Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(3388\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3388}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.ek
\(\chi_{6776}(39,\cdot)\) \(\chi_{6776}(79,\cdot)\) \(\chi_{6776}(95,\cdot)\) \(\chi_{6776}(151,\cdot)\) \(\chi_{6776}(303,\cdot)\) \(\chi_{6776}(359,\cdot)\) \(\chi_{6776}(415,\cdot)\) \(\chi_{6776}(431,\cdot)\) \(\chi_{6776}(655,\cdot)\) \(\chi_{6776}(695,\cdot)\) \(\chi_{6776}(711,\cdot)\) \(\chi_{6776}(767,\cdot)\) \(\chi_{6776}(919,\cdot)\) \(\chi_{6776}(975,\cdot)\) \(\chi_{6776}(1031,\cdot)\) \(\chi_{6776}(1047,\cdot)\) \(\chi_{6776}(1271,\cdot)\) \(\chi_{6776}(1311,\cdot)\) \(\chi_{6776}(1327,\cdot)\) \(\chi_{6776}(1383,\cdot)\) \(\chi_{6776}(1535,\cdot)\) \(\chi_{6776}(1591,\cdot)\) \(\chi_{6776}(1647,\cdot)\) \(\chi_{6776}(1663,\cdot)\) \(\chi_{6776}(1887,\cdot)\) \(\chi_{6776}(1943,\cdot)\) \(\chi_{6776}(1999,\cdot)\) \(\chi_{6776}(2207,\cdot)\) \(\chi_{6776}(2263,\cdot)\) \(\chi_{6776}(2279,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,1,e\left(\frac{2}{3}\right),e\left(\frac{79}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{73}{165}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{1}{10}\right)\) |