Basic properties
| Modulus: | \(4140\) | |
| 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 \(\chi_{1035}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4140.dl
\(\chi_{4140}(97,\cdot)\) \(\chi_{4140}(157,\cdot)\) \(\chi_{4140}(313,\cdot)\) \(\chi_{4140}(337,\cdot)\) \(\chi_{4140}(373,\cdot)\) \(\chi_{4140}(457,\cdot)\) \(\chi_{4140}(493,\cdot)\) \(\chi_{4140}(517,\cdot)\) \(\chi_{4140}(697,\cdot)\) \(\chi_{4140}(733,\cdot)\) \(\chi_{4140}(1033,\cdot)\) \(\chi_{4140}(1213,\cdot)\) \(\chi_{4140}(1417,\cdot)\) \(\chi_{4140}(1537,\cdot)\) \(\chi_{4140}(1597,\cdot)\) \(\chi_{4140}(1717,\cdot)\) \(\chi_{4140}(1753,\cdot)\) \(\chi_{4140}(1813,\cdot)\) \(\chi_{4140}(1897,\cdot)\) \(\chi_{4140}(1993,\cdot)\) \(\chi_{4140}(2077,\cdot)\) \(\chi_{4140}(2113,\cdot)\) \(\chi_{4140}(2137,\cdot)\) \(\chi_{4140}(2173,\cdot)\) \(\chi_{4140}(2317,\cdot)\) \(\chi_{4140}(2353,\cdot)\) \(\chi_{4140}(2797,\cdot)\) \(\chi_{4140}(2857,\cdot)\) \(\chi_{4140}(2977,\cdot)\) \(\chi_{4140}(3073,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,461,1657,3961)\) → \((1,e\left(\frac{1}{3}\right),-i,e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4140 }(2173, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{83}{132}\right)\) |