}(2533,\cdot)\) \(\chi_{4020}(2593,\cdot)\) \(\chi_{4020}(2617,\cdot)\) \(\chi_{4020}(2713,\cdot)\) \(\chi_{4020}(2773,\cdot)\) \(\chi_{4020}(2833,\cdot)\) \(\chi_{4020}(2917,\cdot)\) ...
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
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4020 }(157, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{83}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{16}{33}\right)\) |