Basic properties
| Modulus: | \(9075\) | |
| Conductor: | \(9075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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.gb
\(\chi_{9075}(23,\cdot)\) \(\chi_{9075}(188,\cdot)\) \(\chi_{9075}(287,\cdot)\) \(\chi_{9075}(353,\cdot)\) \(\chi_{9075}(452,\cdot)\) \(\chi_{9075}(617,\cdot)\) \(\chi_{9075}(683,\cdot)\) \(\chi_{9075}(947,\cdot)\) \(\chi_{9075}(1013,\cdot)\) \(\chi_{9075}(1112,\cdot)\) \(\chi_{9075}(1178,\cdot)\) \(\chi_{9075}(1277,\cdot)\) \(\chi_{9075}(1442,\cdot)\) \(\chi_{9075}(1508,\cdot)\) \(\chi_{9075}(1673,\cdot)\) \(\chi_{9075}(1772,\cdot)\) \(\chi_{9075}(1838,\cdot)\) \(\chi_{9075}(2003,\cdot)\) \(\chi_{9075}(2102,\cdot)\) \(\chi_{9075}(2267,\cdot)\) \(\chi_{9075}(2333,\cdot)\) \(\chi_{9075}(2498,\cdot)\) \(\chi_{9075}(2597,\cdot)\) \(\chi_{9075}(2762,\cdot)\) \(\chi_{9075}(2828,\cdot)\) \(\chi_{9075}(2927,\cdot)\) \(\chi_{9075}(3092,\cdot)\) \(\chi_{9075}(3158,\cdot)\) \(\chi_{9075}(3323,\cdot)\) \(\chi_{9075}(3422,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,727,5326)\) → \((-1,e\left(\frac{11}{20}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 9075 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{220}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{13}{220}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{183}{220}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{21}{220}\right)\) |