Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{445}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dk
\(\chi_{4005}(28,\cdot)\) \(\chi_{4005}(127,\cdot)\) \(\chi_{4005}(253,\cdot)\) \(\chi_{4005}(478,\cdot)\) \(\chi_{4005}(883,\cdot)\) \(\chi_{4005}(973,\cdot)\) \(\chi_{4005}(1198,\cdot)\) \(\chi_{4005}(1243,\cdot)\) \(\chi_{4005}(1297,\cdot)\) \(\chi_{4005}(1378,\cdot)\) \(\chi_{4005}(1567,\cdot)\) \(\chi_{4005}(1648,\cdot)\) \(\chi_{4005}(1783,\cdot)\) \(\chi_{4005}(1828,\cdot)\) \(\chi_{4005}(1882,\cdot)\) \(\chi_{4005}(1927,\cdot)\) \(\chi_{4005}(2017,\cdot)\) \(\chi_{4005}(2053,\cdot)\) \(\chi_{4005}(2062,\cdot)\) \(\chi_{4005}(2107,\cdot)\) \(\chi_{4005}(2143,\cdot)\) \(\chi_{4005}(2287,\cdot)\) \(\chi_{4005}(2377,\cdot)\) \(\chi_{4005}(2422,\cdot)\) \(\chi_{4005}(2548,\cdot)\) \(\chi_{4005}(2773,\cdot)\) \(\chi_{4005}(2998,\cdot)\) \(\chi_{4005}(3007,\cdot)\) \(\chi_{4005}(3052,\cdot)\) \(\chi_{4005}(3142,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((3116,802,181)\) → \((1,-i,e\left(\frac{25}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{39}{88}\right)\) |