Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(9075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9075.er
\(\chi_{9075}(134,\cdot)\) \(\chi_{9075}(194,\cdot)\) \(\chi_{9075}(314,\cdot)\) \(\chi_{9075}(404,\cdot)\) \(\chi_{9075}(1019,\cdot)\) \(\chi_{9075}(1139,\cdot)\) \(\chi_{9075}(1229,\cdot)\) \(\chi_{9075}(1784,\cdot)\) \(\chi_{9075}(1844,\cdot)\) \(\chi_{9075}(1964,\cdot)\) \(\chi_{9075}(2609,\cdot)\) \(\chi_{9075}(2669,\cdot)\) \(\chi_{9075}(2789,\cdot)\) \(\chi_{9075}(2879,\cdot)\) \(\chi_{9075}(3434,\cdot)\) \(\chi_{9075}(3494,\cdot)\) \(\chi_{9075}(3614,\cdot)\) \(\chi_{9075}(3704,\cdot)\) \(\chi_{9075}(4259,\cdot)\) \(\chi_{9075}(4319,\cdot)\) \(\chi_{9075}(4439,\cdot)\) \(\chi_{9075}(4529,\cdot)\) \(\chi_{9075}(5084,\cdot)\) \(\chi_{9075}(5144,\cdot)\) \(\chi_{9075}(5264,\cdot)\) \(\chi_{9075}(5354,\cdot)\) \(\chi_{9075}(5909,\cdot)\) \(\chi_{9075}(6089,\cdot)\) \(\chi_{9075}(6179,\cdot)\) \(\chi_{9075}(6734,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{17}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(1844, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) |