Basic properties
Modulus: | \(6760\) | |
Conductor: | \(6760\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.fy
\(\chi_{6760}(37,\cdot)\) \(\chi_{6760}(93,\cdot)\) \(\chi_{6760}(253,\cdot)\) \(\chi_{6760}(397,\cdot)\) \(\chi_{6760}(557,\cdot)\) \(\chi_{6760}(613,\cdot)\) \(\chi_{6760}(773,\cdot)\) \(\chi_{6760}(917,\cdot)\) \(\chi_{6760}(1077,\cdot)\) \(\chi_{6760}(1133,\cdot)\) \(\chi_{6760}(1293,\cdot)\) \(\chi_{6760}(1437,\cdot)\) \(\chi_{6760}(1597,\cdot)\) \(\chi_{6760}(1653,\cdot)\) \(\chi_{6760}(1813,\cdot)\) \(\chi_{6760}(1957,\cdot)\) \(\chi_{6760}(2173,\cdot)\) \(\chi_{6760}(2333,\cdot)\) \(\chi_{6760}(2477,\cdot)\) \(\chi_{6760}(2637,\cdot)\) \(\chi_{6760}(2693,\cdot)\) \(\chi_{6760}(2853,\cdot)\) \(\chi_{6760}(2997,\cdot)\) \(\chi_{6760}(3157,\cdot)\) \(\chi_{6760}(3213,\cdot)\) \(\chi_{6760}(3373,\cdot)\) \(\chi_{6760}(3517,\cdot)\) \(\chi_{6760}(3677,\cdot)\) \(\chi_{6760}(3733,\cdot)\) \(\chi_{6760}(3893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,3381,4057,5241)\) → \((1,-1,-i,e\left(\frac{149}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6760 }(2333, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{8}{39}\right)\) |