Basic properties
Modulus: | \(6534\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6534.bi
\(\chi_{6534}(107,\cdot)\) \(\chi_{6534}(431,\cdot)\) \(\chi_{6534}(701,\cdot)\) \(\chi_{6534}(755,\cdot)\) \(\chi_{6534}(809,\cdot)\) \(\chi_{6534}(1025,\cdot)\) \(\chi_{6534}(1295,\cdot)\) \(\chi_{6534}(1349,\cdot)\) \(\chi_{6534}(1403,\cdot)\) \(\chi_{6534}(1619,\cdot)\) \(\chi_{6534}(1889,\cdot)\) \(\chi_{6534}(1943,\cdot)\) \(\chi_{6534}(1997,\cdot)\) \(\chi_{6534}(2213,\cdot)\) \(\chi_{6534}(2483,\cdot)\) \(\chi_{6534}(2537,\cdot)\) \(\chi_{6534}(2591,\cdot)\) \(\chi_{6534}(2807,\cdot)\) \(\chi_{6534}(3077,\cdot)\) \(\chi_{6534}(3131,\cdot)\) \(\chi_{6534}(3185,\cdot)\) \(\chi_{6534}(3401,\cdot)\) \(\chi_{6534}(3671,\cdot)\) \(\chi_{6534}(3725,\cdot)\) \(\chi_{6534}(3779,\cdot)\) \(\chi_{6534}(3995,\cdot)\) \(\chi_{6534}(4265,\cdot)\) \(\chi_{6534}(4319,\cdot)\) \(\chi_{6534}(4373,\cdot)\) \(\chi_{6534}(4859,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6293,3511)\) → \((-1,e\left(\frac{63}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6534 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) |