Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{89}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dh
\(\chi_{4005}(46,\cdot)\) \(\chi_{4005}(181,\cdot)\) \(\chi_{4005}(226,\cdot)\) \(\chi_{4005}(451,\cdot)\) \(\chi_{4005}(496,\cdot)\) \(\chi_{4005}(541,\cdot)\) \(\chi_{4005}(766,\cdot)\) \(\chi_{4005}(946,\cdot)\) \(\chi_{4005}(1081,\cdot)\) \(\chi_{4005}(1126,\cdot)\) \(\chi_{4005}(1171,\cdot)\) \(\chi_{4005}(1216,\cdot)\) \(\chi_{4005}(1261,\cdot)\) \(\chi_{4005}(1306,\cdot)\) \(\chi_{4005}(1396,\cdot)\) \(\chi_{4005}(1486,\cdot)\) \(\chi_{4005}(1576,\cdot)\) \(\chi_{4005}(1621,\cdot)\) \(\chi_{4005}(1756,\cdot)\) \(\chi_{4005}(1846,\cdot)\) \(\chi_{4005}(1981,\cdot)\) \(\chi_{4005}(2071,\cdot)\) \(\chi_{4005}(2206,\cdot)\) \(\chi_{4005}(2251,\cdot)\) \(\chi_{4005}(2341,\cdot)\) \(\chi_{4005}(2431,\cdot)\) \(\chi_{4005}(2521,\cdot)\) \(\chi_{4005}(2566,\cdot)\) \(\chi_{4005}(2611,\cdot)\) \(\chi_{4005}(2656,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((3116,802,181)\) → \((1,1,e\left(\frac{73}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{88}\right)\) |