Basic properties
| Modulus: | \(29040\) | |
| Conductor: | \(14520\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(44\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{14520}(7283,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 29040.ip
\(\chi_{29040}(23,\cdot)\) \(\chi_{29040}(1607,\cdot)\) \(\chi_{29040}(4247,\cdot)\) \(\chi_{29040}(5303,\cdot)\) \(\chi_{29040}(6887,\cdot)\) \(\chi_{29040}(7943,\cdot)\) \(\chi_{29040}(9527,\cdot)\) \(\chi_{29040}(10583,\cdot)\) \(\chi_{29040}(12167,\cdot)\) \(\chi_{29040}(13223,\cdot)\) \(\chi_{29040}(14807,\cdot)\) \(\chi_{29040}(15863,\cdot)\) \(\chi_{29040}(17447,\cdot)\) \(\chi_{29040}(18503,\cdot)\) \(\chi_{29040}(21143,\cdot)\) \(\chi_{29040}(22727,\cdot)\) \(\chi_{29040}(23783,\cdot)\) \(\chi_{29040}(25367,\cdot)\) \(\chi_{29040}(26423,\cdot)\) \(\chi_{29040}(28007,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{44})\) |
| Fixed field: | Number field defined by a degree 44 polynomial |
Values on generators
\((3631,21781,19361,11617,14401)\) → \((-1,-1,-1,-i,e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 29040 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) |