Basic properties
| Modulus: | \(9075\) | |
| 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 \(\chi_{363}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.ex
\(\chi_{9075}(101,\cdot)\) \(\chi_{9075}(326,\cdot)\) \(\chi_{9075}(701,\cdot)\) \(\chi_{9075}(776,\cdot)\) \(\chi_{9075}(926,\cdot)\) \(\chi_{9075}(1151,\cdot)\) \(\chi_{9075}(1526,\cdot)\) \(\chi_{9075}(1601,\cdot)\) \(\chi_{9075}(1751,\cdot)\) \(\chi_{9075}(2351,\cdot)\) \(\chi_{9075}(2426,\cdot)\) \(\chi_{9075}(2576,\cdot)\) \(\chi_{9075}(2801,\cdot)\) \(\chi_{9075}(3176,\cdot)\) \(\chi_{9075}(3251,\cdot)\) \(\chi_{9075}(3401,\cdot)\) \(\chi_{9075}(3626,\cdot)\) \(\chi_{9075}(4001,\cdot)\) \(\chi_{9075}(4076,\cdot)\) \(\chi_{9075}(4451,\cdot)\) \(\chi_{9075}(4826,\cdot)\) \(\chi_{9075}(4901,\cdot)\) \(\chi_{9075}(5051,\cdot)\) \(\chi_{9075}(5276,\cdot)\) \(\chi_{9075}(5651,\cdot)\) \(\chi_{9075}(5726,\cdot)\) \(\chi_{9075}(5876,\cdot)\) \(\chi_{9075}(6101,\cdot)\) \(\chi_{9075}(6476,\cdot)\) \(\chi_{9075}(6551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,1,e\left(\frac{21}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{19}{22}\right)\) |