Basic properties
Modulus: | \(6760\) | |
Conductor: | \(6760\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 6760.ez
\(\chi_{6760}(29,\cdot)\) \(\chi_{6760}(269,\cdot)\) \(\chi_{6760}(549,\cdot)\) \(\chi_{6760}(789,\cdot)\) \(\chi_{6760}(1069,\cdot)\) \(\chi_{6760}(1309,\cdot)\) \(\chi_{6760}(1589,\cdot)\) \(\chi_{6760}(1829,\cdot)\) \(\chi_{6760}(2109,\cdot)\) \(\chi_{6760}(2349,\cdot)\) \(\chi_{6760}(2629,\cdot)\) \(\chi_{6760}(2869,\cdot)\) \(\chi_{6760}(3149,\cdot)\) \(\chi_{6760}(3389,\cdot)\) \(\chi_{6760}(3669,\cdot)\) \(\chi_{6760}(4189,\cdot)\) \(\chi_{6760}(4429,\cdot)\) \(\chi_{6760}(4949,\cdot)\) \(\chi_{6760}(5229,\cdot)\) \(\chi_{6760}(5469,\cdot)\) \(\chi_{6760}(5749,\cdot)\) \(\chi_{6760}(5989,\cdot)\) \(\chi_{6760}(6269,\cdot)\) \(\chi_{6760}(6509,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5071,3381,4057,5241)\) → \((1,-1,-1,e\left(\frac{10}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6760 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) |