Basic properties
Modulus: | \(4005\) | |
Conductor: | \(1335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1335}(224,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.dg
\(\chi_{4005}(224,\cdot)\) \(\chi_{4005}(359,\cdot)\) \(\chi_{4005}(404,\cdot)\) \(\chi_{4005}(629,\cdot)\) \(\chi_{4005}(674,\cdot)\) \(\chi_{4005}(719,\cdot)\) \(\chi_{4005}(944,\cdot)\) \(\chi_{4005}(1124,\cdot)\) \(\chi_{4005}(1259,\cdot)\) \(\chi_{4005}(1304,\cdot)\) \(\chi_{4005}(1349,\cdot)\) \(\chi_{4005}(1394,\cdot)\) \(\chi_{4005}(1439,\cdot)\) \(\chi_{4005}(1484,\cdot)\) \(\chi_{4005}(1574,\cdot)\) \(\chi_{4005}(1664,\cdot)\) \(\chi_{4005}(1754,\cdot)\) \(\chi_{4005}(1799,\cdot)\) \(\chi_{4005}(1934,\cdot)\) \(\chi_{4005}(2024,\cdot)\) \(\chi_{4005}(2159,\cdot)\) \(\chi_{4005}(2249,\cdot)\) \(\chi_{4005}(2384,\cdot)\) \(\chi_{4005}(2429,\cdot)\) \(\chi_{4005}(2519,\cdot)\) \(\chi_{4005}(2609,\cdot)\) \(\chi_{4005}(2699,\cdot)\) \(\chi_{4005}(2744,\cdot)\) \(\chi_{4005}(2789,\cdot)\) \(\chi_{4005}(2834,\cdot)\) ...
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
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4005 }(224, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{88}\right)\) |