Basic properties
Modulus: | \(8280\) | |
Conductor: | \(8280\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8280.hj
\(\chi_{8280}(157,\cdot)\) \(\chi_{8280}(373,\cdot)\) \(\chi_{8280}(493,\cdot)\) \(\chi_{8280}(517,\cdot)\) \(\chi_{8280}(733,\cdot)\) \(\chi_{8280}(1213,\cdot)\) \(\chi_{8280}(1597,\cdot)\) \(\chi_{8280}(1717,\cdot)\) \(\chi_{8280}(1813,\cdot)\) \(\chi_{8280}(2077,\cdot)\) \(\chi_{8280}(2173,\cdot)\) \(\chi_{8280}(2317,\cdot)\) \(\chi_{8280}(2797,\cdot)\) \(\chi_{8280}(3253,\cdot)\) \(\chi_{8280}(3373,\cdot)\) \(\chi_{8280}(3517,\cdot)\) \(\chi_{8280}(3733,\cdot)\) \(\chi_{8280}(3973,\cdot)\) \(\chi_{8280}(4237,\cdot)\) \(\chi_{8280}(4453,\cdot)\) \(\chi_{8280}(4477,\cdot)\) \(\chi_{8280}(4597,\cdot)\) \(\chi_{8280}(4837,\cdot)\) \(\chi_{8280}(5173,\cdot)\) \(\chi_{8280}(5557,\cdot)\) \(\chi_{8280}(5677,\cdot)\) \(\chi_{8280}(5893,\cdot)\) \(\chi_{8280}(6037,\cdot)\) \(\chi_{8280}(6133,\cdot)\) \(\chi_{8280}(6253,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2071,4141,4601,1657,3961)\) → \((1,-1,e\left(\frac{1}{3}\right),i,e\left(\frac{15}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8280 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{131}{132}\right)\) |