Basic properties
Modulus: | \(6760\) | |
Conductor: | \(3380\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3380}(2719,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6760.gd
\(\chi_{6760}(119,\cdot)\) \(\chi_{6760}(279,\cdot)\) \(\chi_{6760}(479,\cdot)\) \(\chi_{6760}(639,\cdot)\) \(\chi_{6760}(799,\cdot)\) \(\chi_{6760}(839,\cdot)\) \(\chi_{6760}(999,\cdot)\) \(\chi_{6760}(1159,\cdot)\) \(\chi_{6760}(1319,\cdot)\) \(\chi_{6760}(1359,\cdot)\) \(\chi_{6760}(1519,\cdot)\) \(\chi_{6760}(1679,\cdot)\) \(\chi_{6760}(1839,\cdot)\) \(\chi_{6760}(1879,\cdot)\) \(\chi_{6760}(2039,\cdot)\) \(\chi_{6760}(2199,\cdot)\) \(\chi_{6760}(2359,\cdot)\) \(\chi_{6760}(2399,\cdot)\) \(\chi_{6760}(2559,\cdot)\) \(\chi_{6760}(2719,\cdot)\) \(\chi_{6760}(2879,\cdot)\) \(\chi_{6760}(2919,\cdot)\) \(\chi_{6760}(3079,\cdot)\) \(\chi_{6760}(3239,\cdot)\) \(\chi_{6760}(3439,\cdot)\) \(\chi_{6760}(3599,\cdot)\) \(\chi_{6760}(3759,\cdot)\) \(\chi_{6760}(3919,\cdot)\) \(\chi_{6760}(3959,\cdot)\) \(\chi_{6760}(4119,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,3381,4057,5241)\) → \((-1,1,-1,e\left(\frac{133}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 6760 }(2719, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |