Basic properties
Modulus: | \(6760\) | |
Conductor: | \(6760\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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.fn
\(\chi_{6760}(197,\cdot)\) \(\chi_{6760}(293,\cdot)\) \(\chi_{6760}(453,\cdot)\) \(\chi_{6760}(717,\cdot)\) \(\chi_{6760}(813,\cdot)\) \(\chi_{6760}(877,\cdot)\) \(\chi_{6760}(973,\cdot)\) \(\chi_{6760}(1237,\cdot)\) \(\chi_{6760}(1397,\cdot)\) \(\chi_{6760}(1493,\cdot)\) \(\chi_{6760}(1757,\cdot)\) \(\chi_{6760}(1853,\cdot)\) \(\chi_{6760}(1917,\cdot)\) \(\chi_{6760}(2013,\cdot)\) \(\chi_{6760}(2373,\cdot)\) \(\chi_{6760}(2437,\cdot)\) \(\chi_{6760}(2533,\cdot)\) \(\chi_{6760}(2797,\cdot)\) \(\chi_{6760}(2893,\cdot)\) \(\chi_{6760}(2957,\cdot)\) \(\chi_{6760}(3053,\cdot)\) \(\chi_{6760}(3317,\cdot)\) \(\chi_{6760}(3413,\cdot)\) \(\chi_{6760}(3477,\cdot)\) \(\chi_{6760}(3573,\cdot)\) \(\chi_{6760}(3837,\cdot)\) \(\chi_{6760}(3933,\cdot)\) \(\chi_{6760}(3997,\cdot)\) \(\chi_{6760}(4093,\cdot)\) \(\chi_{6760}(4357,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,3381,4057,5241)\) → \((1,-1,i,e\left(\frac{109}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6760 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{37}{39}\right)\) |