Basic properties
| Modulus: | \(8280\) | |
| 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 \(\chi_{1035}(718,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8280.gv
\(\chi_{8280}(97,\cdot)\) \(\chi_{8280}(313,\cdot)\) \(\chi_{8280}(337,\cdot)\) \(\chi_{8280}(457,\cdot)\) \(\chi_{8280}(697,\cdot)\) \(\chi_{8280}(1033,\cdot)\) \(\chi_{8280}(1417,\cdot)\) \(\chi_{8280}(1537,\cdot)\) \(\chi_{8280}(1753,\cdot)\) \(\chi_{8280}(1897,\cdot)\) \(\chi_{8280}(1993,\cdot)\) \(\chi_{8280}(2113,\cdot)\) \(\chi_{8280}(2137,\cdot)\) \(\chi_{8280}(2353,\cdot)\) \(\chi_{8280}(2857,\cdot)\) \(\chi_{8280}(2977,\cdot)\) \(\chi_{8280}(3073,\cdot)\) \(\chi_{8280}(3193,\cdot)\) \(\chi_{8280}(3217,\cdot)\) \(\chi_{8280}(3553,\cdot)\) \(\chi_{8280}(3697,\cdot)\) \(\chi_{8280}(3793,\cdot)\) \(\chi_{8280}(4297,\cdot)\) \(\chi_{8280}(4513,\cdot)\) \(\chi_{8280}(4633,\cdot)\) \(\chi_{8280}(4657,\cdot)\) \(\chi_{8280}(4873,\cdot)\) \(\chi_{8280}(5353,\cdot)\) \(\chi_{8280}(5737,\cdot)\) \(\chi_{8280}(5857,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((1,1,e\left(\frac{2}{3}\right),-i,e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8280 }(1753, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{132}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{19}{132}\right)\) |