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 \(\chi_{3380}(87,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6760.fo
\(\chi_{6760}(87,\cdot)\) \(\chi_{6760}(263,\cdot)\) \(\chi_{6760}(367,\cdot)\) \(\chi_{6760}(503,\cdot)\) \(\chi_{6760}(607,\cdot)\) \(\chi_{6760}(783,\cdot)\) \(\chi_{6760}(887,\cdot)\) \(\chi_{6760}(1023,\cdot)\) \(\chi_{6760}(1127,\cdot)\) \(\chi_{6760}(1303,\cdot)\) \(\chi_{6760}(1407,\cdot)\) \(\chi_{6760}(1647,\cdot)\) \(\chi_{6760}(1823,\cdot)\) \(\chi_{6760}(1927,\cdot)\) \(\chi_{6760}(2063,\cdot)\) \(\chi_{6760}(2167,\cdot)\) \(\chi_{6760}(2447,\cdot)\) \(\chi_{6760}(2583,\cdot)\) \(\chi_{6760}(2687,\cdot)\) \(\chi_{6760}(2863,\cdot)\) \(\chi_{6760}(2967,\cdot)\) \(\chi_{6760}(3103,\cdot)\) \(\chi_{6760}(3207,\cdot)\) \(\chi_{6760}(3383,\cdot)\) \(\chi_{6760}(3487,\cdot)\) \(\chi_{6760}(3623,\cdot)\) \(\chi_{6760}(3727,\cdot)\) \(\chi_{6760}(3903,\cdot)\) \(\chi_{6760}(4007,\cdot)\) \(\chi_{6760}(4143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,3381,4057,5241)\) → \((-1,1,i,e\left(\frac{2}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6760 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{43}{78}\right)\) |