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.fc
\(\chi_{9075}(281,\cdot)\) \(\chi_{9075}(491,\cdot)\) \(\chi_{9075}(536,\cdot)\) \(\chi_{9075}(1106,\cdot)\) \(\chi_{9075}(1316,\cdot)\) \(\chi_{9075}(1361,\cdot)\) \(\chi_{9075}(1421,\cdot)\) \(\chi_{9075}(1931,\cdot)\) \(\chi_{9075}(2141,\cdot)\) \(\chi_{9075}(2186,\cdot)\) \(\chi_{9075}(2246,\cdot)\) \(\chi_{9075}(2966,\cdot)\) \(\chi_{9075}(3011,\cdot)\) \(\chi_{9075}(3071,\cdot)\) \(\chi_{9075}(3581,\cdot)\) \(\chi_{9075}(3836,\cdot)\) \(\chi_{9075}(3896,\cdot)\) \(\chi_{9075}(4406,\cdot)\) \(\chi_{9075}(4616,\cdot)\) \(\chi_{9075}(4661,\cdot)\) \(\chi_{9075}(4721,\cdot)\) \(\chi_{9075}(5231,\cdot)\) \(\chi_{9075}(5441,\cdot)\) \(\chi_{9075}(5486,\cdot)\) \(\chi_{9075}(5546,\cdot)\) \(\chi_{9075}(6056,\cdot)\) \(\chi_{9075}(6266,\cdot)\) \(\chi_{9075}(6311,\cdot)\) \(\chi_{9075}(6371,\cdot)\) \(\chi_{9075}(6881,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{79}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(281, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{19}{110}\right)\) |