Basic properties
| Modulus: | \(2070\) | |
| Conductor: | \(1035\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1035}(958,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2070.bs
\(\chi_{2070}(7,\cdot)\) \(\chi_{2070}(43,\cdot)\) \(\chi_{2070}(67,\cdot)\) \(\chi_{2070}(97,\cdot)\) \(\chi_{2070}(103,\cdot)\) \(\chi_{2070}(157,\cdot)\) \(\chi_{2070}(247,\cdot)\) \(\chi_{2070}(283,\cdot)\) \(\chi_{2070}(313,\cdot)\) \(\chi_{2070}(337,\cdot)\) \(\chi_{2070}(373,\cdot)\) \(\chi_{2070}(457,\cdot)\) \(\chi_{2070}(493,\cdot)\) \(\chi_{2070}(517,\cdot)\) \(\chi_{2070}(697,\cdot)\) \(\chi_{2070}(727,\cdot)\) \(\chi_{2070}(733,\cdot)\) \(\chi_{2070}(787,\cdot)\) \(\chi_{2070}(907,\cdot)\) \(\chi_{2070}(1003,\cdot)\) \(\chi_{2070}(1033,\cdot)\) \(\chi_{2070}(1123,\cdot)\) \(\chi_{2070}(1147,\cdot)\) \(\chi_{2070}(1183,\cdot)\) \(\chi_{2070}(1213,\cdot)\) \(\chi_{2070}(1303,\cdot)\) \(\chi_{2070}(1417,\cdot)\) \(\chi_{2070}(1447,\cdot)\) \(\chi_{2070}(1483,\cdot)\) \(\chi_{2070}(1537,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((461,1657,1891)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2070 }(1993, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{59}{132}\right)\) |